# Statistically, what would the average distance of the closest black hole be?

The closest confirmed black hole is several thousand light years away from earth. Our galaxy has about 100 billion stars. I didn't find any reliable information on the black hole count of ratio versus stars for our galaxy. Some sources say about one in a thousand.

I would like to estimate how close a black hole would be given the data we have. If I did the calculation myself, I would use the volume of the galaxy and the number of stars in it. This would give the average number of stars per some volume, and out of that, the average number of black holes per volume. The distribution of stars would also be have to taken into account, since our part of the galaxy isn't as densely populated. Out of this the statistically approximate distance of the closest black hole could be obtained.

Is anyone equipped with enough information to give me an estimate?

Basically what is needed is the ratio of black holes to stars for our galaxy and then list of x nearest stars and their distances, where x is the ratio.

(I'm asking this because black holes are object of interest, and will have to be visited in the future. Given that our space capabilities might be limited to a distance of a couple of dozens of light years in the near future, this number is interesting.)

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Black holes are generally thought to inhabit the centre of galaxies, therefore the closest one would be at the centre of the Milky Way. – Carl Jun 22 '14 at 8:46
@ Carl There is a supermassive black hole in the center of milky way. Other black holes are spread out in the entire galaxy with the same distribution as the regular stars, only that there is less of them. – this Jun 22 '14 at 11:20
Yeah, sorry, I was thinking just supermassive BHs. This site states that each galaxy has approximately 100 million stellar mass black holes. hubblesite.org/explore_astronomy/black_holes/encyc_mod3_q7.html – Carl Jun 22 '14 at 22:33

I have found a database of the nearest stars within 25 parsecs. The database contains 2608 stars, given the not very accurate estimate of 1 black hole per 1000 stars, would make 2.6 black holes within 81.5 ly( 1 parsec = 3.26 lightyears ).

Taking only the closest 1000 stars from the database, then the maximum distance is 50.9 ly, so there is on average one black hole within that distance. The average distance of all 1000 stars is 35.8 ly, and that is the average distance to that probable black hole.

A more accurate ratio would make this much more interesting. Imagine a ration of 1 to 100. Then the average distance becomes only 14.3 ly.

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I'm still hoping for a better answer. – this Jun 22 '14 at 23:43

This is only a rough estimate. But the number of supernovae in the Milky Way is approximately 2-5 / 100 years (here and here). There is approximately $3 \times 10^{11}$ stars in the Milky Way. Provided the supernovae rate did not change much through the history (which is a big if that probably doesn't work), the total number of supernovae would be $2$-$5\times 10^8$. I do not know how much supernovae will result in a black hole, but if we estimate 10% - 30%, it might not be that wrong. This would lead to $2\times 10^7$ - $1.5\times 10^8$ stellar black holes in the Milky Way. By other words, one star from 2000 - 15000 should be a black hole.

If there is 1000 stars in 50.9 ly around the Sun, with this density there would be one stellar black hole per 100 - 200 ly.

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