# Could we detect dark matter by black holes gaining unexplained mass?

Dark matter is said to interact only gravitationally, so it won't commonly form black holes by itself. But if a black hole is already there, and dark matter encounters the event horizon, it should go in and never come out. This means black holes would vacuum up dark matter and (very slowly) gain mass.

Is this something we could hypothetically measure, as in "these black holes are heavier than they should be for the amount of cosmic gas and background radiation they eat"? (In fact, could this be why the oldest galactic black holes seem to be heavier than we expect?)

• Probably not, our confidence on the exact mass of black holes isn’t very accurate. I don’t know exactly how not confident we are, nor how accurate we could predict the to supposed to be. Dec 8, 2022 at 15:52
• Interesting question. Probably not, for how could we estimate the expected mass of the black hole without dark matter? We estimate a black hole's mass by looking at anomalies of orbits of stars in the neighbourhood. Also we don't know that dark matter is 'something'. Might just be a flaw in our understanding of gravity. Dec 8, 2022 at 16:03

## 2 Answers

The accretion rate is far too small to make much difference to Galactic black holes, but how could this be distinguished from the accretion of normal, baryonic matter in any case?

In fact it is easier for black holes to accrete normal matter, since it is easier for such matter to lose its angular momentum, via friction in an accretion disk, and be able to drop into the black hole.

The effective cross-section for the accretion of non-interacting dark matter is determined by an effective geometric size for the black hole, which will be just dependent on its mass and the speed with which it moves relative to the dark matter. This is the so-called "Hoyle-Lyttleton radius" given by $$R_{\rm HL} = \frac{2GM}{v^2},$$ where $$M$$ is the black hole mass and $$v$$ is its speed with respect to the dark matter background.

The accretion rate is then just $$\frac{dM}{dt} = \pi R_{\rm HL}^2 \rho v,$$ where $$\rho$$ is the density of the dark matter.

For Galactic black holes we might assume $$M=10M_\odot$$, a speed with respect to the Galactic dark matter of 250 km/s (if it is in orbit around the Galaxy at a similar position to the Sun) and $$\rho \simeq 0.01 M_\odot$$/pc$$^3$$ at the Sun's position. Putting the numbers in, we find $$R_{\rm HL}= 4.3\times 10^{10}$$ m (about 0.28 au) and a mass accretion rate of $$10^{-17} M_\odot$$/year.

Thus, even over the $$10^{10}$$ year life of the Galaxy, a stellar black hole increases its mass by a neglible amount due to the accretion of dark matter.

• Well, it was worth a try. Then again, if it was viable, I'm sure the Event Horizon Telescope team would have already done it.
– Hene
Dec 16, 2022 at 9:11

If black holes could gain mass from dark matter then stars should too because stars can become black holes.Since stars don't seem to have anomalous increases in mass, I doubt that black holes do gain mass from dark matter.

• This doesn't work. Firstly, black holes do gain mass, just not much, from dark matter. Secondly dark matter passes right through stars, without interacting with it. Dark matter will fall towards the sun (for example) and fall into the sun, then without stopping they will keep going under their own momentum and fall up out of the sun. Dec 14, 2022 at 23:21
• Why do black holes gain mass from dark matter? Does the event horizon stop dark matter from escaping?
– user48394
Dec 14, 2022 at 23:28
• Yes, the event horizon stips anything from escaping. but see the other answer. Dec 15, 2022 at 6:24