Physics 160 Stellar Astrophysics Prof. Adam Burgasser Lecture 15 Star Evolu?on I: Stellar Timescales & Post Main Sequence Evolu?on 20 November 2013 Announcements • HW #7 now online, due Friday • Errors in last week’s lectures & HW 6 • First observing lab(s) tomorrow (weather pending) Physics 160 Fall 2013 Lecture 15: Star Evolution I: Stellar Lifetimes and Post Main Sequence Evolution 20 November 2013 PRELIMS • Announcements [5 min] MATERIAL [45 min] • [5 min] Review • [15 min] MS timescales • [20 min] Schonberg-ChandreseKhar limit DEMONSTRATIONS/EXERCISES MATERIALS 1 Physics 160 Fall 2013 Review • we’ve walKed through Pre-MS evolution – Jean’s collapse, homologous contraction & fragmentation, adiabatic limit and preferred stellar mass scale, Hayashi & Henyey tracks, disKs/jets/planets • this messy process leads to a distribution of masses – the mass function – which shows a surprisingly universal form • Now let’s see how stars die Timescales • Free-fall – for homologous collapse, ~ 105 yr • Kelvin-Helmholtz – L ~ GM2Δ(1/R)/Δt ~ 105-107 yr (≈40 Myr for Sun) • Nuclear burning timescale: τMS ~ εMc2/L, ε is conversation factor o From Stefan-Boltzmann, density, ideal gas and pressure gradient we can derive scaling relations between L and M and T and M and o τMS ~ 1010 yr (M/Msun)-2.5 Evolution along the MS • H->He => µ -> ½ -> 4/3 • P ~ ρT/µ => core ρ & T increase 4 • L ~ εnuc ~ ρT => Luminosity increases too • Increased energy flow => radius increases • For Sun, ΔL ~ 50%, ΔT ~ 100 K since ZAMS • Faint young Sun paradox: why wasn’t Earth and Mars frozen? (A: internal heating probably played a greater role) Evolving off the MS • He core forms – inert and isothermal (dT/dr ~ net energy flux = 0) • How stable is this? Compute a Jean’s mass! 2 Physics 160 Fall 2013 o Virial equation with added factor – external pressure term o Solve for maximum possible pressure => maximum core radius => maximum core mass ≈ 0.54 Mtotal x (µe/µcore)2 (Schönberg-ChandreseKhar radius) o WorKs out to be 13% Msun for Sun Post MS evolution • Trajectories in HR diagram and primary stages o Main sequence turnoff o Subgiant branch o Red giant phase o Helium flash o Horizontal branch o Asymptotic giant branch & thermal pulsation o Post-AGB – planetary nebulae & white dwarfs (for low mass stars) 3 different greenhouse prescriptions different emissivities evolution of the Sun Sagan & Mullen (1972) .