Two stars, named Ajax and Teucer, are in an eclipsing binary. The binary varies

Question

Two stars, named Ajax and Teucer, are in an eclipsing binary. The binary varies in apparent magnitude from 6.1 out of eclipse to 6.7 when Ajax is fully eclipsing Teucer.

a) What fraction of the total flux from the binary is emitted by Ajax?

b) If the binary is at a distance of 50pc, calculate the total luminosity of the binary system in units of L, given that the absolute magnitude of the Sun is Mv = +4.83.

c) What are the luminosities of Ajax and Teucer? (1 mark) d) Assuming that both Ajax and Teucer are main-sequence stars, what are their masses in units of M?

Explanation / Answer

let flux of Ajax is j1 and Teucer is j2 then the luminosity relation gives us j1 = L1/4r1^2 , in a similar way

j2 = L2/4r2^2

considering the magnitude we use flux ratio relation m1-m2 = -2.5 log (j1/j2)

considering absolute magnitude Mv = +4.83 and using star distance modulus relation we get

m-M= 5log (d/10pc) now d= 50pc or m- 4.83 = 5 log (50/10) or m= 4.83+ 3.49 = 8.32

again in the flux ratio using (6.7- 6.1) = -2.5 log (j1/j2)

or 6/-2.5 =log (j1/j2) or log (j1/j2) = -2.4 or log (L1/4r1^2 /L1/4r2^2 ) =-2.4

using Taucer' luminosity we get Ajax's flux

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