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### The Hydrogen Ionization Front-Photosphere interaction and the Period-Color relations of classical variable stars.

Shashi M. Kanbur,

SUNY Oswego, July 2007

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 (SUNY Oswego undergraduates).
- A. Kanaan, Paulo Henrique, Alexandre Zabot, Vanessa Peixoto (UFSC).

Funding

- NASA/HST Legacy Project
- American Astronomical Society Small Research Award
- American Astronomical Society Chretien International Research Award
- SUNY Oswego

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 co-moving as star pulsates.

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.

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.

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.

Period Color Relations in Cepheids

- There is a PC relation at all phases of pulsation: most workers study the PC relation at mean light.
- But mean light PC relation is an average over the relation at all other phases.
- Insight into PC relation behavior at mean light can be gained by studying PC relation at other phases.

PC/AC relations

- Stefan-Boltzmann law applied to max/min light
- logL(max) – logL(min) = 4logT(max) – 4logT(min)
- An Amplitude-Color (AC) relation.
- PC relation flat at max/min implies an AC relation at min/max light.
- Apply this to variable stars.

Cepheids

- Pop I, core He burning, Z=0.02-Z=0.004. Going up AGB with blueward incursions into instability strip.
- 2-10 solar masses, thousands of solar luminosities, (M-L relation from stellar evolution calculations, 5000
- Consider only fundamental mode here.
- Obey a PLC relation which form the PL or PC relation when integrated over the other variable.

Period-Color Relations in Cepheids

- Galactic Cepheids obey a flat PC relation at maximum light.
- LMC/SMC Cepheids obey a flat/flatter 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 for the LMC.
- LMC Cepheids show a disengagement at all phases for periods greater than 10 days.

Modeling Cepheids

- Full amplitude hydrodynamic models with a Saha ionization equation of state.
- Input parameters include, M, L, Teff, X and Z. M-L come from stellar evolutionary calculations.
- Given M-L is dependent on metallicity and input physics such as convective overshoot.
- Linear models give region of fundamental mode instability.
- Non-linear models develop linear models until a stable limit cycle is reached.
- Codes contain a numerical recipe to model time dependent turbulent convection.
- Interpolation in BaSeL/Kurucz atmosphere with logg and Teff as a function of phase to convert L,T to V band amplitude and V-I colors.
- Microturbulence parameter does not affect broadband colors.

Modeling Cepheids

- Galactic Cepheids: HIF and photosphere engaged at maximum light; disengaged at other phases.
- LMC Cepheids: HIF and photosphere engaged at all phases for short (P<10days) period models. Disengagement around minimum light for long period models.
- SMC Cepheids: Engagement at all phases and periods.
- Short period Cepheid models most discrepant.

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.

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.
- Strong evidence that the mean light LMC PL relation is non-linear.

Tamman et al (2002), Kanbur and Ngeow (2004), Sandage et al (2004), Ngeow et al (2005), Ngeow and Kanbur (2006), Kanbur et al (2007), Koen, Kanbur and Ngeow (2007).

Simulations of the LMC PL Relations

- Recipe:
- log(P) distribution
- G(0,0.23) for
- instability strip
- G(0,0.05) for
- photometric error
- Non-linear and
- linear PL relations

THE LMC PL relation: evidence for non-linearity

- Multi-phase PC/PL relations in the V and I bands using OGLE.
- Statistical tests: F test, Least Absolute deviation, Robust estimation using Tukey’s methods, Non-parametric methods such as LOESS, examination of residuals, testimator, Schwarz Information Criterion.
- All point to a non-linear LMC PL/PC relation using OGLE and MACHO data
- Enough data, reddening errors?

The LMC PL relation: evidence for non-linearity

- Enough long period data? F test IS sensitive to this.
- Add data to the long period end from various sources: Sebo et al (2002), Caldwell and Laney (1991), Gieren (2005).
- Reddening/Extinction errors? Multi-phase relations, evidence from maximum light.
- If Extinction errors, then LMC Cepheids get hotter at maximum light as the period increases – very different to Galactic Cepheids.
- Cepheids in the inner field of NGC 4258 may follow a non-linear PL.

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 2006, van Leeuwen et al 2007)

Cepheid Pulsation and Evolution

- Equally important to understand this effect in terms of pulsation physics.
- Relation to Hertzpsrung progression?
- Why at 10 days?
- Why are SMC photospheric densities greater than that for the LMC/Galactic models - and what are the observational implications of this?
- Period-Color/Amplitude-Color relations.
- Relation to metallicity: Galactic/LMC/SMC Cepheids have different metallicities which changes their L/M ratios and Teff.
- This changes the relative location of the HIF and stellar photosphere and hence the
- Period and phase at which they can interact at low densities.

RR Lyraes

- Periods of the order of hours, Z=0.001 – 0.0001, Population II, mostly in globular clusters.
- Core He burning after He flash, masses 0.55-0.65 solar masses, L about 55-90 times solar and 6000
- Absolute magnitude leads to age and Pop II distance scale.
- Knowledge of absolute magnitude in globular clusters leads to an estimate of the age of globular cluster – galaxy formation.
- Consider only fundamental mode oscillators here.
- Don’t obey a PL relation (maybe PK?)

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.

RR Lyraes

- PC relation at minimum light is flat because HIF is further out in the mass distribution.
- Low density HIF-photosphere interaction only occurs at minimum light.
- At other phases interaction is at high density and os more sensitive to temeprature ie. There is PC(max) relation.
- Working on the situation at maximum light or as the star brightens from minimum.

Future

- 2 weeks of time on SMARTS facilities in Cerro-Tololo, Chile using CPAPIR CCD from Montreal. 20 nights in November 2007/January 2008.
- Same pointings as OGLE/MACHO LMC: develop infra-red light curves for OGLE/MACHO LMC Cepheids: data currently being reduced in SUNY Oswego and NOAO (Lucas Macri).
- Check non-linearity in infra-red.
- PCA templates for IR light curves.
- Definitive test of non-linearity with results from HST Legacy survey.
- Further IR LMC/SMC observations with LNA Brazil plus Antonio Kanaan of UFSC: robotic telescope.
- DIRECT data for M31/M33 CFHT data for M31 in Sloan filters, NGC 4258 (water maser galaxy).
- More modeling, PCA analysis.
- RR Lyraes: M15 observations, modeling, PCA –light curve structure relations.

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