3.6 Star size and transit depth
In the last activity you explored changing the planet size. This time you will explore changing the star size.
Activity _unit5.3.3 Activity 5 Star size and transit depth
If the radius of the star is doubled, what would you expect to happen to the transit depth? Explain your reasoning.
The transit depth depends on the relative areas of the star and the planet. Areas depend on the square of the radius, so doubling the star’s radius will lead to a factor of four change in the transit depth. Because the change is making the star bigger, but not altering the size of the planet, it will reduce the fraction of the starlight blocked out. So, the transit depth should be reduced by a factor of four.
Note that the amount of starlight being blocked hasn’t changed – the planet is still the same size so has the same cross-sectional area. The transit depth though measures the fraction of starlight being blocked.
Adjust the stellar radius to Rstar = 1.24 RSun (check that the other sliders are set to the values Rplanet = 1.75 RJ; Porb = 10 days; i = 90°).
What value of transit depth do these choices lead to?
The transit depth is 2.10%.
If you double the radius of the star to 2.48 RSun, what value would you expect for the transit depth? Explain your reasoning.
The transit depth should be reduced by a factor of four, so you would expect a value of 2.10% ÷ 4 = 0.525%, which can be rounded to 0.53%. You can confirm this with the application.
Adjust the stellar radius to Rstar = 0.60 RSun (check that the other sliders are set to the values Rplanet = 1.75 RJ; Porb = 10 days; i = 90°). Note that the star’s radius is just over half its initial value.
What is the value of the transit depth now?
A transit depth of 8.97%.
If the star’s radius was reduced, you would expect the transit depth to be bigger than it was originally.
Does this value agree with the predictions of Equation 3? Explain your reasoning.
If the star’s radius is reduced, you would expect the transit depth to be greater than it was originally. Compared with the original value, Rstar = 1.24 RSun, the size of the star has been roughly halved. Equation 3 says you should expect the transit depth to be about four times deeper, i.e. it should be about 2.1% × 4 = 8.4%. Because the star is slightly less than half its original size, the transit depth is slightly deeper than 8.4%.
If you are keen on calculations, you can work out the exact value of (1.24/0.6)2 and check the answer given.
Adjust the values of Rstar, and check that the transit depths you obtain always behave as predicted by Equation 3.
Now, suppose that an astronomer has been observing a distant star over a number of weeks, monitoring its brightness. The light curve for the star shows regularly repeating dips that occur every 5.2 days. These dips have the same flat-bottomed shape as Figure 12. Averaging them together, the dips in brightness are measured to be 1.4%.
What is likely to be causing these regular dips in the brightness of the star?
A transiting planet with an orbital period of 5.2 days.
The star undergoes further study using a telescope with a spectrograph. The patterns of absorption lines in the star’s spectrum show that it is an F-type main sequence star, which have radii of 1.3 RSun.
Use the interactive simulation to find out what the radius of the planet could be.
Note that the shape of the dips shows that it is not a grazing transit, so the orbital inclination must be greater than about 85°.