Encyclopedia of the Solar System 2nd ed

698 Encyclopedia of the Solar System

are obtained by integrating the equation of radiative transfer
through a model atmosphere:

Bν(TD)= 2

∫ 1

0

∫∞

0

Bν(T)e(−τ/μ)d(τ/μ)dμ (5)

where Bν(TD) can be compared to the observed disk-
averagedbrightness temperature. The brightnessBν(T)
is given by the Planck function, and the optical depthτν(z)
is the integral of the total absorption coefficient over the al-
titude rangezat frequencyν.The parameterμis the cosine
of the angle between the line of sight and the local verti-
cal. By integrating overμ, one obtains the disk-averaged
brightness temperature, to be compared to the observed
brightness temperature.
Before the integration in Eq. (5) can be carried out, the
atmospheric structure, as composition and temperature-
pressure profile, needs to be defined. Over our region of
interest, the temperature structure can often be approxima-
tel by an adiabatic lapse rate. The temperature, pressure,
and composition of an atmosphere are related to one an-
other through an equation of state, such as the ideal gas law.
Cloud formation and chemical alteration of constituents
due to, for example, photolysis (breakup of molecules by
ultraviolet sunlight), all need to be considered when mak-
ing a model atmosphere. The shape of absorption/emission
lines depend on the temperature and pressure of the en-
vironment, and may vary from relatively narrow lines (e.g.,
Mars, Venus, Titan, Io) to broad quasi-continuum spectra
(e.g., giant planets).

2.4 Terrestrial Planets and the Moon

2.4.1 THE MOON

Lunar radio astronomy dates back to the mid-1940s, well
before the firstApollolanding on the Moon. Since the mid-
1970s, after a decade of “neglect,” there was renewed in-
terest in lunar radio astronomy since radio receivers had
improved substantially and laboratory measurements of
Apollosamples provided a ground-truth for several sites
on the Moon. By using lunar core samples, one could de-
termine a density profile of the soil with depth near the
landing sites, as well as the complex dielectric constant of a
variety of rocks and powders. Both are essential parameters
in modeling radio observations of the Moon.
A microwave image of the full Moon reveals that the
maria are∼5 K warmer than the highlands. This may re-
sult from a difference in albedo (the maria are darker than
the highlands), radio emissivity and/or the microwave opac-
ity. Lunar samples suggest that the microwave opacity in
the highlands is somewhat (factor of∼2) lower than in
the maria, so that deeper cooler layers are probed in the
lunar highlands compared to the maria during full Moon (as
observed); at new Moon the temperature contrast should

be reversed (no observations have yet been reported), since

the temperature increases with depth at night.

2.4.2 MERCURY

Radio images of Mercury show a brightness variation across

the disk, which displays the history of solar insolation. At

short wavelengths, where shallow layers are probed, the day

side temperature is usually highest. However, when deeper

layers are probed, the diurnal heating pattern is less obvi-

ous, and one can distinguish two relatively “hot” regions,

one at longitude 0◦and one at 180◦. This hot–cold pattern

results from Mercury’s 3/2 spin-orbit resonance: Mercury

rotates three times around its axis for every two revolutions

around the Sun. This, combined with the planet’s large or-

bital eccentricity, leads to factor-of-2.5 variation in the aver-

age diurnal insolation as a function of longitude. Mercury’s

peak (noon) surface temperature varies between 700 K for

longitudes facing the Sun at perihelion (longitudes 0◦and

180 ◦)to570K90◦away. While the surface temperature re-

sponds almost instantaneously to changes in illumination,

the subsurface layers do not, and this variation in solar inso-

lation remains imprinted at depths well below the surface.

Figure 3a shows a radio image at 3.6 cm, probing a depth

of∼70 cm. The two hot regions discussed previously are

FIGURE 3 (a) The 3.6 cm thermal emission from Mercury

observed with the VLA. Contours are at 42 K intervals (10% of

maximum), except for the lowest contour, which is at 8 K

(dashed contours are negative). The beamsize is 0.4′′or 1/10 of a

Mercurian radius. Note the two so-called hot regions, discussed

in the text. (b) A residual map of Mercury, which shows the

residuals after subtracting a model image from the observed

map. We further indicated the geometry of Mercury during the

observation, as the direction to the Sun, and the morning

terminator (heavy line). The hot regions have been modeled

extremely well, since they do not show up in this residual map.

However, we see instead large negative (blue) temperatures near

the poles and along the morning side of the terminator. These

are likely caused by shadows on the surface resulting from local

topography, such as craters. Contour intervals are in steps of 10

K, which is roughly 3 times the rms noise in the image. (D. L.

Mitchell and I. de Pater, 1994, Microwave imaging of Mercury’s

thermal emission: Observations and models,Icarus 110 , 2–32.)