Validation of M-dwarf Planets in K2 Campaign Fields 5 – 10

Exoplanets around Low-mass Stars Unveiled by K2

Teruyuki Hirano11affiliation: Department of Earth and Planetary Sciences, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan , Fei Dai22affiliation: Department of Physics, and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA 33affiliation: Department of Astrophysical Sciences, Princeton University, 4 Ivy Lane, Princeton, NJ 08544, USA , Davide Gandolfi44affiliation: Dipartimento di Fisica, Universitá di Torino, via P. Giuria 1, 10125 Torino, Italy , Akihiko Fukui55affiliation: Okayama Astrophysical Observatory, National Astronomical Observatory of Japan, Asakuchi, Okayama 719-0232, Japan , John H. Livingston66affiliation: Department of Astronomy, Graduate School of Science, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo, 113-0033, Japan , Kohei Miyakawa11affiliation: Department of Earth and Planetary Sciences, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan , Michael Endl77affiliation: Department of Astronomy and McDonald Observatory, University of Texas at Austin, 2515 Speedway, Stop C1400, Austin, TX 78712, USA , William D. Cochran77affiliation: Department of Astronomy and McDonald Observatory, University of Texas at Austin, 2515 Speedway, Stop C1400, Austin, TX 78712, USA , Francisco J. Alonso-Floriano88affiliation: Leiden Observatory, Leiden University, 2333CA Leiden, The Netherlands 99affiliation: Departamento de Astrofísica y Ciencias de la Atmósfera, Facultad de Ciencias Físicas, Universidad Complutense de Madrid, 28040 Madrid, Spain , Masayuki Kuzuhara1010affiliation: Astrobiology Center, NINS, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan 1111affiliation: National Astronomical Observatory of Japan, NINS, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan , David Montes99affiliation: Departamento de Astrofísica y Ciencias de la Atmósfera, Facultad de Ciencias Físicas, Universidad Complutense de Madrid, 28040 Madrid, Spain , Tsuguru Ryu1212affiliation: SOKENDAI (The Graduate University for Advanced Studies), 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan 1111affiliation: National Astronomical Observatory of Japan, NINS, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan , Simon Albrecht1313affiliation: Stellar Astrophysics Centre, Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, DK-8000 Aarhus C, Denmark , Oscar Barragan44affiliation: Dipartimento di Fisica, Universitá di Torino, via P. Giuria 1, 10125 Torino, Italy , Juan Cabrera1414affiliation: Institute of Planetary Research, German Aerospace Center, Rutherfordstrasse 2, 12489 Berlin, Germany , Szilard Csizmadia1414affiliation: Institute of Planetary Research, German Aerospace Center, Rutherfordstrasse 2, 12489 Berlin, Germany , Hans Deeg1515affiliation: Instituto de Astrofísica de Canarias, C/ Vía Láctea s/n, 38205 La Laguna, Spain 1616affiliation: Departamento de Astrofísica, Universidad de La Laguna, 38206 La Laguna, Spain , Philipp Eigmüller1414affiliation: Institute of Planetary Research, German Aerospace Center, Rutherfordstrasse 2, 12489 Berlin, Germany , Anders Erikson1414affiliation: Institute of Planetary Research, German Aerospace Center, Rutherfordstrasse 2, 12489 Berlin, Germany , Malcolm Fridlund88affiliation: Leiden Observatory, Leiden University, 2333CA Leiden, The Netherlands 1717affiliation: Department of Space, Earth and Environment, Chalmers University of Technology, Onsala Space Observatory, 439 92 Onsala, Sweden , Sascha Grziwa1818affiliation: Rheinisches Institut für Umweltforschung an der Universität zu Köln, Aachener Strasse 209, 50931 Köln, Germany , Eike W. Guenther1919affiliation: Thüringer Landessternwarte Tautenburg, Sternwarte 5, D-07778 Tautenberg, Germany , Artie P. Hatzes1919affiliation: Thüringer Landessternwarte Tautenburg, Sternwarte 5, D-07778 Tautenberg, Germany , Judith Korth1818affiliation: Rheinisches Institut für Umweltforschung an der Universität zu Köln, Aachener Strasse 209, 50931 Köln, Germany , Tomoyuki Kudo2020affiliation: Subaru Telescope, National Astronomical Observatory of Japan, 650 North Aohoku Place, Hilo, HI 96720, USA , Nobuhiko Kusakabe1010affiliation: Astrobiology Center, NINS, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan 1111affiliation: National Astronomical Observatory of Japan, NINS, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan , Norio Narita66affiliation: Department of Astronomy, Graduate School of Science, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo, 113-0033, Japan 1010affiliation: Astrobiology Center, NINS, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan 1111affiliation: National Astronomical Observatory of Japan, NINS, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan , David Nespral1515affiliation: Instituto de Astrofísica de Canarias, C/ Vía Láctea s/n, 38205 La Laguna, Spain 1616affiliation: Departamento de Astrofísica, Universidad de La Laguna, 38206 La Laguna, Spain , Grzegorz Nowak1515affiliation: Instituto de Astrofísica de Canarias, C/ Vía Láctea s/n, 38205 La Laguna, Spain 1616affiliation: Departamento de Astrofísica, Universidad de La Laguna, 38206 La Laguna, Spain , Martin Pätzold1818affiliation: Rheinisches Institut für Umweltforschung an der Universität zu Köln, Aachener Strasse 209, 50931 Köln, Germany , Enric Palle1515affiliation: Instituto de Astrofísica de Canarias, C/ Vía Láctea s/n, 38205 La Laguna, Spain 1616affiliation: Departamento de Astrofísica, Universidad de La Laguna, 38206 La Laguna, Spain , Carina M. Persson1717affiliation: Department of Space, Earth and Environment, Chalmers University of Technology, Onsala Space Observatory, 439 92 Onsala, Sweden , Jorge Prieto-Arranz1515affiliation: Instituto de Astrofísica de Canarias, C/ Vía Láctea s/n, 38205 La Laguna, Spain 1616affiliation: Departamento de Astrofísica, Universidad de La Laguna, 38206 La Laguna, Spain , Heike Rauer1414affiliation: Institute of Planetary Research, German Aerospace Center, Rutherfordstrasse 2, 12489 Berlin, Germany 2121affiliation: Center for Astronomy and Astrophysics, TU Berlin, Hardenbergstr. 36, 10623 Berlin, Germany , Ignasi Ribas2222affiliation: Institut de Ciències de l’Espai (CSIC-IEEC), Carrer de Can Magrans, Campus UAB, 08193 Bellaterra, Spain , Bun’ei Sato11affiliation: Department of Earth and Planetary Sciences, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan , Alexis M. S. Smith1414affiliation: Institute of Planetary Research, German Aerospace Center, Rutherfordstrasse 2, 12489 Berlin, Germany , Motohide Tamura66affiliation: Department of Astronomy, Graduate School of Science, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo, 113-0033, Japan 1010affiliation: Astrobiology Center, NINS, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan 1111affiliation: National Astronomical Observatory of Japan, NINS, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan , Yusuke Tanaka66affiliation: Department of Astronomy, Graduate School of Science, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo, 113-0033, Japan , Vincent Van Eylen88affiliation: Leiden Observatory, Leiden University, 2333CA Leiden, The Netherlands , Joshua N. Winn33affiliation: Department of Astrophysical Sciences, Princeton University, 4 Ivy Lane, Princeton, NJ 08544, USA hirano@geo.titech.ac.jp
Abstract

We present the detection and follow-up observations of planetary candidates around low-mass stars observed by the K2 mission. Based on light-curve analysis, adaptive-optics imaging, and optical spectroscopy at low and high resolution (including radial velocity measurements), we validate 16 planets around 12 low-mass stars observed during K2 campaigns 5–10. Among the 16 planets, 12 are newly validated, with orbital periods ranging from 0.96–33 days. For one of the planets (K2-151b) we present ground-based transit photometry, allowing us to refine the ephemerides. Combining our K2 M-dwarf planets together with the validated or confirmed planets found previously, we investigate the dependence of planet radius on stellar insolation and metallicity [Fe/H]. We confirm that for periods days, planets with a radius are less common than planets with a radius between 1–2 . We also see a hint of the “radius valley” between 1.5 and 2  that has been seen for close-in planets around FGK stars. These features in the radius/period distribution could be attributed to photoevaporation of planetary envelopes by high-energy photons from the host star, as they have for FGK stars. For the M dwarfs, though, the features are not as well defined, and we cannot rule out other explanations such as atmospheric loss from internal planetary heat sources, or truncation of the protoplanetary disk. There also appears to be a relation between planet size and metallicity: those few planets larger than about 3  are found around the most metal-rich M dwarfs.

methods: observational – techniques: high angular resolution – techniques: photometric – techniques: radial velocities – techniques: spectroscopic – planets and satellites: detection
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1 Introduction

M dwarfs have some advantages over solar-type (FGK) stars in the detection and characterization of transiting planets. Their smaller sizes lead to deeper transits for a given planet radius. In addition, their habitable zones occur at shorter orbital periods, facilitating the study of terrestrial planets in the habitable zone. These advantages are now widely appreciated. Many observational and theoretical studies have focused on M-dwarf planets, including their potential habitability and detectable biosignatures (e.g., Scalo et al., 2007; Shields et al., 2016). However, the number of currently known transiting planets around low-mass stars is much smaller than that for solar-type stars, because low-mass stars are optically faint. In particular, the number of mid-to-late M dwarfs ( K) hosting transiting planets is extremely limited (fewer than 20, as of September 2017). While the planets around early M dwarfs have been investigated in detail with the Kepler sample (Dressing & Charbonneau, 2013, 2015; Morton & Swift, 2014; Mulders et al., 2015a, b; Ballard & Johnson, 2016), the distribution and properties of mid-to-late M-dwarf planetary systems are still relatively unexplored.

Kepler’s second mission, K2 (Howell et al., 2014), has also contributed to the search for transiting planets around M dwarfs. Hundreds of stars have been identified as candidate planet-hosting stars (e.g., Montet et al., 2015; Vanderburg et al., 2016; Crossfield et al., 2016; Pope et al., 2016), many of which have been validated (e.g., Dressing et al., 2017b). Moreover, K2 has observed young stars in stellar clusters (e.g., the Hyades, Pleiades, and Beehive), including many low-mass stars. Several transiting planet candidates around these have already been reported (Mann et al., 2016a, b, 2017b, 2018; Ciardi et al., 2017). These planets are potentially promising targets for follow-up studies such as Doppler mass measurement and atmospheric characterization.

We have been participating in K2 planet detection and characterization in the framework of an international collaboration called KESPRINT111 In 2016, the two independent K2 follow-up teams KEST (Kepler Exoplanet Science Team) and ESPRINT (Equipo de Seguimiento de Planetas Rocosos Intepretando sus Transitos) merged and became the larger collaboration “KESPRINT”. . Making use of our own pipeline to reduce the K2 data and look for transit signals, we have detected 30-80 planet candidates in each of the K2 campaign fields. Through intensive follow-up observations using various facilities all over the world, we have validated or confirmed many transiting planets (e.g., Sanchis-Ojeda et al., 2015; Fridlund et al., 2017; Gandolfi et al., 2017; Guenther et al., 2017). In this paper, we focus on planetary systems around M dwarfs found by the KESPRINT project.

The rest of the paper is organized as follows. In Section 2, we describe the reduction of the K2 data and detection of the planet candidates by our pipeline. Next, we report our follow-up observations, including low- and high-resolution optical spectroscopy, high-contrast imaging, and ground-based follow-up transit observations (Section 3). Section 4 presents the analysis of the follow-up observations, through which we validate 15 planets around M dwarfs. Individual systems of special interest are described in Section 5. In Section 6 we examine the properties of all the transiting planets currently known around M dwarfs, with a focus on the planetary radius. Our conclusions are in Section 7.

2 K2 Photometry and Detection of Planet Candidates

2.1 K2 Light Curve Reduction

Due to the loss of two of its four reaction wheels, the Kepler spacecraft can no longer maintain the pointing stability required to observe its original field of view. The Kepler telescope was re-purposed for a new series of observations under the name K2 (Howell et al., 2014). By observing in the ecliptic, the torque by solar radiation pressure is minimized, significantly improving its pointing stability. The spacecraft must also switch to a different field of view about every three months to maintain pointing away from the Sun. In this operational mode, the photometry is strongly affected by the rolling motion of the spacecraft along its boresight and the variation of pixel sensitivity. To reduce this effect, we adopted an approach similar to that described by Vanderburg & Johnson (2014).

We now briefly describe our light-curve production pipeline. We downloaded the target pixel files from the Mikulski Archive for Space Telescopes.222https://archive.stsci.edu/k2. We then put down circular apertures surrounding the brightest pixel within the collection of pixels recorded for each target. We fitted a 2-D Gaussian function to the intensity distribution at each recorded time. The resultant and positions of the Gaussian function, as a function of time, allowed us to track the rolling motion of the spacecraft. To reduce the intensity fluctuations associated with this motion, we divided the apparent flux variation by the best-fitting piecewise linear relationship between apparent flux and the coordinates and . The systematic correction was described in more detail by Dai et al. (2017).

2.2 Transit Detection

To remove any long-term systematic or instrumental flux variations that may complicate the search of transit signals, we fitted the K2 light curve with a cubic spline with a timescale of 1.5 days. The observed light curve was then divided by the spline fit. The smoothing interval of 1.5 days was chosen to be much longer than the expected duration of planetary transits, which are measured in hours for for short-period planets around dwarf stars. We then searched for periodic transit signals with the Box-Least-Squares algorithm (Kovács et al., 2002). We employed a modification of the BLS algorithm, using a more efficient nonlinear frequency grid that takes into account the scaling of transit duration with orbital period (Ofir, 2014). To quantify the significance of a transit detection, we adopted the signal detection efficiency (SDE) (Ofir, 2014) which is defined by the amplitude of peak in the BLS spectrum normalized by the local standard deviation. A signal was considered significant if the SDE is greater than 6.5. To search for any additional planets in the system, we re-computed the BLS spectrum after removing the transit signal that was detected in the previous iteration, until the maximum SDE dropped below 6.5.

2.3 Initial Vetting

After the transit signals were identified, we performed a quick initial vetting process to exclude obvious false positives. We sought evidence for any alternation in the eclipse depths or a significant secondary eclipse, either of which would reveal the system to be an eclipsing binary (EB). Such effects should not be observed if the detected signal is from a planetary transit. We fitted a Mandel & Agol (2002) model to the odd- and even-numbered transits separately. If the transit depths differed by more than 3, the system was flagged as a likely false positive.

We also searched for any evidence of a secondary eclipse. First we fitted the observed transits with a Mandel & Agol (2002) model. The fit was used as a template for the secondary eclipse. We allowed the eclipse depth and time of opposition to float freely; all the other relevant parameters were held fixed based on the transit model. If a secondary eclipse was detected with more than 3 significance, we then calculated the geometric albedo implied by the depth of secondary eclipse. If the implied albedo was much larger than 1, we concluded the eclipsing object is likely to be too luminous to be a planet. Typically, in each of the K2 Campaigns 5, 6, 7, 8, and 10, approximately M-dwarf planetary candidates survived this initial vetting process.

3 Observations and Data Reductions

We here report the follow-up observations for the planet candidates around M dwarfs detected by our pipeline. The complete list of our candidates will be presented elsewhere (Livingston et al. and other papers in preparation). We attempted follow-up observations for as many M-dwarf planet hosts as possible. Our selection of targets included all planet candidates that had not already been validated (to our knowledge), with a preference for northern-hemisphere targets for which our follow-up resources are best suited. Specifically, we report on the candidates around K2-117, K2-146, K2-122, K2-123, K2-147, EPIC 220187552, EPIC 220194953, K2-148, K2-149, K2-150, K2-151, K2-152, K2-153, and K2-154, for which we conducted both high-resolution imaging and optical spectroscopy. This list of M dwarfs covers about half of all candidate planet-hosts in the K2 Campaign fields 5, 8, and 10. Campaign fields 6 and 7 are located in the southern hemisphere where our telescope resources are limited. The M-dwarf systems we did not follow up are generally fainter objects () for which follow-up observations are difficult and time-consuming.

3.1 Low Dispersion Optical Spectroscopy

We conducted low dispersion optical spectroscopy with the Calar Alto Faint Object Spectrograph (CAFOS) on the 2.2 m telescope at the Calar Alto observatory. We observed planet-host candidates in K2 campaign fields 5 and 8 (K2-117, K2-146, K2-123, EPIC 220187552, EPIC 220194953, K2-149, K2-150, K2-151) on UT 2016 October 28 and 29, and three stars in field 10 (K2-152, K2-153, K2-154) on UT 2017 February 21333As we describe in Section 4.2.1, K2-148 (EPIC 220194974) turns out to be the planet host, although at first we misidentified EPIC 220194953 to be the host of transiting planets and obtained the optical spectrum for EPIC 220194953 with CAFOS.. Following Alonso-Floriano et al. (2015), we employed the grism “G-100” setup, covering with a spectral resolution of . The exposure times ranged from 600 s to 2400 s depending on the magnitude of each star. For long exposures ( s), we split the exposures into several small ones so that we can minimize the impact of cosmic rays in the data reduction. For the absolute flux calibration, we observed Feige 34 as a flux standard on each observing night. We did not observe K2-147 because this target never rises above 25 elevation at Calar Alto.

Figure 1: Wavelengh-calibrated, normalized optical spectra observed by CAFOS. Later M dwarfs are plotted towards the bottom.

We reduced the data taken by CAFOS in a standard manner using IRAF packages; bias subtraction, flat-fielding, sky-subtraction, and extraction of one-dimensional (1D) spectra. Wavelength was calibrated using the revised line list of the comparison lamp (Hg-Cd-Ar) spectrum (Alonso-Floriano et al., 2015). Finally, we corrected the instrumental response and converted the flux counts into the absolute fluxes using the extracted 1D spectrum of Feige 34. The data for one of the targets, K2-123, were not useful because the signal-to-noise ratio (SNR) of the spectrum turned out to be too low. Figure 1 plots the reduced, normalized spectra observed by CAFOS.

3.2 High Dispersion Spectroscopy

In order to estimate stellar physical parameters and check binarity, we obtained high resolution optical spectra with various spectrographs. K2-117, K2-146, K2-123, K2-147, EPIC 220187552, EPIC 220194953, K2-148, K2-149, K2-150, K2-151, and K2-153 were observed by High Dispersion Spectrograph (HDS; Noguchi et al., 2002) on the Subaru 8.2 m telescope between 2015 fall and 2017 summer. For all HDS targets except K2-146, we adopted the standard “I2a” setup and Image Slicer #2 (Tajitsu et al., 2012), covering the spectral region of with a resolving power of . To avoid a telescope auto-guiding error, we adopted the normal slit with its width being () for K2-146, which is the faintest in the optical among our targets.

For K2-123, EPIC 220187552, K2-149, K2-150, and K2-151, we also conducted multi-epoch observations, spanning at least a few days, mainly to check the absence of large RV variations ( km s) caused by stellar companions (i.e., EB scenarios). Except K2-150, the multi-epoch spectra were taken with the iodine (I) cell; the stellar light, transmitted through the cell, is imprinted with the iodine absorption lines which are used for the simultaneous precise calibration of wavelength (e.g., Butler et al., 1996). By using the I cell, we can improve the RV precision by more than tenfold, and can not only rule out the EB scenario but also put a constraint on planetary masses, provided that the spectra are obtained at appropriate orbital phases. The only drawback is that we need to take one additional Ifree spectrum as a template in the RV analysis for each target.

Two-dimensional (2D) HDS data in echelle format were reduced in the standard manner, including flat-fielding, scattered-light subtraction, and extraction of 1D spectra for multiple orders. Wavelength was calibrated based on the Th-Ar emission lamp spectra obtained at the beginning and end of each observing night. Typical SNR’s of the resulting 1D spectra were per pixel around sodium D lines.

RV RV error RV Type Instrument
() (km s) (km s)
K2-122
7343.722376 0.0248 absolute FIES
7395.510251 0.0248 absolute FIES
7398.646686 0.0269 absolute FIES
7399.624305 0.0276 absolute FIES
7370.661943 0.0049 absolute HARPS-N
7370.683403 0.0058 absolute HARPS-N
7372.633972 0.0111 absolute HARPS-N
7372.653348 0.0237 absolute HARPS-N
7400.532625 0.0055 absolute HARPS-N
7400.553493 0.0047 absolute HARPS-N
K2-123
7674.087730 0.0150 relative HDS
7675.115382 0.0162 relative HDS
7676.095845 0.0171 relative HDS
K2-147
7893.706393 0.0127 absolute FIES
7931.617000 0.0122 absolute FIES
K2-149
7674.002138 0.0213 relative HDS
7675.030047 0.0200 relative HDS
7675.998989 0.0209 relative HDS
K2-150
7675.072056 0.171 absolute HDS
7921.089719 0.339 absolute HDS
K2-151
57674.03764 0.0115 relative HDS
7675.094883 0.0114 relative HDS
7676.077393 0.0129 relative HDS
K2-152
7834.755773 0.133 absolute Tull
7954.629452 0.614 absolute Tull
Table 1: Results of RV Measurements

For RV targets observed with the I cell (K2-123, EPIC 220187552, K2-149, and K2-151), we put the reduced 1D spectra into the RV analysis pipeline developed by Sato et al. (2002) and extracted relative RV values with respect to the I-out template spectrum for each target. Among the four targets, the RV fit did not converge for EPIC 220187552, which turns out to be a spectroscopic binary (see Sections 3.3 and 4.1). The results of RV measurements are summarized in Table 1. Figure 2 plots the relative RV variation as a function of orbital phase of each planet candidate; the absence of significant RV variations, along with the typical RV precision of m s for Iin spectra, completely rules out the presence of stellar companions in close-in orbits.

Figure 2: RV values folded by the orbital period of each transiting planet. Relative RV values are plotted for K2-122, K2-123, K2-149, and K2-151, while absolute RV values are shown for K2-147, K2-150 and K2-152. Note that for K2-122, the systemic velocity was subtracted from each dataset to take into account the small RV offset between the FIES and HARPS-N datasets.

We performed the RV follow-up observations of K2-122 and K2-147 using the FIbre-fed Échelle Spectrograph (FIES; Frandsen & Lindberg, 1999; Telting et al., 2014) mounted at the 2.56 m Nordic Optical Telescope (NOT) of Roque de los Muchachos Observatory (La Palma, Spain). We collected 4 high-resolution spectra () of K2-122 between November 2015 and January 2016, and 2 intermediate-resolution spectra () of K2-147 in May and June 2017, as part of the observing programs P52-201 (CAT), P52-108 (OPTICON), and P55-019. Three consecutive exposures of 900-1200 s were secured to remove cosmic ray hits, leading to an SNR of 25-30 per pixel at 5800 Å. We followed the observing strategy described in Buchhave et al. (2010) and Gandolfi et al. (2013), and traced the RV intra-exposure drift of the instrument by acquiring long-exposed (T = 35 s) Th-Ar spectra immediately before and after each observation. The data reduction was performed using standard IRAF and IDL routines, which include bias subtraction, flat fielding, order tracing and extraction, and wavelength calibration. The RVs were determined by multi-order cross-correlation against a spectrum of the M2-dwarf GJ 411 that was observed with the same instrumental set-ups as the two target stars, and for which we adopted an absolute RV of km s.

We also acquired 6 high-resolution spectra () of K2-122 using the HARPS-N spectrograph (Cosentino et al., 2012) mounted at the 3.58 m Telescopio Nazionale Galileo (TNG) of Roque de los Muchachos Observatory (La Palma, Spain). Two consecutive exposures of 1800 s were acquired at 3 different epochs between December 2016 and January 2017, as part of the CAT and OPTICON programs CAT15B_35 and OPT15B_64, using the second HARPS-N fiber to monitor the sky background. Unfortunately, the spectra taken on are affected by poor sky conditions. We reduced the data using the dedicated off-line pipeline. The SNR is between 5 and 20 per pixel at 5800 Å. RVs were extracted by cross-correlating the extracted echelle spectra with the M2 numerical mask (Table 1).

We observed K2-152 and K2-154 with the Harlan J. Smith 2.7 m telescope and its Tull Coudé high-resolution () optical spectrograph (Tull et al., 1995) at McDonald Observatory. We obtained one reconnaissance spectrum of K2-152 in March 2017 and a second one in July 2017. We also collected one spectrum of K2-154 in March 2017. Exposure times ranged from 29 to 50 minutes, due to the faintness of these stars in the optical. The spectra were all bias-subtracted, flat-field divided and extracted using standard IRAF routines. For the wavelength calibration, we use Th-Ar calibration exposures taken adjacent to the science observations. We analyzed the spectra using our Kea code (Endl & Cochran, 2016) to determine stellar parameters. Kea is not well suited to derive accurate parameters for cooler stars, but the results showed that both stars are cool ( K) main sequence stars. In Section 4.1.2, we will perform a more uniform analysis to estimate stellar parameters.

3.3 High Contrast Imaging

In transit surveys, typical false positives arise from background or hierarchical-triple EBs. High resolution imaging is especially useful to constrain background EB scenarios, and thus has intensively been used for planet validations (e.g., Dressing et al., 2017b). To search for nearby companions that could be could be the source of the observed transit-like signal, we conducted high resolution imaging using the adaptive-optics system (AO188; Hayano et al., 2010) with the High Contrast Instrument (HiCIAO; Suzuki et al., 2010) for K2-146 and K2-122 and the Infrared Camera and Spectrograph (IRCS; Kobayashi et al., 2000) for the other systems, both mounted on the Subaru telescope between 2015 winter and 2017 summer.

For the HiCIAO observation, we adopted the same observing scheme as described in Hirano et al. (2016b), except that we employed the angular differential imaging (ADI; Marois et al., 2006) for K2-146. With the three-point dithering and band filter, a total of 11 unsaturated frames after co-addition were obtained with AO for K2-146, resulting in the total exposure time of 1135 s. For K2-122, we obtained three saturated frames (after co-addition) with two-point dithering, corresponding to the total exposure time of 450 s. We also took two unsaturated frames for absolute flux calibration using a neutral-density filter.

HiCIAO data were reduced with the ACORNS pipeline developed by Brandt et al. (2013) for the removal of biases and correlated noises, hot pixel masking, flat-fielding, and distortion correction. We then aligned and median-combined the processed frames to obtain the highest contrast image. The resulting full width at half maximum (FWHM) of the combined images were . We visually inspected the combined images for K2-146 and K2-122, and found two neighboring faint companions to the northwest of K2-146. The brighter of the two is located away from K2-146 with mag, while the fainter is away from K2-146 with mag. Checking the SDSS catalog (Ahn et al., 2012), we identified a star around the coordinate where two faint stars were detected, and found its relative magnitude to be mag. These faint stars are inside the photometric aperture for the K2 light curve, but the optical and near infrared magnitudes imply that these cannot produce the deep transit signal detected for K2-146. We detected no nearby companion in the combined image of K2-122.

Regarding IRCS observations, we conducted AO imaging using each target itself as the natural guide for AO with the band filter. Adopting the fine sampling mode () and five-point dithering, we ran two kinds of sequences for each target. The first sequence consists of long exposures to obtain saturated frames of the targets, which are used to search for faint nearby companions. The total exposure time varied widely for each target, but typically s for a mag star. The saturation radii were less than for all frames. As the second sequence, we also took unsaturated frames with much shorter exposures, and used these frames for absolute flux calibrations.

Following Hirano et al. (2016a), we reduced the raw IRCS data: subtraction of the dark current, flat fielding, and distortion correction, before aligning and median-combining the frames for each target. The combined images were respectively generated for saturated and unsaturated frames. We visually checked the combined saturated image for each target, in which the field-of-view (FoV) is . Most importantly, we found that EPIC 220187552 consists of two stars of similar magnitude separated by from each other (Figure 3). In the same image, we also found a faint star at away from EPIC 220187552 with mag. EPIC 220194953 and K2-148 were both imaged in the same combined frame. K2-147’s combined image also exhibits a possible faint star ( mag) in the south, but with a low SNR, separated by . We found no bright nearby stars in the FoV for the other targets.

Figure 3: contrast curves in the band as a function of angular separation from the centroid for K2 planet-host candidates. The insets display the saturated combined images with FoV of . EPIC 220187552 is clearly a multiple-star system, and we conclude that the candidate is a false positive.

To estimate the detection limit of faint nearby sources in the combined images, we drew contrast curve for each object. To do so, we first convolved the saturated images with each convolution radius being half of FWHM. We then calculated the scatter of the flux counts in the narrow anulus as a function of angular separation from the target’s centroid. Finally, we obtained the target’s absolute flux by aperture photometry using the unsaturated frames for each target with aperture diameter being FWHM, and normalized the flux scatter in the anulus by dividing by the photometric value after adjusting the exposure times for saturated and unsaturated combined images. Figure 3 displays the contrast curves for all objects, along with the combined images of the targets in the insets. Note that as we show in Section 4.2.1, EPIC 220194953 and K2-148 are imaged in the same frame, but since K2-148 is likely the host of transiting planets, we show the contract curve around it.

3.4 Follow-up Transit Observations

3.4.1 OAO 188cm/MuSCAT

On 2016 September 20, we conducted a photometric follow-up observation of a transit of K2-151b with the Multi-color Simultaneous Camera for studying Atmospheres of Transiting exoplanets (MuSCAT; Narita et al., 2015) on the 1.88 m telescope at Okayama Astronomical Observatory (OAO). MuSCAT is equipped with three 1k1k CCDs with a pixel scale of 036 pixel, enabling us to obtain three-band images simultaneously through the SDSS 2nd-generation , , and -band filters. We set the exposure times to 60, 10, and 25 s for the , , and bands, respectively. We observed the target star along with several bright comparison stars for 3.8 h, which covered well the expected 1.5-h duration transit. The sky was photometric except for 0.9 h near the end of the observation, when clouds passed; we omit the data during this period from the subsequent data reduction process. As a result, 166, 749, and 354 images were obtained in the , , and bands, respectively, through clear skies.

The observed images were dark-subtracted, flat-fielded, and corrected for non-linearlity of each detector. Aperture photometry was performed with a customized pipeline (Fukui et al., 2011) for the target star and three similar-brightness stars for comparison, one of which, however, was saturated on the -band images and omitted from the rest of the analysis for this band. The aperture radius for each band was optimized so that the apparent dispersion of a relative light curve (a light curve of the target star divided by that of the comparison stars) was minimized. As a result, the radii of 11, 13, and 12 pixels were adopted for the , , and bands, respectively.

3.4.2 IRSF 1.4 m/SIRIUS

On 2016 October 5 UT, we also conducted a follow-up transit observation with the Simultaneous Infrared Imager for Unbiased Survey (SIRIUS; Nagayama et al., 2003) on the IRSF 1.4 m telescope at South African Astronomical Observatory. SIRIUS is equipped with three 1k1k HgCdTe detectors with the pixel scale of 045 pixel, enabling us to take three near-infrared images in , , and bands simultaneously. Setting the exposure times to 30 s with the dead time of about 8 s for all bands, we continued the observations for 2.4 h covering the expected transit time. As a result, 232 frames were obtained in each band.

The observed frames were analyzed in the same manner as the MuSCAT data. For the flat-fielding, we used 14, 14, and 36 twilight sky frames taken on the observing night for the -, -, and -band data, respectively. We applied aperture photometry for the target and two comparison stars for all bands. However, we found that the brighter comparison star was saturated in the band data and was thus useless. With only the fainter comparison star, we could not achieve a sufficiently high photometric precision to extract the transit signal, and therefore we decided to ignore the -band data from the subsequent analyses. We selected 9 pixels as the optimal aperture radii for both and band data.

4 Data Analyses and Validation of Planet Candidates

4.1 Estimation of Spectroscopic Parameters

4.1.1 Spectral Types

Based on the low resolution spectra obtained by CAFOS, we measured the spectral types (SpT) for the target stars. Following Alonso-Floriano et al. (2015), we measured a suite of (31) spectral indices for each CAFOS spectrum. Alonso-Floriano et al. (2015) found that five indices (TiO 2, TiO 5, PC1, VO-7912, and Color-M) amongst all have the best correlations with SpT and thus we converted each of the measured five indices listed in Table 2 into SpT through the polynomials given by Alonso-Floriano et al. (2015), with revised coefficients (Alonso-Floriano, 2015). We then took the weighted mean of the calculated SpT values to obtain the final value for each target and round those mean spectral types to the nearest standard subtypes (e.g., M0.0, M0.5, M1.0, ), which are listed in Table 3. The scatter of the calculated SpT values from the five indices for each object is generally less than 0.5 subtype, which is comparable to the fiducial measurement error in SpT by the present method. The converted SpT values for K2-117 have a relatively large scatter (standard deviation subtype), which might be due to passage of clouds or other bad weather conditions.

Star TiO 2 TiO 5 PC1 VO-7912 Color-M
K2-117 0.826 0.662 1.037 0.998 0.752
K2-146 0.641 0.423 1.157 1.072 1.045
K2-123 1.061 0.998 0.935 0.980 0.556
EPIC 220187552 0.866 0.730 0.984 0.999 0.733
EPIC 220194953 0.877 0.742 0.978 0.994 0.713
K2-149 0.807 0.635 1.012 1.004 0.778
K2-150 0.697 0.481 1.137 1.049 1.057
K2-151 0.789 0.622 1.023 1.010 0.816
K2-152 0.919 0.775 0.949 0.998 0.748
K2-153 0.662 0.472 1.163 1.073 1.269
K2-154 0.888 0.748 0.955 0.995 0.753
Table 2: Spectral Indices by CAFOS Spectroscopy.

We also checked if the target stars are dwarf stars and not M giants, by inspecting the index “Ratio C” (Kirkpatrick et al., 1991), which is a good indicator of surface gravity. As described in Alonso-Floriano et al. (2015), stars with a low surface gravity should have a value of Ratio C lower than , but all the targets listed in Table 3 show higher Ratio C values, by which we safely conclude that those stars observed by CAFOS are all M dwarfs.

4.1.2 Atmospheric and Physical Parameters

In order to estimate the precise atmospheric and physical parameters of the target stars, we analyzed high resolution optical spectra obtained in Section 3.2. We made use of SpecMatch-Emp developed by Yee et al. (2017). SpecMatch-Emp uses a library of optical high resolution spectra for hundreds of well-characterized FGKM stars collected by the California Planet Search; it matches an observed spectrum of unknown propety to library stars, by which the best-matched spectra and their stellar parameters (the effective temperature , stellar radius , and metallicity [Fe/H]) are found for the input spectrum while the RV shift and rotation plus instrumental line-broadening are simultaneously optimized. SpecMatch-Emp is particularly useful for late-type stars, for which spectral fitting using theoretical models often has large systematics due to imperfection of the molecular line list in the visible region.

Since SpecMatch-Emp is developed for optical spectra obtained by Keck/HIRES, we converted our spectra taken by Subaru/HDS, etc, into the same format as HIRES. To check the validity of applying SpecMatch-Emp to those spectra taken by other instruments, for which spectral resolutions and pixel-samplings are slightly different from those of HIRES, we put several spectra collected by Subaru/HDS in the past campaigns (e.g., Hirano et al., 2014) into SpecMatch-Emp and compared the outputs with literature values. Consequently, we found that the output , , and [Fe/H] are all consistent with the literature values within (typically within ), and we justified the validity of applying SpecMatch-Emp to our new spectra.

Inputting our high resolution spectra to SpecMatch-Emp, we obtained the stellar spectroscopic parameters. We discarded EPIC 220187552 from this analysis, since EPIC 220187552 was found to be a double (in fact triple) star revealed by the AO imaging (Section 3.3). The output parameters (, , and [Fe/H]) are listed in Table 3. To estimate the other stellar parameters (i.e., stellar mass , surface gravity , and luminosity ), we adopted the empirical formulas derived by Mann et al. (2015), who gave empirical relations of stellar mass and radius as a function of the absolute band magnitude and [Fe/H]. Assuming that SpecMatch-Emp’s output parameters follow independent Gaussians with their being the errors returned by SpecMatch-Emp, we performed Monte Carlo simulations and converted , , and [Fe/H] into , , and through the absolute band magnitude. Those estimates are also summarized in Table 3. In the same table, we also list the distance calculated from the apparent and absolute band magnitudes.

EPIC ID K2 ID SpT (K) [Fe/H] (dex) () () (dex) () (pc)
211331236 K2-117 MV
211924657 K2-146 MV
212006344 K2-122
212069861 K2-123
213715787 K2-147
220187552 MV
220194953 MV
220194974 K2-148
220522664 K2-149 MV
220598331 K2-150 MV
220621087 K2-151 MV
201128338 K2-152 MV
201598502 K2-153 MV
228934525 K2-154 MV
Table 3: Stellar Parameters by Optical Low and High Resolution Spectroscopy.

4.1.3 Cross-correlation Analysis

In addition to estimating stellar parameters from the high resolution spectra, we also analyzed the line profile for each target. In the case that a transit-like signal is caused by an eclipsing spectroscopic binary of similar size, we expect to see a secondary line or distortion of the profile in the spectra, depending on the orbital phase of the binary. Using the cross-correlation technique, we computed the averaged spectral line profiles so that we can check for the presence of line blending. In doing so, we cross-correlated each observed spectrum (without the I cell) with the numerical binary mask (M2 mask; see e.g., Bonfils et al., 2013) developed for the RV analysis of HARPS-like spectrographs. From each observed spectrum, we extracted the spectral segments whose wavelengths are covered by the binary mask, and cross-correlated each segment with the mask as a function of Doppler shift (RV). We then took a weighted average of the cross-correlation profiles to get the normalized line profile for each object.

Figure 4: Averaged and normalized cross-correlations between the observed spectra and M2 binary mask. Cross-correlations based on the HDS, HARPS-N, Tull spectra are shown in blue, green, and red, respectively. The Earth’s motion is corrected and RV value is given with respect to the barycenter of the solar system.

Figure 4 displays the line profiles for the observed stars. For the targets with multi-epoch observations, we show the cross-correlation profiles with the highest SNR. Except EPIC 220187552, all stars exhibit single-line profiles, though the cross-correlation continuum looks noisier for particularly cool stars (K2-146 and K2-150), which is most likely due to the more complicated molecular absorption features. EPIC 220187552 clearly shows the secondary line in the cross-correlation profile, as we expected from Figure 3; due to the small angular separation (), the fluxes from the two stars both entered the spectrograph during our HDS observation. The difference in positions of the two lines implies that the two stars have a relative Doppler-shift to each other, suggesting that either of the two has a stellar companion which is most likely responsible for the transit-like signal detected in the K2 light curve. Therefore, we concluded that EPIC 220187552 is a hierarchical triple system, in which two stars among the three are an EB. We will revisit this system in Section 5.

From the cross-correlation profile, we also measured the absolute RV for each target. Since Subaru/HDS (without the I cell) and McDonald 2.7m/Tull are neither stabilized spectrographs nor do they obtain simultaneous reference spectra like HARPS/HARPS-N, it is difficult to trace the small wavelength drift during a night, which prohibits accurate RV measurements. In order to correct for the wavelength drift of each spectrum, we extracted the spectral segment including strong telluric absorption lines (primarily ), and cross-correlated it against a theoretical telluric transmission spectrum at the summit of Mauna Kea, generated by using line-by-line radiative transfer model (LBLRTM; Clough et al., 2005). Stellar RVs and wavelength drifts are measured by inspecting the peaks (bottoms) of the cross-correlation profiles for stellar and telluric segments, respectively. The final RV values (Table 1) are recorded by subtracting the two RV values. Note that the resulting wavelength drift is typically less than km s (less than half a pixel for HDS). Regarding K2-150 and K2-152, we obtained multiple spectra for absolute RV measurements, which are plotted in Figure 2 as a function of the candidates’ phase; no significant RV variation is seen for both objects.

4.2 Light Curve Analysis

4.2.1 Fitting K2 Light Curves

In order to estimate the most precise parameters of each planet candidate, we compared the light curves for the same objects produced by three different pipelines: our own light curves (Section 2.1), ones by Vanderburg & Johnson (2014), and ones by EVEREST (Luger et al., 2016, 2017). As a result, we found that for our sample, the EVEREST light curves generally provided the best precision in terms of the scatter of the baseline flux. We thus used EVEREST light curves to estimate the final transit parameters. For the three targets in K2 field 10, since EVEREST light curves have not been published yet, we employed the light curves by Vanderburg & Johnson (2014).

We reduced the light curves in the following steps. First, using the reduced light curve products, we split each target’s light curve into segments, each spanning days, and detrended each segment by fitting with a fifth-order polynomial to get a normalized light curve. Then, based on the preliminary ephemerides obtained in Section 2, we further extracted small segments around transit signals, in which the baseline spans times the duration of the transit towards both sides from the transit center for each planet candidate. These light curve segments around transits were simultaneously fitted for each planet candidate.

We fitted all the light curve segments simultaneously to obtain the global transit parameters as well as check possible transit timing variations (TTVs). The global transit parameters are the scaled semi-major axis , transit impact parameter , limb-darkening coefficients and for the quadratic law, and planet-to-star radius ratio . We fixed the orbital eccentricity at . In addition to these, we introduced the parameters describing the flux baseline, for which we adopted a linear function of time, and time of the transit center for each transit (segment). To take into account the long cadence of K2 observation, we integrated the transit model by Ohta et al. (2009) over minutes to compare the model with observations.

Figure 5: EVEREST light curves (left panels and top right panel) produced by different apertures (central panel) for EPIC 220194953 and K2-148 (EPIC 220194974). The light curves are folded by the period of K2-148c ( days). The right bottom panel shows a high-resolution image with FoV of taken by Subaru/IRCS; the upper right and lower left stars correspond to EPIC 220194953 and K2-148, respectively.

Following Hirano et al. (2015), we first minimized the statistic by Powell’s conjugate direction method (e.g., Press et al., 1992) to obtain the best-fit values for all the parameters, and fixed the baseline parameters for each segment at these values. We then implemented Markov Chain Monte Carlo (MCMC) simulations to estimate the posterior distribution of the remaining fitting parameters. We imposed Gaussian priors on and based on the theoretical values by Claret et al. (2013); the central values for and were derived by interpolation for each target using the stellar parameters listed in Table 3, and we adopted the dispersion of Gaussians as 0.1. At first we assigned an uncertainty to each K2 data point equal to the observed scatter in neighboring flux values, which sometimes led to a very small or large reduced , presumably due to non-stationary noise. To obtain reasonable uncertainties in the fitted parameter values, we rescaled the flux uncertainties such that the reduced was equal to unity, before performing the MCMC analysis. We adopted the median, and 15.87 and 84.13 percentiles of the marginalized posterior distribution as the central value and its for each fitting parameter.

EPIC 220194953 and K2-148 are separated by , and the photometric apertures used to produce EVEREST light curves for those objects involve at least a part of both stars. In order to identify which of the two stars is the source of transit signals, we analyzed three different light curves provided by EVEREST: the EVEREST version 2.0 light curves for K2-148 (EPIC 220194974) (A) and EPIC 220194953 (B), and EVEREST version 1.0 light curve for EPIC 220194953 (C). The apertures used to produce the three light curves are shown in the central panel of Figure 5. As a result of analyzing and fitting each light curve folded by the period of K2-148c, we found that light curves based on apertures A and B exhibit similar depths in the folded transits, but the one with aperture C shows a much shallower transit (almost invisible; Figure 5). Since a significant fraction of light from K2-148 is missing for aperture C, K2-148 is likely the host of the transiting planet candidates444We also analyzed our own light curves using customized apertures with smaller numbers of pixels, but the transit signals became invisible owing to the larger scatter in flux.. We thus performed the further analysis below based on this assumption. Note that we found a similar trend when the light curve was folded by the period of K2-148b, but with a lower SNR.

To estimate the planetary parameters for K2-148b to K2-148d, we need to know the contamination (dilution) factor from EPIC 220194953 for the photometric aperture we adopt. In doing so, we estimated the flux ratio between EPIC 220194953 and K2-148 in the Kepler () band by the following procedure 555The magnitudes are reported to be 12.856 and 12.975 for EPIC 220194953 and K2-148, respectively. However, the K2 pixel image (band) and our AO image by IRCS (Figure 5; band) both imply that K2-148 is brighter than EPIC 220194953, suggesting EPIC 220194953 is a later-type star the K2-148 and the reported magnitudes are inaccurate.. Adopting the PHOENIX atmosphere model (BT-SETTL; Allard et al., 2013), we first computed the absolute fluxes by integrating the grid PHOENIX spectra for K over the band. We then performed a Monte Carlo simulation, in which and were randomly perturbed for both of EPIC 220194953 and K2-148 assuming Gaussian distributions based on the values in Table 3, and absolute fluxes were interpolated and converted into the photon count ratio between the two stars. Consequently, we found the relative flux contribution from EPIC 220194953 is while that of K2-148 is in the band.

The actual flux contribution from each star depends on which aperture we use. We used aperture A for the light curve fitting (Figure 5). In order to estimate the relative contributions from EPIC 220194953 and K2-148 for this aperture, we summed the total flux counts in the postage stamp (), the counts in the pixels in the upper half of the postage stamp which are “not” in the aperture (), and the counts in the pixels in the lower half of the postage stamp which are not in the aperture (). The resulting ratios and can approximately be considered as the relative flux ratios from EPIC 220194953 and K2-148 that are not inside the photometric aperture. Therefore, by subtracting these ratios from the intrinsic flux ratios above (0.367 and 0.633) and renormalizing them, we finally obtained the relative flux contributions for aperture A as and for EPIC 220194953 and K2-148, respectively. In fitting the transit light curve, we took this dilution factor into account for K2-148.

Figure 6: K2 light curves around transits for individual candidates folded by their periods. Possible TTVs are corrected and all the transits are aligned in these light curves. For K2-148, the flux contamination from EPIC 220194953 is taken into account and the dilution factor is corrected. The best-fit transit curves are shown by the red solid lines.
Planet FPP (days) () () (AU) () K2-117b K2-117c K2-146b K2-122b K2-123b K2-147b K2-148b K2-148c K2-148d K2-149b K2-150b K2-151b K2-152b K2-153b K2-154b K2-154c
Table 4: Planetary Parameters
Figure 7: First double transit event observed for K2-117. The best-fit model is shown by the red solid line.
Figure 8: Seond double transit event observed for K2-117. The best-fit model is shown by the red solid line.
Figure 9: diagrams for mid-transit times for K2 campaign field 5 planets.
Figure 10: diagram for mid-transit times for K2-147b.
Figure 11: diagrams for mid-transit times for K2 campaign field 8 planets.
Figure 12: diagrams for mid-transit times for K2 campaign field 10 planets.

After fitting the light curve segments for each planet candidate, we obtained the transit parameters summarized in Table 4. Figure 6 plots the folded K2 data around the transits (black points) along with the best-fit light curve models (red solid lines) for individual planet candidates. For K2-117, double transit events, in which two planets transit the host star simultaneously, were predicted and identified in two light curve segments, and we fitted these segments separately with only and baseline coefficients floating freely (Figures 7 and 8). Using the optimized datasets, we fitted the observed ’s for each candidate with a linear ephemeris and estimated the orbital period and transit-center zero point , which are also listed in Table 4. We note that in Figure 6, the data for some of the planet candidates exhibits a larger scatter in the residuals during the transits, compared to the data outside of transits. This increased scatter during transits could be ascribed to spot-crossings for relatively active stars (e.g., Sanchis-Ojeda & Winn, 2011), but the large outliers are probably the instrumental artifacts and were clipped in the light curve analysis. In order to check the absence/presence of TTVs, we plot the observed minus calculated () diagrams of for each candidate in Figures 912. Visual inspection suggests that K2-146 exhibits a strong TTV while the other candidates show no clear sign of TTVs. Based on the stellar and transit parameters, we also estimate the planet radius , semi-major axis , and insolation flux from the host star , as also shown in Table 4.

4.2.2 Fitting Ground-based Transits

Because the transit signals of K2-151b are difficult to detect in the ground-based light curves, not all the transit parameters can be constrained from these light curves alone. We therefore fitted these light curves by fixing and at the values determined from the K2 light curves. We also fixed the limb-darkening parameters at the theoretical values of () = (), (), (), (), and () for the , , , , and bands, respectively. For each transit, we fitted the multi-band data simultaneously by allowing for each band and a common to be free. In addition, we simultaneously modeled the baseline systematics adopting a parameterization introduced by Fukui et al. (2016), which takes account of the second-order extinction effect. The applied function is

(1)

where and are the apparent magnitudes of the target star and comparison stars, respectively, is a transit model in magnitude scale, is time, is auxiliary observables such as stellar displacements on the detectors, sky backgrounds, and FWHM of the stellar PSFs, and , , , and a re coefficients to be fitted. For the auxiliary observables, we included only the ones that show apparent correlations with the light curves; the stellar displacements in X direction and sky backgrounds (in magnitude scale) were included for the -band light curve and none was included for the other light curves.

Figure 13: Ground-based transit observation for K2-151 by OAO/MuSCAT (grey dots). The binned flux data for , , and bands are shown by the blue circles, green triangle, and red squares, respectively. The black solid lines indicate the best-fit transit models for individual bands.
Figure 14: Ground-based transit observation for K2-151 by IRSF/SIRIUS (grey dots). The binned flux data for , and bands are shown by the dark-red circles, brown triangles, respectively. The black solid lines indicate the best-fit transit models for individual bands.
bandpass ()
(MuSCAT observation)
(SIRIUS observation)
Table 5: Results of Follow-up Transit Observations for K2-151

To obtain the best estimates and uncertainties of the free parameters, we performed an MCMC analysis using a custom code (Narita et al., 2013). We first optimized the free parameters using the AMOEBA algorithm (Press et al., 1992), and rescaled the error bar of each data point so that the reduced becomes unity. To take into account approximate time-correlated noises, we further inflated each error bar by a factor , which is the ratio of the standard deviation of a binned residual light curve to the one expected from the unbinned residual light curve assuming white noises alone (Pont et al., 2006; Winn et al., 2008). We then implemented 10 and 50 independent MCMC runs with 10 steps each for the MuSCAT and SIRIUS data, respectively, and calculated the median and 16 (84) percentile values from the merged posterior distributions of the individual parameters. The resultant values are listed in Table 5 and the systematics-corrected light curves along with the best-fit transit models are shown in Figures 13 and 14.

We note that the detections of these transit signals are marginal. The improvement by the best-fit transit model over a null-transit one ( are forced to be zero) for the MuSCAT data is 58.7, to which 6.4, 37.8, and 14.5 are contributed from the -, -, and -band data, respectively, corresponding to the 6.5 significance given the number of additional free parameters of four. In the same way, the improvement for the SIRIUS data is 24.2, to which 15.6 and 6.6 are contributed from the - and -band data, respectively, corresponding to the 4.2 significance given the number of additional free parameters of three. Nevertheless, as discussed below, all the values are largely consistent with each other and all the values are well aligned, both supporting that these transit detections are positive.

Figure 15: Observed values of for K2-151b in different bandpasses. The blue horizontal line and its upper and lower shaded areas indicate and its errors in the band.

Based on the results of the ground-based transit observations, we compare the transit depths in different bandpasses. In Figure 15, the value for each band is plotted as a function of wavelength. The blue horizontal line indicates in the band, for which the errors are shown by the blue shaded area. The transit depths in the , , , and bands are consistent with the K2 result within , while the band result exhibits a moderate disagreement. But as is seen in Figure 13, the band light curve seems to suffer from a systematic flux variation, which has not been corrected by our light-curve modeling. A more sophisticated light-curve analysis using e.g., Gaussian processes (see e.g., Evans et al., 2015) may be able to settle this issue.

Figure 16: diagram for mid-transit times for K2-151b. Ground-based transit observations are shown by the green square (MuSCAT) and red triangle (SIRIUS).

In the absence of the follow-up transit observations, we obtained the orbital period as days from the K2 data alone. Our ground-based transit observations were conducted days after the K2 observation for campaign 8 was over, as shown in Figure 16. These follow-up observations improved the precision in the orbital period of K2-151b by a factor of . Figure 16 also implies that the mid-transit times observed by K2 are consistent with the follow-up transit observations, and no clear sign of TTV is seen for K2-151b.

4.3 Validating Planets

We used the open source vespa software package (Morton, 2015b) to compute the false positive probabilities (FPPs) of each planet candidate. Similar to previous statistical validation frameworks (Torres et al., 2011; Díaz et al., 2014), vespa relies upon Galaxy model stellar population simulations to compute the likelihoods of both planetary and non-planetary scenarios given the observations. In particular, vespa uses the TRILEGAL Galaxy model (Girardi et al., 2005) and considers false positive scenarios involving EBs, background EBs (BEBs), as well as hierarchical triple systems (HEBs). vespa models the physical properties of the host star taking into account broadband photometry and spectroscopic stellar parameters using isochrones (Morton, 2015a), and compares a large number of simulated scenarios to the observed phase-folded light curve. Both the size of the photometric aperture and contrast curve constraints are accounted for in the calculations, as well as any other observed constraints such as the maximum depth of secondary eclipses allowed by the data. Finally, vespa computes the FPP for a given planet candidate as the posterior probability of all non-planetary scenarios.

Inputting all available information (e.g., folded K2 light curves, contrast curves from AO imaging, constraint on the depths of secondary eclipses, and spectroscopic parameters of the target stars) from our follow-up observations and analyses, we ran vespa and calculated FPP for each planet candidate. Table 4 summarizes thus derived FPP for our planet candidates; all the FPP values are well below the fiducial criterion of planet validation (), by which the planet candidates listed in Table 4 are statistically validated.

AO observations by Subaru/IRCS and HiCIAO allowed us to obtain high resolution images of candidate planet hosts, but our imaging can only cover the FoV of . Moreover, the targets were not imaged at the exact center of the detector, and nearby stars within K2 photometric apertures may be missing in our high resolution images. In order to ensure that such missing stars are not sources of false positive (i.e., BEBs), we checked the archived catalogs (e.g., Zacharias et al., 2005; Ahn et al., 2012) to look for faint nearby sources for each target. As a consequence, we found that K2-146, K2-147, K2-148, and K2-150 have nearby faint stars, which could be inside the K2 photometric apertures () 666Here, the faint star around K2-146 is different from the two faint sources that we identified in the HiCIAO image. The faint nearby source around K2-148 is also different from EPIC 220194953.. The delta magnitudes of these nearby stars are larger than mag, but smaller than those corresponding to the observed transit depths. Among the four systems, however, the nearby stars around K2-146, K2-148, and K2-150 are located around the edge of the K2 photometric apertures (separation larger than ), and so a significant fraction of light from those faint stars should be missing in the K2 photometry (). Given this loss of light, we found it almost impossible to account for the observed transit depths even for the maximum occultation case (i.e., loss of light during eclipses).

Concerning K2-147, we identified two faint sources around the target, which are separated by ( mag) and ( mag), respectively. Given the observed transit depth of , either of these faint stars could be the source of the observed signal. To prove that this is not the case, we created new K2 light curves using customized apertures for this object, which excluded the pixels around those faint stars. This analysis revealed that the transits are indeed reproduced even after excluding these faint stars, by which we concluded that K2-147 is the source of transits.

Finally, we checked if the stellar densities estimated via transit fitting are consistent with the spectroscopically estimated densities, in order to make sure that the planets are indeed transiting the low-mass host stars. As a result, we found that the stellar densities from the transit modeling all have super-solar densities, suggesting that the planets are transiting low-mass stars, and are in good agreement with spectroscopic values within except K2-117b, for which the two densities are compatible within . Based on all these facts above as well as the vespa calculations and absence of large RV variations for a fraction of systems, we conclude that the candidates in Table 4 are all bona-fide planets 777We note that false positives of an instrumental origin are very unlikely, since our candidates do not include one whose period is close to the known periods associated with instrumental artifacts (e.g., the 6-hour rolling motion)..

5 Individual Systems

5.1 K2-117

The planet candidate K2-117b ( days, ) was first reported by Pope et al. (2016) and recently Dressing et al. (2017b) validated this candidate along with the additional planet K2-117c of similar size (), orbiting the same star with days. We report here independent validations of these planets using our own observational data (AO and a high resolution spectrum), and have performed a more thorough analysis, including the double transit modeling (Figures 7 and 8) and TTV analysis. As shown in Figure 9, no clear TTV signals are seen in the diagram. The two planets exhibit moderate transit depths (), enabling transit follow-up observations from the ground, by which we can refine transit parameters and ephemerides.

5.2 K2-146

K2-146 is the coolest star in our sample, for which we obtain K. Pope et al. (2016) and Dressing et al. (2017b) reported that K2-146 hosts a mini-Neptune candidate in a day orbit with a possible TTV. We have performed a global fit to the K2 light curve allowing every transit center to float freely, and confirmed the TTV as shown in Figure 9. As a result of inputting the TTV-corrected transit curve to vespa, we were able to validate K2-146b as a bona-fide planet. The strong TTV ( minutes) suggests that the object causing TTV is either a very massive planet or has an orbit very close to the mean motion resonance (MMR), although the detailed TTV modeling is beyond the scope of this paper.

K2-146 also exhibits the deepest transit among our sampled stars, making it a very unique target for atmospheric characterizations and TTV modeling by transit follow-ups from the ground and space. However, the predicted transit times are now highly uncertain due to the TTV combined with the long time interval after the K2 observation, and it would be required to cover a long baseline around predicted transits. Fortunately, K2-146 is supposed to be observed by K2 again in the Campaign field 16, by which we can refine the ephemeris and possibly put a constraint on the object inducing the TTV.

K2-146 is very faint in the optical ( mag), but given the magnitudes in the near infrared (e.g., mag) one may be able to constrain the masses of K2-146b and the additional body by RV measurements with upcoming near infrared spectrographs (e.g., IRD; Kotani et al., 2014). Adopting the empirical mass-radius relation for small planets by Weiss & Marcy (2014), the mass of K2-146b is estimated as and the corresponding RV semi-amplitude induced by this planet is m s.

5.3 K2-122

K2-122 is a quite metal-rich early M dwarf (), hosting a close-in Earth-like planet (, days). Pope et al. (2016) reported this system to be a candidate planet-host, which was later validated by Dressing et al. (2017b). In addition to an independent validation by AO imaging and high resolution spectroscopy, we attempted a measurement of the planet mass. As shown in Figure 2, however, RVs measured by FIES and HARPS-N show a small variation. Assuming a circular orbit, we fit the observed RV datasets, for which we find the RV semi-amplitude of m s. This is consistent with a non-detection, but the upper limit of translates to for K2-122b’s mass, suggesting that its composition may be somewhat similar to that of the Earth. Future monitoring with a greater number of RV points would allow for a more robust mass measurement.

5.4 K2-123

The detection of a transiting mini-Neptune () was reported around K2-123 by Pope et al. (2016), and Dressing et al. (2017b) later validated this planet. We have presented our own observations and data analysis including the precise RV measurement (Figure 2), and independently validated K2-123b as a genuine planet in a day orbit.

The relatively large orbital distance ( AU) translates to K2-123b’s equilibrium temperature of K on the assumption that its Bond albedo is 0.3 ( Earth’s albedo). Thus, the planet is near the potential habitable zone, making it an attractive target for further characterizations. Given the moderate transit depth (), the detection of transits is relatively easy with 2-m class ground telescopes, but one may have a small chance to observe a complete transit due to the long orbital period.

5.5 K2-147

K2-147 is a metal-rich M dwarf, orbited by a super-Earth with the ultra-short period (USP; hours). No detection has so far been reported for this planet. According to exoplanet.eu888http://exoplanet.eu/catalog, K2-147b is the seventh validated USP planet ( day) around M dwarfs after Kepler-32f, Kepler-42c, Kepler-732c, KOI-1843.03 (Rappaport et al., 2013), K2-22b (Sanchis-Ojeda et al., 2015), and K2-137b (Smith et al., 2018). Interestingly, these planets show an increasing trend in as a function of the orbital period . We will later discuss the dependence of planetary sizes on insolation flux from host stars.

5.6 Epic 220187552

The transit-like signal was first detected for this target with a period of days and we measured its depth and duration as and hours. As shown in Figures 3 and 4, however, EPIC 220187552 is comprised of at least two stars separated by . The transit curve is also V-shaped, and the preliminary light-curve fitting preferred a grazing transit. We thus conclude that either of the two stars seen in Figure 3 has an eclipsing stellar companion (a late M dwarf or a brown dwarf), which is responsible for the relative Doppler shift in the cross-correlation profile (Figure 4). Indeed, as we described in Section 3.2, multiple spectra were obtained for this target by Subaru/HDS with the I cell but the RV analysis did not converge, which is most likely because the observed spectra (with the I cell) for RV measurement are different in shape from the template (without the I cell), which complicates the fitting procedure.

In Figure 4, the two line positions in the cross-correlation profile are separated by km s. The template spectrum for EPIC 220187552 was taken at , which corresponds to the orbital phase of when folded by the period of EPIC 220187552.01. This phase implies that the left line ( km s) in the cross-correlation profile corresponds to the star with a companion (i.e., EB) and right one ( km s) corresponds to the other star. Assuming a circular orbit () and the orbital inclination of for the EB, we can roughly estimate the secondary-to-primary mass ratio via

(2)

where is the mass of the primary star. When we adopt , we obtain for the mass of the secondary. This would be easily confirmed by taking additional spectra for the absolute RV measurement. EPIC 220187552 provides a good testing bench, where high resolution imaging and/or high dispersion spectroscopy become powerful tools to identify and characterize hierarchical triple systems.

5.7 EPIC 220194953 and K2-148

As we have seen in Section 4.2.1, K2-148 turned out to host three planets, whose radii we estimate as , , and for the innermost ( days), middle ( days), and outermost ( days) planets, respectively. In order to see if EPIC 220194953 and K2-148 are bound to each other (common proper-motion stars), we checked the proper motions of the two stars and found and , for EPIC 220194953 and K2-148, respectively (Smart et al., 2013), indicating that the two stars share the same proper motion within the errorbars. The almost identical RV values (Figure 4), along with the same distance (Table 3) to the stars, all imply that EPIC 220194953 and K2-148 are bound to each other. The separation of between the stars translates to the projected distance of AU from each other. It is of interest that one of the two late-type stars in a wide binary orbit has multiple super-Earths. Searching for planets around EPIC 220194953 also helps us understand the planet formation in cool wide-binary systems.

The period ratio of K2-148b and c is close to the 2:3 MMR. We investigated possible TTVs for the three planets, but no clear signal is seen in Figure 11, likely due to the small planetary masses.

5.8 K2-149

K2-149 is a slightly metal-rich early M dwarf, having a super-Earth () in a 11-day orbit. The RV measurement by Subaru/HDS shows no significant RV variation, supporting the planetary nature of K2-149b.

5.9 K2-150

The validated super-Earth K2-150b is similar to K2-149b in terms of its period ( days) and size (), except that it is orbiting a cooler host star ( K). Two absolute RVs were measured by Subaru/HDS, which are consistent within their errors. Given the moderate-depth transit () for a super-Earth, K2-150 is a good target for ground-based transit observations to refine system parameters and search for a possible TTV.

5.10 K2-151

K2-151 is a metal-poor M dwarf hosting a transiting small planet with days. The size of K2-151b () suggests that it is likely a rocky planet. The relative brightness of the host star allowed us to observe the follow-up transits from the ground, enabling a considerable improvement in the transit ephemeris (Section 4.2.2). We also measured rough RVs, which completely ruled out the EB scenario. K2-151 is also a good target for future precise RV measurements in the near infrared; with mag, new and upcoming spectrographs like IRD and CARMENES (Quirrenbach et al., 2014) may be able to pin down the mass of K2-151b.

5.11 K2-152

The transiting mini-Neptune K2-152 is orbiting the host M dwarf every 33 days. Assuming the Bond albedo of , we estimate the equilibrium temperature of K2-152b as K, putting this planet near the habitable zone. The host star’s brightness ( mag and mag) and moderate transit depth () make this system a good target for further follow-ups including precise RV measurements, either in visible and near infrared, and ground-based transit observations. Based on the mass-radius relation by Weiss & Marcy (2014), the mass of K2-152b is , corresponding to the RV semi-amplitude of m s.

5.12 K2-153

We did not obtain multiple spectra for K2-153, which does not allow us to rule out completely the grazing EB scenario. Our HDS spectrum for K2-153, however, was taken at corresponding to , around which we expect to see the largest line separation in the spectrum if the transit signal is caused by an EB. We carefully inspected the secondary line in the cross-correlation profile, but found no evidence, supporting the result of the vespa validation. K2-153 is a slightly metal-poor, early-to-mid M dwarf orbited by a super-Earth () with days.

5.13 K2-154

We identified and validated two transiting mini-Neptunes ( and ) around K2-154, a slightly metal-rich early M dwarf. The orbital periods are 3.68 and 7.95 days for K2-154b and c, respectively, whose ratio is somewhat close to the 2:1 resonance. We searched for TTVs for this system, but found no clear evidence as shown in Figure 12. A longer-term transit follow-ups with a better precision would be required.

6 Discussion

All together, we have validated 16 planets around 12 of the low-mass stars observed by K2, based on high-resolution imaging and optical spectroscopy. Since the number of planets around M dwarfs has been increasing rapidly, thanks to K2 and other projects, it is tempting to investigate the entire ensemble of M-dwarf planets, seeking patterns among their properties. We focus here on a search for any relationships between planet size, the stellar insolation (the flux received by the planet), and the stellar metallicity. This is because insolation and metallicity are strongly suspected of playing an important role in the formation and evolution of planets, and some possible correlations with planetary radius have already been discussed in the literature (e.g., Owen & Wu, 2013; Buchhave et al., 2014; Dawson et al., 2015; Lundkvist et al., 2016).

System (K) [Fe/H] (dex) ()
K2-3
K2-5
K2-9
K2-18
K2-26
K2-54
K2-72
K2-83
Table 6: Revised Spectroscopic Parameters Based on SpecMatch-Emp

To this end, we created a list of transiting planets around M dwarfs based on information in the NASA Exoplanet Archive999https://exoplanetarchive.ipac.caltech.edu, exoplanet.eu, and exoplanets.org101010http://exoplanets.org. We restricted our sample to confirmed or validated planets around dwarf stars with K. We excluded unvalidated planet candidates. We also excluded 6 systems for which spectroscopic characterization is not available (Kepler-1350, 1582, 1624, 1628, 1646, and 1649).

For some systems, different investigators have reported different values for stellar and planetary parameters, sometimes differing by more than . For the sake of homogeneity, we adopted the stellar parameters of Mann et al. (2013b, a, 2016a, 2016b, 2017b, 2017a) for a majority of the Kepler and K2 stars in our sample, since those were derived based on the same (or similar) observing and reduction schemes. We also used the SpecMatch-Emp code to derive our own versions of the stellar parameters (Table 6), for cases in which high-resolution spectra were available on the ExoFOP website111111https://exofop.ipac.caltech.edu. As noted by Yee et al. (2017), the M-dwarf parameters derived by the SpecMatch-Emp code were calibrated using the sample of Mann et al. (2015), faciliating comparisons. For the other systems, for which high-resolution spectra were not available, we adopted the stellar parameters from the literature (Rojas-Ayala et al., 2012; Biddle et al., 2014; Torres et al., 2015; Hartman et al., 2015; Berta-Thompson et al., 2015; Hirano et al., 2016a; Dressing et al., 2017a; Martinez et al., 2017; Gillon et al., 2017; Dittmann et al., 2017), although no metallicity values were reported by Martinez et al. (2017). Planet radii were estimated based on the revised stellar radii and the values of reported in the literature or by the Kepler team.

Figure 17: Histogram of planet radius, for the validated and well-characterized transiting planets around M dwarfs. The number counts for mid-to-late M dwarfs are shown above those for early M dwarfs.

We split the sample into (1) planets around early M dwarfs (3500-4000 K) and (2) mid-to-late M dwarfs (3500 K), to check for any differences in planet properties associated with stellar mass or effective temperature. By this definition our sample consists of 96 planets around 63 early M dwarfs, and 32 planets around 17 mid-to-late M dwarfs.

Figure 17 shows the distribution of planet sizes, on a logarithmic scale. A larger number of Earth-sized planets () are found around the later-type stars, in spite of the smaller number of such stars in our sample. Although no completeness correction has been applied, it is interesting that Figure 17 shows that both types of stars have deficit of planets with , relative to somewhat smaller or larger planets. This is consistent with the findings of Fulton et al. (2017) and Van Eylen et al. (2017), based mainly on solar-type stars, that planets with sizes between 1.5-2  are rarer than somewhat smaller or larger planets. This paucity has been interpreted as the outcome of photoevaporation on a population of planets with rocky cores () with differing masses of gaseous envelopes and different levels of irradiation (Owen & Wu, 2017), or as the outcome of the erosion of planetary envelopes by internal heat from cooling rocky cores (Ginzburg et al., 2017). The same sort of deficit seen in Figure 17 suggests that the same processes seem to be taking place around M dwarfs.

6.1 Insolation Dependence

Figures 18 and 19 display the planet radius as a function of stellar insolation . In these figures, red circles represent our newly validated planets, blue squares are other K2 planets, and black triangles are planets discovered during the primary Kepler prime mission or by ground-based surveys. Looking at Figures 18 and 19, we note that an important contribution of K2 has been the discovery of relatively large planets (), which were not frequently detected during the Kepler primary mission.

Figure 18: Stellar insolation fluxes vs. radii of planets around early M dwarfs (). Our newly validated planets (red circles), other planets discovered by K2 (blue squares), and planets from the Kepler primary mission and other surveys (black triangles). The cyan rectangle area is the “hot-super-Earth desert” described by Lundkvist et al. (2016). See the text for the upper boundary of (green solid line).
Figure 19: Stellar insolation fluxes vs. radii of planets around mid-to-late M dwarfs (). Symbols and plot ranges are the same as in Figure 18.

Figures 18 and 19 show a lack of larger planets () in the close proximity of M stars. The deficit of close-in planets ( days) was previously reported by, e.g., Howard et al. (2012); Mazeh et al. (2016); Fulton et al. (2017) mainly for solar-type stars. In order to draw a rough boundary above which planets are apparently rare, we took an approach similar to that described in Courcol et al. (2016) for the planet-mass vs. stellar-metallicity diagram. Namely, we computed the cumulative weighted distribution of for each insolation bin with its width being in the space121212The bin size was set to 0.1 in , and thus each bin is overlapping with the neighboring bins. We then estimated the maximum radius for each bin by finding the upper limit of this cumulative distribution. Finally, these upper limits were fitted with a linear function in the space. We restricted this analysis to close-in planets ( days) and excluded hot Jupiters () since they seem to form a different population from their smaller counterparts (e.g., Mazeh et al., 2016).

The green line in Figure 18 represents this estimated boundary line. The moderate slope of the line () implies that only larger planets () are missing in the proximity of the host stars. Owen & Wu (2013) showed that close-in low-mass planets are likely to suffer significant envelope evaporation due to the X-ray and extreme ultraviolet (EUV) radiation from the host star. On the other hand, theoretical works have shown that the gravitational potential of hot Jupiters is so deep that the XUV radiation from host stars cannot significantly strip their envelopes (e.g., Murray-Clay et al., 2009), which is consistent with the presence of the few hot Jupiters seen in Figure 18. Owen & Wu (2013) also noted that the evaporation of hydrogen envelopes should occur within the first 100 Myr, when stars are at the peak of their chromospheric activity. In this light, it is interesting that K2-33b seems to be unusually large for its level of current irradiation; the host is a pre-main-sequence star with an age of Myr. This suggests that K2-33b is actively evaporating, and that its radius will shrink significantly over the next 100 Myr. Note that we did not exclude K2-33b from the analysis to draw the boundary.

The cyan rectangles in Figures 18 and 19 depict the “hot-super-Earth” desert discussed by Lundkvist et al. (2016), for close-in planets around solar-type stars (i.e., and ). Evidently this rectangle is not a good description of the “desert” seen around M dwarfs. Instead, for M dwarfs, the “desert” seems to extend towards much lower insolation. Also interesting is that the observed “desert” is shifted toward lower insolation for the mid-to-late M stars. In Figure 19, we draw a similar upper boundary of for the mid-to-late M sample by the purple dashed line. The derived slope of this boundary () agrees with that for the early-M sample to within . To make this easier to see, the same green line that was drawn in Figure 18 is also drawn in Figure 19.

This result can be understood in the framework of Owen & Wu (2013), which implies that plotting the planet radius against the current bolometric insolation is not the most direct way to seek evidence for photoevaporation. Envelope evaporation is caused specifically by X-ray and EUV irradiation from the star, and not by the bolometric flux. This is especially so for M dwarfs because they emit a higher fraction of X-rays relative to the bolometric flux than solar-type stars. Thus planets around M dwarfs should have been eroded more efficiently, relative to planets around solar-type stars with the same level of bolometric insolation. This was shown in Figure 7 of Owen & Wu (2013), wherein the lack of large planets extends to smaller bolometric fluxes for later-type stars. Owen & Wu (2013) also showed that when is plotted against the empirically estimated X-ray exposure, the maximum planet size at a given X-ray exposure is approximately the same for all types of host stars. Although we do not attempt here to reproduce this type of plot, a comparison between Figures 18 and 19 does suggest a similar pattern. We note that this pattern is also compatible with the scenario in which photoevaporation is responsible for the radius gap (Figure 17), and favors photoevaporation over planetary internal heat as the explanation (Ginzburg et al., 2017), because in the latter case it should be the bolometric luminosity (not the XUV luminosity) that is relevant to atmospheric loss.

Another possible mechanism that could lead to a deficiency of close-in planets with large sizes is high-eccentricity migration (e.g., Rasio & Ford, 1996; Nagasawa & Ida, 2011) coupled with the disruption of planetary envelopes in the vicinity of the Roche limit (Matsakos & Königl, 2016; Giacalone et al., 2017). Since Neptune-sized planets are often observed to have lower mean densities than Jovian or Earth-sized planets, their planetary envelopes should be relatively easy to strip. Mulders et al. (2015b) and Lee & Chiang (2017) suggested that the decline of planet occurrence rate of all sizes at shortest orbital distances ( days) could be the result of disk truncation at these orbital distances. Several mechanisms that truncate the planet populations around different types of stars are discussed in the literature (e.g., Plavchan & Bilinski, 2013; Mulders et al., 2015b), including tidal halting of migrating planets. The lack of planets of all sizes at higher insolation level in Figures 18 and 19 may also be consistent this interpretation. In this picture, the disk truncation likely happens at -day period for both early and mid-to-late M dwarfs to explain the lack of detected planets. However, the “truncation” we observed is not a vertical boundary in the insolation vs. radius plane as one would expect in the disk truncation picture, instead it has a moderate slope. In other words, at high insolation levels, there is only a lack of larger planets but not smaller planets. This would seem to favor the photoevaporation picture rather than the disk truncation picture.

Figures 18 and 19 also suggest a lack of large planets at low insolations (i.e., at longer orbital periods; days). This could be related to the formation process of these larger planets, which somehow is easier in their observed locations; the two figures illustrate that large planets including the hot Jupiters () seem to occur within a relatively narrow range of periods. However, given that the occurrence rate of planets with is known to dwindle dramatically and long-period planets are more affected by detection biases associated with the transit geometry and short span of the K2 monitoring, it is premature to draw any conclusions on those outer planets. Compared to planetary systems around solar-type stars, little is known on the formation and evolution of M-dwarf planets, but measurements of eccentricity for close-in planets and other orbital parameters (e.g., the stellar obliquity) would help to test all these hypotheses for M-dwarf planets.

6.2 Metallicity Dependence

Stellar metallicity is also known to be related to planet size in exoplanetary systems (see, e.g., Buchhave et al., 2014). It is well known that the occurrence rate of giant planets around solar-type stars depends sensitively on [Fe/H] (e.g., Johnson et al., 2010). The occurrence of Earth and Neptune-sized planets were reported to be less dependent on metallicity (e.g., Sousa et al., 2008; Mayor et al., 2011), although some recent studies have shown that such planets are at least somewhat more frequent around metal-rich solar-type stars (e.g., Wang & Fischer, 2015). In particular, there is growing evidence that small close-in planets ( days) are preferentially found around metal-rich stars (Mulders et al., 2016; Dong et al., 2017; Petigura et al., 2017b). Specifically, Wilson et al. (2017) derived the critical period, below which small planets orbit statistically metal-rich host stars ( days).

Figure 20: Host stars’ metallicities from spectroscopy vs. radii of the planets around early M dwarfs (). For multi-planet systems, the largest planets are plotted. Symbols are the same as in Figure 18. Note that contrary to Figures 18 and 19, the scale is logarithmic.
Figure 21: Host stars’ metallicities from spectroscopy vs. radii of the planets around mid-to-late M dwarfs (). For multi-planet systems, the largest planets are plotted. Symbols are the same as in Figure 18.

Here we examine the relationship between and [Fe/H] for M-dwarf planets, based on our new measurements and the parameters available in the literature. Previously, Schlaufman & Laughlin (2010) found a hint that planet-hosting M dwarfs are preferentially found in the region of the diagram where one expects metal-rich stars to be located. Rojas-Ayala et al. (2012) also investigated the metallicity of eight planet-hosting M dwarfs. They found that M-dwarf planets appear to be hosted by systematically metal-rich stars, and that Jovian planet hosts are more metal rich than Neptune-sized planet hosts. Mann et al. (2012), however, found no significant difference in color, a metallicity indicator, between the planet-candidate cool hosts and other cool stars. They ascribed the apparently high metallicity of cool planet-host stars reported in the literature to contamination of the sample by misidentified giant stars.

Figures 20 and 21 show the radii of confirmed and validated transiting planets as a function of stellar metallicity, for early-M hosts (3500-4000 K) and mid-to-late M hosts (3500 K). We restricted the sample to stars with spectroscopic measurements of [Fe/H]. For multi-planet systems, we have plotted only the largest planet. From these figures we see that larger planets () have only been found around metal-rich stars (). This is similar to the situation with solar-type stars (Buchhave et al., 2012). Moreover, the mid-to-late M dwarfs seem to show a trend of increasing planet size with metallicity. For early M dwarfs the correlation (if any) is not obvious; there are many small planets () around super-solar metallicity stars. However, it must be remembered that these results have not been corrected for survey sensitivity. Transit surveys have a strong bias favoring the detection of short-period planets; there may be larger-radius planets that have been missed due to their longer periods. It is most significant that there are no detections of super-Neptune planets around metal-poor M dwarfs (the upper left region in both figures), since such large planets are easier to detect than smaller planets.

Based on RV mass measurements for small planets around solar-type stars, it has been demonstrated that the observed maximum planet mass increases with metallicity (Courcol et al., 2016; Petigura et al., 2017a). A similar trend is seen for planet radius in Figures 20 and 21. To compare the previous finding with the distribution of M-dwarf planets, we draw in Figures 20 and 21 the upper envelope by the green solid line corresponding to Equation (1) of Courcol et al. (2016), where the planet mass is converted into radius assuming (Chen & Kipping, 2017); all the planets except hot Jupiters are below this line. Although the number of systems plotted is much smaller than in previous works for solar-type stars, the upper envelopes of planet radius seem to be pushed towards lower values for coolest stars.

Dawson et al. (2015) advanced an explanation for the paucity of gaseous planets around metal-poor stars. They argued that metal-rich stars possessed protoplanetary disks with a higher surface density of solids, which led to more rapid formation of rocky cores with a critical mass () for gas accretion. If the formation timescale of critical-mass cores is longer than the disk lifetime, gaseous planets are unlikely to form. Although their argument focused on planets around solar-type stars, Figures 20 and 21 suggest that a similar argument might apply to low-mass stars.

To be more quantitative, we computed the Pearson’s correlation coefficient between and [Fe/H]. We found and for early M and mid-to-late M stars, respectively, corresponding to the values of and . This is evidence for some kind of relationship between planet radius and stellar metallicity for cool stars, as has been previously reported for solar-type stars (Buchhave et al., 2014). The mid-to-late M dwarf sample shows a higher correlation coefficient than that of the early M sample, but the number of the systems is also much smaller, which may have led to an apparently higher correlation by chance. To check whether the two samples are drawn from the same distribution, we performed a Monte Carlo simulation in which 17 systems (the number of mid-to-late M systems) are randomly selected from the 57 early M dwarfs, and we computed the probability that the correlation coefficient for the subset of 17 systems is higher than 0.689 (the observed for the mid-to-late M stars). We found that its probability is , implying that the mid-to-late M dwarf sample indeed shows a stronger correlation between and .

Since the envelopes of close-in planets may have been evaporated (at least to some degree) by X-ray and EUV radiation from the star, we also tried to compute the correlation coefficients after removing planets for which the insolation exceeds 100 times the Earth’s insolation, approximately the minimum value for which Figure 18 suggests that shrinkage takes place. We obtained a slightly higher correlation coefficient () for the early-M sample, but with an almost identical statistical significance (), probably due to the smaller sample size. The [Fe/H] correlation is especially strong for coolest M dwarfs (), suggesting that the amount of initial solid material is extremely sensitive to the formation of Neptunian (and jovian) planets with hydrogen-helium envelopes around coolest stars.

Another relevant factor that affects the relation is the correlation between the planet period and its host star’s metallicity. Mulders et al. (2016) and Dong et al. (2017) have recently shown that stars with close-in rocky planets ( days) are preferentially seen around metal-rich stars, and thus the correlation could be in part affected by the correlation. In order to examine such a correlation for M-dwarf planets, we split the whole sample (both early M and mid-to-late M samples) into inner planets ( days) and outer planets ( days), by which the two subsamples have approximately the same numbers of planets, and compared their mean metallicities. Consequently, we found a slightly higher mean metallicity for the inner-planet subsample () than that for the outer-planet subsample (), but in a statistically insignificant manner ( difference). More planets are needed to confirm the correlation.

Following Buchhave et al. (2014), we also computed the mean metallicity for our samples. We found the weighted mean metallicity to be for early M dwarfs, and for mid-to-late M dwarfs. Schlaufman & Laughlin (2010) noted that the mean metallicity of M dwarfs in the solar neighborhood is . Therefore, our result also indicates that the confirmed/validated planet-hosting M dwarfs have systematically high metallicities, The difference in the mean metallicities was also seen by Rojas-Ayala et al. (2012), but here we have extended their argument down to lower-mass stars and have used a larger number of well-characterized systems. We note, however, that unknown selection effects and/or different methodologies for metallicity measurements may have introduced biases in the mean metallicities in the two samples. Homogeneous measurements for volume-limited samples would be required to draw a firm conclusion.

There is no obvious reason why transit surveys should have a detection bias favoring high stellar metallicity, but there might be some effects. For instance, since M dwarfs with higher metallicity are more luminous than lower-metallicity counterparts for a given temperature, it may be somewhat easier to detect planet candidates and conduct follow-up observations for high-metallicity stars, leading to the validation the transiting planets, as we have done in the present paper. Given that we have included a variety of transiting planets detected by many space-based and ground-based surveys, it is not straightforward to account for any detection biases associated with stellar metallicity. We leave this for future work.

7 Conclusions

As a part of our K2 follow-up program (e.g., Sanchis-Ojeda et al., 2015), we have detected tens of planet candidates around M dwarfs in K2 campaign fields 5–10, and conducted follow-up observations for candidate planets around M dwarfs. We have validated 16 transiting planets around 12 low-mass stars, out of which 12 are newly validated planets. All the validated planets are relatively small in size (Earth-sized to mini-Neptunes), with periods ranging from 0.96 to 33 days. We have also identified a hierarchical triple system (EPIC 220187552) based on AO imaging and high resolution spectroscopy.

We also reviewed the relationships between planet size, insolation, and metallicity that are emerging from the growing sample of M-dwarf planets. The planet-radius distribution suggested the same “gap” at around 1.5-2  that was found by Fulton et al. (2017) for a larger sample of mainly solar-type stars. We saw an indication of the “desert” of very hot planets larger than about , although for the coolest M stars the desert begins at significantly lower insolation levels than for solar-type stars. We also confirmed that planets larger than about 3  are preferentially seen around metal-rich stars (). Moreover, we found that the statistical significance of this trend is higher for the coolest M dwarfs. It will be important to try and corroborate these findings with a larger sample and after considering selection biases.

Fortunately, the Transiting Exoplanet Survey Satellite (TESS; Ricker et al., 2015) will be launched and start the transit survey in the near future, which would make it more straightforward to deal with selection biases and extract the true distributions of stellar and planetary parameters with a larger number of sampled stars. To corroborate our findings, homogeneous characterizations of the systems with and without planets are essential.

Some of the new M-dwarf planets offer excellent prospects for further characterization, including Doppler mass measurement with optical or near-infrared spectroscopy (e.g., Kotani et al., 2014). As discussed above, the sizes of M-dwarf planets show some qualitative trends similar to those around solar-type stars, but they also exhibit quantitatively different dependences on stellar insolation and metallicity. Perhaps the mass-radius relation for M-dwarf planets will also be seen to be different from that of planets around solar-type stars (Weiss & Marcy, 2014). Measurements of orbital eccentricity and stellar obliquity could also provide helpful clues to the processes of planet formation and evolution around low-mass stars.

This paper is based on data collected at Subaru Telescope, which is operated by the National Astronomical Observatory of Japan, on observations collected at the Centro Astronómico Hispano Alemán (CAHA) at Calar Alto, operated jointly by the Max–Planck Institut für Astronomie and the Instituto de Astrofísica de Andalucía, and on observations obtained a) with the Nordic Optical Telescope (NOT), operated on the island of La Palma jointly by Denmark, Finland, Iceland, Norway, and Sweden, in the Spanish Observatorio del Roque de los Muchachos (ORM) of the Instituto de Astrofísica de Canarias (IAC); b) with the Italian Telescopio Nazionale Galileo (TNG) operated on the island of La Palma by the Fundación Galileo Galilei of the INAF (Istituto Nazionale di Astrofisica) at the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canaria. The data analysis was in part carried out on common use data analysis computer system at the Astronomy Data Center, ADC, of the National Astronomical Observatory of Japan. We thank Akito Tajitsu, Joanna Bulger, and Ji Hoon Kim, the support astronomers at Subaru, and Jun Hashimoto, Shoya Kamiaka, Yohei Koizumi, and Shota Sasaki for their helps to carry out the Subaru observations. We also thank Santos Pedraz for carrying out the CAFOS observations at the Calar Alto observatory. We are very grateful to the NOT and TNG staff members for their unique and superb support during the observations. T.H. is grateful to Samuel Yee for providing instructions to install SpecMatch-Emp. We are thankful to Christophe Lovis, who provided the numerical mask for the spectral cross-correlation analysis. The discussions with Eric Gaidos, Hiroyuki Kurokawa, Jose Caballero, Alexis Klutsch, and Kento Masuda were very fruitful. This work was supported by Japan Society for Promotion of Science (JSPS) KAKENHI Grant Number JP16K17660. D. G. gratefully acknowledges the financial support of the Programma Giovani Ricercatori – Rita Levi Montalcini – Rientro dei Cervelli (2012) awarded by the Italian Ministry of Education, Universities and Research (MIUR). The research leading to these results has received funding from the European Union Seventh Framework Programme (FP7/2013-2016) under grant agreement No. 312430 (OPTICON). D.M. acknowledge financial support from the Universidad Complutense de Madrid (UCM), the Spanish Ministry of Economy and Competitiveness (MINECO) from project AYA2016-79425-C3-1-P. I.R. acknowledges support by the Spanish Ministry of Economy and Competitiveness (MINECO) and the Fondo Europeo de Desarrollo Regional (FEDER) through grant ESP2016-80435-C2-1-R, as well as the support of the Generalitat de Catalunya/CERCA programme. We acknowledge the very significant cultural role and reverence that the summit of Mauna Kea has always had within the indigenous people in Hawai’i. \softwareIRAF (Tody, 1986, 1993), ACORNS pipeline (Brandt et al., 2013), SpecMatch-Emp (Yee et al., 2017), EVEREST (Luger et al., 2016, 2017), PHOENIX (Allard et al., 2013), vespa (Morton, 2015b), pyfits (Barrett et al., 2012)

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