Solving Eclipsing Binary Homework

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The discussion focuses on solving a homework problem involving two main sequence stars with given apparent magnitudes and radii. The first part requires calculating the apparent brightness of the binary system during an eclipse and determining the necessary radius for star #1 to equalize the depths of the primary and secondary eclipses. The second part involves calculating the B-V colors for both stars, with the participant successfully calculating the temperature of star #1 using Wien's law but seeking guidance on calculating the B-V color for star #2. Suggestions include using the known radius and distance to find effective wavelength relations for star #2. The conversation emphasizes the importance of understanding the relationships between apparent magnitude, brightness, and color indices in binary star systems.
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Homework Statement


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

Homework Equations


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!
 
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shadowpipi said:
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).
That's not what the question is asking.
shadowpipi said:
But how to calculate B-V of #2 with only m_v given?
You also know the radius, and the star is at the same distance as the other star. You can find some relations to calculate λeff.
 
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