I'm trying to determine what the lifetime of a star on the horizontal branch of the Hertzsprung-Russell diagram would be.
Some websites say $10^8$ while others said $10^7,$ so I don't know which one is correct or incorrect.
I know it must be shorter than that of the main sequence (which is about $10^{10}$ years) but by how much and how do you know? Do you use the stellar equations?
There isn't a single value for the lifetime of a horizontal branch star. The lifetime depends upon star mass ($M$), helium core mass ($M_c$) or helium fraction ($Y$), and metalicity ($Z$), where the masses are in units of solar mass.
According to Iben's POST MAIN SEQUENCE EVOLUTION OF SINGLE STARS:
log (lifetime in units of $10^7$ years) $ = 0.74 - 2.2(M_c- 0.5) +log(f)$
$= 0.795+0.506( Y-0.3) + 0.022(log(Z) + 3)+0.077(M -0.8) + log(f)$
where $f$ is a convection factor that is approximately $2$.
In one example of Iben, $Y=0.3$, $Z=0.001$
In another $Y=0.3$, $Z=0.0001$
So $10^8$ years seems like a good estimate for a star of 0.8 solar masses, while $10^7$ years seems too low.
