209th AAS Meeting, January 2007, Seattle, WA
A Theoretical Investigation into Period-Color Relations
for Cepheids in the Small Magellanic Cloud
S. M. Kanbur, G. Feiden (Physics Department, SUNY Oswego) & C.C. Ngeow (Astronomy Department, UIUC)
Abstract: We present preliminary results of a theoretical investigation into the Cepheid Period-Color (PC) relation for the SMC. We
construct a large grid of full amplitude hydrodynamic models of low metallicity Cepheids and develop theoretical PC relations as a function
of phase. We compare these relations with observations and formulate a possible theoretical framework to explain the variation of the PC
relation in the Galaxy, LMC and SMC as a function of phase, metallicity and period. We briefly discuss implications for the Cepheid PeriodLuminosity (PL) relation.
Introduction:
 The Cepheid PL relation is a cornerstone of modern astrophysics. It is of fundamental importance in establishing an extra-galactic
distance scale that is independent of CMB studies. A Cepheid based scale can help to break the degeneracy present between Ω and
Hubble’s constant presented from CMB studies.
 Recent evidence has emerged that the LMC Cepheid PL and Period-Color (PC) relations are non-linear: the data are more consistent
with two lines of differing slopes with a break at a period of 10 days. In contrast, the Galactic and SMC PC relations , and hence the
PL relations, are found to be linear with current data. Since these three galaxies have different metallicity, can metallicity cause such
an effect?
 Kanbur, Ngeow & Buchler (KNB, 2004) and Kanbur & Ngeow (KN, 2006) published theoretical hydrodynamic models of Galactic
and LMC Cepheids, and found that the interaction of the hydrogen ionization front (HIF) and stellar photosphere may play an
important role in explaining the observed properties of PC and PL relations.
 Here we extend the work of KNB and KN by studying a large grid of theoretical models of SMC Cepheids: in particular we analyze
the interaction of the HIF and photosphere in comparison to Galactic and LMC models.
Figure 1: Plots of theoretical
PC relations at maximum (top
panel) and minimum (bottom
panel) light. Open and closed
squares denote models with
two different ML relations
adopted from the literature,
whilst crosses denote the data
obtained from the OGLE
SMC observations. The flat
nature of the maximum light
PC relation is evident.
Method, Analysis & Preliminary Results:
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.
Acknowledgement: GF notes
the support of SUNY Oswego. SK
would like to acknowledge the
HST Grant HST-AR-10673.
References:
Kanbur, S., Ngeow, C. & Buchler, J., 2004, MNRAS,
354, 212.
Kanbur, S., Ngeow, C., 2006, MNRAS, 369, 705.
 Since PL and PC relations are projections of the PLC relation on either two axes, properties of PC relations will
affect the observed PL relations.
 We integrate the time dependent equations of momentum, mass and energy conservation, together with a Saha
equation of state, radiative transfer in the diffusion approximation and a numerical recipe to compute non-local
time dependent turbulent convection. The system is completed by an initial model in hydrostatic equilibrium and
well defined boundary conditions at the center and surface.
 Each model is specified by a mass, luminosity, effective temperature and composition, with X=0.7 and Z=0.004
(for the SMC models), and a variety of mass-luminosity (ML) relations from stellar evolution.
 Fig. 1 displays the theoretical PC relations (open and solid squares) at various phases (maximum and minimum
light) superimposed on observational results from OGLE SMC data.
 The left and right panels of Fig. 2 display the photospheric density at maximum and minimum light for the SMC
models and the GAL+LMC models from KN, respectively.
 The main difference between Galactic, LMC and SMC models is the photospheric density at minimum light: when
the photosphere and HIF interact at low densities, because of the properties of the Saha ionization equation, the
photospheric temperature and hence color is almost independent of period. This does not happen for Galactic
models. This occurs for LMC models with periods greater than 10 days. For SMC models the HIF-photosphere
interaction is at high density for most phases except close to maximum light. This difference in the HIFphotosphere interaction at minimum light is believed to be responsible for the non-linearity and linearity seen in
the LMC and Galactic/SMC PL relations respectively.