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 OswegoSUNY Oswego

CollaboratorsCollaborators

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

Phelps, D. Wallace, J. Young, S. Scott.Phelps, D. Wallace, J. Young, S. Scott.

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 comoving as star HIF and photosphere not comoving 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

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

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.

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 The Cepheid PL/PC relations are really from the PLC relation.from the PLC relation.

Changes in one are reflected in changes in Changes in one are reflected in changes in the other.the other.

Changes in the PC/PL relation at certain Changes in the PC/PL relation at certain phases have some effect in the mean light phases have some effect in the mean light PC/PL relation.PC/PL relation.

If the LMC Cepheid PL relation is truly non-If the LMC Cepheid PL relation is truly non-linear and linear relation is used, then…..linear and linear relation is used, then…..

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…)point uncertainties (Macri et al…)

Cepheid Pulsation and EvolutionCepheid Pulsation and Evolution

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

Relation to Hertzpsrung progression?Relation to Hertzpsrung progression? Why at 10 days? Why at 10 days? Period-Color/Amplitude-Color Period-Color/Amplitude-Color

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

– 4logT(min))– 4logT(min))

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.