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08 Nov 2011
Tatooine star analysis
This a very interesting object: a double star with a planet circling around it. The excellent analysis of the previous posters seems to be the best solution. I wondered however if I would be able to expand on that by adding some numbers. Unfortunately most of the published formulae do not work here, as they all assume that the occulted star is stationary, which is certainly not the case here. So I had to invent some stuff to get to an extended explanation.
The first step involves the double star. As the transits have equal depth and are close to 50%, so both stars are assumed to be equal in size and the orbital plane (circular) has an inclination angle of 90 degrees. Thus we see the orbit edge on. The orbital period can be determined from two transits (i and i+1 - the two green transits) and is 2.976 days. Normally the width of a transitcan be used to calculate the half-major axis of the orbit. However formula 3 of Seager&Mallen;-Ornelas (2002) assumes however that the occulted star does not move, which it does in this case. Thus the observed width (0.13 days) must be doubled to get the correct one. From this the hal-major axis can be determined as 11.3 stellar radii.
To determine the movement of the planet, better timings of the transits are needed. In order to make the three extra transits more clear I subtracted the LC of the double star. This was done by shifting and overlaying an adjacent LC and then subtracting the two. The blue and green lines show where the transits were. The dots shows the results of the subtraction. And you as well that the subtraction did not succeed 100%.
Then these three transits were fitted to determine the transit times. The dermined values, such as the width (T) and impact parameter (b) have not much significance, as the formulae assume a static object. Using the start of the ingress of the first transit (day 55023.31) and the end of the egress of the third transit (day 55024.94), we can determined the speed of the planet. The model of the double star indicates where the stars are and by putting the planet next to the star, we set the position of the planet. I used the configuration indicated by @kianjin in his last animation as starting point.
This resulted in the following animation, which confirms @kianjin’s results. The first transit happens just as star 1 is turning prograde. The planet starts the transit and then star 1 speeds up and moves out under the planet. Transit 2 is when the planet passes in front of star 2. Star 2 is then retrograde, which results in a small transit width. Transit 3 happens when star 2 is retrograde.