# What is the mean separation between a star and its closest neighbor in the Milky Way halo?

My question is inspired by this previous question, Are there any stars that orbit perpendicular to the Milky Way's galactic plane?. In the great answer posted by @ConnorGarcia, one commenter said he would be really jealous of anybody that could see the view of the Milky Way from close to the galactic poles, since a star stream passes close to them. I think, on the flip side, they would envy us due to their near complete isolation. Space travel outside their home system would be much harder, for example. Here on the galactic plane, near the Sun, I guess the average distance to the closest nighboring star is about ~10 Ly or less. The Alpha Centauri system is about 4 Ly away, for example. Regarding the galactic halo, I guess if we picked a random star there, its closest neighbor would be probably located > 100 Ly away. Is this estimate reasonable? Are there reliable figures on that?

I did some rough calculations, and 100 light-years doesn't seem to be a bad guess. If we assume that the average mass of a halo star is $$\sim0.3M_{\odot}$$, as would be expected for a typical IMF, and that the total stellar halo mass is $$\sim10^9M_{\odot}$$ (Deason et al. 2019), then we should expect there to be $$\sim3.3\times10^9$$ halo stars.$$^{\dagger}$$ The halo extends to somewhere near 100 kpc, so if we take it to be roughly spherica-ishl, this leads to an average number density of $$n\approx\frac{3.3\times10^9\;\text{stars}}{\frac{4\pi}{3}(100\;\text{kpc})^3}\approx7.9\times10^{-7}\;\text{pc}^{-3}$$ and a mean inter-star distance of $$l\approx n^{-1/3}\approx108\;\text{pc}$$. So my back-of-the-envelope result differs from yours by only a factor of 3.

Now, the halo has a distinctly non-uniform density. It follows a power law of $$r^{-n}$$, with an index somewhere near $$n\approx3$$. Different surveys have yielded values ranging from $$2.5\lesssim n\lesssim 3.5$$ (ish), depending on the methodology and groups studied. The upshot is that in the outer halo, you'll certainly see much larger separations, whereas closer to the Galactic plane, you could see densities perhaps within a couple orders of magnitude of disk populations.

$$^{\dagger}$$Two things: First, the halo population's mass function should be different than a typical IMF, because it's composed largely of aging Population II stars - but I think $$0.3M_{\odot}$$ is still reasonably close. Second, I also checked the number by actually integrating via a Kroupa IMF (normalizing by total halo mass), (and again, maybe not a totally accurate distribution) and found a value within a factor of 2 of 3.3 billion.

## About 300 light years

Wolfram has previously informed me that if our planet is as big as a flea (1MM), the sun is as big as a pigeon (11CM), the average distance of milky way halo stars is 25000 KM, and the milky way would be as big as the solar system, the disk stars would be about 3700 KM distance.

If the milky way galaxy was as big as the solar system, then it would be filled with 200 billion pigeons and birds (Stars) flying at 8CM/H with an average distance of 25000KM from each other... rare close approches of 160KM of two pigeons would happen every million years in the disk zone, it would be the flea's opportunity to go star-hopping. (i.e. Gliese 71 will approach in 1.2 million years at 0.22 light years / 0.06 parsecs).

• Given HDE 226868's calculation, I must admit that converting back and forth between stars and pigeons seems a bit… complicated? Also, your numbers refer to disk stars, not halo stars; there's most definitely not 5 lyr between those.
– pela
Mar 19 '21 at 8:29
• Oh right, I had just edited it and found 250000km which corresponds to 300 light years which was right and i corrected the question wrong. well spoted. It's very easy to convert to stars to bird sizes using wolfram, I just do 1/earth diameter * sun diameter = pigeon :) They do a lot of that kind of comparison on TV shows and for things like evolution, you know, the last note of the piano of geological timescale is the paleogene. Mar 19 '21 at 19:10