1. Variable Stars: Pulsation, Evolution and applications to Cosmology Shashi M. Kanbur SUNY Oswego, June 2007

2. Stellar Evolution Recall equations of stellar structure. Recall equations of stellar structure. Nuclear energy generation rate ε(ρ,T) slowly changes the composition decreasing the amount of Hydrogen and increasing the amount of Helium on a nuclear time scale – the characteristic time for stellar properties to change as a result of nuclear burning: t nuc ~ 10 10 M/L years. Nuclear energy generation rate ε(ρ,T) slowly changes the composition decreasing the amount of Hydrogen and increasing the amount of Helium on a nuclear time scale – the characteristic time for stellar properties to change as a result of nuclear burning: t nuc ~ 10 10 M/L years. This timescale is much longer than those involved in stellar pulsation. This timescale is much longer than those involved in stellar pulsation. So solve equations of stellar structure, get structure of star at t=0. So solve equations of stellar structure, get structure of star at t=0. Δt ~ t nuc, so X, Y, Z change due to nuclear burning. Δt ~ t nuc, so X, Y, Z change due to nuclear burning. Find X(t+Δt), Y(t+Δt), Z(t+Δt), recalculate stellar stucture with these new values. Find X(t+Δt), Y(t+Δt), Z(t+Δt), recalculate stellar stucture with these new values. Now there is a new ε = ε(ρ,T); recompute changes to X, Y, Z over the next time interval Δt. Now there is a new ε = ε(ρ,T); recompute changes to X, Y, Z over the next time interval Δt. Continue and develop a stellar evolutionary track. Continue and develop a stellar evolutionary track.

3. Hertzsprung –Russell Diagram Plot of T on X axis against L on Y axis. Plot of T on X axis against L on Y axis. Or, plot of color on X axis against magnitude on Y axis. Or, plot of color on X axis against magnitude on Y axis. At each t, star has a certain surface temperature and luminosity. Plot of At each t, star has a certain surface temperature and luminosity. Plot of (T,L) or ((B-V),V) as a function of time is a stellar evolutionary track on a HR diagram. (T,L) or ((B-V),V) as a function of time is a stellar evolutionary track on a HR diagram. HR diagram is the most important diagram in Astronomy. HR diagram is the most important diagram in Astronomy.

5. Aspects of the HR diagram Main Sequence (ms): all stars are nuclear burning hydrogen to helium in their core. Main Sequence (ms): all stars are nuclear burning hydrogen to helium in their core. Mass increases as you go up the ms, but stars do not travel “too much” on the ms. Mass increases as you go up the ms, but stars do not travel “too much” on the ms. Upper ms: high mass, hot stars (why?), convective core, radiative envelope, H burning by CNO cycle: M > 4-8Msun Upper ms: high mass, hot stars (why?), convective core, radiative envelope, H burning by CNO cycle: M > 4-8Msun Lower ms: low mass, cooler stars (why?), radiative core, convective envelope, H burning by proton-proton chain: M < 4 Msun. Lower ms: low mass, cooler stars (why?), radiative core, convective envelope, H burning by proton-proton chain: M < 4 Msun. Sun is a lower main sequence star. Sun is a lower main sequence star. Partially understand in terms of Stefan Boltzmann law: L ~ R 2 T 4 Partially understand in terms of Stefan Boltzmann law: L ~ R 2 T 4

7. Luminosity Classes and Spectral Types Luminsoity Class I: Supergiants, II: Bright giants, III: Giants, IV: Subgiants, V: Main Sequence Luminsoity Class I: Supergiants, II: Bright giants, III: Giants, IV: Subgiants, V: Main Sequence Spectral Type: classifcation of stellar spectra, essentially a temperature sequence, OBAFGKM Spectral Type: classifcation of stellar spectra, essentially a temperature sequence, OBAFGKM Sun is a G2V, Betelgeuse is a M5V Sun is a G2V, Betelgeuse is a M5V Exercise Exercise Exercise

8. Low Mass Stellar Evolution

9. High Mass Stellar Evolution

12. Basics of stellar evolution Governed by Ideal Gas law:P~ρT Governed by Ideal Gas law:P~ρT Star’s battle against gravity. The only weapon it has are the ability of its core to shrink and start nuclear burning of the next element in the core or the same element in a shell around the core. Star’s battle against gravity. The only weapon it has are the ability of its core to shrink and start nuclear burning of the next element in the core or the same element in a shell around the core. Low mass stars do no get hot enough in their core to burn anything heavier than Helium Low mass stars do no get hot enough in their core to burn anything heavier than Helium High mass stars can go until their core is made up of Fe/Si. Then nuclear fusion cannot proceed: Supernova – of type II. High mass stars can go until their core is made up of Fe/Si. Then nuclear fusion cannot proceed: Supernova – of type II.

14. Lifetime on MS High mass stars have lots of fuel but use up their reserves quickly. High mass stars have lots of fuel but use up their reserves quickly. Low mass stars use their store of nuclear fule more sparingly. Low mass stars use their store of nuclear fule more sparingly. t MS ~ M/L ~ M -3, since L~M 4 t MS ~ M/L ~ M -3, since L~M 4 1 Msun star has t MS ~ 10Gy. 1 Msun star has t MS ~ 10Gy. 10 Msun star has t MS ~ 10 Million yrs 10 Msun star has t MS ~ 10 Million yrs 0.1Msun star has t MS ~ 10 Trillion Years. 0.1Msun star has t MS ~ 10 Trillion Years.

15. Clusters Open cluster : loose collection of few (perhaps 20), mostly young stars: in disk of galaxy – considered to be at the same distance. Open cluster : loose collection of few (perhaps 20), mostly young stars: in disk of galaxy – considered to be at the same distance. Thus a plot of apparent magnitude against color, say B-V (a Color-Magnitude diagram) is like plotting temperature against luminosity ( An HR diagram). Thus a plot of apparent magnitude against color, say B-V (a Color-Magnitude diagram) is like plotting temperature against luminosity ( An HR diagram). Pleiades and Hyades clusters. Pleiades and Hyades clusters. Globular clusters: tight collection of many, 10,000-100,000 stars: cant resolve stars in the center. All stars in a GC formed at the same time eg. M3, M15. Globular clusters: tight collection of many, 10,000-100,000 stars: cant resolve stars in the center. All stars in a GC formed at the same time eg. M3, M15.

21. Cluster HR diagrams Subgiant branch: stars which have only just left the main sequence, burning H to He in a thick shell around a He core; short lived phase, only seen in very old clusters. Subgiant branch: stars which have only just left the main sequence, burning H to He in a thick shell around a He core; short lived phase, only seen in very old clusters. Red Giant branch: stars burning H in a shell, outer envelope expanding, core contracting. Red Giant branch: stars burning H in a shell, outer envelope expanding, core contracting. Horizontal branch: low mass stars which are burning He in the core after the He flash. RR Lyraes found here. Horizontal branch: low mass stars which are burning He in the core after the He flash. RR Lyraes found here. Asymptotic giant branch: Core He exhausted, He in a shell around the core, outer envelope expands, cools. Asymptotic giant branch: Core He exhausted, He in a shell around the core, outer envelope expands, cools. White dwarfs in M4. White dwarfs in M4.

25. Main Sequence Fitting HR diagram for local stars whose distances are known. HR diagram for local stars whose distances are known. HR diagram for a cluster whose stars are all assumed to be at the distance – thus m v is just like M V HR diagram for a cluster whose stars are all assumed to be at the distance – thus m v is just like M V Distance modulus (m – M) can be obtained by determining the offste to the main sequence from nearby stars whose distances are known. Distance modulus (m – M) can be obtained by determining the offste to the main sequence from nearby stars whose distances are known.

27. Evolutionary Tracks Evolutionary tracks depend on input physics: convective overhsoot etc. Evolutionary tracks depend on input physics: convective overhsoot etc. These lead to different M-L relations for tracks going through the instability strip: These lead to different M-L relations for tracks going through the instability strip: LogL = a+ blogM LogL = a+ blogM Constant a, b depend on stellar evolutionary input physics. Constant a, b depend on stellar evolutionary input physics. Get, M,L so, input into a stellar pulsation code and get theoretical light curves, compare with observations: Get, M,L so, input into a stellar pulsation code and get theoretical light curves, compare with observations: Compare stellar evolution with stellar pulsation theories. Compare stellar evolution with stellar pulsation theories.