Radial velocity data analysis with compressed sensing techniques

Abstract

We present a novel approach for analysing radial velocity data that combines two features: all the planets are searched at once and the algorithm is fast. This is achieved by utilizing compressed sensing techniques, which are modified to be compatible with the Gaussian processes framework. The resulting tool can be used like a Lomb-Scargle periodogram and has the same aspect but with much fewer peaks due to aliasing. The method is applied to five systems with published radial velocity data sets: HD 69830, HD 10180, 55 Cnc, GJ 876 and a simulated very active star. The results are fully compatible with previous analysis, though obtained more straightforwardly. We further show that 55 Cnc e and f could have been respectively detected and suspected in early measurements from the Lick observatory and Hobby-Eberly Telescope available in 2004, and that frequencies due to dynamical interactions in GJ 876 can be seen.

Radial-velocity fitting challenge

“…Following a private communication with N.C Hara from team 8, It seems that their method is now delivering similar performances in terms of planetary detection as Bayesian framework techniques using red-noise models and with a much shorter computational time (see bottom plot in Fig. 11 and Hara et al 2016). However, following the first results of the RV fitting challenge presented here, techniques using a Bayesian framework and rednoise models seem the most efficient at modeling the effect of stellar signals, and therefore detecting true planetary signals while limiting the number of false positives.…”

“…With more time, each technique can be improved, and the different teams are making progress (see Gregory 2016;Hara et al 2016). The Oxford team also made some important progresses (priv.…”

“…This preliminary method was not very robust, and was greatly improved afterwards. For a precise description of the most recent version, see (Hara et al 2016), where system 2 of the RV Fitting Challenge is treated in detail along with real radial velocity signals.…”

“…A further study shows that the five planets plus the harmonic of the 10.64 days orbit are statistically significant in some sense. This system is treated in detail in (Hara et al 2016). …”

Agatha: disentangling periodic signals from correlated noise in a periodogram framework

“…It has also been analyzed using compressed sensing techniques by Hara et al (2017). Five signals corresponding to the five planets in the Kepler-20 system are injected into simulated noise sampled according to the observational calendar of HARPS measurements of τ Ceti.…”