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

2. Contents Lecture I: Observation Aspects/Theory Lecture I: Observation Aspects/Theory Lecture II: Stellar Pulsation Lecture II: Stellar Pulsation Lecture III: Stellar Evolution Lecture III: Stellar Evolution Lecture IV: Pulsation Modeling Lecture IV: Pulsation Modeling Lecture V: Applications: The distance and age scales. Lecture V: Applications: The distance and age scales.

3. Lecture I: Observational Aspects Classical Cepheids: Cepheids and RR Lyraes. Classical Cepheids: Cepheids and RR Lyraes. Very regular brightness fluctuations ranging from hours to days. Very regular brightness fluctuations ranging from hours to days. Pulsation is due to internal mechanism, not due to binary or occulting effects. Pulsation is due to internal mechanism, not due to binary or occulting effects. Comparitively rare: 1 in a million. Comparitively rare: 1 in a million.

4. Magnitudes and Black Bodies Luminosity: total energy radiated into space/second: Watts, Sun’s luminosity is about 4*10 26 Watts Luminosity: total energy radiated into space/second: Watts, Sun’s luminosity is about 4*10 26 Watts Magnitude, M = -2.5*log L + const. Magnitude, M = -2.5*log L + const. Vega defined to have zero magnitude. Vega defined to have zero magnitude. Absolute and apparent magnitude Absolute and apparent magnitude m v -M V = 5logd – 5; inverse square law, m v -M V = 5logd – 5; inverse square law, B = L/4πd 2 B = L/4πd 2 Magnitudes in certain wavelength ranges, U,B,V, R,I,J, H, K etc. Magnitudes in certain wavelength ranges, U,B,V, R,I,J, H, K etc. Stars are good examples of black bodies, Stefan Boltzmann law: Stars are good examples of black bodies, Stefan Boltzmann law: L = 4πr 2 σT 4 L = 4πr 2 σT 4 Colors: Difference of two magnitudes: eg. B-V, V-I. Colors: Difference of two magnitudes: eg. B-V, V-I. Color: independent of distance, bluer or smaller values of the color index imply hotter stars – Wien’s law. Color: independent of distance, bluer or smaller values of the color index imply hotter stars – Wien’s law.

5. Cepheids Young, population I,high metal content: X=0.7, Z=0.02 Young, population I,high metal content: X=0.7, Z=0.02 Periods range from 2 days to about 100- 120 days. Periods range from 2 days to about 100- 120 days. M: 2-10 solar masses, L: ranges from tens to thousands of solar luminosities – mass- luminosity relation (ML), Teff: 5000-6400K M: 2-10 solar masses, L: ranges from tens to thousands of solar luminosities – mass- luminosity relation (ML), Teff: 5000-6400K Brightness fluctuations of the order of 1 magnitude, surface velocities of the order 40-60km/s. Brightness fluctuations of the order of 1 magnitude, surface velocities of the order 40-60km/s. Located in the disks of spiral galaxies. Located in the disks of spiral galaxies.

6. RR Lyraes Old, population II, low metal content, X=0.7, Z = 0.001 – 0.0001. Old, population II, low metal content, X=0.7, Z = 0.001 – 0.0001. Periods range from 0.2 -0.9 hours. Periods range from 0.2 -0.9 hours. 0.5-0.9 solar masses, tens – hundreds of solar luminosities, Teff: 6000 – 7000K. 0.5-0.9 solar masses, tens – hundreds of solar luminosities, Teff: 6000 – 7000K. Brightness fluctuations of the order of 1 magnitude and velocity fluctuations of the order of 40-60km/s. Brightness fluctuations of the order of 1 magnitude and velocity fluctuations of the order of 40-60km/s. Located in globular clusters and in the field. Located in globular clusters and in the field.

9. Cepheids Fundamental mode, first and second overtone oscillators – some double mode stars. Fundamental mode, first and second overtone oscillators – some double mode stars. Radial Oscillators. Radial Oscillators. Many recent microlensing surveys have produced lots of new data: exciting field. Many recent microlensing surveys have produced lots of new data: exciting field. OGLE, MACHO OGLE, MACHO OGLEMACHO OGLEMACHO SDSS, LSST SDSS, LSST SDSSLSST SDSSLSST Hubble Space Telescope has observed Cepheids in some 30 galaxies in our local group:HST Hubble Space Telescope has observed Cepheids in some 30 galaxies in our local group:HSTHST Amplitude of oscillations generally decreases as wavelength of observation increases. Amplitude of oscillations generally decreases as wavelength of observation increases.

12. Hertzsprung Progression Around P=7d, bumps appear on the descending branch. Around P=7d, bumps appear on the descending branch. At 10 days, bumps area at maximum light. At 10 days, bumps area at maximum light. Around P=12d, bumps appear on ascending branch. Around P=12d, bumps appear on ascending branch. Around P=20d, bumps disappear. Around P=20d, bumps disappear.

18. Fourier Decomposition Need to quantify the structure of the light curve. Need to quantify the structure of the light curve. V = A 0 + Σ k (A k sin(kωt + φ k )), V = A 0 + Σ k (A k sin(kωt + φ k )), ω=2π/P, P the period in days, ω=2π/P, P the period in days, The summations goes from k=1 to N, the order of the fit; typically N is about 8. The summations goes from k=1 to N, the order of the fit; typically N is about 8. A k, φ k : Fourier amplitudes and phases A k, φ k : Fourier amplitudes and phases Use least squares to fit this to observed data points. Use least squares to fit this to observed data points. Compute R k1 =A k /A 1, φ k1 =φ k -kφ 1 and plot these against period. Compute R k1 =A k /A 1, φ k1 =φ k -kφ 1 and plot these against period.

19. Fourier Decomposition and the Hertzsprung progression Major discontinnuity in R k1, φ k1 at a period of 10 days, the center of the Hertzsprung progression. Major discontinnuity in R k1, φ k1 at a period of 10 days, the center of the Hertzsprung progression. Seen in many wavelength bands. Seen in many wavelength bands. Seen in Galaxy, LMC and SMC at about the same period: no significant evidence of a large change in the location at 10 days as a function of metallicity. Seen in Galaxy, LMC and SMC at about the same period: no significant evidence of a large change in the location at 10 days as a function of metallicity. Galaxy: metal rich (Z=0.02), LMC intermediate (Z=0.008), SMC metal poorer or at least has less metals than the LMC (Z=0.004). Galaxy: metal rich (Z=0.02), LMC intermediate (Z=0.008), SMC metal poorer or at least has less metals than the LMC (Z=0.004).

23. RR Lyraes Again fundamental, first and second overtone pulsations: some double mode or beat stars. Again fundamental, first and second overtone pulsations: some double mode or beat stars. Radial oscillators but ….? Radial oscillators but ….? Amplitude generally decreases as wavelength increases. Amplitude generally decreases as wavelength increases. Some stars exhibit the “Blazhko effect”: second periodicity superimposed on the first. Some stars exhibit the “Blazhko effect”: second periodicity superimposed on the first. Use Fourier decomposition as well to characterize light curve structure. Use Fourier decomposition as well to characterize light curve structure.

26. RR Lyraes in M3 Variables in M3 Variables in M3 Variables in M3 Variables in M3

28. The Cepheid Period-Luminosity Relation Empirical relation initially observed by Henrietta Leavit. Empirical relation initially observed by Henrietta Leavit. MACHO PL relation in the LMC MACHO PL relation in the LMC MACHO PL relation in the LMC MACHO PL relation in the LMC

29. The Cepheid PL relation M X = a X + b X logP M X = a X + b X logP How do a X b X vary from galaxy to galaxy or with metallicity? How do a X b X vary from galaxy to galaxy or with metallicity? For a given galaxy, does b X vary with period? For a given galaxy, does b X vary with period? How do a X, b X vary with X, the waveband of observations. How do a X, b X vary with X, the waveband of observations. Interstellar reddening: astronomical objects appear redder than they actually are: Interstellar reddening: astronomical objects appear redder than they actually are:

31. Other types of variable stars Type II Cepheids; population II counterpart of classical Cepheids Type II Cepheids; population II counterpart of classical Cepheids Miras: Long period variables, periods of the order of hundreds of days. Miras: Long period variables, periods of the order of hundreds of days. Semi-regular variables: variable luminosity but no real regularity or repetition. Semi-regular variables: variable luminosity but no real regularity or repetition. Non-Radial Oscillators: eg Sun. Non-Radial Oscillators: eg Sun.

32. Lecture II: Stellar Pulsation.