Fundamentals of Astrophysics Stan Owocki
I Stellar Properties
Chapter 8: Stellar Ages and Lifetimes
8.1 Shortness of chemical burning timescale for the Sun and stars 8.2 Kelvin-Helmholtz timescale for gravitational contraction 8.3 Nuclear burning timescale 8.4 Age of stellar clusters from main-sequence turnoff point 8.5 Questions and exercises What powers stars on the main sequence?
Most stars fall somewhere on the main sequence of the H-R diagram, with
3 L ⎛ M ⎞ ≈ L ⎝⎜ M ⎠⎟ ⊙ ⊙ Shortness of chemical burning timescale
Efficiency of reaction yielding ΔE energy ΔE from mass m ϵ ≡ mc2
For chemical reactions, ΔE~ eV, while mc2~Gev, so ε~10-9
Thus chemical reaction can’t power Sun for long:
3 Kelvin-Helmholz timescale for gravitational contraction
Gravitational binding energy (for constant density Sun)
Suppose luminosity L is powered by gravitational contraction:
The K-H time is how long this can work:
For Sun, we find:
This is longer than tchem, but still << age of Earth (Sun/solar system) 4 Nuclear burning timescale
Hydrogen fusion (requires T~15 MK)
Eγ ~ 0.007 mHe c2 => ε~0.007
Moreover, only central 10% (fraction f=0.1) of Sun is hot enough, so
Such H-fusion time sets the main-sequence lifetime of Sun!
5 Age of a stellar cluster is marked by main-sequence turnoff point On main sequence, luminosity is proportional to cube of mass : which implies that the MS lifetime scales as:
Thus for a cluster with stars born at ~ same time, the MS turnoff indicates cluster age:
old globular cluster => age ~ 8 Gyr
6 Age of a stellar cluster is marked by main-sequence turnoff point
−2/3 L age ≈ 10 Gyr to ( L⊙ ) 7 Age of a stellar cluster is marked by main-sequence turnoff point
−2/3 L age ≈ 10 Gyr to ( L⊙ )
8 Age of a stellar cluster is marked by main-sequence turnoff point
age ≲ 10 Gyr
9 Quick Questions
10 Question What is the main-sequence lifetime of a star with mass M = 16 Msun?
A. 2.5 Myr
B. 25 Myr
C. 250 Myr
D. 2.5 Gyr
E. 25 Gyr Question What is the main-sequence lifetime of a star with mass M = 2 Msun?
A. 2.5 Myr
B. 25 Myr
C. 250 Myr
D. 2.5 Gyr = 10 Gyr/22
E. 25 Gyr Question What is the age of a cluster with main-sequence turnoff at a luminosity Lto = 1000 Lsun?
A. 10 Myr
B. 100 Myr
C. 1 Gyr
D. 10 Gyr
E. It depends on the mass of the turn-off star. Question What is the age of a cluster with main-sequence turnoff at a luminosity Lto = 1000 Lsun?
A. 10 Myr
B. 100 Myr = 10 Gyr/10002/3
C. 1 Gyr
D. 10 Gyr
E. It depends on the mass of the turn-off star.