A type II Cepheid has been located in a distant globular cluster with a period of 10 days,?

Question

what is the star's absolute magnitude?

A.) -1
B.) 0
C.) -4
D.) -6
E.) the absolute magnitude of a Cepheid variable cannot be determined unless its distance is known

Answer 1

For Type I Cepheids, the formula is:
Mv = -2.81 log (P) - 1.43
which gives us
Mv = -2.81 log (10) - 1.43
Mv = -4.24

Type II Cepheids (or W Virginis variables) average 1.5 magnitudes dimmer than Type Is. Which gives us Mv = -2.74

Are you sure they weren't asking for a Type I ?

Answer 2

I disagree with first answer. The whole reason Cepheids are useful is because of the standard candle notion; the period-luminosity relationship. The absolute magnitude CAN be determined and it is from that, that we derive the distance.
for P=10:

Mv=-2.81 log (P) -1.43
Mv= -2.81 (1) - 1.43
Mv= -4.24

What I am not certain about is the difference, if any, in the formula for type II Cepheids. So I think your answer is -4.