Problem set 3 for ASTR 222: From Stars to Cosmology

Due in class Wed Feb 2

You will derive the distance to an open cluster which contains Cepheids using the Hipparcos parallax distances.

Here you can find the data for parallaxes from the Hipparcos satellite for all stars it observed with distances less than 20 pc and good parallax values (errors of less than 5 milli-arcseconds).
(a) What is the V magnitude and B-V color of the nearest star in the list?
(b) What is the V magnitude and B-V color of the most luminous star in the list?
(c) plot up the H-R diagram for these stars. Are there any white dwarfs there? What are their V magnitudes?

The open cluster (NGC 7790) contains 3 Cepheid variables. Here is the photometry from a recent study of the cluster.

(a) Plot the color-magnitude (H-R) diagram for the cluster.

(b) correct for interstellar reddening as follows. The best estimate of reddening towards the cluster is E(B-V)=0.51, so you need to subtract 0.51 from the B-V color and 3.31*E(B-V) from the V magnitude.

(c) do the main sequence fit by comparing the Hipparcos HR diagram with the open cluster HR diagram in the color region where they both have data. What is your estimate of the distance to the cluster (with error)?

(d) The three Cepheid variables in the cluster have the following periods and V apparent magnitudes:

Cepheid	P (days)	mean V (mag)
CEa Cas	5.14087	10.90
CEb Cas	4.47928	11.02
CF Cas	4.87522	11.14

What are the mean absolute V magnitudes for the three Cepheids? Remember you will need to subtract the reddening to the cluster first.