# How big would a black hole have to be to absorb the Sun?

How big would a slow moving black hole have to be to absorb or otherwise destroy the Sun?

• Same question for Earth: physics.stackexchange.com/q/2743/2451 , physics.stackexchange.com/q/172403/2451 – Qmechanic Feb 7 '19 at 2:28
• I was thinking that a small enough black hole, say one a bit more than the Planck mass and at rest relative to the sun and at it's center, would evaporate faster than it could accumulate mass. How big would it have to be to accumulate matter gravitationally as fast as it radiates due to Hawking radiation? – Victor Ganora Feb 7 '19 at 2:46

Here's an answer based on thermodynamics (see also). Heat only flows from hot to cold. A black hole's Hawking temperature is

$$k T = \frac{\hbar c^3}{8\pi GM}$$

So any black hole with mass $$M\gtrsim2\times10^{19}\,\mathrm{kg} \approx 4\times10^{-6}\,M_\text{earth}$$ has a surface temperature that's cooler than the temperature anywhere inside the Sun. If such a black hole were to appear inside the Sun (which wouldn't necessary cause drama in the outer solar system --- that's not much mass), there would be some mass accumulation as nearby parts of the Sun's atmosphere fell onto the event horizon. But the radiation from the hot Sun would also fall onto the black hole more rapidly than the Hawking radiation from the black hole was emitted. A black hole in such a situation would have nothing to stop it from eventually consuming the entire Sun, which would be curtains for us. It would be amusing to compute what such a devourment would look like and how long it would take.

A black hole with a mass larger than a couple of nano-Earths ($$10^{-9}\,M_\text{earth}$$) would be hotter than the Sun's photosphere but cooler than its core. An object like that would definitely accrete mass if it were at rest in the core, but in the less-dense regions of the Sun there would be a competition between mass accretion and Hawking radiation. Computing how that competition would play out would be interesting, but doing it seriously would involve some knowledge about hydrodynamics and accretion that I don't have.

There is some minimum black hole mass where the Hawking radiation wins out over the mass accretion, even in cold, relatively dense matter. For example, consider a black hole in its last second before evaporation, with mass $$10^5\rm\,kg$$ and radiating at $$10^{21}\rm\,W$$, and a Schwarzchild radius smaller than a proton. That object isn't going to gravitationally accrete mass at anything like its evaporation rate, even in a medium as dense as the Sun's core. (Degenerate matter raises as many questions as it answers; leave it alone for now.) So there are black holes that are too low-mass/high-temperature to absorb the Sun without evaporation, and the burst of power in the last instants of evaporation would be a pretty small fraction of the Sun's total luminosity: possibly strong enough to make waves on the photosphere if it happened near the surface, but easily absorbed by the Sun's bulk if it happened in the radiative zone or in the core. But I'm not claiming in this answer to compute what that minimum mass is --- too many unknowns are involved.

• Takes no account of accretion luminosity and radiation pressure. – ProfRob Feb 7 '19 at 7:16
• @RobJeffries "but doing it seriously would involve some knowledge about hydrodynamics and accretion that I don't have." The goal here was just to argue that both limits exist. – rob Feb 7 '19 at 7:18

The odds of a roaming stellar blackhole entering the solar system is less than 1 in a trillion. There are two predominant types of a black hole in the universe. The first are supermassive black holes found churning at the center of galaxies. These don’t pose any threat to us at least until our galaxy collides with the Andromeda galaxy in a few billion years.

The other types of black holes are stellar mass black holes. The smallest of which is just 3.2 solar masses in size.

If one of these passed near the solar system, it would perturb the Ort cloud as such that it would shower the solar system with both massive and small comets.

If the black hole made its way into the solar system, we probably won't notice it at first, unless it began to eat a gas giant forming an accretion disk.

By the time it reaches the asteroid belt between Jupiter and Mars, the Earth would begin to be torn apart.

The sun and the black hole would begin to orbit each other. Gas would be sucked off the sun. As the sun lost mass it would begin to swell to a red giant. More and more mass would be lost until you are left with just a white dwarf. They would then orbit each other radiating gravity waves until further weakening the sun, until it is finally ripped apart.

The closest known black hole is Cygnus X-1 6000-7000 light years away and is 14.2 solar mass.

• "The sun and the black hole would begin to orbit each other" needs some justification. – S. McGrew Feb 7 '19 at 2:40
• "As the Sun lost mass it would begin to swell" needs justification. "The odds of a roaming stellar blackhole entering the solar system is less than 1 in a trillion. " needs justification and a timescale. – ProfRob Feb 7 '19 at 7:24