Context : 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 .

Aims : 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 .

Methods : Simulations of the cooling and contraction were conducted for ice giants with masses of 5 , 10 , 20 , and 50 M _ { \oplus } 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 .

Results : We find for a nominal 10 M _ { \oplus } 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 R _ { \oplus } , and an intrinsic luminosity of 0.006 L _ { \textrm { \tiny \jupiter } } .
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 \mu m pick up the intrinsic flux .

Conclusions : 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 M _ { \oplus } 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 .