Why are stars so small and rare in the greater scheme of things?

I did a few back of the envelope calculations based on figures I found online.

If the distance between the earth and sun is 1 metre, then:

the sun is about 0.93 cm

earth is about 0.85 mm

nearest star about 4.3 light years away = 271.925 km away. So if the sun is a marble with diameter less than 1 cm, you can go 271.925 km in all directions before you reach another little star like that.

milky galaxy with roughly 100,000 light year diameter and thickness 1,000 light years = 6,323,837 km diameter and 6,324 km thickness roughly

Does this imply that the conditions for stars to form are much less commonplace than we might think, but that it is only because space is so vast that we see billions of them?

Sin City

Id say because space is to vast and your looking at our solar system
whats the difference in space the closer to the center of the milkyway
or how close are binary stars to each other?

Sin City

Sin City wrote: »

Id say because space is to vast and your looking at our solar system
whats the difference in space the closer to the center of the milkyway
or how close are binary stars to each other?

I read this on wikipedia, (calculations different to mine but give a similar picture)

" While the Andromeda Galaxy contains about 1 trillion (1012) stars and the Milky Way contains about 300 billion (3×1011), the chance of even two stars colliding is negligible because of the huge distances between the stars. For example, the nearest star to the Sun is Proxima Centauri, about 4.2 light-years (4.0×1013 km; 2.5×1013 mi) or 30 million (3×107) solar diameters away. If the Sun were a ping-pong ball, Proxima Centauri would be a pea about 1,100 km (680 mi) away, and the Milky Way would be about 30 million km (19 million mi) wide. Although stars are more common near the centres of each galaxy, the average distance between stars is still 160 billion (1.6×1011) km (100 billion mi). That is analogous to one ping-pong ball every 3.2 km (2.0 mi). Thus, it is extremely unlikely that any two stars from the merging galaxies would collide. "

So while you're correct in saying stars are closer to each other near the centre of the galaxy, they're still very far apart relative to their size. Like to take the example here, imagine a ping pong ball sitting in space, and then having to go in all directions for over 3 km to find another such objects - and that is near the centre of the galaxy.

Binary stars are indeed much closer to each other though - using the metric of the earth being 1 metre away from the sun, binary stars are tens of metres away from each other as opposed to tens or hundreds of kms.

mickmackey1

That's why they call it 'space'.

Zubeneschamali

mickmackey1 wrote: »

That's why they call it 'space'.

You may think it's a long way down the road to the Chemists, but that's just peanuts compared to space.

Rubecula

space is big and getting bigger stars are big but not getting bigger

Capt'n Midnight

It's because gravity is weak.

But if gravity was stronger then all the stars and stuff would be a lot closer together, too close. Our universe is a lot more interesting seeing as how it's more than a ginormous black hole.

If gravity was weaker then gas might be too spread out to collapse into stars.


very roughly speaking the universe is as dense as it needs to be

ps200306

Deleted User wrote: »

Does this imply that the conditions for stars to form are much less commonplace than we might think, but that it is only because space is so vast that we see billions of them?

It's a good question but the answer is no. Consider the next level up the organisational hierarchy: galaxies. If our Milky Way was a 1 cm marble, the nearest galaxy would be only 25 cm away, the local group of galaxies would be only a metre across, and even the Virgo Supercluster of 50,000 (mostly dwarf) galaxies would be just ten metres across. If sparseness of distribution was an indicator of difficulty of formation, it would seem strange that galaxies would form much more easily than the stars they are made of. (That said, there are huge regions totally devoid of galaxies, but that's another story).

No, the answer to why stars are so far apart has to do with how they form. As you know, this is by the gravitational collapse of large clouds of gas. How large? That depends on a number of factors. Gravity is universal, so without some counteracting force every patch of gas in the universe would collapse. The opposing force is, of course, gas pressure -- the random thermal motions of atoms in the gas cloud. The higher the temperature, the higher the pressure.

So star formation relies on sufficiently high gas cloud density and sufficiently low temperature. The precise relationships were worked out by James Jeans in an essay of 1917 entitled "Problems of cosmogony and stellar dynamics" (published as a book in 1919). The condition necessary for stellar collapse is called the Jeans Instability Criterion. Rather than get into the nitty gritty here, you can read about it on Wikipedia.

Suffice it to say that star formation generally needs very low temperatures for gravity to overcome the gas pressure in the very rarefied gas that is typical of our galaxy's interstellar medium. Even at that it only happens in the densest molecular clouds, with number densities of one to ten thousand atoms per cubic centimetre (which is more than a thousand trillion times less dense than the air in your sitting room). The dust in the outer layers of molecular clouds can shield the internal environment from stellar radiation, creating so-called cold cores with temperatures below 30K (-240°C) and there may also be random density fluctuations.

To see how the Jeans criterion applies to molecular clouds, have a look at the worked examples here. Lower densities require higher volumes to enclose the amount of mass necessary for collapse. At a temperature of 30K, the calculated radius of the required gas cloud for the range of densities we mentioned is between 0.37 and 1.18 parsec, or roughly one to four light years. The mass would be one hundred to several hundred times the mass of our Sun. It should be immediately obvious that it takes quite a large volume of space to make a star.

What happens next is complicated. Once collapse begins it is relentless, because collapse causes the density to increase which puts the gas cloud ever further beyond the Jeans criterion. But this can mean that initially overdense regions within the cloud can become Jeans unstable in their own right. Thus the cloud tends to fragment into smaller regions which continue to collapse on their own. All the while, the temperature is rising as the gas is compressed which puts a major brake on the collapse, and a lot of energy has to be radiated away in order for collapse to continue. Meanwhile, the shrinkage of the cloud results in the collapsing cores starting to spin by conservation of angular momentum. Some of the fragments will fission into pairs as a result, which is the reason that the majority of stars in the galaxy are binaries. Ternary and higher systems are rare though, because it's very hard to organise a stable configuration of more than two co-orbiting stars in a three-dimensional universe.

As you know, the collapsing protostars eventually get hot enough to commence core nuclear fusion, and settle down to life as normal stars. Early on in the birth process, though, they develop strong stellar winds which prevent any more material falling onto them from the protostellar cloud and the process of mass accretion is halted at that point. Not only that, but over time they will blow away the entire original cloud of gas so that star formation in the whole region will come to a halt. The stars that have formed are usually only loosely gravitationally bound to each other, and they drift off into space over time. Our own Sun formed in a cloud similar to the nearby Orion nebula which is still a site of active star formation.

Anyway, how does this all pertain to the original question? Well, the Jeans instability criterion means that clouds up to several light years across are needed in order to form stars given the highest gas densities typical of our galaxy. Although there may be several hundred solar masses in such a cloud, most of that is blown away by various processes without being incorporated into stars, and the stars that do form will drift off into lower density regions of the galaxy. We should not be surprised, therefore to find typical separations of several light years between stars in our neck of the woods.

All that said, conditions vary greatly across different regions, different galaxies, and different epochs of cosmic history. Violent events such as supernova explosions and galaxy mergers can trigger bouts of very active star formation by sweeping up gas and compressing it. In the early universe we believe that the galaxies themselves were formed by huge streamers of cold gas falling into denser concentrations with dark matter cores. The centres of galaxies have higher concentrations of stars as do the large agglomerations of stars called globular clusters -- which themselves might be the remaining cores of galaxies stripped of most of their stars by gravitational interactions with bigger systems.

Brilliant answer, thanks