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

[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.

 

[Bosko]

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

I believe they are around, but we haven't detected most of them yet.
They seem like the best candidate for dark matter to me.

I'm a mathematician, so maybe some of the following thinking isn't quite right:

We have stars that are larger than several solar masses.
The bigger they are, the faster they burn hydrogen, helium, silicon, C-N-O... and so on until iron, so they live shorter than smaller stars.

Eventually they explode as supernovae and the explosion itself may clear the surrounding space of some of the smaller objects.

The black hole continues to move around the galactic center at the same speed and in the same place where the large star once was.

It does not emit any radiation and is relatively small in size.

It may be possible to estimate how many there are in total, how they are distributed compared to other objects in our galaxy, and as a percentage of the total number, what is the expected mass.

 

[Vanadium 50]

If you want stellar-mass black holes to be dark matter, you need 1000x as many of them. Then you need to really explain why don't see more. Then you also have to explain why they preferentially populate the halo, a region that has never seen high rates of star formation. Then you need to explain whyu LIGO doesn't see mergers - 10,000x as many means 100,000,000 as many mergers. Then you have to explain why there is no diffuse x-ray background coming from these halo holes, and why we don't see gravitational lensing from them.

I might have forgotten some. But this looks really tough to make work.

 

[timmdeeg]

In addition the Milky Way is thought to be within a much larger halo of dark matter. Very unlikely that stellar black holes are out there.

 

[Orodruin]

They seem like the best candidate for dark matter to me.

They would be so-called MACHOs (Massive Compact Halo Objects). That they form (all of the) dark matter is excluded by Milky Way microlensing searches.

They would also fail to explain the dark matter impact on the early Universe.

 

[Vanadium 50]

And, at the risk of piling on, if you had DM as former stars, you run into problems with Big Bang nucleosynthesis, with lithium abundance (why is there any left?) and with remnant red dwarfs of which there should be a zillion.

 

[Bosko]

If you want stellar-mass black holes to be dark matter, you need 1000x as many of them. Then you need to really explain why don't see more.

They will be on average 10x closer and without detection ... only by gravity ...
I'm just thinking:
What else could it be?
How big were the first stars (after the Big Bang)
How many of them became black holes?
How was the black hole in the center of our galaxy (4 million suns) formed...

Then you also have to explain why they preferentially populate the halo, a region that has never seen high rates of star formation.

What else could it be?
I'm just guessing...
If we apply Gauss's law of gravity to the curved space-time of general relativity.
Then the approximation by classical Newton's gravity would not be precise enough.
Simplified...
$$g= \frac {GM} {r^2} \frac {4\pi} {4\pi}$$
What if the surface of the sphere deviates significantly from the surface of the sphere in flat space $4r^2\pi$. Especially when calculating g in the galactic plane.

you need to explain whyu LIGO doesn't see mergers - 10,000x as many means 100,000,000 as many mergers. Then you have to explain why there is no diffuse x-ray background coming from these halo holes, and why we don't see gravitational lensing from them.

I might have forgotten some. But this looks really tough to make work.

I tried ... :-)

 

[Vanadium 50]

What else could it be?

This is a terrible argument. There are already three messages showing that this does not fit the data. Further, one can use the same argument for any theory - "maybe invisible pink unicorns are dark matter. After all, what else could it be?"

Oh, it could be supersymmetry, axions, sterile neutrinos, shadow matter, dark photons, non-SUST WIMPs, modified gravity....

But it is not composed of stellar mass black holes. Previous messages explained why.

 

[Bosko]

They would be so-called MACHOs (Massive Compact Halo Objects). That they form (all of the) dark matter is excluded by Milky Way microlensing searches.

I wonder what would be obtained if a curved space-time were constructed in accordance with the measured values of gravity.

They would also fail to explain the dark matter impact on the early Universe.

I'm looking for an explanation of the influence of dark matter on the early Universe... I didn't know.
Thanks

 

[Orodruin]

What else could it be?

A lot of different things. There is a veritable plethora as mentioned above.

I wonder what would be obtained if a curved space-time were constructed in accordance with the measured values of gravity.

Huh? The galactic scale gravity is very weak. You will not get an appreciable difference to Newtonian gravity.

I'm looking for an explanation of the influence of dark matter on the early Universe... I didn't know.
Thanks

There are many. Some have already been mentioned above. Nucleosynthesis, the CMB spectrum, structure formation, etc. They all depend on the dark matter being present at the corresponding eras.

 

[Bosko]

This is a terrible argument...

I'm not trying to defend my position.
I'm just asking myself.
If there are not enough arguments for a good explanation, I look at where it most likely could be.