A Machine Learning Inspired Method Reveals the Mass of K2-167 b Zoe L. de Beurs1,2, Andrew Vanderburg1,2, Christopher J. Shallue3, Joseph E. Rodriguez4, Sebastian Zieba5,10, Annelies Mortier6,7, Lars Buchhave8, Luca Malavolta9, HARPS-N Telescope Collaboration Discovering earth-mass exoplanets orbiting bright nearby stars requires precise radial velocity (RV) observations. Currently, we are limited by spurious RV signals introduced by the host star in the form of stellar activity (i.e. faculae, starspots). These stellar signals can mimic or hide exoplanet signals. Inspired by our successful implementation of a neural network stellar activity mitigation method on solar data (de Beurs et al. 2020), we designed a simplified machine learning (ML) method that can be applied to extrasolar stars. As a proof-of-concept, we tested this method on one star: K2-167. K2-167 was first found to host a transiting super-Earth by the K2 mission (Vanderburg et al. 2016b; Mayo et al. 2018). Recently, the planetary signal was re-detected by TESS (Ikwut-Ukwa et al. 2020). K2-167 is an ideal test case for our method. It is the brightest star observed by K2 that hosts a validated planet, and it is a relatively active, yet slowly rotating F7. HARPS-N began observing K2-167 in late 2015, but stellar activity has prevented a confident detection of the planet’s RV signal, even with the aid of state-of-the-art methods like GP regression. Our strategy is to use a simplified ML method to identify and interpret the subtle changes to stellar spectra that are caused by stellar activity. Background Data K2 – K2-167 was observed during K2 Campaign 3 from 2014 November 17 to 2015 January 23. After extraction, the lightcurves were reprocessed by using the methods described in Vanderburg & Johnson (2014) and Vanderburg et al. (2016a). TESS – K2-167 was observed by Camera 1 during TESS Sector 2 from 2018 Aug22 to Sept 20. The lightcurves were generated using NASA’s SPOC pipeline. HARPS-N – HARPS-N is a vacuum-enclosed cross-dispersed echelle spectrograph designed to achieve high-precision RVs (Cosentino et al. 2012). We collected 76 precise RV observations of K2-167 between Aug 2015 and Oct 2016. CCF Input Representation – For our ML model, we have to pre- process our data products into a uniform format such that the model becomes sensitive to shape changes due to stellar activity, not translational shifts caused by Keplerian shifts. We describe this input representation in detail in de Beurs et al. 2020. Results o We find that our simplified approach to stellar activity corrections yields a significant improvement in both the RV scatter (by a factor of ~ 2) and the precision with which we recover the mass of the transiting planet (improving a 2.3σ significance detection into a 4.0σ significance detection; Figure 3). Our MCMC fit found that the mass of 6.12!".$% &".%" 𝑀', the orbital period and phase of the detection agrees with the known 9.97857 day period from transit observations Future Directions o In the future, these or similar techniques could be widely applied to solar-type (FGK) stars, help measure masses of planets from TESS to fulfill the level 1 science requirement, and eventually help detect habitable-zone Earth-mass exoplanets. o We plan to further validate our method with HARPS-N Rocky Planet Targets and young planets orbiting young active stars Acknowledgments We thank the Office of Undergraduate Research, TIDES Advanced Research Fellowship, Dean’s Scholars, and the Junior Fellows Honors Program for their generous support. References Dumusque et al. 2014; de Beurs et al. 2020; Haywood PhD Thesis 2015; Vanderburg & Johnson 2014; Vanderburg et al. 2016a. Vanderburg et al. 2016b; Mayo et al. 2018; Shallue & Vanderburg, AJ 155, 94, 2018; Cosentino et al. 2012; Ikwut-Ukwa et al. 2020; Akeson et al. 2013 zdebeurs@mit.edu Figure 4: Periodogram: HARPS-N Raw (a) and Corrected (b) RVs in Fourier space. The peaks in the top panel that correspond to stellar activ