2013

A Cepheid in a nearby galaxy

Round: Theory
Points: 10
Level: Bronze
Taught in: Section 8.8

Adapted from IOAA 2013 (Volos), theory problem S4. We have restated it in our own words and kept the original data. The original gave a period-luminosity graph and a light curve. We give the readings from them instead. The solution was last checked on 21 October 2026.

A classical Cepheid in a galaxy of the Local Group has a light curve that varies between visual magnitudes 14.1 and 14.8 with a period of about 11 days. A graph of the period-luminosity relation gives an absolute magnitude of $- 4.2$ for this period.

(a) Estimate the distance of the Cepheid. [8 points]

(b) Revise the estimate for an extinction of $A = 0.25$ magnitudes towards the Cepheid. [2 points]

I solved it without the solution

Answer(a) About 54 kpc. (b) About 48 kpc, closer than before, since part of the faintness is caused by dust. The official solution adds the extinction instead of taking it off, and also misprints the powers of ten, giving 57.5 kpc and then 64.5 kpc. A careful reading of the light curve, which spends longer near minimum, gives a mean nearer 14.5, which moves both answers out by about 2%.

This problem also appears among the olympiad problems of Section 8.8, Other variable stars and reading light curves, which teaches the ideas it uses. Equation and figure numbers refer to the course.