New period-luminosity and period-color relations of classical Cepheids

• Published in: Astronomy and astrophysics (Berlin) 2004-09, Vol.424 (1), p.43-71
• Main Authors: Sandage, A., Tammann, G. A., Reindl, B.
• Format: Article
• Language: English
• Subjects: cosmology: distance scale; galaxies: Magellanic Clouds; stars: variables: Cepheids
• ISSN: 0004-6361; 1432-0746
• DOI: 10.1051/0004-6361:20040222

Photometric data for 593 Cepheids in the LMC, measured by Udalski et al. in the OGLE survey, augmented by 97 longer period Cepheids from other sources, are analyzed for the period-color (P-C) and period-luminosity (P-L) relations, and for the variations of amplitude, light curve shape, and period across the instability strip at constant absolute magnitude. Both the P-C and P-L relations have different slopes for periods smaller and larger than 10 days. The break at 10 days is also seen in the period-amplitude relations, and the compound Fourier combinations of R21 and $\Phi_{21}$ introduced by Simon and Lee. 
The LMC Cepheids are bluer than Galactic Cepheids in the B, V, and I color bands, part of which is due to differential Fraunhofer line blanketing and part to real differences in the temperature boundaries of the instability strip. The LMC strip is hotter by between $80\;$K and $350\;$K depending on the period. Hence, both the slopes and (necessarily) the zero points of the P-L relations in B, V, and I must differ between LMC and the revised relations (also given here) for the Galaxy, and in fact they do. The LMC Cepheids are brighter by up to $0.5\;$mag at $\log P = 0.4$ (2 days) and fainter by $0.2\;$mag at $\log P = 1.5$ (32 days). These facts complicate the use of Cepheid as precision distance indicators until the reason is found (metallicity differences or other unknown differences) for the non-universality of the P-L and P-C relations. 
The very large data base permits mapping of various Cepheid properties at different positions within the instability strip, both at constant period and at constant absolute magnitude over the range of $2 < P < 40$ days and $-2 > M_{V} > -5$. Amplitude of the light curves are largest near the blue edge of the strip for periods between 2 and 7 days and longer than 15 days. The sense is reversed for periods between 7 and 15 days. The shape of the light curves varies systematically across the strip. Highly peaked curves (of large amplitude) that necessarily have large values of R21 of about 0.5, occur near the blue edge of the strip. More symmetrical (small amplitude) light curves that have, thereby, small values of R21, generally occur near the red edge of the strip. Consequently, there is a strong correlation of R21 with color within the strip at a given absolute magnitude. Strong correlations also exist between color and period, and color and amplitude at given absolute magnitudes, for the same reason that has long