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..