The Hydrogen Ionization The Hydrogen Ionization Front-Photosphere Front-Photosphere

interaction and the Period-interaction and the Period-Color relations of classical Color relations of classical

variable stars.variable stars.

Shashi M. Kanbur,Shashi M. Kanbur,

SUNY Oswego, July 2007SUNY Oswego, July 2007

CollaboratorsCollaborators

Chow Choong Ngeow.Chow Choong Ngeow. D. Leonard, N. Tanvir, M. Hendry.D. Leonard, N. Tanvir, M. Hendry. L. Macri, T. Barnes, S. Nikolaev.L. Macri, T. Barnes, S. Nikolaev. A. Nanthakumar, C. Koen.A. Nanthakumar, C. Koen. G. Feiden, D. Crain, R. Stevens, C. Phelps, G. Feiden, D. Crain, R. Stevens, C. Phelps,

D. Wallace, J. Young, S. Scott (SUNY D. Wallace, J. Young, S. Scott (SUNY Oswego undergraduates).Oswego undergraduates).

A. Kanaan, Paulo Henrique, Alexandre A. Kanaan, Paulo Henrique, Alexandre Zabot, Vanessa Peixoto (UFSC).Zabot, Vanessa Peixoto (UFSC).

FundingFunding

NASA/HST Legacy ProjectNASA/HST Legacy Project American Astronomical Society Small American Astronomical Society Small

Research AwardResearch Award American Astronomical Society American Astronomical Society

Chretien International Research Chretien International Research AwardAward

SUNY OswegoSUNY Oswego

The Hydrogen Ionization front The Hydrogen Ionization front (HIF).(HIF).

Region of rapid temperature change near Region of rapid temperature change near the surface of a star where the the surface of a star where the temperature is changing and hence temperature is changing and hence hydrogen is ionizing.hydrogen is ionizing.

Together with this there is a very sharp Together with this there is a very sharp rise in opacity.rise in opacity.

Stellar photosphere is defined as the Stellar photosphere is defined as the location where optical depth = 2/3.location where optical depth = 2/3.

HIF and photosphere not co-moving as star HIF and photosphere not co-moving as star pulsates.pulsates.

The HIF-photosphere interactionThe HIF-photosphere interaction

In certain situations, the photosphere can In certain situations, the photosphere can lie at the base of the HIF.lie at the base of the HIF.

Further movement in very hard due to Further movement in very hard due to opacity wall.opacity wall.

Then the temperature of the photosphere Then the temperature of the photosphere is very close to the temperature at which is very close to the temperature at which Hydrogen ionizes.Hydrogen ionizes.

In this situation, the color of the star is the In this situation, the color of the star is the temperature at which Hydrogen ionizes.temperature at which Hydrogen ionizes.

The HIF-photosphere interactionThe HIF-photosphere interaction

Saha ionization equation used in stellar Saha ionization equation used in stellar pulsation models.pulsation models.

Temperature at which Hydrogen ionizes is Temperature at which Hydrogen ionizes is somewhat independent of density for low somewhat independent of density for low densities.densities.

Thus, when the HIF-photosphere are Thus, when the HIF-photosphere are engaged, temperature of stellar engaged, temperature of stellar photosphere is somewhat independent of photosphere is somewhat independent of global stellar properties, such as period, at global stellar properties, such as period, at low densities.low densities.

This can lead to changes in the period-This can lead to changes in the period-color relation.color relation.

The Period-Color RelationThe Period-Color Relation

Because the photosphere and HIF are Because the photosphere and HIF are either engaged or not, such changes can either engaged or not, such changes can be sudden.be sudden.

Only occurs when the interaction is at low Only occurs when the interaction is at low densities.densities.

Because the HIF lies further in the mass Because the HIF lies further in the mass distribution as the L/M ratio changes, the distribution as the L/M ratio changes, the nature and extent of the HIF-photosphere nature and extent of the HIF-photosphere interaction changes with period and interaction changes with period and metallicity and pulsation phase.metallicity and pulsation phase.

Period Color Relations in CepheidsPeriod Color Relations in Cepheids

There is a PC relation at all phases of There is a PC relation at all phases of pulsation: most workers study the PC pulsation: most workers study the PC relation at mean light.relation at mean light.

But mean light PC relation is an But mean light PC relation is an average over the relation at all other average over the relation at all other phases.phases.

Insight into PC relation behavior at Insight into PC relation behavior at mean light can be gained by mean light can be gained by studying PC relation at other phases.studying PC relation at other phases.

PC/AC relationsPC/AC relations

Stefan-Boltzmann law applied to Stefan-Boltzmann law applied to max/min lightmax/min light

logL(max) – logL(min) = 4logT(max) logL(max) – logL(min) = 4logT(max) – 4logT(min)– 4logT(min)

An Amplitude-Color (AC) relation.An Amplitude-Color (AC) relation. PC relation flat at max/min implies an PC relation flat at max/min implies an

AC relation at min/max light.AC relation at min/max light. Apply this to variable stars.Apply this to variable stars.

CepheidsCepheids

Pop I, core He burning, Z=0.02-Z=0.004. Pop I, core He burning, Z=0.02-Z=0.004. Going up AGB with blueward incursions Going up AGB with blueward incursions into instability strip.into instability strip.

2-10 solar masses, thousands of solar 2-10 solar masses, thousands of solar luminosities, (M-L relation from stellar luminosities, (M-L relation from stellar evolution calculations, 5000<Teff<6000Kevolution calculations, 5000<Teff<6000K

Consider only fundamental mode here.Consider only fundamental mode here. Obey a PLC relation which form the PL or Obey a PLC relation which form the PL or

PC relation when integrated over the other PC relation when integrated over the other variable.variable.

Period-Color Relations in CepheidsPeriod-Color Relations in Cepheids

Galactic Cepheids obey a flat PC relation at Galactic Cepheids obey a flat PC relation at maximum light.maximum light.

LMC/SMC Cepheids obey a flat/flatter PC relation LMC/SMC Cepheids obey a flat/flatter PC relation at maximum light for Cepheids with periods at maximum light for Cepheids with periods greater than 10 days.greater than 10 days.

In Galactic Cepheids, HIF and photosphere are In Galactic Cepheids, HIF and photosphere are only engaged at maximum light.only engaged at maximum light.

In SMC/LMC Cepheids, always engaged, but only In SMC/LMC Cepheids, always engaged, but only at low densities for Cepheids with periods greater at low densities for Cepheids with periods greater than 10 days for the LMC.than 10 days for the LMC.

LMC Cepheids show a disengagement at all LMC Cepheids show a disengagement at all phases for periods greater than 10 days.phases for periods greater than 10 days.

Modeling CepheidsModeling Cepheids Full amplitude hydrodynamic models with a Saha ionization Full amplitude hydrodynamic models with a Saha ionization

equation of state.equation of state. Input parameters include, M, L, Teff, X and Z. M-L come Input parameters include, M, L, Teff, X and Z. M-L come

from stellar evolutionary calculations.from stellar evolutionary calculations. Given M-L is dependent on metallicity and input physics Given M-L is dependent on metallicity and input physics

such as convective overshoot.such as convective overshoot. Linear models give region of fundamental mode instability.Linear models give region of fundamental mode instability. Non-linear models develop linear models until a stable limit Non-linear models develop linear models until a stable limit

cycle is reached.cycle is reached. Codes contain a numerical recipe to model time dependent Codes contain a numerical recipe to model time dependent

turbulent convection.turbulent convection. Interpolation in BaSeL/Kurucz atmosphere with logg and Interpolation in BaSeL/Kurucz atmosphere with logg and

Teff as a function of phase to convert L,T to V band Teff as a function of phase to convert L,T to V band amplitude and V-I colors.amplitude and V-I colors.

Microturbulence parameter does not affect broadband Microturbulence parameter does not affect broadband colors.colors.

Modeling CepheidsModeling Cepheids Galactic Cepheids: HIF and photosphere Galactic Cepheids: HIF and photosphere

engaged at maximum light; disengaged at engaged at maximum light; disengaged at other phases.other phases.

LMC Cepheids: HIF and photosphere LMC Cepheids: HIF and photosphere engaged at all phases for short engaged at all phases for short (P<10days) period models. (P<10days) period models. Disengagement around minimum light for Disengagement around minimum light for long period models.long period models.

SMC Cepheids: Engagement at all phases SMC Cepheids: Engagement at all phases and periods.and periods.

Short period Cepheid models most Short period Cepheid models most discrepant.discrepant.

Figure 2: The photospheric density (1/V, where V is the specific volume) at maximum (top) and minimum (bottom) light in the theoretical models. The left panel shows the results from the SMC models with two ML relations. The rights panel show the comparison between the LMC models (open and solid squares) and the Galactic models (crosses). The right panel is adopted from KN.

SMC LMC & GAL

The Cepheid PL relation and H0The Cepheid PL relation and H0 The Cepheid PL/PC relations are really from the The Cepheid PL/PC relations are really from the

PLC relation.PLC relation. Changes in one are reflected in changes in the Changes in one are reflected in changes in the

other.other. Changes in the PC/PL relation at certain phases Changes in the PC/PL relation at certain phases

have some effect in the mean light PC/PL relation.have some effect in the mean light PC/PL relation. Strong evidence that the mean light LMC PL Strong evidence that the mean light LMC PL

relation is non-linear.relation is non-linear.Tamman et al (2002), Kanbur and Ngeow (2004), Tamman et al (2002), Kanbur and Ngeow (2004),

Sandage et al (2004), Ngeow et al (2005), Ngeow Sandage et al (2004), Ngeow et al (2005), Ngeow and Kanbur (2006), Kanbur et al (2007), Koen, and Kanbur (2006), Kanbur et al (2007), Koen, Kanbur and Ngeow (2007).Kanbur and Ngeow (2007).

Simulations of the LMC PL Simulations of the LMC PL RelationsRelations

Recipe:1. log(P) distribution

2. G(0,0.23) for instability strip

3. G(0,0.05) forphotometric error

4. Non-linear andlinear PL relations

THE LMC PL relation: evidence for THE LMC PL relation: evidence for non-linearitynon-linearity

Multi-phase PC/PL relations in the V and I Multi-phase PC/PL relations in the V and I bands using OGLE.bands using OGLE.

Statistical tests: F test, Least Absolute Statistical tests: F test, Least Absolute deviation, Robust estimation using Tukey’s deviation, Robust estimation using Tukey’s methods, Non-parametric methods such as methods, Non-parametric methods such as LOESS, examination of residuals, LOESS, examination of residuals, testimator, Schwarz Information Criterion.testimator, Schwarz Information Criterion.

All point to a non-linear LMC PL/PC relation All point to a non-linear LMC PL/PC relation using OGLE and MACHO datausing OGLE and MACHO data

Enough data, reddening errors?Enough data, reddening errors?

The LMC PL relation: evidence for The LMC PL relation: evidence for non-linearitynon-linearity

Enough long period data? F test IS sensitive to Enough long period data? F test IS sensitive to this.this.

Add data to the long period end from various Add data to the long period end from various sources: Sebo et al (2002), Caldwell and Laney sources: Sebo et al (2002), Caldwell and Laney (1991), Gieren (2005).(1991), Gieren (2005).

Reddening/Extinction errors? Multi-phase Reddening/Extinction errors? Multi-phase relations, evidence from maximum light.relations, evidence from maximum light.

If Extinction errors, then LMC Cepheids get hotter If Extinction errors, then LMC Cepheids get hotter at maximum light as the period increases – very at maximum light as the period increases – very different to Galactic Cepheids.different to Galactic Cepheids.

Cepheids in the inner field of NGC 4258 may Cepheids in the inner field of NGC 4258 may follow a non-linear PL.follow a non-linear PL.

The Cepheid PL relations and H0The Cepheid PL relations and H0

Can affect H0 by as much as 2% (Ngeow Can affect H0 by as much as 2% (Ngeow and Kanbur 2006).and Kanbur 2006).

If the goal is to reduce errors on the If the goal is to reduce errors on the accuracy of H0 estimates to below 5% via accuracy of H0 estimates to below 5% via a method independent of CMB (Spergel et a method independent of CMB (Spergel et al 2006), then this is important especially al 2006), then this is important especially as..as..

Other work is attempting to reduce zero Other work is attempting to reduce zero point uncertainties (Macri et al 2006, van point uncertainties (Macri et al 2006, van Leeuwen et al 2007)Leeuwen et al 2007)

Cepheid Pulsation and EvolutionCepheid Pulsation and Evolution

Equally important to understand this effect in terms of Equally important to understand this effect in terms of pulsation physics.pulsation physics.

Relation to Hertzpsrung progression?Relation to Hertzpsrung progression? Why at 10 days? Why at 10 days? Why are SMC photospheric densities greater than that for Why are SMC photospheric densities greater than that for

the LMC/Galactic models - and what are the observational the LMC/Galactic models - and what are the observational implications of this?implications of this?

Period-Color/Amplitude-Color relations.Period-Color/Amplitude-Color relations. Relation to metallicity: Galactic/LMC/SMC Cepheids have Relation to metallicity: Galactic/LMC/SMC Cepheids have

different metallicities which changes their L/M ratios and different metallicities which changes their L/M ratios and Teff.Teff.

This changes the relative location of the HIF and stellar This changes the relative location of the HIF and stellar photosphere and hence thephotosphere and hence the

Period and phase at which they can interact at low Period and phase at which they can interact at low densities.densities.

RR LyraesRR Lyraes Periods of the order of hours, Z=0.001 – 0.0001, Periods of the order of hours, Z=0.001 – 0.0001,

Population II, mostly in globular clusters.Population II, mostly in globular clusters. Core He burning after He flash, masses 0.55-0.65 Core He burning after He flash, masses 0.55-0.65

solar masses, L about 55-90 times solar and solar masses, L about 55-90 times solar and 6000<Teff <7000K. On the horizontal branch.6000<Teff <7000K. On the horizontal branch.

Absolute magnitude leads to age and Pop II Absolute magnitude leads to age and Pop II distance scale.distance scale.

Knowledge of absolute magnitude in globular Knowledge of absolute magnitude in globular clusters leads to an estimate of the age of clusters leads to an estimate of the age of globular cluster – galaxy formation.globular cluster – galaxy formation.

Consider only fundamental mode oscillators here.Consider only fundamental mode oscillators here. Don’t obey a PL relation (maybe PK?)Don’t obey a PL relation (maybe PK?)

RR LyraesRR Lyraes

PC relation at minimum light is flat.PC relation at minimum light is flat. AC relation at maximum light such AC relation at maximum light such

that higher amplitude stars are that higher amplitude stars are driven to bluer colors at maximum driven to bluer colors at maximum light.light.

PC relation at minimum light used to PC relation at minimum light used to estimate reddening.estimate reddening.

Could also use AC relations.Could also use AC relations.

RR LyraesRR Lyraes PC relation at minimum light is flat PC relation at minimum light is flat

because HIF is further out in the mass because HIF is further out in the mass distribution.distribution.

Low density HIF-photosphere interaction Low density HIF-photosphere interaction only occurs at minimum light.only occurs at minimum light.

At other phases interaction is at high At other phases interaction is at high density and os more sensitive to density and os more sensitive to temeprature ie. There is PC(max) relation.temeprature ie. There is PC(max) relation.

Working on the situation at maximum light Working on the situation at maximum light or as the star brightens from minimum.or as the star brightens from minimum.

FutureFuture 2 weeks of time on SMARTS facilities in Cerro-Tololo, Chile using 2 weeks of time on SMARTS facilities in Cerro-Tololo, Chile using

CPAPIR CCD from Montreal. 20 nights in November 2007/January CPAPIR CCD from Montreal. 20 nights in November 2007/January 2008.2008.

Same pointings as OGLE/MACHO LMC: develop infra-red light Same pointings as OGLE/MACHO LMC: develop infra-red light curves for OGLE/MACHO LMC Cepheids: data currently being curves for OGLE/MACHO LMC Cepheids: data currently being reduced in SUNY Oswego and NOAO (Lucas Macri).reduced in SUNY Oswego and NOAO (Lucas Macri).

Check non-linearity in infra-red.Check non-linearity in infra-red. PCA templates for IR light curves.PCA templates for IR light curves. Definitive test of non-linearity with results from HST Legacy Definitive test of non-linearity with results from HST Legacy

survey.survey. Further IR LMC/SMC observations with LNA Brazil plus Antonio Further IR LMC/SMC observations with LNA Brazil plus Antonio

Kanaan of UFSC: robotic telescope.Kanaan of UFSC: robotic telescope. DIRECT data for M31/M33 CFHT data for M31 in Sloan filters, NGC DIRECT data for M31/M33 CFHT data for M31 in Sloan filters, NGC

4258 (water maser galaxy).4258 (water maser galaxy). More modeling, PCA analysis.More modeling, PCA analysis. RR Lyraes: M15 observations, modeling, PCA –light curve structure RR Lyraes: M15 observations, modeling, PCA –light curve structure

relations.relations.