Encyclopedia of the Solar System 2nd ed

The Solar System at Radio Wavelengths 697

an array of antennas is needed to construct an image that
shows both the large and small scale structure of a radio
source. At short spacings, the entire object can be “seen,”
but details on the planet are washed out due to the low res-
olution of such baselines. At longer baselines, details on the
planet can be distinguished, but the large-scale structure of
the object gets resolved out, and hence would be invisible
on the image unless short spacing data are included as well.
Hence, arrays of antennas are crucial to image an object.

2. Thermal Emission from Planetary Bodies

2.1 Thermal or Blackbody Radiation

Any object with a temperature above absolute zero emits
a continuous spectrum of electromagnetic radiation at all
frequencies, which is its thermal or “blackbody” radiation.
A blackbody radiator is defined as an object that absorbs
all radiation that falls on it at all frequencies and all angles
of incidence; none of the radiation is reflected.Blackbody
radiationcan be described by Planck’s radiation law, which,
at radio wavelengths, can usually be approximated by the
Rayleigh–Jeans law:

Bν(T)=

2 ν^2

c^2

kT (1)

whereBνTis the brightness (W/m^2 /Hz/sr),νthe frequency
(Hz), T the temperature (K), kBoltzmann’s constant
(1.38× 10 −^23 J/deg(K)) andcthe velocity of light (3×
108 m/s). With a radio telescope, one measures theflux
densityemitted by the object. A common unit is the flux
unit or Jansky, where 1 Jy =10−^26 W/m^2 /Hz. This flux den-
sity can be related to the temperature of the object:

S=

abT

4. 9 × 106 λ^2

Jy (2)

withλthe observing wavelength (in m), 2aand 2bare the
equatorial and polar diameters (in arc seconds), andTthe
temperature (in K). Usually, planets do not behave like a
blackbody, and the temperatureTin Eq. (2) is called the
brightness temperature, defined as the temperature of an
equivalent blackbody of the same brightness.

2.2 Radio Emission from a Planet’s (Sub)surface

Radio observations can be used to extract information about
the (sub)surface layers of planetary bodies. The temper-
ature structure of the (sub)surface layers of airless bod-
ies depends upon a balance between solar insolation, heat
transport within the crust, and reradiation outward. The
fraction of the solar flux absorbed by the surface depends
upon the object’s albedo,A, while the energy radiated by the
surface (at a given temperature) depends upon its emissiv-

ity,e(which is 1 for a blackbody,e= 1 −A). During the day,

a planet’s surface heats up and reaches its peak temperature

at noon or early afternoon (the exact time depends upon the

body’s thermal inertia—see later); at night the object cools

off. Its lowest temperature is reached just before sunrise.

Because it takes time for the heat to be carried downward,

there will be a phase lag in the diurnal heating pattern of

the subsurface layers with respect to that at the surface, and

the amplitude of the variation will be suppressed. At night,

heat is carried upward and radiated away from the surface.

Hence, while during the day the surface is hotter than the

subsurface layers, at night the opposite is true.

The amplitude and phase of the diurnal temperature

variations and the temperature gradient with depth in the

crust are largely determined by the thermal inertia and the

thermal skin depth of the material. The thermal inertia,γ,

measures the ability of the surface layers to store energy,

and depends on the thermal conductivityK, the densityρ,

heat capacityC:γ=

√

KρC.

The amplitude of diurnal temperature variations is

largest at the surface, and decreases exponentially into the

subsurface, with ane-folding scale length equal to the ther-

mal skin depth:

Lt=

√

(KP

πρC

)

. (3)

wherePis the rotational period.

For the terrestrial planets, using thermal properties of

lunar soils and the proper rotation rates, the skin depths

are of order a few centimeters (Earth and Mars) to a few

tens of centimeters (Moon, Mercury, and Venus, because

of their slow rotation). The 1/edepth to which a radio wave

at wavelengthλprobes into the subsurface is given by

Lr=λ/(2π

√

εrtan) (4)

whereεris the real part of the dielectric constant, and tan

is the “loss tangent” (or absorptivity) of the material—

the ratio of the imaginary to the real part of the dielec-

tric constant. Radio waves typically probe∼10 wavelengths

into the crust. By observing at different wavelengths, one

can thus determine the diurnal heating pattern of the Sun

in the subsurface layers. Such observations can be used to

constrain thermal and electrical properties of the crustal

layers. The thermal properties relate to the physical state of

the crust (e.g., rock versus dust), while the electrical prop-

erties are related to the mineralogy of the surface layers

(e.g., metallicity).

2.3 Radio Emission from a Planet’s Atmosphere

Radio spectra of a planet’s atmosphere can be interpreted by

comparing observed spectra with synthetic spectra, which