This entry contains some ideas on stellar mass black holes orbiting a supermassive black hole and traveling through a jet. While this (quick) calculation was mostly done for fun, if anyone has any comments or ideas on how to improve this, please don’t hesitate to e-mail me.
This paper suggest that there is a number of stellar-mass black holes trapped in the vicinity of the supermassive black hole of an AGN. This might lead to mergers in the accretion disks binary black holes and have implications for the LIGO detection of gravitational waves from these objects.
When reading this paper (and listening to the talk by the author), I was wondering about what would happen in a radio loud AGN, i.e., when such a stellar mass black hole would orbit through the relativistic outflow. Would this black hole be able to accrete and produce mini-jets?
In order to estimate the accretion, a few colleagues and I looked at the Bondi accretion. The Bondi radius gives a distance within which the average speed plasma velocity is smaller than the escape velocity. This was not derived with a relativistic plastic in mind, but was originally intended for gas accretion by a stationary star. While a relativistic plasma traveling in (mostly) one direction (and we’re not considering shocks or other jet features) is a complication, the Bondi radius gives us a rough estimate for the accretion that could occur:
with the mass of the black hole M●, the gravitational constant G and the speed of the sound in the medium cs . For a jet the sound speed is given by 0.37 c, which of course is not the same throughout the jet and might not be an exact value, but it will be sufficient for this estimate. (The initial proper sound speed is given as γsβsc~0.4 c
For a stellar mass black hole of 10×M⊙, this yields
while the gravitational radius of this black hole is
We can use this to estimate a mass accretion rate within the Bondi radius, by using the surface of the Bondi sphere
with ρ = 1 e±/cm3.
Even if this is a few orders of magnitude off (lots of assumptions!), an accretion rate of 10-29 M⊙/yr is too low to significantly increase the black hole mass, and will not allow the stellar mass black hole to form jets or produce any other kind of (observable) phenomenon.
In short: Stellar mass black holes can travel through a relativistic jet completely unharmed!
Thanks to: M. Lucchini, P. Polko, and J. Wilms for the input.