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

to cosmologyto cosmology

Shashi M. KanburShashi M. KanburSUNY OswegoSUNY Oswego

June 2007June 2007

Hubble’s LawHubble’s Law Cosmological Principle plus general relativity yield Cosmological Principle plus general relativity yield

Friedmann’s equations.Friedmann’s equations. The most important parameter in these equations The most important parameter in these equations

is Hubble’s constant, His Hubble’s constant, H00.. Empirically, we have Hubble’s law:Empirically, we have Hubble’s law: V = HV = H0 0 × D,× D, Where V = speed of recession and D is the Where V = speed of recession and D is the

distance.distance. Measure V by Doppler shifts. Hence can measure Measure V by Doppler shifts. Hence can measure

HH00 if D is known. if D is known. Find distances and recession velocities far out in Find distances and recession velocities far out in

the “Hubble Flow”.the “Hubble Flow”.

The Extra-Galactic Distance Scale The Extra-Galactic Distance Scale (Nearby)(Nearby)

Measurement of distance is crucial in Astronomy.Measurement of distance is crucial in Astronomy. Most accurate distances are by parallax: due to the motion Most accurate distances are by parallax: due to the motion

of the Earth around the Sun.of the Earth around the Sun. d = 1/pd = 1/p Unfortunately, this is only possible for the nearest stars (e.g Unfortunately, this is only possible for the nearest stars (e.g

αα Centauri: parallax of 0.75” at a distance of 1.33pc. Centauri: parallax of 0.75” at a distance of 1.33pc. Good out to about 100pc, can only get 10% accuracy for Good out to about 100pc, can only get 10% accuracy for

distances out to a few pc.distances out to a few pc. Many measured by Hipparcos (10% accuracy out to about Many measured by Hipparcos (10% accuracy out to about

100pc).100pc). New missions SIM (10% accuracy out to about 25000pc), New missions SIM (10% accuracy out to about 25000pc),

GAIA (10% accuracy out to about 10000pc).GAIA (10% accuracy out to about 10000pc). Parallax distances used to turn m into M for local stars: Parallax distances used to turn m into M for local stars:

create local HR diagram.create local HR diagram. Then main sequence fitting of young open clusters eg. Then main sequence fitting of young open clusters eg.

Pleiades and Hyades clusters.Pleiades and Hyades clusters.

The Extra-Galactic Distance Scale The Extra-Galactic Distance Scale (Far away)(Far away)

Tully-Fisher relation: rate at which a Tully-Fisher relation: rate at which a galaxy spins is related to its intrinsic galaxy spins is related to its intrinsic luminosity: faster a galaxy spins the more luminosity: faster a galaxy spins the more luminous is the galaxy. Why?luminous is the galaxy. Why?

For circular motion, star of mass m at For circular motion, star of mass m at radius r in a galaxy of mass M and radius radius r in a galaxy of mass M and radius R,R,

mVmVcc22/R = GMm/R/R = GMm/R22, so M~V, so M~Vcc

22/R,/R, The more massive a galaxy, the brighter it The more massive a galaxy, the brighter it

will be.will be.

Cepheids and the Extra-Galactic Cepheids and the Extra-Galactic Distance ScaleDistance Scale

Cepheids are important in that they Cepheids are important in that they connect the near and far distance ladder connect the near and far distance ladder and are currently one of the most accurate and are currently one of the most accurate primary distance scale tools.primary distance scale tools.

Period-Luminosity (PL) relation.Period-Luminosity (PL) relation. Actually we have the Period-Luminosity-Actually we have the Period-Luminosity-

Color (PLC) relation.Color (PLC) relation. Need Period-Mean Density theorem, Need Period-Mean Density theorem,

Stefan-Boltzmann law and the existence of Stefan-Boltzmann law and the existence of the instability strip.the instability strip.

Cepheids and the Extra Galactic Cepheids and the Extra Galactic Distance ScaleDistance Scale

Period-mean density theorem plus Stefan-Period-mean density theorem plus Stefan-Boltzmann yields a relation of the form:Boltzmann yields a relation of the form:

logL = a + blogTlogL = a + blogTee + clogP, + clogP, with an observational counterpart:with an observational counterpart: MMvv = a’ + b’(V-I) + c’logP (*) = a’ + b’(V-I) + c’logP (*) Currently (*) has been found in the Currently (*) has been found in the

LMC,SMC but not in our Galaxy. Why?LMC,SMC but not in our Galaxy. Why? Averaging these equations over color or Averaging these equations over color or

logTlogTee yields, yields, logL = c+dlogP,logL = c+dlogP, MMvv = c’ + d’logP. = c’ + d’logP.

Cepheids and the Extra-Galactic Cepheids and the Extra-Galactic Distance ScaleDistance Scale

Key Project on the Hubble Space Key Project on the Hubble Space Telescope (HST) observed Cepheids Telescope (HST) observed Cepheids in local group galaxies and used the in local group galaxies and used the Cepheid PL relation to get distances.Cepheid PL relation to get distances.

These distances, in turn, enabled the These distances, in turn, enabled the calibration of many secondary calibration of many secondary distance indicators like the TF distance indicators like the TF relation far out in the Hubble flow:relation far out in the Hubble flow:

Estimate HEstimate H00 to 10% error. to 10% error.

Assumptions and Methods IAssumptions and Methods I Cepheid PL relation in V and I bands is well Cepheid PL relation in V and I bands is well

characterized by Cepheids in the Large characterized by Cepheids in the Large Magellanic Cloud (LMC):Magellanic Cloud (LMC):

MMvv = -2.760[±0.03](logP – 1) – 4.218[±0.02], = -2.760[±0.03](logP – 1) – 4.218[±0.02], σσVV = = ±0.16.±0.16.

MMII = -2.962[±0.02](logP – 1) – 4.904[±0.01], = -2.962[±0.02](logP – 1) – 4.904[±0.01], σσVV=±0.11.=±0.11.

Assume this is true universally, except perhaps Assume this is true universally, except perhaps for a metallicity dependence of the zero point.for a metallicity dependence of the zero point.

The LMC is the “calibrator galaxy”The LMC is the “calibrator galaxy” Observe Cepheids in the target galaxy.Observe Cepheids in the target galaxy.

Distance Measurement with LMC Distance Measurement with LMC Cepheid PL RelationCepheid PL Relation

Distancemodulus

Calibrated (LMC) PL relation

Data in target galaxy

Tanvir (1997)

Assumptions and Methods IIAssumptions and Methods II Metallicity correction: change distance modulus Metallicity correction: change distance modulus

by a certain amount determined empirically.by a certain amount determined empirically. Observe in V and I bands to correct for reddening: Observe in V and I bands to correct for reddening:

reddening of light due to interaction with reddening of light due to interaction with interstellar dust.interstellar dust.

Use V and I bands simulatneously to correct for Use V and I bands simulatneously to correct for reddeningreddening

μμ00 = = μμVV – 2.45( – 2.45(μμVV – – μμII)) Assume all Cepheids in the target galaxy are at Assume all Cepheids in the target galaxy are at

the same distance.the same distance. Assume Assume μμ00 = 18.5 magnitudes and there is no = 18.5 magnitudes and there is no

depth effect in the LMC.depth effect in the LMC.

Future IFuture I KP estimate of HKP estimate of H0 0 ~ 72±8km/s/Mpc.~ 72±8km/s/Mpc. CMB estimate of HCMB estimate of H0 0 ~ 71 ± 3km/s/Mpc.~ 71 ± 3km/s/Mpc. But estimating many other cosmological But estimating many other cosmological

parameters, such as parameters, such as ΩΩ, can only be , can only be estimated through a convolution with Hestimated through a convolution with H00..

An independent estimate of HAn independent estimate of H0 0 accurate to accurate to a few percent can help this situation.a few percent can help this situation.

Need a more accurate Cepheid distance Need a more accurate Cepheid distance scale.scale.

Future IIFuture II Different calibrator galaxy? NGC 4258 has Different calibrator galaxy? NGC 4258 has

an accurate geometric distance due to an accurate geometric distance due to water maser measurements: water maser measurements: μμ0 0 ~ 29.28 ~ 29.28 ±0.15 mag.±0.15 mag.

Known more accurately than the distance Known more accurately than the distance to the LMC.to the LMC.

Recent progress on the metallicity Recent progress on the metallicity dependence of the zero point of the PL dependence of the zero point of the PL relation.relation.

But what about change of slope with But what about change of slope with period?period?

Future IIIFuture III Strong statistical, observational and Strong statistical, observational and

theoretical evidence to indicate that theoretical evidence to indicate that in the LMC, the following model is in the LMC, the following model is more consistent with the data:more consistent with the data:

MMvv = a + blogP, logP < 1, = a + blogP, logP < 1, MMv v = a’ + b’logP, logP > 1.= a’ + b’logP, logP > 1. In B,V,I,J,H, marginally linear in K.In B,V,I,J,H, marginally linear in K. Effects estimates of HEffects estimates of H00 to 1-2%. to 1-2%.

Future IVFuture IV Why, in terms of Physics?Why, in terms of Physics? What, in terms of what effect on the What, in terms of what effect on the

distance scale?distance scale? How in terms of how widespread this How in terms of how widespread this

is?is? Combination of Combination of

statistical/theoretical/numerical/obsestatistical/theoretical/numerical/observational work.rvational work.

RR LyraesRR Lyraes Population II (Z=0.001 to Z=0.0001)Population II (Z=0.001 to Z=0.0001) Periods of the order of hours, M ~ 0.55Msun to Periods of the order of hours, M ~ 0.55Msun to

0.65Msun.0.65Msun. Hundreds of solar luminosities.Hundreds of solar luminosities. TTeffeff~6000K to 7000K~6000K to 7000K RRab, RRc, RRd (fundamental, first overtone and RRab, RRc, RRd (fundamental, first overtone and

double mode oscillatorsdouble mode oscillators Mostly found in globular clustersMostly found in globular clusters All stars in a cluster at the same distance and All stars in a cluster at the same distance and

same age but chemically homogeneous.same age but chemically homogeneous. But stars evolve at different rates.But stars evolve at different rates. Globular clusters in halo: distribution of ages in a Globular clusters in halo: distribution of ages in a

globular cluster can tell us how halo collapsed.globular cluster can tell us how halo collapsed.

Globular Cluster HR diagramsGlobular Cluster HR diagrams A: Main Sequence (H burning in the core)A: Main Sequence (H burning in the core) B: Red Giant Branch (H shell burning)B: Red Giant Branch (H shell burning) C: Helium Flash occurs here (Onset of core C: Helium Flash occurs here (Onset of core

He burning)He burning) D: Horizontal Branch Steady State core He D: Horizontal Branch Steady State core He

burningburning E: Hertzsprung gap: Separates Blue HB E: Hertzsprung gap: Separates Blue HB

and Red HBand Red HB F: White Dwarfs: Outer envelope lost, F: White Dwarfs: Outer envelope lost,

Carbon core remains.Carbon core remains.

Globular Cluster AgesGlobular Cluster Ages Absolute ages: fit theoretical stellar evolutionary isochrones Absolute ages: fit theoretical stellar evolutionary isochrones

to CMD diagrams.to CMD diagrams. Stellar Isochrone: locus of points on a HR diagram which Stellar Isochrone: locus of points on a HR diagram which

have the same age for all masses.have the same age for all masses. CMD: color-magnitude diagram: HR diagram: TCMD: color-magnitude diagram: HR diagram: Teffeff vs. L. vs. L. Need transformation between color and TNeed transformation between color and Teff,eff, magnitude and L magnitude and L

(bolometric correction).(bolometric correction). Luminosity of the main sequence turnoff (MSTO): MLuminosity of the main sequence turnoff (MSTO): MVV(TO) is a (TO) is a

good stellar clock to determine globular cluster ages.good stellar clock to determine globular cluster ages. But: uncertainty of 0.02mag. In color means an error of 0.1 But: uncertainty of 0.02mag. In color means an error of 0.1

mag. In derived distance modulus and hence an error of 1.5 mag. In derived distance modulus and hence an error of 1.5 Gyr in age.Gyr in age.

MMVV(TO) is the bluest point on the main sequence for a gc: (TO) is the bluest point on the main sequence for a gc: same color over a large range in magnitude.same color over a large range in magnitude.

MMVV(BTO) is brighter than the main sequence but 0.05 mag. (BTO) is brighter than the main sequence but 0.05 mag. redder – easier to measure, twice as accurate.redder – easier to measure, twice as accurate.

Globular Cluster AgesGlobular Cluster Ages Can measure relative cluster ages and leave the zero point for a Can measure relative cluster ages and leave the zero point for a

separate problem.separate problem. Brightness difference between HB and MSTOBrightness difference between HB and MSTO Brightness of HB set by the core mass of stars evolving up the GB.Brightness of HB set by the core mass of stars evolving up the GB. But as the cluster ages, its MSTO decreases, but core mass of But as the cluster ages, its MSTO decreases, but core mass of

stars going up the GB tends to be the same.stars going up the GB tends to be the same. As a cluster ages, its HB stars tend to be bluer at constant As a cluster ages, its HB stars tend to be bluer at constant

brightness, but the MSTO decreases with increasing age. Thusbrightness, but the MSTO decreases with increasing age. Thus ΔΔMMVV(HB-MSTO) increases with cluster age.(HB-MSTO) increases with cluster age. But metallicity also plays a role:But metallicity also plays a role: MMVV(HB) = a+b[M/H](HB) = a+b[M/H] MMVV(HB) ~ M(HB) ~ MVV(RR Lyraes in GC)(RR Lyraes in GC) Also degeneracy between age and distance: Can simulate an older Also degeneracy between age and distance: Can simulate an older

of younger GC by moving it closer or further away.of younger GC by moving it closer or further away. Thus need to know the distance to GC’sThus need to know the distance to GC’s Thus need to know MThus need to know MVV(RR Lyraes)(RR Lyraes)

RR Lyraes and GC agesRR Lyraes and GC ages Getting MGetting MVV(RR) amounts to obtaining (RR) amounts to obtaining

a population II distance scale.a population II distance scale. But how? Don’t obey a PL like But how? Don’t obey a PL like

Cepheids excpet perhaps in the K?Cepheids excpet perhaps in the K? Stellar pulsation modesl: obsrevation Stellar pulsation modesl: obsrevation

with theory.with theory. Light curve structure against MLight curve structure against MVV

relation.relation. Metallicity complication.Metallicity complication.

Oosterhoff DichotomyOosterhoff Dichotomy Two types of GC’s: OoI, OoII, based Two types of GC’s: OoI, OoII, based

on mean period their fundamental on mean period their fundamental mode RR Lyrae stars.mode RR Lyrae stars.

Why? And what implications for Why? And what implications for age/distance estimation? Hot topic age/distance estimation? Hot topic right now.right now.

Period-Color/Amplitude Color Period-Color/Amplitude Color relations as a function of phase.relations as a function of phase.