Sustained super-Eddington accretion around neutron stars & black holes

Recently, it was shown that the formation of a photon-trapping surface might not be sufficient to ensure unimpeded super-Eddington (SE) accretion. In light of this finding, here we derive a condition such that sustained and unimpeded SE accretion could be achieved in optically thick slim accretion disks surrounding neutron stars (NSs) and black holes (BHs). For this, we calculate a semi-analytic approximation of the self-similar global radial velocity expression for an advection-dominated flow. Neglecting the influence of relativistic jets on the accretion flow, we find that for Eddington fraction $\dot{m} \gtrsim 1.5 (\epsilon/0.1)^{3/5}$ ($\epsilon$ being the accretion efficiency) sustained SE accretion might be possible in slim disks around BHs irrespective of their spin. The same condition holds for NSs when $\epsilon > 0.03$. The presence of a surface magnetic field might truncate the disk at the magnetosphere of the NS, resulting in lower efficiencies and consequently changing the condition to $\dot{m} > 0.013 \epsilon^{-19/31}$. Our approach suggests that sustained SE accretion might almost always be possible around NSs and BHs hosting accretion disks.