Abstract:
Matter falling onto black holes is hot, fully ionized and has to be necessarily transonic.
Since the electrons are responsible for radiative cooling via processes like synchrotron,
bremsstrahlung and inverse-Compton, the electron gas and proton gas are supposed to
settle into two separate temperature distribution. But the problem with two-temperature
flow is that there is one more variable than the number of equations. Accretion flow in its
simplest form is radial, which has two constants of motion, while the flow variables are
the radial bulk three-velocity, electron and proton temperatures. Therefore, unlike single
temperature flow, in the two-temperature regime, there are multiple transonic solutions,
nonunique for any given set of constants of motion with a large variation in sonic points.
We invoked the second law of thermodynamics to find a possible way to break the
degeneracy, by showing only one of the solutions among all possible, has maximum
entropy and therefore is the correct solution. By considering these correct solutions,
we showed that the accretion efficiency increase with the increase in the mass accretion
rate. We showed that radial flow onto super-massive black hole can radiate with efficiency
more than 10%, if the accretion rate is more than 60% of the Eddington accretion rate,
but accretion onto stellar-mass black hole achieve the same efficiency, when it is close to
the Eddington limit. We also showed that dissipative heat quantitatively affects the two
temperature solution. In the presence of explicit heat processes, the Coulomb coupling
is weak.
