Re: Astrophysics question: main sequence evolution

sigidunum@xxxxxxxxx wrote:

As main sequence dwarf stars age, they get brighter. Our sun had only
around 0.7 times its current luminosity when it entered the main
sequence 4.5 billion years ago. It will have about 2.2 times its
current luminosity when it leaves, 6.5 billion years in the future.
So, over 11 billion years, it will increase its brightness about
threefold.

This is why the main sequence is a band rather than a line -- stars of
the same mass and temperature can differ in brightness, depending on
their age.

So, my question: does the difference between lowest main sequence
luminosity and highest change with changing stellar mass?

IOW, the sun's luminosity will change by about a factor of three. For
a more massive star, will this figure be bigger or smaller?

My very tentative guess is that it would be bigger, and that more
massive stars would get brighter faster. But that's just a guess.

Why I ask: it occurs to me that this could place another limit on the
development of life. A middle-F dwarf, for instance, would have about
1.5 solar masses and would spend around two billion years on the main
sequence. Two billion years sounds like a plausible period of time for
complex life to evolve. However, if the star's luminosity changes
drastically over that period, then it seems a lot less likely.

Anyway. Does anyone know the answer to this?

Roughly speaking, the evolutionary track of lower mass stars (about 5 solar masses and lower) on the H-R diagram tends to initially move upward and to the right (as hydrogen in the core is burned), then dramatically to the right and slightly down (as hydrogen in the core is exhausted and shell sources are created), and then finally further to the right and dramatically upward (as the core contracts further and finally helium burning is initiated). For very large stars, there is subsequently more zigging back and forth across the H-R diagram as further stages of nuclear burning are achieved.

These three phases correspond to the main sequence, leaving the main sequence for the subgiants, and then leaving the subgiants to become a true giant, respectively. For a one solar mass star, the length of the first period is about 9.9 billion years, the second about 0.5 billion years, and the third about another 0.5 billion years.

Since you're only concerned with the steady brightening of the star over the main sequence, we can ignore the latter two stages (since they occur so rapidly anyway). The answer to your question is that for stars in the range 1-15 solar masses, the total change in luminosity between zero-age main sequence and the point where the track just starts to dramatically cut across to the right _decreases_ with increasing stellar mass, though it falls of asymptotically. For a 1.0 solar mass star, the ratio in luminosities is about a factor of 3; for a 3.0 solar mass star, the ratio is about 2. For a 5.0 solar mass star, the ratio is still about 2. For higher mass stars, the total stellar lifetime is so short that it doesn't really matter for your question, as there isn't enough time for complex life to evolve anyway; even a 5.0 solar mass star has a lifetime of only about 100 million years.

For more information, see _Principles of Stellar Evolution and Nucleosynthesis_, by Clayton.

--
Erik Max Francis && max@xxxxxxxxxxx && http://www.alcyone.com/max/
San Jose, CA, USA && 37 20 N 121 53 W && AIM erikmaxfrancis
Smaller than the eye can see / Bigger than the mind can conceive
-- India Arie
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