Variable Stars: Pulsation, Variable Stars: Pulsation, Evolution and application to Evolution and application to

Cosmology.Cosmology.Shashi M. KanburShashi M. Kanbur

SUNY Oswego, July 2007SUNY Oswego, July 2007

ContentsContents

Lecture I: Observation Lecture I: Observation Aspects/TheoryAspects/Theory

Lecture II: Stellar PulsationLecture II: Stellar Pulsation Lecture III: Stellar EvolutionLecture III: Stellar Evolution Lecture IV: Pulsation ModelingLecture IV: Pulsation Modeling Lecture V: Applications: The distance Lecture V: Applications: The distance

and age scales.and age scales.

Lecture I: Observational AspectsLecture I: Observational Aspects

Classical Cepheids: Cepheids and RR Classical Cepheids: Cepheids and RR Lyraes.Lyraes.

Very regular brightness fluctuations Very regular brightness fluctuations ranging from hours to days.ranging from hours to days.

Pulsation is due to internal Pulsation is due to internal mechanism, not due to binary or mechanism, not due to binary or occulting effects.occulting effects.

Comparitively rare: 1 in a million.Comparitively rare: 1 in a million.

Magnitudes and Black BodiesMagnitudes and Black Bodies Luminosity: total energy radiated into space/second: Watts, Luminosity: total energy radiated into space/second: Watts,

Sun’s luminosity is about 4*10Sun’s luminosity is about 4*102626 Watts 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 magnitudeAbsolute and apparent magnitude mmvv-M-MVV = 5logd – 5; inverse square law, = 5logd – 5; inverse square law, B = L/4B = L/4ππdd22

Magnitudes in certain wavelength ranges, U,B,V, R,I,J, H, K Magnitudes in certain wavelength ranges, U,B,V, R,I,J, H, K etc.etc.

Stars are good examples of black bodies, Stefan Boltzmann Stars are good examples of black bodies, Stefan Boltzmann law:law:

L = 4L = 4ππrr22σσTT44

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 Color: independent of distance, bluer or smaller values of

the color index imply hotter stars – Wien’s law.the color index imply hotter stars – Wien’s law.

CepheidsCepheids Young, population I,high metal content: Young, population I,high metal content:

X=0.7, Z=0.02X=0.7, Z=0.02 Periods range from 2 days to about 100-Periods range from 2 days to about 100-

120 days.120 days. M: 2-10 solar masses, L: ranges from tens M: 2-10 solar masses, L: ranges from tens

to thousands of solar luminosities – mass-to thousands of solar luminosities – mass-luminosity relation (ML), Teff: 5000-6400Kluminosity relation (ML), Teff: 5000-6400K

Brightness fluctuations of the order of 1 Brightness fluctuations of the order of 1 magnitude, surface velocities of the order magnitude, surface velocities of the order 40-60km/s.40-60km/s.

Located in the disks of spiral galaxies.Located in the disks of spiral galaxies.

RR LyraesRR Lyraes

Old, population II, low metal content, Old, population II, low metal content, X=0.7, Z = 0.001 – 0.0001.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 0.5-0.9 solar masses, tens – hundreds of

solar luminosities, Teff: 6000 – 7000K.solar luminosities, Teff: 6000 – 7000K. Brightness fluctuations of the order of 1 Brightness fluctuations of the order of 1

magnitude and velocity fluctuations of the magnitude and velocity fluctuations of the order of 40-60km/s.order of 40-60km/s.

Located in globular clusters and in the Located in globular clusters and in the field.field.

CepheidsCepheids Fundamental mode, first and second overtone Fundamental mode, first and second overtone

oscillators – some double mode stars.oscillators – some double mode stars. Radial Oscillators.Radial Oscillators. Many recent microlensing surveys have produced Many recent microlensing surveys have produced

lots of new data: exciting field.lots of new data: exciting field. OGLEOGLE, , MACHOMACHO SDSSSDSS, , LSSTLSST Hubble Space Telescope has observed Cepheids Hubble Space Telescope has observed Cepheids

in some 30 galaxies in our local group:in some 30 galaxies in our local group:HSTHST Amplitude of oscillations generally decreases as Amplitude of oscillations generally decreases as

wavelength of observation increases.wavelength of observation increases.

Hertzsprung Progression Hertzsprung Progression

Around P=7d, bumps appear on the Around P=7d, bumps appear on the descending branch.descending branch.

At 10 days, bumps area at maximum At 10 days, bumps area at maximum light.light.

Around P=12d, bumps appear on Around P=12d, bumps appear on ascending branch.ascending branch.

Around P=20d, bumps disappear.Around P=20d, bumps disappear.

Fourier DecompositionFourier Decomposition Need to quantify the structure of the light Need to quantify the structure of the light

curve.curve. V = AV = A00 + + ΣΣkk(A(Akksin(ksin(kωωt + t + φφkk)),)), ωω=2=2ππ/P, P the period in days,/P, P the period in days, The summations goes from k=1 to N, the The summations goes from k=1 to N, the

order of the fit; typically N is about 8.order of the fit; typically N is about 8. AAk,k,φφkk: Fourier amplitudes and phases: Fourier amplitudes and phases Use least squares to fit this to observed Use least squares to fit this to observed

data points.data points. Compute RCompute Rk1k1=A=Akk/A/A11, , φφk1k1==φφkk-k-kφφ11 and plot and plot

these against period.these against period.

Fourier Decomposition and the Fourier Decomposition and the Hertzsprung progressionHertzsprung progression

Major discontinnuity in RMajor discontinnuity in Rk1k1, , φφk1k1 at a period at a period of 10 days, the center of the Hertzsprung of 10 days, the center of the Hertzsprung progression.progression.

Seen in many wavelength bands.Seen in many wavelength bands. Seen in Galaxy, LMC and SMC at about the Seen in Galaxy, LMC and SMC at about the

same period: no significant evidence of a same period: no significant evidence of a large change in the location at 10 days as large change in the location at 10 days as a function of metallicity.a function of metallicity.

Galaxy: metal rich (Z=0.02), LMC Galaxy: metal rich (Z=0.02), LMC intermediate (Z=0.008), SMC metal poorer intermediate (Z=0.008), SMC metal poorer or at least has less metals than the LMC or at least has less metals than the LMC (Z=0.004).(Z=0.004).

RR LyraesRR Lyraes Again fundamental, first and second Again fundamental, first and second

overtone pulsations: some double mode or overtone pulsations: some double mode or beat stars.beat stars.

Radial oscillators but ….?Radial oscillators but ….? Amplitude generally decreases as Amplitude generally decreases as

wavelength increases.wavelength increases. Some stars exhibit the “Blazhko effect”: Some stars exhibit the “Blazhko effect”:

second periodicity superimposed on the second periodicity superimposed on the first.first.

Use Fourier decomposition as well to Use Fourier decomposition as well to characterize light curve structure.characterize light curve structure.

RR Lyraes in M3RR Lyraes in M3

Variables in M3Variables in M3

The Cepheid Period-Luminosity The Cepheid Period-Luminosity RelationRelation

Empirical relation initially observed Empirical relation initially observed by Henrietta Leavit.by Henrietta Leavit.

MACHO PL relation in the LMCMACHO PL relation in the LMC

The Cepheid PL relationThe Cepheid PL relation

MMX X = a= aXX + b + bXXlogPlogP How do aHow do aXX b bXX vary from galaxy to galaxy or vary from galaxy to galaxy or

with metallicity?with metallicity? For a given galaxy, does bFor a given galaxy, does bXX vary with vary with

period?period? How do aHow do aXX, b, bXX vary with X, the waveband vary with X, the waveband

of observations.of observations. Interstellar reddening: astronomical Interstellar reddening: astronomical

objects appear redder than they actually objects appear redder than they actually are:are:

Other types of variable starsOther types of variable stars

Type II Cepheids; population II Type II Cepheids; population II counterpart of classical Cepheidscounterpart of classical Cepheids

Miras: Long period variables, periods Miras: Long period variables, periods of the order of hundreds of days.of the order of hundreds of days.

Semi-regular variables: variable Semi-regular variables: variable luminosity but no real regularity or luminosity but no real regularity or repetition.repetition.

Non-Radial Oscillators: eg Sun.Non-Radial Oscillators: eg Sun.

Lecture II: Stellar Pulsation.Lecture II: Stellar Pulsation.