2008ApJ...686..779S

A graphical and an algebraic demonstration is made to show why the slope and zero point of the Cepheid period-luminosity (P-L) relation is rigidly coupled with the slope and zero point of the Cepheid instability strip in the HR diagram. In this way it is shown why it is logically inconsistent to adopt a fixed P-L slope for all galaxies if the intrinsic color-period relations differ in slope for some of them. The graphical demonstration of this inconsistency uses an arbitrary (toy) ridgeline in the instability strip, while the algebraic demonstration uses the pulsation equation into which the observed P-L relations for the Galaxy and the LMC are put to predict the temperature zero points and slopes of the instability strips. Agreement between the predicted and the observed slopes in the instability strips argue that the observed P-L differences between the Galaxy and LMC are real. The direct evidence for different P-L slopes in different galaxies is displayed by comparing the Cepheid data in the Galaxy, the combined data in NGC 3351 and NGC 4321, in M31, LMC, SMC, IC 1613, NGC 3109, and in Sextans A+B. The P-L slopes for the Galaxy, NGC 3351, NGC 4321, and M31 are nearly identical and are the steepest in the sample. The P-L slopes decrease monotonically with metallicity in the order listed, showing that the P-L relation is not the same in different galaxies, complicating their use in calibrating the extragalactic distance scale.