Two main sequence stars have the following properties:
#1: apparent magnitude m_v=2.5, λ_eff = 551nm radius r=1.6R_sun
#2: m_v = 5.77, r = 1.25R_sun
1) Calculate the apparent brightness of the system when #2 is in front of #1. Assuming that #1 has constant apparent brightness, what radius is required for #1 to make the depth of the primary eclipse equal to that of the secondary eclipse (the properties of #2 don't change).
2)Further: B-V colors of the two stars have to be calculated
a) m_v1 - m_v2 = -2.5*log(F_1/F_2)
b) λ_max = 2898/T
c) B-V= m_b - m_v =-0.865+(8540/T)
The Attempt at a Solution
1)I already calculated the apparent brightness of the binary system, when there is no eclipse, using eq. a and the relation of fluxes (m_system=m_2+2.5*log(F_2/F_system).
2)for #1 I did the following:
using Wien's displacement law (eq. b) I calculated T (not sure if I can use the effective wavelength as max wavelength), and then calculated B-V using eq. c. From that I calculated m_b. But how to calculate B-V of #2 with only m_v given?
Thanks for any suggestions!