Task 1

Note: It is highly recommended that your read the Introduction before you start at this exercise.

The Period-Luminosity relation for Cepheid variables has been revised many times since Henrietta Leavitt’s first measurements. Today the best estimate of the relation is:

M = –2.78 log (P) – 1.35

where M is the absolute magnitude of the star and P is the period measured in days.

Light curves for the 12 Cepheids in M100 that have been measured with Hubble are shown below.

Our goal is to calculate the distance to M100. If you remember the distance equation, you will know that the absolute magnitude alone is not enough to calculate the distance — you also need the apparent magnitude.

Choose the distance equation

Apart from problems in measuring the amount of light received accurately and calibrating the magnitudes that were measured, for a hundred years astronomers have discussed which apparent magnitude, m, to use in the distance equation for a Cepheid that is actually varying in magnitude.

Think about a method to estimate the apparent magnitude, m, using the curves.

At the beginning of the 20th century astronomers measured the minimum apparent magnitude (m_min) and the maximum apparent magnitude (m_max) and then took the average (<m>) of the two.

If we do that we now have all the information we need to calculate the distance to M100.