Cepheid variable star

Some stars are seen to vary in brightness and, for this reason, are called variable stars. This light curve shows how the brightness changes with time for a typical cepheid variable, with a period of about 6 days.

Plot of a Cepheid Light Curve. In this graph the vertical axis is labeled “Magnitude,” and goes from 4.4 (at the bottom) to 3.4 in increments of 0.2. The horizontal axis is labeled “Time (days),” ranging from 0 to 18 in increments of 1 day. The plotted curve begins at day zero near magnitude 4.1. The curve dips to the minimum magnitude of 4.3 at day 1.5, then rises rapidly to the maximum magnitude of 3.6 at day 3. The curve slowly dips down again to magnitude 4.3 at day 7. The curve repeats two more times to day 18, giving the plot the appearance of a saw blade.

Periods and average luminosities turn out to be directly related, the longer the period (the longer the star takes to vary), the greater the luminosity.

Period-Luminosity Relation for Cepheid Variables (we are able to obtain its linear regression by this graphic).

How to Use a Cepheid to Measure Distance.

Find a cepheid variable star and measure its period.
Use the period-luminosity relation to calculate the star's luminosity.
Measure the star's apparent brightness.
Compare the luminosity with the apparent brightness to calculate the distance with the following formula: d=10^(m-M+5)/5 .