The luminosity generated by accretion onto a black hole is given by $L = \epsilon \dot{m} c^2$, where $\dot{m}$ is the mass accretion rate and $\epsilon$ is the radiative efficiency. I read that the natural limit of the $\epsilon$ is 0.5. But I can't think why. Does it have something to do with Eddington limit?
$\begingroup$
$\endgroup$
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
A limit to the radiative efficiency of matter accreted by a black hole is the energy of the innermost stable orbit (ISCO), $1-E_{isco}$. This is the energy per unit mass of a particle orbiting at the ISCO, which is generally lower than one, signifying that the particle has lost energy as it has sunk into the gravitational well. The most energy (percentage wise) that a particle can have lost during the accretion process is $1-E_{isco}$. After reaching the ISCO a particle will plunge into the black hole quite promptly and there is little opportunity to convert energy into in electromagnetic radiation.
The ISCO energy of a black hole is a monotonicaly decreasing function of the black hole’s spin, with it tending to $1/\sqrt{3}\approx 0.577$. So the maximal radiative efficiency is given by roughly $\epsilon=0.422$, which is close to 0.5.
