A Cepheid has period and mean apparent magnitude

PHYSICS · Multi-part · Fermi University Physics · Astrophysics & Cosmology · Observational foundations and instrumentation · Stellar structure, energy generation and evolution

Stars from the Inside, Ch Pulsating stars: the kappa mechanism, the Leavitt law and asteroseismology

Problem

A Cepheid has period Π=15.0 d\Pi = 15.0\,\mathrm{d} and mean apparent magnitude Vˉ=16.80\bar V = 16.80. Independent reddening measurements give AV=1.20 magA_V = 1.20\,\mathrm{mag} along the line of sight. Using the calibrated Galactic Leavitt law MV=−2.43(log⁡10Π−1)−4.05M_V = -2.43(\log_{10}\Pi - 1) - 4.05 (with Π\Pi in days), someone works the distance as follows: "log⁡10(15.0)=1.176\log_{10}(15.0) = 1.176, so MV=−2.43(0.176)−4.05=−4.48M_V = -2.43(0.176) - 4.05 = -4.48. The distance modulus is μ=Vˉ−MV=16.80−(−4.48)=21.28\mu = \bar V - M_V = 16.80 - (-4.48) = 21.28. Hence d=10(μ+5)/5 pc=105.256 pc=1.8×105 pc=180 kpcd = 10^{(\mu+5)/5}\,\mathrm{pc} = 10^{5.256}\,\mathrm{pc} = 1.8\times10^{5}\,\mathrm{pc} = 180\,\mathrm{kpc}." ((a)) Identify the error in this working. ((b)) Recompute the correct distance in kiloparsecs. ((c)) By what factor was the distance overestimated?

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