Astrophysics - Apparent Magnitude of stars in a close binary system?

Astrophysics - Apparent Magnitude of stars in a close binary system


1. The problem statement, all variables and given/known data





2 solar type stars are in a close binary system. Each indivual star has an apparent brightness of m = 10 mag.





Determine the apparent magnitudes of the combined system of the 2 stars assuming they cannot be resolved as individual objects. Determine the minimum brightness for this eclipsing binary when 100%, 75%, 50% and 25% of the stellar survace are covered during the eclipse.





2. Relevant equations





m1 - m2 = -2.5 log(f1/f2)





3. The attempt at a solution





m1 - m2 = -2.5 log (f1/f2)


10-10 = -2.5log(f1/f2)


f1/f2 =1


f1=f2





m1+2 - m2 = -2.5 log (f1+f2 \ f2) f1 = f2


m1+2 - m2 = -2.5 log (2f1 \ f1)


m1+2 - m2 = -2.5 log 2


m1+2 = -2.5log2 + 5 mag


m1+2=4.247425011


m1+2 = 4.25 mag





Then I'm not sure how to continue from here - any help would be most appreciated!|||Assuming f is light flux, you want to compare the magnitude change for a doubling of flux.


m(double)-m(single) = 螖m = -2.5log10(2) = -0.752575


m(single) = 10


m(double) = m(single)-螖m = 9.247425


You added 5 instead of 10 to 螖m. Was there a reason for this?


For the eclipse questions, you have a flux ratio of 1, 1.25, 1.5 and 1.75 relative to one star. If the "minimum brightness" answers are expected as apparent magnitudes, just substitute these values as the argument to log10.