Frequency distribution

[AstroSmurf]

I wonder if there's a site with histograms or whatever on the number of stars known with a certain spectral class and luminosity; basically, the Hertzsprung-Russell diagram only in numerical terms.

The reason why I ask is that I'm part of a space strategy game project, and I would like to make the game map be reasonably close to the 'real world' in terms of what kind of stars there are, and how many of each type.

[daver]

I wonder if there's a site with histograms or whatever on the number of stars known with a certain spectral class and luminosity; basically, the Hertzsprung-Russell diagram only in numerical terms.

The reason why I ask is that I'm part of a space strategy game project, and I would like to make the game map be reasonably close to the 'real world' in terms of what kind of stars there are, and how many of each type.

I googled a bit, and found hints that the data you want is out there, but i couldn't find exactly what the data was. So i'll make up something.

I'd guess the actual mass distribution would be roughly exponential modified by the lifespan of a star of that mass (take a uniformly distributed random number, take the natural log, multiply by some constant (probably around -2) to get the initial mass of the star in solar masses. Pick an age for the star (you might want to decide if you're in a star-forming region, and hence would have a disproportionate number of young stars, but you'd probably just want to multiply a random number by 14 billion), determine at what stage in its lifespan a star of that age would be.(you're going to want to include double stars; in which case you may as well give both stars the same age). You might determine metalicity as a function of age as well.

This model likely gives more brown dwarfs and rogue planets than are actually present. Most likely there's a cutoff (proto-stars below a certain mass either don't form or get incorporated into other stars--they don't ignite and disperse their parent cloud). So you could rather arbitrarily multiply your initial random number by .95 before taking its log to determine stellar mass.

[Darkwing]

I remember there being tables, etc with specifics on that stuff in my old astronomy textbooks, but essentially what daver said is right. Very few high mass stars, and as the mass goes down, the numbers go up.

[dgruss23]

James Kaler's textbook Astronomy! gave this table which actually was taken from a 1973 source. The numbers are fractions out of 1:

O - 4 x 10^-7
B - 1.4 x 10^-3
A - 7 x 10^-3
F - 0.036
G - 0.09
K - 0.11
M - 0.72

F to M Giants and Supergiants are only 10^-3 to 10^-4.