<p>There can be no closer white dwarf. The <a href="https://public.nrao.edu/news/pressreleases/cold-white-dwarf" rel="noreferrer">coolest, oldest</a> white dwarfs (3000K), would be rare, but are still luminous enough <span class="math-container">$6\times10^{-6} L_{\odot}$</span> to have been easily detected at distances closer than Sirius. At the distance of Sirius, such an object would have a visual magnitude of around 12-13 and would be brighter at near infrared wavelengths where all sky surveys such as 2MASS would definitely have spotted it from its parallax.</p>

<p>Neutron stars and black holes could be almost undetectable but are expected to be roughly 10 and 100 times rarer respectively. Calculated as follows:</p>

<p>Let us assume that <span class="math-container">$N$</span> stars have ever been born in the Milky Way galaxy, and given them masses between 0.1 and 100<span class="math-container">$M_{\odot}$</span>. Next, assume that stars have been born with a mass distribution that approximates to the Salpeter mass function - <span class="math-container">$n(m) \propto m^{-2.3}$</span>. Then assume that all stars with mass <span class="math-container">$m&gt;25M_{\odot}$</span> end their lives as black holes, all stars with <span class="math-container">$8&lt;m/M_{\odot}&lt;25$</span> end their lives as neutron stars and about <em>half</em> the stars with <span class="math-container">$0.9&lt;m/M_{\odot}&lt;8$</span> end their lives as white dwarfs (the other half are still alive as main sequence stars, as are all stars born with lower masses).</p>

<p>So, if <span class="math-container">$n(m) = Am^{-2.3}$</span>, then
<span class="math-container">$$N = \int^{100}_{0.1} A m^{-2.3}\ dm$$</span>
and thus <span class="math-container">$A=0.065N$</span>.</p>

<p>The number of black holes created will be 
<span class="math-container">$$N_{BH} = \int^{100}_{25} Am^{-2.3}\ dm = 6.4\times10^{-4} N$$</span>
i.e 0.064% of stars in the Galaxy become black holes. NB: The finite lifetime of the galaxy is irrelevant here because it is much longer than the lifetime of black hole progenitors. </p>

<p>In a similar way, the number of neutron stars 
<span class="math-container">$$N_{NS} = \int^{25}_{8} Am^{-2.3}\ dm = 2.6\times10^{-3}N$$</span>
and the number of white dwarfs
<span class="math-container">$$N_{WD} = 0.5\times \int^{8}_{0.9} Am^{-2.3}\ dm = 0.027 N$$</span></p>

<p>Now we use these results as scaling factors to apply to the local stellar population. There are about 1000 "normal" stars in a sphere of 15 pc radius, thus a density of 0.07 pc<span class="math-container">$^{-3}$</span>. Thus one uses the results above to calculate the density of compact remnants and then take <span class="math-container">$(3/4\pi n)^{1/3}$</span> as an estimate of the average distance to one of them. This gives an expectation value of 18 pc to the nearest black hole, 11 pc to the nearest neutron star and 5 pc to the nearest white dwarf.</p>

<p>Thus the distance to the nearest white dwarf is roughly as expected. For reasons discussed in <a href="http:///astronomy.stackexchange.com/questions/4725/statistically-what-would-the-average-distance-of-the-closest-black-hole-be" rel="noreferrer">my answer to this related question</a> the distance calcuated to the nearest black hole and neutron star remnants is likely to be an <em>underestimate</em> because many escape from the Galaxy or have very high velocity dispersions and much larger Galactic scale heights than normal stars. So whilst it is <em>possible</em> that an unseen one exists closer than Sirius, it is highly unlikely.</p>

<p>How could such an object be detected? An old, cold neutron star or black hole could be completely undetectable at all wavelengths of electromagnetic radiation - though it could be fruitful to examine carefully any candidate detections [see below] for signs of X-ray emission due to accretion from the interstellar medium). But your question has I think the correct suggestion. The objects would likely have a substantial proper motion and so there is a decent chance that you would see a "moving" gravitational lensing signature. This would still be very small unless the object just happened to pass directly in front of a background star - but such a microlensing event would be transient and may not be observed. More likely is that Gaia would pick up the subtle shifts in the positions of background stars changing over the 5 years of its mission. As per your other question: <a href="https://astronomy.stackexchange.com/questions/16578/will-gaia-detect-inactive-neutron-stars?rq=1">Will Gaia detect inactive neutron stars?</a></p>

CC BY-SA 4.0
2019-10-16T13:40:39.517Z
I think there's a small error in lower bound of the integral for $N_\mathrm{WD}$; shouldn't it be 0.9 rather than 1, according to what you write in the beginning (and according to your result of 0.027). But why do you start at 0.9, and not at 0.1? Is it because stars of M<0.9 are _all_ assumed to be still on the MS?
pela
CC BY-SA 4.0
2019-10-16T14:28:03.560Z
Yes, it should be 0.9. Of course it is (slightly) composition dependent. The lower limit is indeed set by the lifetime on the main sequence. Lower mass stars are not white dwarfs (yet) - that is spelled out in the brackets at the end of para. 3.
ProfRob
CC BY-SA 4.0
2019-10-16T14:56:58.643Z
Ah yes, sorry, I missed the "_…as are all stars born with lower masses_". Thanks! And yes, a shallower IMF at low masses would yield a smaller number of WDs. But I thought actually the number was larger? Salpeter assumed 10% WDs, but that's probably outdated. Do you happen to have any references for observed numbers?
pela
CC BY-SA 4.0
2019-10-16T16:46:18.083Z
@Pela Well the mass function isn't Salpeter down to the lowest masses and so low mass stars are over-represented in my calculation I expect. I could do something more realistic and it might bump the WD density up by a factor of 2, but wouldn't change the NS and BH numbers.
ProfRob
CC BY-SA 4.0
2019-10-16T16:47:49.290Z
Yes, that's what I meant. Anyway, thanks for a great answer.
pela
CC BY-SA 4.0
2016-07-23T09:42:16.333Z
2019-10-16T14:28:33.620Z
2019-10-16T14:28:33.620Z
ProfRob
<p>Neutron stars and black holes are hard to detect when they are solitary, and there seems to be big uncertainties about how common they are. White dwarfs are much easier to detect and the nearest one is Sirius B only 2.6 parsec from here. Should we expect to have exotic company even closer by? How likely is it that we have a yet undetected compact star remnant nearby, as in as close as our nearest active star? What are the odds of spotting one of them nearby?</p>

<p>How could a yet undetected one be discovered? Could one of the upcoming sky surveying telescopes catch it or would one have to rely on a rare microlensing event? How would it then be observed? Would such an exotic object, say, just one parsec away, give important insights in physics given its relativistic effects and strange composition?</p>

CC BY-SA 3.0
2016-07-23T10:38:41.967Z
related: http://astronomy.stackexchange.com/questions/4725/statistically-what-would-the-average-distance-of-the-closest-black-hole-be
ProfRob
<black-hole><observational-astronomy><neutron-star>
How far away is the nearest compact star remnant likely to be?
LocalFluff
# How far away is the nearest compact star remnant likely to be?

(Asked by: username_0 on 2016-07-23)

Neutron stars and black holes are hard to detect when they are solitary, and there seems to be big uncertainties about how common they are. White dwarfs are much easier to detect and the nearest one is Sirius B only 2.6 parsec from here. Should we expect to have exotic company even closer by? How likely is it that we have a yet undetected compact star remnant nearby, as in as close as our nearest active star? What are the odds of spotting one of them nearby?

How could a yet undetected one be discovered? Could one of the upcoming sky surveying telescopes catch it or would one have to rely on a rare microlensing event? How would it then be observed? Would such an exotic object, say, just one parsec away, give important insights in physics given its relativistic effects and strange composition?

**Tags:** black-hole, observational-astronomy, neutron-star

> **Comments:**
> **username_1**: related: http://astronomy.stackexchange.com/questions/4725/statistically-what-would-the-average-distance-of-the-closest-black-hole-be  

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## 1 answers

### Answer by username_1 on 2016-07-23. Score: 18 | Accepted answer

There can be no closer white dwarf. The [coolest, oldest](https://public.nrao.edu/news/pressreleases/cold-white-dwarf) white dwarfs (3000K), would be rare, but are still luminous enough $6\times10^{-6} L\_{\odot}$ to have been easily detected at distances closer than Sirius. At the distance of Sirius, such an object would have a visual magnitude of around 12-13 and would be brighter at near infrared wavelengths where all sky surveys such as 2MASS would definitely have spotted it from its parallax.

Neutron stars and black holes could be almost undetectable but are expected to be roughly 10 and 100 times rarer respectively. Calculated as follows:

Let us assume that $N$ stars have ever been born in the Milky Way galaxy, and given them masses between 0.1 and 100$M\_{\odot}$. Next, assume that stars have been born with a mass distribution that approximates to the Salpeter mass function - $n(m) \propto m^{-2.3}$. Then assume that all stars with mass $m>25M\_{\odot}$ end their lives as black holes, all stars with $8<m/M\_{\odot}<25$ end their lives as neutron stars and about *half* the stars with $0.9<m/M\_{\odot}<8$ end their lives as white dwarfs (the other half are still alive as main sequence stars, as are all stars born with lower masses).

So, if $n(m) = Am^{-2.3}$, then
$$N = \int^{100}\_{0.1} A m^{-2.3}\ dm$$
and thus $A=0.065N$.

The number of black holes created will be
$$N\_{BH} = \int^{100}\_{25} Am^{-2.3}\ dm = 6.4\times10^{-4} N$$
i.e 0.064% of stars in the Galaxy become black holes. NB: The finite lifetime of the galaxy is irrelevant here because it is much longer than the lifetime of black hole progenitors.

In a similar way, the number of neutron stars
$$N\_{NS} = \int^{25}\_{8} Am^{-2.3}\ dm = 2.6\times10^{-3}N$$
and the number of white dwarfs
$$N\_{WD} = 0.5\times \int^{8}\_{0.9} Am^{-2.3}\ dm = 0.027 N$$

Now we use these results as scaling factors to apply to the local stellar population. There are about 1000 "normal" stars in a sphere of 15 pc radius, thus a density of 0.07 pc$^{-3}$. Thus one uses the results above to calculate the density of compact remnants and then take $(3/4\pi n)^{1/3}$ as an estimate of the average distance to one of them. This gives an expectation value of 18 pc to the nearest black hole, 11 pc to the nearest neutron star and 5 pc to the nearest white dwarf.

Thus the distance to the nearest white dwarf is roughly as expected. For reasons discussed in [my answer to this related question](http:///astronomy.stackexchange.com/questions/4725/statistically-what-would-the-average-distance-of-the-closest-black-hole-be) the distance calcuated to the nearest black hole and neutron star remnants is likely to be an *underestimate* because many escape from the Galaxy or have very high velocity dispersions and much larger Galactic scale heights than normal stars. So whilst it is *possible* that an unseen one exists closer than Sirius, it is highly unlikely.

How could such an object be detected? An old, cold neutron star or black hole could be completely undetectable at all wavelengths of electromagnetic radiation - though it could be fruitful to examine carefully any candidate detections [see below] for signs of X-ray emission due to accretion from the interstellar medium). But your question has I think the correct suggestion. The objects would likely have a substantial proper motion and so there is a decent chance that you would see a "moving" gravitational lensing signature. This would still be very small unless the object just happened to pass directly in front of a background star - but such a microlensing event would be transient and may not be observed. More likely is that Gaia would pick up the subtle shifts in the positions of background stars changing over the 5 years of its mission. As per your other question: [Will Gaia detect inactive neutron stars?](https://astronomy.stackexchange.com/questions/16578/will-gaia-detect-inactive-neutron-stars?rq=1)

> **Comments:**
> **username_2**: I think there's a small error in lower bound of the integral for $N_\mathrm{WD}$; shouldn't it be 0.9 rather than 1, according to what you write in the beginning (and according to your result of 0.027). But why do you start at 0.9, and not at 0.1? Is it because stars of M<0.9 are _all_ assumed to be still on the MS?  
> **username_1**: Yes, it should be 0.9. Of course it is (slightly) composition dependent. The lower limit is indeed set by the lifetime on the main sequence. Lower mass stars are not white dwarfs (yet) - that is spelled out in the brackets at the end of para. 3.  
> **username_2**: Ah yes, sorry, I missed the "_…as are all stars born with lower masses_". Thanks! And yes, a shallower IMF at low masses would yield a smaller number of WDs. But I thought actually the number was larger? Salpeter assumed 10% WDs, but that's probably outdated. Do you happen to have any references for observed numbers?  
> **username_1**: @username_2 Well the mass function isn't Salpeter down to the lowest masses and so low mass stars are over-represented in my calculation I expect. I could do something more realistic and it might bump the WD density up by a factor of 2, but wouldn't change the NS and BH numbers.  
> **username_2**: Yes, that's what I meant. Anyway, thanks for a great answer.  

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