Thermal emission spectra for a variety of cometary nucleus models were evaluated by a radiative transfer technique adapted from modeling of terrestrial ice and snow fields. It appears that millimeter wave sensing from an interplanetary spacecraft is the most effective available means for distinguishing between alternate models of the nucleus and for evaluating the thermal state of the layer which is below the instantaneous surface where modern theories of the nucleus indicate that sublimation of the cometary volatiles actually occurs

Brandt, J. C.

Hobbs, R. W.

Maran, S. P.

English

NASA Technical Reports Server

MILLIMETER WAVE RADIOMETRY AS A MEANS OF
DETERMINING COMETARY SURFACE AND SUBSURFACE TEMPERATURES
Robert W. Hobbs
John C. Brandt
Stephen P. Maran
Laboratory for Astronomy and Solar Physics
NASA-Goddard Space Flight Center
Greenbelt, Maryland 20771
Abstract
Thermal emission spectra for a variety of cometary nucleus models are evaluated by a
radiative transfer technique adapted from modeling of terrestrial ice and snow fields. It
appears that millimeter wave sensing from an interplanetary spacecraft is the most effective
available means for distinguishing between alternate models of the nucleus and for evaluating
the thermal state of the layer —which is below the instantaneous surface— where modern
theories of the nucleus indicate that sublimation of the cometary volatiles actually occurs.
Introduction
Although the cometary nucleus has never been directly resolved, its general nature has been
deduced. According to the icy conglomerate model (Whipple 1950), a cometary nucleus is a solid,
inhomogeneous mixture of ices and refractory material. The uppermost layer of the nucleus of a
comet that has been exposed to solar heating is now thought to be a crust of refractory material,
from which the volatiles have been removed by sublimation. This crust is supposedly an open
structure (c.f., Mendis and Brin, 1977) through which flow the gases sublimating from the frozen
volatiles below. Its thickness depends upon the comet's heliocentric distance, previous exposure
in the inner solar system, and other factors. The crust must serve as an insulating layer, with
its external surface in rough equilibrium with solar radiation. The interface between the crust
and the region below would be at the sublimation temperature of the dominant ice component. This
temperature is very important physically. It is determined by the balance among the heat input
from the sun and any other source, the heat going into sublimation, and heat conducted inward to
the even colder central part of the nucleus. This interface layer is the source of the gases that
make up the coma and tail of the comet. To understand the nature and physical state of the
nucleus it is necessary to determine the temperature gradients in the outer nucleus and the
temperature at this interface.
Thermal Sensing
Millimeter wave radiometry is a demonstrated technique for remote sensing of terrestrial ice
fields (c.f., Chang et &]_, 1976). Experimenters have been able to determine basic ice field
parameters, such as temperature gradients and particle sizes. Measurements have been made from
both earth-orbiting spacecraft and from aircraft, and thus much flight-proven hardware exists.
It seems logical to consider this technology for application to the investigation of the icy
conglomerate nucleus of a comet.
Millimeter wave radiometry should be considered in the context of other applicable technology,
notably infrared radiometry. With no interference from dust in the coma, both techniques w i l l
yield data on the thermal state of the nucleus. However, infrared measurements wil l tell only the
temperature of the external surface, and will not provide hard data on the temperature of the
interface layer where sublimation occurs. They also are subject to interference from infrared
radiation by superheated dust particles in the inner coma, observed in some comets, which would
effectively screen the nucleus from observation. Dust comas are, however, transparent to
millimeter waves. In addition, millimeter waves of different wavelengths enable observation of
96
https://ntrs.nasa.gov/search.jsp?R=19820006130 2020-03-21T10:13:32+00:00Z
the radiation emerging at different depths in the nucleus. In particular, multi-channel
millimeter wave radiometry will enable the determination of the interface layer temperature and
the thermal gradient in the vicinity.
Nucleus Models
We have made models of the outer nucleus to establish the validity of the proposed use of
millimeter wavelengths to probe the cometary surface and subsurface layers. Numerical solutions
to the radiative transfer equation originally developed at Goddard Space Flight Center for the
investigation of terrestrial snow and ice fields have been modified to deal with a two-component
(refractory and volatile) medium. In a multi-layer, plane-parallel aproximation, the models are
used to predict the brightness temperature of the hypothetical comet nucleus as a function of
wavelength. The work takes into account Mie scattering and Fresnel reflection and transmission
coefficients at the surface, and except for horizontal inhomogeneities, it should be realistic.
Parameters that can be modeled include surface temperature, subsurface temperature gradient,
relative fractions of the volatile and refractory components in the various layers, indices of the
refraction of the two components, particle size and layer thickness.
In the present models, we have assumed that the two components are water ice and sand
particles. The top layer of each model is composed solely of the refractory material; its
thickness is varied from model to model. Internal to the crust, the layers are composed of equal
fractions of water ice particles and sand particles acting as independent spheres. All of the
models assume a surface temperature of 250 K, representitive of a comet slightly closer to the sun
than 1 a.u. The results in Figure 1 show that the majority of the variation of brightness
temperature as a function of wavelength takes place at the short millimeter wavelengths. Thus, to
discriminate among a variety of models, one should choose several wavelengths in the short
millimeter range. We have picked sample wavelengths of 1.7, 3.4, 6.9 mm and 3 cm as they are
typical of what is already feasible in a state-of-the-art spacecraft radiometer system.
To illustrate how millimeter wave radiometry could be used to deduce physical parameters of
the cometary subsurfce layers, Figure 2 shows the expected temperature variation for three models
with different crust thicknesses. The temperature gradient and particle sizes for the three models
in Figure 2 are the same. As can be seen, temperature measurements at the three millimeter
wavelengths will discriminate between these three models.
Figure 3 is a plot of the expected brightness temperature as a function of wavelength for two
models having the same particle size and same crust thickness, but with different temperature
gradients. From brightness temperature measurements at the three short millimeter wavelengths it
should be possible to deduce the temperature gradient. To further illustrate the effectiveness of
millimeter wave radiometry to sample different depths below the comet surface we have calculated
for each of these models the depth at which half the radiation at a given wavelength arises from
above and one half from below. A sample of such calculations is shown in Figure 4. We conclude
that millimeter wave radiometry is the most suitable way to remotely sense the cometary subsurface
layers. Short of a physical landing on a comet surface, it may be the ony feasible way to
investigate the energy balance, temperature structure, and physical nature of the nucleus1
near-surface layers.
Instrument Concept and Spectrometry
We have developed a design for a multi-frequency millimeter wave radiometer for an
interplanetary spacecraft. A schematic drawing is shown in Figure 5. This system would weigh
about 10 kg exclusive of the one meter antenna and a 3 cm radiometer channel which we anticipate
would be part of another spacecraft system. The choice of wavelengths was of course influenced^ by
the existence of the 183-GHz water vapor band. Our design incorporates spectrometer channels at
both 183 GHz and at 93 GHz in order to observe the emission of water and perhaps other molecular
species.
The 183 GHz water vapor band is more easily excited than the typically observed 23 GHz water
vapor band and of course cannot be observed from below the earth's atmosphere. Water is regarded
as the principal component of comets, although direct detection of water in a comet has not been
97
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Figure 1. Brightness temperature as a function of wavelength for a variety of
two component comet models. Vertical bars are typical wavelengths of
observation 1.7, 3.4, 6.9 and 30 mm.
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Figure 2. Brightness temperature as a function of wavelength for models with different
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99
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Figure 3. Brightness temperature as a function of wavelength for models with
different temperature gradients through the surface crust.
100
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WEIGHTING FUNCTION W(Z)
Figure 4. Weighting function as a function of depth below model comet
surface. The horizontal bars indicate the depth at which the
integrated weighting function becomes one-half.
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confirmed. The spectrometer channels will also permit measurements of other molecular species
such as HCN and HNC from a vantage point close to the comet, eliminating the effect of beam
dilution which limits the sensitivity of molecular line observations from the ground. Millimeter
wave radiometry of comets cannot at the present time be carried out from the ground unless a comet
were to come extremely close to the earth. Even the most sensitive millimeter wave radiometer
systems used on the largest current millimeter wave telescopes are still two orders of magnitude
short of making meaningful measurements of comets at distances of 1 a.u. or more from the earth.
A millimeter wave radiometer system would be a valuable component of any interplanetary
spacecraft. It could probe the surface layers of icy satellites, comets and asteroids alike.
References
Chang, T. C., Gloersen, P., Saxmugge, T., Wilheit, T. T., and Zwally, H. J., 1976,
^J. of Glaciology _16, 23.
Mendis, D. A. and Bnn, G. D. 1977, The Moon 17, 359.
Whipple, F. L. 1950, Ap. J. Ill, 375.
103


Millimeter wave radiometry as a means of determining cometary surface and subsurface temperature

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