The transiting multi-planet system HD3167: a 5.7 MEarth Super-Earth and a 8.3 MEarth mini-Neptune
Davide Gandolfi, Oscar Barragán, Artie P. Hatzes, Malcolm Fridlund, Luca Fossati, Paolo Donati, Marshall C. Johnson, Grzegorz Nowak, Jorge Prieto-Arranz, Simon Albrecht, Fei Dai, Hans Deeg, Michael Endl, Sascha Grziwa, Maria Hjorth, Judith Korth, David Nespral, Joonas Saario, Alexis M. S. Smith, Giuliano Antoniciello, Javier Alarcon, Megan Bedell, Pere Blay, Stefan S. Brems, Juan Cabrera, Szilard Csizmadia, Felice Cusano, William D. Cochran, Philipp Eigmüller, Anders Erikson, Jonay I. González Hernández, Eike W. Guenther, Teruyuki Hirano, Alejandro S. Mascareño, Norio Narita, Enric Palle, Hannu Parviainen, Martin Pätzold, Carina M. Persson, Heike Rauer, Ivo Saviane, Linda Schmidtobreick, Vincent Van Eylen, Joshua N. Winn, Olga V. Zakhozhay
DDraft version June 9, 2017
Preprint typeset using L A TEX style AASTeX6 v. 1.0
THE TRANSITING MULTI-PLANET SYSTEM HD 3167:A 5.7 M ⊕ SUPER-EARTH AND A 8.3 M ⊕ MINI-NEPTUNE
Davide Gandolfi , Oscar Barrag´an , Artie P. Hatzes , Malcolm Fridlund , Luca Fossati , Paolo Donati ,Marshall C. Johnson , Grzegorz Nowak , Jorge Prieto-Arranz , Simon Albrecht , Fei Dai ,Hans Deeg , Michael Endl , Sascha Grziwa , Maria Hjorth , Judith Korth , David Nespral ,Joonas Saario , Alexis M. S. Smith , Giuliano Antoniciello , Javier Alarcon , Megan Bedell ,Pere Blay , Stefan S. Brems , Juan Cabrera , Szilard Csizmadia , Felice Cusano , William D. Cochran ,Philipp Eigm¨uller , Anders Erikson , Jonay I. Gonz´alez Hern´andez , Eike W. Guenther ,Teruyuki Hirano , Alejandro S. Mascare˜no , Norio Narita , Enric Palle , Hannu Parviainen ,Martin P¨atzold , Carina M. Persson , Heike Rauer , Ivo Saviane , Linda Schmidtobreick ,Vincent Van Eylen , Joshua N. Winn , Olga V. Zakhozhay Dipartimento di Fisica, Universit´a di Torino, via P. Giuria 1, 10125 Torino, Italy; email: davide.gandolfi@unito.it Th¨uringer Landessternwarte Tautenburg, Sternwarte 5, D-07778 Tautenberg, Germany Leiden Observatory, University of Leiden, PO Box 9513, 2300 RA, Leiden, The Netherlands Department of Earth and Space Sciences, Chalmers University of Technology, Onsala Space Observatory, 439 92 Onsala, Sweden Space Research Institute, Austrian Academy of Sciences, Schmiedlstrasse 6, 8042, Graz, Austria INAF - Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, 50125, Florence, Italy Department of Astronomy, The Ohio State University, 140 West 18th Ave., Columbus, OH 43210, USA Instituto de Astrof´ısica de Canarias, C/ V´ıa L´actea s/n, 38205 La Laguna, Spain Departamento de Astrof´ısica, Universidad de La Laguna, 38206 La Laguna, Spain Stellar Astrophysics Centre, Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, DK-8000 Aarhus C, Denmark Department of Astrophysical Sciences, Princeton University, 4 Ivy Lane, Princeton, NJ 08544, USA Department of Physics and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA02139, USA Department of Astronomy and McDonald Observatory, University of Texas at Austin, 2515 Speedway, Stop C1400, Austin, TX 78712, USA Rheinisches Institut f¨ur Umweltforschung an der Universit¨at zu K¨oln, Aachener Strasse 209, 50931 K¨oln, Germany Nordic Optical Telescope, Apartado 474, 38700, Santa Cruz de La Palma, Spain Institute of Planetary Research, German Aerospace Center, Rutherfordstrasse 2, 12489 Berlin, Germany European Southern Observatory, Alonso de Cordova 3107, Santiago, Chile Department of Astronomy and Astrophysics, University of Chicago, 5640 S. Ellis Ave, Chicago, IL 60637, USA Landessternwarte K¨onigstuhl, Zentrum f¨ur Astronomie der Universit¨at Heidelberg, K¨onigstuhl 12, D-69117 Heidelberg INAF - Osservatorio Astronomico di Bologna, Via Ranzani, 1, 20127, Bologna, Italy Department of Earth and Planetary Sciences, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokio 152-8551, Japan Observatoire Astronomique de l’Universit´e de Gen`eve, 1290 Versoix, Switzerland Department of Astronomy, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan Astrobiology Center, NINS, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan National Astronomical Observatory of Japan, NINS, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan Center for Astronomy and Astrophysics, TU Berlin, Hardenbergstr. 36, 10623 Berlin, Germany Main Astronomical Observatory, National Academy of Sciences of the Ukraine, 27 Akademika Zabolotnoho St. 03143, Kyiv, Ukraine
ABSTRACTHD 3167 is a bright (V=8.9 mag) K0 V star observed by the NASA’s K2 space mission during itsCampaign 8. It has been recently found to host two small transiting planets, namely, HD 3167 b, anultra short period (0.96 d) super-Earth, and HD 3167 c, a mini-Neptune on a relatively long-periodorbit (29.85 d). Here we present an intensive radial velocity follow-up of HD 3167 performed withthe FIES@NOT, [email protected], and HARPS-N@TNG spectrographs. We revise the systemparameters and determine radii, masses, and densities of the two transiting planets by combining the K2 photometry with our spectroscopic data. With a mass of 5 . ± . M ⊕ , radius of 1 . ± . R ⊕ ,and mean density of 8 . +1 . − . g cm − , HD 3167 b joins the small group of ultra-short period planets a r X i v : . [ a s t r o - ph . E P ] J un Gandolfi et al. known to have a rocky terrestrial composition. HD 3167 c has a mass of 8 . +1 . − . M ⊕ and a radius of2 . +0 . − . R ⊕ , yielding a mean density of 2 . +0 . − . g cm − , indicative of a planet with a compositioncomprising a solid core surrounded by a thick atmospheric envelope. The rather large pressure scaleheight ( ∼
350 km) and the brightness of the host star make HD 3167 c an ideal target for atmosphericcharacterization via transmission spectroscopy across a broad range of wavelengths. We found evidenceof additional signals in the radial velocity measurements but the currently available data set does notallow us to draw any firm conclusion on the origin of the observed variation.
Keywords: stars: fundamental parameters — stars: individual: HD 3167 — planets and satellites:detection — planets and satellites: individual: HD 3167 b, HD 3167 c INTRODUCTIONBack in 1995 the discovery of 51 Peg b demonstratedthat gas-giant planets ( R p ≈ R Jup ) could have orbitalperiods of a few days and thus exist quite close to theirhost star (Mayor & Queloz 1995). Space-based tran-sit search missions such as
CoRoT (Baglin & Fridlund2006),
Kepler (Borucki et al. 2010), and K2 (Howell etal. 2014) have established that these close-in planets canhave radii down to Neptune-like (Barrag´an et al. 2016;David et al. 2016) and even Earth-like values (Queloz etal. 2009; Howard et al. 2009; Pepe et al. 2013). Close-in exoplanets have challenged planet formation theoriesand play an important role in the architecture of exo-planetary systems (e.g., Winn & Fabrycky 2015; Hatzes2016).Based on the occurrence rate of planets and planetcandidates discovered by Kepler we know that short-period super-Earths ( R p = 1 - 2 R ⊕ , M p = 1 - 10 M ⊕ ) andsub-Neptunes ( R p = 2 - 4 R ⊕ , M ⊕ = 10 - 40 M ⊕ ) are ex-tremely common in our Galaxy. About 26% of solar-likestars in the Milky Way host small planets ( R p < R ⊕ )with orbital periods shorter than 100 days (see, e.g.,Marcy et al. 2014; Burke et al. 2015). These planets arenot represented in our Solar System and were thereforecompletely unknown to us until a few years ago.Although Kepler has provided us with a bonanza ofsuch small planets, little is known about their masses,compositions, and internal structures. Mass determina-tions with a precision that allows us to distinguish be-tween different internal compositions (better than 20 %)have been possible only for a few dozen super-Earthsand sub-Neptunes. The small radial velocity (RV) vari-ation induced by such planets and the faintness of most
Kepler host stars (
V >
13 mag) make RV follow-up ob-servations difficult. These observations either place toomuch demand on telescope time, or they are simply un-feasible with state-of-the-art facilities.A special class of close-in objects is composed of ex-oplanets with ultra-short orbital periods ( P orb < ∝ P − / ) and the inducedRV variation is large ( ∝ P − / ). Very short orbital pe- riods are also advantageous because they are (often)much shorter than the rotation period of the star, al-lowing the correlated noise due to stellar rotation to bemore easily distinguished from the planet-induced RVsignal (Hatzes et al. 2011). To date about 80 ultra-short period exoplanets have been discovered , mainlyfrom transit surveys starting with CoRoT-7b (L´eger etal. 2009). Masses, however, have only been determinedfor two dozen of these objects. About half of these aregas-giant planets with masses between 1 and 10 M Jup .The rest are small planets in the super-earth regime withmasses between about 5 and 10 M ⊕ .Using time-series photometric data from the K2 spacemission, Vanderburg et al. (2016) recently announcedthe discovery of two small transiting planets around thebright (V=8.9 mag) K0 dwarf star HD 3167. The in-ner planet, HD 3167 b, has a radius of R p =1.6 R ⊕ andtransits the host star every 0.96 days. By our defini-tion, HD 3167 b qualifies as an ultra-short period planet.The outer planet, HD 3167 c, has a radius of 2.9 R ⊕ andan orbital period of 29.85 days. The brightness of thehost star makes the system amenable to follow-up ob-servations such as high-precision RV measurements forplanetary mass determination.As part of the ongoing RV follow-up program of K2 transiting planets successfully carried our by our consor-tium KESPRINT (e.g., Sanchis-Ojeda et al. 2015; Grziwaet al. 2016; Van Eylen et al. 2016; Barrag´an et al. 2017;Fridlund et al. 2017; Guenther et al. 2017; Nowak etal. 2017), we herein present the results of an intensiveRV campaign we conducted with the FIES, HARPS,and HARPS-N spectrographs to accurately measure themasses of the two small planets transiting HD 3167. Thepaper is organized as follows. In § § K2 data and describe our high-resolution spectroscopic observations. The propertiesof the host star are reported in §
4. We present thedata modeling in § § See exoplanets.org and exoplanet.eu ; as of May 2017. ass determinations of HD 3167 b and HD 3167 c Figure 1 . K2 light curve of HD 3167 from Vanderburg et al. (2016).2. K2 PHOTOMETRY K2 observed HD 3167 during its Campaign 8 for about80 days – between January and March 2016 – with anintegration time of about 29.4 minutes (long cadencemode). For our analysis presented in § . We referthe reader to Vanderburg et al. (2016) for a detailed de-scription of both the K2 data of HD 3167 and the detec-tion of the two transiting planets. For the sake of claritywe reproduce in Fig. 1 the full light curve of HD 3167presented in Vanderburg et al. (2016). SPECTROSCOPIC FOLLOW-UPWe used the FIbre-fed ´Echelle Spectrograph (FIES;Frandsen & Lindberg 1999; Telting et al. 2014) mountedat the 2.56m Nordic Optical Telescope (NOT) of Roquede los Muchachos Observatory (La Palma, Spain) to ac-quire 37 high-resolution spectra (R ≈ ◦ C. Ob-servations of RV standard stars performed by our teamsince 2011, have shown that long-exposed ThAr spec-tra taken immediately before and after short-exposedtarget’s observations ( T exp ≤
20 min) allow us to tracethe intra-night RV drift of the instrument to within ∼ Publicly available at . that the inter-night stability of the instrument is 2 to 4times worse.The FIES observations were carried out as part ofthe OPTICON and NOT observing programs 16A/055,P53-016, and P53-203. We set the exposure time to 15 -20 min and acquired long-exposed ( T exp ≈
35 sec) ThArspectra immediately before and after the target obser-vations. We took at least 2 spectra separated by 1-2hours per night except on one night. The data were re-duced using standard routines, which include bias sub-traction, flat fielding, order tracing and extraction, andwavelength calibration. Radial velocities were derivedvia multi-order cross-correlations, using the stellar spec-trum with the highest S/N ratio as a template . Themeasured RVs are listed in Table 5 along with their 1- σ internal uncertainties and the signal-to-noise (S/N) ratioper pixel at 5500 ˚A.We also acquired 50 spectra with the HARPS spec-trograph (R ≈
115 000; Mayor et al. 2003) and 32spectra with the HARPS-N spectrograph (R ≈ < − ). They are mounted at the ESO-3.6m telescope of La Silla observatory (Chile) and at the3.58m Telescopio Nazionale Galileo (TNG) of Roque delos Muchachos Observatory (La Palma, Spain).The HARPS and HARPS-N observations were per-formed as part of the ESO observing programs 097.C-0948 and 098.C-0860, and of the TNG/CAT programsA33TAC 15 and CAT16B 61. We used the simultaneousFabry Perot calibrator and set the exposure times to 15 -40 minutes depending on sky conditions and schedulingconstraints. We followed the same multi-visit strategy Epoch 2457605.
Gandolfi et al.
Table 1 . Spectroscopic parameters of HD 3167 as derived from the FIES (top), HARPS (middle), and HARPS-N (bottom)data using the three methods described in Sect 4.1.Method T eff (K) log g (cid:63) (cgs) [Fe/H] (dex) v mic (km s − ) v mac (km s − ) v sin i (cid:63) (km s − ) FIES
Method 1 5288 ±
75 4.53 ± ± ± ± ± ±
95 4.56 ± ± ± ± ± ±
76 4.44 ± ± ± HARPS
Method 1 5295 ±
70 4.54 ± ± ± ± ± ±
80 4.54 ± ± ± ± ± ±
112 4.41 ± ± ± HARPS-N
Method 1 5275 ±
62 4.51 ± ± ± ± ± ±
70 4.52 ± ± ± ± ± ±
121 4.40 ± ± ± adopted for the FIES observations, i.e., we acquired atleast 2 spectra per night in most of the observing nights.The data were reduced using the dedicated HARPS andHARPS-N off-line pipelines and radial velocities wereextracted by cross-correlating the extracted echelle spec-tra with a G2 numerical mask. We tested also the K0and the K5 mask but found neither a significant im-provement of the error bars, nor a significant variationof the relative amplitude of the detected RV variation.The HARPS and HARPS-N radial velocity measure-ments and their uncertainties are also listed in Table 5,along with the S/N ratio per pixel at 5500 ˚A, the full-width half maximum (FWHM) and bisector span (BIS)of the cross-correlation function (CCF), and the Ca ii H & K chromospheric activity index log R (cid:48) HK . Five outof the 50 HARPS spectra are affected by poor sky andseeing conditions. They are not listed in Table 5 andwere not used in our analysis. STELLAR PROPERTIES4.1.
Spectroscopic parameters
We combined separately the FIES, HARPS, andHARPS-N data to produce three co-added spectra ofhigher S/N ratio and determine the spectroscopic pa-rameters of the host star. The stacked FIES, HARPS,and HARPS-N spectra have S/N ratios of 500, 560, and480 per pixel at 5500 ˚A, respectively. We derived thespectroscopic parameters using three independent meth-ods as described in the next three paragraphs. Resultsfor each method and spectrum are listed in Table 1. – Method 1 . This uses a customized
IDL softwaresuite that implements the spectral synthesis program
SPECTRUM (V2.76; Gray & Corbally 1994) to com-pute synthetic spectra using ATLAS 9 model atmospheres(Castelli & Kurucz 2004). The code fits spectral fea-tures that are sensitive to different photospheric param-eters, adopting the calibration equations of Bruntt etal. (2010) and Doyle et al. (2014) to determine the mi-croturbulent ( v mic ) and macroturbulent ( v mac ) veloci-ties. It uses the wings of the Balmer lines to obtain afirst guess of the effective temperature ( T eff ), and theMg i i i D lines to refine the effective temperature estimateand derive the surface gravity (log g (cid:63) ). The iron abun-dance [Fe/H] and projected rotational velocity v sin i (cid:63) are measured by fitting many isolated and unblendediron lines. – Method 2 . This uses the spectral analysis package SME (V4.43; Valenti & Piskunov 1996; Valenti & Fischer2005) along with both
ATLAS 12 and
MARCS model at-mospheres (Kurucz 2013; Gustafsson et al. 2008).
SME calculates synthetic spectra and fits them iteratively tothe observed high-resolution echelle spectra using a chi-squared minimization procedure. Micro and macro tur-bulent velocities are estimated using the same calibra-tion equations adopted by the first method. T eff , log g (cid:63) ,[Fe/H], and v sin i (cid:63) are derived by fitting the same spec-tral features as in the previous paragraph. – Method 3 . This is based on the classical equiva-lent width (EW) technique applied to about 100 Fe i and 10 Fe ii lines. It uses the public version of theline list prepared for the Gaia -ESO Survey (Heiter et Publicly available at . ass determinations of HD 3167 b and HD 3167 c VALD3 atomic database(Ryabchikova et al. 2011). T eff is obtained by removingtrends between the abundance of a given element andthe respective excitation potential; log g (cid:63) is derived byassuming the ionization equilibrium condition, i.e., byrequiring that for a given species the same abundance(within the uncertainties) is obtained from lines of twoionization states (typically neutral and singly ionizedspecies); v mic and [Fe/H] are estimated by minimizingthe slope of the relationship between abundance and thelogarithm of the reduced EWs. Equivalent widths aremeasured using the code DOOp (Cantat-Gaudin et al.2014), a wrapper of
DAOSPEC (Stetson & Pancino 2008).The photospheric parameters are derived with the code
FAMA (Magrini et al. 2013), a wrapper of
MOOG (Snedenet al. 2012).The three techniques provide consistent results, re-gardless of the used spectrum and/or method. Whilewe have no reason to prefer one method over theother, we adopted the results of
Method 1 applied onthe FIES, HARPS, and HARPS-N spectra. The fi-nal adopted values for T eff , log g (cid:63) , [Fe/H], and v sin i (cid:63) are the averaged estimates we obtained using the firstmethod; the corresponding uncertainties are defined asthe square root of the individual errors added in quadra-ture, divided by three. We obtained T eff = 5286 ±
40 K,log g (cid:63) = 4.53 ± ± v sin i (cid:63) = 1.8 ± − (Table 2). Our results are infairly good agreement with the spectroscopic parametersderived by Vanderburg et al. (2016).4.2. Stellar mass, radius, and age
We followed the same method adopted by Vander-burg et al. (2016) and derived the mass, radius, andage of HD 3167 using
PARAM , an on-line interface forBayesian estimation of stellar parameters . Briefly, PARAM interpolates the apparent visual magnitude, par-allax, effective temperature and iron abundance onto
PARSEC model isochrones (Bressan et al. 2012), adopt-ing the initial mass function from Chabrier (2001). Weused our spectroscopic parameters ( § V = 8.941 ± Hipparcos ’ parallax(21.82 ± . Following themethod outlined in Gandolfi et al. (2008) and using thebroad-band photometry available in the EPIC input cat-alog, we found that the interstellar reddening is indeedconsistent with zero ( A v = 0.02 ± ± Available at http://stev.oapd.inaf.it/cgi-bin/param . Gaia ’s first data release does not report the parallax ofHD 3167. set the interstellar absorption to zero and did not correctthe apparent visual magnitude.HD 3167 has a mass of M (cid:63) = 0 . ± . M (cid:12) and aradius R (cid:63) = 0 . ± . R (cid:12) , implying a surface grav-ity of log g (cid:63) = 4.51 ± § ± Stellar activity and rotation period
The average Ca ii H & K activity index log R (cid:48) HK , asmeasured from the HARPS and HARPS-N spectra,is − ± − ± . Wechecked if the extrinsic absorption, either from the in-terstellar medium (ISM) or from material local to thesystem, biases the measured values of log R (cid:48) HK (Fos-sati et al. 2013, 2015). The far-ultraviolet (FUV) stel-lar emission, which originates in the chromosphere andtransition region, provides instead an unbiased measureof the stellar activity (Fossati et al. 2015). We mea-sured the excess of the chromospheric FUV emission– directly proportional to stellar activity – by estimat-ing the difference between the measured GALEX FUVflux and the photospheric flux derived from a MARCSmodel with the same photospheric parameters as thestar (Gustafsson et al. 2008) rescaled to fit the observedoptical (Johnson and Tycho) and infrared (2MASS andWISE) photometry of HD 3167. The fit accounts for theinterstellar extinction reported in § − s − , indicative of a low level of stellar activ-ity (Shkolnik et al. 2014), in agreement with the log R (cid:48) HK value. This provides evidence that the Ca ii activity in-dex log R (cid:48) HK is very likely not biased by extrinsic ab-sorption.The light curve of HD 3167 displays a 0.08 % flux dropoccurring during the first half of the K2 observationsand lasting for about 35-40 days (Fig. 1). If the vari-ation were due to an active region moving in and outof sight as the star rotates around its axis, then therotation period of the star should be at least twice aslong, i.e., 70-80 days. Such a long rotation period seemsto be unlikely for a K-type dwarf and is inconsistentwith our v sin i (cid:63) measurement and stellar radius deter-mination (see below). Figure 2 shows the distributionof the rotation period of 3591 late G- and early K-typedwarfs as measured by McQuillan et al. (2014) using Kepler light curves. We selected only
Kepler stars withphotospheric parameters similar to those of HD 3167,i.e., objects with 5170 ≤ T eff ≤ g (cid:63) ≥ As comparison, the activity index of the Sun varies between − . − . Gandolfi et al.
Figure 2 . Rotation period distribution of
Kepler field starswith 5170 ≤ T eff ≤ g (cid:63) ≥ (cgs). None of the “HD 3167’s Kepler twins” has a ro-tation period longer than 70 days. Moreover, only 9objects have a rotational period exceeding 50 days. Asboth the K2 light curves of HD 3167 – as extracted byLuger et al. (2016) and Aigrain et al. (2016) – displaythe same feature, we conclude that the observed 0.08 %flux drop is very likely an instrumental artifact causedby the spacecraft pointing jitter.Figure 3 shows the Lomb-Scargle (LS) periodogram(Lomb 1976; Scargle 1982) of the K2 light curve ofHD 3167 following the subtraction of the best fittingtransit models of planet b and c ( § ∼
75 days due to the flux drop describedin the previous paragraph, there are 2 additional sig-nificant peaks at 14 and 23.5 days with a Scargle’s falsealarm probability (FAP) lower than 0.1 %. Since the pe-riod ratio is close to 0.5, we interpreted the former as thefirst harmonic of the latter. With an amplitude of about0.04 %, the 23.5-day signal is clearly visible in the firsthalf of the K2 time series data, whereas is barely visiblein the second half of the photometric data (Fig. 1). Asa sanity check, we split the light curve into two chunksof ∼
40 days and calculated the LS periodogram of eachchunk. The 23.5-day signal is detected also in the sec-ond half of the light curve but with a lower significance.This is likely due to the 80 % higher noise level of thesecond half of the K2 data with respect to the first half,as pointed out by Vanderburg et al. (2016).We interpreted the 23.5-day signal as the rotation pe-riod of the star and attributed the peak at 14 days to thepresence of active regions located at opposite stellar lon-gitudes. We measured a rotation period and uncertaintyof P rot = 23.52 ± R (cid:48) HK activity index (Su´arez Mascare˜no et Figure 3 . Lomb-Scargle periodogram of the K2 light curveof HD 3167. The horizontal dashed line marks the 0.1% FAPas defined in Scargle (1982). Table 2 . Stellar parameters.Parameter ValueEffective Temperature T eff (K) 5286 ± (a) log g (cid:63) (cgs) 4.53 ± (b) log g (cid:63) (cgs) 4.51 ± ± v sin i (cid:63) (km s − ) 1.8 ± A v (mag) 0.02 ± M (cid:63) ( M (cid:12) ) 0 . ± . R (cid:63) ( M (cid:12) ) 0 . ± . ± P rot (day) 23.52 ± (c) (pc) 45.8 ± a From spectroscopy. b From spectroscopy and isochrones. c Hipparcos ’ distance from van Leeuwen (2007). al. 2015). It is also worth noting that the distributionof the rotational periods of HD 3167’s
Kepler twins ispeaked between 20 and 25 days (Fig. 2).The spectroscopically derived projected rotational ve-locity of the star v sin i (cid:63) = 1.8 ± − , combinedwith the stellar radius R (cid:63) = 0 . ± . R (cid:12) , impliesan upper limit on the rotation period of 23.5 ± DATA ANALYSIS5.1.
Periodogram analysis of the radial velocities ass determinations of HD 3167 b and HD 3167 c <
10 m s − ) is expected given, e.g., thedifferent detector, optics, wavelength coverage of the twoinstruments. The generalized Lomb-Scargle (GLS; Zech-meister & K¨urster 2009) periodograms of the HARPSand HARPS-N RVs show a significant peak at the or-bital period of HD 3167 b, with a false alarm probability (FAP) of about 10 − and 10 − , respectively (top andmiddle panel of Figure 4). We conclude that the signalof the inner planet HD 3167 b is clearly present in bothdata sets. The GLS periodogram of the HARPS datadisplays a significant peak at ∼
32 days (FAP=10 − ),which is close to the orbital period of HD 3167 c (29.85days). However, the outer transiting planet remains un-detected in the HARPS-N data, owing to the unevensampling of the orbital phase of the outer transitingplanet with this instrument (Fig. 9).On three occasions we observed HD 3167 nearly si-multaneously (within 10 minutes) with HARPS andHARPS-N. We used these measurements to measure theoffsets of the RV, FWHM, BIS and log R (cid:48) HK between thetwo data sets and calculate the periodograms of the com-bined data. We found ∆ RV (HS − HN) = 8.0 ± − ,∆ FWHM (HS − HN) = 0.068 ± − , ∆ BIS (HS − HN) = 0.009 ± − , and ∆ log R (cid:48) HK (HS − HN) = − . ± . − ) and a moderately significant peak at theorbital period of HD 3167 c.It’s worth noting that the three periodograms showalso the presence of a significant peak at 23.8 days(0.042 c/d), which is close to the rotation period of thestar. We stress, however, that this peak corresponds to The FAPs reported in this subsection have been calculatedusing Eq. 24 of Zechmeister & K¨urster (2009) and should be re-garded as preliminary estimates. Deriving reliable FAPs througha bootstrap analysis – as presented in § Epochs 2457611, 2457646, and 2457692.
Figure 4 . GLS periodograms of the HARPS (top panel),HARPS-N (middle panel), and HARPS+HARPS-N (bottompanel) RV measurements. The vertical dashed lines mark theorbital periods of HD 3167 b (0.96 d) and HD 3167 c (29.85 d). the 1-day alias of the orbital period of HD 3167 b. Theperiodogram of the RV residuals – as obtained followingthe subtraction of the signals of the two planets – showno peaks at 0.042 c/d (Fig. 6).5.2.
Orbital solution of HD 3167 b
We performed a Keplerian fit of the FIES, HARPS,and HARPS-N RV data following the floating chunk off-set (FCO) method described in Hatzes et al. (2011). TheFCO method exploits the reasonable assumption that,
Gandolfi et al. for ultra-short period planets, RV measurements takenon a single night mainly reflect the orbital motion of theplanet rather than other, longer period phenomena suchas stellar rotation, magnetic activity, and additionalplanets. If we can sample a sufficient time segment ofthe Keplerian curve, then these nightly “chunks” canbe shifted until the best fit to the orbital motion isfound. This method was successfully used to determinethe mass of the ultra-short period planets CoRoT-7b(Hatzes et al. 2011) and Kepler-78b (Hatzes 2014).The ultra-short period planet HD 3167 b is well suitedfor application of the FCO method. This technique isparticularly effective at filtering out the RV jitter due toactivity. The star has an estimated rotation period ofabout 23.5 days ( § ∼ § pyaneti (Barrag´an et al.2016), a MCMC-based software suite that explores theparameter space using the ensemble sampler with theaffine invariance algorithm (Goodman & Weare 2010).Following Hatzes et al. (2011), we divided the RVs intothree subsets of nightly measurements – one per in-strument – and analyzed only those radial velocitiesfor which multiple measurements were acquired on thesame night, leading to a total of 12, 15, and 11 chunksof nightly FIES, HARPS, and HARPS-N RVs, respec-tively. The best fitting orbital solution of HD 3167 bwas found keeping period and transit ephemeris fixedto the values derived by our joint analysis described in § K b and the 38 nightly offsets to vary. We also fitted for √ e b sin ω (cid:63), b and √ e b cos ω (cid:63), b , where e b is the eccen-tricity and ω (cid:63), b is the argument of periastron of the star(Ford 2006). We adopted uniform uninformative pri-ors within a wide range for each parameter and ran 500independent Markov chains. The burn-in phase was per-formed with 25000 iterations using a thin factor of 50,leading to a posterior distribution of 250000 indepen-dent data points for each fitted parameter. The finalestimates and their 1- σ uncertainties were taken as themedian and the 68 % of the credible interval of the pos- Figure 5 . Upper panel : FIES (triangles), HARPS (circles),and HARPS-N (squares) RV measurements and circular or-bital solution of HD 3167 b (solid line) derived using the FCOmethod. Different colors represent measurements for differ-ent observing nights.
Lower panel : Residuals to the circularmodel. terior distributions.We obtained a best fitting non-zero eccentricity of e b = 0.112 ± √ e b sin ω (cid:63), b = √ e b cos ω (cid:63), b = 0). Fig-ure 5 displays our FIES, HARPS, and HARPS-N mea-surements along with the best fitting circular (thick line)and eccentric model (dashed line). Different symbolsrefers to different instrument, whereas different colorsrepresent different nights. We note that the best fittingeccentric solution might be driven by the uneven distri-bution of data points along the RV curve (Fig. 5). Inorder to asses the significance of our result we created10 sets of synthetic RVs that sample the best fittingcircular solution at the epochs of our real observations.We added Gaussian noise at the same level of our mea-surements and fitted the simulated data allowing foran eccentric solution. We found that there is a ∼ K b = 3.82 ± − which translates into a mass of M b = 5.40 ± M ⊕ forHD 3167 b. We note that the eccentric solution providesa planetary mass that is consistent within 1- σ with theresult from the circular model.5.3. Transit and RV joint analysis
We performed a joint modeling of the K2 and RVmeasurements with pyaneti . The photometric data in-cludes 6 and 15 hours of K2 data-points centered aroundeach transit of HD 3167 b and c. We detrended the seg- ass determinations of HD 3167 b and HD 3167 c exotrending . Briefly, we fit-ted a second order polynomial to the out-of-transit dataand removed outliers using a 3-sigma-clipping algorithmapplied to the residuals of the preliminary best fittingtransit models derived using the formalism of Mandel &Agol (2002) coupled to a non-linear least square fittingprocedure. As for the RV data sets, we used only theHARPS and HARPS-N measurements because of thelong-term instability of the FIES spectrograph ( § K2 long cadence data, we in-tegrated the transit models over 10 steps. We adoptedthe same Gaussian likelihood as defined in Barrag´an etal. (2016). For each planet i we fitted for the orbitalperiod P i , time of first transit T ,i , scaled semi-majoraxis a i /R (cid:63) , impact parameter b i , planet-to-star radiusratio R i /R (cid:63) , and RV semi-amplitude variation K i . Weassumed a circular orbit for the inner planet and fittedfor √ e c sin ω (cid:63),c and √ e c cos ω (cid:63),c for the outer planet.The 30-minute integration time of K2 smears out theshape of planetary transits increasing the degeneracybetween the scaled semi-major axis a/R (cid:63) and the impactparameter b (Csizmadia et al. 2011). We therefore setGaussian priors for the stellar mass and radius usingthe values derived in § a i /R (cid:63) of bothplanets from their orbital periods through Kepler’s thirdlaw.We explored the parameter space with 500 indepen-dent chains created from random priors for each param-eter, as listed in the second column of Table 3. Theconvergence of the MCMC chains was checked with theGelman-Rubin statistic. Once all chains converged, weran 25000 more iterations with a thin factor of 50. Thisled to a posterior distribution of 250000 independentpoints for each fitted parameter.The two-planet model provides a poor fit to theHARPS and HARPS-N measurements with a RV χ of597 and χ / dof = 8 .
7, suggesting that additional signalsmight be present in the data, as discussed in the nextsection.5.4.
Frequency analysis of the RV residuals
After fitting the two transiting planets, we in-spected the RV residuals to look for additional sig-nals in the Doppler data. The upper panel of Fig. 6shows the GLS periodogram of the RV residuals(thick black line). There are 3 significant peaks at f =0.094 c/d ( P =10.7 d), f =0.119 c/d ( P =8.4 d),and f =0.167 c/d ( P =6.0 d). We assessed their FAP Available at https://github.com/oscaribv/exotrending . Figure 6 . Top panel : GLS periodograms of the HARPSand HARPS-N RV residuals. The vertical dashed bluelines mark the frequencies f =0.094 c/d, f =0.119 c/d, and f =0.167 c/d whose FAP is less than 10 − , as derived using abootstrap randomization procedure. Middle-panel : DiscreteFourier transform of the HARPS and HARPS-N RV residu-als. The dotted red line marks the window function shiftedto the right by f =0.094 c/d and mirrored to the left of thisfrequency. Lower panel : Window function. The red arrowsmark the two peaks presented in the main text. following the Monte Carlo bootstrap method describedin K¨urster et al. (1997). We computed the GLS peri-odograms of 10 fake data sets obtained by randomlyshuffling the RV measurements, keeping the observationtime-stamps fixed. The FAP is defined as the fractionof those periodograms whose highest power exceeds thepower spectrum of the original observed data at any fre-quency. We found no false positives out of our 10 trials,implying that f , f , f have a FAP lower than 10 − .As a sanity check, we employed the program Period04 (Lenz & Breger 2004) to calculate the discrete Fouriertransform (DFT) of the RV residuals. We used thepre-whitening technique (see, e.g., Hatzes et al. 2010)to subsequently identify significant peaks in the powerspectrum and remove the corresponding signal from thedata. Briefly, we performed a least squares sine-fit tothe amplitude and phase at the first dominant frequencyfound by the DFT and subtracted the fit from the timeseries. We then reiterated the process to identify andsubtract the next dominant Fourier component. The it-eration was stopped once we reached the level of thenoise. We regarded as significant only those signalswhose amplitudes are more than 4 times the Fouriernoise level (Breger et al. 1993). The Fourier fit of theRV residuals was obtained with only two dominant fre-0
Gandolfi et al. quencies, namely, f =0.094 c/d and f =0.167 c/d, withan amplitude of 1.4 and 1.1 m s − , respectively.The periodogram of the sampling pattern - the so-called “window function” - shows two peaks at 0.025 c/d(40 d) and 0.039 c/d (25 d). They are highlighted by twored arrows in the lower panel of Fig. 6. We note that thebeat frequency between f =0.094 c/d and f =0.119 c/dis equal to 0.025 c/d, which corresponds to one of thetwo frequencies seen in the window function. This ledus to suspect that f and f are aliases of one anotherand share the same physical origin. We verified thishypothesis using again the pre-whitening technique. Weperformed a least-squares sine-fit to the amplitude andphase at either f or f , subtracted the best fit from theRV time series, and recalculated the GLS periodogramof the new residuals. Regardless of which of the twosignals is fitted and subtracted first, by removing oneof the two we also remove the other, as expected fromalias peaks, confirming our hypothesis. We note thatthe subtraction of the signal at either f or f does notremove f =0.167 c/d, which remains significant in theGLS periodogram of the new residuals.The middle panel of Fig. 6 shows the DFT of the RVresiduals (thick black line), along with the window func-tion shifted to the right by f =0.094 c/d and mirroredto the left of this frequency (red dotted line). It is evi-dent that f , along with most of the side lobes seen tothe right and left of f , is an alias of the latter relatedto the observing window. We conclude that f is verylikely the actual periodicity. We also note that f isnot an alias of f , as there is no peak detected in the“shifted” window function at this frequency, corroborat-ing our pre-whitening analysis.To further assess which of the two signals is the actualperiodicity, we performed a least-squares multi-sine fitto the amplitude and phase at the frequency couples f , f , and f , f . We then created synthetic RVs residualsusing the best fitting parameters, added white noise,sampled the simulated data at the epochs of our realobservations, and calculated the GLS periodograms. Wefound that “fake” data sets obtained from the couple f , f reproduce better the observed periodogram thanthe couple f , f . This further supports the fact thatthe RV residuals contain only two significant signals at f =0.094 c/d ( P =10.7 d) and f =0.167 c/d ( P =6.0 d).What are the sources of the two signals at 6.0 and 10.7days detected in the RV residuals? Are they due to ac-tivity, additional planets, or both? We note that the twoperiods are close to the first and third harmonic of therotational period of the star ( P rot = 23.52 ± ∼
90 and ∼
180 degrees in longitude could account for the two pe- riodicities. To further investigate this hypothesis, wecalculated the GLS periodograms of the activity indica-tors – namely, the full width at half-maximum (FWHM)and bisector span (BIS) of the cross-correlation profile,and the Ca ii H & K activity index (log R (cid:48) HK ) – but foundno significant peak. We stress, however, that this can-not be used to exclude that activity is the source of theobserved RV variation. Given the amplitude of the twosignals (1.2 and 1.4 m s − ) and low projected rotationalvelocity of the star (1.8 ± − ), the suppression ofgranular blueshift in magnetized regions of the photo-sphere of HD 3167 is expected to be the source of theobserved “jitter”. Based on observations of the Sun asa star, Haywood et al. (2016) recently found that thetraditional activity indicators perform poorly in tracingthe RV jitter of slowly rotating stars with low level ofmagnetic activity, such as in the case of HD 3167.We further investigated the nature of the addi-tional signals detected in the RV residuals using thestacked Bayesian generalized Lomb-Scargle (BGLS) pe-riodogram proposed by Mortier & Collier Cameron(2017). This tool exploits the BGLS algorithm describedin Mortier et al. (2015), which in turn is a Bayesian ver-sion of the GLS periodogram of Zechmeister & K¨urster(2009). As described in Mortier & Collier Cameron(2017), the stacked BGLS periodogram relies on the as-sumption that the power (or probability) of a coherentRV signal – such as that produced by a bona fide or-biting planet – is expected to increase by adding moredata points. On the contrary, the RV signal producedby stellar activity is usually incoherent, since its ampli-tude, phase, period vary with time, due to the evolutionof active regions, differential rotation, and magnetic cy-cle. Its significance can thus increases or decreases asmore RV measurements are added to the data set. Thetool calculates the BGLS periodogram for n out of NRVs (where n ≤ N ), adds the next point, recalculatesthe BGLS periodogram, and iterate the process till thelast available measurement.Figure 7 shows the BGLS periodogram (upper panel)and the stacked BGLS periodogram (lower panel) of theHARPS and HARPS-N RV residuals. As expected, thetwo dominant peaks at 6.0 and 10.7 days are clearlyvisible along with their aliases related to the observingwindow. We note that both signals do not seem to showa steadily increasing power (or probability) as we wouldexpect from signals arising from presence of planets. Isthis enough to claim that the two periodic signals aredue to activity? Following Johnson et al. (2016), wecreated a data set of synthetic RV residuals containingtwo sinusoidal signals at the same period, phase, andamplitude as the observed data. We added Gaussiannoise and sampled the simulated RVs at the time stampsof our observations. ass determinations of HD 3167 b and HD 3167 c
30 20 15 10 9 8 7 6 5 4
Period (d) l og P Frequency (c/d) N o b s e r v a t i o n log P Figure 7 . Stacked BGLS periodogram of the HARPS andHARPS-N RV residuals.
The BGLS periodogram and stacked BGLS peri-odogram of the synthetic data are shown in Fig. 8.As is evident from a visual inspection, Fig. 7 and 8share roughly the same peaks and a similar pattern.None of the two simulated coherent signals shows asteadily increasing power. Given the data, this simula-tion proves that our sampling of two truly coherent sig-nals at 6.0 and 10.7 days can mimic the trend expectedfrom activity-induced RV variation in the stacked BGLSperiodogram.We conclude that, although we found evidence thatthere are two additional signals with periods of 6.0 and10.7 days in the HARPS and HARPS-N measurements,the sampling of our observations, as well as the limitednumber of RVs and their noise level do not allow us toassess whether the two signals are due to activity, or arerather induced by two additional orbiting planets. Wethus include the two signals in our analysis but warn thereader that more observations are needed to unveil theirtrue nature. RESULTSWe used the code pyaneti to perform the final jointmodeling of the K2 and RV measurements. We fittedthe transit and RV curves of HD 3167 b and c followingthe guidelines presented in § §
30 20 15 10 9 8 7 6 5 4
Period (d) l og P Frequency (c/d) N o b s e r v a t i o n log P Figure 8 . Stacked BGLS periodogram of the simulated RVresiduals. sponding phases and amplitudes. To account for addi-tional instrumental noise not accounted by the nominalRV error bars and/or imperfect treatment of the vari-ous sources of RV variations (e.g., stellar activity and/oradditional planets), we added jitter terms to the equa-tion of the likelihood for the HARPS and HARPS-N RVdata following the method described in Dumusque et al.(2014).We report our results in Table 4. The parameter esti-mates and their error bars were taken to be the medianand the 68 % credible interval of the final posterior prob-ability distribution of each parameter. Fig. 9 shows the K2 transit light curves and best fitting transit models,as well as the HARPS and HARPS-N RVs and best fit-ting Keplerian models of HD 3167 b and c. The RV fitsto the two additional signals at 6.0 and 10.7 days areshown in Fig. 10.The mass of HD 3167 b is in very good agree-ment with the value we derived using the FCOmethod corroborating our analysis (cfr. § (HS − HN) = 8.3 ± − ) agrees with the valuepresented in § (HS − HN) = 8.0 ± − ). Fi-nally, our values of the planetary radii agree within lessthan 1- σ with those found by Vanderburg et al. (2016).Does the inclusion of the 6.0 and 10.7-day signals biasthe mass determinations of HD 3167 b and HD 3167 c ?A two-planet model fit that included only planetb and c gives RV semi-amplitude variations of K b = 3.74 ± − and K c = 2.29 ± − , re-spectively. By adding only the 10.7-day signal we get K b =4.06 ± − and K c =2.04 ± − . By2 Gandolfi et al.
HD3167bHD3167bHD3167c HD3167c
Figure 9 . Transit light curves and RV curves of HD 3167 b (upper panels) and HD 3167 c (lower panels). The best fittingtransit and Keplerian models are overplotted with thick black lines. The K2 data points are shown with red circles (left panels).The HARPS and HARPS-N RV measurements are plotted with red circles and blue diamonds, respectively, along with theirnominal uncertainties (right panels). adding both the 10.7-day and the 6.0-day signal weobtain K b = 4.02 ± − and K c = 1 . +0 . − . m s − ,proving that the RV semi-amplitude variations – andthus the determination of the planetary masses ofHD 3167 b and HD 3167 c – are not significantly affectedby the inclusion of the two additional signals. DISCUSSION AND SUMMARYThe ultra-short period planet HD 3167 b has amass of M b =5 . ± . M ⊕ and a radius of R b =1 . ± . R ⊕ , yielding a mean density of ρ b =8 . +1 . − . g cm − . Figure 11 displays the positionof HD 3167 b on the mass-radius diagram compared tothe sub-sample of small transiting planets ( R ≤ R ⊕ )whose masses and radii have been derived with a preci-sion better than 20 %. Theoretical models from Zeng etal. (2016) are overplotted using different lines and col-ors. The precision of our mass determination (14 %) al-lows us to conclude that HD 3167 b is a rocky terrestrialplanet with a composition consisting of ∼
50 % silicateand ∼
50% iron.HD 3167 b adds to the sample of low-mass, close-in planets with a RV-determined mass and a bulk densitysuggestive of a mostly rocky composition. Planets be-longing to this sample have a restricted Jeans escapeparameter Λ (cid:46)
20 (Table 3). This parameter, defined asΛ = GM pl m H k B T eq R p l , (1)has been introduced by Fossati et al. (2017) who foundthat the hydrogen-dominated atmospheres of exoplanetswith Λ (cid:46)
20 lie in the “boil-off” regime (Owen & Wu2016; Cubillos et al. 2017), where the escape is drivenby the atmospheric thermal energy and low planetarygravity. Fossati et al. (2017) also found that the at-mosphere of hot ( T eq (cid:38) M p (cid:46) M ⊕ )planets with Λ (cid:46)
20 shrinks to smaller radii so that theiratmosphere evolves out of the “boil-off” regime in lessthan about 500 Myr.Because of the very large escape rates after thedispersal of the proto-planetary disc, planets such asHD 3167 b have lost quickly (within a few hundreds Myr)their primary hydrogen-dominated atmosphere, as sup-ported, e.g., by the non-detection of a hydrogen ex-osphere around the ultra-short period planet 55 Cnc e ass determinations of HD 3167 b and HD 3167 c RV signal at 10.7 dRV signal at 6 d
Figure 10 . Radial velocity curves of the two signals at 10.7days (upper panel) and 6.0 days (lower panel) and best-fitting models. The HARPS and HARPS-N RV measure-ments are plotted with red circles and blue diamonds, re-spectively, along with their nominal uncertainties. (Ehrenreich et al. 2012). We remark that this fast es-cape is not driven by the high-energy stellar flux, butby the high temperature of the lower atmosphere andlow planetary gravity. This implies that these plan-ets subsequently developed a secondary, possibly CO -dominated, atmosphere while the host star was stillyoung and hence active. This led to the fast escape –this time instead driven by the high-energy stellar flux– also of the secondary atmosphere (Kulikov et al. 2006;Tian 2009), leaving behind the strongly irradiated rockysurface. It is therefore foreseeable that the high sur-face temperature led then to the formation of magmaoceans on the day side (Miguel et al. 2011; Demory etal. 2016), which out-gases and sputters minerals, form-ing a tenuous atmosphere not too dissimilar from thatof Mercury (e.g. Pfleger et al. 2015). Over time lighterelements escape from the atmosphere, leaving behind apossibly extended exosphere composed mostly by heavyrefractory elements that could be detected in transit atultraviolet and optical wavelengths. This picture wouldbe reinforced if the orbit of HD 3167 b had a non-zeroeccentricity, as this would lead to tidal heating and thus Table 3 . Low-mass ( M (cid:46) M ⊕ ) planets with RV-determined masses, Λ (cid:46)
20, and bulk densities suggestive ofa mostly rocky composition (mean density ρ p > − ).Except for HD 3167 b, all values are taken from Cubillos etal. (2017). Planet Λ ρ p g cm −
55 Cnc e 15.6 5.14CoRoT-7 b 15.6 7.97GJ 1132 b 18.4 5.79HD 219134 b 20.6 5.94Kepler-10 b 8.9 6.31Kepler-78 b 5.5 6.43Kepler-93 b 18.1 6.82Kepler-97 b 12.3 5.93HD 3167 b 15.6 8.00 to a more extended magma ocean. The detection of theexosphere would then enable for the first time the studyof the mineralogy of a rocky planet orbiting a star otherthan the Sun.With a mass of M c =8 . +1 . − . M ⊕ and a radius of R c =2 . +0 . − . R ⊕ the outer planet HD 3167 c has amean density of ρ b =2 . +0 . − . g cm − , which is consis-tent with a composition comprising a solid core sur-rounded by a thick atmosphere. HD 3167 c joins thesmall group of low-density mini-Neptunes with precisemass and radius determinations (Fig. 11).HD 3167 c is expected to have a completely differentnature with respect to the inner planet b. Despite thelack of mass measurements, Vanderburg et al. (2016)noticed that HD 3167 c may be a primary target fortransmission spectroscopy. The rather large pressurescale height of about 350 km and the brightness of thehost star (V=8.9 mag) make HD 3167 c an ideal targetfor transmission spectroscopy observations across a widerange of wavelengths, from the far-ultraviolet to the in-frared. One can expect the planet to have a rather largehydrogen-rich cloud made of gas escaping from the plan-etary upper atmosphere under the effect of the high-energy stellar radiation, similarly to GJ 436 b (Kulow etal. 2014; Ehrenreich et al. 2015). This cloud would bedetectable at Ly α during primary transit. Such obser-vations would then provide us with crucial informationabout the properties of the upper planetary atmosphereand its environment (e.g., stellar wind density and veloc-ity). Observations at longer wavelengths would insteadgive us the opportunity to study the lower atmosphereand infer its chemical composition and physical proper-ties. HD 3167 c appears to be one of the best candidatesto investigate the atmosphere of a low-mass planet.4 Gandolfi et al.
Mass ( M ⊕ ) R ad i u s ( R ⊕ ) HD3167bHD3167c H O MgSiO 50% H OMgSiO Fe 50% MgSiO Fe Figure 11 . Mass-radius diagram for well-characterized (5- σ precision level or better) super-Earths and Neptunes. From bottomto top, the solid curves are theoretical models (Zeng et al. 2016) for planets with a composition of 100% iron (brown), 50% silicateand 50% iron (dashed red), 100% silicate (beige), 50% silicate and 50% water (dashed blue), water (light blue). HD 3167 b &HD 3167 c are highlighted with different symbols and colors. We found evidence for two additional signals with pe-riods of 6.0 and 10.7 days in the HARPS and HARPS-Ndata. The respective RV semi-amplitude variations are1 . +0 . − . m s − and 1 . ± .
25 m s − . If the signalswere caused by two additional orbiting planets, theirminimum masses would be 4 . +0 . − . M ⊕ and 3 . ± . M ⊕ , respectively. According to the forecasting model ofChen & Kipping (2017), the two putative planets wouldhave radii of ∼ R ⊕ , implying that K2 wouldhave likely detected their transits if the two planets weretransiting HD 3167. We searched the light curve for ad-ditional transit signals using the DST code of Cabrera etal. (2012), but found none. The null detection of thetransits of the two putative additional planets requiresthat their orbits are inclined by at least 2-3 degrees rel-ative to the orbits of planet b and c. Although a dy-namical N-body simulation carried out with mercury6 (Chambers 1999) shows that such a compact planetarysystem would be stable for at least 10 years, we stressagain that our current data set does not allow us toassess whether the two signals are due planets and/or activity. Additional RV observations are needed to un-veil the real nature of the two signals.We are extremely grateful to the NOT, ESO, TNGstaff members for their unique and superb supportduring the observations. We thank Xavier Bonfils,Fran¸cois Bouchy, Martin K¨urster, Jorge Melendez, andNuno Santos who kindly agreed to exchange HARPStime with us. D. G. would like to acknowledge theinspiring discussions with Conny Konnopke, NuccioLanza, Paul Robertson, Rodrigo Diaz, Elisa DelgadoMena, and Aldo Bonomo. D. G. gratefully acknowl-edges the financial support of the Programma Gio-vani Ricercatori – Rita Levi Montalcini – Rientro deiCervelli (2012) awarded by the Italian Ministry ofEducation, Universities and Research (MIUR). M. F.and C. M. P. acknowledge generous support from theSwedish National Space Board. L. F. acknowledges theAustrian Forschungsf¨orderungsgesellschaft FFG project“TAPAS4CHEOPS” P853993. Sz. C. thanks the Hun-garian OTKA Grant K113117. H. J. D. and D. N. ac-knowledge support by grant ESP2015-65712-C5-4-R of ass determinations of HD 3167 b and HD 3167 c a ) with the Nordic Optical Telescope (NOT), op-erated on the island of La Palma jointly by Denmark,Finland, Iceland, Norway, and Sweden, in the SpanishObservatorio del Roque de los Muchachos (ORM) of the Instituto de Astrof´ısica de Canarias (IAC); b ) with theItalian Telescopio Nazionale Galileo (TNG) also oper-ated at the ORM (IAC) on the island of La Palma bythe INAF - Fundaci´on Galileo Galilei; c ) the 3.6m ESOtelescope at La Silla Observatory under programs ID097.C-0948 and 098.C-0860. This paper includes datacollected by the Kepler mission. Funding for the
Ke-pler mission is provided by the NASA Science Missiondirectorate.
Facilities:
Kepler (K2), NOT (FIES), ESO-3.6m(HARPS), TNG (HARPS-N)
Software:
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Parameter Prior a Value
Model Parameters for HD 3167 b
Orbital period P orb (day) U [0 . , . . ± . T (BJD TDB − U [7394 . , . . +0 . − . Scaled semi-major axis a/R (cid:63) N [4 . , .
18] 4 . +0 . − . Scaled planet radius R p /R (cid:63) U [0 , .
5] 0 . ± . b U [0 ,
1] 0 . +0 . − . Radial velocity semi-amplitude variation K (m s − ) U [0 , . ± . √ e sin ω F [0] 0 √ e cos ω F [0] 0 Derived Parameters for HD 3167 b
Planet mass M p ( M ⊕ ) · · · . ± . R p ( R ⊕ ) · · · . ± . ρ b (g cm − ) · · · . +1 . − . Eccentricity e · · · a (AU) · · · . ± . i p ( ◦ ) · · · . +1 . − . Transit duration τ (hours) · · · . ± . (b) T eq (K) · · · ± Model Parameters for HD 3167 c
Orbital period P orb (day) U [29 . , . . +0 . − . Transit epoch T (BJD TDB − U [7394 . , . . ± . a/R (cid:63) N [46 . , .
4] 46 . ± . R p /R (cid:63) U [0 , .
5] 0 . +0 . − . Impact parameter, b U [0 ,
1] 0 . +0 . − . Radial velocity semi-amplitude variation K (m s − ) U [0 , . +0 . − . √ e sin ω U [ − ,
1] 0 . +0 . − . √ e cos ω U [ − ,
1] 0 . +0 . − . Derived Parameters for HD 3167 c
Planet mass M p ( M ⊕ ) · · · . +1 . − . Planet radius R p ( R ⊕ ) · · · . +0 . − . Mean density ρ c (g cm − ) · · · . +0 . − . Eccentricity e · · · . +0 . − . Argument of periastron w (cid:63) · · · +134 − Semi-major axis of the planetary orbit a (AU) · · · . ± . i p ( ◦ ) · · · . ± . τ (hours) · · · . +0 . − . Equilibrium temperature (b) T eq (K) · · · ± Signal with period of 10.7 days
Period P orb (days) U [9 . , .
0] 10 . +0 . − . Radial velocity semi-amplitude variation K (m s − ) U [0 , . +0 . − . Signal with period of 6.0 days
Period P orb (days) U [5 . , .
5] 5 . +0 . − . Radial velocity semi-amplitude variation K (m s − ) U [0 , . ± . Other Parameters
Systemic velocity γ HARPS (km s − ) U [19 . , . . ± . γ HARPS − N (km s − ) U [19 . , . . ± . σ HARPS (m s − ) U [0 ,
10] 1 . +0 . − . RV jitter term σ HARPS − N (m s − ) U [0 ,
10] 0 . +0 . − . Parameterized limb-darkening coefficient q U [0 ,
1] 0 . +0 . − . Parameterized limb-darkening coefficient q U [0 ,
1] 0 . +0 . − . Linear limb-darkening coefficient u · · · . +0 . − . Quadratic limb-darkening coefficient u · · · . +0 . − . a U [ a, b ] refers to uniform priors between a and b , N [ a, b ] to Gaussian priors with mean a and standard deviation b , and F [ a ] to a fixed a value. b Assuming zero albedo. Gandolfi et al.
Table 5 . FIES, HARPS, HARPS-N radial velocity measurements and activity indicators of HD 3167.
BJD
TDB RV σ RV CCF BIS CCF FWHM log R (cid:48) HK σ log R (cid:48) HK S/N per pixel − − ) (km s − ) (km s − ) (km s − ) (dex) (dex) @ 5500 ˚A FIES
HARPS