  The recently renewed interest in a possible additional major body in the
outer solar system prompted us to study the thermodynamic evolution of such an
object. We assumed that it is a smaller version of Uranus and Neptune. We
modeled the temporal evolution of the radius, temperature, intrinsic
luminosity, and the blackbody spectrum of distant ice giant planets. The aim is
also to provide estimates of the magnitudes in different bands to assess
whether the object might be detectable. Simulations of the cooling and
contraction were conducted for ice giants with masses of 5, 10, 20, and 50
Mearth that are located at 280, 700, and 1120 AU from the Sun. The core
composition, the fraction of H/He, the efficiency of energy transport, and the
initial luminosity were varied. The atmospheric opacity was set to 1, 50, and
100 times solar metallicity. We find for a nominal 10 Mearth planet at 700 AU
at the current age of the solar system an effective temperature of 47 K, much
higher than the equilibrium temperature of about 10 K, a radius of 3.7 Rearth,
and an intrinsic luminosity of 0.006 Ljupiter. It has estimated apparent
magnitudes of Johnson V, R, I, L, N, Q of 21.7, 21.4, 21.0, 20.1, 19.9, and
10.7, and WISE W1-W4 magnitudes of 20.1, 20.1, 18.6, and 10.2. The Q and W4
band and other observations longward of about 13 microns pick up the intrinsic
flux. If candidate Planet 9 has a significant H/He layer and an efficient
energy transport in the interior, then its luminosity is dominated by the
intrinsic contribution, making it a self-luminous planet. At a likely position
on its orbit near aphelion, we estimate for a mass of 5, 10, 20, and 50 Mearth
a V magnitude from the reflected light of 24.3, 23.7, 23.3, and 22.6 and a Q
magnitude from the intrinsic radiation of 14.6, 11.7, 9.2, and 5.8. The latter
would probably have been detected by past surveys.
