[PAE20-P06] Transit Observations and Light-curve Analyses on TRAPPIST-1 d & e for Mass Estimation
Keywords:TRAPPIST-1, earth-sized exoplanets, transiting planets, TTV, mass estimation, MuSCAT
Previous researches  used the transit data of the TRAPPIST survey, Spitzer, K2 mission and other telescopes for the TTV analysis, but the size of dataset is still not big enough to measure the masses precisely. In this study, we conducted new transit observations and light curve analyses on TRAPPIST-1 d and e, in order to derive the accurate transit center times for TTV analysis.
Using the MuSCAT camera installed on 188-cm telescope at the Okayama Atrophysical Observatory, we observed consecutive transits of TRAPPIST-1 d & e in z-band, on November 5, 2017. We analyzed the derived light-curve by model fitting. We assumed that model is a combination of transit model and systematics model. For the transit model, we used the python module 'PyTransit' and adapted it for a double transit. In this study we chose the radius ratio and transit center time as free parameters, and used literature values from previous research for the other values (semimajor axis, impact parameter, orbital period, limb-darkening parameters). We approximated the systematics model as linear combination of factors, such as the position of the point of telescope and airmass. In order to select the best parameter set, we used the Bayesian Information Criterion(BIC) We chose 10 good parameter sets and then did more robust model fitting using Markov chain Monte Carlo (MCMC). We used the emcee.EnsembleSampler to minimize chi-square, and calculated the time of transit center and its standard deviation, using long enough chains (100 walkers and 2000 steps, taking into account the autocorrelation).
As a result, we were able to add one new data point to each TTV data set of TRAPPIST-1 d and e (from Wang et al.(2017) FIG.3) to constrain the TTV model. From this study, we can restrict the masses of TRAPPIST-1 c, d, e and f, which are in orbital resonance with TRAPPIST-1 d and e.
 Gillon et al., 2017, Nature, Vol 542
 Wang et al., 2017, ArXiv e-prints, 1704.04290