Shashi M. Kanbur, SUNY Oswego

1. The Hydrogen Ionization Front-Photosphere interaction and the Period-Color relations of classical variable stars. Shashi M. Kanbur, SUNY Oswego

2. Collaborators • Chow Choong Ngeow • D. Leonard, N. Tanvir, M. Hendry • L. Macri, T. Barnes, S. Nikolaev • A. Nanthakumar, C. Koen • G. Feiden, D. Crain, R. Stevens, C. Phelps, D. Wallace, J. Young, S. Scott.

3. The Hydrogen Ionization front (HIF). • Region of rapid temperature change near the surface of a star where the temperature is changing and hence hydrogen is ionizing. • Together with this there is a very sharp rise in opacity. • Stellar photosphere is defined as the location where optical depth = 2/3. • HIF and photosphere not comoving as star pulsates.

6. The HIF-photosphere interaction • In certain situations, the photosphere can lie at the base of the HIF. • Further movement in very hard due to opacity wall. • Then the temperature of the photosphere is very close to the temperature at which Hydrogen ionizes. • In this situation, the color of the star is the temperature at which Hydrogen ionizes.

7. The HIF-photosphere interaction • Saha ionization equation used in stellar pulsation models. • Temperature at which Hydrogen ionizes is somewhat independent of density for low densities. • Thus, when the HIF-photosphere are engaged, temperature of stellar photosphere is somewhat independent of global stellar properties, such as period, at low densities. • This can lead to changes in the period-color relation.

8. The Period-Color Relation • Because the photosphere and HIF are either engaged or not, such changes can be sudden. • Only occurs when the interaction is at low densities. • Because the HIF lies further in the mass distribution as the L/M ratio changes, the nature and extent of the HIF-photosphere interaction changes with period and metallicity and pulsation phase.

9. Period-Color Relations in Cepheids • Galactic Cepheids obey a flat PC relation at maximum light. • LMC/SMC Cepheids obey a flat PC relation at maximum light for Cepheids with periods greater than 10 days. • In Galactic Cepheids, HIF and photosphere are only engaged at maximum light. • In SMC/LMC Cepheids, always engaged, but only at low densities for Cepheids with periods greater than 10 days. • LMC Cepheids show a disengagement at all phases for periods greater than 10 days.

14. SMC LMC & GAL 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.

15. The Cepheid PL relation and H0 • The Cepheid PL/PC relations are really from the PLC relation. • Changes in one are reflected in changes in the other. • Changes in the PC/PL relation at certain phases have some effect in the mean light PC/PL relation. • If the LMC Cepheid PL relation is truly non-linear and linear relation is used, then…..

16. The Cepheid PL relations and H0 • Can affect H0 by as much as 2% (Ngeow and Kanbur 2006). • If the goal is to reduce errors on the accuracy of H0 estimates to below 5% via a method independent of CMB (Spergel et al 2006), then this is important especially as.. • Other work is attempting to reduce zero point uncertainties (Macri et al…)

17. Cepheid Pulsation and Evolution • Equally important to understand this effect in terms of pulsation physics. • Relation to Hertzpsrung progression? • Why at 10 days? • Period-Color/Amplitude-Color relations. • logL(max) – logL(min) = 4(logT(max) – 4logT(min))

18. RR Lyraes • PC relation at minimum light is flat. • AC relation at maximum light such that higher amplitude stars are driven to bluer colors at maximum light. • PC relation at minimum light used to estimate reddening. • Could also use AC relations.