Variable Stars: Pulsation, Variable Stars: Pulsation, Evolution and applications Evolution and applications

to Cosmologyto Cosmology

Shashi M. KanburShashi M. Kanbur

SUNY Oswego, June 2007SUNY Oswego, June 2007

Stellar EvolutionStellar Evolution Recall equations of stellar structure.Recall equations of stellar structure. Nuclear energy generation rate Nuclear energy generation rate εε((ρρ,T) slowly changes the ,T) slowly changes the

composition decreasing the amount of Hydrogen and composition decreasing the amount of Hydrogen and increasing the amount of Helium on a nuclear time scale – increasing the amount of Helium on a nuclear time scale – the characteristic time for stellar properties to change as a the characteristic time for stellar properties to change as a result of nuclear burning: tresult of nuclear burning: tnuc nuc ~ 10~ 101010M/L years.M/L years.

This timescale is much longer than those involved in stellar This timescale is much longer than those involved in stellar pulsation.pulsation.

So solve equations of stellar structure, get structure of star So solve equations of stellar structure, get structure of star at t=0.at t=0.

ΔΔt ~ tt ~ tnucnuc, so X, Y, Z change due to nuclear burning., so X, Y, Z change due to nuclear burning. Find X(t+Find X(t+ΔΔt), Y(t+t), Y(t+ΔΔt), Z(t+t), Z(t+ΔΔt), recalculate stellar stucture t), recalculate stellar stucture

with these new values.with these new values. Now there is a new Now there is a new εε = = εε((ρρ,T); recompute changes to X, Y, ,T); recompute changes to X, Y,

Z over the next time interval Z over the next time interval ΔΔt.t. Continue and develop a stellar evolutionary track. Continue and develop a stellar evolutionary track.

Hertzsprung –Russell DiagramHertzsprung –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 Or, plot of color on X axis against

magnitude on Y axis.magnitude on Y axis. At each t, star has a certain surface At each t, star has a certain surface

temperature and luminosity. Plot oftemperature and luminosity. Plot of (T,L) or ((B-V),V) as a function of time is a (T,L) or ((B-V),V) as a function of time is a

stellar evolutionary track on a HR diagram.stellar evolutionary track on a HR diagram. HR diagram is the most important diagram HR diagram is the most important diagram

in Astronomy.in Astronomy.

Aspects of the HR diagramAspects of the HR diagram Main Sequence (ms): all stars are nuclear burning Main Sequence (ms): all stars are nuclear burning

hydrogen to helium in their core.hydrogen to helium in their core. Mass increases as you go up the ms, but stars do Mass increases as you go up the ms, but stars do

not travel “too much” on the ms.not travel “too much” on the ms. Upper ms: high mass, hot stars (why?), Upper ms: high mass, hot stars (why?),

convective core, radiative envelope, H burning by convective core, radiative envelope, H burning by CNO cycle: M > 4-8MsunCNO cycle: M > 4-8Msun

Lower ms: low mass, cooler stars (why?), Lower ms: low mass, cooler stars (why?), radiative core, convective envelope, H burning by radiative core, convective envelope, H burning by proton-proton chain: M < 4 Msun.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 Partially understand in terms of Stefan Boltzmann

law: L ~ Rlaw: L ~ R22TT44

Luminosity Classes and Spectral Luminosity Classes and Spectral TypesTypes

Luminsoity Class I: Supergiants, II: Luminsoity Class I: Supergiants, II: Bright giants, III: Giants, IV: Bright giants, III: Giants, IV: Subgiants, V: Main SequenceSubgiants, V: Main Sequence

Spectral Type: classifcation of stellar Spectral Type: classifcation of stellar spectra, essentially a temperature spectra, essentially a temperature sequence, OBAFGKMsequence, OBAFGKM

Sun is a G2V, Betelgeuse is a M5VSun is a G2V, Betelgeuse is a M5V ExerciseExercise

Low Mass Stellar EvolutionLow Mass Stellar Evolution

High Mass Stellar EvolutionHigh Mass Stellar Evolution

Basics of stellar evolutionBasics of stellar evolution Governed by Ideal Gas law:P~Governed by Ideal Gas law:P~ρρTT Star’s battle against gravity. The only Star’s battle against gravity. The only

weapon it has are the ability of its core to weapon it has are the ability of its core to shrink and start nuclear burning of the shrink and start nuclear burning of the next element in the core or the same next element in the core or the same element in a shell around the core.element in a shell around the core.

Low mass stars do no get hot enough in Low mass stars do no get hot enough in their core to burn anything heavier than their core to burn anything heavier than HeliumHelium

High mass stars can go until their core is High mass stars can go until their core is made up of Fe/Si. Then nuclear fusion made up of Fe/Si. Then nuclear fusion cannot proceed: Supernova – of type II.cannot proceed: Supernova – of type II.

Lifetime on MSLifetime on MS

High mass stars have lots of fuel but High mass stars have lots of fuel but use up their reserves quickly.use up their reserves quickly.

Low mass stars use their store of Low mass stars use their store of nuclear fule more sparingly.nuclear fule more sparingly.

ttMSMS ~ M/L ~ M ~ M/L ~ M-3-3, since L~M, since L~M44

1 Msun star has t1 Msun star has tMSMS ~ 10Gy. ~ 10Gy. 10 Msun star has t10 Msun star has tMSMS ~ 10 Million yrs ~ 10 Million yrs 0.1Msun star has t0.1Msun star has tMS MS ~ 10 Trillion ~ 10 Trillion

Years.Years.

ClustersClusters Open cluster : loose collection of few (perhaps Open cluster : loose collection of few (perhaps

20), mostly young stars: in disk of galaxy – 20), mostly young stars: in disk of galaxy – considered to be at the same distance.considered to be at the same distance.

Thus a plot of apparent magnitude against color, Thus a plot of apparent magnitude against color, say B-V (a Color-Magnitude diagram) is like say B-V (a Color-Magnitude diagram) is like plotting temperature against luminosity ( An HR plotting temperature against luminosity ( An HR diagram).diagram).

Pleiades and Hyades clusters.Pleiades and Hyades clusters. Globular clusters: tight collection of many, Globular clusters: tight collection of many,

10,000-100,000 stars: cant resolve stars in the 10,000-100,000 stars: cant resolve stars in the center. All stars in a GC formed at the same time center. All stars in a GC formed at the same time eg. M3, M15.eg. M3, M15.

Cluster HR diagramsCluster HR diagrams Subgiant branch: stars which have only just left Subgiant branch: stars which have only just left

the main sequence, burning H to He in a thick the main sequence, burning H to He in a thick shell around a He core; short lived phase, only shell around a He core; short lived phase, only seen in very old clusters.seen in very old clusters.

Red Giant branch: stars burning H in a shell, outer Red Giant branch: stars burning H in a shell, outer envelope expanding, core contracting.envelope expanding, core contracting.

Horizontal branch: low mass stars which are Horizontal branch: low mass stars which are burning He in the core after the He flash. RR burning He in the core after the He flash. RR Lyraes found here.Lyraes found here.

Asymptotic giant branch: Core He exhausted, He Asymptotic giant branch: Core He exhausted, He in a shell around the core, outer envelope in a shell around the core, outer envelope expands, cools.expands, cools.

White dwarfs in M4.White dwarfs in M4.

Main Sequence FittingMain Sequence Fitting

HR diagram for local stars whose HR diagram for local stars whose distances are known.distances are known.

HR diagram for a cluster whose stars HR diagram for a cluster whose stars are all assumed to be at the distance are all assumed to be at the distance – thus m– thus mvv is just like M is just like MVV

Distance modulus (m – M) can be Distance modulus (m – M) can be obtained by determining the offste to obtained by determining the offste to the main sequence from nearby stars the main sequence from nearby stars whose distances are known.whose distances are known.

Evolutionary TracksEvolutionary Tracks Evolutionary tracks depend on input physics: Evolutionary tracks depend on input physics:

convective overhsoot etc.convective overhsoot etc. These lead to different M-L relations for tracks These lead to different M-L relations for tracks

going through the instability strip:going through the instability strip: LogL = a+ blogMLogL = a+ blogM Constant a, b depend on stellar evolutionary input Constant a, b depend on stellar evolutionary input

physics.physics. Get, M,L so, input into a stellar pulsation code and Get, M,L so, input into a stellar pulsation code and

get theoretical light curves, compare with get theoretical light curves, compare with observations:observations:

Compare stellar evolution with stellar pulsation Compare stellar evolution with stellar pulsation theories.theories.