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I read that a black hole can sometime "choke" on a star:

"...the disrupted stellar matter was generating so much radiation that it pushed back on the infall. The black hole was choking on the rapidly infalling matter."

Why does a black hole choke? How do astronomers manage to observe this rare event?

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There is a limit to how quickly a black hole can accrete matter. As a star gets close to a black hole it may be tidally disrupted and pulled apart. The material from the star will then fall toward the black hole and as it does so, the gravitational potential energy will go into heating it up. Now the stellar material would not normally be able to fall directly into the black hole - angular momentum must be conserved, so first it will form an "accretion disk". Viscosity in the disk can transport angular momentum outwards, allowing material to then fall through the event horizon. The ultimate rate at which the black hole can swallow mass will be controlled by the rate at which material can reach the inner parts of the accretion disk.

If the accretion disk is very hot and luminous, there could be a limit to how fast material can be added to it. This is known as the Eddington limit. Basically what happens is that the radiation from the inner parts of the accretion disk is so intense that it can "blow away" any new material falling towards the black hole. This is then a self-regulating phenomenon because the luminosity of the disk is derived from the material falling onto it - and so an equilibrium will be set up that limits the accretion rate to that which produces only enough luminosity that allows the accretion to proceed. This limit on the accretion rate is what the article you refer to means by "choking".

An estimate of the maximum accretion rate is set by equating the accretion luminosity and the Eddington luminosity (the maximum luminosity that an object may have before radiation pressure will halt accretion). This in turn depends on the efficiency $\epsilon \sim 0.1$ with which gravitational potential energy is turned into radiation as material falls into the black hole.

The journal paper that reports this discovery - Vinko et al. (2015) - analyse the light curve of the event and suggest this is black hole of $10^{5}$ to $10^{6}$ solar masses, tidally disrupting and swallowing a star of about a solar mass.

The Eddington luminosity (for spherical accretion) would be $\leq 3\times 10^{10}$ solar luminosities , but this thing had a peak luminosity (even in X-rays) of $10^{11}$ solar luminosities indicating that it must be in the regime where radiation pressure would reduce the accretion rate. To supply this luminosity would require $\epsilon \dot{M} c^2 \sim 10^{11} L_{\odot}$. For $\epsilon \sim 0.1$ this gives a peak mass accretion rate $\dot{M} \sim 2\times 10^{-4} M_{\odot}$ per day. Thus it would take more than 10 years to "swallow" the star even at this peak rate.

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I read that a black hole can sometime "choke" on a star: "...the disrupted stellar matter was generating so much radiation that it pushed back on the infall. The black hole was choking on the rapidly infalling matter."

I read the report and thought it was reasonable, and in line with Rob's answer. But note that there's no certainty that this is what actually happened. They saw a very bright "optical transient" event, circa ten times brighter than a normal supernova. See the paper on the arXiv: A Luminous, Fast Rising UV-Transient Discovered by ROTSE: a Tidal Disruption Event? There's a question mark on the end of the title, they don't know for sure. And see this from the news article:

"To narrow it down from four possibilities, they studied Dougie with the orbiting Swift telescope and the giant Hobby-Eberly Telescope at McDonald, and they made computer models. These models showed how Dougie's light would behave if created by different physical processes. The astronomers then compared the different theoretical Dougies to their telescope observations of the real thing."

They came up with what they thought was the best fit. But we don't know for sure that this was actually a black hole "choking" on a star.

Why does a black hole choke?

We don't know for sure. Note in the paper on page 8 and 9 they talk about an off-axis GRB interpretation. It's possible that this is what happened. Or something else altogether. The tidal disruption idea looks like a good fit, but they don't know for certain. Anyway, have a look at the summary on page 12 for a nice round-up:

"The tidal disruption scenario was explored by fitting the event to an amended version of the model presented in Guillochon et al. (2014). The TDE model yielded a good fit to the photometric and spectral evolution of the flare, with the highest-likelihood models suggesting a disruption of a solar-mass star by a black hole."

How do astronomers manage to observe this rare event?

They didn't actually observe a black hole choking on a star. What they saw was an optical transient. Something that looked like a supernova, but didn't fit the supernova pattern. So they think it was the disruption of a star by a black hole.

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    $\begingroup$ This is fair comment, I don't understand a down vote. Read the paper- the conclusion is not unequivocal. $\endgroup$ – Rob Jeffries Dec 24 '15 at 10:54
  • $\begingroup$ There are malicious downvoters I'm afraid Rob. $\endgroup$ – John Duffield Dec 24 '15 at 13:16

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