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The upper atmosphere of Neptune: An analysis of occultation observations
ICAFLUS
The
13, 59-65 (1974)
Upper
KATHY
Atmosphere
RAGES,
JOSEPH
of’ Neptune: An Observations VEVERKA,
Laboratory for Planetary Studies,
AND
Analysis
LAWRENCE
of
Occultation
WASSERMAN,
University,Ithaca, New York 14850
Cornell AND
K. C. FREEMAN Mount Strondo
and Siding
Spring
Observatories,Research School of Physical National
Sciences,
Australian
University
Received February 6, 1974
; revised May 6, 1974
An analysis of available observations of the April 7,196s occultation of BD -17” 4388 by Neptune yields upper atmosphere temperatures of -140°K near the 5 x 10’4cm-3 level. The temperature structure of the atmosphere at these levels is complicated andnonisothermal. Diurnal temperature variations are certainly less than 10°K and may be absent. The average temperature decreases by less than 15°K between 0” and 55” latitude.
I. INTR~DUOTI~N
Veverka, 1973). By a formal inversion of the light curve, Veverka et al. (1974a) have shown that the Mount Stromlo emersion curve indicates a nonisothermal atmosphere with an approximate scale height of 55km. This value agrees with those obtained by Kovalevsky and Link from the inversion of the Japanese light curves. However, the analysis of Kovalevsky and Link is based, not on the actual observed light curves, but on “mean curves” in which the spikes have been averaged out by some unspecified process. We feel that such averaging is unnecessary and must destroy some information. In the present paper we analyze all available light curves of the occultation event, using one and the same technique described in detail by Wasserman and Veverka (1973) and used by Veverka et al. (1974a, 1974b). In this method, the observed light curves are inverted point by point to yield the atmospheric refractivity as a function of height. Assuming that the atmosphere of Neptune consists mostly of hydrogen and helium, these refractivity profiles can be converted into temperature vs number density profiles
The occultation of BD -17” 4388 by Neptune on April 7, 1968 was observed photoelectrically at the Mount Stromlo Observatory in Australia (Freeman and Lyngb, 1969, 1970), and at the Dodaira and Okayama stations of the Tokyo Astronomical Observatory in Japan (Kovalevsky and Link, 1969). Immersion and emersion light curves were obtained at each site. From these curves it is possible to derive refractivity and temperature vs number density profiles for six points on Neptune. The immersion and emersion events occurred at the sunset and sunrise limbs, respectively. The latitude range covered on Neptune was 13”N to 55”s. Previous analyses of these occultation light curves were carried out by Freeman and Lynga (1970) and Kovalevsky and Link (1969). Freeman and Lynga attempted to fit the Mount Stromlo emersion light curve to an isothermal atmosphere model and obtained a scale height of about 30 km. Unfortunately, such curve fitting techniques can be very misleading when dealing with light curves dominated by spikes (Brinkmann, 197 1; Wasserman and Copyright 0 1974 by Academic Press, Inc. All rights of reproduction in any form reserved. Printed in Great Britain
59
60
RAGESET AL.
using methods described in the above papers. Thus, for the first time, the four Japanese light curves are analyzed without neglecting spikes. In addition, the Mount Stromlo immersion light curve is analyzed for the first time. Finally, for the sake of completeness, we reproduce the reanalysis of the Mount Stromlo emersion curve published by Veverka et al. (1974a). II. OBSERVEDLIGHT CURVES AND CALCULATEDATMOSPHERICSTRUCTURE Pertinent data concerning the light curves are gathered in Table I. Kovalevsky and Link (1969) reproduce facsimiles of the Japanese observations from which we have read points every 0.5sec. Facsimiles of the Mount Stromlo curves have never been published. The record of the emersion event given by Freeman and Lynga (1969), their Fig. la, is a point by point copy based on the original chart recording. In this study, however, we have used facsimiles of the original chart recordings of the Mount Stromlo immersion and emersion events. Since the time scale is more compressed than in the chart recordings of the Japanese events, points were read at only I-set intervals from the Mount Stromlo curves. Due to this time scale compression, there is some difficulty in reading values from the Mount Stromlo light curves near maximum where scintillation is evident. This is especially true of the emersion curve. This uncertainty in graph reading introduces small uncertain-
ties into the refractivity profile at the beginning of the calculation. This problem is dealt with in detail by Veverka et al. (1974a). According to that discussion, it seems that reading errors do not significantly affect the major portion of the calculated refractivity profile. Their effect on the calculated temperature profile is more pronounced, and large errors may be introduced into the upper portions of such profiles, as well as into inferred temperature gradients. It is therefore advisable to record occultation observations in digital form and with high time resolution whenever possible. In general, the signal to noise ratio is highest for the Mount Stromlo data and lowest for the Dodaira observations. The star’s velocity normal to the limb was at Mount Stromlo and 15.7 km/set 17.4km/sec for the Japanese observatories, computed from the ephemeris of Neptune using the corrections given by Freeman and Lynga (1970), and the star’s position corrected to the time of the event. All observations were made photoelectrically with V filters. The calculated refractivity profiles are shown in Fig. 1. The initial portions of such curves are not reliable since they are based on the incorrect assumption that the refractivity (and hence the density) is zero at the starting point of the calculation. Approximately four scale heights are needed for this error to become negligible (Wasserman and Veverka, 1973). Since all the refractivity profiles in Fig. 1 have quasilinear portions we can
TABLE I DATA STJMM~RYFOR 7 APRIL 1968 NEPTUNE OCCULTATION.BASED ON KOVALEVSKY AND LINK (1969) AND FREEMAN AND LYNGB (1970)
Telescope Place Mount Stromlo Mount Stromlo Dodaira Dodaira Okayama Okayama
Event
(cm)
Immersion Emersion Immersion Emersion Immersion Emersion
127 127 91 91 91 91
Neptune latitude of event -55” -2” -40” +13” -40” +13”
45’ 04’ 05’ 46’ 34’ 12’
Original analysis None Freeman and LyngB (1970) Kovalevsky and Link (1969) Kovalevsky and Link ( 1969) Kovalevsky and Link ( 1969) Kovalevsky and Link (1969)
NEPTUNE
,&u
100
200 x.3 Z(klIl,
400
61
UPPER ATMOSPHERE
define a quasi scale height I?: for each profile (Table II). On the average H - 50km, so that the first 200 km of the refractivity profiles are influenced by the assumed boundary condition and are therefore uncertain. The small wiggles in the refractivity profiles are related to the light curve spikes. The refractivity profiles in Fig. 1 can be used to derive the temperature vs number density plots shown in Fig. 2 according to the method outlined in Veverka et al. (1974a). The upper portions of these curves, again corresponding to about four scale heights from the beginning of the calculation are not meaningful since they correspond to unreliable portions of the re. and refractivity profiles (Wasserman Veverka, 1973). These portions have therefore been omitted in Fig. 2. It should be noted that even the temperature profiles shown may still be affected by uncertainties in reading data points from chart recordings (Veverka et al., 1974a) but we have no reason to expect such errors to be large. The composition of Neptune’s atmosphere was assumed to be 100% H, in calculating the Fig. 2 profiles. Methane and ammonia are unlikely to make any significant contribution to the observed re-
ou
Z(km)
FIG. 1. Refractivity profiles for Neptune’s upper atmosphere calculated from occultation light curves. The zero point of the depth scale (z) is arbitrary and corresponds to the initial point of each calculation. Consequently it is not the same for all curves shown. Note that for z 5 200km the profiles are uncertain and are shown dashed. A mean Neptune radius of 25 OOOkm was used in the calculations. (Refractivity equals the real part of the index of refraction minus one.)
TARLE
II
SUMXGZY OF RESULTS Quasi scale height Event
3
(kH,)
Temperature at lOi
crnm3
(“K)
at 3 x 1014cm-3
Mount Stromlo (Immersion)
55.0
146
148
Mount Stromlo (Emersion)
55.0
140
147
Dodaira (Immersion) Dodaira (Emersion )
53.0
133
144
52.5
132
142
Okeyama (Immersion)
48.8
128
127
Okayama, (Emersion)
59.3
160
144
62
RAGESETAL.
r
Id2
MT STROMLO IMMERSION
r MT
c
STROMLC
Id2 Id3
DODAIRA IMMERSION
DODAIRA EMERSION
It is then necessary in the Appendix. to assume that the atmosphere is well mixed at the levels in question. This means assuming a reasonable value for the eddy diffusion coef6cient : 2 5 x lo5 cm2 see-’ (Veverka et al.,1974a). Should the actual eddy diffusion coefficient be considerably smaller, the atmosphere at these levels would not be well-mixed, and the algorithm used to generate the profile in Fig. 2 would be invalid if the atmosphere is not made up predominantly of molecular hydrogen. III. Discussion OFRESULTS
d3 l.5‘E e IO14
OKAYAMA EMERSION
OKAYAMA IMMERSION
co
120 14c 130 180 x)0 T(“K)
FIG. 2. Temperature/number density profiles for Neptune’s upper atmosphere calculated from the refractivity profiles in Fig. 1. The calculation assumes that the atmosphere at these levels consists only of molecular hydrogen. Portions corresponding to the first 200km of the refractivity profile are uncertain and have been omitted.
fractivity, but helium cannot be ignored. Veverka et ab. (1974a) give temperature vs number density profiles based on the Mount Stromlo emersion curve, for three assumed compositions of Neptune’s atmosphere: (a) 100% H,; (b) 50% H, ; 50% He; and (c) 20% H,; 80% He by number. They argue that cases (b) and (c) lead to unacceptably high temperatures in Neptune’s upper atmosphere. In fact, there is no evidence to indicate that the helium fraction in Neptune’s atmosphere differs from the accepted solar value : f(He) = 0.10, by number. For small admixtures of helium, the appropriate temperature vs number density profiles can be obtained from those shown in Fig. 2 by the procedure outlined
We consider the results presented in Figs. 1 and 2 to be superior to previous analyses. As mentioned above the analysis of the Mount Stromlo emersion curve published by Freeman and Lynga (1970) is based on curve fitting to a very spiky light curve, a procedure which can yield results. (Wasserman and misleading Veverka, 1973; Veverka et al., 1974a). Our analysis of the Japanese results is in fair agreement with that of Kovalevsky and Link (1969) even though these authors essentially ignored spikes and smoothed the Dodaira and Okayama light curves for each event. Their Fig. 7, showing calculated temperatures and scale heights, is in part misleading, since it does not indicate that some of the values shown are grossly affected by the boundary conditions of the problem. Ignoring such values, their graphs give scale heights of 50-63 km on emersion and 45-52 km on immersion; corresponding temperatures are 130170°K and 120-140”K, respectively. These are in fair, but not good, agreement with our values. Table II gives the c_alculated values of the quasi scale height H, and the temperatures at number densities of 3 x 10L4cm-3 from the six and 1014cmP3 derived light curves studied. It is clear that the atmosphere is not isothermal. The spike associated wiggles are typically 2-lOoK in amplitude ; their apparent vertical scale is of the order of 10km. It is evident from the published light curves that the Dodaira observations have the lowest signal to
63
NEPTUNE UPPER ATMOSPHERE
noise. This is probably why the shape of the Dodaira emersion temperature vs number density profile differs from the other five curves. It appears to indicate a strong negative temperature gradient between n = 3 x 10’4cm-3 and n = 3 x lOI cmP3, whereas this feature is absent in the other curves. In general, temperature gradients obtained from occultation curves can have significant systematic errors (Wasserman and Veverka, 1973), but we expect the calculated temperatures to be accurate to about *lo% below the 10’“cm3 levels. IV. SEARCH FOR DIURNAL
AND LATITUDE
VARIATIONS
The six occultation curves make it possible to compare temperatures at a given pressure level at various latitudes, and to look for diurnal changes in temperature. The occultation geometry was such that the emersions took place at the sunrise limb and the immersions at the sunset limb (Kovalevsky and Link, 1969). The latitudes of the various events taken from Freeman and Lynga (1970) are given in Table I. The latitude range covered is from 13”N to 55”s. The calculated quasi scale height is shown as a function of latitude in Fig. 3. The open symbols indicate points on the sunrise limb ; the full symbols represent ’
I
70 60-
o
50-
1
l
o Mount Stromlo
n
0 Dodaira
AAOkayama A
points on the sunset limb. Since the quasi scale heights are only approximate quantities (the atmosphere is not isothermal!) the error bars on the points in Fig. 3 are realistically &lo%. No pronounced latitude or diurnal trend is evident. The two Mount Stromlo points ought, perhaps, be given greatest weight, and they are identical. In searching for latitude and diurnal effects, it is better to compare temperatures at a given pressure level. Two such plots are shown in Fig. 4, for pressures of 5.3 and 1.8 dynes/cm2, corresponding to number densities of 3 x 1014crnv3 and lOI crnm3 at T = 128”K, respectively. Again, no definite diurnal or latitude variation is evident, but note that all sunset temperatures are measured at higher latitudes than the sunrise temperatures. Is it possible that in Figs. 3 and 4 latitude effects precisely offset diurnal effects? Fortunately, the magnitude of the diurnal effects can be estimated. It is likely that the main cause of night-time cooling in this part of Neptune’s atmosphere is radiation from the 7.7t~m band of methane. In that case, we find, following Wasserman (1974), an overnight cooling d T 212°K. In this calculation we have used a methane mixing ratio of 1% (by number) consistent with available spectroscopic information (McElroy, 1969 ; Freeman and Lynga, 1970). Thus the amount of diurnal cooling at these levels is insignificant and any temperature variations in Fig. 4 may be attributed to latitude effects.
.
n
:
403020IO00
I 30”
I 60” Latitude
I 900
FIG. 3. Latitude dependence of the observed quasi scale height (see text for definition). The open symbols are emersion observations on the sunrise limb; the full symbols represent immersion observations on the sunset limb.
FIG. 4. Latitude
dependence
of temperature
at two pressure levels in Neptune’s atmosphere. The open symbols are emersion observations on the sunrise limb; the full symbols represent immersion observations on the sunset limb. (1 mb = lo3 dynes/cm*).
64
RAGESET AI,.
The apparent temperature variation with latitude is about 15°K between the equator and latitude 55’. A slightly larger latitude variation would result if the Mount Stromlo immersion point were ignored, but there are no grounds for doing this. In fact, judging from the quality of the light curves, the Mount Stromlo points should probably be given greater weight than the Japanese observations. In our calculations, we assumed a constant value of g = 1090cm sece2. This assumption does not significantly affect any of our results, including Figs. 3 and 4. If the oblateness of Neptune is 2% (Kovalevsky and Link, 1969) and the rotation period close to 15hr, then g at the equator is about 2% lower than the value adopted above; at latitude 55”, it is about 2% higher. This variation is less than the present uncertainty in Neptune’s surface gravity.
V. LATERAL EXTENT OF SPIKE LAYERS Freeman and Lynga (1970) discussed the correlation of spikes in various observed light curves. Since the same spikes were observed by two Mount Stromlo telescopes, they concluded that spike producing layers extend laterally for at least 200m on Neptune. They found only a weak correlation among the spikes in the Japanese light curves, and none between the Japanese and Australian results. From this they obtained an upper limit of 260km on the lateral scale of spike layers on Neptune. The fine structure of the temperature profiles shown in Fig. 2 supports these conclusions. The lower portions of the two Japanese immersion curves are perhaps similar, but the correlation is not striking. No correlation is evident between the two Japanese emersion profiles, but this could be due to systematic errors in the Dodaira profile (see above). We prefer to conclude that there is no evidence of a correlated atmospheric structure in any of the profiles in Fig. 2 and suspect that the lateral scale for spike producing layers onNeptune is 0.2 < 1 Q 260km. Their vertical scale
has been estimated to be lo-15km (Freeman and Lynga, 1970). But, in some cases, the actual scale could be much smaller, since the apparent diameter of the star at Neptune was about 10km. VI. CONCLUSIONS An analysis of available light curves of the April 7, 1968 occultation of BD -17’ 4388 by Neptune, leads to very consistent results. The approximate scale height of the atmosphere between density levels of 1013cm-3 and 10’5cm-3 is about 55km, but this region of the atmosphere is not isothermal. Numerous 2-lOoK temperature fluctuations are present. These correspond to the light curve spikes and are probably due to a density layering of the upper atmosphere (Freeman and Lynga, 1969; Veverka et al., 1974a). Such layering has also been observed in the Jovian atmosphere and may be a manifestation of the dissipation of gravity waves (Veverka et al., 1974b). On Neptune, the lateral extent of such layers is: 0.2km < 1 < 260km, and their vertical scale is 5 10km. The temperature near n = 5 x 10’4cm-3 is about 140°K. Diurnal variations at this level are probably less than 2°K. An upper limit of 0-15’K on the variation of temperature with latitude between the equator and 60” latitude is indicated.
APPENDIX. VARIATION OF INFERRED TEMPERATURESWITH ASSUMED HYDROGEN/HELIUM RATIO The temperature data presented in this paper were obtained for a 100% H, atmosphere. The results can be modified easily if helium is present, provided that the atmosphere is well mixed at the levels in question. Using the following notation : T P p n g
= = = = =
temperature (“K) pressure (dynes/cm2) density (gm/om3) number density (cm-‘) acceleration due to (cm/sec2)
gravity
65
NEPTUNEUPPERATMOSPHERE
M, = TV= k= v= n=
mass of a hydrogen atom (gm) mean molecular weight Boltzmann’s constant (erg/K) refractivity index of refraction (VZ n - 1) f = helium fraction by number N, = Loschmidt’s number = 2.7 x lOI crna3 >
we have for the temperature
at some level
2:
this paper may be scaled using relation (1) and approximation (4). ACKNOWLEDGMENTS We are grateful to P. Gierasoh, C. Sagan, J. Elliot, and R. French for discussions. This work was supported in part by NASA Grant NGR33-010-082, and in part by the Atmospheric Sciences section of the National Science Foundation Grant GA 23946.
REFERENCES
s“(4 ‘,v(d)
dz’
Since V(Z) is known from the refractivity profile, the inferred temperature T(z) is simply proportional to the mean molecular weight at a given depth. In particular, T(f) =
T(f = 0)(1+f)
(1)
at a given depth z. But, at a given depth z, v(z) is fixed and n(z) = (N&J
- 44,
(2)
where the subscript zero refers to conditions at STP. Near 5000& v,(H,)/v,(He) N 1.410.35 so that at a given level x
-=n(f) n(f = 0) or
vo(f= 0) _
vm -
n(f) = n(f
1
1 - 0.75f’
= 0). (1 _ ;.75f)
(3)
If f is close to the solar value (O.l), n(f) = 1.08n(f
= 0) - n(f = 0)
(4)
at any given level z. Hence to a good approximation the temperatures given in
BRINKMANN, R. T. (1971). Occultation by Jupiter. Nature (London) 230, 515-516 FREEMAN, K. C., AND LYNG& G. (1969). The occultation of BD -17” 4388 by Neptune. III. Discussion. Proc. Ast. Sot. Australia 1, 203-204. FREEMAN, K. C., AND LYNG& G. (1970). Data for Neptune from occultation observations. Ap. J. 160, 767-780. KOVALEVSKY, J., AND LINK, F. (1969). Dism&ire, aplatissement et proprietes optiques de la haute atmosphere de Neptune d’apres l’occultation de l’etoile BD -17” 4388. Astron. Astrophys. 2, 398-412. MCELROY, M. B. (1969). Atmospheric composition of the Jovian planets. J. A&on. Sot. 26, 798-812. VEVERKA, J., WASSERMAN, L., AND SAGAN, C. (1974a) On the upper atmosphere of Neptune. Ap.J. 189,569~575. VEVEREA, J., WASSERMAN, L., ELLIOT, J., SAGAN, C., AND LILLER, W. (1974b). The occultation of Beta Scorpii by Jupiter. I. The structure of the Jovian upper atmosphere. A&on. J., 79, 73-84 WASSERMAN, L. H. (1974). The occultation of Beta Scorpii by Jupiter. IV. Diurnal temperature v&&ions and the methane mixing ratio in the Jovian upper atmosphere. Icarus 22, 105-110. WASSERMAN, L. AND VEVERKA, J. (1973). On the reduction of occultation light curves. Icarus 20, 322-345.
The
13, 59-65 (1974)
Upper
KATHY
Atmosphere
RAGES,
JOSEPH
of’ Neptune: An Observations VEVERKA,
Laboratory for Planetary Studies,
AND
Analysis
LAWRENCE
of
Occultation
WASSERMAN,
University,Ithaca, New York 14850
Cornell AND
K. C. FREEMAN Mount Strondo
and Siding
Spring
Observatories,Research School of Physical National
Sciences,
Australian
University
Received February 6, 1974
; revised May 6, 1974
An analysis of available observations of the April 7,196s occultation of BD -17” 4388 by Neptune yields upper atmosphere temperatures of -140°K near the 5 x 10’4cm-3 level. The temperature structure of the atmosphere at these levels is complicated andnonisothermal. Diurnal temperature variations are certainly less than 10°K and may be absent. The average temperature decreases by less than 15°K between 0” and 55” latitude.
I. INTR~DUOTI~N
Veverka, 1973). By a formal inversion of the light curve, Veverka et al. (1974a) have shown that the Mount Stromlo emersion curve indicates a nonisothermal atmosphere with an approximate scale height of 55km. This value agrees with those obtained by Kovalevsky and Link from the inversion of the Japanese light curves. However, the analysis of Kovalevsky and Link is based, not on the actual observed light curves, but on “mean curves” in which the spikes have been averaged out by some unspecified process. We feel that such averaging is unnecessary and must destroy some information. In the present paper we analyze all available light curves of the occultation event, using one and the same technique described in detail by Wasserman and Veverka (1973) and used by Veverka et al. (1974a, 1974b). In this method, the observed light curves are inverted point by point to yield the atmospheric refractivity as a function of height. Assuming that the atmosphere of Neptune consists mostly of hydrogen and helium, these refractivity profiles can be converted into temperature vs number density profiles
The occultation of BD -17” 4388 by Neptune on April 7, 1968 was observed photoelectrically at the Mount Stromlo Observatory in Australia (Freeman and Lyngb, 1969, 1970), and at the Dodaira and Okayama stations of the Tokyo Astronomical Observatory in Japan (Kovalevsky and Link, 1969). Immersion and emersion light curves were obtained at each site. From these curves it is possible to derive refractivity and temperature vs number density profiles for six points on Neptune. The immersion and emersion events occurred at the sunset and sunrise limbs, respectively. The latitude range covered on Neptune was 13”N to 55”s. Previous analyses of these occultation light curves were carried out by Freeman and Lynga (1970) and Kovalevsky and Link (1969). Freeman and Lynga attempted to fit the Mount Stromlo emersion light curve to an isothermal atmosphere model and obtained a scale height of about 30 km. Unfortunately, such curve fitting techniques can be very misleading when dealing with light curves dominated by spikes (Brinkmann, 197 1; Wasserman and Copyright 0 1974 by Academic Press, Inc. All rights of reproduction in any form reserved. Printed in Great Britain
59
60
RAGESET AL.
using methods described in the above papers. Thus, for the first time, the four Japanese light curves are analyzed without neglecting spikes. In addition, the Mount Stromlo immersion light curve is analyzed for the first time. Finally, for the sake of completeness, we reproduce the reanalysis of the Mount Stromlo emersion curve published by Veverka et al. (1974a). II. OBSERVEDLIGHT CURVES AND CALCULATEDATMOSPHERICSTRUCTURE Pertinent data concerning the light curves are gathered in Table I. Kovalevsky and Link (1969) reproduce facsimiles of the Japanese observations from which we have read points every 0.5sec. Facsimiles of the Mount Stromlo curves have never been published. The record of the emersion event given by Freeman and Lynga (1969), their Fig. la, is a point by point copy based on the original chart recording. In this study, however, we have used facsimiles of the original chart recordings of the Mount Stromlo immersion and emersion events. Since the time scale is more compressed than in the chart recordings of the Japanese events, points were read at only I-set intervals from the Mount Stromlo curves. Due to this time scale compression, there is some difficulty in reading values from the Mount Stromlo light curves near maximum where scintillation is evident. This is especially true of the emersion curve. This uncertainty in graph reading introduces small uncertain-
ties into the refractivity profile at the beginning of the calculation. This problem is dealt with in detail by Veverka et al. (1974a). According to that discussion, it seems that reading errors do not significantly affect the major portion of the calculated refractivity profile. Their effect on the calculated temperature profile is more pronounced, and large errors may be introduced into the upper portions of such profiles, as well as into inferred temperature gradients. It is therefore advisable to record occultation observations in digital form and with high time resolution whenever possible. In general, the signal to noise ratio is highest for the Mount Stromlo data and lowest for the Dodaira observations. The star’s velocity normal to the limb was at Mount Stromlo and 15.7 km/set 17.4km/sec for the Japanese observatories, computed from the ephemeris of Neptune using the corrections given by Freeman and Lynga (1970), and the star’s position corrected to the time of the event. All observations were made photoelectrically with V filters. The calculated refractivity profiles are shown in Fig. 1. The initial portions of such curves are not reliable since they are based on the incorrect assumption that the refractivity (and hence the density) is zero at the starting point of the calculation. Approximately four scale heights are needed for this error to become negligible (Wasserman and Veverka, 1973). Since all the refractivity profiles in Fig. 1 have quasilinear portions we can
TABLE I DATA STJMM~RYFOR 7 APRIL 1968 NEPTUNE OCCULTATION.BASED ON KOVALEVSKY AND LINK (1969) AND FREEMAN AND LYNGB (1970)
Telescope Place Mount Stromlo Mount Stromlo Dodaira Dodaira Okayama Okayama
Event
(cm)
Immersion Emersion Immersion Emersion Immersion Emersion
127 127 91 91 91 91
Neptune latitude of event -55” -2” -40” +13” -40” +13”
45’ 04’ 05’ 46’ 34’ 12’
Original analysis None Freeman and LyngB (1970) Kovalevsky and Link (1969) Kovalevsky and Link ( 1969) Kovalevsky and Link ( 1969) Kovalevsky and Link (1969)
NEPTUNE
,&u
100
200 x.3 Z(klIl,
400
61
UPPER ATMOSPHERE
define a quasi scale height I?: for each profile (Table II). On the average H - 50km, so that the first 200 km of the refractivity profiles are influenced by the assumed boundary condition and are therefore uncertain. The small wiggles in the refractivity profiles are related to the light curve spikes. The refractivity profiles in Fig. 1 can be used to derive the temperature vs number density plots shown in Fig. 2 according to the method outlined in Veverka et al. (1974a). The upper portions of these curves, again corresponding to about four scale heights from the beginning of the calculation are not meaningful since they correspond to unreliable portions of the re. and refractivity profiles (Wasserman Veverka, 1973). These portions have therefore been omitted in Fig. 2. It should be noted that even the temperature profiles shown may still be affected by uncertainties in reading data points from chart recordings (Veverka et al., 1974a) but we have no reason to expect such errors to be large. The composition of Neptune’s atmosphere was assumed to be 100% H, in calculating the Fig. 2 profiles. Methane and ammonia are unlikely to make any significant contribution to the observed re-
ou
Z(km)
FIG. 1. Refractivity profiles for Neptune’s upper atmosphere calculated from occultation light curves. The zero point of the depth scale (z) is arbitrary and corresponds to the initial point of each calculation. Consequently it is not the same for all curves shown. Note that for z 5 200km the profiles are uncertain and are shown dashed. A mean Neptune radius of 25 OOOkm was used in the calculations. (Refractivity equals the real part of the index of refraction minus one.)
TARLE
II
SUMXGZY OF RESULTS Quasi scale height Event
3
(kH,)
Temperature at lOi
crnm3
(“K)
at 3 x 1014cm-3
Mount Stromlo (Immersion)
55.0
146
148
Mount Stromlo (Emersion)
55.0
140
147
Dodaira (Immersion) Dodaira (Emersion )
53.0
133
144
52.5
132
142
Okeyama (Immersion)
48.8
128
127
Okayama, (Emersion)
59.3
160
144
62
RAGESETAL.
r
Id2
MT STROMLO IMMERSION
r MT
c
STROMLC
Id2 Id3
DODAIRA IMMERSION
DODAIRA EMERSION
It is then necessary in the Appendix. to assume that the atmosphere is well mixed at the levels in question. This means assuming a reasonable value for the eddy diffusion coef6cient : 2 5 x lo5 cm2 see-’ (Veverka et al.,1974a). Should the actual eddy diffusion coefficient be considerably smaller, the atmosphere at these levels would not be well-mixed, and the algorithm used to generate the profile in Fig. 2 would be invalid if the atmosphere is not made up predominantly of molecular hydrogen. III. Discussion OFRESULTS
d3 l.5‘E e IO14
OKAYAMA EMERSION
OKAYAMA IMMERSION
co
120 14c 130 180 x)0 T(“K)
FIG. 2. Temperature/number density profiles for Neptune’s upper atmosphere calculated from the refractivity profiles in Fig. 1. The calculation assumes that the atmosphere at these levels consists only of molecular hydrogen. Portions corresponding to the first 200km of the refractivity profile are uncertain and have been omitted.
fractivity, but helium cannot be ignored. Veverka et ab. (1974a) give temperature vs number density profiles based on the Mount Stromlo emersion curve, for three assumed compositions of Neptune’s atmosphere: (a) 100% H,; (b) 50% H, ; 50% He; and (c) 20% H,; 80% He by number. They argue that cases (b) and (c) lead to unacceptably high temperatures in Neptune’s upper atmosphere. In fact, there is no evidence to indicate that the helium fraction in Neptune’s atmosphere differs from the accepted solar value : f(He) = 0.10, by number. For small admixtures of helium, the appropriate temperature vs number density profiles can be obtained from those shown in Fig. 2 by the procedure outlined
We consider the results presented in Figs. 1 and 2 to be superior to previous analyses. As mentioned above the analysis of the Mount Stromlo emersion curve published by Freeman and Lynga (1970) is based on curve fitting to a very spiky light curve, a procedure which can yield results. (Wasserman and misleading Veverka, 1973; Veverka et al., 1974a). Our analysis of the Japanese results is in fair agreement with that of Kovalevsky and Link (1969) even though these authors essentially ignored spikes and smoothed the Dodaira and Okayama light curves for each event. Their Fig. 7, showing calculated temperatures and scale heights, is in part misleading, since it does not indicate that some of the values shown are grossly affected by the boundary conditions of the problem. Ignoring such values, their graphs give scale heights of 50-63 km on emersion and 45-52 km on immersion; corresponding temperatures are 130170°K and 120-140”K, respectively. These are in fair, but not good, agreement with our values. Table II gives the c_alculated values of the quasi scale height H, and the temperatures at number densities of 3 x 10L4cm-3 from the six and 1014cmP3 derived light curves studied. It is clear that the atmosphere is not isothermal. The spike associated wiggles are typically 2-lOoK in amplitude ; their apparent vertical scale is of the order of 10km. It is evident from the published light curves that the Dodaira observations have the lowest signal to
63
NEPTUNE UPPER ATMOSPHERE
noise. This is probably why the shape of the Dodaira emersion temperature vs number density profile differs from the other five curves. It appears to indicate a strong negative temperature gradient between n = 3 x 10’4cm-3 and n = 3 x lOI cmP3, whereas this feature is absent in the other curves. In general, temperature gradients obtained from occultation curves can have significant systematic errors (Wasserman and Veverka, 1973), but we expect the calculated temperatures to be accurate to about *lo% below the 10’“cm3 levels. IV. SEARCH FOR DIURNAL
AND LATITUDE
VARIATIONS
The six occultation curves make it possible to compare temperatures at a given pressure level at various latitudes, and to look for diurnal changes in temperature. The occultation geometry was such that the emersions took place at the sunrise limb and the immersions at the sunset limb (Kovalevsky and Link, 1969). The latitudes of the various events taken from Freeman and Lynga (1970) are given in Table I. The latitude range covered is from 13”N to 55”s. The calculated quasi scale height is shown as a function of latitude in Fig. 3. The open symbols indicate points on the sunrise limb ; the full symbols represent ’
I
70 60-
o
50-
1
l
o Mount Stromlo
n
0 Dodaira
AAOkayama A
points on the sunset limb. Since the quasi scale heights are only approximate quantities (the atmosphere is not isothermal!) the error bars on the points in Fig. 3 are realistically &lo%. No pronounced latitude or diurnal trend is evident. The two Mount Stromlo points ought, perhaps, be given greatest weight, and they are identical. In searching for latitude and diurnal effects, it is better to compare temperatures at a given pressure level. Two such plots are shown in Fig. 4, for pressures of 5.3 and 1.8 dynes/cm2, corresponding to number densities of 3 x 1014crnv3 and lOI crnm3 at T = 128”K, respectively. Again, no definite diurnal or latitude variation is evident, but note that all sunset temperatures are measured at higher latitudes than the sunrise temperatures. Is it possible that in Figs. 3 and 4 latitude effects precisely offset diurnal effects? Fortunately, the magnitude of the diurnal effects can be estimated. It is likely that the main cause of night-time cooling in this part of Neptune’s atmosphere is radiation from the 7.7t~m band of methane. In that case, we find, following Wasserman (1974), an overnight cooling d T 212°K. In this calculation we have used a methane mixing ratio of 1% (by number) consistent with available spectroscopic information (McElroy, 1969 ; Freeman and Lynga, 1970). Thus the amount of diurnal cooling at these levels is insignificant and any temperature variations in Fig. 4 may be attributed to latitude effects.
.
n
:
403020IO00
I 30”
I 60” Latitude
I 900
FIG. 3. Latitude dependence of the observed quasi scale height (see text for definition). The open symbols are emersion observations on the sunrise limb; the full symbols represent immersion observations on the sunset limb.
FIG. 4. Latitude
dependence
of temperature
at two pressure levels in Neptune’s atmosphere. The open symbols are emersion observations on the sunrise limb; the full symbols represent immersion observations on the sunset limb. (1 mb = lo3 dynes/cm*).
64
RAGESET AI,.
The apparent temperature variation with latitude is about 15°K between the equator and latitude 55’. A slightly larger latitude variation would result if the Mount Stromlo immersion point were ignored, but there are no grounds for doing this. In fact, judging from the quality of the light curves, the Mount Stromlo points should probably be given greater weight than the Japanese observations. In our calculations, we assumed a constant value of g = 1090cm sece2. This assumption does not significantly affect any of our results, including Figs. 3 and 4. If the oblateness of Neptune is 2% (Kovalevsky and Link, 1969) and the rotation period close to 15hr, then g at the equator is about 2% lower than the value adopted above; at latitude 55”, it is about 2% higher. This variation is less than the present uncertainty in Neptune’s surface gravity.
V. LATERAL EXTENT OF SPIKE LAYERS Freeman and Lynga (1970) discussed the correlation of spikes in various observed light curves. Since the same spikes were observed by two Mount Stromlo telescopes, they concluded that spike producing layers extend laterally for at least 200m on Neptune. They found only a weak correlation among the spikes in the Japanese light curves, and none between the Japanese and Australian results. From this they obtained an upper limit of 260km on the lateral scale of spike layers on Neptune. The fine structure of the temperature profiles shown in Fig. 2 supports these conclusions. The lower portions of the two Japanese immersion curves are perhaps similar, but the correlation is not striking. No correlation is evident between the two Japanese emersion profiles, but this could be due to systematic errors in the Dodaira profile (see above). We prefer to conclude that there is no evidence of a correlated atmospheric structure in any of the profiles in Fig. 2 and suspect that the lateral scale for spike producing layers onNeptune is 0.2 < 1 Q 260km. Their vertical scale
has been estimated to be lo-15km (Freeman and Lynga, 1970). But, in some cases, the actual scale could be much smaller, since the apparent diameter of the star at Neptune was about 10km. VI. CONCLUSIONS An analysis of available light curves of the April 7, 1968 occultation of BD -17’ 4388 by Neptune, leads to very consistent results. The approximate scale height of the atmosphere between density levels of 1013cm-3 and 10’5cm-3 is about 55km, but this region of the atmosphere is not isothermal. Numerous 2-lOoK temperature fluctuations are present. These correspond to the light curve spikes and are probably due to a density layering of the upper atmosphere (Freeman and Lynga, 1969; Veverka et al., 1974a). Such layering has also been observed in the Jovian atmosphere and may be a manifestation of the dissipation of gravity waves (Veverka et al., 1974b). On Neptune, the lateral extent of such layers is: 0.2km < 1 < 260km, and their vertical scale is 5 10km. The temperature near n = 5 x 10’4cm-3 is about 140°K. Diurnal variations at this level are probably less than 2°K. An upper limit of 0-15’K on the variation of temperature with latitude between the equator and 60” latitude is indicated.
APPENDIX. VARIATION OF INFERRED TEMPERATURESWITH ASSUMED HYDROGEN/HELIUM RATIO The temperature data presented in this paper were obtained for a 100% H, atmosphere. The results can be modified easily if helium is present, provided that the atmosphere is well mixed at the levels in question. Using the following notation : T P p n g
= = = = =
temperature (“K) pressure (dynes/cm2) density (gm/om3) number density (cm-‘) acceleration due to (cm/sec2)
gravity
65
NEPTUNEUPPERATMOSPHERE
M, = TV= k= v= n=
mass of a hydrogen atom (gm) mean molecular weight Boltzmann’s constant (erg/K) refractivity index of refraction (VZ n - 1) f = helium fraction by number N, = Loschmidt’s number = 2.7 x lOI crna3 >
we have for the temperature
at some level
2:
this paper may be scaled using relation (1) and approximation (4). ACKNOWLEDGMENTS We are grateful to P. Gierasoh, C. Sagan, J. Elliot, and R. French for discussions. This work was supported in part by NASA Grant NGR33-010-082, and in part by the Atmospheric Sciences section of the National Science Foundation Grant GA 23946.
REFERENCES
s“(4 ‘,v(d)
dz’
Since V(Z) is known from the refractivity profile, the inferred temperature T(z) is simply proportional to the mean molecular weight at a given depth. In particular, T(f) =
T(f = 0)(1+f)
(1)
at a given depth z. But, at a given depth z, v(z) is fixed and n(z) = (N&J
- 44,
(2)
where the subscript zero refers to conditions at STP. Near 5000& v,(H,)/v,(He) N 1.410.35 so that at a given level x
-=n(f) n(f = 0) or
vo(f= 0) _
vm -
n(f) = n(f
1
1 - 0.75f’
= 0). (1 _ ;.75f)
(3)
If f is close to the solar value (O.l), n(f) = 1.08n(f
= 0) - n(f = 0)
(4)
at any given level z. Hence to a good approximation the temperatures given in
BRINKMANN, R. T. (1971). Occultation by Jupiter. Nature (London) 230, 515-516 FREEMAN, K. C., AND LYNG& G. (1969). The occultation of BD -17” 4388 by Neptune. III. Discussion. Proc. Ast. Sot. Australia 1, 203-204. FREEMAN, K. C., AND LYNG& G. (1970). Data for Neptune from occultation observations. Ap. J. 160, 767-780. KOVALEVSKY, J., AND LINK, F. (1969). Dism&ire, aplatissement et proprietes optiques de la haute atmosphere de Neptune d’apres l’occultation de l’etoile BD -17” 4388. Astron. Astrophys. 2, 398-412. MCELROY, M. B. (1969). Atmospheric composition of the Jovian planets. J. A&on. Sot. 26, 798-812. VEVERKA, J., WASSERMAN, L., AND SAGAN, C. (1974a) On the upper atmosphere of Neptune. Ap.J. 189,569~575. VEVEREA, J., WASSERMAN, L., ELLIOT, J., SAGAN, C., AND LILLER, W. (1974b). The occultation of Beta Scorpii by Jupiter. I. The structure of the Jovian upper atmosphere. A&on. J., 79, 73-84 WASSERMAN, L. H. (1974). The occultation of Beta Scorpii by Jupiter. IV. Diurnal temperature v&&ions and the methane mixing ratio in the Jovian upper atmosphere. Icarus 22, 105-110. WASSERMAN, L. AND VEVERKA, J. (1973). On the reduction of occultation light curves. Icarus 20, 322-345.