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

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

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

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

  2. 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.

  3. 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.

  4. 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.

  5. Cepheids • Young, population I,high metal content: X=0.7, Z=0.02 • 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 • Brightness fluctuations of the order of 1 magnitude, surface velocities of the order 40-60km/s. • Located in the disks of spiral galaxies.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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).

  11. 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.

  12. RR Lyraes in M3 • Variables in M3

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

  14. 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:

  15. 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.

  16. Lecture II: Stellar Pulsation.

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