The Neptune central flash data obtained from the August 20, 1985 occultation was analyzed. The three main objectives of the analysis, which combined the study of the CTIO data with the ESO data obtained by the Meudon groups were: deduce the oblateness, equatorial radius, and pole positon angle of Neptune from a combined analysis of the limb-occultation and central-flash data; determine the temperature/absorption profile in Neptune's atmosphere in the region probed by the occultation data (from 1 microbar to about 0.2 mbar), as well as atmospheric distortions produced by waves or turbulence; and search for additional Neptune ring arcs. Results were discussed in terms of the three main objectives

Hubbard, W. B.

English

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'University of Arizona
•tnient of Planetary Sciences
and Planetary Laboratory
NASA Grant NSG 7045
"Interiors of the Giant Planets-
Semiannual Report #24
Period October 1, 1985 - April 1, 1986
(NASA-CR-177154) INTEBIOBS OF THE GIANT N86-32386
PLANETS Semiannual Eeport, 1 Oct. ,,1985 - 1
Apr.,.1986 (Arizona. Oni-v., Tucson,), 7 p
CSCL 03B Onclas
v G3/91 . 43304
Submitted: 18 September 1986
W. B. Hubbard
Principal Investigator
https://ntrs.nasa.gov/search.jsp?R=19860022914 2020-03-20T13:19:46+00:00Z
I. Personnel working on this grant during this reporting period:
Dr. W. B. Hubbard (Principal Investigator, 1/4 time)
Ms. Charlene Lobb (Secretary, 1/4 time)
II. Overview and Summary
Occultation and Geodesy:
Hubbard analyzed data from the Aug. 20, 1985 Neptune occultation, which
showed a pronounced central flash. This work was done in collaboration with
Meudon Observatory planetary astronomers. A new oblateness and equatorial
radius for Neptune was found. The data provide constraints on Neptune's
methane abundance at the 0.3-mbar level. A new determination of Neptune's
pole position was obtained. A paper on the radius of Ceres was completed, in
collaboration with several other groups.
Foreign Travel:
None supported by this grant.
III. Occultations
As stated in the previous report, analysis of the Neptune central flash
data obtained from the Aug. 20, 1985 occultation was a principal focus of
this reporting period. There were three main objectives of the analysis,
which combined the study of the CTIO data with the ESO data obtained by the
Meudon group (this was a collaborative effort):
(1) deduce the oblateness, equatorial radius, and pole position angle of
Neptune from a combined analysis of the limb-occultation and central-flash
data;
(2) determine the temperature/absorption profile in Neptune's atmosphere in
the region probed by the occultation data (from 1 /ibar to about 0.2 mbar),
as well as atmospheric distortions produced by waves or turbulence;
(3) search for additional Neptune ring arcs.
All of the above program was well advanced by the end of this reporting
period, with a paper on topic (1) prepared and submitted for publication.
Here is a summary of the principal results obtained for each of these topics:
(1) The 8/20/85 data provided measurements of the immersion and emersion
occultation profiles at six stations, two in the earth's southern hemisphere
and four in the northern hemisphere. We fitted to the immersion/emersion
timings to obtain the limb profile at a pressure level of 1 pbar, and
simultaneously fitted to the CTIO and ESO central flash intensity data.
Results of this analysis are presented in Table 1.
The parameters were e, the scale height at the level probed by the
central flash Hg (the ratio of H^  to the true scale height at the central
flash level is equivalent to the transmission factor) , the coordinates
Xgty of the projected geometrical center of Neptune in the sky plane,
and the projected position angle of Neptune's north pole in the sky plane,
p . The model was also dependent on the equatorial radius of Neptune a,,,
n u
the Neptune -centered declination of the earth, ft , and the scale height at
the immersion/emersion level, H,,. The fitting procedure does not provide a
meaningful constraint on /3 , which must be derived from independent
information.
The inferred scale height at the flash level Hf corresponds to a
temperature of about 100 K at a pressure of 0.24 mbar. If the actual
temperature at this level is higher, then the transmission is reduced from
unity by the ratio of the inferred to actual temperatures. At the
half -intensity points on the limb, the region probed by the rays has a scale
height HQ of 52 km (average of results from ESO and CTIO) , corresponding to
a temperature of 153 K for solar-composition gas. The corresponding pressure
is 1.0 pbar. Table 1 presents the oblateness e at this level in the
atmosphere. In the fitting procedure, allowance is made for the variation of
e with depth. We estimate the altitude difference between the l-/ibar
level and the 0.24 -mbar level to be approximately 285 km, or 0.011 in units
of aQ. If we let
where ft is the radius in units of a0, then the surface value of r; is
given by hydrostatic-equilibrium theory (Zharkov & Trubitsyn 1978), assuming
a constant rotation rate:
_ _ q 15 J2
»J ~ •* ~ ~2~ ~i~
where J2 is the second- degree zonal harmonic of Neptune's gravity field.
Employing eq. (2), we find the oblateness at the flash level ef - 0.983
e, where e is the oblateness at the 1-pbar level. The intensity
pattern in the central flash is computed using ef. The corrections
XQ, y to the relative positions of Neptune and the occulted star show
that the ephemeris position of Neptune must be moved to the west and south
(assuming no correction to the predicted star position) .
Using the nominal Neptune pole position at the time of the occultation,
computed from Harris' (1984) paper, we obtain p - 22.9° and ft -
n o
-25.0°. This position assumes that the angle e between Neptune's rotation
vector and the angular momentum vector of the Neptune -Triton system is
•3.6°. If e is taken to be zero, corresponding to negligible Triton mass,
then Harris' ephemeris gives p - 21.6°, ft - -21.7°. According to
the results given in Table 1, the best-fit value of p from solution 1 is
20.9°. This result is within one probable error of the Harris' pole
position for zero Triton mass, but cannot be regarded as strong support for
this interpretation as opposed to the one for a nominal Triton mass, since we
have no constraint on ft . We use the value of ft corresponding to the
nominal Harris ephemeris, i.e. ft - -25.0°, although the value of p
• n
is adjusted to fit the central flash intensities and tines observed at ESO
and CTIO. The value of e given in Table 1 thus corresponds to ft -
-25.0°. To within errors of order e2, the inferred oblateness scales
as (cos ft )"2. Thus if ft were revised to -21.7° from -25.0°, values
of e which we derive would have to be reduced by five percent.
The value of a0 given in Table 1 includes a correction of 100 km for
refractive and general-relativistic bending of the rays (Hubbard et
al., 1985).
TABLE 1. Parameters of general solution
Hf - 35 km (Ho - 52 km)
e (1 /ibar) - 0.0204 ± 0.0014
KO - -25715.27 km
yo - -6117.32 km
pn - 20.9°
aj (1 /ibar) - 25260 ± 10 km
Is Neptune far less centrally-condensed than Uranus? Let us review this
question by first computing the second-degree response coefficient A2 for
Uranus. This quantity is given by
(3)
where
q - (A)
w is the planet's angular rotation velocity (assumed uniform), G is the
gravitational constant, and M is the planet's mass. In eq. (3), the second-
degree zonal harmonic J2 is normalized to a0. Eq. (3) is valid to order
q2-
For Uranus we use J2 - 3.352 x 10"3 (Elliot 1982). For a
rotation period of 16.31h, we would have q - 0.0355, but the recent Voyager
2 measurement of the rotation rate of the deep Uranian interior gives a
rotation period of 17.24h (Warwick et al., 1986), which implies q -
0.0318, and thus f^  - 0.105 for Uranus.
For Neptune we employ the equation
-1 2e o /cv
- j- - 3. (5)
'2
Taking Harris' lower bound for J2 and our upper bound for e, we obtain
Aj - 0.114, and thus q - 0.0325 and the rotation period P - 14.8h. If
we take Harris' upper bound for J2 and our lower bound for e, we obtain
A, - 0.171, q - 0.0251, P - 16.9h.
We conclude that despite improved error bars on Neptune's oblateness,
there is still substantial uncertainty in its degree of central condensation
as measured by Ag. There is evidence that Neptune is less centrally-
condensed than Uranus, but a definitive resolution of this matter must await
a determination of the rotation period of Neptune's deep interior, as would
be provided by a measurement of the rotation period of a magnetosphere. When
significant differential rotation is present in a planetary atmosphere, as is
apparently the case for Uranus, the oblateness may differ substantially from
that corresponding to uniform rotation, for a fixed value of J2 (Hubbard,
1986). This may explain the substantial discrepancy between the Voyager
value for Uranus' deep rotation period and the value derived by Elliot (1982)
on the basis of an occultation measurement of the oblateness, P — 15.5h
± 1.3h. It may also account for the discrepancy between the rotation
period for Neptune which we obtain, P - 15.9h ± 1.0h, and the rotation
period of 18.2h proposed by Belton et al. (1981).
(2) A paper on the interpretation of the 8/20/85 Neptune central flash data
has been prepared and submitted to Nature (Lellouch et al., 1986). Fitting
to the central flash data alone gives e - (2.08 * 0.19) x 10"2, in good
agreement with the solution given in Table 1, and, assuming a stratospheric
temperature of 120 K at 0.3 mbar, an atmospheric transmission of 0.70 ± 0.20
for an integrated column density of 1.9 km-atm. The opacity at the central
flash level is attributed to CH4 absorption, and the inferred value for the
CH4 mixing ratio is 0.6% with a factor 10 uncertainty. This may indicate
supersaturation of methane in Neptune's atmosphere. However, if the
atmospheric temperature is 100 K at the 0.23-mbar level, the central flash
intensity level is entirely explained and there is no significant opacity.
(3) The 8/20/85 occultation at CTIO did not reveal any Neptune ring arcs,
although one was detected in Hawaii. This result is consistent with the
emerging picture of these features, according to which they have typical
azimuthal lengths which do not exceed 103 km.
A major paper on the profile of Ceres was submitted to Icarus during
this reporting period (see Papers Submitted). This represents the outcome of
analysis of data from 13 sites for the occultation of a star by Ceres on 13
November 1984, to which we contributed data from 3 sites. The analysis gives
an equatorial radius for Ceres of 479.6 ± 2.4 km and a polar radius of 453.4
* 4.5 km. These results will provide a fundamental calibration of the
asteroid size scale.
IV. Publications and presentations during this reporting period
(a) Published papers:
JHK Photometry of Candidate Stars for Occultation by Neptune, by F.
Vilas and D. J. Mink, PASP 98, 116-117, 1986
Occultation detection of a Neptunian ringlike arc, by W. B. Hubbard, A.
Brahic, B. Sicardy, L.-R. Elicer, F. Roques, and F. Vilas, Nature 319, 636-
640, 1986.
1981N1: A Neptune Arc?, by W. B. Hubbard, Science 231, 1276-1278, 1986.
(b) Papers submitted for publication:
Evolution of Super-Jupiters, submitted December 1985 for publication in
proceedings of "Astrophysics of Brown Dwarfs", conference at George Mason
University, October 14-15, 1985.
The phase diagram of hydrogen with other elements, and applications to
Jovian planet interiors. Submitted to Proceedings of NATO Advanced Study
Institute, Newcastle upon Tyne, England, 1985.
The 1985 August 20 occultation by Neptune: The central flash
determination of Neptune's oblateness and methane stratospheric mixing ratio,
by E. Lellouch, W. B. Hubbard, B. Sicardy, F. Vilas, and P. Bouchet,
submitted to Nature.
The size, shape, density, and albedo of Ceres from its occultation of
BD+8°471, by 37 authors (Millis et al.), including W. B. Hubbard, submitted
to Icarus.
(c) External presentations;
Evolution of Super-Jupiters, by W. B. Hubbard, "Astrophysics of Brown
Dwarfs" conference at George Mason University, October 14-15, 1985.
VII. Financial Status
Expenditures are on schedule.


Interiors of the giant planets

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