Question about eclipsing binaries

[badhex]

Hello all, 

I'm working through an assignment for my astronomy studies and I'm struggling to figure out what method I need to use to understand the flux contributed by each star.

I'm not looking for someone to solve the actual question for me obviously so I've changed the numbers below anyway, I'm just a bit stumped on what method I need to use. 

Any ideas gratefully received! 

 

An eclipsing binary varies in apparent magnitude from mag. 6 out of eclipse to mag. 7 when star B is fully eclipsing star A. 
What fraction of the total flux from the binary is emitted by star B? 

Edited January 4, 2023 by badhex

[vlaiv]

Let's call brightness of Star A - a and brightness of star B - b

If stars are side by side, total brightness will be: a+b

But when star B is fully eclipsing star A - total brightness will be just b. No light from A will reach us as B is in the way so we will only have brightness of B - which is b

Magnitude system represents ratio of two values so we can write b/(a+b) and magnitude of that ratio is 1 (change from 6 to 7).

1 = -2.5 * log(b/(a+b)) =>

b / (a+b) = 0.39794 0.3981

b = 0.39794  0.3981 * (a+b)

b = 39.81% of total flux (a+b is total flux)

Edited January 4, 2023 by vlaiv
For some reason I got the numbers wrong

[badhex]

11 hours ago, vlaiv said:

Let's call brightness of Star A - a and brightness of star B - b

If stars are side by side, total brightness will be: a+b

But when star B is fully eclipsing star A - total brightness will be just b. No light from A will reach us as B is in the way so we will only have brightness of B - which is b

Magnitude system represents ratio of two values so we can write b/(a+b) and magnitude of that ratio is 1 (change from 6 to 7).

1 = -2.5 * log(b/(a+b)) =>

b / (a+b) = 0.39794 0.3981

b = 0.39794  0.3981 * (a+b)

b = 39.81% of total flux (a+b is total flux)

Thanks Vlaiv, this is very helpful. Actually I should have written that my very first assumption was that whilst fully eclipsed, the light we see is just from star B, which gives me something to go on, but then I started to doubt if I was correct with that assumption and got myself in a bit of a muddle. 

I'm just re-reading the chapter on magnitudes, luminosity etc. and then I'm going to sit down and work through your equations on my own and make sure I understand exactly what's happening, then have a crack at the actual question in the assignment. There are a bunch of other parts to the question relating to the luminosities and mass of the stars, but I think now that I have a place to start I should be able to figure that out. 

Thanks again!

[badhex]

Okay, so thanks to your answer Vlaiv as well as re-reading various bits, I've realised that where I was getting confused was that I was thinking of the binary as a special case, when in fact all I'm doing is comparing two magnitudes, which is something I'm fairly comfortable with. It doesn't actually matter that one of the magnitudes for comparison is a binary, the calculation is the same, and once I know the Flux ratio, I can then just divide 1/(flux ratio) to find the percentage.

 

Edited January 5, 2023 by badhex

[badhex]

Just following up to say thanks for the hints @vlaiv, assignment now submitted!