Temperature Differences in the Cepheid Instability Strip Require Differences in the Period-luminosity Relation in Slope and Zero Point

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. The graphical demonstration uses an arbitrary (toy) ridge line 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 measured slopes in the instability strips argue that the observed P-L differences between the Galaxy and LMC are real. In another proof, the direct evidence for different P-L slopes in different galaxies is shown by comparing the Cepheid data in the Galaxy, the combined data in NGC3351 and NGC4321, in M31, LMC, SMC, IC1613, NGC3109, and in Sextans A+B. The P-L slopes for the Galaxy, NGC3351, NGC4321, 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. Subject headings: stars: variables: Cepheids — P-L relations — distance scale