K-Stacker: an algorithm to hack the orbital parameters of planets hidden in high-contrast imaging
Authors: Le Coroller H. , Nowak M. , Delorme P. , Chauvin G. , Gratton R. , Devinat M. , Bec-Canet J. , Schneeberger A. , Estevez D. , Arnold L. , Beust H. , Bonnefoy M. , Boccaletti A. , Desgrange C. , Desidera S. , Galicher R. , Lagrange A. M. , Langlois M. , Maire A. L. , Menard F. , Vernazza P. , Vigan A. , Zurlo A. , Fenouillet T. , Lambert J. C. , Bonavita M. , Cheetham A. , D’orazi V. , Feldt M. , Janson M. , Ligi R. , Mesa D. , Meyer M. , Samland M. , Sissa E. , Beuzit J.-L. , Dohlen K. , Fusco T. , Le Mignant D. , Mouillet D. , Ramos J. , Rochat S. , Sauvage J. F. 
Published: May 2020

Context. Recent high-contrast imaging surveys, using the Spectro-Polarimetic High contrast imager for Exoplanets REsearch (SPHERE) or the Gemini Planet Imager in search of planets in young, nearby systems, have shown evidence of a small number of giant planets at relatively large separation beyond 10–30 au, where those surveys are the most sensitive. Access to smaller physical separations between 5 and 30 au is the next step for future planet imagers on 10 m telescopes and the next generation of extremely large telescopes in order to bridge the gap with indirect techniques such as radial velocity, transit, and soon astrometry with Gaia. In addition to new technologies and instruments, the development of innovative observing strategies combined with optimized data processing tools is participating in the improvement of detection capabilities at very close angular separation. In that context, we recently proposed a new algorithm, Keplerian-Stacker, which combines multiple observations acquired at different epochs and takes into account the orbital motion of a potential planet present in the images to boost the ultimate detection limit. We showed that this algorithm is able to find planets in time series of simulated images of the SPHERE InfraRed Dual-band Imager and Spectrograph (IRDIS) even when a planet remains undetected at one epoch.
Aims. Our goal is to test and validate the K-Stacker algorithm performances on real SPHERE datasets to demonstrate the resilience of this algorithm to instrumental speckles and the gain offered in terms of true detection. This will motivate future dedicated multi-epoch observation campaigns of well-chosen, young, nearby systems and very nearby stars carefully selected to search for planets in emitted and reflected light, respectively, to open a new path concerning the observing strategy used with current and future planet imagers.
Methods. To test K-Stacker, we injected fake planets and scanned the low signal-to-noise ratio (S/N) regime in a series of raw observations obtained by the SPHERE/IRDIS instrument in the course of the SPHERE High-contrast ImagiNg survey for Exoplanets. We also considered the cases of two specific targets intensively monitored during this campaign: β Pictoris and HD 95086. For each target and epoch, the data were reduced using standard angular differential imaging processing techniques and then recombined with K-Stacker to recover the fake planetary signals. In addition, the known exoplanets β Pictoris b and HD 95086 b previously identified at lower S/N in single epochs have also been recovered by K-Stacker.
Results. We show that K-Stacker achieves a high success rate of ≈100% when the S/N of the planet in the stacked image reaches ≈9. The improvement of the S/N is given as the square root of the total exposure time contained in the data being combined. At S∕N < 6−7, the number of false positives is high near the coronagraphic mask, but a chromatic study or astrophysical criteria can help to disentangle between a bright speckle and a true detection. During the blind test and the redetection of HD 95086 b, and β Pic b, we highlightthe ability of K-Stacker to find orbital solutions consistent with those derived by the current Markov chain Monte Carlo orbital fitting techniques. This confirms that in addition to the detection gain, K-Stacker offers the opportunity to characterize the most probable orbital solutions of the exoplanets recovered at low S/N.