The Fermi Paradox and the Drake Equation – Star Formation

As we discussed in the last post, using the Drake Equation as a way of thinking about the Fermi Paradox, an estimate of the number of civilizations in our galaxy with which communication might be possible, N, is given by:

N = R * f_p * n_e * f_l * f_i * f_c * L

Today, we’ll talk about the first term, R = the average rate of star formation per year in our galaxy.

Caveat: I’m an amateur (hopefully in the best sense of the word), with a day job, a family, and a writing career. These estimates are chock-full of back-of-the-envelope-calculations (BOTEC) and rules of thumb. I’ll show my work, and professional astronomers are welcome to comment.

Average rate of star formation

More accurately, we’re interested in the rate of star formation a few billion years ago, on the assumption other intelligent life would only evolve billions of years after its home stellar system formed, just like us. I’ll assume the rate of star formation has been constant over that time frame. I’ll also assume the number of stars in our galaxy is in equilibrium–the number that form each year is equal to the number that die each year. (“leave the main sequence,” to be more technical).

One more assumption: I will ignore class L, T, and Y red and brown dwarf stars, on the assumption they have such low luminosity, any planets they might have would receive insufficient sunlight for life to arise.

From our equilibrium assumption, if we estimate the number of stars dying each year, we have an estimate for how many formed per year in the time frame of interest. Next question: approximately how many stars die each year?

Answer: approximately the number of stars of each spectral classification in the galaxy divided by the main sequence lifespan for that spectral type.  (Number of stars from here * 100 billion stars in our galaxy, main sequence lifespan for a typical star of that classification estimated from here):

spectral type	Number in galaxy	max lifespan (yrs)	number at max lifespan
O	30000	5000000	0.006
B	130000000	50000000	2.6
A	600000000	1000000000	0.6
F	3000000000	2000000000	1.5
G	7600000000	10000000000	0.76
K	12100000000	30000000000	0.4033333333
M	76450000000	200000000000	0.3822

Summing up and rounding a bit, we get R = 6.25. In other words, a star is born about every two months.

Note, about half of those stars, spectral types O-A, have maximum lifespans less than 1 billion (=1000 million) years, and another quarter (spectral type F) live less than 2 billion years. This will matter when discussing f_i in a few posts.

One down, six to go. Till next time.