I How close is Earth to the closest black hole?

[mfb]

We know 60 black holes in our galaxy today.

Gaia is expected to find a few thousand. It is basically guaranteed that many of them will be closer than the currently closest known.
As these are double systems, we might have to wait for the final data release, 2022-2024.

 

[stefan r]

... find a few thousand. ...

I the article

https://www.sciencenews.org/article/we-share-milky-way-100-million-black-holes​

says

The Milky Way teems with black holes — about 100 million of them.​

...

The arxiv article says 10⁵ black holes in the milky way. Did someone miss by x10³?

 

[mfb]

That is a good question. Both numbers are recent, and a factor 1000 is large even for astrophysical uncertainties.

Gaia will measure roughly 1% of the stars in our galaxy, measuring O(1%) of the black holes in binary systems doesn't look unreasonable.

 

[Buzz Bloom]

The arxiv article says 10⁵ black holes in the milky way. Did someone miss by x10³?

Hi stefen:

Here is a quote from the https://arxiv.org/pdf/1703.02551.pdf article.
... a galaxy like the Milky Way should host millions of ∼30M_sun black holes ...
I confess that the bulk of the article is over my head. However, Figure 2 seems to show the basis for estimating the MW BHs.
https://en.wikipedia.org/wiki/Milky_Way says the mass of the MW is ~10¹² solar masses.

As I read this chart, the black line gives the number of BHs of mass greater than 10 solar masses. The X-axis shows the mass of a galaxy. One has to extrapolate the black line since the max Y-axis value is 10⁸.

Regards,
Buzz

 

[Buzz Bloom]

Out of curiosity, Buzz, what are the median and quartile distances?

Hi JMz:

I will have to go back and explore the Monte Carlo data. It will try to post the answer later today or tomorrow.

Regards,
Buzz

 

[Buzz Bloom]

Gaia is expected to find a few thousand.

Hi mfb:

Thanks very much for the link. The previous abstract about GAIA failed to mention anything about finding black holes.

Regards,
Buzz

 

[snorkack]

That is a good question. Both numbers are recent, and a factor 1000 is large even for astrophysical uncertainties.

The article contains a bland statement that most black holes should be binaries with a luminous partner.

Absurd on its face.

Luminous stars are short lived. A great majority of black holes should not have a luminous partner now, even if they had one at some point of evolution.

 

[mfb]

The article contains a bland statement that most black holes should be binaries with a luminous partner.

Absurd on its face.

Luminous stars are short lived. A great majority of black holes should not have a luminous partner now, even if they had one at some point of evolution.

Why do you expect binary stars to have symmetric masses?

 

[snorkack]

Why do you expect binary stars to have symmetric masses?

I did not.

On closer examination, it turns out that the article does interpret "luminous" apparently to mean "giving off any, even small amount of light", and expressly considers binaries of black hole and low mass old main sequence star - although these are hard to detect.

So: binary systems of a black hole and a massive star should commonly form, but are short-lived.
Binary systems of a black hole and a low mass main sequence star may form less often, but then last longer.

 

[stefan r]

Hi mfb:

Thanks very much for the link. The previous abstract about GAIA failed to mention anything about finding black holes.

Regards,
Buzz

I believe all the black holes GAIA will find have luminous companions. Gaia is looking at momentum and position.

Why do you expect binary stars to have symmetric masses?

There is this paper

...massive stars preferentially have massive companions...

If they came from the same cloud at the same time my first guess would be somewhat similar stars form. They have nearly identical metalicity and were probably kick started by the same shockwave. Most of the poster image open clusters are all the same color. The small dim companions do not show up as well in the poster so that is not an accurate measurement. In pictures of stellar nurseries like Orion nebula you have a group of B and O stars blowing material away and smaller stars forming in the remnants. Again that is not statistical evidence but would be a good first guess.

 

[Buzz Bloom]

Hi @JMz:

I have looked over my spreadsheet and my source articles, and I have decided I need to make some revisions, primarily because some of the more recently found references seem to be more reliable. When I complete this, I will report the means and standard deviations as well as quartile numbers with standard deviations from multiple Monte Carlo runs.

I have listed below the various variable values I will use in the next version, and the sources for the data, as well as a few comments.

https://www.sciencenews.org/article/we-share-milky-way-100-million-black-holes
It is difficult to judge from this abstract any range and confidence limits.
However, I guess that it is plausible to assume that the 1 sigma base 10 logarithmic stdev is 0.5

https://en.wikipedia.org/wiki/Milky_Way#Size_and_mass​

The total mass of all the stars in the Milky Way is estimated to be between
4.6×10¹⁰ M☉ and 6.43×10¹⁰ M☉.
Average: 5.515 10¹⁰ M☉.
Stdev = 1.3 10¹⁰ M☉.
Geometric average: 5.44 10¹⁰ M☉.

https://en.wikipedia.org/wiki/Stellar_classification​

Average mass of a MW star is 0.54 M☉.
Estimated number of stars: 10 +/- 2.4 x 10¹⁰ M☉ or 10^{11 +/- log₁₀(2.4)}
It is not clear whether I should consider this to be a Gaussian distribution, or the logarithm to be a Gaussian distribution.
Estimated number of stars per BH = 1000 - Stdev to be calculated.

http://www.atlasoftheuniverse.com/12lys.html​

33 stars within 12.5 ly (bigger than brown dwarfs)
1000 stars at this density would require a sphere of radius (1000/33)^(1/3) * 12.5 = 39 ly.
Average distance from center for a random point is 39 * 3/4 ~= 29 ly.

Regards,
Buzz

 

[JMz]

Hi @JMz:

I have looked over my spreadsheet and my source articles, and I have decided I need to make some revisions, primarily because some of the more recently found references seem to be more reliable. When I complete this, I will report the means and standard deviations as well as quartile numbers with standard deviations from multiple Monte Carlo runs.

I have listed below the various variable values I will use in the next version, and the sources for the data, as well as a few comments.

https://www.sciencenews.org/article/we-share-milky-way-100-million-black-holes
It is difficult to judge from this abstract any range and confidence limits.
However, I guess that it is plausible to assume that the 1 sigma base 10 logarithmic stdev is 0.5

https://en.wikipedia.org/wiki/Milky_Way#Size_and_mass​

The total mass of all the stars in the Milky Way is estimated to be between
4.6×10¹⁰ M☉ and 6.43×10¹⁰ M☉.
Average: 5.515 10¹⁰ M☉.
Stdev = 1.3 10¹⁰ M☉.
Geometric average: 5.44 10¹⁰ M☉.

https://en.wikipedia.org/wiki/Stellar_classification​

Average mass of a MW star is 0.54 M☉.
Estimated number of stars: 10 +/- 2.4 x 10¹⁰ M☉ or 10^{11 +/- log₁₀(2.4)}
It is not clear whether I should consider this to be a Gaussian distribution, or the logarithm to be a Gaussian distribution.
Estimated number of stars per BH = 1000 - Stdev to be calculated.

http://www.atlasoftheuniverse.com/12lys.html​

33 stars within 12.5 ly (bigger than brown dwarfs)
1000 stars at this density would require a sphere of radius (1000/33)^(1/3) * 12.5 = 39 ly.
Average distance from center for a random point is 39 * 3/4 ~= 29 ly.

Regards,
Buzz

This is turning into a substantial project for you, isn't it? :-)
FWIW, log-Normal will give virtually the same answers as Normal, because the SD is not large compared to the mean. (And if log-N isn't close enough to right, then the right answer is almost dependent on observational and model uncertainties in the published research, so a Normal will likely be even further from the mark.)

 

[Buzz Bloom]

FWIW, log-Normal will give virtually the same answers as Normal, because the SD is not large compared to the mean.

Hi JMz:

I will accept your advice and calculate the variables as log normal.

Regards,
Buzz

 

[Buzz Bloom]

Out of curiosity, Buzz, what are the median and quartile distances?

Hi JMz:

I completed the revised spreadsheet, and I used the Box-Muller method for generating Gaussian random numbers.

Input values

33 stars with 12.5 ly - assumed this was a good approximation of star population density in the Earth region.

http://www.atlasoftheuniverse.com/12lys.html
​

N_BH = random number of BHs in MW is a log Gaussian distribution.
log₁₀ N_BH = 8 +/- 0.5

https://www.sciencenews.org/article/we-share-milky-way-100-million-black-holes
​

The total mass of all the stars in the Milky Way is estimated to be between
Mstars[/SUB = 4.6×10^10 M☉ and 6.43×10^10 M☉.
M_stars random number of the mass of stars (stellar mass units) in MW is a log Gaussian distribution.

https://en.wikipedia.org/wiki/Milky_Way#Size_and_mass​

Average mass of a MW star is 0.54 M☉.
https://en.wikipedia.org/wiki/Stellar_classification

N_stars random number of stars in MW is a log Gaussian distribution.
N_stars = M_stars / 0.54
log₁₀ N_stars = 10^(11 +/-0.11) M☉.
ρ = N_stars / N_BH
ρ is also a log Gaussian distribution.
log₁₀ ρ = 3 +/- √(0.5² + 0.11²) = 3 +/- 0.512.

Monte Carlo

I generated 25 runs of 100 random numbers for ρ. I sorted each run of 100 to get percentile values.
I calculated the m=average, and std=standard deviations for each percentile from the 25 runs.
I will report below these m and std values for the following percentiles:

16, 25, 50, 75, 84.​

The 16th and 84th percentile values would correspond to to m-std and m+std for a Gaussian distribution rather than a log Gaussian distribution.

R = 12.5 × (ρ/33)^1/3
I also calculated values m, m-std and m+srd corresponding to 10³, 10^2.488, and 10^3.512 values of ρ.

For each of these eight ρ values, I calculate the corresponding radius R of a sphere containing the corresponding number of stars, and the average distance D to a point in the sphere from the center.
D = 3 R / 4

Regards,
Buzz

 

[JMz]

The only question that comes to mind (beyond previously mentioned stellar-evolution & galaxy-evolution questions that might influence our expectations of BH density vs. position in the MW) is: You cite 0.54 M_☉ as the MW mean, but does that closely match the mean for the stars in the local neighborhood, 12 LY? I am just wondering if there is a selection effect. (Obviously, we have known about all the bright nearby stars since antiquity, but not the fainter ones.)

My guess is, Yes, over that distance, we know them all. But if there were a selection effect, it would favor brighter stars, for which there would be far fewer in the MW as a whole, so the BH/star ratio would need to be adjusted upward. But even that is surely just a minor adjustment: Even a large adjustment will only change the distance estimate by a cube root.

 

[Buzz Bloom]

You cite 0.54 M☉ as the MW mean, but does that closely match the mean for the stars in the local neighborhood, 12 LY?

Hi JMz:

That's a good question, but I will need a break for a while before I can explore it.

The list of the 33 stars with their characteristics is in
http://www.atlasoftheuniverse.com/12lys.html .
The data I use to arrive 0.54 is in
https://en.wikipedia.org/wiki/Stellar_classification .

If you have the time you might get the characteristics for each of 33 stars, and look up the mass for each type, and calculate their average mass.

Regards,
Buzz

 

[JMz]

Hi JMz:

That's a good question, but I will need a break for a while before I can explore it.

The list of the 33 stars with their characteristics is in
http://www.atlasoftheuniverse.com/12lys.html .
The data I use to arrive 0.54 is in
https://en.wikipedia.org/wiki/Stellar_classification .

If you have the time you might get the characteristics for each of 33 stars, and look up the mass for each type, and calculate their average mass.

Regards,
Buzz

A quick check: Another link on the first page you listed is http://www.atlasoftheuniverse.com/nearstar.html, which gives spectral class and lists them in order of distance. The ones closer than 12 LY (and even the rest within 20 LY) are overwhelmingly class M or sometimes K. These are all low-mass stars (no red giants to complicate the relationship to spectral class). So I do believe that they are typical of the average mass in the MW, about 1/2 solar.

 

[QuasBlackWorm MIT]

But I really hope Proxima Centauri implodes oh itself and becomes a black hole soon
That should make my field of science much more interesting

 

[mfb]

It won't. Proxima Centauri will live for many billion years and then become a white dwarf.

 

[JMz]

It won't. Proxima Centauri will live for many billion years and then become a white dwarf.

In fact, this suggests a time scale that greatly understates Proxima's lifetime. It is estimated that it will last 5 to 10 trillion years. (And no black hole, ever.)