A Testimator Approach to Detecting Heteroskedasticity in the Cepheid PL Relation
The Cepheid Period–Luminosity (PL) relation is crucial to establish the size scale of the Universe independent of the Cosmic Microwave Background. A greater understanding of its systematics and underlying physics is therefore vital. Here we adapt the testimator approach, previously used to study a possible nonlinearity in the slope of the PL relation, to look at possible variations in the dispersion of the PL relation as a function of period—or heteroskedasticity. We describe the mathematics behind our new test and some test calculations. We then apply it to Large Magellanic Cloud Cepheid PL data using published reddenings, and show that there is a reduction in the variance of the PL relation around 10 days. While this could be due to errors in reddenings, analysis of multiphase PL relations suggest that this is a real feature. We close with a discussion of the possible implications of this result for the extra-galactic distance scale and stellar pulsation.
KeywordsError Variance Linear Regression Model Cosmic Microwave Background Size Scale Constant Error
SMK and SR thank SUNY Oswego for supporting this research. CCN thanks the funding from National Science Council (of Taiwan) under contract NSC 98-2112-M-008-013-MY3.