Question

Distances to local galaxies are determined by measuring the brightness of stars, called Cepheid variables, that can be observed individually and that have absolute brightness at a standard distance that are well known. Explain how the measured brightness would vary with distance as compared with the absolute brightness.

Short answer

The apparent brightness will depend upon the distance from the star according to the below expression,

\(m - M = {5^{{\rm{log}}\left( {{\rm{D/10}}} \right)}}\)

Step-by-step solution

Definition of Cepheid variables.

The relation between brightness and absolute brightness is given by,

\(m - M = {5^{{\rm{log}}\left( {{\rm{D/10}}} \right)}}\)

Here\(m\)is the brightness,\(M\)is the absolute brightness and\(D\)is the distance from the star.

Step 2: Variation of measured brightness with distance

Cepheid variables are pulsating stars, and their period is uniquely and directly related to the luminosity of the star. This means that we can determine a star's absolute luminosity - the absolute measure of radiated light - simply by measuring its period of oscillation. We also know that the measured intensity of radiation emitted by such an object decreases with distance, similar to how a candle becomes less and less bright as we move further away.

Knowing the initial amount of radiation and how the intensity of radiation decreases with distance allows us to calculate the distance to the star using the received intensity.