Limb-darkening scans of Jupiter

ICARUS

27,407-415

(1976)

Limb-Darkening

Scans of Jupiter

C. B. PILCHER AND T. D. KUNKLE Institute for Astronomy,

University of Hawaii,

Honolulu,

Hawaii

96822

Received September 23, 1975 An area scanning photometer has been used to obtain photometrically calibrated limb-darkening scans of Jupiter at four wavelengths : 6190,6300,7250, and 8200s. The first and third of these correspond to methane absorptions and the second and fourth to continuum regions near the 4-O and 3-O H2 quadrupole bands, respectively. Single-scattering albedos have been calculated for several areas on the planet at all four wavelengths assuming a semi-infinite, homogeneous, isotropically scattering atmosphere. The values obtained at the wavelengths of the quadrupole bands range from 0.98 over the NEB to 20.99 over the NTrZ and the bright band in the southern hemisphere. The single-scattering albedo values are used to show that the 5t~m-emitting equatorial regions of the planet may be relatively clear and the tropical regions relatively cloudy.

As our understanding of the nature of the atmosphere of Jupiter has increased, it has become increasingly apparent that measurements with high spatial resolution are usually necessary if any physically realistic interpretation is to result. In particular, Hunt (1973) has shown that center-to-limb (CTL) observations of the equivalent widths of absorption lines provide information for a determination of the vertical cloud structure of the Jovian atmosphere. One of the parameters in models used to interpret these observations is the single-scattering albedo of the cloud 1973; Hunt and particles, 5, (Hunt, Margolis, 1973). There is ample evidence from Pioneer spacecraft images that this quantity is spatially variable over distances much smaller than those observable from the surface of the Earth (Swindell and Doose, 1974; Baker et al., 1975). It is therefore imperative, in interpreting CTL spectral observations, to have accurate contemporaneous measurements of the nearby continuum intensity taken with approximately the same spatial resolution. In this paper we present representative photometric measurements of this type of several areas on Jupiter in the form of Copyright 0 1976 by Academic Press, Inc. AN rights of reproduction in any form reserved. Printed in Great Britain

limb-darkening scans taken through narrow-band (30-50 A) interference filters isolating continuum regions near the 3-O and 4-O hydrogen quadrupole bands. The results of scans measured through filters isolating two regions dominated by methane absorption are also discussed.

OBSERVATIONSAND DATA REDUCTION Jupiter was observed in October and December of 1974 with an area scanning photometer (Rakos, 1974) on one of the 61 cm telescopes of the Mauna Kea Observatory. The details of the observations and a description of the characteristics of the interference filters used are given, respectively, in Tables I and II. The photometer was equipped with a GaAs phototube in order to achieve high quantum efficiency out to 9000A. Circular apertures of 1 arc set and about 12arc set, respectively, were used for observations of Jupiter and the standard star 29Psc. The reflectivity of Jupiter in units of I/F, where I is the measured Jovian specific intensity and aF is the solar flux at Jupiter, was calculated using the monochromatic magnitudes of 29Psc relative to those of a Lyr given by Oke (1964), the 407

PILCHER

408 TABLE

AND

KUNKLE

TABLE

I

VALUES USED IN DATAREDUCTION

THE OBSERVATIONS

Date

Time (UT) Begin/End

7rPC Are8

Filter@ h(A)

Oct. 14 Oct. 14

7:29/8:46 9: 14/10:03

SEB, SEB,/STrZ”

2, 3, 4 2, 3,4

Oct. Oct. Oct. oat. Oct. Dec.

7:12/7:65 8:16/8:49 8:68/9:36 7:36/8:46 9:07/9:33 5:30/6: 14

NEB NTrZ C.M.’ C.M.’ NTrZ NTrZ

3, 3, 3, 1, 3, 1,

4:58/6:35 6:17/7:05

SEB, SEB,/STrZ*

:: :

16 16 16 18 18 1

Dec. 2 1

4 4 4 2, 3, 4 4 2

o Filter 1= 6190 A; Filter 2 = 6300 A; Filter 3 = 7260 A; Filter 4 = 8200 A. * The center of the bright b8nd formed by the SEB, and the STrZ. c Central Meridian.

TABLE

II

FILTEIM A, (4

Ah(A)

6190 6300 7250 8200

30 30 50 60

III

CH, Continuum (Hz 4-O) CH, Continuum (H, 3-O)

o Full-width-at-half-m8ximum

tr8nsmission.

6190 6300 7250 8200

Am(aLyr29Psc)” 5.14 5.14 5.16 5.17

m(aLyr)*

(erg cm-* see-’ A-i)

0.13 0.15 0.30 0.43

6.97 6.85 5.56 4.35

0 From Oke (1964). * From Hayes and Latham (1975). A vdue of 3.39 x 10~pergsom-*see-‘A-’ was adopted from these 8uthors for the flux from a 0.0 magnitude star at 5656A. c The solar flux from Arvesen et QL. (1969) extr8polated to 4.9SAU.

absolute brightness of a Lyr given by Hayes and Latham (1975), and the solar fluxes determined by Arvesen et al. (1969). The values adopted from these workersinterpolated where necessary-are shown in Table III. Because of our desire to obtain high spatial resolution while limited by the area scanner to a maximum scan length of about 4.5mm, we chose to scan the planet (diameter N 44arc set during the October observations) at a plate scale of 5arc secl mm in several overlapping scans. A complete observation through a particular filter usually consisted of ten scans: two

1.0 SEBn

8200A

F

FIU. 1. The results of fitting together the overlapping sc8ns of the north component of the South Equatorial Belt (SEB,) taken 8t 8200 A. The vertical scale is reflectivity in units of I/F where 1 is the measured Jovian speoiflc intensity 8nd rF is the solar flux at Jupiter. Numbers along the d8t8 curve denote the ends of individual sc8ns.

JUPITER

LIMB-DARKENING

IO

nated by the “white” noise of the photon counting statistics. It is thus possible to fdter the data by setting the Fourier transform to zero above some critical frequency, fC, and computing the inverse transform. The results of this calculation for the data of Fig. 1 are shown in Fig. 3. The high precision of this “cut-off filter” can be demonstrated by superimposing the filtered data on the original scans. For comparison, an optimal filter of the type described by Brault and White (197 1) was also applied to these data. No significant difference between the results obtained with the two filters was observed ; in consequence we have applied the “cut-off filter” to all of the data. Plotted at the bottom of Fig. 3 is the total scatter in the original data for each point in the scan. This is plotted rather than standard deviations because differences between overlapping scans are sometimes due to errors in repositioning the telescope. A standard deviation calculation is of questionable value for this kind of error. Some differences between overlapping scans are also introduced by the rotation of Jupiter during an observation (the last scan in an overlapping sequence was typically measured 30-70 minutes after the first). The scatter in the data may therefore be somewhat more useful than standard deviations in assessing the uncertainties in the intensities given in the filtered scans. Unfortunately, we found that the least-

8

Iti

6

$ 5 4 2

0 0

0.5

1.00

SPATIAL

FREQUENCY

1.5

2.00

f,

(ARCSEC-‘1

FIG. 2. The power spectrum (Fourier transform) of the data of Fig. 1. The frequency beyond which the power spectrum was set equal to zero for filtering purposes isf,. The Nyquist frequency is fN.

scans at each of five positions along the area being observed. The scans for a particular observation were then fit together using a digital least-squares technique and averaged. Figure 1 shows a representative fit of ten scans of the northern component of the South Equatorial Belt (SEB,) observed at SZOOA. The Fourier transform of the average of these data is shown in Fig. 2. It can be seen that the signal is predominately at frequencies below about 0.5 (arc set)-’ ; the power spectrum above that frequency is domiIO

C

409

SEB, 82OOA

II

El

UT 181

mm m

Tn&

BloazLz?D3l5,II

FIG. 3. The averaged and filtered data of Fig. 1 (see text and Fig. 2). The total scatter of the original data are shown at the bottom of the figure. Superimposed are calculated limb-darkening curves for a semi-infinite, homogeneous, isotropically scattering atmosphere with two different values of c&, the single-scattering albedo. The overall length of the averaged scan is not meaningful for reasons described in the text.

410

PILCHERAND KUNKLE

squares fitting process did not produce a unique value for the apparent width of the planet in a given observation. For example, if we arbitrarily tried to fit together eight or nine of the ten scans shown in Fig. 1, the result would likely show a different apparent width of the planet than that shown in Fig. 1. In the extreme cases (which the data of Fig. 1 are not), fitting together different subsets of a complete set of ten scans produced apparent overall scan lengths that differed from the nominal value (that obtained using all ten scans) by as much as 10%. Thus, no reliance can be placed on the apparent overall scan lengt,h in these observations. RESULTS AND DISCUSSION For comparison with the observations, we have computed limb-darkening curves for semi-infinite, homogeneous, isotropioally scattering atmospheres with different values of &,. The emergent intensity was calculated using the expression given by Chandrasekhar (1960) and the values of the H- functions for isotropic scattering tabulated by Carlstedt and Mullikin (1966). All geometrical factors were approximately accounted for under the assumption that the Earth and the Sun both lie in Jupiter’s equatorial plane. Separate sets of curves were calculated for the October and December observations when the phase angles were 8.0” and 11.4”, respectively. Two of these curves calculated for the latitude of the SEB, are shown in Fig. 3. It can be

seen that over much of the scan, allowing for variations along the belt, a curve intermediate between the curves shown would provide a reasonable match t,o the data. This result is suggested by t,he well known similarit,y relations (van de Hulst and Grossman, 1968 ; Hansen, 1969) that state that the reflection properties of a homogeneous anisotropically scattering atmosphere can be simulated by a homogeneous isotropioally scattering atmosphere in which the optical thickness and single-scattering albedo are related to the anisotropic values by simple scaling factors. The deviations of the data from a curve for a single value of 9, over the central regions of the planetary disk are undoubtedly due in part to the inhomogeneous nature of the Jovian atmosphere. Values of b, between 0.985 and 0.989 match the data over most of the SEB,. Values of 6, can also be determined from scans taken along the Jovian central meridian. Two examples of this type of scan at 8200A are shown superimposed in Fig. 4 ; the locations along the scan of several belts and zones are indicated using the notation of Peek (1958). Figure 5 shows similar data for 725OA. The planet clearly shows much more structure in the meridional than in the east-west scans. The scatter in the 82OOA data of October 18, plotted at the bottom of Fig. 4, is relatively large to either side of the NEB. As mentioned above, this is probably due to a combination of rotation of the planet during the observations and errors in repositioning the telescope. The data of

1.0 C

CENTRAL

MERIDIAN

8200A

FIG. 4. Two averaged and filtered scans of the central meridian at 82008. Vertical scale is the same as Fig. 1. The positions of several bands &re indicated using the notetiofi of Peek (1958). The apparent displacement of the north limbs relative to each other is an artifact of the data reduction process. The scatter plot is for the d&a of October 18.

JUPITER

411

LIMB-DARKENING

IO

CENTRAL

MERIDIAN

72508

FIG. 5. Same as Fig. 4 except in the 7250A methane absorption band. The scatter plot is for the d&a of October 18.

TABLE

IV

JOVIANREFLECTIVITIES"

Area

NTrZ

NEB

NEB/EZ EZ SEB,

SEB, SEB,/STrZ

Date Oct. Oct. Oct. Oct. Dec.

16 16 18 18 1

Oct. Oct. Oct. Oct.

16 16 17 18

63008

8200A

I% (4-O)

Hz (3-O)

IIP (Center/Max)

-

WC

-

0.72 -

0.991 -

0.69/0.69

0.986-0.990

-

-

0.6310.64 0.62

-

0.97&0.980 0.976 -

Oct. 16 Oct. 18

0.61

Oct. 16 Oct. 18

0.71

0.986

0.7110.73 -

0.984-0.988 -

0.70 0.70/0.71

0.985 0.984-0.987

Oct. Oct. Oct. Dec.

14 16 18 1

-

-

0.974 -

-

IIP (Center/Max)

WC

0.78 0.73/0.75 0.71 0.7310.73 -

0.995 0.991-0.993 0.991 0.991-0.993 -

0.66 0.6610.67 0.63/0.64 0.62

0.981 0.973-0.979 0.973-0.979 0.974

0.63 0.60

0.976 0.971

0.76 0.73

0.991 0.988

0.7310.73 0.74 0.71 -

0.986-0.989 0.990 0.987 -

Oct. 16 Oct. 18

0.76

0.992

0.79 0.75

0.995 0.993

Oct. 14 Dec. 2

0.7810.79 0.7510.76

0.992-0.996 0.991-0.993

0.79/0.79 -

0.993-0.996 -

a Reflectivities are given in units of I/F where I is the speci6c intensity of Jupiter and TF is the solar flux at Jupiter. Single values of I/F and G, are shown for scans along the central meridian ; two values are shown for each quantity for scans parallel to the equator. In the latter case, the I/F values are those at the center of the disk and the maximum observed in tha;t scan; the GE values are the limits observed over approximately the central half of the disk.

412

PILCHER

AND KUNKLE

October 16 in Fig. 4 are systematically higher than those of October 18. Since these scans were separated in time by 4.7 rotation periods of the planet, it is possible that part of this difference is real, but it also seems likely that at least part is due to unknown systematic errors. This possibility, combined with uncertainties produced by actual photometric variations on the planet, combine to yield a total maximum internal error of +4% in I/F. Systematic errors whose existence is known and are applicable to all of the data include errors in the following quantities taken from the literature cited above: the solar flux ($3%), the monochromatic magnitudes of 29Psc relative to those of CLLyr (&-2%), the colors of cxLyr (f2%), and the absolute measurement of the flux from

a Lyr at 5566 A (*2%). An additional error of +2% is introduced by an uncertainty in the solid angle subtended by the aperture used for the Jovian observations. Assuming that these errors add as the square-root-of-the-sum-of-the-squares, the additional systematic error in I/F is f5%. The total absolut’e error in any I/F value presented here may therefore be as large as &9%. However, the relative errors in the entire data set are no larger than f3-4% and the values derived from a single scan (such as one of the meridional scans) generally have a relative uncertainty of &l-2%. Tabulations of I/F and ijC values for the continuum regions near the 3-O and 4-O H, quadrupole bands are presented in Table IV. Similar values for the methane

TABLE

V

JOVIANREFLECTIVITIES' 6190 A

7250 i%

CH,

Area

Date

IIF (Center/Max)

CH,

wv

IIP (Center/Max)

“V

NTrZ

Oct. Oct. Oct. Oct. Dec.

16 16 18 18 1

0.59 0.67/0.69

0.974 0.968-0.972

0.40 0.40/0.40 0.39 0.39/0.39 -

0.92 0.91-0.92 0.91 0.90-0.91 -

NEB

Oct. Oct. Oct. Oct.

16 16 17 18

0.51/0.62 0.62

0.948-0.966 0.964

0.36 0.37/0.38 0.36lO.36 0.34

0.89 0.88-0.90 0.87-0.89 0.88

NEB/EZ

Oct. 18

0.60

0.949

EZ

Oct. 16 Oct. 18

0.57

0.966

SEB,

Oct. 14 Oct. 16 Dec. 1

0.66 0.67/0.67

Oct. I6 Oct. 18

0.62

Oct. 14 Dec. 2

0.63/0.64

Oct. 18 SEB, SEB,/STrZ

-

0.962 0.962/0.967 0.977 0.977-0.982

0.39 0.39 0.3qo.39 0.39 0.38 -

0.90 0.90 0.89-0.91 0.91 0.90 -

0.41 0.40

0.92 0.91

0.40/0.41 -

0.91-0.92 -

a Same as Table IV except 0, substituted for 8, to indicate region of absorption.

JUPITER

absorption bands at 6190 and 72508 are presented in Table V (8, is used to designate the single-scattering albedo in a region of absorption). These values are substantially lower than those reported for the same regions of the planet by P&her et al. (1972), but are in excellent agreement with the recent measurements by Orton (1975). Much of the discrepancy between the measurements presented here and earlier results can be attributed to an inaccuracy in the published flux from J3, the satellite used as a comparison standard by Pilcher et al., as shown by Morrison et al. (1974). However, the B, values presented here are still substantially higher than those used in earlier studies of the H, quadrupole bands(DanielsonandTomasko, 1969; Fink and Belton, 1969; Pilcher et al., 1972). The ii,, values given in Table V can be used to calculate a parameter that is a measure of the relative densities of the gaseous absorber (in this case methane) and the cloud particles. Using a slightly modified form of the notatidn of Chamberlain (1970), we have cTc= o/(fc + a)

(1)

6, = a/(Q” + K + 0):

(2)

and

where o is the volume scattering coefficient, K is the cloud volume absorption coefficient, and ay is the gas volume absorption coefficient at frequency v. The desired parameter is aJu, given by .%,/a = l/G, - l/G,.

413

LIMB-DARKENING

(3)

Figure 6 shows the values of this parameter for several areas on Jupiter derived from two independent sets of scans along the central meridian at 7250 and 82008. Similar results from meridional scans at 6190 and 6300A are shown in Fig. 7 along with a few points from east-west observations. The error bars correspond to an estimated f2% maximum relative uncertainty in the intensity measurements from a single meridional scan. The eastwest measurements are shown in Fig. 7 without error bars because of the difficulty in determining their relative uncertainty;

I

Tl

4

SEBS

i E

FIG. 6. Plot of CY,/U versus position along Jovian central meridian calculated from meridional data at 7250 and 82OOA given in Tables IV and V. Data of October 16 and October 18 are for same latitudes but are shown slightly displaced for clarity. av is the gas volume absorption coefficient and o is the volume scattering coefficient. The error bars correspond to a &2% relative uncertainty in I/P.

0.04 ~’ 0.03

c

NEB

)

-I

FIG. 7. Same as Fig. 6 except calculated from data at 6190 and 63008. X’s are calculated from east-west data and areshown without error bars (see text).

however, it is likely that the errors in these measurements are somewhat larger than those for the meridional scan shown in the same figure. Although the errors in general are fairly large, the combined data shown in these two illustrations strongly suggest higher values for a,,/cr, and hence for the gas/cloud density ratio, over the comparatively dark equatorial regions of the planet (NEB, EZ, SEB,) than over the brighter SEB, and north and south tropical zones. (At the time of these

414

PILCEER AND KUNKLE

observations, the SEB, was the brightest region on t,he planet-as illustrated in Fig. 4-and merged visually with the STrZ to form a broad, bright zone in the southern hemisphere. In discussing cloud structure, it is thus reasonable to consider the SEB, along with the tropical zones rather than with the SEB,.) Relatively high values of the gas/cloud density ratio most likely occur over regions of the planet where one or more of the cloud layers thought to exist in the atmosphere (cf. Weidenshilling and Lewis, 1973) are thin or absent. The conclusion that this is the case over the equatorial regions of the planet is consistent with the interpretation of the 5pm emission observed from these areas. Several workers (Westphal et al., 1974; Rieke and Westphal, 1975, Keay et al., 1973) have suggested that this emission is present due to the absence of a high cloud layer that blocks 5pm radiation from the rest of the planet. Further photometric observations of the type presented here and more sophisticated atmospheric models should help to determine if this conclusion is correct.

ACKNOWLEDGMENTS We would like to thank K. D. Rakes for making the area scanner available to us, and T. J. Jones for assistance with the observations. This work was supported in part by NASA grant NGL 12-001-067.

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Tran-sfer,

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JUPITER

LIMB-DARKENING

SWINDELL, W., AND DOOSE, L. R. (1974). The imaging experiment on Pioneer 10. J. Geophys. Res. 79, 36343644; see also results presented by T. Gehrels at Jupiter Workshop, May 1975. VAN DE HULST, H. C., AND GROSSMAN, K. (1968). Multiple light scattering in planetary atmospheres. In The Atmospheres of Venzcs and Mars (J. C. Brandt and M. B. McElroy,

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