The Habitable-zone Planet Finder Detects a Terrestrial-mass Planet Candidate Closely Orbiting Gliese 1151: The Likely Source of Coherent Low-frequency Radio Emission from an Inactive Star
Suvrath Mahadevan, Guðmundur Stefánsson, Paul Robertson, Ryan C. Terrien, Joe P. Ninan, Rae J. Holcomb, Samuel Halverson, William D. Cochran, Shubham Kanodia, Lawrence W. Ramsey, Alexander Wolszczan, Michael Endl, Chad F. Bender, Scott A. Diddams, Connor Fredrick, Fred Hearty, Andrew Monson, Andrew J. Metcalf, Arpita Roy, Christian Schwab
DDraft version February 5, 2021
Typeset using L A TEX twocolumn style in AASTeX63
The Habitable-zone Planet Finder Detects a Terrestrial-mass Planet Candidate Closely OrbitingGliese 1151: The Likely Source of Coherent Low-frequency Radio Emission from an Inactive Star
Suvrath Mahadevan ,
1, 2
Guðmundur Stefánsson , ∗ Paul Robertson , Ryan C. Terrien , Joe P. Ninan ,
1, 2
Rae J. Holcomb , Samuel Halverson , William D. Cochran ,
7, 8
Shubham Kanodia ,
1, 2
Lawrence W. Ramsey ,
1, 2
Alexander Wolszczan ,
1, 2
Michael Endl ,
7, 8
Chad F. Bender , Scott A. Diddams ,
10, 11
Connor Fredrick ,
10, 11
Fred Hearty ,
1, 2
Andrew Monson ,
1, 2
Andrew J. Metcalf ,
12, 10, 11
Arpita Roy , and Christian Schwab Department of Astronomy & Astrophysics, The Pennsylvania State University, 525 Davey Laboratory, University Park, PA, 16802, USA Center for Exoplanets and Habitable Worlds, 525 Davey Laboratory, University Park, PA, 16802, USA Princeton University, Department of Astrophysical Sciences, 4 Ivy Lane, Princeton, NJ 08540, USA Department of Physics and Astronomy, The University of California, Irvine, Irvine, CA 92697, USA Department of Physics and Astronomy, Carleton College, One North College Street, Northfield, MN 55057, USA Jet Propulsion Laboratory, 4800 Oak Grove Drive, Pasadena, CA 91109, USA McDonald Observatory and Department of Astronomy, The University of Texas at Austin, 2515 Speedway, Austin, TX 78712, USA Center for Planetary Systems Habitability, The University of Texas at Austin, 2515 Speedway, Austin, TX 78712, USA Steward Observatory, The University of Arizona, 933 N. Cherry Ave, Tucson, AZ 85721, USA Time and Frequency Division, National Institute of Standards and Technology, 325 Broadway, Boulder, CO 80305, USA Department of Physics, University of Colorado, 2000 Colorado Avenue, Boulder, CO 80309, USA Space Vehicles Directorate, Air Force Research Laboratory, 3550 Aberdeen Ave. SE, Kirtland AFB, NM 87117, USA Space Telescope Science Institute, 3700 San Martin Dr., Baltimore, MD 21218, USA Department of Physics and Astronomy, Macquarie University, Balaclava Road, North Ryde, NSW 2109, Australia
ABSTRACTThe coherent low-frequency radio emission detected by LOFAR from Gliese 1151, a quiescent M4.5dwarf star, has radio emission properties consistent with theoretical expectations of star-planet in-teractions for an Earth-sized planet on a 1-5 day orbit. New near-infrared radial velocities from theHabitable-zone Planet Finder (HPF) spectrometer on the 10 m Hobby-Eberly Telescope at McDonaldObservatory, combined with previous velocities from HARPS-N, reveal a periodic Doppler signatureconsistent with an m sin i = 2 . ± . M ⊕ exoplanet on a 2.02-day orbit. Precise photometry from theTransiting Exoplanet Survey Satellite (TESS) shows no flares or activity signature, consistent witha quiescent M dwarf. While no planetary transit is detected in the TESS data, a weak photometricmodulation is detectable in the photometry at a ∼ day period. This independent detection of acandidate planet signal with the Doppler radial-velocity technique adds further weight to the claim ofthe first detection of star-exoplanet interactions at radio wavelengths, and helps validate this emergingtechnique for the detection of exoplanets. INTRODUCTIONPlanets in close-in orbits orbit are embedded in a mag-netized stellar wind from the expanding stellar corona.As they orbit, short-period planets can perturb the flowof the magnetized wind, which can carry substantialamounts of energy towards the host star via sub-Alfvénicinteractions (Neubauer 1980; Saur et al. 2013; Turnpen-
Corresponding author: Suvrath [email protected] ∗ Henry Norris Russell Fellow ney et al. 2018). This incoming energy can heat up thechromosphere of the star, causing a hot spot on the sur-face of the star, which can cause variability that is mod-ulated by the orbital period of the planet. Shkolnik et al.(2005, 2008) and Cauley et al. (2019) detected chromo-spheric modulations in hot Jupiter systems, which theyinterpret as evidence for Star-Planet Interactions (SPI),and Turner et al. (2020) discuss promising candidate de-tections of circularly polarized emission from τ Boötisand ν Andromedae. In addition to hot Jupiters, M-dwarf planet systems with close-in rocky planets—suchas the TRAPPIST-1 system (Gillon et al. 2017)—havealso been suggested as capable of producing SPI (Pineda a r X i v : . [ a s t r o - ph . E P ] F e b Mahadevan et al. & Hallinan 2018; Turnpenney et al. 2018; Fischer & Saur2019). Recently, Pérez-Torres et al. (2021) announcedthe detection of circularly polarized 1.6 GHz radio emis-sion from Proxima Centauri that could be consistentwith sub-Alfvénic interactions with its 11.2-day planet.Continued monitoring at radio wavelengths will help todistinguish between sub-Alfvénic interactions and othermechanisms (eg. Zic et al. 2020).Vedantham et al. (2020) reported evidence for low-frequency highly circularly polarized radio emission at150 MHz in GJ 1151 using the LOFAR Telescope Array(the LOw-Frequency ARray; van Haarlem et al. 2013).GJ 1151 is a nearby bright ( J = 8 . ) M4.5 dwarf witha quiet chromosphere. The origin of the radio emission,which is observed to be transient and highly circularlypolarized (circular polarization fraction of ± ), ismost consistent with sub-Alfvénic star-planet interac-tions between a rocky planet in a 1 to 5 day orbit aroundthe host star.To search for the presence of a potential rocky planetcompanion and exclude more massive companions, Popeet al. (2020) obtained precise radial velocities (RVs) us-ing the HARPS-N spectrograph. Their observations,yielding 19 RVs over a span of three months, allowedthem to place upper limits on the mass of a potentialplanetary companion of m sin i < . ⊕ with periodsbetween 1 and 5 days.We report on a rocky planet candidate revealed inadditional precise RVs obtained in the near-infrared us-ing the Habitable-zone Planet Finder (Mahadevan et al.2012, 2014) on the 10m Hobby-Eberly Telescope. To-gether, the HPF RVs and the HARPS-N RVs fromPope et al. (2020) reveal a planet with an orbital pe-riod of P = 2 .
02 days and an RV semi-amplitude of K = 4 . ± . − , translating to a mass of m sin i =2 . ± . M ⊕ , where i is the inclination of the orbit. Givenits short period, the planet is capable of sub-Alfvénic in-teractions with its host star, and is likely source of thecoherent radio emission observed by Vedantham et al.(2020). Photometric data from the Transiting Exo-planet Survey Satellite (TESS; Ricker et al. 2015) con-fidently rules out transits of the planet candidate, butthe data show hints of modulation at ∼
100 ppm level, which could constitute the photometricsignature of the SPI interaction.This paper is structured as follows. Section 2 detailsthe observations. Section 3 presents the analysis of theHPF and HARPS-N RVs along with the TESS photo-metric data. In Section 4, using the SPI model fromSaur et al. (2013) and Turnpenney et al. (2018), wedemonstrate that the planet candidate satisfies the sub-Alfvénic criterion and is capable of SPI, and we further discuss the energetics of the sub-Alfvénic interactions.We summarize our key findings in Section 5. DATA2.1.
HARPS-N Radial Velocities
Pope et al. (2020) obtained time-series Doppler spec-troscopy of GJ 1151 using the HARPS-N spectrometer(Cosentino et al. 2012) at Telescopio Nazionale Galileo(TNG). The HARPS-N time series consists of 21 obser-vations compiled over a time baseline of approximately3 months between December 2018 and February 2019.The standard HARPS-N RV pipeline did not offer suf-ficient Doppler precision for a star as cool as GJ 1151,so Pope et al. (2020) extracted their own RVs using the wobble (Bedell et al. 2019) spectral analysis code. Fromthe 21 HARPS-N spectra, Pope et al. (2020) provided19 wobble
RVs; one spectrum (BJD=2458475.75494602)was explicitly excluded for having low signal-to-noise,while another (BJD=2458491.64178017) was excludedfor unspecified reasons. The wobble
RVs exhibitan RMS scatter of 3.8 m s − , with a mean single-measurement error of 2.9 m s − .In our analysis, we have incorporated the wobble RVsas presented by Pope et al. (2020). For our analysis ofstellar magnetic activity (§3.2), we have also used the1D extracted HARPS-N spectra from the TNG archiveto derive the Ca II H&K ( S HK ; Vaughan et al. 1978;Gomes da Silva et al. 2011) and H α ( I H α ; Robertsonet al. 2013) activity indices.2.2. HPF Radial Velocities
HPF is a stabilized fiber-fed near-infrared (NIR) spec-trograph on the 10 m Hobby-Eberly Telescope (HET)covering the z , Y , and J bands from − at aspectral resolution of R ∼ . To enable precise RVsin the NIR, HPF is actively temperature stabilized tothe milli-Kelvin level (Stefansson et al. 2016). HET isa fully queue-scheduled telescope (Shetrone et al. 2007),and all of the observations presented here were executedas part of the HET queue.HPF uses a Laser-Frequency Comb (LFC) calibrator(Metcalf et al. 2019) to provide long-term accurate andprecise instrument drift correction and monitoring. Wedid not obtain simultaneous LFC observations to mini-mize the possibility of contaminating the target spec-trum, but performed the drift correction using LFCframes obtained throughout the night. We have previ-ously demonstrated that we can achieve a drift-correctedprecision at the <
30 cm s − level (Stefansson et al.2020) using this technique.We used the HxRGproc (Ninan et al. 2018) package toperform bias, non-linearity, and cosmic-ray corrections, terrestrial mass planet candidate orbiting GJ 1151 l n ( B F ) a) RV Periodogram Period (d) W i ndo w Period (d) l n ( B F ) b) Periodogram Focus
470 480 490 500 510 520 530 5401050510 R V ( m / s ) c) Time-Series RVs HARPS-N (2019)HPF (2020)
900 920 940 960 980 1000 1020
BJD - 2458000 R V ( m / s ) R V ( m / s ) d) Phase-folded RVs HPFHARPS-N
Phase (Per = 2.018d) R e s i dua l ( m / s ) HPF RMS = 3.4 m/s HARPS-N RMS = 3.0 m/s
Figure 1.
HARPS-N and HPF radial velocities of GJ 1151. In a , we show the Bayes factor periodogram of the combinedHARPS-N+HPF RV series, along with the corresponding window function. The section of the periodogram near the 2.02-daypeak is detailed in b . In c , we show the time-series RVs with the Keplerian model to the planet overlaid. The 5 earliest HPFRVs are not shown to facilitate visibility. In d , we show all RVs phased to the 2.018-day period of the planet. The planet modelis shown as a black curve, with 1, 2, and 3- σ uncertainty regions shaded in gray. RVs and associated activity indicators areavailable in machine readable format. Mahadevan et al. along with slope and variance image generation of theraw HPF up-the-ramp data. Following the slope andvariance image generation, the HPF 1D spectra were ex-tracted using the methods and algorithms discussed byNinan et al. (2018), Kaplan et al. (2019), and Metcalfet al. (2019). To extract RVs from the 1D HPF spec-tra, we used an adapted version of the SpEctrum RadialVelocity AnaLyzer (SERVAL; Zechmeister et al. 2018)code which is further described by Metcalf et al. (2019)and Stefansson et al. (2020). Briefly, SERVAL uses thetemplate-matching method (Anglada-Escudé & Butler2012) to extract precise RVs. For the RV extraction, wefollowed Stefansson et al. (2020), using the 8 HPF or-ders cleanest of tellurics covering the wavelength rangefrom 854-889nm and 994-1076nm. Following Metcalfet al. (2019) and Stefansson et al. (2020), we maskedtellurics and sky-emission lines, to minimize their effecton the RV determination. To further minimize the im-pact of sky-emission lines on the RV determination, wesubtracted the sky-background estimated using the ded-icated HPF sky-fiber. Barycentric correction of our RVswas performed using barycorrpy (Kanodia & Wright2018). barycorrpy also corrects for secular accelera-tion (Kürster et al. 2003), which for GJ 1151 is 0.61 m s − yr − . The secular acceleration is negligible acrossthe baseline of the HARPS-N RVs, but significant forour HPF velocities.Overall, we obtained 50 high resolution spectra withHPF in 25 visits with HPF, obtaining two spectra pervisit with an exposure time of 969s per exposure. Thespectra cover a time baseline of 458 days from March15 2019 to June 25 2020. The median S/N of the HPFspectra was 217 per 1D extracted pixel at µ m . We ex-cluded from our analysis two of the spectra due to lowS/N of 28 and 38 due to poor weather, which left 48 highquality spectra obtained in 24 visits. Following Stefans-son et al. (2020), we binned the resulting RV points perHET visit, resulting in a median RV error of 2.7 m s − ,and an effective exposure time of 32 minutes. The HPFRVs are shown alongside the HARPS-N velocities in Fig-ure 1. The RVs and associated activity indicators usedin this work are provided in machine readable format as‘Data Behind Figure’ 1.2.3. TESS Photometry
As part of its all-sky survey for transiting exoplan-ets, the Transiting Exoplanet Survey Satellite (TESS;Ricker et al. 2015) observed GJ 1151 for 27 days duringSector 22 (18 February–18 March 2020) of the missionin two orbits (Orbit 51 and 52). GJ 1151 is listed asTIC 11893637 in the TESS Input Catalog (TIC; Stas-sun et al. 2018, 2019). TESS pixel data surrounding GJ 1151 were averaged into 2-minute stacks, which werereduced to lightcurves by the Science Processing Op-erations Center (SPOC) at NASA Ames (Jenkins et al.2016), which we retrieved using the lightkurve package(Lightkurve Collaboration et al. 2018). We analyzed thePresearch Data Conditioning Single Aperture Photom-etry (PDCSAP) lightcurve, which contains systematics-corrected data using the algorithms originally developedfor the
Kepler data analysis pipeline. The PDCSAPlightcurve uses pixels chosen to maximize the SNR ofthe target and has removed systematic variability byfitting out trends common to many stars (Smith et al.2012; Stumpe et al. 2014). Data from
Gaia demonstratethat there are no nearby stars within 1 arcmin that arewithin 5 TESS magnitudes of GJ 1151, resulting in min-imal dilution of the TESS light curve.To clean the available TESS data, we removed allpoints with non-zero quality flags (4563 in total) whichindicate known problems (e.g., Tenenbaum & Jenkins2018). We removed an additional 6 points that we iden-tified as σ outliers, leaving a total of 14050 points thatwe used for subsequent analysis, with a median errorbarof 1392ppm. The median-normalized TESS PDCSAP light curve is discussed in Subsection 3.4.From the TESS Data Release Notes for Sector 22,’momentum dump’ events—when the TESS reactionwheel speeds are reset by removing angular momen-tum through thruster firing to keep the pointing of thetelescope stable—occurred every 6.625 days, and 6.75days in Orbits 51, and 52, respectively. These eventsare known to impact the photometry (see e.g., Huanget al. 2018), and we specifically highlight those events inFigure 2. ANALYSIS3.1.
Period Search in RV Data
When analyzing the combined HARPS-N+HPF RVswith frequency analysis tools such as periodograms, weconsistently find evidence for a periodic signal near 2days. For the sake of brevity, we will present resultsfrom the Bayes Factor Periodogram, or BFP (Feng et al.2017). The BFP is particularly useful for this analysis,as it offers an unambiguous measure of a signal’s sta-tistical significance, which is crucial when attempting todetect a low-amplitude exoplanet with a small number ofobservations. However, other periodograms such as thegeneralized Lomb-Scargle (GLS; Zechmeister & Kürster2009) or Bayesian Lomb-Scargle (BGLS; Mortier et al.2015) offer qualitatively similar results.The BFP works by comparing the Bayesian Informa-tion Criterion (BIC) of a periodic signal at each can-didate frequency with that of a noise model. Peri- terrestrial mass planet candidate orbiting GJ 1151 ln( BF ) ≥ are con-sidered statistically significant. While the Agatha im-plementation of this algorithm from Feng et al. (2017)offers the option to account for correlated noise usingone or more moving average terms, the model selec-tion feature of
Agatha prefers a white noise model forour data. Our BFPs were all evaluated for periods − . < log ( P ) < with an oversampling factor of15.In Figure 1a, we show the BFP for the combinedHARPS-N+HPF time series. The RV periodogramshows two distinct sets of peaks. The first occurs ataround 2 days, with peaks at 2.02 and 1.98 days. Thesecond feature sits at approximately 0.7 days. Thesepeaks are all aliases of each other; specifically, each fre-quency is separated by 1 day − . The “1-day alias" prob-lem is common to time-series Doppler searches (Dawson& Fabrycky 2010). Interestingly, the ambiguity between1.98 and 2.02 days is extremely similar to the alias ob-served for YZ Ceti b, another low-mass exoplanet orbit-ing a mid-M dwarf (Robertson 2018). The periodogramssuggest that 2.02 days is the true signal period, a hy-pothesis we confirm via model comparison in §3.3.The HPF RVs alone show statistically significantpower near 2 days. The HARPS-N velocities alonedo not show significant power at any period, but thestrongest peak occurs near the 0.7-day alias of the 2-dayperiod. While the power in the combined periodogramis approximately equal to that of the HPF power spec-trum, the appearance of at least one alias of the samesignal in HARPS-N, as well as the consistency of theHARPS-N RVs with the 2-day signal (Figure 1c) wouldappear to rule out instrumental systematics as the originof the signal.3.2. Ruling out an Astrophysical False Positive
Magnetic features such as starspots and plage can cre-ate periodic RV signals (e.g., Boisse et al. 2011; Robert-son et al. 2014), and the 2-day period of our candidatesignal would be consistent with many young, rapidly ro-tating M dwarfs (Newton et al. 2016). However, we findinstead that GJ 1151 appears to be quiet and slowly-rotating, and that its rotation should not be the astro-physical origin of the signal.By all indications, GJ 1151 is a slow rotator. Newtonet al. (2016) estimated its rotation period to be 117.6days based on MEarth photometry. Reiners et al. (2018)placed an upper limit on its rotational velocity of < km s − , which we agree with based on our own v sin i analysis of the high-resolution HPF spectra, from whichwe also obtain an upper limit of v sin i < − . ItsX-ray luminosity L X = 5 . × erg s − (Foster et al. 2020) implies a stellar age of approximately 5 Gyr and arotation period between 70 and 90 days, according to theempirical relationship of Engle & Guinan (2011). Fur-thermore, data from TESS, HARPS-N, and HPF disfa-vor a short rotation period. For the HARPS-N and HPFtime series, we performed periodicity searches for fourspectral activity indicators: S HK and I H α from HARPS-N, and the chromatic index (CRX) and differential linewidth (dLW) from HPF (Zechmeister et al. 2018). Wesee no evidence for periodic astrophysical variability inany of the spectral activity tracers. Likewise, the TESSlightcurve shows no evidence for a stellar rotation pe-riod of P ≤ days. Finally, the complete absence ofdetectable flares in the TESS lightcurve, and the lack ofemission in chromospheric lines such as H α , are inconsis-tent with GJ 1151 being young and active. Further still,the kinematics of this star are consistent with an olderage as would be expected for a slow rotator: U V W =(-26.9, -65.0, -33.4) km s − , placing it at the boundaryof thin and thick disk membership.Aside from arguments related to the difference be-tween the star’s likely rotation period and the RV pe-riod, the RV data themselves are inconsistent withactivity-driven variability. The RVs show no correla-tions with any of the spectral activity indicators. Also, ifwe model the 2.02-day signal using the optical HARPS-N RVs and NIR HPF RVs separately, we find consis-tent amplitudes. On the other hand, if the signal werecreated by starspots, we would expect a smaller ampli-tude at NIR wavelengths (e.g., Marchwinski et al. 2015).Thus, we conclude that it is extremely unlikely that theobserved 2-day Doppler signal is caused by stellar vari-ability. 3.3. Orbit Modeling
Given the evidence that GJ 1151 is a quiet, slowly-rotating star, we modeled the 2-day variability as a Ke-plerian exoplanet orbit. We used the Markov ChainMonte Carlo (MCMC) orbit-fitting code radvel (Ful-ton et al. 2018) to compute the model. We adoptedmostly uninformative priors for the model parameters,although for the additional white-noise terms (“jitters", σ HARPSN / HPF ) we adopted the jitter prior suggested byFord & Gregory (2007) with a “reference value" σ = 1m s − and maximum σ max = 100 m s − . This prior waschosen to facilitate Bayesian model comparison, partic-ularly to a zero-planet model, for which a uniform priorcan allow the noise terms to grow enough to absorb realastrophysical variability. We fixed the planet’s eccen-tricity to zero, both because our data are not numerousenough to constrain it, and because we expect a planet Mahadevan et al.
Parameter Prior Posterior
Orbital Parameters
Period P (days) N (2 . , .
1) 2 . ± . Time of inferior conjunction T C (BJD - 2458400) U (72 . , . . ± . √ e sin ω · · · √ e cos ω · · · K (m s − ) U (0 , . ± . Instrument Parameters
HARPS-N zero-point offset γ HARPSN (m s − ) U ( − ,
20) 0 . ± . HPF zero-point offset γ HPF (m s − ) U ( − , − . ± . HARPS-N jitter σ HARPSN (m s − ) ∝ ( σ + σ ) − . +1 . − . HPF jitter σ HPF (m s − ) ∝ ( σ + σ ) − . ± Inferred Parameters
Minimum mass m sin i ( M ⊕ ) . ± . Semimajor axis a (AU) . +0 . − . Semimajor axis a ( a/R ∗ ) . ± . Table 1.
Priors and 1-dimensional posterior distributions for the orbital and instrumental parameters for our 1-planet RVmodel to GJ 1151. N ( a, b ) denotes a normal prior with median value a , and standard deviation b ; U ( a, b ) denotes a uniformprior with lower limit value a and upper limit value b . so close to the star to be tidally circularized (e.g Rasio& Ford 1996).For each model considered, we compared to a zero-planet model in which we account for the RV variabil-ity using only a zero-point offset and a jitter term foreach instrument. We performed model selection usingthe Bayes factor ln BF = ∆ BIC , where BIC is theBayesian Information Criterion, which scales a model’slog-likelihood value to include a complexity penalty formodels with more free parameters (Kass & Raftery1995).Our preferred model is for an exoplanet with P = 2 . days. When compared to the zero-planet model, it hasa Bayes factor ln BF = 12 . , indicating a high level ofsignificance. This Bayes factor also agrees well with theresult of our periodogram analysis. While the alias ofthe 2.02-day period at P = 1 . days appears as a strongpeak in our periodogram analysis, if we choose a periodprior tightly constrained at 1.98 days, the posterior dis-tribution still prefers the 2.02-day period. Additionally,we also note that while a model treating the signal asa Keplerian with P = 0 . days is also favored over the zero-planet model, its Bayes factor is significantly lowerthan that of the 2-day model, and we therefore concludeit is simply an alias of the true period.Given the multi-modal nature of the period posterior,we additionally fit the RV datasets using the dynesty dynamic nested sampler (Speagle 2019) available in the juliet (Espinoza et al. 2018) package. Nested sam-plers are efficient at accurately exploring multi-modalsolutions (Speagle 2019). From the nested sampler,we observe a clear highest mode at 2.02 days ( P =2 . +0 . − . days ), with a significantly smaller modeseen at 1.98 days. To quantify the preference for the 2.02day solution over the 1.98 day solution we ran two sets of6 RV-fits each in juliet to get an accurate view of theresulting variance in log evidence values ( ln Z values).To sample the 2.02 day solution, we ran the first set witha uniform prior on the period from 2.0 to 2.04 days, andto sample the 1.98 day solution, we ran the second setwith a uniform prior from 1.96 days to 2.0 days on theperiod. In doing so, we obtain a ln Z = − . ± . and ln Z = − . ± . for the 2.02 day and 1.98 daysolutions, respectively, where we report the values as the terrestrial mass planet candidate orbiting GJ 1151 ∆ ln Z = 3 (20 to 1 pos-terior odds) statistical preference for that solution overthe 1.98 day solution.The planet candidate presented here is fully consis-tent with the expected planet occurrence around mid M-dwarfs: Hardegree-Ullman et al. (2019) suggest a planetoccurrence of . +2 . − . for small ( . ⊕ to . ⊕ ) short-period ( P <
10 days ) planets around M4-M4.5 dwarfs.There remains a possibility that further planets orbit inthe system. However, as seen from Figure 1 with thecurrent RVs, we do not see clear evidence of additionalperiodic signals. Additional precise RVs could shed fur-ther constraints on any additional planets in the system.The prior distributions and adopted posterior valuesof the planet’s orbital model are shown in Table 1. Ad-ditionally, we show the orbit superimposed over the RVdata in Figure 1.3.4.
TESS Photometry
Transit Search
Given the short orbital period period of the planet,and the small radius of the host star, the planet hasa high geometric transit probability. From our best-fit RV model, assuming a circular orbit, we estimate asemi-major axis of a = 0 .
017 AU . Using a stellar radiusof R = 0 . R ⊕ , we obtain a geometric transit proba-bility of R ∗ /a = 5 . . Thus, we looked for evidence oftransits at the expected times inferred from our best-fitRV solution in photometry available from TESS.Figure 2a shows the available photometry from TESS,and Figure 2b shows the expected transit of GJ 1151bphased at the best-fit ephemerides from our RV fit.To estimate the expected transit depth, we predictedthe most likely radius of the planet from its minimummass value of m min = 2 . M ⊕ (assuming inclination is i = 90 ◦ ) using the parametric mass-radius relation im-plemented in the forecaster (Chen & Kipping 2017)package. Using forecaster , we obtain a radius of R = 1 . +0 . − . R ⊕ , which corresponds to an expectedtransit depth of ∼ . As seen from Figure 2b,the expected transit depth of the planet is significantlydeeper than TESS’s single-point 2min photometric pre-cision on this target ( ), and the data confi-dently rule out transits at this ephemeris. In addition,to search for evidence of other periodic transiting plan-ets in the system, we used the Box-Least-Squares (BLS)algorithm (Kovács et al. 2002). In examining BLS pe-riodograms from periods from 0.5 to 30 days, we seeno significant evidence of transiting planets in the sys-tem from the TESS data. We additionally note that although sub-Alfvénic star-planet interactions are capa-ble of creating flares, we see no clear signatures of flaresin the TESS data (Fischer & Saur 2019).3.4.2. Periodogram Analysis
Figure 2d shows Generalized Lomb Scargle (GLS) Pe-riodograms of the available TESS photometry, show-ing the GLS of i) all of the available photometry (Or-bits 51 and 52; top panel), ii) photometry from Orbit51 (middle panel), and iii) photometry from Orbit 52(bottom panel). In Orbit 51, we see a clear peak at ∼ − , which we attribute to the systematic noisein the photometry that occurred during the TESS mo-mentum dump in this orbit (see Figure 2a). From theGLS Periodogram of Orbit 52, which overall shows lesscorrelated noise structures, we do not see a clear sys-tematic jump during the TESS momentum dump, andwe see no clear peak at 6-7 days. In the GLS Peri-odogram of Orbit 52, and in the periodogram of bothorbits, we see evidence of a moderately significant peakat the .
02 day period we see in the RVs (False AlarmProbability of ∼ ∼ a/R ∗ = 18 . and assuming m p sin i = 2 . M ⊕ ,we obtain a maximum possible amplitude expected fromellipsoidal variations of ∼ .
01 ppm , which is negligiblein comparison to the observed
100 ppm signal in TESS.We conclude that the
100 ppm photometric modulationis not due to ellipsoidal variations.Instead, we surmise that the 2 day photometric sig-nal could represent the photometric counterpart of thestar-planet interaction between the planet and the star.However, due to the limited significance of the signalin the TESS photometry (False Alarm Probability of ∼
1% in Figure 2), we urge further precise photometricfollow-up of this system to characterize this potentiallow-amplitude signal.3.4.3.
Starspot Modulation
Given that we have identified photometric periodicitymatching that of our proposed exoplanet candidate, weconsidered the possibility that the RV signal is causedby starspot modulation rather than a planet. This spotcould be created by H- opacity supplied by the incom-ing electron beam from the possible sub-Alfvénic inter-action, similar to stellar spots observed in photometryof late M-dwarfs with corresponding radio modulations(see e.g., Littlefair et al. 2008; Hallinan et al. 2015). To
Mahadevan et al.
Figure 2. a) Available photometry from TESS from Sector 22, obtained in two orbits: TESS Orbit 51 and 52. The unbinned2min TESS cadence is shown in black, and 30min bins in blue. No transits are seen. b) TESS photometry folded on the expectedtransit ephemeris from our best-fit RV fit. The red curve shows a nominal expected transit model if the planet were transiting.The data rule out such transits to a high degree of confidence. c) TESS photometry of both orbits phased to the 2.02day periodof the RV planet shows a ∼ ∼ estimate the spot size from the 100ppm TESS signal,we created a starspot model with SOAP 2.0 (Dumusqueet al. 2014), which predicts both photometric and RVvariability for given stellar parameters and starspot con-figurations. For the purposes of this test, we assumedthe stellar rotation period P rot = 2 . days. We used asimple model of a single equatorial starspot with a spot-photosphere temperature difference ∆ T = 600 K, whichis a moderate contrast for M stars (Reiners et al. 2010).Scaling the spot radius to match the observed photo-metric amplitude, we found that a radius equal to 1% ofthe stellar radius produces the desired 100 ppm bright-ness variation. However, the expected RV amplitude ofsuch a spot is of order 0.2 m s − , which is too small by afactor of ∼
20 to explain the RV periodicity we observe.Furthermore, as we have discussed in §3.2, multiple linesof evidence suggest that P rot is significantly longer than2 days. Thus, we find it is unlikely that starspot modu- lation is the origin of either the photometric or Dopplersignal at 2 days. DISCUSSION4.1.
Sub-Alfvénic Interaction
To study the Alfvén interaction of the planet can-didate and estimate the resulting Poynting fluxes, webroadly follow Vedantham et al. (2020), using the modelframeworks of Saur et al. (2013) and Turnpenney et al.(2018), and that of Lanza (2009), to describe the ener-getics of the star-planet interactions. These models as-sume that the planet is a conductive perturber orbitingin a magnetized expanding stellar corona described asa Parker-wind (Parker 1958). For the Parker-wind, weassumed a coronal temperature of T corona = 2 × K ,which results in a sound speed of c s ∼
129 km s − . Fol-lowing Vedantham et al. (2020), we assumed a base num-ber density of n base = 10 g cm − , which we scaled as n ∝ d − where d is the distance from the star. terrestrial mass planet candidate orbiting GJ 1151 Table 2.
Summary of input parameters and posterior parameters describing the energetics of the star-planet interactions forthe ST model (Saur et al. 2013, and Turnpenney et al. 2018), and the Lanza model (Lanza 2009). N ( a, b ) denotes a normalprior with median value a , and standard deviation b ; J ( a, b ) denotes a log-uniform prior with lower limit value a and upperlimit value b ; U ( a, b ) denotes a uniform prior with lower limit value a and upper limit value b .Parameter Parameter Description Value Notes Prior Parameters R ∗ Stellar Radius ( R (cid:12) ) N (0 . , . TICv8 (Stassun et al. 2019) M ∗ Stellar Mass ( M (cid:12) ) N (0 . , . TICv8 (Stassun et al. 2019) P rot Stellar Rotation (days)
Newton et al. (2016) T C Temperature of Stellar Corona (K) × Adopted from Vedantham et al. (2020) n base Base Number Density ( cm − ) × Adopted from Vedantham et al. (2020) B ∗ Stellar Magnetic Field (T) J (0 . , . Nominal M-dwarf stellar magnetic field B exo Planet Magnetic Field (G) J (0 . , Nominal planet magnetic field R p Planet Radius ( R ⊕ ) N (1 . , . Estimated from m sin i Posterior Parameters log ( M A ) Alfvén Mach number − . ± . ( S total , ST ) Poynting Flux, ST model ( ergs s − ) . +0 . − . log ( S total , Lanza ) Poynting Flux, ST model ( ergs s − ) . +1 . − . To estimate if our planet candidate satisfies the cri-terion for sub-Alfvénic interactions, we estimate theAlfvén Mach number of the planet, which is given by, M A = v rel /v A , (1)where v rel is the relative velocity of the stellar windas seen by the orbiting planet, and v A is the Alfvénspeed. Assuming a circular orbit with a period of P = 2 .
02 days , the planet has a Keplerian orbital ve-locity of v orb ∼
94 km s − at its orbital distance of a/R ∗ = 18 . . As the magnetic field of GJ 1151 is notcurrently well constrained, if we adopt the nominal valueof B ∗ = 0 .
01 T assumed by Vedantham et al. (2020), weobtain an Alfvén speed of v A ∼ − and anAlfvén Mach number of M A = 0 . at the orbital dis-tance of the planet. As the Mach number is less than 1,the planet is capable of sub-Alfvénic interactions withits host star. We further note the planet also satisfiesthe second criterion for sub-Alfvénic interactions – thatthe radial wind speed is less than the radial componentof the Alfvén speed, which is a necessary condition sothat one of the two Alfvén-wings points towards the star(see discussion in Saur et al. 2013).As the planet is capable of sub-Alfvénic interactions,and has a small Alfvén Mach number, we estimate thetotal Poynting flux of the system with S total = 2 π v rel R B µ ε, (2)where v rel is the relative velocity of the stellar wind asseen by the orbiting planet, B is the total magneticfield at the position of the planet, µ is the vacuum permeability constant, and R eff is the effective radiusof the planet. The ε parameter describes the efficiencyof the star-planet interactions, and its parameterizationdiffers in the model of Saur et al. (2013) and Turnpenneyet al. (2018) (hereafter in the ST Model), and the modelof Lanza (2009) (hereafter the Lanza Model). In the STmodel ε parameter is given by ε = M A ¯ α sin ( θ ) , (3)where M A is the Alfvén Mach number of the system, θ is the angle between the total magnetic field B at theposition of the planet and the total stellar wind velocity,and ¯ α , is a parameter denoting the sub-Alfvénic interac-tion efficiency, where we follow Vedantham et al. (2020)and assume it is equal to unity.In the model of Lanza (2009), ε is given by ε = γ/ , (4)where γ is a parameter ranging from 0 to 1. Here wefollow Vedantham et al. (2020) and assume γ = 0 . .To estimate the effective radius of the planet, givenour mass estimate of m sin i = 2 . ± . M ⊕ , we use the forecaster (Chen & Kipping 2017) mass-radius rela-tions to predict a likely minimum radius of the planet of R p = 1 . +0 . − . R ⊕ . If the planet has an inherent mag-netic field, this will increase the effective radius R eff ofthe interaction (see Equation 57 in Saur et al. 2013) by R eff = R exo (cid:18) B exo B (cid:19) / (cid:115) (cid:18) Θ M (cid:19) , (5)where R exo is the radius of the planet, B exo is the equa-torial magnetic field of the planet, and Θ M is the angle0 Mahadevan et al. between the planet magnetic moment and the stellarmagnetic field at the location of the planet. We followVedantham et al. (2020), and assume that the planet hasa magnetic field of , and assume that the magneticmoment nominally has a Θ M = 90 ◦ angle between thestellar magnetic field, resulting in (cid:113) Θ M ) ∼ S total , ST ∼ × W , and S total , Lanza ∼ × W for the ST and Lanza mod-els, respectively. Assuming a Poynting flux-to-radioemission conversion efficiency of (cid:15) r = 1% , we obtaina Poynting radio power of P radio , ST = 8 × W , and P radio , Lanza = 9 × W , for the two models, respec-tively. Given the distance of d = 8 .
04 pc to the host star,we can also calculate the resulting spectral flux den-sity of F radio , ST = 0 . , and F radio , Lanza = 52 mJy ,where we followed followed Vedantham et al. (2020) as-suming a bandwidth of ∆ ν equal to the electron gy-rofrequency on the surface of the star, and assumed abeam solid angle Ω = 0 . . These spectral flux den-sities broadly agree with the observed LOFAR value of ∼ . from Vedantham et al. (2020). As a compari-son to other M-dwarf systems, this spectral flux densityis similar—but somewhat higher—to the spectral fluxdensity of ∼ mJy for the M4-dwarf planet GJ 876 bas estimated by Turnpenney et al. (2018).To visualize the sensitivity of the models to differentinput parameters as a function of orbital distance of theplanet, we performed a Monte Carlo sampling assum-ing nominal input priors summarized in Table 2. Figure3 shows the Alfvén mach number, along with the re-sulting Poynting flux estimates using the ST and theLanza models, as a function of distance from the star.The solid curves show the median models and the cor-responding shaded regions show the σ credible inter-vals. From Figure 3a, we see that for even the broadset of input parameters in Table 2, the system is sub-Alfvénic ( log ( M A ) < ) at the orbital location of theplanet. In Figure 3b, we additionally compare our re-sulting Poynting flux estimates from the ST and Lanzamodels to the radio observation constraint from Vedan-tham et al. (2020) (grey shaded region in Figure 3b).We see that the ST and Lanza models flank the radioconstraint presented by Vedantham et al. (2020) whichassumes a B ∗ = 0 .
01 T , with both the ST and Lanzamodels being consistent with the observed radio con-straint at the 1-2 σ level for the assumed parameters. Figure 3. a) Alfvén Mach numbers as a function of dis-tance from the host star. The solid curve shows the medianmodel, and the grey filled region shows the σ credible inter-val around the median model. The grey vertical dashed linesshow the orbital distance of the planet. b) Total Poyntingflux as a function of distance of the star as calculated withthe ST model (blue solid curve) and the Lanza model (redsolid curve). The blue and red shaded regions show the cor-responding σ credible intervals around the median model.The grey region in the lower panel shows the radio constraintfrom Vedantham et al. (2020) assuming a fixed B ∗ = 0 .
01 G . We conclude that the planet candidate we report here iscompatible with being the source of the radio emissiondetected by Vedantham et al. (2020).In the near future, The Square Kilometre Array(SKA), a next generation radio telescope, is expectedwill come online which is anticipated to improve on theflux density sensitivity to that of LOFAR by a factor of10-30 resulting in a flux density sensitivity of ∼ µ Jy Zarka et al. (2015) in the 50-250MHz range. With itsimproved precision, SKA is expected to enable the de-tection of additional planets exhibiting coherent radioemission around nearby stars. SUMMARYWe report on a planetary companion orbiting the qui-escent M4.5 dwarf GJ 1151 in a 2.02 day orbit. From ra-dial velocities obtained with the Habitable-zone Planet terrestrial mass planet candidate orbiting GJ 1151 m sin i = 2 . ± . M ⊕ .The planet has an Alfvén Mach number of M A = 0 . ,and thus satisfies the criterion for sub-Alfvénic interac-tion with its host star. We estimate the resulting Poynt-ing fluxes of the star-planet system using two differentmodels, which we show are consistent with the radioconstraints reported by Vedantham et al. (2020) at the − σ level. Given this consistency, we conclude that itis highly likely that the planet is the source of the radioemission. To confirm that SPI interactions with the RVplanet candidate we report is the true source of the radioemission, we urge continued radio follow-up observationsto demonstrate a corresponding 2.02day periodicity atradio wavelengths.Further, using data from the TESS spacecraft we areable to rule out transits of the reported RV planet. Fromthe TESS photometry, we see a photometric modulationat ∼ ∼ Facilities:
HPF/HET, HARPS-N, TESS.
Software: astropy (Astropy Collaboration et al.2013), astroquery (Ginsburg et al. 2018), barycorrpy (Kanodia & Wright 2018), batman (Kreidberg 2015), dynesty (Speagle 2019), forecaster (Chen & Kipping2017),
GNU Parallel (Tange 2011),
HxRGproc (Ninanet al. 2018),
Jupyter (Kluyver et al. 2016), juliet (Espinoza et al. 2018), matplotlib (Hunter 2007), numpy (Van Der Walt et al. 2011), pandas (McKinney2010), radvel (Fulton et al. 2018),
SERVAL (Zechmeisteret al. 2018),
SOAP 2.0 (Dumusque et al. 2014), tesscut (Brasseur et al. 2019).2
Mahadevan et al.
REFERENCES