Question

A particular type II Cepheid variable has a period of 10 days, and an apparent magnitude of 3.2. What is the distance of that Cepheid variable? (Refer to the enclosed figure.)

-6 -5 2 -4 -2 0.25 0.63 1.64.0 10.0 25.0 63.1 Period (days) Figure 3.5 Period-Luminosity Relation for Cepheids Harlow Shapley's estimates fitted all Cepheids onto one curve (solid white line), with luminosity increasing for the longer-period variables. Walter Baade divided Cepheids into two classes, Population (solid black line) and Population II (dashed black line), the latter type being fainter than Population I Cepheid stars with the same period. The magnitude scale is a logarithmic measure of brightness. The brightness increases by a factor of 2.5 for each smaller number (the smaller, or more negative, the magnitude, the brighter the star). [From "Pulsating Stars and Cosmic Distances" by Robert P. Kraft. Copyright 1959 by Scientific American, Inc. All rights reserved.l

Answer 1

Knowing the period of the Cepheid we can now determine its mean absolute magnitude, M, by interpolating on the period-luminosity plot. Interpolating we get, so, absolute magnitude (luminosity), M = -4.8 apparent magnitude, m = 3.2 The magnitude-distance relation of a Cepheid reads, m - M = 5 log_10 (d/10) 3.2 + 4.8 = 5 log_10 (d/10) 8/5 = log_10 d - 1 log_10 d = 13/5 Therefore d = 10^13/5 = 398.10 parsees