# Why are stars so far apart?

So, this is mere musing, but it seems that stars are quite extremely far apart. I tried to determine the mean distance between nearest neighbors for stars (in just our galaxy) but I'm not sure what it is, though a first approximations I would guess that the mean is around 5 ly with some 0.5 standard deviation or so!

However, assuming I didn't screw up, the distance between two sun-massed objects required to generate 1,000N of force between them is an incredible 54.3 million ly.  If you change that to 1 billion Newtons, the distance is one galactic radius -- 54000~ ly!

I'm probably mis-estimating how much even 1kN of force would effect solar trajectories over time, but I still can't help but feel that our solar neighbors are very far away given the spheres of interaction that I would expect.

Any insights?

• This force is why Sun revolves around the galactic center of mass. – Mithoron Mar 4 '15 at 0:55
• Favorite counterexample: "The average star density in a Globular Cluster is about 0.4 stars per cubic parsec. In the dense center of the cluster, the star density can increase from 100 to 1000 per cubic parsec." astro.keele.ac.uk/workx/globulars/globulars.html – Wayfaring Stranger Jun 23 '16 at 16:15

Most stars are of a solar-mass or below. The average number of companions that each stars has (in the sense of being part of binary or higher multiple systems) systems ranges from 0.75 for stars of a solar mass to approximately 0.35 (not a well-established number) for the more numerous M-dwarfs. Let's take a compromise value, say 0.5. The separation distribution of these multiples peaks at around 50 AU for solar-type stars, reducing to about 5 AU for low-mass M dwarfs. Again, lets take a compromise value of 20 AU. See Duchene & Kraus (2013) for all the details.

So if we take 1000 stars, then 333 of them (roughly speaking) are companions to another 333 stars, while 333 are isolated single stars. (NB This does not mean the frequency of multiple systems is 50%, because some of the companions will be in higher order multiple systems)

Thus, taking your calculation of the separation between stellar systems of 5 light years ($= 3.2\times10^{5}$ AU), then the mean separation is: $$\bar{D} = 0.667\times 20 + 0.333 \times 3.2\times10^{5} \simeq 10^{5} AU,$$ but the median separation is 20 AU!

This is of course sophistry, because I'm sure your question is really, why are stellar systems so far apart?

Stars (and stellar systems) are born in much denser environments. The number density of stars in the Orion Nebula Cluster (ONC - the nearest very large stellar nursery) is about 1 per cubic light year. The equivalent number for the solar neighbourhood is 0.004 stars per cubic light year. Thus the average interstellar separation in the ONC is 1 light year, but in the solar neighbourhood it is about 6.3 light years.

The reason for this separation at birth is the Jeans length - the critical radius at which a clouds self-gravity will overcome its thermal energy and cause it to collapse. It can be expressed as $$\lambda_J = c_s \left( \frac{\pi}{G\rho } \right)^{1/2},$$ where $c_s$ is the sound speed in a molecular cloud and $\rho$ its density. For star forming giant molecular clouds $c_s = 0.2$ km/s and $\rho=10^{-23}$ kg/m$^3$. So clouds of scale hundreds of light years could collapse. As they do, the density increases and the Jeans length becomes smaller and allows the cloud to fragment. Exactly how far the fragmentation goes and the distribution of stellar masses it produces is an area of intense research, but we know observationally that it can produce things like the ONC or sometimes even more massive and dense clusters.

From there we know that a new born cluster of stars tends not to survive very long. For various reasons - outflows, winds and ionising radiation from newborn stars are able to heat and expel the remaining gas; star formation appears to have an average efficiency of a few to perhaps 20-30%. Expelling the gas, plus the tidal field of the galaxy breaks up the cluster and disperses it into the field, which gives us the lower field star (or system) density that we see around us.

Once the stars are part of the field they essentially don't interact with each other; they are too far apart to feel the influence of individual objects and move subject to the overall gravitational potential of the Galaxy. so your consideration of the force between stars is not really relevant.

Most of the universe is pretty empty in terms of the density you're used to in daily life. It's perhaps not that stars are far apart, but that they are pretty compact. This is because baryonic matter (as opposed to dark matter) can lose energy via electromagnetic radiation and hence condense to smaller and denser objects. This is only opposed by angular momentum (which cannot be simply radiated away) forcing disc-like structures such as the Galaxy and proto-stellar and -planetary discs.

In the Milky Way, the density of stars varies a lot between the stellar halo, the disc, the central bulge, and the cores of star clusters.

Your concept of spheres of interaction is flawed, however. Each star feels the combined force of all other stars, even those on the far side of the Galaxy. The resulting total gravitational potential of the Galaxy can be approximated as smooth in space and time. This is because individual star-star gravitational interactions are comparatively weak and have negligible effect. Combined they would eventually scatter a star off its orbit, but the time scale for that is much longer than the Hubble time. For the dense cores of star clusters, the situation is different and so-called two-body relaxation effects their structure over their life time.

Binary stars are not very far apart. Which begs the question, how did they get so close together, if most star systems are quite far apart.

• They were born from the same collapsed part of their "mother" molecular cloud. Fragmenting into two or more stars is actually quite common. The chances of two stars meeting each other are very small, and even if they did, they wouldn't be able to capture each other gravitationally due to energy conservation. For this to happen, a three-body encounter is required, which is even less likely. – pela Feb 16 '15 at 13:56

Stars are far apart from other celestial bodies because of mass, temperature, elements. The way in which a star burns, henceforth its mass, depending on its given place in the cosmos. A large star burns hot and dies fast, while a small or dwarf star such as our own star (the sun), burns at a more consecutive speed, and burns longer, now to ask a question about why stars are so far apart, I feel that their make up, and the way they behave is quite important; to why they are far apart. All of this has to do with the type of the star itself, they are all different so I feel that my answer is valid.

• I find my second answer to be more accurate – jenni selman Feb 16 '15 at 0:55

What is far apart? In our universe there are zillions upon zillions of stars, some of them live fast and die young, so to speak.They burn their fuel at a very fast rate; witch causes them to have much shorter life spans. While some stars burn much slower, which then causes them to live longer, there are many different ways in which they react to each other. Some stars are in binary form, they are dependent upon each others gravity for their survival. Astronomers, with the help of the Hubble space telescope have discovered a star cluster, full of thousands of stars circling a massive black hole,measuring speeds of up to twelve million miles an hour.Visit http//www.Hubble.com for more information.

• This does not answer the question. – HDE 226868 Dec 14 '14 at 20:26
• How does it not? Explain? – jenni selman Feb 16 '15 at 0:17
• It barely talks about stars being close to one another, and it doesn't explain why stars are far apart in a given region of a galaxy. – HDE 226868 Feb 16 '15 at 0:18
• Binary stars are some of the closest know stars to be CLOSE to each other, can you name any other type of star closer or farther apart? – jenni selman Feb 16 '15 at 0:25
• Small stars don't live fast and die young. Small stars live for billions of years, while large stars burn out fast, on the scale of millions of years. Check out Wikipedia's article on stellar evolution. – pela Feb 16 '15 at 13:49

The Stars are far apart because the Universe has been expanding for billions of years at a fast rate of speed. So since the Stars have been moving away from one another for so long it is only natural that the Stars are so far apart.

• This is not true. Cosmological expansion only applies on really, really, really big scales. See, for example, this. – HDE 226868 Dec 11 '14 at 23:26
• The Stars in other Galaxies are moving away from us though because the Galaxies are moving away from each other, is this not true ? Except for Andromeda which is moving towards us – Peter U Dec 12 '14 at 0:33
• Absolutely, but the question talked about stars in our galaxy, as per the Wolfram search. – HDE 226868 Dec 12 '14 at 0:34
• How about this then, matter is spread very, very thinly in Space and enormous distance is required to collect enough matter to form a Star. This is the reason they are so far apart. – Peter U Dec 12 '14 at 1:01
• No, stellar nurseries (aka Giant Molecular Clouds, if you want to sound cool) are pretty dense. – HDE 226868 Dec 12 '14 at 1:01