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Estimation of initial auroral proton energy fluxes from Doppler profiles
Journal of Atmospheric and Terrestrial Physics,Vol. 58, No. 16, pp. 1871-1883, 1996 Copyright © 1996 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0021-9169/96 $15.00+0.00
~Perg
amon
0021-9169(95)00179--4
Estimation of initial auroral proton energy fluxes from Doppler profiles F. Sigernes The University Courses on Svalbard, N-9170 Longyearbyen, Svalbard, Norway
(Received in final form 20 June 1995; accepted 5 July 1995) Abstract--An energetic auroral proton entering the atmosphere will, by charge exchange in collisions with atmospheric constituents, alternate between being a proton H + and a neutral hydrogen atom H. This study provides a ptocedure to evaluate the auroral Doppler shifted and broadened hydrogen Balmer profile as a function of initial energy, flux, pitch angle and view angle relative to the geomagnetic field. The differential proton energy flux entering the atmosphere is deduced using ground-based measurements of H~ and Hp from Nordlysstasjonen in Adventdalen, Longyearbyen. The main assumptions are that the geomagnetic field lines are: parallel and vertical, and that the pitch angle of the H/H+-particle is preserved in collisions with atmospheric constituents before being thermalized. This numerical method estimates the fate of the auroral H/H %particle in the atmosphere, and from measured Doppler profiles the corresponding incoming particle flux can be deduced. Optimization of the method will continue through extensive use of observational dat~.. Copyright © 1996 Elsevier Science Ltd
INTRODUCTION Vegard (1939) was lLhefirst to discover the presence of auroral Balmer hydrogen emissions using a groundbased spectrograph. Later observations of the Balmer lines confirmed that they were Doppler displaced and broadened, and therefore caused by neutralized protons penetrating into the atmosphere (Vegard, 1948, 1950; Gartlein, 1950). Meinel (1951) was the first to make a detailed study of hydrogen emissions viewed parallel and perpendicular to the magnetic field. Since this discovery, numerous measurements of the Doppler profiles have been carried out (cf. Galperin, 1963; Vallance Jones, 1974; Deehr et al., 1980; Henriksen et al., 1985), which gave results in agreement with Meinel's observations. r h e theory of the Balmer lines has been extensively developed since the work of Chamberlain (1961), Eather (1967) and Omholt (1971). Both in-situ measurements (Reasoner et al., 1968; cf. Soraas el al., 1974) and recently obtained laboratory cross sections (Van Zyl and Neumann, 1980) have made it possible to develop numerical models explaining :~ome of the characteristics of proton aurora (Jasperse and Basu, 1982; Rees, 1982; Van Zyl et al., 1984; Kc,zelov and Ivanov, 1992). A simple method of calculating synthetic Doppler profiles as a function of initial particle flux and energy at arbitrary view angles relative to the magnetic field is presented. The pitch angle distribution is assumed
either to be isotropic or cosine. Each calculated profile is convolved with the instrument function of an EbertFastie spectrometer (Fastie, 1952; Sivjee et al., 1979). By means of a library of such synthetic Doppler profiles it is possible to deconvolve an observed profile caused by auroral protons into an energy spectrum giving the flux of protons at given energies. The aim is to create a simple tool for on-going programs related to auroral morphology, especially in the dayside aurora where the influence of proton precipitation has become more and more important to the scientific community. It may seem superfluous to obtain an estimate of particle fluxes through ground-based Doppler profiles, since particle fluxes can be obtained directly by satellites and rockets. Doppler profiles and particle fluxes are indeed independent parameters. However, again, limitations imposed on satellite and rocket measurements by their transient nature make the ground-based techniques useful, considering their temporal and spatial resolution. Indeed, both kinds of observations are necessary to obtain full information on the proton precipitation during auroras (Omholt, 1971). The method presented here is meant as additional support. Doppler profiles of the hydrogen Balmer lines observed from Nordlysstasjonen in Adventdalen, Longyearbyen, are the data treated by this method, and the results are discussed. This study is a con-
1871
F. Sigernes
1872
tinuation of the work initiated by Sigernes et al. (1994).
with the vector r pointing to the origin of the emitter's v,'v/v j-coordinate system. The spherical components of r are
THE D O P P L E R SHIFTED AND BROADENED
r~ = r sin ;~cos,1
(4)
ry = r sin )~sin )I
(5)
r= = r cos Z
(6)
HYDROGEN BALMER PROFILE
The line-of-sight velocity of an emitting particle is found by representing the observer O and the emitter E in two-coordinate systems (Fig. 1). The observer O is located at the origin of the xyz-coordinate system. Since the observer actually represents an Ebert-Fastie spectrometer capable of obtaining auroral spectra in the north-south magnetic meridian plane at an arbitrary angle relative to the magnetic field, the x-axis is defined to point towards the geomagnetic north, the y-axis west and the z-axis is aligned parallel with the magnetic field. Also, since the field of view of the instrument is only 5 degrees, the emitter E is defined at the origin of the parallel reference Vx'Vy'Vz'-coordinate system. The vector r connects the two origins. The components of the velocity vector v of the emitter in spherical coordinates are
where Z is the angle between the viewing direction and the magnetic field, q the corresponding azimuth angle, and r the length of r. Note that t/is taken to be zero in our case. The component of v projected onto r gives the absolute value of the line of sight velocity vector Vs (Howard, 1987), namely v= -
Iv'rl r
(7)
The components ofv are defined similarly and equation (7) becomes v= = v[yl
(8)
(9)
where
v=, = v s i n 0 c o s ¢
(1)
? = sin 0sinx cos(q$-q)+ cos0cosg.
vy = vsin0sinff
(2) (3)
According to equation (8) the emitter moves with velocity v, pitch angle 0 and phase angle ¢ at height h = rz, while the observer in its reference frame senses the velocity v=. The sign of the angular function ? gives information on whether the emitter is approaching or receding from the observer. The Doppler shifted wavelength 2, which the observer can detect from an emission with centre wavelength 20, is
t~z, ---- t) COS 0
where 0 is the pitch angle relative to the magnetic field, ~b the azimuth angle, and v the magnitude of v. The observer is at the origin of the xyz-coordinate system
Vz,
Vs ~
where c is the speed of light. The emission rate of (H+/H)-particles at an arbitrary height is given by (Sigernes et al., 1994)
Vy,
A. E ~
~
'
3
0
: Vx'
, !
i ll
Y
,, X
n--1
. . . NM(~ff
~. A,m
['~"
photons -1
lh sT vlA L
(II)
m=l
I
r
~'.m - -
i ,11 I X
O Fig. 1. Configuration of observer O and emitter E in two frames of reference.
where A,m is the probability of transition from the nth to mth energy level, a ~ =) the corresponding effective excitation cross section (Van Zyl and Neumann, 1980), NM the concentration of all atmospheric atoms and molecules at height h, and F the (H+/H)-particle flux. Expression (I I) is valid when collisional quenching is negligible. The energy degradation of the (H+/H)-particle in the upper atmosphere was calculated based on the fundamental hypothesis that the pitch angle is preserved in the interaction with atmospheric constitu-
Estimation of initial auroral proton energy fluxes from Doppler profiles ents, and that the magnetic field is homogeneous and vertical in the main collisional region. Physical reasons for this hypothesis were given by Sigernes et al. (1993). The instantaneous energy K at height h for a (H +/H)particle with initial kinetic energy eo at the top of the atmosphere h = H, pitch angle 0 and random phase angle 4) is (12)
K(eo,h,O,dp) = e o - W(eo,h,O,dp)
1873
by (H+/H)-particles with initial flux f(eo), view angle and wavelength 2. The differential energy photon flux integrated from the top of the atmosphere, h = H, down to the lower height level, h = h0, can then be expressed as ho
~
An m
D~(eo,2)= ~
L E.-, h'ffiH 4¢=0 i E A.m m=l
W is the total energy loss given by ( ]t ) W(eo,h,O,(a) = ~ o ~
h dK ~
h' =H
,
--d~x(K(e°'h ,O,(a))"
p(h') PO
,
× NM(h')a~')(K(eo,h',Oi, c~'))f(eo) • n(h',Oi,c~')AOAc~Ah'
photons ] cm2 s sr/~ keV_] (16)
Ah
(13) where P0 = 1.23 × 10-3 g/cm 3. The energy loss was found by adding up the energy-dependent stopping power, dK/dx, at each height interval above height h. The energy-dependent stopping power used in these calculations was faund by Sigemes et al. (1994) to be a compromise between experimental results obtained by Reid (1961) and Dalgarno (1962). The mass density p as a function of height from 200 km down to 90 km is obtained from the MSIS-86 model (Hedin, 1987) for different solar activities and geomagnetic conditions. The particle flux 5~" is related to the initial flux by the expression.
The wavelength 2 reaching the observer is calculated by equation (10) when vs is given, and no significant quenching of the upper state occurs. Since it is assumed that the initial particle flux is independent of the pitch angle distribution, equation (16) takes the form
[ photons q D.~m(e0,2) = f(eo)" B~.m(e0,2)LcmZs sr A keV J (17) where B~,,. are the terms left after extractingffrom the summation.
o~(K(eo,h,O,q~)) = . ~ ( e o - W(eo,h,O,(~)) = f(eo)
INSTRUMENTATIONAND CALCULATEDDOPPLER
V-particles .] • n(h,O,~) [_cm2 s sr keVJ
(14)
where f is the initial H+/H-particle flux at energy e0, and n the pitch angle distribution. Sincefis the H ÷/Hparticle flux, the proton flux is given as fp = f-Fp, where Fp is the proton flux fraction (Van Zyl and Neumann, 1980). The (H+/H)-particle flux is then assumed to be in equilibrium, and the top of the atmosphere is set to 200 km. According to equations (8) and (12), the line-ofsight kinetic energy of a (H+/H)-particle is given by 1
2
mv~ --=K(eo,h,O,dp)" y2(0,~b,r/,Z)
(15)
where m is the mass. Equations (15) and (10) are the key equations in constructing the Doppler profile as a function of initial energy, view angle and height. The main idea is to solve equation (15) with 0 as the only unknown. For each fixed phase angle ~b, initial energy eo, line-of-sight velocity v, viewing direction ~, and height h, equation (15) has two solutions denoted as 0~ where i~[1,2]; r/ is in our case zero. Adding up all solutions of 0i around ~b makes it possible to construct the differential energy photon flux produced
PROFILES
Ebert-Fastie spectrometers were used to measure Doppler profiles. Their construction is based on one large spherical mirror, one plane diffraction grating, and a pair of slits. The light from the entrance slit is reflected and made parallel by the spherical mirror onto the grating. The same mirror focuses the diffracted and parallel light from the grating onto the exit plane. When the grating turns, the image of the entrance slit is observed at the exit slit in different wavelengths, determined by the angular position of the grating. The grating is blazed at a fixed angle in order to produce a maximum efficiency at the desired spectral order and wavelength region used. Filters in front of the entrance slit are used to prevent overlapping orders. A perfect instrument with no defects such as spherical aberration, astigmatism or grating ghosts has an instrument function R(2) = Ef(2) •F:(2) • GA COS fl" T#(2) • A(R)/L~,
(18) where EI is the efficiency of the grating, FI the transmission fraction of the order sorting filter, GA the
1874
F. Sigernes
illuminated grating area, fl the diffraction angle, Tg the geometric transmission coefficient, Lj the focal length of the mirror, and A a triangular function with a baselength of twice the bandpass. Normally the entrance and exit slits have the same width. Then the bandpass is the instrumental line width, the half-width of an infinitely narrow line passing through the instrument and recorded. A light-pipe transfers the image at the exit slit to the detector. The detectors are photomultiplier tubes mounted in Peltier cooled housings, improving the sensitivity and the signal-to-noise ratio of the tubes. They are of the GaAs type, and since the spectral response of these tubes covers a wide range from ultraviolet to 9300 A, the quantum efficiency is nearly independent of wavelength. The entrance optics to the spectrometers is a periscope, which can be turned in different directions along the geomagnetic meridian filling the field of view of the spectrometers. In order to obtain the Doppler profile as measured by an Ebert-Fastie spectrometer, it is necessary to convolve the intensities calculated in equation (17) with the instrument function J~m(eo,2) = f(eo)" B~,m(eo,2)*R(2)
(19)
Equation (19) can now be used to produce a library of Doppler profiles, produced by a monoenergetic beam of protons, as a function of view angle. Figure 2 shows the calculated Doppler profile of H~ as a function of view angle relative to the magnetic field when the initial energy is 10 keV. The profiles are calculated with an instrument function of an EbertFastie spectrometer with a one-meter focal-length mirror scanning in the first spectral order with a bandpass of 7 A. The grating is blazed at 53 ° and has 1200 grooves per millimeter. The pitch angle distribution is cosine in the upper panel (A) and isotropic in the lower panel (B). The horizontal profiles in panels (A) and (B), Z = 90°, are symmetrical about the centre wavelength 20, and the corresponding zenith profiles, = 0 °, have their characteristic tails shifted towards the blue part of the spectrum and minor redshifts due to instrumental broadening. The wavelength of the peak intensity of the zenith profile in panel (A) is about 1 A less than the corresponding wavelength in panel (B). As the view angle increases, the peak intensity of the profiles in panel (B) drops faster than in panel (A). The pitch angle distributions are defined to be normalized at the top of the atmosphere (Sigerues et al. 1993). Accordingly, the cosine and isotropic distributions equal ncos (h, 0, ~b) = (l/n) cos 0 and his o (h,O,~) = l/2n, respectively. The cosine particle flux will then be less than or greater than the isotropic flux,
dependent on whether the absolute value of the pitch angle is less or greater than 60°:
fleo)noos(h,O,49) > f(eo)niso(h,O,~)
101 < 60 °
f(eo)n¢os(h,O,dp) < f(eo)niso(h,O,c~)
101 > 60 ° (20)
This effect is clearly seen in the half-widths of the profiles shown in Fig. 2. The zenith profile shown in panel (A) has a larger half-width compared to that of the zenith profile shown in panel (B). This is simply due to the fact that the main fraction of the cosine particle flux has pitch angles less than 60 °, which leads to a larger contribution to the tail of the profile in panel (A) compared to that of the tail in panel (B). Furthermore, as the view angle increases, a decrease of the half-widths in panel (A) and a corresponding increase in panel (B) are observed, respectively. In the present study, the incident (H+/H)-particle flux is assumed to be in equilibrium according to the flux fractions given by Van Zyl and Neumann (1980). The top of the atmosphere was therefore defined at 200 km. Above ~ 200 km, Kozelov (1993) found that the convergence of the magnetic field causes a small fraction of the incident flux to be mirrored and transported out of the atmosphere. Now, since the light productive height region was measured by Soraas et al. (1974) and calculated by Sigernes et al. (1994) to be centred at approximately 115 km, well below mirroring heights, it seems that collisional scattering in the low-energy range is the only alternative left in order to explain the observed redshifts in the Doppler profiles. But this is only speculation and reveals the need to include both a converging magnetic field model and collisional scattering in future model calculations in order to explain the minor redshifts observed. In this study we concentrate only on downward oriented fluxes.
AN ESTIMATEOF THE INITIALDIFFERENTIALH÷/HENERGY PARTICLE FLUX USING GROUND-BASED SPECTROMETRIC OBSERVATIONS
The method which now will be presented is based on the use of the above-calculated Doppler profiles (equation (19)) as a library in obtaining a fit to the measured quantifies, and thereby deducing the initial energy particle flux. The total intensity of a Doppler profile at any given wavelength 2 is the summed contributions from particles with initial and degraded energies
IXnm(l~)= ~ J ~ ( E , 2 ) d E J
(21)
Estimation of initial auroral proton energy fluxes from Doppler profiles
1875
3.0x10 - 6
2.5x10 - 6 >
2.0xl 0 - 6
.< ~
1.5x10-6
z i-._z 1 . 0 × 1 0 - 6
5.0x10 - 7
0 6530
:"'
6540
. . . . . . .
6550
I . . . . . . . . .
I . . . . . . . . .
6560 6570 WAVELENGTH [A]
I . . . . . . . .
3.0x10 - 6
I . . . . . . .
6580
6590
' ' I ' ' ' ' ' ' ' ' ' I
. . . . .
6600
'''
(B) CALCULATED Hm PROFILES
2.5xl 0 - 6
O" k
ISOTROPIC PITCH ANGLE
10,~X
DISTRIBUTION INITIAL ENERGY 10 keV
' ~ 2-0x10-6
30
~-
4oL....
~
1.5xi 0 - 6 :-
Z
VIEW ANGLE 0-90"
5o[.... 60"
~7 1.0x10-6
_ 70" 80"
5.0x10 - 7
0 65~m
~ i . , i i , I i i
654o
655o
656o
657o
658o
659o
WAVELENGTH [A] Fig. 2. Calculated monoenergetic H~ Doppler profiles as a function of view angle relative to the magnetic field. The initial flux consists of one test particle with 10 keV kinetic energy for each of the pitch angle values used. Panel (A) shows the profiles calculated with a cosine pitch angle distribution while panel (B) shows the corresponding profiles using an isotropic pitch angle distribution. The instrument function is derived using a one-meter Ebert-Fastie spectrometer scanning in the second order.
66oo
F. Sigernes
1876
Alternatively, equation (21) can be expressed as a discrete summation
IXnm(,~)= f J~,m(E,2)dE
(22)
where N is the total number of energy bins of variable width AEi. If we now consider the total Doppler profile consisting of a number of discrete intensities at M wavelengths, a set of M linear equations each similar to equation (22) is obtained. In matrix notation we can write I]m = ~'~nXm° f(E)AE
(23)
where ll,xm is the matrix of monoenergetic intensities at discrete wavelengths with the number of rows equal to the size of the I,X,,intensity vector and the number of columns equal to the number of energy bins; indicates the viewing direction. An example of l~,x,, is displayed in Fig. 3, where each monoenergetic H# profile, f/°2(Ei,2) = B~42(Ei,2)*R(2), represents column i in f/°2. The initial energy ranges from 1 to 70 keV, and the view angle is zero relative to the magnetic field. The pitch angle distribution is isotropic in panel (A) and cosine in panel (B). Each profile is calculated with an instrument function of a one-meter Ebert-Fastie spectrometer scanning in the second order, having a bandpass of 6 ]k. The intensity increases as the initial particles penetrate deeper into the more dense atmosphere with increasing energy, and the tail of the profiles becomes larger, indicating a wider energy range of the emitting particles contributing to the profile. Again we notice that the peak wavelengths of the cosine profiles are slightly blueshifted compared to the corresponding isotropic wavelengths. Also, the profiles in panel (B) have higher intensities and are wider compared with the profiles in panel (A), which is due to the properties of the particle fluxes used (see equation (20)). Our task is to solve M linear equations simultaneously in order to determine N values of the differential energy flux,f (E3, where U,m (2) is obtained by a ground-based spectrometer. Since M can be set greater than N, and the matrix f~,, in most cases becomes singular or close to singular, the method of Singular Value Decomposition (SVD) is used (Press et al., 1992). The energy range and the width of the energy bins AE are predetermined by analysing the shape of the measured Doppler profile I z . Since the measured Doppler profile I,Zmactually represents the velocity distribution along the line of sight of the emitting particles, the width of energy bins AE can
be estimated assuming the kinetic line-of-sight energy bins to be equally representative. Also, the width of the Doppler profile itself gives an indication of the initial energy range responsible for contributing to the profile, and an optimal result in respect to convergence and computation time is obtained by proper sampling of this range. An initial energy spectrum, f(E) = 8 × 10 7 E - 2 protons/cm 2 s sr keV, measured by the PROTON I rocket launched into a post-breakup auroral glow from Andoya on 13 February 1972 (Soraas et al., 1974) is used to calculate, according to equation (23), an H a Doppler profile with known characteristics. During this flight the pitch angle distribution was reported to be isotropic. Figure 4 shows in the upper panel (A) the measured energy spectrum (solid line). Equation (23) is then used to calculate the corresponding H a Doppler profile shown in panel (B) (solid line). It is unfortunate that no measured Doppler profile exists for the energy spectrum in panel (A). In order to test the mathematics of the procedure described above a set of values from the Doppler profile in panel (B), marked with diamonds, was used to obtain the initial energy spectrum. The result of this test is shown by diamonds in panel (A). This test indicates that the described method for deducing initial energy particle spectra from corresponding measured ground-based Doppler profiles may give reasonable results. In this case the instrument function used corresponds to a one-meter Ebert--Fastie spectrometer scanning in the second order with a bandpass of 1.5 ,~. The total intensity of the profile in panel (B) must be multiplied by a factor of 0.7 in order to fit the reported intensity of 170 R, measured by interference filter photometers (Soraas et al., 1974). This discrepancy could be interpreted to mean that the emission cross sections for H# are 30% too high. However, both the absolute calibration of the instruments and uncertainties related to the calculation of the instrument function could well be of similar magnitude. It must be emphasized that this is only a test of the calculating procedures presented, and cannot be seen as a verification of the method itself. One of the main objects of this work is to provide a tool for studying proton precipitation in the dayside aurora. Newell et al. (1991) have identified particle spectra from the DMSP satellites corresponding to the ionospheric cusp as proposed by Vasyliunas (1979). Since the measured particle flux is highly fieldaligned, well within the atmospheric loss cone, we assume the pitch angle distribution to be cosine. The upper panel (A) of Fig. 5 shows the ion cusp spectrum obtained by fitting a Gaussian function to the data obtained by the DMSP F7 satellite crossing the
Estimation of initial auroral proton energy fluxes from Doppler profiles
1877
, , , , , , , , , I , , , , , , , , r l , ~ , , , , , , , I , , , , , , , , , i , , , , , , , , , i , , , , , , , , , i , , , ,
(A) CALCULATED
3.0x10 -6
Hp -
MONOENERGETIC
ZENITH DOPPLER PROFILES 2.5x10 -6
ISOTROPIC PITCH ANGLE DISTRIBUTION 70 keV ENERGY RANGE (1 -
70) keY
/~._.,~,_ i / N\ //...~\
2.0xl 0 -6 /
rl,-
_~ 1 . 5 x 1 0 - 6 z
60 keV 50 keV
,o
ov
i
Z -
-
1.OxlO-6 -
20 keY
5.0x10 -7
,OkoV
0 4810
4.0xl 0-6
4820
.........
I .........
(B) CALCULATED
4830
4840 4850 WAVELENGTH [A]
I ......... Hp -
I .........
I .........
4860
:
4870
I .........
i ....
MONOENERGETIC
ZENITH DOPPLER PROFILES 3.Ox10 - 6 .< >
COSINE PITCH ANGLE DISTRIBUTION ENERGY RANGE (1 -
'~' 2.0x10 -6 Z I..ul F--
//
z /
/
1.0x10 -6
~ 70) keY
/
70 keV 60 keY
/
50 keY
/
40 keY
/
,.30 keY 20 keV
/ /
0 4810
4820
48,.30
10 keY
4840 4850 WAVELENGTH [A]
4860
4870
Fig. 3. Calculated monoenergetic zenith H~ Doppler profiles as a function of initial energy (1-70 keV). The initial particle flux is unity. The pitch angle distribution is isotropic in panel (A) and cosine in panel (B). The instrument function used represents a one-meter Ebert-Fastie spectrometer scanning in the first order.
_
1878
F. Sigernes v
~
J
i
r
i
i
6x10 7 (A) ISOTROPIC PITCH ANGLE DISTRIBUTION
>
SOLID LINE - TEST SPECTRUM DIAMONDS
4x10 7
- CALCULATED
tO
o X
3
2x10 7
l,
,
1
.... i O
10 INITIAL ENERGY [keV]
. . . . . .
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I
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. . . . .
I
. . . . . . . . .
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. . . . .
30
25
(B) ZENITH H PROFILE
< 20
_z 10
5
4820
4830
4840 4850 WAVELENGTH [A]
4860
4870
]Fig. 4. Panel (A) shows the differential irutial energy particle spectrum (solid line) measured by the PROTON I rocket launched into a post.breakup auroral glow from Andoya on 13 February 1972 (Soraas et al., 1974). It is used to generate the H# Doppler profile in panel (B) (sofid line). The pitch angle distribution was isotropic. Thus several values of the Hp profile are obtained, shown by diamonds, and the corresponding initial energy particle flux calculated by the described method. These calculated values are shown by diamonds in panel (A).
Estimation of initial auroral proton energy fluxes from Doppler profiles '
'
'
~
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1879
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(A)
>
/
6x106
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INITIAL ENERGY [keY]
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,
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(B) COSINE PITCH ANGLE DISTRIBUTION
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-
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DIAMONDS - CALCULATED
-z 10 z
ZENITH Hp PROFILE
tO
¢" ~I
bJ I---
5
0
~AA~.,t.
4820
AA~I.
A A A A A A A A ~ - A A ~ I ~ ' ~ P ~ f ,
48.30
, , I , , , , , , , , ,
4840 4850 WAVELENGTH [A]
, ~ A ~ A A A ~
4860
4870
Fig. 5. Panel (A) shows the differential initial cusp particle spectrum (solid line) measured by the DMSP F7 satellite crossing the southern hemisphere 26 January 1984. It is used to generate the H~ Doppler profile in panel (r 0 (solid line). The pitch angle distribution is cosine. The calculated values of the flux and the resulting profile using the method described are shown in panels (A) and (B) (diamonds), respectively. The instrument function used represents a one-meter Ebert-Fastie spectrometer scanning in the second order.
1880
F. Sigernes
southern hemisphere on 26 January 1984 (solid line). The same procedure as described in Fig. 4 is applied to the lower panel (B). We noticed that the Doppler profile is well reproduced throughout the entire wavelength region. The synthetic initial energy flux has a small fluctuating behaviour around 3 keV. This is due to the choice of monoenergetic profiles and the width of the energy bins used. A rather crude energy resolution in the tail of the profile can produce this effect. Therefore this method requires proper sampling of the initial energy range. Also, the signal-to-noise ratio of a measured Doppler profile has to be high, which may result in poor time resolution. The calculated profile in panel (B) corresponds well both in intensity and shape to ground-based spectral observations carried out during several years at Nordlysstasjonen in Adventdalen, Svalbard (74.9°N, 114.6°E geomagnetic coordinates, geomagnetic noon ~ 0830 UT). Henriksen et al. (1985) have reported narrow auroral dayside H~ profiles confined within 10 A, corresponding to about 1 keV initial energy of the precipitating protons. In other words, the particle flux of the precipitating protons can be close to the flux in panel (A). Again, it must be emphasized that the only true proper test of the method can be made by comparing satellite or rocket measurements that coincide, which in itself is a difficult task not yet performed with ground-based sites. It is therefore a crucial point to be addressed in the future for continuation and optimization of the method presented. On 12 January 1992 measurements of auroral dayside hydrogen emissions were carried out at Nordlysstasjonen. The Sun was then more than 6 degrees below the horizon, which permitted optical measurements throughout most of the daytime period. The dayside auroral oval was in the zenith between 0700 and 1100 UT. Throughout this time period polewardmoving auroral forms were seen, which broke away from the stationary oval and moved poleward into the polar cap. Associated with each poleward-moving auroral form was a burst of H~ and H~ emissions, which stretched over much of the sky (Sigernes et al., 1995). A half-meter Ebert-Fastie spectrometer was fixed in the geomagnetic zenith scanning the secondorder wavelength region (65174579) A with a bandpass of 2.5 .&. The upper panel (A) of Fig. 6 shows the obtained intensities of HE plotted as a function of time and wavelength. The scaled bar to the left indicates intensities in Rayleighs. Absolute calibration of the spectrometer was done with a diffuse re-emitting screen covering the field of view of the instrument and a tungsten lamp as the comparative source situated in a tower 30 m away. Overlapping OH(6, 1) rotational emission airglow
intensities are filtered out by the method described by Herzberg (1950). Each scan of the spectrometer took 12 s. In order to improve the signal-to-noise ratio, a summation of several scans was required, which resulted in a time resolution of about 2 rain for the processed data records. The next panel (A2) shows a sample of a data record obtained during maximum activity around 10 UT. The middle panel (B) shows the resulting initial particle flux (diamonds) calculated by using each processed data record as input to the method described above. The pitch angle distribution is cosine. The main part of the calculated flux values are distributed in the energy range less than 5 keV. The average values (solid line) have the order of magnitude of 106 protons/cm 2 s sr keV and a "bulk" energy close to 2 keV. Maximum flux values are one order of magnitude higher than the mean values and correspond to the most intense part of panel (A). In the low-energy range, less than 1 keV, the mean flux is represented as a low-energy tail connecting to the "bulk"-flux. This is a typical shape of the initial flux (Sigernes et al., 1993). Calculations applying an isotropic pitch angle distribution are shown in the lower panel (C). The obtained isotropic flux tends to be wider than the cosine flux shown in panel (B). It should be mentioned that the monoenergetic profiles calculated applying a cosine pitch angle distribution were better than the corresponding isotropic profiles conditioned to the measured profiles both in shape and in respect to convergence of the method described. The order of magnitude and the initial energy range of the calculated particle fluxes are found to be reasonable estimates of dayside proton precipitation.
CONCLUDING REMARKS
A procedure to obtain an estimate of the initial auroral proton energy fluxes through deconvolving observed ground-based Doppler hydrogen profiles is outlined and utilized. A satisfactory agreement between measurements and calculations is demonstrated, indicating that the underlying physical reasoning of this method is realistic. The calculated Doppler profiles are found to be strongly dependent on whether the pitch angle distribution is isotropic or cosine. Monoenergetic Doppler profiles viewed perpendicular to the magnetic field are found to have a characteristic symmetrical shape, where the isotropic profiles are wider than the corresponding cosine profiles. Profiles viewed parallel to the magnetic field have characteristic blueshifted tails and redshifts due to instrumental broadening. The
Estimation of initial auroral proton energy fluxes from Doppler profiles
1881
&OxlO ?
?S.
2"s~J07
o
¢
'~1~
10 7 7
.,.0. 2
~L,~,07 L~
12
dJ~/~t a 2
4
. . . . . . . . .
O ISOl'HK]t~~TCtt ~ 01SIIqlOtf/'d~ O OtAtt0tC5 - Ct~t.C~TED ~ , t L r T [ n.UX
eO~ 7 2.0xl 0
8
Ce) . . . . . . . . .
H
2.~107H
S
e sQm uk~
- U~N FLt~
1
Se
• i
.....
, .........
, .........
, .........
, .........
t..
2
4
a
mmav[~'1
B
Fig. 6. Upper panel (A): Daytime zenith H~ Doppler profiles observed at Nordlysstasjonen in Adventdalen, Svalbard, on 12 January 1992 at 00:00 to 14:49 UT. The intensity is given in Rayleighs.Middle panel (A2): Sample of the H~ Doppler profile obtained at 09:56:37 UT from panel (A). Middle panel (B): Calculated particle spectra obtained from the H~ profiles shown in panel (A), applying cosine pitch angle distributions (diamonds). Also shown is the mean flux (solid line).Bottom panel (C): Calculated particle spectra obtained from the Ho profiles shown in panel (A), applying isotropic pitch angle distributions (diamonds). Also shown is the mean flux (solid line). The spread of the diamonds indicates the variation of the particle fluxes during the observing period. peak intensity of the isotropic profiles are shifted about 1 .A towards shorter wavelengths compared to the corresponding cosine profiles. The blueshift is found to be more dominant in the cosine compared to the isotropic case, resulting in larger half-widths, respectively. A Doppler profile applying a typical initial dayside particle spectrum obtained by in-situ measurements (Newell et al., 1991) corresponds well both in shape and intensity to ground-based spectral observations by Henriksen et aL (1985). A 1 keV "bulk" energy of the initial particle flux resulted in a Doppler profile confined within 10 ,~. Through deconvolving dayside ground-based mea:sured Doppler profiles made from
Nordlysstasjonen, Svalbard, on 12 January 1992, assuming a cosine pitch angle distribution, the main part of the initial particle flux is found to have an order of magnitude of 106 protons/cm 2 s sr keV with a "bulk" flux centred near 2 keV. Only downward oriented fluxes are obtained in these calculations. Redshifts produced by factors other than instrumental broadening are not considered. Extensive high-resolution ground-based measurements of the auroral Doppler shifted hydrogen lines have to be carried out in order to optimize model calculations and to promote progress. Corresponding energy particle spectra and Doppler profiles are needed.
REFERENCES Chamberlain J. W.
1961
Physics of the Aurora and Airglow, Academic Press,
New York.
1882
F. Sigernes
Dalgarno A.
1962
Deehr C. S., Sivjee G. G., Egeland A., Henriksen K., Sandholt P. E., Smith R., Sweeney P., Duncan C. and Gilmer J. Eather R. H.
1980
Fastie W. G.
1952
Galperin Y. I.
1963
Gartlein C. W.
1950
Hedin A. E.
1987
Henriksen K., Fedorova N. I., Totunova G. F., Deehr C. S., Romick G. J. and Sivjee G. G. Herzberg G.
1985
Howard A.
1987
Jasperse J. R. and Basu B.
1982
Kozelov B. V.
1993
Kozelov B. V. and Ivanov V. E.
1992
Meinel A. B. NeweU P. T., Burke W. J., Meng C.-I., Sanchez E. R. and Greenspan M. Omholt A. Press W. H., Teukolsky S. A., Vetterling W. T. and Flannery B. P.
1951 1991
1967
1950
1971 1992
Reasoner D. L., Eather R. H. and O'Brien B. J.
1968
ReesM. H.
1982
Reid G. C.
1961
Sigernes F., Fasel G., Deehr C. S., Minow J., Smith R. W., Lorentzen D. A., Wetjen L. T. and Henriksen K. Sigernes F., Lorentzen D. A., Deehr C. S. and Henriksen K. Sigernes F., Lorentzen D. A., Deehr C. S. and Henriksen K.
1995
Sivjee G. G., Romick G. J. and Rees M. H.
1979
Saraas F., Lindalen H. R., Mfiseide K., Egeland A., Sten T. A. and Evans D. S. Vallance Jones A.
1974
Van Zyl B. and Neumann H.
1980
Van Zyl B., Gealy M. W. and Neuman H.
1984
Vasyliunas V. M.
1979
1993 1994
1974
Range and energy loss. In Atomic and Molecular Processes, Ch. 15, Academic Press, New York. Ground based observations of F-region aurora associated with the magnetospheric cusp. J. 9eophys. Res. 85, 2185. Auroral proton precipitation and hydrogen emissions. Rev. Geophys. 5, 207. Image forming properties of the Ebert-monochromator, J. Opt. Soc. Am. 42, 647. Proton bombardment in aurora. Planet. Space. Sci. 10, 187. Aurora spectra showing broad hydrogen lines. Trans. Am. #eophys. Un. 31, 18 1987. MSIS-86 thermospheric model. J. yeophys. Res. 92, 4649. Hydrogen emissions in the polar cleft. J. atmos, terr. Phys. 47, 1051. Spectra of Diatomic Molecules, D. Van Nostrad Co., Inc., New York. Elementary Linear Alyebra, John Wiley & Sons, New York. Transport theoretic solutions for auroral proton and H atom fluxes and related quantities. J. yeophys. Res., 87, 811. Influence of the dipolar magnetic field on transport of proton-H atom fluxes in the atmosphere. Ann. Geophys. 11, 697. Monte Carlo calculations of proton-hydrogen atom transport in N2. Planet. Space Sci. 40, 1503. Doppler shifted auroral emission. Astrophys. J. 113, 50. Identification and observation of the plasma mantle at low altitude. J. 9eophys. Res. 96, 35. The Optical Aurora, Springer, Berlin. Numerical recipes in FORTRAN: The Art of Scientific Computing, Cambridge University Press, New York. Detection of alpha particles in auroral phenomena. J. 9eophys. Res. 73, 4185. On the interaction of auroral protons with the earth's atmosphere. Planet. Space Sci. 30, 463. A study of the enhanced ionization produced by solar protons during a polar cap absorption event. J. 9eophys. Res. 66, 4071. Calculations and ground-based observations of pulsed proton events in the dayside aurora. J. atmos, terr. phys. (in press). Modulation of the auroral proton spectrum in the upper atmosphere. J. atmos, terr. Phys. 55, 1289. Calculation of auroral Balmer volume emission height profiles in the upper atmosphere. J. atmos, terr. Phys. 56, 503. Intensity. ratio and center wavelengths of OII (73207330 A) line emissions. Astrophys. J. 229, 432. Proton precipitation and the H a emission in a postbreakup auroral glow. J. #eophys. Res. 79, 1851. Aurora, D. Reidel Publishing Company, DordrechtHolland. H, and H~ emission cross sections for low-energy H and H ÷ collisions with N2 and 02. J. Geophys. Res. 85, 6006. Prediction of photon yields for proton aurorae in N2 atmosphere, J. 9eophys. Res. 89, 1701. Interaction between the magnetospheric boundary layers and the ionosphere, Proceedings of Magnetospheric Boundary Layer Conference. Eur. Space Ayency Spec. Publ., p. 148.
Estimation ofinitial auroral proton energy fluxes ~omDoppler profiles Vegard L.
1939
VegardL.
1948
Vegard L.
1950
1883
Hydrogen showers in the auroral region. Nature 144, 1089. Report on recent work in ionospheric phenomena and solar and terrestrial relationships. In Emission Spectra of the Night Sky and Aurorae, The Physical Society, London. Nouvelles recherches sur le spectre des aurores boreales. C. R. Acad. Sci., Paris 230, 1884.
~Perg
amon
0021-9169(95)00179--4
Estimation of initial auroral proton energy fluxes from Doppler profiles F. Sigernes The University Courses on Svalbard, N-9170 Longyearbyen, Svalbard, Norway
(Received in final form 20 June 1995; accepted 5 July 1995) Abstract--An energetic auroral proton entering the atmosphere will, by charge exchange in collisions with atmospheric constituents, alternate between being a proton H + and a neutral hydrogen atom H. This study provides a ptocedure to evaluate the auroral Doppler shifted and broadened hydrogen Balmer profile as a function of initial energy, flux, pitch angle and view angle relative to the geomagnetic field. The differential proton energy flux entering the atmosphere is deduced using ground-based measurements of H~ and Hp from Nordlysstasjonen in Adventdalen, Longyearbyen. The main assumptions are that the geomagnetic field lines are: parallel and vertical, and that the pitch angle of the H/H+-particle is preserved in collisions with atmospheric constituents before being thermalized. This numerical method estimates the fate of the auroral H/H %particle in the atmosphere, and from measured Doppler profiles the corresponding incoming particle flux can be deduced. Optimization of the method will continue through extensive use of observational dat~.. Copyright © 1996 Elsevier Science Ltd
INTRODUCTION Vegard (1939) was lLhefirst to discover the presence of auroral Balmer hydrogen emissions using a groundbased spectrograph. Later observations of the Balmer lines confirmed that they were Doppler displaced and broadened, and therefore caused by neutralized protons penetrating into the atmosphere (Vegard, 1948, 1950; Gartlein, 1950). Meinel (1951) was the first to make a detailed study of hydrogen emissions viewed parallel and perpendicular to the magnetic field. Since this discovery, numerous measurements of the Doppler profiles have been carried out (cf. Galperin, 1963; Vallance Jones, 1974; Deehr et al., 1980; Henriksen et al., 1985), which gave results in agreement with Meinel's observations. r h e theory of the Balmer lines has been extensively developed since the work of Chamberlain (1961), Eather (1967) and Omholt (1971). Both in-situ measurements (Reasoner et al., 1968; cf. Soraas el al., 1974) and recently obtained laboratory cross sections (Van Zyl and Neumann, 1980) have made it possible to develop numerical models explaining :~ome of the characteristics of proton aurora (Jasperse and Basu, 1982; Rees, 1982; Van Zyl et al., 1984; Kc,zelov and Ivanov, 1992). A simple method of calculating synthetic Doppler profiles as a function of initial particle flux and energy at arbitrary view angles relative to the magnetic field is presented. The pitch angle distribution is assumed
either to be isotropic or cosine. Each calculated profile is convolved with the instrument function of an EbertFastie spectrometer (Fastie, 1952; Sivjee et al., 1979). By means of a library of such synthetic Doppler profiles it is possible to deconvolve an observed profile caused by auroral protons into an energy spectrum giving the flux of protons at given energies. The aim is to create a simple tool for on-going programs related to auroral morphology, especially in the dayside aurora where the influence of proton precipitation has become more and more important to the scientific community. It may seem superfluous to obtain an estimate of particle fluxes through ground-based Doppler profiles, since particle fluxes can be obtained directly by satellites and rockets. Doppler profiles and particle fluxes are indeed independent parameters. However, again, limitations imposed on satellite and rocket measurements by their transient nature make the ground-based techniques useful, considering their temporal and spatial resolution. Indeed, both kinds of observations are necessary to obtain full information on the proton precipitation during auroras (Omholt, 1971). The method presented here is meant as additional support. Doppler profiles of the hydrogen Balmer lines observed from Nordlysstasjonen in Adventdalen, Longyearbyen, are the data treated by this method, and the results are discussed. This study is a con-
1871
F. Sigernes
1872
tinuation of the work initiated by Sigernes et al. (1994).
with the vector r pointing to the origin of the emitter's v,'v/v j-coordinate system. The spherical components of r are
THE D O P P L E R SHIFTED AND BROADENED
r~ = r sin ;~cos,1
(4)
ry = r sin )~sin )I
(5)
r= = r cos Z
(6)
HYDROGEN BALMER PROFILE
The line-of-sight velocity of an emitting particle is found by representing the observer O and the emitter E in two-coordinate systems (Fig. 1). The observer O is located at the origin of the xyz-coordinate system. Since the observer actually represents an Ebert-Fastie spectrometer capable of obtaining auroral spectra in the north-south magnetic meridian plane at an arbitrary angle relative to the magnetic field, the x-axis is defined to point towards the geomagnetic north, the y-axis west and the z-axis is aligned parallel with the magnetic field. Also, since the field of view of the instrument is only 5 degrees, the emitter E is defined at the origin of the parallel reference Vx'Vy'Vz'-coordinate system. The vector r connects the two origins. The components of the velocity vector v of the emitter in spherical coordinates are
where Z is the angle between the viewing direction and the magnetic field, q the corresponding azimuth angle, and r the length of r. Note that t/is taken to be zero in our case. The component of v projected onto r gives the absolute value of the line of sight velocity vector Vs (Howard, 1987), namely v= -
Iv'rl r
(7)
The components ofv are defined similarly and equation (7) becomes v= = v[yl
(8)
(9)
where
v=, = v s i n 0 c o s ¢
(1)
? = sin 0sinx cos(q$-q)+ cos0cosg.
vy = vsin0sinff
(2) (3)
According to equation (8) the emitter moves with velocity v, pitch angle 0 and phase angle ¢ at height h = rz, while the observer in its reference frame senses the velocity v=. The sign of the angular function ? gives information on whether the emitter is approaching or receding from the observer. The Doppler shifted wavelength 2, which the observer can detect from an emission with centre wavelength 20, is
t~z, ---- t) COS 0
where 0 is the pitch angle relative to the magnetic field, ~b the azimuth angle, and v the magnitude of v. The observer is at the origin of the xyz-coordinate system
Vz,
Vs ~
where c is the speed of light. The emission rate of (H+/H)-particles at an arbitrary height is given by (Sigernes et al., 1994)
Vy,
A. E ~
~
'
3
0
: Vx'
, !
i ll
Y
,, X
n--1
. . . NM(~ff
~. A,m
['~"
photons -1
lh sT vlA L
(II)
m=l
I
r
~'.m - -
i ,11 I X
O Fig. 1. Configuration of observer O and emitter E in two frames of reference.
where A,m is the probability of transition from the nth to mth energy level, a ~ =) the corresponding effective excitation cross section (Van Zyl and Neumann, 1980), NM the concentration of all atmospheric atoms and molecules at height h, and F the (H+/H)-particle flux. Expression (I I) is valid when collisional quenching is negligible. The energy degradation of the (H+/H)-particle in the upper atmosphere was calculated based on the fundamental hypothesis that the pitch angle is preserved in the interaction with atmospheric constitu-
Estimation of initial auroral proton energy fluxes from Doppler profiles ents, and that the magnetic field is homogeneous and vertical in the main collisional region. Physical reasons for this hypothesis were given by Sigernes et al. (1993). The instantaneous energy K at height h for a (H +/H)particle with initial kinetic energy eo at the top of the atmosphere h = H, pitch angle 0 and random phase angle 4) is (12)
K(eo,h,O,dp) = e o - W(eo,h,O,dp)
1873
by (H+/H)-particles with initial flux f(eo), view angle and wavelength 2. The differential energy photon flux integrated from the top of the atmosphere, h = H, down to the lower height level, h = h0, can then be expressed as ho
~
An m
D~(eo,2)= ~
L E.-, h'ffiH 4¢=0 i E A.m m=l
W is the total energy loss given by ( ]t ) W(eo,h,O,(a) = ~ o ~
h dK ~
h' =H
,
--d~x(K(e°'h ,O,(a))"
p(h') PO
,
× NM(h')a~')(K(eo,h',Oi, c~'))f(eo) • n(h',Oi,c~')AOAc~Ah'
photons ] cm2 s sr/~ keV_] (16)
Ah
(13) where P0 = 1.23 × 10-3 g/cm 3. The energy loss was found by adding up the energy-dependent stopping power, dK/dx, at each height interval above height h. The energy-dependent stopping power used in these calculations was faund by Sigemes et al. (1994) to be a compromise between experimental results obtained by Reid (1961) and Dalgarno (1962). The mass density p as a function of height from 200 km down to 90 km is obtained from the MSIS-86 model (Hedin, 1987) for different solar activities and geomagnetic conditions. The particle flux 5~" is related to the initial flux by the expression.
The wavelength 2 reaching the observer is calculated by equation (10) when vs is given, and no significant quenching of the upper state occurs. Since it is assumed that the initial particle flux is independent of the pitch angle distribution, equation (16) takes the form
[ photons q D.~m(e0,2) = f(eo)" B~.m(e0,2)LcmZs sr A keV J (17) where B~,,. are the terms left after extractingffrom the summation.
o~(K(eo,h,O,q~)) = . ~ ( e o - W(eo,h,O,(~)) = f(eo)
INSTRUMENTATIONAND CALCULATEDDOPPLER
V-particles .] • n(h,O,~) [_cm2 s sr keVJ
(14)
where f is the initial H+/H-particle flux at energy e0, and n the pitch angle distribution. Sincefis the H ÷/Hparticle flux, the proton flux is given as fp = f-Fp, where Fp is the proton flux fraction (Van Zyl and Neumann, 1980). The (H+/H)-particle flux is then assumed to be in equilibrium, and the top of the atmosphere is set to 200 km. According to equations (8) and (12), the line-ofsight kinetic energy of a (H+/H)-particle is given by 1
2
mv~ --=K(eo,h,O,dp)" y2(0,~b,r/,Z)
(15)
where m is the mass. Equations (15) and (10) are the key equations in constructing the Doppler profile as a function of initial energy, view angle and height. The main idea is to solve equation (15) with 0 as the only unknown. For each fixed phase angle ~b, initial energy eo, line-of-sight velocity v, viewing direction ~, and height h, equation (15) has two solutions denoted as 0~ where i~[1,2]; r/ is in our case zero. Adding up all solutions of 0i around ~b makes it possible to construct the differential energy photon flux produced
PROFILES
Ebert-Fastie spectrometers were used to measure Doppler profiles. Their construction is based on one large spherical mirror, one plane diffraction grating, and a pair of slits. The light from the entrance slit is reflected and made parallel by the spherical mirror onto the grating. The same mirror focuses the diffracted and parallel light from the grating onto the exit plane. When the grating turns, the image of the entrance slit is observed at the exit slit in different wavelengths, determined by the angular position of the grating. The grating is blazed at a fixed angle in order to produce a maximum efficiency at the desired spectral order and wavelength region used. Filters in front of the entrance slit are used to prevent overlapping orders. A perfect instrument with no defects such as spherical aberration, astigmatism or grating ghosts has an instrument function R(2) = Ef(2) •F:(2) • GA COS fl" T#(2) • A(R)/L~,
(18) where EI is the efficiency of the grating, FI the transmission fraction of the order sorting filter, GA the
1874
F. Sigernes
illuminated grating area, fl the diffraction angle, Tg the geometric transmission coefficient, Lj the focal length of the mirror, and A a triangular function with a baselength of twice the bandpass. Normally the entrance and exit slits have the same width. Then the bandpass is the instrumental line width, the half-width of an infinitely narrow line passing through the instrument and recorded. A light-pipe transfers the image at the exit slit to the detector. The detectors are photomultiplier tubes mounted in Peltier cooled housings, improving the sensitivity and the signal-to-noise ratio of the tubes. They are of the GaAs type, and since the spectral response of these tubes covers a wide range from ultraviolet to 9300 A, the quantum efficiency is nearly independent of wavelength. The entrance optics to the spectrometers is a periscope, which can be turned in different directions along the geomagnetic meridian filling the field of view of the spectrometers. In order to obtain the Doppler profile as measured by an Ebert-Fastie spectrometer, it is necessary to convolve the intensities calculated in equation (17) with the instrument function J~m(eo,2) = f(eo)" B~,m(eo,2)*R(2)
(19)
Equation (19) can now be used to produce a library of Doppler profiles, produced by a monoenergetic beam of protons, as a function of view angle. Figure 2 shows the calculated Doppler profile of H~ as a function of view angle relative to the magnetic field when the initial energy is 10 keV. The profiles are calculated with an instrument function of an EbertFastie spectrometer with a one-meter focal-length mirror scanning in the first spectral order with a bandpass of 7 A. The grating is blazed at 53 ° and has 1200 grooves per millimeter. The pitch angle distribution is cosine in the upper panel (A) and isotropic in the lower panel (B). The horizontal profiles in panels (A) and (B), Z = 90°, are symmetrical about the centre wavelength 20, and the corresponding zenith profiles, = 0 °, have their characteristic tails shifted towards the blue part of the spectrum and minor redshifts due to instrumental broadening. The wavelength of the peak intensity of the zenith profile in panel (A) is about 1 A less than the corresponding wavelength in panel (B). As the view angle increases, the peak intensity of the profiles in panel (B) drops faster than in panel (A). The pitch angle distributions are defined to be normalized at the top of the atmosphere (Sigerues et al. 1993). Accordingly, the cosine and isotropic distributions equal ncos (h, 0, ~b) = (l/n) cos 0 and his o (h,O,~) = l/2n, respectively. The cosine particle flux will then be less than or greater than the isotropic flux,
dependent on whether the absolute value of the pitch angle is less or greater than 60°:
fleo)noos(h,O,49) > f(eo)niso(h,O,~)
101 < 60 °
f(eo)n¢os(h,O,dp) < f(eo)niso(h,O,c~)
101 > 60 ° (20)
This effect is clearly seen in the half-widths of the profiles shown in Fig. 2. The zenith profile shown in panel (A) has a larger half-width compared to that of the zenith profile shown in panel (B). This is simply due to the fact that the main fraction of the cosine particle flux has pitch angles less than 60 °, which leads to a larger contribution to the tail of the profile in panel (A) compared to that of the tail in panel (B). Furthermore, as the view angle increases, a decrease of the half-widths in panel (A) and a corresponding increase in panel (B) are observed, respectively. In the present study, the incident (H+/H)-particle flux is assumed to be in equilibrium according to the flux fractions given by Van Zyl and Neumann (1980). The top of the atmosphere was therefore defined at 200 km. Above ~ 200 km, Kozelov (1993) found that the convergence of the magnetic field causes a small fraction of the incident flux to be mirrored and transported out of the atmosphere. Now, since the light productive height region was measured by Soraas et al. (1974) and calculated by Sigernes et al. (1994) to be centred at approximately 115 km, well below mirroring heights, it seems that collisional scattering in the low-energy range is the only alternative left in order to explain the observed redshifts in the Doppler profiles. But this is only speculation and reveals the need to include both a converging magnetic field model and collisional scattering in future model calculations in order to explain the minor redshifts observed. In this study we concentrate only on downward oriented fluxes.
AN ESTIMATEOF THE INITIALDIFFERENTIALH÷/HENERGY PARTICLE FLUX USING GROUND-BASED SPECTROMETRIC OBSERVATIONS
The method which now will be presented is based on the use of the above-calculated Doppler profiles (equation (19)) as a library in obtaining a fit to the measured quantifies, and thereby deducing the initial energy particle flux. The total intensity of a Doppler profile at any given wavelength 2 is the summed contributions from particles with initial and degraded energies
IXnm(l~)= ~ J ~ ( E , 2 ) d E J
(21)
Estimation of initial auroral proton energy fluxes from Doppler profiles
1875
3.0x10 - 6
2.5x10 - 6 >
2.0xl 0 - 6
.< ~
1.5x10-6
z i-._z 1 . 0 × 1 0 - 6
5.0x10 - 7
0 6530
:"'
6540
. . . . . . .
6550
I . . . . . . . . .
I . . . . . . . . .
6560 6570 WAVELENGTH [A]
I . . . . . . . .
3.0x10 - 6
I . . . . . . .
6580
6590
' ' I ' ' ' ' ' ' ' ' ' I
. . . . .
6600
'''
(B) CALCULATED Hm PROFILES
2.5xl 0 - 6
O" k
ISOTROPIC PITCH ANGLE
10,~X
DISTRIBUTION INITIAL ENERGY 10 keV
' ~ 2-0x10-6
30
~-
4oL....
~
1.5xi 0 - 6 :-
Z
VIEW ANGLE 0-90"
5o[.... 60"
~7 1.0x10-6
_ 70" 80"
5.0x10 - 7
0 65~m
~ i . , i i , I i i
654o
655o
656o
657o
658o
659o
WAVELENGTH [A] Fig. 2. Calculated monoenergetic H~ Doppler profiles as a function of view angle relative to the magnetic field. The initial flux consists of one test particle with 10 keV kinetic energy for each of the pitch angle values used. Panel (A) shows the profiles calculated with a cosine pitch angle distribution while panel (B) shows the corresponding profiles using an isotropic pitch angle distribution. The instrument function is derived using a one-meter Ebert-Fastie spectrometer scanning in the second order.
66oo
F. Sigernes
1876
Alternatively, equation (21) can be expressed as a discrete summation
IXnm(,~)= f J~,m(E,2)dE
(22)
where N is the total number of energy bins of variable width AEi. If we now consider the total Doppler profile consisting of a number of discrete intensities at M wavelengths, a set of M linear equations each similar to equation (22) is obtained. In matrix notation we can write I]m = ~'~nXm° f(E)AE
(23)
where ll,xm is the matrix of monoenergetic intensities at discrete wavelengths with the number of rows equal to the size of the I,X,,intensity vector and the number of columns equal to the number of energy bins; indicates the viewing direction. An example of l~,x,, is displayed in Fig. 3, where each monoenergetic H# profile, f/°2(Ei,2) = B~42(Ei,2)*R(2), represents column i in f/°2. The initial energy ranges from 1 to 70 keV, and the view angle is zero relative to the magnetic field. The pitch angle distribution is isotropic in panel (A) and cosine in panel (B). Each profile is calculated with an instrument function of a one-meter Ebert-Fastie spectrometer scanning in the second order, having a bandpass of 6 ]k. The intensity increases as the initial particles penetrate deeper into the more dense atmosphere with increasing energy, and the tail of the profiles becomes larger, indicating a wider energy range of the emitting particles contributing to the profile. Again we notice that the peak wavelengths of the cosine profiles are slightly blueshifted compared to the corresponding isotropic wavelengths. Also, the profiles in panel (B) have higher intensities and are wider compared with the profiles in panel (A), which is due to the properties of the particle fluxes used (see equation (20)). Our task is to solve M linear equations simultaneously in order to determine N values of the differential energy flux,f (E3, where U,m (2) is obtained by a ground-based spectrometer. Since M can be set greater than N, and the matrix f~,, in most cases becomes singular or close to singular, the method of Singular Value Decomposition (SVD) is used (Press et al., 1992). The energy range and the width of the energy bins AE are predetermined by analysing the shape of the measured Doppler profile I z . Since the measured Doppler profile I,Zmactually represents the velocity distribution along the line of sight of the emitting particles, the width of energy bins AE can
be estimated assuming the kinetic line-of-sight energy bins to be equally representative. Also, the width of the Doppler profile itself gives an indication of the initial energy range responsible for contributing to the profile, and an optimal result in respect to convergence and computation time is obtained by proper sampling of this range. An initial energy spectrum, f(E) = 8 × 10 7 E - 2 protons/cm 2 s sr keV, measured by the PROTON I rocket launched into a post-breakup auroral glow from Andoya on 13 February 1972 (Soraas et al., 1974) is used to calculate, according to equation (23), an H a Doppler profile with known characteristics. During this flight the pitch angle distribution was reported to be isotropic. Figure 4 shows in the upper panel (A) the measured energy spectrum (solid line). Equation (23) is then used to calculate the corresponding H a Doppler profile shown in panel (B) (solid line). It is unfortunate that no measured Doppler profile exists for the energy spectrum in panel (A). In order to test the mathematics of the procedure described above a set of values from the Doppler profile in panel (B), marked with diamonds, was used to obtain the initial energy spectrum. The result of this test is shown by diamonds in panel (A). This test indicates that the described method for deducing initial energy particle spectra from corresponding measured ground-based Doppler profiles may give reasonable results. In this case the instrument function used corresponds to a one-meter Ebert--Fastie spectrometer scanning in the second order with a bandpass of 1.5 ,~. The total intensity of the profile in panel (B) must be multiplied by a factor of 0.7 in order to fit the reported intensity of 170 R, measured by interference filter photometers (Soraas et al., 1974). This discrepancy could be interpreted to mean that the emission cross sections for H# are 30% too high. However, both the absolute calibration of the instruments and uncertainties related to the calculation of the instrument function could well be of similar magnitude. It must be emphasized that this is only a test of the calculating procedures presented, and cannot be seen as a verification of the method itself. One of the main objects of this work is to provide a tool for studying proton precipitation in the dayside aurora. Newell et al. (1991) have identified particle spectra from the DMSP satellites corresponding to the ionospheric cusp as proposed by Vasyliunas (1979). Since the measured particle flux is highly fieldaligned, well within the atmospheric loss cone, we assume the pitch angle distribution to be cosine. The upper panel (A) of Fig. 5 shows the ion cusp spectrum obtained by fitting a Gaussian function to the data obtained by the DMSP F7 satellite crossing the
Estimation of initial auroral proton energy fluxes from Doppler profiles
1877
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Fig. 5. Panel (A) shows the differential initial cusp particle spectrum (solid line) measured by the DMSP F7 satellite crossing the southern hemisphere 26 January 1984. It is used to generate the H~ Doppler profile in panel (r 0 (solid line). The pitch angle distribution is cosine. The calculated values of the flux and the resulting profile using the method described are shown in panels (A) and (B) (diamonds), respectively. The instrument function used represents a one-meter Ebert-Fastie spectrometer scanning in the second order.
1880
F. Sigernes
southern hemisphere on 26 January 1984 (solid line). The same procedure as described in Fig. 4 is applied to the lower panel (B). We noticed that the Doppler profile is well reproduced throughout the entire wavelength region. The synthetic initial energy flux has a small fluctuating behaviour around 3 keV. This is due to the choice of monoenergetic profiles and the width of the energy bins used. A rather crude energy resolution in the tail of the profile can produce this effect. Therefore this method requires proper sampling of the initial energy range. Also, the signal-to-noise ratio of a measured Doppler profile has to be high, which may result in poor time resolution. The calculated profile in panel (B) corresponds well both in intensity and shape to ground-based spectral observations carried out during several years at Nordlysstasjonen in Adventdalen, Svalbard (74.9°N, 114.6°E geomagnetic coordinates, geomagnetic noon ~ 0830 UT). Henriksen et al. (1985) have reported narrow auroral dayside H~ profiles confined within 10 A, corresponding to about 1 keV initial energy of the precipitating protons. In other words, the particle flux of the precipitating protons can be close to the flux in panel (A). Again, it must be emphasized that the only true proper test of the method can be made by comparing satellite or rocket measurements that coincide, which in itself is a difficult task not yet performed with ground-based sites. It is therefore a crucial point to be addressed in the future for continuation and optimization of the method presented. On 12 January 1992 measurements of auroral dayside hydrogen emissions were carried out at Nordlysstasjonen. The Sun was then more than 6 degrees below the horizon, which permitted optical measurements throughout most of the daytime period. The dayside auroral oval was in the zenith between 0700 and 1100 UT. Throughout this time period polewardmoving auroral forms were seen, which broke away from the stationary oval and moved poleward into the polar cap. Associated with each poleward-moving auroral form was a burst of H~ and H~ emissions, which stretched over much of the sky (Sigernes et al., 1995). A half-meter Ebert-Fastie spectrometer was fixed in the geomagnetic zenith scanning the secondorder wavelength region (65174579) A with a bandpass of 2.5 .&. The upper panel (A) of Fig. 6 shows the obtained intensities of HE plotted as a function of time and wavelength. The scaled bar to the left indicates intensities in Rayleighs. Absolute calibration of the spectrometer was done with a diffuse re-emitting screen covering the field of view of the instrument and a tungsten lamp as the comparative source situated in a tower 30 m away. Overlapping OH(6, 1) rotational emission airglow
intensities are filtered out by the method described by Herzberg (1950). Each scan of the spectrometer took 12 s. In order to improve the signal-to-noise ratio, a summation of several scans was required, which resulted in a time resolution of about 2 rain for the processed data records. The next panel (A2) shows a sample of a data record obtained during maximum activity around 10 UT. The middle panel (B) shows the resulting initial particle flux (diamonds) calculated by using each processed data record as input to the method described above. The pitch angle distribution is cosine. The main part of the calculated flux values are distributed in the energy range less than 5 keV. The average values (solid line) have the order of magnitude of 106 protons/cm 2 s sr keV and a "bulk" energy close to 2 keV. Maximum flux values are one order of magnitude higher than the mean values and correspond to the most intense part of panel (A). In the low-energy range, less than 1 keV, the mean flux is represented as a low-energy tail connecting to the "bulk"-flux. This is a typical shape of the initial flux (Sigernes et al., 1993). Calculations applying an isotropic pitch angle distribution are shown in the lower panel (C). The obtained isotropic flux tends to be wider than the cosine flux shown in panel (B). It should be mentioned that the monoenergetic profiles calculated applying a cosine pitch angle distribution were better than the corresponding isotropic profiles conditioned to the measured profiles both in shape and in respect to convergence of the method described. The order of magnitude and the initial energy range of the calculated particle fluxes are found to be reasonable estimates of dayside proton precipitation.
CONCLUDING REMARKS
A procedure to obtain an estimate of the initial auroral proton energy fluxes through deconvolving observed ground-based Doppler hydrogen profiles is outlined and utilized. A satisfactory agreement between measurements and calculations is demonstrated, indicating that the underlying physical reasoning of this method is realistic. The calculated Doppler profiles are found to be strongly dependent on whether the pitch angle distribution is isotropic or cosine. Monoenergetic Doppler profiles viewed perpendicular to the magnetic field are found to have a characteristic symmetrical shape, where the isotropic profiles are wider than the corresponding cosine profiles. Profiles viewed parallel to the magnetic field have characteristic blueshifted tails and redshifts due to instrumental broadening. The
Estimation of initial auroral proton energy fluxes from Doppler profiles
1881
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Fig. 6. Upper panel (A): Daytime zenith H~ Doppler profiles observed at Nordlysstasjonen in Adventdalen, Svalbard, on 12 January 1992 at 00:00 to 14:49 UT. The intensity is given in Rayleighs.Middle panel (A2): Sample of the H~ Doppler profile obtained at 09:56:37 UT from panel (A). Middle panel (B): Calculated particle spectra obtained from the H~ profiles shown in panel (A), applying cosine pitch angle distributions (diamonds). Also shown is the mean flux (solid line).Bottom panel (C): Calculated particle spectra obtained from the Ho profiles shown in panel (A), applying isotropic pitch angle distributions (diamonds). Also shown is the mean flux (solid line). The spread of the diamonds indicates the variation of the particle fluxes during the observing period. peak intensity of the isotropic profiles are shifted about 1 .A towards shorter wavelengths compared to the corresponding cosine profiles. The blueshift is found to be more dominant in the cosine compared to the isotropic case, resulting in larger half-widths, respectively. A Doppler profile applying a typical initial dayside particle spectrum obtained by in-situ measurements (Newell et al., 1991) corresponds well both in shape and intensity to ground-based spectral observations by Henriksen et aL (1985). A 1 keV "bulk" energy of the initial particle flux resulted in a Doppler profile confined within 10 ,~. Through deconvolving dayside ground-based mea:sured Doppler profiles made from
Nordlysstasjonen, Svalbard, on 12 January 1992, assuming a cosine pitch angle distribution, the main part of the initial particle flux is found to have an order of magnitude of 106 protons/cm 2 s sr keV with a "bulk" flux centred near 2 keV. Only downward oriented fluxes are obtained in these calculations. Redshifts produced by factors other than instrumental broadening are not considered. Extensive high-resolution ground-based measurements of the auroral Doppler shifted hydrogen lines have to be carried out in order to optimize model calculations and to promote progress. Corresponding energy particle spectra and Doppler profiles are needed.
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Estimation ofinitial auroral proton energy fluxes ~omDoppler profiles Vegard L.
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Hydrogen showers in the auroral region. Nature 144, 1089. Report on recent work in ionospheric phenomena and solar and terrestrial relationships. In Emission Spectra of the Night Sky and Aurorae, The Physical Society, London. Nouvelles recherches sur le spectre des aurores boreales. C. R. Acad. Sci., Paris 230, 1884.