\[ \frac{T_{t,m}}{T_{t,e}} = (\frac{E_m}{E_e})^{1/4} (\frac{M_m}{M_e})^{-1/6} \]

with \(T_{t,e}=34 K\) and \(T_{CO_2}(gas|p=0.1atm) > 180 K\)

For \(M_m = M_e\) and \(T_{t,m} = 180 K\) we get \(E_{crit} \geq 780 E_⊕\)

Assuming \(E\propto M\), then \(M_{crit} \geq 5 × 10^8 M_⊕\)

\(E_{crit} = 5×10^{30} \text{erg/s} \gg E_⊕=4×10^{20} \text{erg/s}\)