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The Hydrogen Ionization
Front-Photosphere
interaction and the PeriodColor relations of classical
variable stars.
Shashi M. Kanbur,
SUNY Oswego, July 2007
Collaborators
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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
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NASA/HST Legacy Project
American Astronomical Society Small
Research Award
American Astronomical Society
Chretien International Research
Award
SUNY Oswego
The Hydrogen Ionization front
(HIF).
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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
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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
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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 periodcolor relation.
The Period-Color Relation
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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
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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
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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
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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<Teff<6000K
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
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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
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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
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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).
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Simulations of the LMC PL
Relations
Recipe:
1. log(P) distribution
2. G(0,0.23) for
instability strip
3. G(0,0.05) for
photometric error
4. Non-linear and
linear PL relations
THE LMC PL relation: evidence for
non-linearity
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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
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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
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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
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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
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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<Teff <7000K. On the horizontal branch.
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
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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
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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
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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.