Geocoronal hydrogen studies using Fabry–Perot interferometers, part 1: Instrumentation, observations, and analysis

ARTICLE IN PRESS Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 1520–1552 www.elsevier.com/locate/jastp Geocoronal hydrogen studies ...

Download PDF

883KB Sizes 0 Downloads 12 Views

Report

PDF Reader
Full Text

ARTICLE IN PRESS

Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 1520–1552 www.elsevier.com/locate/jastp

Geocoronal hydrogen studies using Fabry–Perot interferometers, part 1: Instrumentation, observations, and analysis E.J. Mierkiewicza,, F.L. Roeslera, S.M. Nossala, R.J. Reynoldsb a

Department of Physics, University of Wisconsin– Madison, Madison, WI, USA Department of Astronomy, University of Wisconsin– Madison, Madison, WI, USA

b

Available online 3 July 2006

Abstract Ground-based Fabry–Perot observations of the solar excited Balmer a emission line of neutral atomic hydrogen have become one of the primary means of studying the distribution and behavior of hydrogen in the thermosphere+exosphere. This ﬁrst of two companion papers on ‘‘Geocoronal Hydrogen Studies Using Fabry–Perot Interferometers’’, will outline the technique of Fabry–Perot spectroscopy as applied to geocoronal hydrogen. Representative high spectral resolution data sets will be discussed which will serve to highlight advances in instrumentation and in the interpretation of geocoronal Balmer a intensity and line proﬁle observations. A second companion paper will address long-term observations of the Balmer a emission. r 2006 Elsevier Ltd. All rights reserved. Keywords: Geocoronal hydrogen; Techniques and methods; Fabry–Perot spectroscopy

1. Introduction Balmer a (6563 A˚) ‘‘nightglow’’ is the result of solar Lyman b scattering by atmospheric atomic hydrogen. This scattering is nonconservative and results in Balmer a ﬂuorescence 12% of the time. The Balmer a column emission rate (also referred to as intensities in the following) is dependent upon the hydrogen density proﬁle, the solar Lyman b line center excitation ﬂux, and the observational viewing geometry. A portion of the signal is also due to multiple scattering of Lyman b into the Earth’s Corresponding author. Tel.: +1 608 2621152.

E-mail address: [email protected] (E.J. Mierkiewicz). 1364-6826/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.jastp.2005.08.024

shadow (see e.g., Anderson et al., 1987; Bishop et al., 2001) and from cascade contributions from hydrogen excitation by higher order solar Lyman series lines (Meier, 1995; Nossal et al., 1998). Typical zenith Balmer a intensities are in the range of 2–15 Rayleighs. Ground-based observations of the geocoronal Balmer a column emission include contributions from both the exosphere and the thermosphere. Although ground-based Fabry–Perot observations of geocoronal hydrogen have been made over the last several decades with increasing instrumental capabilities (Reynolds et al., 1973; Atreya et al., 1975; Meriwether et al., 1980; Yelle and Roesler, 1985; Shih et al., 1985, Kerr et al., 1986, 2001a, b; Kerr and Tepley, 1988; He et al., 1993; Nossal et al.,

ARTICLE IN PRESS E.J. Mierkiewicz et al. / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 1520–1552

1993, 1997, 1998, 2001, 2004; Bishop et al., 2001, 2004; Mierkiewicz, 2002; and references therein), recent advances in detector technology, such as the charged-coupled-device (CCD), and its application to Fabry–Perot spectroscopy (e.g., CCD annular summing spectroscopy), have greatly improved the quality and quantity of geocoronal Balmer a emissions data. Scientiﬁc areas of focus include: High resolution observations of the geocoronal hydrogen Balmer a line proﬁle and its relation to excitation mechanisms and exospheric physics. Retrieval of geocoronal hydrogen parameters such as the hydrogen column abundance [H], the hydrogen density proﬁle H(z), and the photochemically initiated hydrogen ﬂux f(H). Long-term observations of the geocoronal hydrogen column emission intensity for the investigation of natural variability, such as solar cycle trends, and of potential anthropogenic change due to increases in atmospheric concentrations of warming gases. This paper will discuss the technique of Fabry– Perot spectroscopy as applied to ground-based geocoronal hydrogen Balmer a observations, including strategies for obtaining data of sufﬁcient precision and scope to address the scientiﬁc areas of focus outlined above. Observations by the Wisconsin group and collaborators (Reynolds et al., 1973; Yelle and Roesler, 1985; Shih et al., 1985; Harlander and Roesler, 1989; Nossal et al., 1993, 1997, 1998, 2001, 2004; Coakley et al., 1996; Bishop et al., 2001, 2004; Mierkiewicz, 2002) will be used to illustrate capabilities and challenges associated with using Fabry–Perot spectroscopy as a means to explore the hydrogen geocorona. 2. Overview of the geocorona and scientiﬁc motivation The tenuous uppermost reach of a neutral planetary atmosphere is commonly referred to as an exosphere or corona (Chamberlain and Hunten, 1987). The existence of a diffuse hydrogen corona at the top of the Earth’s atmosphere (i.e., the geocorona), and its loss by thermal escape, was predicted as early as the mid-19th century, although at the time it was thought to be almost entirely molecular hydrogen. The modern era of geocoronal research began in earnest in the 1950s with the detection of hydrogen Lyman a (Byram et al., 1957)

1521

and Balmer a (Prokudina, 1959; Shefov, 1959) emissions in the night sky. Although there was early controversy as to the source of these emission lines (e.g., terrestrial or interplanetary), they were eventually revealed to be the result of solar Lyman series photons interacting with geocoronal atomic hydrogen (see e.g., Tinsley, 1974; Donahue, 1977). For excellent overviews of the geocorona with a historical perspective, see e.g., Chamberlain (1963), Tinsley (1974), Donahue (1977). The primary source of geocoronal hydrogen is the photodissociation of H2O, CH4, and H2, molecular species which originate in the troposphere and are transported to higher regions of the atmosphere (see e.g., Brasseur and Solomon, 1986; Dessler et al., 1994). At altitudes above 90 km, direct photoproduction of atomic hydrogen is balanced by its upward diffusion through the thermosphere, with an estimated global mean escape rate of a few 108 atoms cm2 s1 by Jeans evaporation and other nonthermal processes (see e.g., Donahue, 1977; Chamberlain and Hunten, 1987). As a daughter of H2O and CH4, the distribution of atomic hydrogen in the mesosphere and thermosphere, and its associated vertical transport ﬂux, are recognized as important parameters in understanding the chemistry of the upper atmosphere and coupling processes between atmospheric regions (Hunten and Strobel, 1974; Liu and Donahue, 1974a–c; Yung et al., 1989). Planetary escape and the distribution of atomic hydrogen into the interplanetary medium are of interest with regard to planetary evolution (see e.g., Walker, 1977) and exospheric phenomena (see e.g., Chamberlain and Hunten, 1987). The interaction between the hydrogen exosphere, plasmasphere and ring current is also of interest given the use of energetic neutral atom (ENA) imaging of the magnetosphere with the IMAGE satellite (Burch, 2000). Until recently, the full utilization of ground-based Balmer a nightglow measurements to extract parameters of more general aeronomic interest (i.e., [H], H(z), and f(H)) has been hampered by apparent inconsistencies with satellite Lyman a data sets (Donahue, 1966; Tinsley and Meier, 1971; Anderson et al., 1987) and in situ atomic hydrogen density measurements (e.g., Breig et al., 1985). Recent radiative transport analysis of satellite and ground-based data by Bishop (2001) and Bishop et al. (2001), using the spherical nonisothermal radiative transport code LYAO_RT (Bishop, 1999), thermospheric atomic hydrogen density proﬁles

ARTICLE IN PRESS 1522

E.J. Mierkiewicz et al. / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 1520–1552

derived from a three-parameter (the atomic hydrogen mesospheric peak density ½Hpeak , exobase density ½Hc , and ﬂux f(H)) diffusive ﬂow algorithm (Bishop, 2001), and updated solar Lyman series ﬂux estimates by Warren et al. (1998), appears to resolve these inconsistencies. Bishop et al. (2001) were able to obtain good agreement in the hydrogen distributions corresponding to the best forward-model ﬁts to Balmer a and Lyman a data sets taken during periods of similar solar–geophysical conditions, and have shown that, in the context of limited data sets, the apparent discrepancies among satellite and ground-based data sets were mainly the result of cumulative uncertainties in solar line center ﬂuxes, calibration sources, and simplifying assumptions used in radiative transfer modeling techniques. The work by Bishop et al. (2001) removes a long standing obstacle to relating ground-based geocoronal studies to aeronomic issues of more general interest, and is signiﬁcant motivation for future ground-based Balmer a observations and data/ model comparisons. Extensive geocoronal Balmer a data sets are now being obtained with two similarly designed Fabry– Perot CCD annular summing spectrometers located at Pine Bluff, WI and Kitt Peak, AZ. Complementing these ground-based measurements, satellite missions, e.g., EURD (Garcı´ a Primo, 2001), FUSE (Feldman et al., 2001), IMAGE/GEO (Østgaard et al., 2003), are providing large data sets of FUV and EUV emission measurements including geocoronal Lyman line intensities. With the data sets now available (see e.g., Bishop et al., 2004), updated solar Lyman line center ﬂux observations (e.g., Warren et al., 1998), the use of astronomical standards for absolute radiance calibrations (see e.g., Scherb, 1981), and reﬁned radiative transport modeling for site speciﬁc observations (Bishop, 1999), the goal of developing the Balmer a emission as a diagnostic of the upper atmosphere (e.g., as a tracer of atmospheric chemistry, variability, and exospheric characteristics) appears to be within reach. 3. The Fabry–Perot interferometer Interferometric instruments offer sensitivity gains on the order of 1.5–2 orders of magnitude per spectral element over slit spectrometers with dispersing elements of similar size, when used to study spatially extended diffuse emissions (Roesler, 1974). The interferometer devised by Fabry and

Perot (1901) employs multiple-beam interference by division of amplitude in which a large number of mutually coherent wavefronts are produced. This division occurs through multiple reﬂections between two optically ﬂat partially reﬂecting plates, spaced some distance l, and held parallel; this is the etalon. Light which passes through an etalon gives rise to an annular (due to the azimuthal symmetry of the system) interference pattern at inﬁnity. The condition for total constructive interference is satisﬁed whenever 2ml cos y ¼ ml,

(1)

where m is the index of refraction of the material between the plates, l is the plate spacing, and y is the angle of incidence with respect to the optical axis. That is, there is maximum transmission through the etalon (a bright fringe) whenever the path difference between the plates 2ml cos y is an integral number of wavelengths ml, where l is the vacuum wavelength and m is the order of interference. For any given l, multiple orders are transmitted. For light at normal incidence (i.e., ‘‘on-axis’’), Eq. (1) reduces to lo ¼ 2ml=m,

(2)

where lo is the wavelength transmitted on-axis, in order m, for a given optical spacing ml. The wavelength transmitted at an angle y off-axis, ly , is given by ly ¼ lo cos y

(3)

or, in terms of wavenumber s (where s ¼ 1=l), so ¼ sy cos y,

(4)

where so ¼ m=2ml. For a ﬁxed m, l, and m, sy increases as y increases (i.e., one goes from the red wing to the blue wing of the spectrum as y increases). 3.1. Pressure scanning and pressure tuning In order to work successfully as a spectrometer, a Fabry–Perot interferometer requires a means by which to record a spectral interval. If conﬁned to a single element detector, such as a photomultiplier tube (PMT), the interferometer must be scanned through the desired spectral interval, sequentially sampling one spectral resolution element dl at a time. Although there are a number of ways to accomplish this (e.g., mechanical, tilt, or pressure scanning) the method most commonly

ARTICLE IN PRESS E.J. Mierkiewicz et al. / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 1520–1552

used in geocoronal Balmer a studies involves pressure scanning (see e.g., Atreya et al., 1975; Meriwether et al., 1980; Shih et al., 1985; Yelle and Roesler, 1985; Harlander and Roesler, 1989; Kerr et al., 1986; Kerr et al., 2001a, b; Nossal et al., 1993). In a pressure scanning system, the etalon, with a ﬁxed spacing l, is housed inside a sealed, windowed chamber, within which the gas pressure can be varied. A change in the chamber pressure P results in a change in the index m between the plates, and hence in the optical spacing ml. Thus, by Eq. (1), for a ﬁxed y (i.e., ‘‘on-axis’’), a Fabry–Perot can be scanned across a desired spectral interval by slowly changing the gas pressure within the etalon chamber. A standard technique to select y when pressure scanning is to center an aperture, which is coupled to the single element detector, in the image plane of a post etalon ‘‘ringpimaging’’ lens. The angular ﬃﬃﬃﬃﬃﬃﬃﬃﬃ diameter b (¼ 2y ¼ 8=R) of this aperture, as seen from the lens, must be carefully selected in order to avoid degrading the resolving power R of the system or limiting the maximum possible etendue (Roesler, 1974). N2 and the higher index gas SF6 are commonly used scan gases during pressure scanning. For an etalon chamber ﬁlled with N2, where mo ðN2 Þ 1:00029 near 6563 A˚, 1:9 A˚ are scanned per atmosphere. For SF6, where mo ðSF6 Þ 1:00072 near 6563 A˚, 4:7 A˚ are scanned per atmosphere; the higher index gas SF6 results in a larger spectral shift for a given DP. For further details see e.g., Roelser (1974). In the CCD annular summing conﬁguration (discussed in Section 3.2) the radial position of an annular fringe on the CCD can be adjusted by increasing or decreasing the etalon chamber pressure. For a given l, by Eq. (1), an increase in P (i.e., an increase in the optical spacing ml) results in an increase in y, or, in terms of the image of the annular fringe in the image plane of a ring imaging lens, an increase in P moves the fringe outward; conversely a decrease in P results in a decrease in y (i.e., the annular fringe moves inward). 3.2. Annular summing: the basics The ‘‘angular dispersion in wavelength’’ given by Eq. (3) can be used in conjunction with modern image plane detectors in order to record a limited spectral interval in a single exposure. In particular, the technique of annular summing spectroscopy, which involves imaging the Fabry–Perot’s annular

1523

fringe pattern onto a low noise, cryogenically cooled, CCD, has enabled a dramatic increase in the sensitivity of Fabry–Perot observations of faint diffuse sources such as the geocorona (Coakley et al., 1996). From Eq. (4), the wavenumber range Ds from normal incidence out to an angle y (where y is small), is found to be Ds y2 . so 2

(5)

For Ds composed of N nested nonoverlapping resolution elements of width ds ¼ so =Ro , where Ro is the theoretical resolving power of the system, and N is an integer, Eq. (5) becomes Nds y2N , ¼ so 2

(6)

where yN is the outer angular radius of the Nth resolution element. Or, in terms of the outer angular radius of the ﬁrst (i.e., central) resolution element (who’s inner radius is zero), pﬃﬃﬃﬃﬃ yN ¼ N y 1 , (7) where sﬃﬃﬃﬃﬃﬃﬃﬃ sﬃﬃﬃﬃﬃﬃ 2ds 2 . y1 ¼ ¼ so Ro

(8)

The ‘‘angular area’’ O subtended by each annular resolution element is conserved, pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ pﬃﬃﬃﬃﬃ pð N y1 Þ2 pð N 1y1 Þ2 ¼ py21 ¼ 2p=Ro ¼ O. (9) Equivalently, equal area annuli (Of 2 ) in the focal plane of a ring imaging lens (of focal length f ) correspond to equal spectral intervals. In this case, Eq. (7) becomes pﬃﬃﬃﬃﬃ rN ¼ N r1 , (10) where sﬃﬃﬃﬃﬃﬃ 2 r 1 y1 f ¼ f Ro

(11)

is the radius of the central resolution element; refer to Fig. 1. Using the property that equal area annuli in the Fabry–Perot’s interference pattern correspond to equal spectral intervals, the CCD image of the Fabry–Perot’s annular interference pattern can be divided into equal area annular bins, and

ARTICLE IN PRESS 1524

E.J. Mierkiewicz et al. / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 1520–1552

3.3. PMTs vs. CCDs

r1

rN-1

P rN

P Fig. 1. Ring image cartoon of the 1st and Nth Fabry–Perot annuli on a square (P P) CCD array. The 1st annulus, or central resolution element, has a radius of r1 ; the inner and outer radii of the Nth annuli (i.e., resolution element) are rN1 and rN , respectively. The areas of the 1st and Nth annuli are equal. Note, the pﬃﬃﬃﬃﬃ maximum possible radius on the CCD is rmax ¼ ðPsÞ=2 ¼ N r1 , where P is the number of pixels along each dimension of the square array; s is the size of the pixels. Refer to Roesler et al. (1994).

reassembled, with the aid of software, to provide a useful spectral proﬁle; refer to Fig. 2. Although CCD annular summing spectroscopy is the main focus of this paper, other techniques for the application of the CCD to Fabry–Perot spectroscopy can be found in the literature (see e.g., Hays, 1990; Killeen et al., 1983; Conde, 2002). Conde (2002) discusses a method for retrieving spectra from two-dimensional images of Fabry–Perot fringe images using discrete cross-correlation techniques and observed fringes of a highly monochromatic laser. The method does not assume perfectly circular fringes and actually corrects for distortions that are present in the ring imaging optical system (distortions which can lead to wavelength errors in local regions of the fringe image). For experiments designed to resolve spectral variations across the fringe pattern (e.g., wind determination from all-sky images), these distortions can impact interpretation of the data (Conde, 2002). When integrating over the entire fringe, as is the case in the geocoronal observations discussed in this paper, the average of these errors across the entire fringe are small.

A principle advantage of the CCD/annular summing technique over the more traditional PMT/scanning systems is that light is collected simultaneously in all spectral elements. If there were no other differences between PMTs and CCDs, this multichannel advantage of the CCD/annular summing system leads to an N-fold gain in efﬁciency which is equal to the number of spectral elements sampled within the desired spectral range. As such, signal-to-noise ratios equivalent to those obtained with a PMT/scanning system can be obtained with the annular summing technique in a fraction of the time. Furthermore, any changes in the background during an exposure (e.g., due to variations in atmospheric transmission) affect all the spectral elements in the same way. The high quantum efﬁciency of modern CCDs (80% at Balmer a) combines with multichannel detection to yield a gain in sensitivity of a factor of 10 or more (depending on the details of the problem) over more traditional single-channel PMT/scanning Fabry–Perots (Coakley et al., 1996). Further details regarding the annular summing technique and its application to aeronomy are found in Coakley et al. (1996), including: parameter choices for optimizing performance by the use of a standard format CCD array, read and photon noise considerations in the calculation of signal-to-noise ratios for different applications (e.g., low light levels, large backgrounds, etc.), demonstration observations, and direct comparisons to PMT/ scanning systems. 4. Wisconsin Fabry–Perot facilities Mid-latitude geocoronal hydrogen Balmer a observations by Wisconsin observers now span 1977 to the present with some gaps in the data record (Reynolds et al., 1973; Yelle and Roesler, 1985; Shih et al., 1985; Nossal et al., 1993, 1997, 1998, 2001, 2004; Bishop et al., 2001, 2004; Mierkiewicz, 2002). The majority of these observations were made from Wisconsin, with additional observations from Haleakala (HI) (Harlander and Roesler, 1989; Bishop et al., 2001), and Kitt Peak (AZ) (Nossal et al., 2001, 2004). All of these observations were made with similarly designed large aperture (150 mm), double etalon Fabry–Perot spectrometers (see e.g., Roesler et al., 1979, 1994), and all tied to a single nebular calibration source

ARTICLE IN PRESS E.J. Mierkiewicz et al. / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 1520–1552

1525

(b)

(a)

relative intensity

30

20

10

0 0 (c)

20

40

60

80

bin number

Fig. 2. (a) An example of a geocoronal Balmer a fringe imaged onto the PBO CCD in a 600 s integration. The CDD is an array of 512 512 24 mm square pixels, binned 2 2. The radial position of the fringe is selected so that there is nearly equal spectral baseline to red (toward the fringe center) and blue (toward the edge of the CCD) of the emission. Using the property that equal area annuli in the Fabry–Perot’s interference pattern correspond to equal spectral intervals, (a) is divided into equal area annular bins indicated by alternating white and black annuli in (b); the radius of the ﬁrst resolution element (r1 ) is 22 binned pixels, corresponding to a spectral interval of 3.75 km/s; 20 bins, or resolution elements (i.e., 75 km/s), are shown in (b). (c) The resulting line proﬁle (5 over sampling, 0.75 km/s sample bin). The Abscissa in (c) is in terms of bin number, where 1 bin ¼ 0:75 km=s; bin 0 corresponds to the central sample bin, hence wavelength decreases from left to right. A two cluster Gaussian ﬁt to the data and the residuals (i.e., the difference between the data and ﬁt) are also included in (c).

ARTICLE IN PRESS 1526

E.J. Mierkiewicz et al. / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 1520–1552

(NGC 7000) (Scherb, 1981). Earlier observations, compiled in Nossal et al. (1993), made use of a scanning photo-multiplier detection system, while later observations make use of the CCD camera for annular summing detection (see e.g., Coakley et al., 1996). Each instrument was coupled to a siderostat or situated next to another Fabry–Perot that was coupled to a siderostat. In the later case, the instrument with the ﬁxed pointing was cross calibrated with the instrument with the pointing/ tracking capability. For geocoronal studies, the siderostat allows observations to be made in directions away from signiﬁcant galactic emission and/or toward directions where the Doppler shift between the terrestrial and galactic Balmer a emission is large. The siderostat’s pointing and tracking capability also allows nebular calibration sources to be used for relative and absolute intensity calibration, and keeps the galactic background ﬁxed during an integration. The pointing capability also facilitates observations in multiple viewing geometries. Such observations are useful to constrain forward resonance radiative transfer modeling (see e.g., Bishop et al., 2001). 4.1. PBO and WHAM Fabry– Perots The Wisconsin group is currently operating two CCD annular summing Fabry–Perot spectrometers for geocoronal studies (see e.g., Nossal et al., 2001; Mierkiewicz, 2002). One instrument is located at the Pine Bluff Observatory (PBO) near Madison, WI (43:07 N, 270:33 E); refer to Figs. 3 and 4. The PBO Fabry–Perot has an optical ﬁeld-of-view on the sky of 1:5 , and a spectral range at Balmer a of 75 km/ s (1:6 A˚) with 3.75 km/s (0:08 A˚) spectral resolution (R ¼ l=Dl 80; 000). With a spectral resolution of 3.75 km/s, the PBO Fabry–Perot is capable of resolving the 7 km=s full-width at half-maximum (fwhm) geocoronal Balmer line proﬁle, as well as providing intensity data. The second instrument, the Wisconsin Ha Mapper (WHAM), has been in operation at Kitt Peak Observatory, AZ (31:98 N, 248:40 E), since 1997. Although WHAM is used primarily for making astronomical observations of interstellar medium emissions (Haffner et al., 2003), the terrestrial emissions present in the WHAM astronomical Balmer a spectra offer a rich resource for studying the geocorona (Nossal et al., 2001). Dedicated WHAM geocoronal observations are also con-

Fig. 3. The Wisconsin group is currently operating two CCD annular summing Fabry–Perot spectrometers for geocoronal studies. One instrument is located at Kitt Peak Observatory, AZ (31:98 N, 248:40 ). The second instrument (shown here) is located at Pine Bluff Observatory (PBO), WI (43:07 N, 270:33 ). The PBO Fabry-Perot has an optical ﬁeld-of-view on the sky of 1:4 , and a spectral range at Balmer a of 75 km/s (1:6 A˚) with 3.75 km/s (0:08 A˚) spectral resolution. The PBO Fabry–Perot is capable of resolving the 7 km=s full-width at half-maximum geocoronal Balmer line proﬁle, as well as providing intensity data. Broadband etalon coatings and a N2 pressure control system allows the PBO 75 km/s spectral window to be set anywhere between 4500 and 9000 A˚.

ducted. WHAM can detect galactic Balmer a emission as faint as 0:05R in a 30 s exposure, covering a 200 km/s (4.4 A˚) spectral region with 12 km/s spectral resolution from a 1 beam on the sky (Tufte, 1997). With this sensitivity, hundreds of spectra can be collected in a single clear night. Over 40,000 Balmer a spectra have been collected as part of the WHAM galactic survey since 1997. Although not capable of fully resolving the geocoronal Balmer a line proﬁle, WHAM’s sensitivity makes it an exceptional instrument for geocoronal Balmer a intensity observations. 4.2. Dual etalon configuration A double etalon Fabry–Perot, in which two etalons are combined in series, assists in isolating the geocoronal emission line. This conﬁguration

ARTICLE IN PRESS E.J. Mierkiewicz et al. / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 1520–1552

Fig. 4. Basic optical diagram of the siderostat and dual-etalon Fabry–Perot annular summing spectrometer located at Pine Bluff Observatory (not to scale). Light from the sky is directed by the plane mirror siderostat through the input optics (L1 and L2) and into the etalons (E1 and E2). A series of post-etalon optics (L3, L4, and L5) image L1 and the Fabry–Perot fringe pattern onto the CCD. (The distance between L1 and L2 is 4000 mm.) The ﬁeld-of-view for a 100 mm ﬁeld stop is 1:4 .

enables high spectral purity and contrast by extending the free spectral range Q (i.e., the spectral distance between adjacent orders of transmission) and suppressing the broad Lorentzian wings of a single etalon’s transmission (i.e., Airy) function (Roesler, 1974). The second etalon also sharpens the common transmission peak of the two etalon system (Daehler and Roesler, 1968). For geocoronal studies, the extended free spectral range of the two etalon system allows spectrally broad (25 km=s) nebular emissions to be used as absolute intensity references. The WHAM and PBO etalons are made of fused silica with highly reﬂective (91 1% near Balmer a) broadband (4500–9000 A˚) multi-layer dielectric coatings on their inward facing surfaces modiﬁed from the Trauger (1976) design by Tscharnack (unpublished). The outside surfaces of each etalon

1527

are wedged 0.01 rad in order to throw off reﬂections from any plane parallel surface that is not the coated inner surface. The plates are ﬂat to l=200. The PBO Fabry–Perot has a resolving etalon with a ﬁxed gap of l ¼ 0:149 cm, corresponding to a wavenumber free spectral range of Qs ¼ 3:36 cm1 . The addition of a second lower resolution etalon, with a ﬁxed gap of l ¼ 0:0524 cm (Qs ¼ 9:54 cm1 ), extends the free spectral range of the resolving etalon, by suppressing unwanted multiple orders of interference. The WHAM resolving etalon has a ﬁxed plate spacing of l ¼ 0:0471 cm, corresponding to a wavenumber free spectral range of Qs ¼ 10:62 cm1 ; the plate spacing and wavenumber free spectral range of the second, lower resolution, etalon are 0.0201 cm and 24:88 cm1 , respectively (Tufte, 1997; Haffner et al., 2003). In a dual etalon system, where each etalon is housed within its own pressure chamber, the pressure difference between the two chambers can be adjusted to align (i.e., pressure tune) the transmission peaks of each etalon to a desired wavelength. Broadband etalon coatings and a N2 pressure control system allows the PBO 75 km/s spectral window to be set anywhere between 4500 and 9000 A˚. The SF6 pressure control system used by WHAM allows the WHAM 200 km/s spectral interval to be set anywhere from 4800 to 7320 A˚; the optical elements in the WHAM Fabry–Perot are optimized for Balmer a and b (4861 A˚) which ultimately limit the full 4500–9000 A˚ range of the broadband etalon coatings. For the PBO and WHAM geocoronal observations, once the etalons are tuned for Balmer a, the chamber pressure is set so that radial position of the Balmer a fringe on the CCD has nearly equal baseline to the red and blue of line center. Unlike PMT/scanning systems once the etalons are pressure tuned, and the ring is placed in an optimal position on the CCD, a ﬁxed pressure is maintained for the duration of each exposure. Pressure control systems, appropriate for ﬁxed-pressure operation, allow the chamber pressures to be maintained to within 0.1 mm Hg. Figs. 5a–f show the theoretical transmission function for each of the PBO and WHAM etalons, along with their combined transmission functions, shown here with each of the two PBO and WHAM etalons tuned to Balmer a. It can be seen in Figs. 5c and f that the combined transmission functions each have a single strong transmission peak at their tuned wavelength, along with some very weak ‘ghost’

ARTICLE IN PRESS 1528

E.J. Mierkiewicz et al. / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 1520–1552

Fig. 5. The theoretical transmission function of the PBO (a) and WHAM (d) resolving and suppression (b and e) etalons shown here with each set of etalons tuned to Balmer a. The combined PBO (c) and WHAM (f) transmissions are also shown. The suppression etalon(s) removes unwanted multiple orders passed by the resolving etalon(s) alone, signiﬁcantly extending the free spectral range of the spectrometer. An interference ﬁlter proﬁle is also indicated by the dotted curve in (a) and (e). The dotted vertical lines (a–f) indicate the position of two strong OH airglow emissions at 15254:34 and 15218:81 cm1 .

ARTICLE IN PRESS E.J. Mierkiewicz et al. / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 1520–1552

peaks that appear where only one etalon has a transmission peak. When designing multi-etalon systems, care must be taken in selecting the spacer ratios in order to ensure that unwanted emission lines are not located at one of these ghost peaks. For example, the PBO spacer choices virtually eliminates spectral contamination at Balmer a from two nearby OH airglow lines at 15254:34 and 15218:81 cm1 (indicated by vertical dashed lines in Figs. 5a–f). Although the addition of a second etalon extends the free spectral range of the resolving etalon, a ‘premonochrometer’ (e.g., an interference ﬁlter) is still required in order to suppress unwanted multiple orders of transmission that lie beyond the extended free spectral range of the dual etalon system. This ﬁlter can have a much broader pass band than would be necessary for a single etalon system. For illustrative proposes a 20 A˚ (fwhm) ﬁlter proﬁle is indicated by dashed lines in Figs. 5a and d. 5. The PBO Fabry–Perot: an example of an annular summing spectrometer The ﬁrst application of a Fabry–Perot annular summing spectrometer to the study of the geocoronal Balmer a emission was implemented by adding a CCD imager to an existing PMT/scanning Fabry–Perot (Coakley et al., 1996). Although this retroﬁtted Fabry–Perot contributed to an important new understanding of geocoronal Balmer a excitation and emission, the data set was limited in coverage, and instrumental vignetting within the retroﬁtted instrument compromised the full advantage of the annular summing technique (Nossal et al., 1997, 1998). In 1999 the entrance and exit optics of the demonstration instrument were redesigned and the instrument was rebuilt in order to minimize vignetting and facilitate improved intensity, wavelength, and linewidth calibration (Mierkiewicz, 2002; Mierkiewicz et al., 1999). This newly designed CCD/ annular summing Fabry–Perot is currently installed and operated at the University of Wisconsin’s PBO. 5.1. Optical system The PBO Fabry–Perot is coupled to a plane mirror siderostat. Light from a 2 beam on the sky evenly illuminates 150 mm etalons (1:4 beam on the sky when the etalons are stopped down to 100 mm), ﬁlling angles corresponding to a 75 km/s spectral

1529

interval. The resulting fringe pattern is imaged onto a 1:2 cm2 CCD with 24 mm square pixels binned 2 2. A schematic drawing of the PBO Fabry–Perot optical system is shown in Fig. 4. The three main parts of this optical system are the siderostat, the input optics, and the exit optics. 5.1.1. The siderostat The siderostat allows pointing and tracking; this is especially important for nebular calibration, for sampling a wide range of viewing geometries, and for avoiding regions of signiﬁcant galactic emission. Light from a selected region of the sky is reﬂected by the primary mirror of the siderostat to a secondary mirror, and into the input optics train (lenses L1 and L2 in Fig. 4). The primary mirror is moved in right-ascension a and declination d by stepper motors; each step corresponds to 7.5 s of time in a and 30 in d. When tracking, the stepper motor driving the motion in a is triggered one step (moving east to west) every 7.5 sidereal seconds. In order to adjust for pointing errors due to slight drifts in the tracking mechanism and small misalignments in the axes, offsets from bright stars are used to verify the pointing. A ﬂoat glass port window (91% transmission at 6300 A˚), located between L1 and L2, isolates the temperature controlled Fabry–Perot observing room from the night air. 5.1.2. Input optics Eq. (5) can be rewritten in terms of velocity Dv y2FP , (12) c 2 where c is the speed of light and Dv is the spectral range, in units of velocity, from on-axis out to an angle yFP . By Eq. (12), the desire to cover a 75 km/s spectral interval translates into a 1:28 half-angle for the cone of rays passing through the etalon. The role of the input optics is to map the 2 ﬁeld-ofview on the sky into this 1:28 half-angle cone and to eliminate spatial and spectral confusion at the detector. A pair of lenses (L1 and L2 in Fig. 4) accomplishes this task. Lens L1 (f L1 4300 mm, d L1 ¼ 200 mm) is located near the base of the siderostat (refer to Fig. 4). Lens L2 (f L2 4000 mm, d L2 ¼ 160 mm) sits 250 mm above etalon chamber E1. L1 and L2 are uncoated BK-7, plano-convex single element lenses. The distance between L1 and L2 is f L2 . With this L1–L2 spacing, the image of the Fabry–Perot fringe

ARTICLE IN PRESS E.J. Mierkiewicz et al. / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 1520–1552

1530

plane formed by L2 is located near L1. Furthermore, the ring image corresponding to a 75 km/s spectral interval formed by L2 at L1 ﬁts comfortably within the diameter of L1 (d L1 ). The net result is that light from all points on the sky is uniformly distributed across the 75 km/s spectral interval. The L1–L2 combination (f eff ¼ 4028 mm) images the sky near the top of etalon chamber E1; a ﬁeld stop at this location allows the ﬁeld-of-view on the sky to be selected. This sky image plane location is also useful in terms of checking the siderostat’s pointing error, and off-setting from bright stars to faint nebular calibration regions. A fold-mirror/ Fresnel-lens combination can be inserted into the beam near the sky image plane, allowing the entrance optics to act as a ﬁnder-scope. The majority of geocoronal Balmer a data is collected at PBO with the system stopped down to d ¼ 100 mm due to efﬁciency losses of the etalons at diameters much larger than 100 mm, refer to Fig. 6. A ﬁeld-stop of 100 mm corresponds to a 1:4 ﬁeld on the sky.

In many Fabry–Perot systems there are no input optics. In this case, the sky and the Fabry–Perot’s annular fringe pattern are conjugate. Thus, when the annular fringe pattern is imaged onto a CCD, so is the sky. The spectral information contained in the fringe pattern is still intact at the detector, but the amount of light reaching any point on an annular fringe is determined by the conjugate fringe on the sky (i.e., spatial and spectral features are recorded at the CCD). This is not a problem when a PMT/ scanning Fabry–Perot is used for geocoronal observations, as a single element detector effectively integrates all the light from the resolution element to which it is coupled. With the CCD/annular summing technique, however, spatial structure on the sky, due primarily to the galactic Balmer a background (see e.g., Haffner et al., 2003), will distort the annular fringe at the CCD, and may lead to misinterpretations of the geocoronal line proﬁle data. 5.1.3. Exit optics The exit optics image the desired spectral range onto the CCD with appropriate sampling given

60

50

relative intensity

40

30

20

10

0 0

50

100

150

iris diameter (mm) Fig. 6. Relative intensity of nightsky OI 6300 A˚ emission vs. iris diameter (i.e., as a function of ﬁeld-stop setting). The dotted curve indicates the theoretical response of the PBO Fabry–Perot as the etalon area is increased. At an iris setting of 100 mm the PBO Fabry–Perot begins to depart from its theoretical response. (An iris setting of 100 mm corresponds to a 1:4 ﬁeld-of-view on the sky.) Nightsky OI was used for this study as it is very bright airglow emission relative to Balmer a.

ARTICLE IN PRESS E.J. Mierkiewicz et al. / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 1520–1552

the detector and pixel size. The ﬁrst element in this optical chain is a ring imaging lens L3 (f L3 ¼ 760 mm) which immediately follows etalon chamber E2. An aperture located in the focal plane of L3 can be used to limit the spectral interval and is also useful for alignment procedures. L4 (f L4 ¼ 254 mm) re-collimates the light imaged by L3, allowing the collimated beam to ﬁt through a 50 mm interference ﬁlter (16 A˚ fwhm at Balmer a). The interference ﬁlter is used to suppress unwanted orders transmitted by the two etalon system. L5 (f L5 ¼ 85 mm) re-images this ﬁltered beam onto the CCD, a 512 512 array of 24 mm square pixels binned 2 2. Refer to Fig. 7. The effective focal length f eff of the ring imaging system (L3, L4, and L5) determines the radius of the fringe pattern on the CCD. For a given angle yFP , f rCCD ¼ f L3 L5 tan yFP ¼ ðf eff Þ tan yFP . (13) f L4 For the PBO Fabry–Perot, f eff is calculated to be 254 mm. It is critical to choose these lenses carefully in order to match the Fabry–Perot’s annular fringe pattern to the CCD (i.e., its area and pixel size), which ensures that the desired spectral interval not only ﬁts on the chip, but that it is also adequately sampled (Coakley et al., 1996). In order to reduce the impact of CCD read noise in applications which are read noise limited (refer to Section 9), it is important to keep the number of pixels per annular resolution element to a minimum, yet maintain an adequately sampled resolution element out to the edge of the desired spectral interval. This last point is of particular importance so as to not degrade the resolving power of the system as one moves radially outward from the center of the annular interference pattern. Thus, care must be taken when designing E2

fL3

fL4

fL5

CCD

L3

L4

L5

Fig. 7. Fabry–Perot exit optics ‘‘ray trace’’ cartoon (not to scale). The exit optics image a 75 km/s spectral range onto a 1:2 cm2 CCD array (512 512 24 mm pixels binned 2 2). (The interference ﬁlter which sits between L4 and L5, and the fold mirror after L3 are not included in this cartoon for simplicity.)

1531

the exit optics in order to ensure that the radial width of the outermost annular resolution element is at least two pixels wide, thereby satisfying the Nyquist sampling theorem (which requires at least two samples per resolution element). 5.2. Annular summing at PBO The CCD image of the Fabry–Perot’s annular fringe pattern is divided into equal area annular bins in software, the area of which is selected so as to subdivide each nested resolution element into smaller spectral intervals, where a resolution element is deﬁned by the fwhm of the spectrometer’s instrumental function. For the PBO Fabry–Perot, this width is 3.75 km/s (R ¼ 80; 000). By Eq. (8) the angular radius of the ﬁrst 3.75 km/s resolution element is found to be, sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 2 y1 ¼ (14) ¼ 0:005 rad ¼ 0:28 80; 000 which, by Eq. (13), with f eff ¼ 254 mm, corresponds to a radius of the ﬁrst resolution element r1 on the CCD of r1 ¼ ð245 mmÞ tanð0:28 Þ ¼ 1:24 mm

¼ 25:8 pixels.

1 pixel 48 103 mm

ð15Þ

Note, in the standard mode of operation at PBO, the CCD is binned 2 2, thus, hereafter, pixels refer to binned (i.e., 48 mm) pixels. Exact values for f eff and r1 are determined by calibration measurements discussed below. The desired 75 km/s spectral interval on the chip corresponds to 75=3:75 ¼ 20 annular resolution elements. The radius of the 20th annular resolution element is determined by Eq. (10), pﬃﬃﬃﬃﬃ r20 ¼ 20 25:8 pixels 115 pixels. (16) The radius of the 19th annular resolution element is r19 112 pixels. Thus, the radial width of the 20th resolution element is 1152112 ¼ 3 pixels, which, as it is greater than two pixels wide, is adequately sampled. In the annular ring-summing procedure, each annular resolution element is sampled several times by choosing an appropriate sample area, the area of which is picked such that the last annular resolution element contains at least two annular samples. Given that the radial width of the 20th resolution element of the PBO spectrometer is 3 pixels across,

ARTICLE IN PRESS 1532

E.J. Mierkiewicz et al. / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 1520–1552

an outermost annular sample bin of one pixel radial width, with an outside radius of r ¼ 115 pixels, is a reasonable sample choice. This sample corresponds to an annular area of 720 pixels, or equivalently, a radius of the ﬁrst sample bin (or ‘‘data point’’) of r1dp ¼ 15 pixels. There is no harm in over sampling, so long as the sample bin is not so small that equal area bins eventually fail to contain pixels. In fact, there is an advantage to over sampling in that it yields a well determined instrumental function or proﬁle (IP) which can be ﬁt with minimal error (i.e., several data points across the fwhm of the IP reduce uncertainties in ﬁtting procedures). A sample bin corresponding to r1dp ¼ 10 pixels is used in the PBO data analysis. Spectral dispersion measurements (refer to Section 5.4) indicate a spectral interval per sample bin of 0.75 km/s 15th the size of a 3.75 km/s resolution element . Knowing that r1dp ¼ 10 pixels corresponds to 0.75 km/s spectral interval per sample bin, the initial effective focal length estimate of the ring imaging system, which assumed the optical system to be perfect and all lenses simple, was reﬁned and determined to be f eff ¼ 214:7 mm. Based on this measured effective focal length, the radius of the ﬁrst annular (3.75 km/s) resolution element is determined to be 22 pixels and the radial width of the outer most annular resolution element is 2:5 pixels (still adequately sampled with r1dp ¼ 10 pixel sample bin at the 20th annular resolution element). 5.2.1. The annular summing algorithm Once the size of a sample bin (i.e., the area of a circle with radius r1dp ) is selected, and the center of the annular fringe pattern is determined (refer to Section 5.2.2), a computer algorithm divides the CCD array into equal area annular elements, and performs the annular ‘‘ring-sum’’. For each pixel in the CCD array, the annular summing algorithm calculates an area, the value of which corresponds to the area of an imaginary circle of which the pixel is the radius (centered on the center of the fringe pattern). The area assigned to each pixel is divided by the area of the sample bin, and the result is rounded down to the nearest integer; this integer corresponds to the equal area annular bin in which each pixel falls (e.g, bin 0, bin 1, etc.). Refer to Figs. 2a and b. Once each pixel is assigned to an equal area bin, the mean pixel value in each bin is determined (out to some maximum bin maxdp). During this procedure each bin is ﬁltered to remove any ‘‘hot’’ pixels

(e.g., due to cosmic ray hits) using a two pass 3s ﬁlter. Any pixel value which is 3s away from the mean value of the bin to which it belongs is removed as shown in Fig. 8a–f. After the ﬁnal ﬁlter pass, the average pixel value (in ADU) per bin is plotted as a function of bin number to obtain a useful line proﬁle (refer to Fig. 8e). The bin spacing is eventually calibrated to a known spectral interval (refer to Section 5.4) and the line intensity is determined via nebular calibration (refer to Section 6). The PBO ring-summing and line center algorithms are modeled on earlier algorithms by Coakley (1995) and Coakley et al. (1996). Prior to ring-summing all CCD frames were bias subtracted; a pixel-by-pixel subtraction technique was used in which a mean bias image was subtracted from the fringe image. 5.2.2. The ring center algorithm An accurate ring center determination is important in order to avoid signiﬁcant distortion of the line proﬁle. A narrow fringe, corresponding to the thorium 6554 A˚ emission produced in a thorium– argon hollow cathode laboratory lamp, is used to determine the center of the annular fringe pattern. A ﬁrst guess for the annular fringe center is determined ‘‘by eye’’. This procedure involves plotting a circle over the CCD image of the thorium fringe, with a radius approximately equal to the radius of the fringe; the circle center is varied until the circle overlays the fringe. The ﬁrst guess for annular center is used as the basis for a computer grid search using a ‘‘medium’’ and ‘‘ﬁne’’ grid. The medium grid search uses a 5 5 grid, with 0.5 pixel resolution. The best center choice is determined by performing successive annular sums of the thorium 6554 A˚ fringe about each grid point, recording the line-width of a single Gaussian ﬁt to the 6554 A˚ line. The best center is deﬁned as that which results in the narrowest 6554 A˚ line width. The ﬁne grid search uses a 7 7 grid with 0.1 pixel shifts from the best center returned by the medium grid search. During the analysis of the PBO data, the previous night’s medium grid search result is used as a ﬁrst guess for the ﬁne grid center search. On the rare occasion in which a 6554 A˚ data is not available, the center choice from the closest night with a center determination is used. On nights with more than one 6554 A˚ scan, typical of most nights, an average center determined from all 6554 A˚ data is used in the analysis.

ARTICLE IN PRESS E.J. Mierkiewicz et al. / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 1520–1552

1533

40 (a)

(b)

bin 75

20

bin75

20

10

0

0 40 (d)

20

20

10

0

0 40 (f)

(e)

20

20

0

frequency

relative intensity

(c)

10

0 0

20

40 60 bin number

80

100

-20

-10

0

10 value

20

30

40

Fig. 8. A two pass, 3s ﬁlter was used to eliminate ‘‘hot’’ pixels. (a) Ring-sum of a typical Balmer a nightsky CCD image before ﬁltering. A number of noisy bins are apparent (see e.g., bin number 75, circled in a, c, and e). (b) The unﬁltered pixel value frequency distribution (300 pixels) in bin 75. (c–d) Pixels with ADU counts outside the 3s limit are removed. (e–f) This procedure is repeated and noisy bins due to a few hot pixels are ﬁltered. There are typically 1 or 2 hot pixels per bin in a 10 min integration.

5.3. Instrumental function (IP) The IP is a measure of a spectrometer’s response to a delta function input spectrum. The etalon spacer choice, plate reﬂectivity, and defect terms all combine to determine this response and thus, the achieved resolving power (i.e., the fwhm of the IP) of a Fabry–Perot. The IP is used when analyzing data in order to differentiate the portion of the observed line width due to the instrument from that arising from the emission under study. In the case of the PBO Fabry–Perot, the measured IP is convolved with a model ﬁt to the geocoronal data in order to account for the line broadening due to the instrument (refer to Section 8.3). Thorium is a heavy, even–even nucleus, and is therefore a very narrow emission with no hyperﬁne structure (Roesler, private communication). The predicted width of the thorium emission produced in a hollow cathode lamp (with a typical discharge 1 temperature of 1000 K) is 0.42 km/s; 10 th the expected measured line width for a spectrometer

working at a resolving power of 80,000. Thus, the thorium emission can be used as a measure of the spectrometer’s achieved spectral resolving power, where it is assumed that all observed broadening to the thorium emission is due to instrumental effects. Neglecting the inherent width of the thorium emission introduces a negligible 4 K systematic error in temperature when interpreting the Balmer a line proﬁle in terms of an effective temperature (Nossal et al., 1997). The thorium 6554 A˚ line is the brightest thorium line in the spectral vicinity of Balmer a. As such, reﬂectivity and phase shifts in the etalon coatings are not expected to have a dramatic effect on thorium 6554 A˚ relative to Balmer a (6563 A˚). This line is used at PBO to determine the Fabry–Perot’s IP. Note, it is important to measure the IP at the same position on the CCD as the spectral feature under study is observed, in this way uncertainties due to imperfections in the optical imaging of the ring pattern onto the CCD will be minimized (Coakley et al., 1996).

ARTICLE IN PRESS E.J. Mierkiewicz et al. / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 1520–1552

1534

In order to isolate the thorium 6554 A˚ emission line from other nearby features (refer to Fig. 9a), the spectral range near the 6554 A˚ emission is ﬁt with a four component model and a sloping background. Once ﬁt, the three components corresponding to ‘‘background features’’ are subtracted, thereby isolating the 6554 A˚ emission line (refer to Figs. 9b and c). The PBO IP is deﬁned as the region 15 bins from the center of the ﬁt component corresponding to the thorium 6554 A˚ emission line (refer to Fig. 9d). The average measured fwhm of the thorium 6554 A˚ emission line by the PBO Fabry– Perot is 3.75 km/s (i.e., R ¼ 80; 000). 5.4. Dispersion calibration The dispersion (i.e., the spectral interval per sample interval or bin) across the CCD chip can be calculated by imaging the emissions from two narrow laboratory lamp lines on the CCD with an

accurately known wavelength difference. Note, it is important to use laboratory lamp lines with wavelengths close to that of the emission line under study as the spectral dispersion depends on wavelength. One method involves using a hydrogen–deuterium (H–D) lamp. The Balmer a line of hydrogen differs in wavelength from the Balmer a line of deuterium by 1.78 A˚ (82 km/s). By scattering light from a H–D laboratory lamp off a white card located above the Fabry–Perot, and knowing the spectral interval between the observed H and D lines, the corresponding spectral interval per annular bin is determined. This method works well for lower resolving power systems such as WHAM (see e.g., Tufte, 1997), but the broad H–D emission lines and their complex line ratios, which depend on the properties of the lamp, lead to unacceptable uncertainties at high resolving powers (Roesler, private communication).

(a)

bin number

(b)

bin number

(c)

bin number

(d)

∆ bin from V3

Fig. 9. (a) The thorium 6554 A˚ line (bright line near bin 50) was used as an instrumental proﬁle in the PBO analysis. The average measured fwhm of this emission was found to be 3.75 km/s, corresponding to a resolving power of 80,000. The full 75 km/s range in (a) is ﬁt with a four component model and a sloping background. (b) The three components corresponding to ‘‘background features’’ in the spectra are isolated, and subtracted (c). (d) The IP itself is deﬁned as the region 15 bins from the center of component V3.

ARTICLE IN PRESS E.J. Mierkiewicz et al. / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 1520–1552

Estimates of the spectral interval per data point can also be determined by taking two images of a known calibration line (e.g., thorium 6554 A˚) at two different absolute chamber pressures (i.e., the theoretical shift in spectral interval with a change in pressure can be determined, and thus the corresponding measured shift in ring position can be used to calculate the spectral interval per annular bin). To fully exploit this technique a fringe counting method, e.g., using a Michelson gas refractometer with a well determined fringe interval, is needed in order to get enough accuracy in the change in m with the change in pressure (see e.g., Coakley, 1995). In the case of the PBO Fabry–Perot system, the spectral interval per sample interval was determined with a method analogous to the H–D lamp technique, only in this case images of two pairs of two well known narrow thorium lines were used: 6564.4443, 6565.0698, and 6560.0576, 6558.8755 A˚. The known spectral intervals between these lines allowed the 0.75 km/s spectral interval per sample bin of the PBO spectrometer to be determined. This

1535

technique was made possible due to the optical design of the PBO Fabry–Perot in which a 75 km/s spectral interval (and hence a number of thorium calibration lines) could be obtained in one exposure. Small differences in the spectral interval per data point can be calculated by changing the location on the CCD chip at which the laboratory emission lines are imaged (see e.g., Tufte, 1997). 6. Intensity calibration The absolute intensity of each geocoronal Balmer a spectrum is based on a comparison of the integrated area of the geocoronal line with that from a nebular calibration source (obtained on the same night if possible); refer to Fig. 10. The primary calibration source is a 0:8 region of NGC 7000 (i.e., the North American Nebula, NAN), centered at að1950Þ ¼ 20h 56m 17s , dð1950Þ ¼ 44 240 0300 , with a Balmer a surface brightness of 850 50R (Scherb, 1981). Accurate pointing capabilities are required to consistently repeat an intensity calibration using the same patch of NAN.

80

relative intensity

60

40

20

0 0

20

40

60

80

bin number Fig. 10. Typical NAN spectrum and 1-component Gaussian ﬁt. The intensity of the 0:8 NAN calibration region deﬁned by Scherb (1981) is 850 50 Rayleighs. Using the bootstrap method described in Section 6.2, the surface intensity of NAN in the PBO Fabry–Perot’s 1:4 ﬁeld-of-view is 650 Rayleighs. The abscissa is in terms of bin number, where 1 bin ¼ 0:75 km=s; bin 0 corresponds to the central sample bin, hence wavelength decreases from left to right.

ARTICLE IN PRESS 1536

E.J. Mierkiewicz et al. / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 1520–1552

Nebular calibration offers the advantage of longterm source stability and calibration by line rather than continuum emission. As nebular sources are diffuse, they ﬁll the Fabry–Perot’s ﬁeld-of-view in much the same way as the geocorona. In addition, as these sources are outside of the Earth’s atmosphere, they are subject to the same (lower) atmospheric extinction process as the geocorona itself, thereby minimizing this source of uncertainty. All Wisconsin geocoronal data sets (past and present) use NAN as an absolute intensity calibration, thereby providing internal consistency between data sets and less uncertainty when searching for longterm trends (see e.g., Nossal et al., 2006). The standard stars a Boo and a Tau, and the planetary nebula NGC 7662 were used in the initial NAN Balmer a calibration (Scherb, 1981). This calibration was checked against a black body (Nossal, 1994), and its accuracy has also been corroborated with a comparison to the Southern Balmer a Sky Survey Atlas of Gaustad et al. (2001). Several spectra of NAN, or of a secondary calibration source when NAN is not available, are obtained during every night of observations to allow for correction of night to night variations in atmospheric transmission. The absolute intensities for all geocoronal observations for a given night are then derived by comparison to the calibration source spectrum, including a correction for atmospheric extinction. 6.1. Extinction correction and absolute intensity determination The atmospheric extinction coefﬁcient can be determined by observing a nebular calibration source throughout the night and monitoring the intensity of the nebular source as a function of the airmass of the observation, where airmass is deﬁned as the secant of the zenith angle (ZA) of the observation. By the Beer– Lambert Law, I NAN ¼ I NAN et secðZANAN Þ

(17)

or lnðI NAN Þ ¼ lnðI NAN Þ t secðZANAN Þ,

(18)

where I NAN is the intensity of NAN at the top of the atmosphere (i.e., unextincted), t is the atmospheric extinction coefﬁcient, and ZANAN is the ZA of NAN at the time of observation. By observing NAN at a number of zenith angles, and plotting the natural logarithm (ln) of its measured

intensity (or its integrated area under the line ANAN , where ANAN / I NAN ) as a function of airmass, secðZANAN Þ, the extinction coefﬁcient t is determined, where t is the slope of this extinction curve; refer to Fig. 11. The average clear sky Balmer a extinction at PBO from 2000–2001 was t 0:14. An extinction coefﬁcient of 0:14 corresponds to transmissivity (i.e., T ¼ I=I ) of 0:86 at ZA of 20 , in good agreement with earlier measurements at PBO by Reynolds and others (Reynolds, private communication). The atmospheric Balmer a extinction coefﬁcient for clear sky conditions at Kitt Peak Observatory is t 0:08. For a given ﬁeld-of-view, the ratio of the integrated area of the geocoronal emission line (ADU/s bin) to the integrated area of a corresponding NAN scan (ADU/s bin) is equal to the ratio of their intensities I geo et secðZAgeo Þ Ageo I geo ¼ ¼ . ANAN I NAN I NAN et secðZANAN Þ

(19)

Thus, if I NAN is known, and Ageo and ANAN are observed, I geo can be determined, i.e., I geo ¼ I NAN

Ageo tðsecðZAgeo ÞsecðZANAN ÞÞ e , ANAN

(20)

where I geo and I NAN are the intensity of the geocorona and NAN at the top of the atmosphere (i.e., unextincted), t is the atmospheric extinction coefﬁcient, ZAgeo and ZANAN are the zenith angles of the geocorona and NAN at the time of their observation, and Ageo and ANAN are their respective observed integrated areas. 6.2. Adjusting the NAN calibration for differing fields-of-view There are differences in the intensity of the NAN calibration associated with differences in ﬁelds-ofview; because of the spatial structure of NAN and efﬁciency differences within a Fabry–Perot when different areas of the etalons are illuminated (see e.g., Fig. 6), the intensity of the calibrated 0:8 region of NAN cannot simply be scaled to a new ﬁeld-of-view. The Balmer a intensity from a 0:8 patch of NAN viewed by the Wisconsin scanning Fabry–Perots was measured to be 850 50R (Scherb, 1981). The NAN Balmer a intensity from the WHAM 1:0 ﬁeld is estimated to be 800R 80. Mierkiewicz (2002) measured the intensity of the patch of NAN viewed by the 1:4 ﬁeld-of-view of the PBO annular summing Fabry–Perot to be

ARTICLE IN PRESS E.J. Mierkiewicz et al. / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 1520–1552

1537

6

ln(area)

4

2

0 0

1

2

3

4

5

sec(z) Fig. 11. NAN extinction curves (combined data from 11-03-00 and 11-24-00) for three different ﬁeld-stops: 56 mm (0:8 ), 100 mm (1:4 ), and no stop (2:0 ). The average extinction at PBO (for all ﬁelds-of-view) is t 0:14. Taking the ratios of the y-intercept, ANAN ð2:0 Þ=ANAN ð0:8 Þ ¼ 2:58 and ANAN ð1:4 Þ=ANAN ð0:8 Þ ¼ 2:24.

650R by conducting an alternating series of observations of NAN and the nightsky at the new Fabry–Perot’s 1:4 ﬁeld-of-view, and a stopped down ﬁeld, which matched the original 0:8 ﬁeld of Scherb (1981), thereby ‘‘bootstrapping’’ from one ﬁeld-of-view to the other. Three ﬁeld-stops were used in this procedure: 56 mm (corresponding to a 0:8 ﬁeld on the sky), 100 mm (1:4 on the sky), and no stop (2 on the sky); refer to Figs. 11 and 12. The 56 mm ﬁeld-stop corresponds to a ﬁeld-of-view on the sky which matches the original Scherb (1981) NAN calibration (0:8 ). A 100 mm ﬁeld-stop (1:4 ) is the standard mode of operation with the PBO instrument. The question is, if I NAN ¼ 850 Rayleighs for a 0:8 ﬁeld-of-view, what is I NAN for a 1:4 ﬁeld-ofview? Assuming for the moment that there is no extinction, Eq. (19) becomes I geo I NAN

¼

Ageo . ANAN

observations have nearly identical viewing geometries, then I geo ð2:0 Þ ¼ I geo ð0:8 Þ and Eq. (21) becomes, I NAN ð2:0 Þ ¼ I NAN ð0:8 Þ

ANAN ð2:0 Þ Ageo ð0:8 Þ . ANAN ð0:8 Þ Ageo ð2:0 Þ

(22) By ﬁtting a fourth-order polynomial to these three sets of geocoronal observations (i.e., no stop, a 100 mm stop and a 56 mm stop), the average ratios of the geocoronal emission for the three different ﬁelds-of-view is determined; refer to Fig. 12. For example, Ageo ð2:0 Þ=Ageo ð0:8 Þ ¼ 3:53. Note, this ratio is expected to be 7 if the system were perfect, refer to Fig. 6. In this way, by Eq. (22), Figs. 11 and 12, it was determined that: I NAN ð1:4 Þ ¼ 650R and I NAN ð2:0 Þ ¼ 620R. 7. Observation strategies

(21)

Also, assuming that the geocoronal emission is essentially uniform over a few degree ﬁeld and

Due to the extremely faint Balmer a signal (2–15 Rayleighs), observations are restricted to times when the sun is well below the horizon

ARTICLE IN PRESS 1538

E.J. Mierkiewicz et al. / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 1520–1552

Fig. 12. Geocoronal Balmer a intensity (combined data from 11-03-00 and 11-24-00) vs. shadow altitude (km) for three different ﬁeldstops (56, 100 mm, and no stop). Each curve is ﬁt with a fourth order polynomial; the ratios of the coefﬁcients of these ﬁts (between the shadow altitude range of 435 and 4173 km) were used in ‘‘bootstrapping’’ from the Scherb (1981) 0:8 NAN calibration to the PBO Fabry–Perot’s 1:4 (Ageo ð1:4 Þ=Ageo ð0:8 Þ ¼ 2:94) and 2 (Ageo ð2:0 Þ=Ageo ð0:8 Þ ¼ 3:53) ﬁelds-of-view.

(i.e., the solar depression angle (SDA) is 10 or larger). This SDA restriction is necessary in order to reduce the sky background to a manageable level. In addition, spectral contamination from solar features, in particular a deep solar Fraunhofer absorption line at Balmer a, precludes geocoronal Balmer a observations in the presence of scattered sunlight. As such, observations are also limited to periods when the moon is below the horizon, restricting observations to a 2 week period centered around new moon. Observations also require clear nights. As discussed in Section 5, entrance optics couple the PBO Fabry–Perot to a fully pointable siderostat, which allows observations to be made over a wide range of viewing geometries while also avoiding regions of signiﬁcant galactic Balmer a emission. Recent work by Haffner et al. (2003) to produce a velocity resolved map of Balmer a emissions from the interstellar medium is used to select low galactic emission regions for geocoronal observations; refer to Fig. 13. This map also offers the ability to accurately ﬁt and account for the galactic compo-

nent in each geocoronal spectra, an especially important tool in the interpretation of geocoronal line proﬁles. Observations are also kept at least 20 in galactic latitude b away from the galactic plane (b ¼ 0) when possible. Due to the orbital velocity of the Earth, and the peculiar velocity of the sun with respect to the local standard of rest (LSR) (v ¼ 20:0 km=s toward a1900 ¼ 18:0h , d1900 ¼ þ30:0 ), there is a velocity separation (VLSR) between the geocentric rest frame and zero LSR, the magnitude of which depends on the direction in the sky and the time of year. As the majority of the local galactic Balmer a emission occurs near 0 km/s LSR (Haffner, 1999), the galactic component of emission in each geocoronal spectrum will usually be located near VLSR. In some look directions, nonlocal galactic Balmer a, Doppler shifted from 0 km/s LSR by differential galactic rotation, can also contaminate geocoronal observations. Refer to Fig. 14. In general, observation directions are selected in order to maximize the spectral shift (i.e., VLSR) between the geocoronal rest frame and the LSR.

ARTICLE IN PRESS E.J. Mierkiewicz et al. / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 1520–1552

1539

Fig. 13. Wisconsin Ha Mapper (WHAM) all sky survey of galactic Balmer a integrated intensities (37,565 spectra, velocity integrated emission from 80 to þ80 km=s LSR) (Haffner et al., 2003). This map was used to select regions of low galactic emission for geocoronal observations. Not only does the WHAM map guide our observations to regions of low galactic emission, its line intensity, line width, and spectral shift information allow a detailed accounting for the galactic Balmer a component in any of our spectra (ﬁgure is courtesy of L.M. Haffner).

Such a scheme makes it easy to resolve the relatively broad (20 km=s fwhm) galactic Balmer a emission from the narrow (7 km=s fwhm) geocoronal line, thereby minimizing the galactic component’s effect on the retrieval of accurate geocoronal intensities and reducing uncertainties in the interpretation of geocoronal line proﬁles due to galactic contamination. In order to explore the red-wing of the geocoronal emission proﬁle for signatures of cascade emission, free of galactic contamination, observation look directions in which the galactic emission is Doppler shifted to the blue of the telluric emission are favored. Individual observations (spectra) are obtained with right-ascension (a) and declination (d) held ﬁxed (i.e., tracking at the sidereal rate). In this way the interstellar hydrogen background remains constant for each geocoronal spectrum. In order to limit the effects of the lower atmosphere, and to simplify the interpretation of the line proﬁles, observations are also made as close to the zenith as possible given the aforementioned restrictions.

8. Reduction 8.1. Geocoronal Balmer a fine structure Balmer a (6563 A˚) is the result of the ðn ¼Þ3 ! 2 transition of atomic hydrogen and is composed of seven ﬁne structure components; refer to Fig. 15 and Table 1. Geocoronal Balmer a ﬂuorescence arises primarily from solar Lyman b (resonance) excitation. The only electric dipole allowed Lyman b transitions populate the 32 P3=2;1=2 levels as shown in Fig. 15. These levels subsequently decay 88% of the time to the ground state (12 S 1=2 ), and 12% to the 22 S 1=2 state, the latter resulting in the Balmer a emission (see e.g., Bethe and Salpeter, 1957). Thus, Balmer a resonance–ﬂuorescence is a blend of two ﬁne structure components (32 P3=2 ! 22 S1=2 and 32 P1=2 ! 22 S 1=2 ) in a 2:1 intensity ratio with a vacuum wavenumber line center of gravity of 15233:3280417 cm1 (lair ¼ 6562:74 A˚) (Garcia and Mack, 1965). Note, the line center of gravity of the solar excited Balmer a resonance–ﬂuorescence emission is blue shifted 2:3 km=s from the mean

ARTICLE IN PRESS 1540

E.J. Mierkiewicz et al. / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 1520–1552

S

P

D j=5/2 j=3/2

n=3

j=1/2

relative intensity

Geocoronal Balmer α j=3/2 n=2

Galactic Balmer α

j=1/2

n=1 j=1/2

-100

-50 arbitrary velocity

0

50

Fig. 14. Sample WHaM Balmer a spectrum with galactic and geocoronal emissions. The telluric emission feature is the tall narrow peak (7 km=s fwhm), the broader emissions (20 km=s fwhm) 25 and 75 km=s to the blue of the geocoronal line are galactic in origin. Careful observation planning minimizes the overlap of these emissions. In addition, regions of signiﬁcant galactic emission are generally avoided. The geocoronal emission intensity in this scan is 5R; the spectra was obtained in 30 s. Spectral displacement is expressed in velocity units. Zero velocity is placed at an arbitrary location (ﬁgure is courtesy of L.M. Haffner).

Fig. 15. An energy level diagram showing the seven allowed Balmer a transitions of atomic hydrogen. For Lyman b excitation, indicated by the solid lines on the ﬁgure, only the 32 P1=2;3=2 levels are populated, resulting in only two allowed Balmer a transitions (dashed lines on the ﬁgure). The dotted lines indicate the other ﬁve possible ﬁne structure transitions (not present in direct Lyman b excitation). Note, the energy spacing is not to scale.

Table 1 Balmer a emission components Component Transition

2

32 S1=2 ! 2 2 P1=2 15233.301551 6562.752 0.90 32 P1=2 ! 2 2 S 1=2 15233.255771 6562.772 0.0

3

8.2. Cascade

lair (A˚)b Dv (km/s)c

32 D3=2 ! 2 2 P1=2 15233.399279 6562.710 2.824 32 P3=2 ! 2 2 S 1=2 15233.364177 6562.725 2.133

1

Balmer a wavelength (lmean ¼ 6562:79 A˚) which contains the full suite of ﬁne structure components (Garcia and Mack, 1965).

sðcm1 )a

4 6

32 D5=2 ! 2 2 P3=2 15233.06954 6562.852 3.665 32 D3=2 ! 2 2 P3=2 15233.033406 6562.868 4.376

7

32 S1=2 ! 2 2 P3=2 15232.935678 6562.910 6.299

5

a

Vacuum wavenumbers from Garcia and Mack (1965). lair ¼ lvac =m, where m ¼ 1:0002762 at Balmer a. c Velocity intervals are referenced to component 4. b

Cascade processes result in additional Balmer a ﬁne structure components not present in direct solar Lyman b excitation (refer to Fig. 15). Solar Lyman lines beyond Lyman b excite geocoronal hydrogen atoms to energy states n43, some of which decay into n ¼ 3, populating terms (in addition to 3P) which are not allowed by direct Lyman b excitation (i.e., 3S and 3D). These terms subsequently decay to n ¼ 2, adding emission line components from all seven possible Balmer a transitions to the two components allowed by direct excitation. The net result is that the geocoronal Balmer a emission is a blend of nine line components, grouped into two

clusters. One cluster contains the two components from direct solar Lyman b excitation. The other cluster contains seven components from cascade processes. Note, the 32 P3=2 ! 22 S1=2 and 32 P1=2 ! 22 S 1=2 transitions are counted twice (i.e., these transitions include contributions from both direct excitation and cascade processes). The intensity I of a particular emission line is determined by the population of ‘‘emitting’’ atoms

ARTICLE IN PRESS E.J. Mierkiewicz et al. / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 1520–1552

(i.e., the column density N) and the emission rate g. Because the absorption line width of geocoronal hydrogen is much less than the solar emission line width, detailed knowledge of the exciting solar Lyman line shape is necessary in order to calculate geocoronal hydrogen excitation and subsequent emission rates (i.e., the solar Lyman line center ﬂux is primarily responsible for the excitation of geocoronal hydrogen). Using the high spectral resolution data set from the 1962 ultraviolet solar spectrum experiment of Tousey et al. (1963, 1965) (Lyman a through k), combined with the absolute ﬂuxes of Hinteregger et al. (1981) and a pseudocontinuum for Lyman 10 through the Lyman continuum (based on the observations Vernazza and Reeves (1978)), Meier (1995) calculated the excitation and emission g-factors for the parent terms of Balmer a (3P, 3S, and 3D). It was assumed that atomic hydrogen resides in the ground-state, and that only solar Lyman lines participated in the excitation (i.e., no collisional excitation, etc.) (Meier, 1995). The ‘‘ﬁne-structure’’ splitting of each term into its respective j levels was not explicitly solved in Meier’s (1995) calculations, but this can be determined via the intensity ratios for lines within a multiplet. Meier’s (1995) Balmer a emission g-factors, partitioned among all seven ﬁne-structure components, for both direct and cascade induced emission, are presented in Table 2. Note, the 3S transitions (where the 3S parent term is predominately populated by cascade from Lyman g excitation) are favored over the other Balmer a cascade contributions by an order of magnitude (Meier, 1995), with the largest contribution 7.7 km/s to the red of the centroid wavelength of the two directly excited emission contributions (see e.g., Nossal et al., 1998). In the absence of large Doppler shifts, Table 2 Emission g-factors for Balmer a (direct and cascade) (Meier, 1995) Component

Transition

g direct (s1 )

g cascade (s1 )

1

32 D3=2 ! 22 P1=2 32 P3=2 ! 22 S1=2

0

9:34 1010 2:29 1010

2 3 4 5 6 7

32 S1=2 ! 22 P1=2 32 P1=2 ! 22 S1=2 32 D5=2 ! 22 P3=2 2

2

3 D3=2 ! 2 P3=2 32 S1=2 ! 22 P3=2

7

2:64 10 0

7

1:32 10 0 0 0

9:00 109 1:15 1010 1:68 109 10

1:86 10 1:80 108

1541

or complications due to multiple scattering or extinction, the ratios of the emission g-factors are equal to the ratios of the line intensities (Meier, 1995). Based on the Tousey et al. (1963, 1965) data set, Meier (1995) calculated cascade contribution of 7% to the total Balmer a emission (near solar minimum conditions). More recently, Warren et al. (1998) presented high resolution disk averaged solar line proﬁles (obtained with SOHO/SUMER) for Lyman b through l (also for solar minimum conditions). Revised calculations based on the Warren et al. (1998) data set adjusts Meier’s (1995) cascade numbers somewhat lower (to 4% at Balmer a) (Meier, private communication). 8.3. Fits to the data In the case of the high resolution Pine Bluff Fabry–Perot, individual measured spectra are reduced using a four-parameter ﬁt procedure incorporating nine Gaussian line components grouped into two clusters, convolved with an IP (measured several times a night); refer to Fig. 2c. The ﬁrst cluster contains the two ﬁne structure lines directly excited by Lyman b scattering with a ﬁxed 2:1 emission ratio. The second cluster contains the full set of seven Balmer a ﬁne structure components with lines set in the line ratios given in Meier (1995). The transitions, spectral positions, and g-factors for the full set of seven Balmer a ﬁne structure components are listed in Tables 1 and 2. The four free parameters in this ﬁtting procedure are the total intensities of each of the two clusters, the line width (common to all ﬁne structure components), and the spectral position. Lower resolution WHAM column emission intensity observations are typically reduced using a two Gaussian line component model, which accounts for the two geocoronal Balmer a ﬁne structure components directly excited by Lyman b, convolved with an IP. In both the PBO and WHAM ﬁts, the model parameters are iterated subject to the above constraints to produce a least squares, best-ﬁt to the data using the Voigt-ﬁt code of R.C. Woodward, personal communication. 8.3.1. Data bins Because geocoronal hydrogen ﬂuorescence is primarily solar excited, the altitude of the Earth’s shadow at the time of an observation can be used as

ARTICLE IN PRESS 1542

E.J. Mierkiewicz et al. / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 1520–1552

a ﬁrst order determination of the base of the observed column emission. The shadow altitude is deﬁned as the radial distance at which the (groundbased) observer’s line-of-site (i.e., slant path) intersects the Earth’s terminator (shadow line) (more speciﬁcally, in the case of Balmer a, the shadow of Lyman b ‘‘black region’’ at 102 km due to O2 screening). This shadow altitude is uniquely speciﬁed by the SDA, the relative solar azimuth, and the zenith distance of the observation (see e.g., Tinsley, 1974). Various slant paths (deﬁned by the ZA and azimuth of the observation) can correspond to any given shadow altitude. Note, it is the total emission (i.e., the ‘‘column’’ emission) along the line-of-site which is collected by ground-based geocoronal observations. As the SDA changes, the changing height of the Earth’s shadow provides a means by which to study the altitude structure of the exosphere. Shadow altitude and SDA are usually used as indices with which to compare data sets (see e.g., Nossal et al., 2001). As various slant paths can correspond to any given shadow altitude, the data is grouped into bins based on the zenith angle of the observation (OZA) in order to partially account for differences in viewing geometry between various data points (Nossal et al., 2001). The OZA bins are deﬁned as follows: OZAp15 , 15 oOZAp30 , 30 oOZAp45 , 45 oOZAp60 . Only data collected with an OZAs p45 are included in the PBO data presented in this paper. 9. Signal-to-noise ratio estimate for the PBO Fabry–Perot Although the high quantum efﬁciency of modern CCDs combines with multichannel detection to yield a large gain in sensitivity over more traditional single-channel PMT/scanning Fabry–Perots (Coakley et al., 1996), the limitations imposed by ampliﬁer noise associated with the reading of the charge on the CCD must be considered. An estimate for the signal-to-noise ratio obtained with the PBO CCD annular summing Fabry–Perot follows. The number of photons per second, N line , above the background level hitting the detector in one resolution element (l=Ro , where Ro is the theoretical resolving power) is given by N line ¼ ð0:8ÞAO

I line 106 dl , Dlline 4p

(23)

where 0.8 is the average transmitted intensity of the line within the fwhm, I line is the integrated intensity of the source in Rayleighs, A is the area of the etalon plates, O ¼ ð2p=Ro Þ is the solid angle subtended by a resolution element, is the efﬁciency of the optical system (including the quantum efﬁciency of the detector), and dl=Dlline is inverse of the number of resolution elements in the observed line width Dlline . The signal is then the product of the rate (N line ) and the integration time T. Noise terms include contributions from the sky background, CCD dark current, and read noise. The background count rate in one resolution element (N back ) can be estimated in the same way as N line , but with the continuum background intensity I back integrated over a resolution element (i.e., I back dl), N back ¼ AO

ðI back dlÞ 106 . 4p

(24)

The signal-to-noise ratio is then S N line T ¼ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ , N est ðN þ N þN ÞT þ R2 p line

back

dark

(25)

n

where T is the total integration time, Rn the rms read noise, p is the number of pixels in one resolution element, and N dark is total dark current per resolution element (note, N dark ¼ Dp, where D is the dark current per pixel per second). The signal-to-noise ratio obtained in 600 s in a resolution element centered on a geocoronal Balmer a emission line with I line ¼ 5R (a typical intensity for a shadow altitude of 2500 km) in the presence of a 2R/A˚ (0.16 Rayleigh per resolution element) background will be estimated. The efﬁciency of the optical system is assumed to be ¼ 0:08. The resolving power of the PBO Fabry–Perot is R ¼ 80; 000, the etalon diameter used for this observation is 10 cm. With a 3.75 km/s resolution element and a geocoronal line width of 7 km=s, dl=Dlline ¼ 0:5. By Eq. (23), N line ¼ 79 e =s and N back ¼ 6 e =s. With a measured dark current of D ¼ 0:001 e =pixel=s and p ¼ 1520 pixels, N dark ¼ 1:52 e =s. The read noise for the PBO CCD is Rn ¼ 10 e =pixel. From Eq. (25), ðS=NÞest ¼ 100 for a 600 s integration on a 5R line. It is clear from this analysis that the PBO Fabry–Perot is read noise dominated; N back þ N dark do not contribute signiﬁcantly to the total signal-to-noise ratio. Given the form of Eq. (25), the

ARTICLE IN PRESS E.J. Mierkiewicz et al. / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 1520–1552

read noise term can be overcome if N line þ N back is large, or if the integration time is long enough to make the read noise term small in comparison to the integrated signal. Reducing the number of pixels read will also reduce the magnitude of the total read noise contribution. For further discussion of criteria to reduce the number of pixels read per resolution element, using a standard format CCD array, see Coakley et al. (1996). Circular format CCDs (Killeen et al., 1983) and circle-to-line converters (Hays, 1990) are also discussed by Coakley et al. (1996). In the circle-to-line interferometric optical system (CLIO) of Hays (1990), an annular segment is projected onto a CCD as a straight line. This system permits reading only a column of pixels, with 10 pixels per resolution element. If all other variables in the S=N estimate above remain the same, this reduction in pixels read leads to ðS=NÞest ¼ 200 or 2 that obtained with the annular summing method for the case outlined above. This estimate is an upper limit assuming perfect efﬁciency for the CLIO optic. The estimated signal-to-noise ratio can also be compared with experimental data by using the total counts recorded by the CCD, e.g., using Fig. 2c, S Lcp ¼ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ , (26) N rec ðLcp þ Bcp þ DTpÞ þ R2n p where L is 0.8 of the recorded number of counts per pixel above the background signal B in analog-todigital units (ADU) on the peak of the line in time T, c is the conversion from ADU to photoelectrons, which depends on the CCD gain setting, and again p is the number of pixels in a resolution element. D is the measured dark current (¼ 0:001 e =pixel=s). From the data in Fig. 2c, where the CCD gain was c ¼ 1:22 e =ADU, L ¼ 0:8 30 ADU per pixel on the line and B ¼ 10 ADU per pixel on the background. The calculation for the observed signal-to-noise ratio gives ðLcÞp ¼ 44; 506 e /resolution element, ðBcÞp ¼ 18; 544 e /resolution element, ðDTÞp ¼ 912 e /resolution element, and R2n p ¼ 152; 000, yielding ðS=NÞrec ¼ 96 for a 600 s integration; this is in agreement with the S=N estimated from instrumental parameters. 10. Sample PBO geocoronal hydrogen balmer a observations Processing of the sample PBO data set presented here includes bias subtraction, ﬁltering to remove

1543

cosmic rays, and ‘‘ring-summing’’. The data has not been ﬂatﬁelded. In general, ﬂatﬁeld images are typically needed to correct for variations in sensitivity due to vignetting within the instrument, and to correct for pixel-to-pixel variations in the quantum efﬁciency of the CCD. As each annular element used in the PBO analysis contains 300 pixels, pixels-to-pixel variations are averaged out. There is no evidence for any large scale structure on the chip beyond the ﬁxed pattern noise which is removed by the bias subtraction. The carefully designed optical system of the PBO Fabry–Perot greatly reduced the magnitude of instrumental vignetting associated with the CCD demonstration observations. The result is a nearly ﬂat (i.e., unvignetted) 75 km/s spectral region with an estimated 10% loss in efﬁciency from the red to the blue end of the 75 km/s spectral window. In addition to pixel-to-pixel variations in sensitivity, thermal noise (i.e., the accumulation of electrons by the CCD even in the absence of light) is also an issue which must be addressed when using CCDs. Cooling of the CCD helps reduce this dark current. The PBO CCD was cooled to approximately 110 C, resulting in a dark contribution of o0:001 e /pixel/s, an insigniﬁcant fraction of the total noise during a typical 600 s nightsky integration (refer to Section 9). Furthermore, a ring-sum test on a number of dark frames indicates no structure which might adversely affect the annular summed data. Dark frame subtraction was not included in this analysis. Nine Gaussian line components, which are divided into two clusters (one cluster corresponding to direct solar excitation, the other to cascade emission), are convolved with an IP (measured several times a night) and ﬁt to each spectrum. There are four free parameters in this ﬁtting procedure: line width, line center, and the area of each of the two clusters. These ﬁt parameters are tracked over the course of a night, new moon period, etc. A tropospheric scattering model developed by Leen (1979) is available to assess the impact of the lower atmosphere on the Balmer a observations; an important consideration as the geocoronal emission is a spatially extended source and thus, a faction of the total observed Balmer a intensity is due to emission from outside of the Fabry–Perot’s line-ofsight, scattering into its line-of-sight. This effect is estimated to contribute between 14% and 26% to the total observed Balmer a intensity, the magnitude

ARTICLE IN PRESS 1544

E.J. Mierkiewicz et al. / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 1520–1552

of which depends on the OZA (Leen, 1979; Shih et al., 1985; Yelle and Roesler, 1985). Reﬁned tropospheric scattering corrections are needed in order to reduce the uncertainty in the absolute Balmer a intensity determination. The PBO data presented here has not been corrected for tropospheric scattering. The data is corrected for atmospheric extinction (refer to Section 6.1). The absolute intensity calibration of the PBO data set is based on comparisons with NGC 7000 (refer to Section 6). 10.1. Intensity data Geocoronal Balmer a intensity data from 1484 spectra collected over 71 nights between 8 January 2000 and 11 December 2001 (OZAp45 ) are plotted in Figs. 16a and b as a function of shadow altitude. (Shadow altitude and VLSR calculations were determined by an algorithm provided by J. Percival of the University of Wisconsin’s Space Astronomy Lab.) These observations span an interval near solar maximum, with solar/geophysical conditions ﬂuctuating from moderate to high activity during the two years of data presented here. Observations obtained before midnight local time (Fig. 16a) and after midnight local time (Fig. 16b) are grouped together. A number of trends are immediately apparent. The predominate variations in the Balmer a intensities in Figs. 16a and b are associated with line-of-sight variations in the Earth’s shadow altitude; more speciﬁcally the shadow altitude of the Lyman b black region at 102 km due to O2 screening. As the shadow altitude increases, less hydrogen is directly illuminated by solar Lyman b radiation and the emission intensity decreases. Eventually a plateau is reached as contributions to Balmer a from the multiple scattering of Lyman b into the Earth’s shadow become a large fraction of the total emission. It is also clear from Figs. 16a and b that the dawn intensities are, on average, typically 20% brighter than dusk intensities for similar shadow altitudes, with the dusk to dawn intensity asymmetry most apparent at shadow altitudes p2000 km. The magnitude of this dusk to dawn intensity asymmetry is consistent with the earlier observations by Tinsley (1970) and others. 10.2. Doppler widths Balmer a Doppler width data, obtained during the same period as Figs. 16a and b, is plotted as a

function of shadow altitude in Fig. 16c. In this case only spectra in which jVLSRjX10 km=s were included in Fig. 16c. Although most geocoronal observations from PBO were restricted to regions away from the galactic plane (toward regions of low galactic emission), the addition of a VLSR data cut reduces the uncertainty associated with Doppler width determination due to galactic contamination. The WHAM Balmer a galactic survey is being explored as a way to explicitly model the galactic component which is present at some level in almost every geocoronal spectrum. Employing an accurate model of the galactic component in the geocoronal ﬁtting procedure has great potential for reducing uncertainties associated with geocoronal line proﬁle and cascade determination given the ever present galactic background. A decrease in Doppler width with shadow altitude is a persistent feature in every night of PBO observations in which a wide range of shadow altitudes were observed; refer to Fig. 16c. The extent and quality of the 2000–2001 PBO Balmer a data set enables a detailed investigation into this line proﬁle narrowing which was ﬁrst reported by Meriwether et al. (1980) and later observed by Yelle and Roesler (1985) and Kerr et al. (1986). The Nossal et al. (1997) CCD/annular summing demonstration observations show signiﬁcantly less proﬁle narrowing with altitude than the other observers. Although the narrowing trends observed in the 2000–2001 PBO data set are in good qualitative agreement with earlier observations, signiﬁcant line proﬁle perturbations detected by some of these observers (e.g., Meriwether et al., 1980; Kerr et al., 1986) or the Lorentzian-like proﬁles observed at very high shadow altitudes (e.g., Yelle and Roesler, 1985) were not detected in the 2000–2001 PBO data set. In terms of an effective temperature, the decrease in Doppler width with shadow altitude displayed in Fig. 16c represents a 500 K decrease, starting at 850 K near 500 km, and decreasing with shadow altitude to 350 K near 20,000 km. Although it is possible to speculate on potential sources of this decrease (e.g., contributions from satellite atoms at high shadow altitudes or multiple scattering of Lyman b into the Earth’s shadow illuminating cooler hydrogen below the exobase) detailed radiative transport modeling is necessary for full interpretation of the Balmer a line proﬁle. In fact, as anticipated by Meriwether et al. (1980) and Yelle and Roesler (1985), and deﬁnitively concluded by Anderson et al. (1987), the effects of multiple

ARTICLE IN PRESS E.J. Mierkiewicz et al. / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 1520–1552

am

20

20

15

15

intensity (R)

intensity (R)

pm

10 5 0

1545

10 5

0

(a)

2000 4000 6000 8000 shadow altitude (km)

0 10000

10000 (b)

8000 6000 4000 2000 shadow altitude (km)

0

8

DopW (km/s)

7 6 5 4 3 0

5.0x103

1.0x104 shadow altitude (km)

1.5x104

2.0x104

0

5.0x103

1.0x104 shadow altitude (km)

1.5x104

2.0x104

(c)

20

% cascade

10 0 -10 -20 (d)

Fig. 16. 2000–2001 PBO data set. (a–b) Combined Balmer a intensities vs. shadow altitude (km); the data is separated into (a) ‘‘pm’’ and (b) ‘‘am’’ observations. Low shadow altitude intensities for the morning exosphere are typically 20% brighter than evening intensities for the same viewing geometry. (c) Combined Doppler widths (‘‘pm’’ and ‘‘am’’ plotted together) vs. shadow altitude (km), where jVLSRjX10 km=s. A persistent narrowing of the proﬁle with shadow altitude is apparent in the majority of the PBO data. (d) Combined % cascade contributions to the total Balmer a intensity vs. shadow altitude (km) (‘‘pm’’ and ‘‘am’’ plotted together). Two limits were used to restrict the cascade data set: VLSRo 10 km=s or VLSR435 km=s, and a pointing direction at least 60 in galactic latitude (i.e., well out of the galactic plane). Plotting symbols: s correspond to OZA p15 , &s correspond to 15 o OZA p30 , and ns corresponds to 30 o OZA p45 .

scattering on the line proﬁle cannot be neglected when interpreting this type of observation. 10.3. Cascade In the initial CCD/annular summing geocoronal demonstration observations by Nossal et al. (1998), a 10% enhancement to the red-wing of the geocor-

onal Balmer a proﬁle was detected. This enhancement appeared to be consistent with cascade induced emission, although the observed value was slightly higher than 7% contribution predicted by Meier (1995). Revised calculations by Meier (private communication), based on the SOHO/SUMER data of Warren et al. (1998), reduce the cascade contribution to 4%. Shemansky et al., 1999, personal

ARTICLE IN PRESS E.J. Mierkiewicz et al. / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 1520–1552

(a)

relative intensity

communication have argued that photoelectron impact excitation of the 3S, 3D terms may be sufﬁcient to enhance the 3S ! 2P and 3D ! 2P components of Balmer a as needed to explain the net 10% red-wing enhancement reported by Nossal et al. (1998), particularly in view of the recent reduction in cascade contributions by Meier. As previously discussed, each Balmer a spectra in the PBO data set was ﬁt with a two cluster Gaussian model which takes into account both direct solar excitation and cascade contributions to the emission. The PBO data set indicates a cascade contribution at Balmer a of 5 3%; refer to Fig. 16d. Note, the observations presented here, and those of Nossal et al. (1998), are near solar maximum; Meier’s (1995) and more recent cascade calculations are based on solar observations conducted near solar minimum. Only 18% of the PBO data initially included in Figs. 16a and b were deemed useful for cascade studies. Two limits were used to restrict this data set in order to achieve an accurate cascade determination: VLSR o 10 km=s or VLSR435 km=s, and a pointing direction at least 60 in galactic latitude (i.e., well out of the galactic plane). These requirements helped to ensure that even small amounts of galactic emission (i.e., at the sub Rayleigh level) were not mistakenly ﬁt as cascade contributions. The improved optical system of the PBO Fabry–Perot, with its 75 km/s spectral baseline centered on Balmer a, allows better identiﬁcation and characterization of galactic emission; refer to Figs. 17a and b. The arrows in Figs. 17a and b indicate the position of the LSR at the time of the observation; 25 km/s to the red of the geocoronal line in Fig. 17a and 26 km=s (to the blue) in Fig. 17b. The galactic emission is rather broad (25 km=s); thus even when signiﬁcantly Doppler shifted from the geocoronal line center, galactic contributions from the wings of the galactic emission may overlap and be mistakenly ﬁt as geocoronal emission. Also, in regions of the sky where the galactic emission is known to be extremely faint (typically 0:25R), if the emission is near the red wing, this sub Rayleigh signal can look exactly like cascade emission which is also a sub Rayleigh component to the Balmer a emission. Although care was taken in the original CCD/annular summing observations by Nossal et al. (1998) to avoid regions with high amounts of galactic emission, without the beneﬁt of an extended baseline it is possible that at least some galactic emission went unnoticed.

vlsr = 25 km/s

0

20

40

60

80

100

(b)

relative intensity

1546

vlsr = -26 km/s

0

20

40 60 bin number

80

100

Fig. 17. (a–b) Geocoronal Balmer a with small galactic contributions. The arrows indicate VLSR at the time of the observations. (a) 25 km/s to the red (toward bin 0) of the geocoronal emission. (b) 26 km=s to the blue (toward bin 100) of the geocoronal emission. As galactic Balmer a is rather broad (20 km=s fwhm), even when signiﬁcantly Doppler shifted from the geocoronal line center, galactic contributions from the wings of the galactic emission may overlap the geocoronal proﬁle and be mistakenly ﬁt as geocoronal emission. The Abscissa is in terms of bin number, where 1 bin ¼ 0:75 km=s; bin 0 corresponds to the central sample bin, hence wavelength decreases from left to right in a and b.

Furthermore, even though many observers have relied on VLSR to restrict their observations to times/look-directions when the galactic component is Doppler shifted away from the geocoronal line, the extended baseline of the PBO Fabry–Perot, the high sensitivity of the CCD annular summing technique, and the completion of the WHAM survey, make it possible to search for galactic contributions after the observations are conducted, and quantify the magnitude of the galactic contamination.

ARTICLE IN PRESS E.J. Mierkiewicz et al. / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 1520–1552

Explicit modeling of the galactic component will allow less restrictive cascade data cuts, and eventually a more thorough investigation into the cascade emission. For example, theory predicts a shadow altitude dependence on cascade contributions; this limited (i.e., restricted) cascade data set is currently inconclusive on this account. At higher shadow heights, where a larger portion of the Balmer a emission is attributable to multiple scattering, the cascade contribution to the line is expected to be less important than at lower shadow heights where the dominant emission arises from single scattering. In addition to the galactic emission masking cascade contributions, recent work by Hausen et al. (2002) indicates that faint atmospheric lines (some of which are time dependent) populate the spectral regions about the Balmer a emission. As the full potential of this data set is explored, these faint lines will be investigated with the high resolution PBO Fabry–Perot. 11. Discussion and the future Fabry–Perot spectrometers are particularly well suited for detailed studies of faint diffuse emissions, such as geocoronal Balmer a, because they are capable of simultaneously achieving high spectral resolution and high throughput (Roesler, 1974; Hernandez, 1988). High spectral resolution enables detailed line proﬁle studies and is necessary to unambiguously isolate the geocoronal line from the galactic background, now known to be signiﬁcant in almost every direction on the sky (Reynolds, 1997; Haffner et al., 2003). High throughput provides the temporal resolution needed to investigate, and limit, the variations in the Balmer a emission due to changes in viewing geometry, local time, and atmospheric conditions. The double etalon, siderostat, and multi-element detection using a CCD are instrumental attributes particularly advantageous for ground-based geocoronal Balmer series observations. It is a basic goal of the current analysis efforts to search for signatures of upper atmospheric conditions that might be derived from Balmer airglow measurements. Because hydrogen column emission intensities involve nonnegligible complications from multiple scattering, such retrievals currently require a forward modeling approach. This capability is provided by the resonance radiative transfer code LYAO_RT (Bishop, 1999, 2001), which accounts

1547

for nonisothermal conditions and multiple scattering in spherical coordinates but does not account for the complications of cascade or collisional excitations. LYAO_RT is usually used with thermospheric temperatures and density proﬁles of the major thermospheric species (N2, O2, O) provided by the empirical mass spectrometer incoherent scatter (MSIS) model of Hedin (1991), although other thermospheric atmosphere models can just as easily be used. The atomic hydrogen density proﬁle [H](z) at thermospheric altitudes is generated by direct integration of the vertical diffusion equation using user-input parameters for the densities at the thermospheric upper boundary (exobase density) and the mesospheric peak (85 km) and for the photochemical upward ﬂux. The speciﬁcation of the population of exospheric hydrogen atoms on satellite orbital trajectories is made via two additional parameters using the analytic model of Bishop (1991). Recently, Bishop et al. (2004) used same-night ground-based Balmer a data from PBO and geocoronal Lyman b measurements from the Espectro´grafo Ultravioleta extremo para la Radiacio´n Difusa (EURD) instrument on the Spanish satellite MINISAT-1 (provided by J.F. Go´mez and C. Morales of the Laboratorio de Astroﬁsica Espacial y Fı´ sica Fundamental, INTA, Madrid, Spain) in order to investigate the modeling constraints imposed by two sets of independent geocoronal measurements, both of which rely on astronomical calibration methods. These data sets were acquired during the dark of the moon period of early March 2000. Bishop et al. (2004) developed a data–model comparison search procedure employing a large, extensive grid of input parameters (deﬁning a seven-dimensional parameter space containing over 60,000 thermospheric–exospheric nightside pairings). Using search criteria deemed ‘‘reasonable’’ (e.g., requiring the implied morning and evening solar Lyman b line-center ﬂuxes derived separately from each data set to agree to within 20%) and line-of-sight integrations for the pointing direction of each intensity measurement, it turned out that only a very small region of the seven-dimensional parameter space yielded good ﬁts to both data sets, two examples of which are shown in Fig. 18. Although the initial parameter binning in the Bishop et al. (2004) study was coarse, and both the PBO and EURD data sets require further processing, the study does substantiate the idea that such

ARTICLE IN PRESS 1548

E.J. Mierkiewicz et al. / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 1520–1552

(a)

(b)

Fig. 18. Two examples of candidate solutions from the data–model comparison search procedure by Bishop et al. (2004). Forward modeling ﬁts are to ground-based Fabry–Perot Balmer a data from the Pine Bluff Observatory (4 March 2000) and to satellite EURD (1–6 March 2000) Lyman a data using global resonance radiative transfer modeling; model results are indicated by s. Search parameter values for exobase densities nexo and ﬂuxes f are given in the PBO panels (left), vertical column densities above 102 km (N b ) are given in the EURD panels (right). T exo ¼ 1293 K for the ‘‘pm’’ case and T exo ¼ 1023 K for the ‘‘am’’ case in the two solutions shown.

data–model comparison search procedures offer the possibility of deriving useful geophysical parameters from Balmer a data. It is anticipated that reﬁned searches building upon the coarse grid of Bishop et al. (2004) will lead to further constraints on forward modeling inputs; addition of a constraint regarding the effective Doppler widths from the PBO data can also be exercised. Another approach to investigate what might be genuinely retrievable from ground-based data and to quantify hydrogen abundance variations under varying solar and seasonal conditions is the forward-modeling analysis of WHAM column emission measurements taken in multiple viewing geometries, a continuation of the work started in Nossal et al. (2001). In that study, data–model case comparisons demonstrated that the WHAM geocoronal data have sufﬁcient signal-to-noise ratios to distinguish and rank goodness-of-ﬁt for different model scenarios to within 5% in their associated upper atmospheric hydrogen column abundance (Nossal et al., 2001).

In addition to observations of Balmer a, the sensitivity gains afforded by the CCD annular summing technique is prompting a new look at geocoronal Balmer b, ﬁrst isolated by Reynolds et al. (1973). Initial observations with WHAM and PBO indicate that a detailed study of the geocoronal Balmer b emission is possible as shown in Fig. 19. Because of the differing transport properties of Lyman b and Lyman g in the terrestrial atmosphere, the latter of which is responsible for the direct excitation of geocoronal Balmer b, measurements of the variation of both Balmer emissions with SDA and viewing geometry has the potential to improve upper atmospheric hydrogen distribution determinations. For example, LYAO_RT model atomic hydrogen density proﬁles can be systematically varied in order to obtain consistent ﬁts to both the Balmer a and Balmer b emissions. Fitting, in terms of replicating the SDA and other viewing geometry variations of both emissions, may provide a tight constraint on LYAO_RT atomic hydrogen distributions that is independent of other model

ARTICLE IN PRESS E.J. Mierkiewicz et al. / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 1520–1552

1549

time (utc)

Rayleighs

Hα

Hβ

time (local) Fig. 19. Representative Balmer a (upper curve) and Balmer b (lower curve) intensities vs. time (local and UT), as measured with WHAM on 24 May 2001. Alternating ‘‘blocks’’ of Balmer a and Balmer b observations were conducted with 30 s and 60 s integration times per observation, respectively. The CCD annular summing technique has made this kind of observation possible for the ﬁrst time. All observations are within 10 of the zenith.

parameters such as the solar line center ﬂux and absolute intensity calibration (Bishop, private communication). Although ground-based observations of geocoronal hydrogen, via its solar excited Balmer a emission line, have been made over the last several decades with increasing instrumental capabilities, the technique of Fabry–Perot CCD annular summing spectroscopy is enabling a tremendous leap forward in the quality and quantity of geocoronal emissions data. Extensive geocoronal Balmer a data sets are being obtained with two Fabry–Perot spectrometers which have been designed to take full advantage of this CCD annular summing technique. Data presented from the PBO Fabry– Perot demonstrates that a carefully designed optical system, with a 75 km/s spectral baseline, enables better identiﬁcation and characterization of galactic emission. Understanding the galactic Balmer a background is critical to the interpretation Balmer a line proﬁles. In addition to advances in instrumentation, recent modeling work (see e.g., Bishop et al., 2004), shows great promise for deriving geophysical parameters of general aeronomic interest from Balmer a emission data. These advances, and the fact that atomic hydrogen plays several

unique roles in the terrestrial atmosphere, combine to warrant a systematic study of the Balmer a emission. Acknowledgments The authors would like to acknowledge the valuable assistance of J. Bishop. We would also like to acknowledge the contributions of R.C. Woodward, J. Percival, K. Jaehnig, M. Coakley, I. Yegingil, L.M. Haffner, G. Madsen and S. Tufte. We also thank J. Harlander and F. Scherb for their long-term contributions to the Wisconsin geocoronal research program. We also thank the editor and two reviewers for their helpful comments. This work has been funded by the NSF through grants ATM-9908775 and ATM-0228465. WHAM is funded by the NSF through AST-0204973. References Anderson Jr., D.E., Meier, R.R., Hodges Jr., R.R., Tinsley, B.A., 1987. Hydrogen Balmer alpha intensity distributions and line proﬁles from multiple scattering theory using realistic geocoronal models. Journal of Geophysical Research 92, 7619.

ARTICLE IN PRESS 1550

E.J. Mierkiewicz et al. / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 1520–1552

Atreya, S.K., Hayes, P.B., Nagy, A.F., 1975. Doppler proﬁle measurements of the geocoronal hydrogen Balmer alpha line. Journal of Geophysical Research 80, 635. Bethe, H.A., Salpeter, E.E., 1957. Quantum Mechanics of Oneand Two-Electron Atoms. Academic, San Diego, CA. Bishop, J., 1991. Analytic exosphere models for geocoronal applications. Planetary and Space Science 39, 885–893. Bishop, J., 1999. Transport of resonant atomic hydrogen emissions in the thermosphere and geocorona: model description and applications. Journal of Quantitative Spectroscopy Radiative Transfer 61, 473–491. Bishop, J., 2001. Thermospheric atomic hydrogen densities and ﬂuxes from dayside Lyman a measurements. Journal of Atmospheric and Solar Terrestrial Physics 63., 331–340. Bishop, J., Harlander, J., Nossal, S., Roesler, F.L., 2001. Analysis of Balmer a intensity measurements near solar minimum. Journal of Atmospheric and Solar-Terrestrial Physics 63, 341–353. Bishop, J., Mierkiewicz, E.J., Roesler, F.L., Gomez, J.F., Morales, C., 2004. Data–model comparison search analysis of coincident PBO Balmer a, EURD Lyman b geocoronal measurements from March 2000. Journal of Geophysical Research doi:10.1029 /2003JA010165. Brasseur, G., Solomon, S., 1986. Aeronomy of the Middle Atmosphere. D. Reidel Publishing Company, Dordrecht, Holland. Breig, E.L., Sanatani, S., W.B., Hanson, 1985. Thermospheric hydrogen: the long-term solar inﬂuence. Journal of Geophysical Research 90, 5247–5260. Byram, E.T., Chubb, T.A., Friedman, H., Kupperian, J., 1957. Far ultra-violet radiation in the night sky. In: Zelikoff, M. (Ed.), The Threshold of Space. Pergamon Press, Oxford, pp. 203–210. Burch, J.L., 2000. IMAGE Mission Overview. Space Science Reviews 91, 1–14. Chamberlain, J.W., 1963. Planetary coronae and atmospheric evaporation. Planetary and Space Science 11, 901–960. Chamberlain, J.W., Hunten, D.M., 1987. Theory of Planetary Atmospheres: An Introduction to their Physics and Chemistry, second ed., Academic, San Diego, CA, pp. 330–415. Coakley, M.M., 1995. Application of the CCD Fabry–Perot annular summing technique to thermospheric O 1D. Ph.D. Thesis, University of Wisconsin, Madison. Coakley, M.M., Roesler, F.L., Reynolds, R.J., Nossal, S., 1996. Fabry–Perot/CCD annular summing spectroscopy: study and implementation for aeronomy applications. Applied Optics 35, 6479. Conde, M., 2002. Deriving wavelength spectra from fringe images from a ﬁxed-gap single-etalon Fabry–Perot spectrometer. Applied Optics 41, 2672. Daehler, M., Roesler, F.L., 1968. High contrast in a polyetalon Fabry–Perot spectrometer. Applied Optics 7, 1240. Dessler, A.E., Weinstock, E.M., Hintsa, E.J., Anderson, J.G., Webster, C.R., May, R.D., Elkins, J.W., Dutton, G.S., 1994. An examination of the total hydrogen budget of the lower stratosphere. Geophysical Research Letters 21, 2563–2566. Donahue, T.M., 1966. The problem of atomic hydrogen. Annales de Geophysique 22, 175–188. Donahue, T.M., 1977. Hydrogen. In: Studies in Geophysics: The Upper Atmosphere and Magnetosphere. National Academy of Sciences, pp. 72–83.

Fabry, C., Perot, A., 1901. On a new form of interferometer. Astrophysical Journal 13, 265. Feldman, P.D., Sahnow, D.J., Kruk, J.W., 2001. High-resolution FUV spectroscopy of the terrestrial day airglow with the Far Ultraviolet Spectroscopic Explorer. Journal of Geophysical Research 106, 8119–8129. Garcia, J.D., Mack, J.E., 1965. Energy level and line tables for one–electron atomic spectra. Journal of the Optical Society of America 55, 654. Garcı´ a Primo, M.A., 2001. Spanish MINISAT Program: objectives and operational results. Astrophysics and Space Science 276, 3–12. Gaustad, J.E., McCullough, P.R., Rosing, W., Van Buren, D., 2001. A robotic wide-angle H-alpha survey of the southern sky. Publicaitions of the Astronomical Society of the Paciﬁc 113, 1326. Haffner, L.M., 1999. The warm ionized medium: distribution, kinematics, and physical conditions. Ph.D. Thesis, University of Wisconsin, Madison. Haffner, L.M., Reynolds, R.J., Tufte, S.L., Madsen, G.J., Jaehnig, K.P., Percival, J.W., 2003. The Wisconsin H-Alpha Mapper Northern Sky Survey. Astrophysical Journal, Supplement Series 149, 405–422. Harlander, J., Roesler, F.L., 1989. Observations of geocoronal Balmer a from Mt. Haleakala, Hawaii, (abstract). EOS Transactions of the American Geophysics Union 70, 1238. Hausen, N.R., Reynolds, R.J., Haffner, L.M., Tufte, S.L., 2002. Interstellar Ha line proﬁles toward HD 93521 and the Lockman Window. Astrophysical Journal 565, 1060–1068. Hays, P.B., 1990. Circle to line interferometer optical system. Applied Optics 29, 1482–1489. He, X., Kerr, R.B., Bishop, J., Tepley, C.A., 1993. Determining exospheric hydrogen density by reconciliation of H a measurements with radiative transfer theory. Journal of Geophysical Research 98, 21611. Hedin, A.E., 1991. Extension of the MSIS thermospheric model into the middle and lower atmosphere. Journal of Geophysical Research 96, 1159–1172. Hernandez, G., 1988. Fabry–Perot interferometers. Cambridge University Press, Cambridge. Hinteregger, H.E., Fukui, K., Gilson, B.R., 1981. Geophysical Research Letters 8, 1147. Hunten, D.M., Strobel, D.F., 1974. Production and escape of terrestrial hydrogen. Journal of the Atmospheric Sciences 31, 305–317. Kerr, R.B., Tepley, C.A., 1988. Ground-based measurements of exospheric hydrogen density. Geophysical Research Letters 15, 1329–1332. Kerr, R.B., Atreya, S.K., Meriwether, J.W., Tepley, C.A., Burnside, R.G., 1986. Simultaneous H a line proﬁle and radar measurements at Arecibo. Journal of Geophysical Research 91, 4491–4512. Kerr, R.B., Garcia, R., He, X., Noto, J., Lancaster, R.S., Tepley, C.A., Gonzalez, S.A., Friedman, J., Doe, R.A., Lappen, M., McCormack, B., 2001a. Periodic variations of geocoronal Balmer a brightness due to solar driven exospheric abundance variations. Journal of Geophysical Research 106 (A12), 28797–28817. Kerr, R.B., Garcia, R., He, X., Noto, J., Lancaster, R.S., Tepley, C.A., Gonzalez, S.A., Friedman, J., Doe, R.A., Lappen, M.,

ARTICLE IN PRESS E.J. Mierkiewicz et al. / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 1520–1552 McCormack, B., 2001b. Secular variability of the geocoronal Balmer a brightness: magnetic activity and possible human inﬂuences. Journal of Geophysical Research 106 (A12), 28819–28829. Killeen, T.L., Kennedy, B.C., Hays, P.B., Symanow, D.A., Ceckowski, D.H., 1983. Image plane detector for the dynamics explorer Fabry–Perot interferometer. Applied Optics 22, 3503–3513. Leen, T., 1979. Application of radiative transfer theory to photometric studies of astronomical objects. Thesis, University of Wisconsin, Madison, WI. Liu, S.C., Donahue, T.M., 1974a. The aeronomy of hydrogen in the atmosphere of the earth. Journal of the Atmospheric Sciences 31, 1118–1136. Liu, S.C., Donahue, T.M., 1974b. Mesospheric hydrogen related to exospheric escape mechanisms. Journal of the Atmospheric Sciences 31, 1466–1470. Liu, S.C., Donahue, T.M., 1974c. Realistic model of hydrogen constituents in the lower atmosphere and escape ﬂux from the upper atmosphere. Journal of the Atmospheric Sciences 31, 2238–2242. Meier, R.R., 1995. Solar Lyman-series line proﬁles and atomic hydrogen excitation rates. Astrophysical Journal 452, 462. Meriwether Jr., J.W., Atreya, S.K., Donahue, T.M., Burnside, R.G., 1980. Measurements of the spectral proﬁle of Balmer alpha emission from the hydrogen geocorona. Geophysical Research Letters 7, 967. Mierkiewicz, E.J., 2002. Fabry–Perot observations of the hydrogen geocorona. Ph.D. Thesis, University of Wisconsin, Madison, WI. Mierkiewicz, E.J., Roesler, F.L., Bishop, J., S. Nossal, 1999. A systematic program for ground–based Fabry–Perot observations of the neutral hydrogen exosphere: instrumental characteristics. In: Optical Spectroscopic Techniques and Instrumentation for Atmospheric and Space Research III: Proceedings of the International Society for Optical Engineering, vol. 3756, SPIE. p. 323. Nossal, S., 1994. Fabry–Perot observations of geocoronal hydrogen Balmer-a emissions. Ph.D. Thesis, University of Wisconsin, Madison, WI. Nossal, S., Roesler, F.L., Reynolds, R.J., Scherb, F., 1993. Solar cycle variations of geocoronal Balmer a emission. Journal of Geophysical Research 98, 3669. Nossal, S., Roesler, F.L., Coakley, M.M., Reynolds, R.J., 1997. Geocoronal hydrogen Balmer a line proﬁles obtained using Fabry–Perot annular summing spectroscopy: effective tem perature results. Journal of Geophysical Research 102 (A7), 14541–14553. Nossal, S., Roesler, F.L., Coakley, M.M., 1998. Cascade excitation in the geocoronal hydrogen Balmer a line. Journal of Geophysical Research 103, 381–390. Nossal, S.M., Mierkiewicz, E.J., Roesler, F.L., Reynolds, R.J., Hoffner, L.M., 2006. Geocoronal hydrogen studies using Fabry–Perot interferometers, Part 2: Long-term observations. Journal of Atmospheric and Solar-Terrestrial Physics, in Press, doi:10.1016/j.jastp.2005.08.025 Nossal, S., Roesler, F.L., Reynolds, R.J., Haffner, M., Tufte, S., Bishop, J., Percival, J., 2001. Geocoronal Balmer a intensity measurements using the WHAM Fabry–Perot facility. Journal of Geophysical Research 106, 5605–5616. Nossal, S.M., Roesler, F.L., Mierkiewicz, E.J., Reynolds, R.J., 2004. Observations of solar cyclical variations in geocoronal

1551

Ha column emission intensities Geophysical Research Letters 31, L06110, doi:10.1029/2003GL018729. Østgaard, N., Mende, S.B., Frey, H.U., Gladstone, G.R., Lauche, H., 2003. Neutral hydrogen density proﬁles derived from geocoronal imaging. Journal of Geophysical Research 108(A7), 1300, doi:10.1029/2002JA009749. Prokudina, V.S., 1959. On the observations of the line l 6562 A˚ in the spectrum of the night sky. Spectral, electrophotometrical and radar researches of aurora and airglow, vol. 1, pp. 43–44 (Results of IGY, USSR Academy of Sciences. Moscow). Reynolds, R.J., 1997. Ionizing the galaxy. Science 277, 1446. Reynolds, R.J., Roesler, F.L., Scherb, F., 1973. Low-intensity Balmer emissions from the interstellar medium and geocorona. Astrophysical Journal 179, 651–658. Roesler, F.L., 1974. Fabry–Perot instruments for astronomy. In: Martin, Carlton (Eds.), Methods of Experimental Physics, Part A: Optical and Infrared, vol. 12, Academic Press, New York, p. 531. Roesler, F.L., Reynolds, R.J., Scherb, F., Ogden, P.M., 1979. Instrumental aspects of the Wisconsin interstellar emission program. In: Hack, M.(Ed.), High Resolution Spectroscopy, Proceedings of the Fourth Colloquium on Astrosphysics of the Trieste Observatory: High Resolution Spectroscopy, 1978. Obs. Astron. de Trieste, Trieste, Italy, pp. 600–609. Roesler, F.L., Reynolds, R.J., Scherb, F., 1994. Fabry–Perot spectroscopy of extremely faint astronomical sources. In: Tridimensional Optical Spectroscopic Methods in Astrophysics, Proceedings of IAU Colloquium, vol. 149, Marseille, France. Scherb, F., 1981. Hydrogen production rates from ground-based Fabry–Perot observations of comet Kohoutek. Astro physical Journal 243, 644. Shefov, N.N., 1959. Intensity of some emissions of the twilight and night sky. Spectral, Electrophotometrical and Radar Researches of Aurora and Airglow, vol. 1, pp. 18 (Results of IGY, USSR Academy of Science, Moscow). Shih, P., Roesler, F.L., Scherb, F., 1985. Intensity variations of geocoronal Balmer alpha emission, 1. Observational results. Journal of Geophysical Research 90, 477. Shemansky, et al., 1999. Personal communication. Tinsley, B.A., 1970. Variations of Balmer—a emission and related hydrogen distributions. Space Research 10, 582–590. Tinsley, B.A., 1974. Hydrogen in the upper atmosphere. Fundamentals of Cosmic Physics 1, 201–300. Tinsley, B.A., Meier, R.R., 1971. Balmer a distributions over a solar cycle: comparisons of observations with theory. Journal of Geophysical Research 76, 1006–1016. Tousey, R., Purcell, J.D., Austin, W.E., Garrett, D.L., Widing, K.G., 1963. Extreme ultraviolet spectrum of the Sun. Space Research 4, 703. Tousey, R., Austin, W.E., Purcell, J.D., Widing, K.G., 1965. Newphotographic spectra of the Sun in the extreme ultraviolet. Annales de Astrophysique 28, 755. Trauger, J.T., 1976. Broadband dielectric mirror coatings for Fabry–Perot spectroscopy. Applied Optics 15, 2998–3005. Tufte, S.L., 1997. The WHAM spectrometer: design performance characteristics and ﬁrst results. Ph.D. Thesis, University of Wisconsin, Madison. Vernazza, J.E., Reeves, E.M., 1978. Astrophysical Journal, Supplemental Series 37, 485.

ARTICLE IN PRESS 1552

E.J. Mierkiewicz et al. / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 1520–1552

Walker, J.C.G., 1977. Evolution of the atmosphere. Macmillan Publishing, New York. Warren, H.P., Mariska, J.T., Wilhelm, K., 1998. High-resolution observations of the solar hydrogen Lyman lines in the quiet sun with the SUMER instrument on SOHO. Astrophysical Journal Supplemental Series 119, 105–120. Woodward, 2006. Personal communication

Yelle, R.V., Roesler, F.L., 1985. Geocoronal Balmer alpha line proﬁles and implications for the exosphere. Journal of Geophysical Research 90, 7568. Yung, Y.L., Wen, J.S., Moses, J.I., Landry, B.M., Allen, M., Hsu, K.J., 1989. Hydrogen and deuterium loss from the terrestrial atmosphere: a quantitative assessment of nonthermal escape ﬂuxes. Journal of Geophysical Research 94, 14971–14989.

Geocoronal hydrogen studies using Fabry–Perot interferometers, part 1: Instrumentation, observations, and analysis

Geocoronal hydrogen studies using Fabry–Perot interferometers, part 1: Instrumentation, observations, and analysis

Recommend Documents