The Mid­Infrared Period­Luminosity Relations for Classical Cepheids

Chow-Choong Ngeow (IANCU)

withMarcella Marconi, Ilaria Musella, Michele Cignoni (INAF),

Shashi M. Kanbur (SUNY-Oswego) & Hilding Neilson (Argelander Institute for Astronomy)

Graduate Institute of Astronomy, National Central UniversityGraduate Institute of Astronomy, National Central University

The Need of Accurate & Independent Measurement of H

o in Cosmology

Macri et al (2006)

Freedman & Madore (2010)

I. Empirical P-L Relations

Deriving MIR P-L Relations From Spitzer Archival Data

SAGE: Meixner et al (2006)

The MIR P-L Relation: LMC

● Ngeow & Kanbur (2008):

– SAGE single epoch data

– OGLE­II Cepheids (N~600)

● Ngeow et al. (2009):

– SAGE two epoch data

– OGLE­III Cepheids     (N ~ 1800)

● Open squares: rejected outliers using sigma­clipping method

The MIR P-L Relation: SMC

Ngeow & Kanbur (2010)

A Note on SMC MIR P-L Relations

● SMC P­L relation is known to exhibit break at log(P)=0.4 in optical

● Confirmed the break in MIR P­L relation

● Due to evolutionary effect (Baraffe et al 1998)

Ngeow & Kanbur (2010)

The AKARI LMC Data

Ngeow et al. (2010)

AKARI SAGE Ita et al (2008)

The AKARI P-L Relation

Slope for N3 P-L Relation: -3.25 ± 0.05 Ngeow et al. (2010)

In contrast to SAGE data, AKARI data include MJD information   →apply random­phase correction for single­phase epoch data

Summary of Empirical MIR P-L Slopes for MC Cepheids

● LMC:– N3: ­3.25 ± 0.05

– 3.6 micron: ­3.25 ± 0.01

– 4.5 micron: ­3.21 ± 0.01

– 5.8 micron: ­3.18 ± 0.02

– 8.0 micron: ­3.20 ± 0.04

● SMC:– 3.6 micron: ­3.23 ± 0.02

– 4.5 micron: ­3.18 ± 0.02

– 5.8 micron: ­3.23 ± 0.04

– 8.0 micron: ­3.25 ± 0.05

Empirical Multi-Band P-L Slopes

Expected MIR P-L Slopes

● L=4 Rπ 2Bλ(T); for B

λ(T) ~ T (Rayleigh­Jean approx.)

● Then, MIRAC

= ­5aRlog(P) + a

Tlog(P) +  const., adopt a

R=0.68 

(Gieren et al (1999)

● Beaulieu et al (2001): log(T) – (V­I) conversion

– LMC (V­I) P­C relation from Sandage et al (2004)

– SMC (V­I) P­C relation from Sandage et al (2009)

● Slope of IRAC band P­L:    

– LMC: ­5 x 0.68 + 0.18 = ­3.22

– SMC: ­5 x 0.68 + 0.19 = ­3.21

See Neilson et al (2010) for more details

Application I: IC 1613

Data from Freedman et al (2008)

Application II: NGC 6822

Data from Madore et al (2009)

II. Theoretical P-L Relations

The Theoretical Slopes

Synthetic P-L relations from pulsation models with different input Y and Z (models from Marcella Marconi,Ilaria Musella & Michele Cignoni)

Non-linear pulsations models include time-dependent treatment of pulsation and convection

Evolution M-L relation

~1000 pulsators with 5 -11 Solar mass populated the instability strip according to a given mass law

Convert to IRAC mag using stellar atmosphere models

Theoretical Vs. Empirical: GAL

GAL1: ''Old'' IRSB; GAL2: ''New'' IRSB; GAL3: HST parallaxes; From Marengo et al (2010)

Theoretical Vs. Empirical: LMC

LMC1: Madore et al (2009); LMC2: Ngeow et al (2009)

Comparison for BVIJK Slopes

Theoretical Vs. Empirical: SMC

SMC: Ngeow & Kanbur (2010)

Take Home Points

● Empirical mid­IR P­L relations based on LMC and SMC Cepheids

– Slopes found to be around ­3.2

– Applied to IC 1613 and NGC 6822

● Synthetic P­L relations compared to empirical counterparts

– Empirical P­L relations in good agreement to some synthetic P­L relations