In this paper the synthetic period-luminosity ( P-L ) relations in Spitzer ’ s IRAC bands , based on a series of theoretical pulsation models with varying metal and helium abundance , were investigated .
Selected sets of these synthetic P-L relations were compared to the empirical IRAC band P-L relations recently determined from Galactic and Magellanic Clouds Cepheids .
For the Galactic case , synthetic P-L relations from model sets with ( Y = 0.26 , Z = 0.01 ) , ( Y = 0.26 , Z = 0.02 ) and ( Y = 0.28 , Z = 0.02 ) agree with the empirical Galactic P-L relations derived from the Hubble Space Telescope parallaxes .
For Magellanic Cloud Cepheids , the synthetic P-L relations from model sets with ( Y = 0.25 , Z = 0.008 ) agree with both of the empirical Large Magellanic Cloud ( LMC ) and Small Magellanic Cloud ( SMC ) P-L relations .
Analysis of the synthetic P-L relations from all model sets suggested that the IRAC band P-L relations may not be independent of metallicity , as the P-L slopes and intercepts could be affected by the metallicity and/or helium abundance .
We also derive the synthetic period-color ( P-C ) relations in the IRAC bands .
Non-vanishing synthetic P-C relations were found for certain combinations of IRAC band filters and metallicity .
However , the synthetic P-C relations disagreed with the [ 3.6 ] - [ 8.0 ] P-C relation recently found for the Galactic Cepheids .
The synthetic [ 3.6 ] - [ 4.5 ] P-C slope from ( Y = 0.25 , Z = 0.008 ) model set , on the other hand , is in excellent agreement to the empirical LMC P-C counterpart , if a period range of 1.0 < \log ( P ) < 1.8 is adopted .