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Variable Stars: Pulsation, Evolution and application to Cosmology. Shashi M. Kanbur SUNY Oswego, July 2007 Contents Lecture I: Observation Aspects/Theory Lecture II: Stellar Pulsation Lecture III: Stellar Evolution Lecture IV: Pulsation Modeling Lecture V: Applications: The distance and age scales. Lecture I: Observational Aspects Classical Cepheids: Cepheids and RR Lyraes. Very regular brightness fluctuations ranging from hours to days. Pulsation is due to internal mechanism, not due to binary or occulting effects. Comparitively rare: 1 in a million. Magnitudes and Black Bodies Luminosity: total energy radiated into space/second: Watts, Sun’s luminosity is about 4*1026 Watts Magnitude, M = -2.5*log L + const. Vega defined to have zero magnitude. Absolute and apparent magnitude mv-MV = 5logd – 5; inverse square law, B = L/4πd2 Magnitudes in certain wavelength ranges, U,B,V, R,I,J, H, K etc. Stars are good examples of black bodies, Stefan Boltzmann law: L = 4πr2σT4 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. Cepheids Young, population I,high metal content: X=0.7, Z=0.02 Periods range from 2 days to about 100120 days. M: 2-10 solar masses, L: ranges from tens to thousands of solar luminosities – massluminosity relation (ML), Teff: 5000-6400K Brightness fluctuations of the order of 1 magnitude, surface velocities of the order 40-60km/s. Located in the disks of spiral galaxies. RR Lyraes Old, population II, low metal content, X=0.7, Z = 0.001 – 0.0001. Periods range from 0.2 -0.9 hours. 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. Located in globular clusters and in the field. Cepheids Fundamental mode, first and second overtone oscillators – some double mode stars. Radial Oscillators. Many recent microlensing surveys have produced lots of new data: exciting field. OGLE, MACHO SDSS, LSST Hubble Space Telescope has observed Cepheids in some 30 galaxies in our local group:HST Amplitude of oscillations generally decreases as wavelength of observation increases. Hertzsprung Progression Around P=7d, bumps appear on the descending branch. At 10 days, bumps area at maximum light. Around P=12d, bumps appear on ascending branch. Around P=20d, bumps disappear. Fourier Decomposition Need to quantify the structure of the light curve. V = A0 + Σk(Aksin(kωt + φk)), 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. Ak,φk: Fourier amplitudes and phases Use least squares to fit this to observed data points. Compute Rk1=Ak/A1, φk1=φk-kφ1 and plot these against period. Fourier Decomposition and the Hertzsprung progression Major discontinnuity in Rk1, φk1 at a period of 10 days, the center of the Hertzsprung progression. 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. 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). RR Lyraes Again fundamental, first and second overtone pulsations: some double mode or beat stars. Radial oscillators but ….? Amplitude generally decreases as wavelength increases. Some stars exhibit the “Blazhko effect”: second periodicity superimposed on the first. Use Fourier decomposition as well to characterize light curve structure. RR Lyraes in M3 Variables in M3 The Cepheid Period-Luminosity Relation Empirical relation initially observed by Henrietta Leavit. MACHO PL relation in the LMC The Cepheid PL relation MX = aX + bXlogP How do aX bX vary from galaxy to galaxy or with metallicity? For a given galaxy, does bX vary with period? How do aX, bX vary with X, the waveband of observations. Interstellar reddening: astronomical objects appear redder than they actually are: Other types of variable stars Type II Cepheids; population II counterpart of classical Cepheids Miras: Long period variables, periods of the order of hundreds of days. Semi-regular variables: variable luminosity but no real regularity or repetition. Non-Radial Oscillators: eg Sun. Lecture II: Stellar Pulsation.