AST 613: Exoplanets: HW 3 #1-5

1)
All 3 algorithms used the same step size (0.0000243) and range (0.37026 to 324.22235) for this comparison.

Box-Least-Squares

It is not clear that there is any signal of a transiting exoplanet here, with the peaks not standing out from the noise. (A peak power of ~25 does not seem meaningful when the average is ~7 to 15, though it corresponds to a peak in both others)

Lomb-Scargle

This algorithm shows what seem to be actual signals, notably the one at ~4.2 days. My p-value calculations are ambiguous, with the most significant 3 tending to hit zero with all the software I tried. (eg: libreoffice)

Plavchan

This algorithm also shows what appear to be actual signals, though with a different pattern. Again, there is a large peak around 4.2 days. The smaller ones to to have periods that are multiples of it. Outside of the universal step-size and interval tunings, this algorithm also lets one focus on the most extreme points as they are the most likely to have actual planets.

2)
Using systemic, I get a planet at 4.2308 days with a mass of 0.47814 Mj and eccentricity of 0.01409. This is close to exoplanets.org's values, with differences ranging from rounding error/displayed digits to almost 10%. These values are at/within the 1-sigma errors at exoplanet.org, however. (4.230785 ± 3.6×10-5 days, 0.461 ± 0.0164 Mj*sin(i), eccentricity 0.013 ± 0.012)

The 4.23 day signal has a p-value of 1.58e-179, with 4 of the next 5 signals near it. The residual periodogram generally shows p-values around 1, with the only exceptions being relatively suspicious (1 day, and 12 synodic lunar cycles).

3)

4)
It is not clear that true anomaly actually only goes between 0 and 2 pi radians, but it should have no effect on orbital distance. Link to code: https://github.com/pdn4kd/freezing-tyrion/blob/master/HW3-4.py