I Where Are the Missing Black Holes in the Milky Way?

[Vanadium 50]

TL;DR Summary

A simple calculation suggests there should be many black holes relatively nearby. Why don't we detect them?

Where should the nearest black hole be?

Something like 0.1% of stars end up as BH's, so that suggests about 100 million in the Milky Way. The easiest thing to do, instead of a complicated geometry problem, is to recognize that the cube root of 0.1% is 0.1, so that we expect BH's to have separations roughly 10x that of stars.

That, in turn, suggests that there should be one around 50 ly from us. However, the nearest identified one is more like 1500 ly. This implies a density 25,000-30,000 times lower. Now, one can say "maybe we just don't see them", but we should see the ones in binary systems due to the gravitational pull on the companion star, and indeed, this is how the nearest (and 2nd nearest) ones were discovered.

This also suggests that 99.9+% do not have accretion disks sufficient to make them bright x-ray sources.

So where are they?

 

[Borg]

How many of the the 0.1% are in binary systems? Could we extrapolate from large stars that we can see that would likely become black holes in the future?

 

[Vanadium 50]

How many of the the 0.1% are in binary systems?

About half of all stars are in multiple star systems.

 

[FactChecker]

In a random uniform distribution, there is more clustering than many would expect. That is even without a gravitational force to pull things together and make more clustering. With gravity, the high number of multiple star systems may be just the tip of the iceberg.

 

[Vanadium 50]

If you want to say clustering gives you a factor of 2, I will buy it. But not a factor of 30,000. SNe are from short-lived stars, so they occur in regions of active star formation, but after time passes, they should get mixed in with the rest of the galaxy. After all, 4 billion years ago the sun was in a region of active star formation, and now, not so much.

Another way to look at it: say the lifetime of a progenitor is 20 million years and say the milky way is 10 billion years old. So there should be 500 black holes for every visible progenitor.

Betelgeuse, Spica and Rigel are all good candidates (possibly Antares, al;though it may be a little small), and the most distant is half the distance to the nearest black hole. So we expect 3x8x500 = 12,000 black holes within 1600 light years. We see one. Double the distance, and we should see 100,000. We see 2.

You ca say, half are solitary, and of the other half, maybe half are perpendicular to our field of view, and I'll even toss in 1% for the possibility that the period is so long we just haven't looked hard enough. That still leave us coming up around two orders of magnitude short.

So where are they?

 

[Ibix]

A couple of thoughts.

How long lived is the accretion disc of a stellar mass black hole? The hole's long range gravitational behaviour isn't different from a star, so it's not going to be accumulating all that much matter, and it's radiating heat from gravitational infall of the disc. That'll run out and go dark on some timescale - how long? If the radiation loss is enough bigger than the accretion that the lifetime is short compared to stellar lifetimes then there could be a lot of quiescent holes out there.

Are black hole/star binaries likely to be very common? I'd tend to suspect a point-blank supernova isn't going to do all that much good to a nearby star. Distant binaries would obviously fair better, but then the wobble due to the dark companion is harder to spot.

 

[Vanadium 50]

So, lets look at various points:

Accretion disks: I don't know how long they last, or perhaps more relevantly, how often they are replenished by new dust and gas. But orbit perturbations don't depend on this.

Companion disruption: this can happen, for sure, but it takes a lot to do this, and SNe only last for weeks. Maybe as much energy impinges on the companion ad the companion itself produces: that's a lot, nut a year or two later things are more or less as they were. Also, much of the SN energy is in neutrinos from the p -> n process, so the companions will have n -> p: essentially replenishing fuel.

Further, there are neutron stars with planets. These are often more energetic SNe, and surely a planet is less robust than a star.

Finally, there exist stars that are so cliose that they touch. W Ursae Majoris, for example. Their disruption is dominated by mass transfer, not energy.

It is absolutely true that these become harder to spot with distance from the companion. Periods get long. But the amplitude of variation is much larger for a star than a planet. And going back to W Ursae Majoris, it's only 170 ly away. Its period is only 9 hours. So short-period binaries are not that rare. I estimated 1%, which may be wrong, but 0.01% seems very small.

There really are only three possibilities, and I don't see how any of them fit what is known:

1. We never made these black holes
2. We made them, but none are nearby
3. They are nearby, but we just can't detect them.

 

[Ibix]

I was thinking (3), that accretion discs might cool faster than they reheat from new infalling matter so we don't see many of them. But I don't know how to do the calculations - d1.25 in this astro.princeton.edu pdf may help, but I haven't had a chance to read in detail.

 

[Vanadium 50]

I was still thinking more along the lines of picking them up as really heavy planets - accretion disks are just a bonus. There are such objects - called microquasars - but a handful, not hundreds.

Note that my three options are not mutually exclusive. Anu or all could be true.

 

[Dr_Nate]

Something like 0.1% of stars end up as BH's, so that suggests about 100 million in the Milky Way.

Are 0.1% of stellar mass objects now BHs, or will we in the future see 0.1% of them be BHs?

 

[Vanadium 50]

Are 0.1% of stellar mass objects now BHs, or will we in the future see 0.1% of them be BHs?

The estimate is "now", but I don't think this is known to this accuracy - another 5 billion years is ony a factor of 1.5, and after the Milky Way-Andromeda collision, there will be much less star formation.

 

[anuttarasammyak]

For first generation of stars there are abundant materials so many black holes were produced. Recycle by recycle fewer BH. It’s my thought on Christmas.

 

[Vanadium 50]

As a sanity check, the same calculation with white dwarfs suggests that the nearest one should be around 9 ly from us. The nearest one is Sirius B, around 9 ly away from us.

 

[anuttarasammyak]

Does the news this month https://www.icrr.u-tokyo.ac.jp/en/news/14513/ say something new to your question ?

 

[Vanadium 50]

No. The title says "distant universe". That's more than tens of light years.

 

[mfb]

Binary stars that formed together tend to have similar masses, if one becomes a black hole then the other one is likely to become a black hole, too.

The supernova comes with a big mass loss, that can eject the other star.

Even if you have a visible star orbiting a black hole, you need the orbit to be close in order to detect it.

But most importantly, where is that large radial velocity dataset for tons of different stars? Radial velocity method exoplanet searches look at a handful of stars at a time. Gaia is making a big dataset. A look at early data gave us the nearest two black holes we know, we can expect more with the full dataset and further analysis.

 

[Vanadium 50]

Binary stars that formed together tend to have similar masses, if one becomes a black hole then the other one is likely to become a black hole, too.

Can you point me to a reference? This is trivially true, in the sense that most stars are red dwarfs, and red dwarfs have similar masses. If I picked two stars at random, odds are that they will have similar masses. But it sounds like you mean more than this.

Looking at the nearest stars (a less biased dataset) and I have a mass ratio of 1,2 for alpha centauri, 2.0 for Sirius, 2,4 for Procyon, 1.1 for 61 Cygnui and 1.3 for 40 Eridani. Gliese 169 is 2.9. I could look at the SN progenitor candidates, which is a more biased (but possibly more relevant) sample, and get Spica 1.6, Rigel 7.0 (!), Betelgeuse (solitary) and Antares 2.5.

I don't think this is it.

 

[Vanadium 50]

Onto the other issues:

"Maybe the orbits are hard to find" was addressed. I assumed we were missing 99% of them. Maybe it's 99.99%, buto accept this as an answer, I'd like to see an estimate. While it is true that there are binaries with such large separations that finding them via gravitational perturabtions is impossible (Proxima Centauri is an example), there are many we should. Note that the amplitude will be much larger than for typical planets.

"The primary won't survive" argument has two problems: one is my argument on energetics and neutrino chemistry above. The other argument is that the two companion stars to the Gaia black holes (obviously) survived. They are close - not W Ursae Majoris close, but a couple of AUs. So that argument doesn't seem to fit the data.

The argument that maybe its in the data but we haven't got to it yet sounds plausible. But we've found over a thousand exoplanets this way. That argument is getting less and less likely over time. Even now, it looks kind of marginal at best.

 

[snorkack]

I was thinking (3), that accretion discs might cool faster than they reheat from new infalling matter so we don't see many of them. But I don't know how to do the calculations - d1.25 in this astro.princeton.edu pdf may help, but I haven't had a chance to read in detail.

I did read it.
The issue is that it takes "accretion rate" as a fixed parameter.
Which is not obvious!
If you have a compact object, the infalling matter might pass by at close hyperbolic orbits without colliding with anything or losing any energy, and escape back to infinity. So one thing to figure out about accretion is how a compact object intercepts infalling matter. Which is especially critical for a black hole - for a brown or white dwarf or neutron star, infalling matter that meets the surface heats it up, but for black hole, any energy reaching event horizon is swallowed up and only energy intercepted by something outside the horizon can be emitted.
About black holes and binaries: compare pulsars
https://www.aanda.org/articles/aa/full_html/2017/12/aa31518-17/aa31518-17.html
Something like 3...7% of solitary pulsars move less than 60 km/s relative to original speed
This suggests that black holes in binaries are rare relative to black hole precursors, not because the explosion damages the second component but because great majority of black holes take off at a great speed and leave their partner behind as a solitary star. And this would especially afflict distant binaries because of lower escape velocity of the black hole from the distant binary.

 

[sbrothy]

As always it's me with the naive questions, but isn't it possible to detect them with (some variation of?) the "transit method" used to detect extra solar planets?

 

[Ibix]

As always it's me with the naive questions, but isn't it possible to detect them with (some variation of?) the "transit method" used to detect extra solar planets?

Stellar mass holes are small (the Sun's Schwarzschild radius is only about 3km) so transit across something as big as a star won't block or lens much light. So I don't think it would be a very sensitive technique compared to spotting the wobble induced by the hole's gravity.

Maths might prove me wrong, of course.

 

[Vanadium 50]

I agree with @Ibix : these BH's are tiny. Further, if you have a transit, how do you know it wasn't an asteroid? There are probably many tens of thousands of asteroids this size in our solar system.

 

[snorkack]

I agree with @Ibix : these BH's are tiny. Further, if you have a transit, how do you know it wasn't an asteroid? There are probably many tens of thousands of asteroids this size in our solar system.

Because a black hole transit would look completely different? Almost all lensing!

 

[Orodruin]

Because a black hole transit would look completely different? Almost all lensing!

My intuition tells me the transit would actually make the companion brighter rather than dimmer exactly because of the lensing effect collecting a larger solid angle of the light from the companion into the forward direction. Essentially microlensing.

This would not be the case for an asteroid.

 

[Vanadium 50]

Given the size of the lens, I expect this is far too small to see in photometry. How do you know its not a sunspot?

 

[sbrothy]

Because a black hole transit would look completely different? Almost all lensing!

Wouldn't this actually be beneficial in this endeavor? I mean the more unique the event and so forth..... But yes, I realize the sheer sizes involved makes "my idea" unrealistic to put it very politely.

 

[Vanadium 50]

Asteroids lens and occult. Black holes lens and occult. Presumably the two have different ratios of the two effects, bit if both are too small to detect, does this difference really matter?

Gravity must make this a lot easier: Gaia BH1 has a companion 10,000x heavier than Jupiter, a little closer in. So the gravitationally induced "wiggle" is 10,000x bigger. Why look at one in a billion effect when you have one that is so much lartger?

 

[Vanadium 50]

I did some more looking at binary star periods. This is non-trivial, as there is a high degree of selection bias, especially for dim stars. But the shortest period exoplanet known has a period of 2 years, and something like 10-15% of binary stars have periods less than this. So my 1% estimate seems close, and if anything, maybe a bit high.

These were mostly small MS stars...because most stars are small, MS stars.

 

[TeethWhitener]

1) The galaxy looks much more like a square than a cube.
2) the center of the galaxy has about 30 times the stellar density of the edge.
Both of these together easily give two orders of magnitude.

 

[Vanadium 50]

The galaxy looks much more like a square than a cube.

Not on the 50ly scale. Or even at the 300 ly scale, which is what you get when you replace the cube with a square.

the center of the galaxy has about 30 times the stellar density of the edge.

Not relevant. To estimate where the nearest BH is, I used the local density, which is appropriate. We can argue if my 5 ly should be 6, but that's the scale. For example, the nearest star to the sun is Alpha Centauri at 4.3 ly; the 2nd nearest star to that is Barnard's Star (6 ly) and the nearest star to that is Ross 154 at 5.4 ly.

If we were living in the galactic center, the nearest BH would likely be closer, but I am estimating what we should see in our own neighborhood.

 

[sbrothy]

It just occured to me that I don't even know how big these BHs are supposed to be. What scale are we talking about?

 

[Vanadium 50]

Stellar-mass black holes are a few km in diameter.

 

[sbrothy]

Stellar-mass black holes are a few km in diameter.

Thanks. But yes, that is peanuts to space.

 

[TeethWhitener]

Seems @Vanadium 50 isn't the only one thinking about this:
https://www.euronews.com/next/2023/...ean Space,light-years from Earth respectively.
My guess is that non-accreting black holes are very very hard to detect, and really their only signature is gravitational, e.g., can only be seen in their action on the dynamics of "nearby" star clusters (as in the paper linked to the news article above).

 

[sbrothy]

For such a stellar mass BH, how big would it's gravitational size of influence be? I mean how far out would it bend space-time?

 

[256bits]

After all, 4 billion years ago the sun was in a region of active star formation, and now, not so much.

Where was the sun, radially speaking, when it formed.
There is radial migration of stars during there lifetime ( and subsequently sBH also, during which some mergers would have occurred decreasing the apparent density ). I think the sun has moved outwards 1000 ly from its formation location.

Having said that, I do quite expect the galaxy evolution to have a bearing on where the older black holes are residing, perhaps in more stable orbits farther out on the order of another 1000 ly or so ( solar is only 4 billion years old ) or on an inward migration path closer to the galactic centre.

Homogenuous star formation, time wise and space wise, all across the galactic disk and bulge most likely not a thing from Milky Way beginnings to now.

 

[Vanadium 50]

Where was the sun, radially speaking, when it formed.

I'm old, but not so old I remember that!

Individual stars move in, out and around. I expect the net effect is one of mixing. I know of no study that suggests we can look at a spiral and tell how old the galaxy is (as opposed to its component stars), so I expect the BH density to still match the star density.

If the BH density does not match the star density, there needs to be some mechanism that treats BH's differently. What is it? It's hard to make it gravotational, as gravity is pretty doggone democratic.

Mergers go as the density squared, so that explanation has a built-in problem for answering the original question. Placing BH's predominantly in binary BH systems would fix the problem, but again, what is the mechanism for that? (You also have an issue with why the progenitor cloud sepaarted into two large symmetric pieces as opposed to the alternatives, but maybe this can be finessed)

 

[Vanadium 50]

For such a stellar mass BH, how big would it's gravitational size of influence be?

Gravity goes out forever.

A related question is "how close to its visblee companion does it have to be to be detectable?" This looks like a few AUs. We see exoplanets with periods of up to two years. A black hole with a similar period would be somewhere between Mars and Jupiter (although Jupiter is pushing it). Hence "a few AUs".

The effect could not be confused with an expolanet. The period of the orbintal perturbation would be the same, but the magnitude would be thousands of times larger.

 

[sbrothy]

Gravity goes out forever.

A related question is "how close to its visblee companion does it have to be to be detectable?" This looks like a few AUs. We see exoplanets with periods of up to two years. A black hole with a similar period would be somewhere between Mars and Jupiter (although Jupiter is pushing it). Hence "a few AUs".

The effect could not be confused with an expolanet. The period of the orbintal perturbation would be the same, but the magnitude would be thousands of times larger.

Gravity goes out forever.

A related question is "how close to its visblee companion does it have to be to be detectable?" This looks like a few AUs. We see exoplanets with periods of up to two years. A black hole with a similar period would be somewhere between Mars and Jupiter (although Jupiter is pushing it). Hence "a few AUs".

The effect could not be confused with an expolanet. The period of the orbintal perturbation would be the same, but the magnitude would be thousands of times larger.

I'm almost sorry I didn't/couldn't vote for you for the "Community Spirit Award". I know how bad you suffer fools. You've been most patient. :)

 

[Vanadium 50]

Start a write-in campaign.

 

[Orodruin]

Stellar-mass black holes are a few km in diameter.

In Schwarzschild radius (or 2x Schwarzschild radius). The actual optical size of a black hole corresponds to a factor $\sqrt{27/4}$ larger disc, making the optical size of a stellar mass black home correspond to that of a disc with about 15 km diameter in a flat spacetime.

The solid angle with relevant sized lensing effect will of course be even larger.

 

[snorkack]

Indeed. Consider Algol B and suppose it were a black hole instead.
The black hole deflects a lot of light at small angles. Which means that there are directions where the light is deflected away from and directions where light is concentrated to. But a lot of deflection merely shifts Algol A. Very little is actually intercepted.
What would Algol lightcurve look like with a black hole B?

 

[Vanadium 50]

correspond to that of a disc with about 15 km diameter in a flat spacetime.

Do you think this is a viable way to spot a BH 50ly away against a star with a diameter of a million km?

 

[Orodruin]

Do you think this is a viable way to spot a BH 50ly away against a star with a diameter of a million km?

Again, I don't think the signal you would be looking for is a decrease in luminosity. I think it is an increase in luminosity from microlensing. The actual effect would have to be computed.

 

[Vanadium 50]

But even an increase - does this sound plausible?

The sun's variability is about 0.15%. To beat that, you need your 15 km (optically) object to concentrate 50,000 km worth of stellar area's light and send it to Earth. To me, this seems implausible - you have an extended source and a small lens. But even if this were correct, I see two problems: one is how you distinguish such an effect from other transients, like flares, and (maybe more importantly) it would make BH's easier to spot, not harder. So it makes the problem worse, not better.

 

[snorkack]

But even an increase - does this sound plausible?

The sun's variability is about 0.15%. To beat that, you need your 15 km (optically) object to concentrate 50,000 km worth of stellar area's light and send it to Earth. To me, this seems implausible - you have an extended source and a small lens.

The lens is huge. Sun deflects light rays passing 700 000 km from Sun by 1,75 seconds. A black hole of 1 solar mass would also deflect light rays passing 700 000 km from it by 1,75 seconds but it would deflect rays that pass closer by a larger angle.

But even if this were correct, I see two problems: one is how you distinguish such an effect from other transients, like flares

That would be by predictable shape of lensing?

 

[mfb]

Can you point me to a reference?

It's more complicated than I remembered. here are some plots. For low mass stars, the smaller star is often much smaller (but they don't form black holes). For O type stars the curve inverts and similar masses are more likely, see figure 4.

For Sirius and Procyon you compared the active stars with the white dwarfs, which lost most of their mass at the end of their life.

It's certainly not a big effect, but binary black holes are another way black holes can disappear from view.

But we've found over a thousand exoplanets this way.

Most exoplanet discoveries came from transits with short orbital periods. You won't find any black holes in these datasets. Most of the remaining discoveries were radial velocity measurements of small sets of stars - finding a black hole there is unlikely, too. Exoplanets are fare more common.

A transit should lead to an increased brightness. Let's look at a 5 solar mass black hole 5 AU away from a star with a radius of 1 million km, directly along our line of sight. Without lensing, the star appears like a disk ~1 million km wide as it passes the black hole. The black hole deflects light at 1 million km distance by 2 r_s/r = 3E-5. Multiplying that by 5 AU we get 22,000 km. If we look 1,022,000 km away from the black hole, we still see the star. If the surface brightness stays the same over most of the area (I don't know if that is true, however) then we would expect a ~4.5% increase in brightness from this effect. To estimate the size of the black area in the center we want a deflection by 1 million km/(5 AU), which we'll get at r = 2 r_s * 5 AU/(1E6 km) = 22,000 km (it's not coincidence that these numbers match). This reduces our light collection by pi*0.022^2 which is much smaller than the 4.5% increase.

Are we likely to see a 4.5% luminosity increase for a few hours that repeats every few years? If we only see it once, we won't be able to identify it as a black hole. We would need to observe the star at least once per day for 10+ years to have a high chance. I'm not aware of projects doing that for many stars. Vera Rubin will observe stars every few days, but that means it'll miss most transits.

 

[Orodruin]

Vera Rubin will observe stars every few days

So there is an afterlife!!

 

[Vanadium 50]

here are some plots.

That paper is discussing wide binaries (which I admit we would not see (part of the 99%) caused by encounters. I am assuming a more general class of binaries. That author is, however, using some of the data I used in my estimate (Duquennoy).

Also, O-type stars have a natural tendency to be the same mass. Too heavy, and they don't last long and/or shed mass. Too light and they are B's. You could say that about all stars, but spectral class O doesn't fo from 0 to 9 like the others. O2 is as high as it goes, and there weren't any discovered when I was in grad school. (There were a handful of O3's -- but for all intents and purposes, O's go from O5 to O9)

Since we're discussing progenitor masses, it's fair to say this is not well understood. I think it's fair to say that the minimum mass is not fully understood, especially in binary systems where mass transfer is a possibility. LIGO has seen a deficit in small (<5 solar mass) BH mergers - this may be the same puzzle. If you need a heavy progenitor to make a heavy black hole, the number of black holes goes down, so the nearest ones are farther away.

"Where are they?" would then have the simple answer "We never made them to begin with".

 

[Vanadium 50]

As far as lensing and photometry, 4/5% should be observable. However, no new light is created - so you are depleting some other portion of the light curve. That may actually help, as peak-to-trough goes up. It may hurt, in that you may need an unusually good alignment and/or a short observation time to make this all work out. Certainly if you need many repetitions your observing time goes way up.

Once your observing time goes up, I think you are better off with spectroscopy. That's unambiguous.