What do we know about accretion rates of micro black holes? Suppose a relative small black hole (mass about $10^9$ kilograms) would be thrown into the sun. Eventually this black hole will swallow all matter into the star, but how much time will pass before this happens?

Are there any circumstances where the black hole would trigger a gravitational collapse in the core, and result in a supernova?

There seems to be some margin for the accretion heating to counter or exceed the heating from fusion, so it could throw the star over the temperature threshold for carbon-12 fusion and above. The black hole is converting nearly 80% - 90% of the rest-mass of the accretion matter to heat, while fusion is barely getting about 0.5% - 1%.

Bonus question: Could this be used to estimate a bound on primordial micro black holes with the fraction of low-mass stars going supernova?

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    $\begingroup$ Related: worldbuilding.stackexchange.com/q/6426. $\endgroup$ – HDE 226868 Jun 19 '15 at 17:54
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    $\begingroup$ dat feeling when answers on a scifi SE have better physics than on the physics SE ;) $\endgroup$ – lurscher Jun 19 '15 at 17:57
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    $\begingroup$ Worldbuilding. Not Sci-fi. We get touchy about that. :-) $\endgroup$ – HDE 226868 Jun 19 '15 at 17:57
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    $\begingroup$ Supernovae occur due to two processes: core-collapse or thermonuclear run-away; both require a more-massive-than-our-sun star (even with the paltry 1e9 kg added) $\endgroup$ – Kyle Kanos Jun 19 '15 at 19:04
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    $\begingroup$ I think his question was more along the lines if a black hole eats the inside of a star, could the star collapse into that space that the black hole consumed. A kind of smaller core-collapse scenario. I'm pretty sure the answer is no, cause a mini black hole and it's accretion disk would heat up the inside of the star. It would be very different than a core collapse, it would probobly expand the star. And you'd need a bigger black hole than 1e9 KG. One that wouldn't evaporate in a poof of Hawking radiation. $\endgroup$ – userLTK Jun 19 '15 at 20:48

The micro black hole would be unable to accrete very quickly at all due to intense radiation pressure.

The intense Hawking radiation would have an luminosity of $3.6 \times 10^{14}$ W, and a roughly isotropic flux at the event horizon of $\sim 10^{48}$ W m$^{-2}$.

The Eddington limit for such an object is only $6 \times 10^{9}$ W. In other words, at this luminosity (or above), the accretion stalls as matter is driven away by radiation pressure. There is no way that any matter from the Sun would get anywhere near the event horizon. If the black hole was rotating close to the maximum possible then the Hawking radiation would be suppressed and accretion at the Eddington rate would be allowed. But this would then drop the black hole below its maximum spin rate, leading to swiftly increasing Hawking radiation again.

As the black hole evaporates, the luminosity increases, so the accretion problem could only become more severe. The black hole will entirely evaporate in about 2000 years. Its final seconds would minutely increase the amount of power generated inside the Sun, but assuming that the ultra-high energy gamma rays thermalised, this would be undetectable.

EDIT: The Eddington limit may not be the appropriate number to consider, since we might think that the external pressure of gas inside the Sun might be capable of squeezing material into the black hole. The usual Eddington limit is calculated assuming that the gas pressure is small compared with the radiation pressure. And indeed that is probably the case here. The gas pressure inside the Sun is $2.6 \times 10^{16}$ Pa. The outward radiation pressure near the event horizon would be $\sim 10^{40}$ Pa. The problem is that the length scales are so small here that it is unclear to me that these classical arguments will work at all. However, even if we were to go for a more macroscopic 1 micron from the black hole, the radiation pressure still significantly exceeds the external gas pressure.

Short answer: we wouldn't even notice - nothing would happen.

Bonus Question: The answer to this is it doesn't have a bearing on the supernova rate, because the mechanism wouldn't cause supernovae. Even if the black hole were more massive and could grow, the growth rate would be slow and no explosive nucleosynthesis would occur because the gas would not be dense enough to be degenerate.

Things change in a degenerate white dwarf, where the enhanced temperatures around an accreting mini-black hole could set off runaway thermonuclear fusion of carbon, since the pressure in a degenerate gas is largely independent of temperature. This possibility has been explored by Graham et al (2015) (thanks Timmy), who indeed conclude that type Ia supernova rates could constrain the density of micro black holes in the range $10^{16}$ to $10^{21}$ kg.

  • $\begingroup$ that relies heavily on the micro black hole being Schwarzschild. If the micro black hole is spinning near extremality, it would be cooler and allow accretion $\endgroup$ – lurscher Jun 19 '15 at 19:50
  • $\begingroup$ @lurscher see my edit. The luminosity would need to be reduced by a factor of $10^5$ to allow accretion. Even then the accretion timescale would be very long and if it did accrete something it would no longer be maximally rotating and would start to evaporate. I think the black hole needs to be several orders of magnitude more massive. $\endgroup$ – ProfRob Jun 19 '15 at 20:06
  • $\begingroup$ that sounds good! but I'm a little unconvinced that accretion would make the black hole necessarily drift away from extremality. Wouldn't the accretion rates that counterrotate the black hole be lower than the accretion rate of the mass rotating in the same direction? $\endgroup$ – lurscher Jun 19 '15 at 20:48
  • $\begingroup$ @lurscher Where would the specific angular momentum come from to ensure that J/M remained maximal? $\endgroup$ – ProfRob Jun 19 '15 at 21:07
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    $\begingroup$ I don't see how the Eddington limit is relevant here. That measures what the black hole can suck in, it says nothing about what the pressure of the star's matter can press in. $\endgroup$ – Loren Pechtel Jun 21 '15 at 4:37

The intense flux of Hawking radiation of about $10^{13}$ Watt will prevent any solar matter from coming close to the event horizon. So, the Hawking radiation creates a small bubble preventing it from growing by accretion.

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    $\begingroup$ Power output of the sun is $10^{26}\,\rm W$ so I'm not convinced something so small as $10^{13}\,\rm W$ could be described as intense or prevent accretion. $\endgroup$ – Kyle Kanos Jun 19 '15 at 19:17
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    $\begingroup$ I think his point was, a black hole of that size would be much hotter than the inside of the sun and being that much hotter, it would lose mass to the sun faster than it can absorb matter from it. A black hole that small couldn't form an accretion disk either, so any matter eating would be more random collisions. (an accretion disk speeds up the rate a black hole takes in matter). Also, the heat of the black hole would push matter away from it. For the entire sun, the additional hawking radiation would be irrelevant but around the black hole, it would prevent the hole from eating much. $\endgroup$ – userLTK Jun 19 '15 at 19:37
  • $\begingroup$ the assumption that it will radiate Hawking radiation relies heavily on the micro black hole being of the Schwarzschild type. If the micro black hole is spinning near extremality, it might be cooler and allow accretion $\endgroup$ – lurscher Jun 19 '15 at 19:53
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    $\begingroup$ @KyleKanos you are confusing power with power density. The radius of the sun is about 7 x 10^8 m. From your link, surface emission is ~60 MW/sq m. For a black hole at a distance of 1 nm, emission power is about 8 x 10^29 W/sq m. That's a factor of about 10^21 greater for the black hole. $\endgroup$ – WhatRoughBeast Jun 19 '15 at 20:00
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    $\begingroup$ Ah. Sorry. Perils of the Socratic Method, and all that. $\endgroup$ – WhatRoughBeast Jun 19 '15 at 20:06

This might help: http://xaonon.dyndns.org/hawking/

10^9 KG gives it:

a temperature of 1.227203e+14 Kelvin

and a luminosity of 3.563442e+14 watts

and a size about 500 times smaller than a proton by radius - that would make an absorption rate equivalent to its Hawking radiation pretty difficult because it's over five orders of magnitude hotter than the inside of the sun and at the same time, much smaller than an atom.

At that mass, a black hole wouldn't even create a good pocket of very dense material gravitationally pulled material around it. At just the distance of one atomic radius, even in the densely packed center of the sun, its gravity would drop off well over a million fold.

At that size, it's hard to imagine that it would have even significant tidal effects either. If such a black hole existed and you were able to approach it (ignoring the Hawking radiation it shoots out), you'd have to get about 3 inches from it to even feel a 1 G force from it - which would feel strange because the tidal forces would drop off the gravitation rapidly, but as long as you kept a reasonable distance, it wouldn't feel dangerous - perhaps like what it feels like holding a magnet, but you're the magnet.

Now if it was to pass through you it would likely leave a bullet sized hole - so that wouldn't be fun - and its radiation would also be lethal, but if you keep your distance, it would seem gravitationally pretty wimpy until you were very close.

So, if you want a black hole that would eat the sun, I think you have to go bigger - as a ballpark guess, maybe 10^13 or 10^14 kg - give or take and even then, I expect it would take a long time to eat the sun.

Now as to eating the core leading to collapse, a black hole that small wouldn't have a noticeable effect, but as it gets bigger, two things would happen.

It could create a small area of higher pressure, essentially an accretion disk inside the sun and, the formation of the accretion disk would create additional heat as well as those lovely jets that shoot out the poles. The extra heat would likely push matter away from the center of the sun faster than the pocket of high gravity would drag things towards it. The net effect would be complicated because in the localized area you'd have more energy, but that more energy would heat up the sun, causing the sun to expand. It would also have a stirring effect of sorts from the jets of energy. The total effect is, for me, very hard to say.

Now, as the micro black hole gets bigger, the sun would eventually look less and less like a sun and more and more like an accretion disk with two jets shooting out. The intermediate stages are complicated, but the beginning (not much difference) and end (black hole accretion disk) aren't hard to predict.

Now, on going supernova, that, I don't think so because black holes, while eating, shoot out too much heat in the process. A star goes nova because the core cools and in cooling it collapses and in collapsing - well, you know the rest. A black hole would provide steady and consistent heat while it eats, so I see no mechanism for a nova moment - and that's basically how a nova works - it happens kind of all at once. A nova is like a perfect storm, where, everything falls in very fast and then all that matter bounces off of itself and explodes outwards. A core collapse is a very different event than a black hole with an accretion disk.

Maybe I missed something, but that's my take on this rather improbable scenario, and for the record, I don't believe micro black holes exist.

  • $\begingroup$ Low-mass stars don't collapse, they go through runaway nuclear fusion. $\endgroup$ – Kyle Kanos Jun 19 '15 at 19:19
  • $\begingroup$ @ Lursher, Oh, I'm sure locally, near the black hole inside the star, it could create all kinds of reactions, perhaps even making some heavy molecules. The problem is one of how the energy would behave. The jets would react with the matter in the star, but eventually the Jets would break through the star. I think this scenario would eventually stir up the star a lot, but I don't see how it would look like a super-nova. Granted, my answer is purely speculative. $\endgroup$ – userLTK Jun 19 '15 at 19:28
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    $\begingroup$ Are the 7 significants digits warranted for the temperature and luminosity? $\endgroup$ – Peter Mortensen Jun 20 '15 at 16:51
  • $\begingroup$ That would be a no. I just copy/pasted from the website. $\endgroup$ – userLTK Jun 20 '15 at 17:08

It appears that for white-dwarfs, the answer is supernova, if the masses are large enough: see http://arxiv.org/abs/1505.04444, a blog discussing the paper is here: http://astrobites.org/2015/06/03/detonating-white-dwarfs-with-black-holes/

On the grounds that the link above specifically discussed white-dwarfs, I am guessing that for the lower density of a normal star, a micro-black-hole actually passes straight through, presumably gaining some mass.

The paper does indeed discuss primordial micro black holes, and states "primordial black holes with masses ∼ $10^{20}$ gm - $10^{24}$ gm cannot be a significant component of dark matter."

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    $\begingroup$ The gas in the Sun is neither degenerate, nor made of carbon, so the conditions that might ignite a runaway detonation in a white dwarf are not present. $\endgroup$ – ProfRob Jun 21 '15 at 18:22
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    $\begingroup$ Just be patient and wait a few billion years then :-) $\endgroup$ – user1998586 Jun 24 '15 at 7:52
  • $\begingroup$ Yes, I see your (tongue in cheek?) thinking, but the problem is that a small black hole of $10^{9}$ kg evaporates in 2000 years. $\endgroup$ – ProfRob Jun 24 '15 at 9:32

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