K2 DISCOVERS A BUSY BEE: AN UNUSUAL TRANSITING NEPTUNE FOUND IN THE BEEHIVE CLUSTER

We identified the star K2-95 as a potential M dwarf target and high probability member of the Praesepe cluster for our K2 Campaign 5 proposal (GO5006—PI Schlieder). Other groups also proposed this star as a potential K2 target (GO5011—PI Beichman, GO5048—PI Guzik, GO5095—PI Agueros, GO5097—PI Johnson).

K2-95 was observed during K2 Campaign 5 with nearly continuous photometry from 2015 April 27 to July 10. We extracted the photometry from the pixel data which we downloaded from the MAST.²¹

Our photometric extraction pipeline is described in more detail in Petigura et al. (2015) and Crossfield et al. (2015). During K2 operations, the telescope is torqued by solar radiation pressure which causes it to slowly roll around the boresight. This motion causes stars to drift across the CCD by about 1 pixel every 6 hr. As stars are sampled by different pixels, intra-pixel sensitivity and flat-fielding variations cause the apparent brightness of the star to change. Thruster fires to correct for this drift affect the pointing and therefore pixel position greatly, giving the overall photometry a saw-tooth shape. We solve for the roll angle between each frame and an arbitrary reference frame and model the time- and roll-dependent brightness variations using a Gaussian process. Further, we adjust the size of our square extraction aperture to minimize the residual noise in the corrected light curve. This balances two competing effects: larger apertures yield smaller systematic errors while smaller apertures include less background noise. Our final square extraction aperture is r = 1 pixel $\approx 4^{\prime\prime}$. The resulting, de-trended light curve exhibits slow, periodic, ∼1% modulations with a period of about 24 days. We attribute this modulation to spots on the rotating stellar surface. The timescale of this variation is long compared to other M dwarfs in Praesepe and places K2-95 among the slowest rotators in the cluster (see also Section 3.5). This variation is fitted and removed to produce the final light curve which is shown in the top panel of Figure 1.

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We searched through the optimized light curve with the TERRA algorithm which is described in more detail by Petigura et al. (2013). In short, it searches for periodic box-shaped photometric dimmings and fits them with a model from Mandel & Agol (2002). Using TERRA, we detected a transit signal in the K2-95 light curve with a period of $P=10.132\,\mathrm{days}$ and a signal-to-noise ratio (S/N) of 23.97. The phase-folded light curve is shown in the bottom panel of Figure 1, centered around the transit event. We subtracted the best-fitting model transit and iterated the TERRA algorithm to search for other transits but did not detect any secondary signals. Visual inspection also did not reveal any additional transit features.

We observed K2-95 with the 2.0 m Fraunhofer telescope Wendelstein (Hopp et al. 2014), using the Wide Field Imager (WFI) (Kosyra et al. 2014) on Mt. Wendelstein in the Bavarian Alps. An independent transit detection from a ground-based facility serves not only for period confirmation and estimation of its uncertainty, but as evidence for the planetary nature of the transit from a common eclipse depth at different wavelengths. Multi-band transit photometry can be used to characterize the planet's atmosphere or rule out false-positive detections (Mislis et al. 2010; Southworth et al. 2012; Mancini et al. 2013; Ciceri et al. 2016). The limb darkening coefficients differ across photometric bands and can be used to differentiate between planetary signals and those of shallow-eclipse eclipsing binaries (EBs). K2-95 was followed up in the i'-band on UT 2016 April 16 during suboptimal weather with seeing between $1^{\prime\prime}$ and $3^{\prime\prime}$ and cirrus activity which led to aborting the observations after about three hours, or around mid-transit. However, due to the relative isolation of the target and reference stars on the CCD, the data were still salvageable and we could identify the transit after binning the data in 30 minutes intervals. The light curve seen in Figure 2 shows the expected transit depth of 0.7% and agrees very well with the overlaid best-fitting transit model from the K2 data, adjusted for the respective i'-band limb darkening coefficients. This light curve is already time-corrected and indicates a slight shift in phase. This implies that our initial period estimate may have been off by a few seconds per cycle, an effect seen in the follow-up of previous K2 planet discoveries (see Beichman et al. 2016), but it is still inside the period uncertainty (see also Section 4.2) of ≈60 s. Following up transiting planets over larger baselines and therefore improving period accuracy is a valuable step in preserving the ephemeris for future studies.

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We observed our target with the near-infrared cross-dispersed spectrograph (SpeX, Rayner et al. 2003) on the 3.0 m NASA Infrared Telescope Facility on Mauna Kea. While K2 targets are already pre-characterized with broadband photometry, spectral typing is essential for more accurate stellar properties. K2-95 was observed on UT 2015 December 09 under excellent conditions with a clear sky and an average seeing of $0\buildrel{\prime\prime}\over{.} 5$. We used the instrument's short cross-dispersed mode (SXD) with the 0.3 × $15^{\prime\prime}$ slit which provides a wavelength range of 0.68–2.5 $\,\mu {\rm{m}}$ and a resolution of R ≈ 2000. The target was placed at two locations along the slit and was observed in an ABBA pattern with 16 × 185 s integrations for a total integration time of 2960 s. For telluric correction and wavelength calibration, we observed an A0 standard star plus arc and flat lamp exposures right after the target. We reduced the data with the SpeXTool package (Vacca et al. 2003; Cushing et al. 2004) which performs flat fielding, sky subtraction, bad pixel removal and subsequently spectral extraction and combination, telluric correction, wavelength+flux calibration and order merging. We achieved a median S/N of 70 per resolution element in the J- ($1.25\,\mu {\rm{m}}$), 80 in the H- ($1.6\,\mu {\rm{m}}$) and 60 in the K-band ($2.2\,\mu {\rm{m}}$). We compare the JHK-band spectra to late-type standards from the IRTF Spectral Library (Rayner et al. 2009), seen in Figure 3. The best visual match for K2-95 lies between M2 and M3 standards across all infrared bands.

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We obtained a high-resolution optical spectrum of K2-95 using the HIRES echelle spectrometer on the 10 m Keck I telescope (Vogt et al. 1994) on UT 2015 December 23. High-resolution spectroscopy can be used to rule out false-positive detection scenarios such as EBs by searching for secondary line features that are created by a possible companion star. Our observation followed the procedures of the California Planet Search (CPS, Howard et al. 2010). We used the "C2" decker, providing a spectral resolution of R = 55,000, and subtracted the sky from the stellar spectrum. We utilized the HIRES exposure meter to automatically terminate the exposure when S/N = 32 per pixel was achieved. The HIRES spectrum was reduced using standard CPS procedures and cover ∼3600–8000 Å. Two additional spectra were obtained on UT December 24 and 29 using a redder setting of HIRES at R = 48,000; these data are described in J. Pepper et al. (2016, in preparation).

We obtained high-resolution NIR images of K2-95 using NIRC2 on the 10 m Keck II telescope using the target as a natural guide star to drive the AO system. High-resolution imaging is a useful tool for constraining the probability of a blended background star. We observed the target on UT 2016 January 16 in the K-band, following a multi-point dither pattern with integration times short enough to avoid saturation. We used the dithered images to subtract the sky background and remove dark current, then aligned, flat-fielded, and stacked the individual images. The star appears single and has no close companions within several arcseconds. To estimate the sensitivity of the NIRC2 observations, we injected fake sources with S/N = 5 into the combined image at separations that are integral multiples of the star's FWHM. We show our final image and the 5σ sensitivity curve in the left panel of Figure 4.

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We also obtained speckle imaging of K2-95 in two narrow band filters centered at 880 and 692 nm using the DSSI camera (Horch et al. 2009) on the 8 m Gemini North telescope on UT 2016 January 16. We followed a standard observing procedure where the star was centered in the field, guiding was established, and many images were taken using 60 ms exposures. The data were reduced and combined into a final reconstructed image using the techniques described in Horch et al. (2011) and Howell et al. (2012). These procedures perform automatic model fits (single, double, triple) and provide estimates of the magnitude difference and separation for multiple systems. K2-95 was found to be a single star. We measured the background sensitivity of the reconstructed DSSI image, using a series of concentric annuli centered on the target. The innermost annulus is at the telescope diffraction limit where our sensitivity is zero. The sensitivities in the subsequent annuli are interpolated using a cubic spline to produce a smooth sensitivity curve. The 880 nm reconstructed DSSI image and sensitivity curve are shown in the right panel of Figure 4.

Data taken from photographic plates, now digitally scanned and available online²² , cover several decades of astrometry. Our target was first observed in 1954 by the Digital Sky Survey (DSS) in the red and blue channels with an additional epoch from 1989 and 1990, respectively. We show the DSS-red plates from 1954 and 1989 in Figure 5. The images are centered on the epoch 2015 coordinates of the target in the EPIC database (08:37:27.059, +18:58:36.07) and the K2 aperture is overlaid as a green square. The target's proper motion of 1.4 arcsec over the course of 35 years results in a visible shift in position, seen in comparison of the middle and left panels in Figure 5. There is no indication for a background star at the 2015 epoch position, based on the archival data. If there is a star still hidden in the background it must be quite faint, in which case it would not significantly dilute the transit signal.

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We apply the index-based methods of Mann et al. (2013a, 2013b, 2015) and equivalent width (EW)-based methods of Newton et al. (2014, 2015) to our SpeX spectrum in order to estimate the metallicity, temperature, radius, and luminosity of K2-95. These approaches are empirically calibrated by using wide M dwarf binary companions and nearby bright M dwarf standards with interferometrically measured radii. Our SpeX spectrum, shown in Figure 3, suffers from poor telluric correction in the J- and H-bands. These residuals result from the long exposure time of the target which led to a large time baseline (nearly one hour) and non-ideal airmass difference (>0.1) between the target and A0 calibrator. To avoid the systematic effects introduced when using the index-based methods of Mann et al. (2013b) in regions of poor telluric correction (Mann et al. 2013a; Newton et al. 2015) we use only their K-band relations. Prior to any analyses, the spectrum was shifted by its RV estimated via cross-correlation with an M dwarf standard.

To estimate the star's metallicity, we use IDL software provided by A. Mann and E. Newton.²³ Using the Mann et al. (2013a) K-band index relations, we estimate a metallicity $[\mathrm{Fe}/{\rm{H}}]=0.09\pm 0.09\ \,\mathrm{dex}$. The K-band EW-based methods of Newton et al. (2014) provide $[\mathrm{Fe}/{\rm{H}}]=0.12\pm 0.14\ \,\mathrm{dex}$. The uncertainties were estimated using Monte Carlo sampling. These estimates are consistent with each other and also with the metallicity of Praesepe, $[\mathrm{Fe}/{\rm{H}}]=0.12\pm 0.04\ \,\mathrm{dex}$ (Boesgaard et al. 2013).

We estimate the effective temperature using the K-band index relations of Mann et al. (2013b) and the H-band EW-based relations of Newton et al. (2015) using IDL software provided by A. Mann and E. Newton.²⁴ The K-band relations provide ${T}_{\mathrm{eff}}=3460\pm 73\,{\rm{K}}$ where the adopted uncertainty is the scatter in the polynomial relation. The H-band relations yield ${T}_{\mathrm{eff}}=3481\pm 100\,{\rm{K}}$. The uncertainty was estimated using Monte Carlo sampling of the measurement error in the spectrum. These consistent effective temperatures are used to estimate the radius and luminosity of the star using the aforementioned empirical calibrations. Following the Mann et al. (2013b) relations, we estimate ${R}_{* }=0.393\pm 0.036\,{R}_{\odot }$ and ${L}_{* }=0.017\pm 0.006\,{L}_{\odot }$. The Newton et al. (2015) relations provide ${R}_{* }=0.411\pm 0.034\,{R}_{\odot }$ and ${L}_{* }=0.024\pm 0.006\,{L}_{\odot }$. These fundamental parameters, estimated using different methods, are consistent at the $\lt 1\sigma$ level. We adopt the means of these estimates for further analyses and calculate conservative uncertainties by adding the individual errors in quadrature. The final values are provided in Table 1. The methods of Mann et al. (2013b) also provide estimates of the star's mass and density, ${M}_{* }=0.361\pm 0.069\,{M}_{\odot }$ and ${\rho }_{* }=7.81\pm 1.90\,{\rm{g}}\,{\mathrm{cm}}^{-3}$, respectively. We further use the H20_K2 index (Rojas-Ayala et al. 2012) to estimate the spectral type of the star. We find K2-95's type to be M3.0 ± 0.5, consistent with visual comparisons to standard stars and our spectroscopic temperature estimates.

We utilize the spectral energy distribution (SED) fitting code from Obermeier et al. (2016) as an additional layer of our stellar type characterization. In contrast to spectroscopy, this approach relies on broadband photometry. We extract the Pan-STARRS1 3π data (version PV3) for this star and cross-match its coordinates with the 2MASS catalog. For the synthetic stellar SED catalog, we use the newest version of the PARSEC isochrones package (Bressan et al. 2012) which includes improvements for low-mass stars that were calibrated for Praesepe (Chen et al. 2014). The age of the cluster is known (Brandt & Huang 2015a), therefore we restrict the synthetic model population to 800 Myr and Praesepe's metallicity of ($[\mathrm{Fe}/{\rm{H}}]=0.12\,\mathrm{dex}$). Since the isochrone models are for nonrotating stars, we furthermore include a second set of isochrones at 650 Myr. We create a tenth-order polynomial to interpolate between the distance-dependent extinction values given in the 3D dust map from Green et al. (2015) and²⁵ iteratively fit distance and extinction until both converge. We find that the final photometric fits for temperature and radius, ${T}_{\mathrm{eff}}=3386\pm 100\,{\rm{K}}$ and ${R}_{* }=0.43\pm 0.070\ {R}_{\odot }$, agree very well with the spectroscopic results and the extinction is negligible with $E(B-V)=0.0016$. The better fit was for the 650 Myr model with a marginally better ${\chi }^{2}$ of 7.83 against 7.97. We also estimate a distance of 171  ± 15 pc which is consistent with a Praesepe cluster membership and the derived distance of 172  ± 14 pc based on kinematic distance and K-band magnitude.

We use the methodology and algorithm of Kolbl et al. (2015) to search for blended background stars or close spectroscopic binary companions in our HIRES spectrum. The secondary line analysis compares the observed spectrum to a suite of about 600 well characterized, slowly rotating HIRES spectra of FGKM stars from the CPS and attempts to identify residuals consistent with a fainter secondary star. For faint, late-type stars like K2-95, this method is sensitive to spectroscopic companions projected within one half the HIRES slit width (04), with approximate V-band fluxes as small as 3% of the primary flux and ${\rm{\Delta }}\mathrm{RV}\gt 10\,\mathrm{km}\,{{\rm{s}}}^{-1}$. This sensitivity range complements our high-resolution imaging. The algorithm also measures the barycentric corrected primary RV using telluric lines. The analysis revealed no secondary lines within the above sensitivity limits. Using the color–temperature conversions of Pecaut & Mamajek (2013), we estimate that the Kolbl et al. (2015) analysis of our HIRES spectrum rules out a large range of close companions on circular orbits down to ∼M5.5 types on ∼75 day or shorter orbits. Additionally, we measure $\mathrm{RV}=35.2\pm 0.2\,\mathrm{km}\,{{\rm{s}}}^{-1}$, consistent with other Praesepe members. The combined RV constraints from our multi-epoch HIRES observations are described further in Section 4.1.

We also use the HIRES spectrum to investigate Hα emission at 6563 Å. Hα emission is a magnetic activity indicator in low-mass stars and can be used to place coarse constraints on a star's age (West et al. 2008). Kafka & Honeycutt (2006) and Douglas et al. (2014) present Hα measurements for low-mass Praesepe members, including K2-95. They find that M3 type stars in Praesepe exhibit a wide range of emission levels, with equivalent widths (EWs) spanning approximately 0 to −8 Å (where negative EWs represent emission). K2-95 is on the low end of the emission distribution for stars of similar spectral type in their studies, with only a hint of weak emission. We show a portion of our HIRES spectrum surrounding Hα in Figure 6 compared to a field age planet host with similar spectral type, K2-9 (Montet et al. 2015; Schlieder et al. 2016). The Hα line morphology of K2-95 is different from the weak absorption observed in the older star K2-9; it exhibits narrow emission peaks in the line wings. This profile is consistent with model predictions for weakly active low-mass dwarfs (Cram & Mullan 1979) and similar to Hα profiles observed for the slowest rotating M dwarfs in the younger Pleiades cluster (P∼15 days, Stauffer et al. 2016). We conservatively estimate ${\mathrm{EW}}_{{\rm{H}}\alpha }=-0.1\pm 0.1$ which is consistent with previous EW measurements and broadly consistent with expectations for an M3 dwarf in Praesepe.

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We further cross-correlated our HIRES spectrum with a slowly rotating, rotationally broadened M dwarf standard to place constraints on the projected rotational velocity v sin i. This analysis revealed that the star has a low rotational velocity with the best-match broadened spectrum having v sin i <3 km s⁻¹. This low v sin i and the long rotation period (∼24 days) estimated from de-trended K2 photometry are consistent with the slowest rotating Praesepe M dwarfs presented in Douglas et al. (2014). Both indications of slow rotation are also consistent with the low level of magnetic activity inferred from the Hα line. The slow rotation of this intermediate-age M dwarf is remarkable when considering its close-in planet (see Section 4) and may indicate differences in angular momentum evolution due to initial conditions, the primordial disk, planet formation, or planet migration. In contrast, the very similar Hyades M dwarf planetary system K2-25 is among the fastest rotating M dwarfs in that cluster with a period of ∼1.9 days (Douglas et al. 2014; David et al. 2016a; Mann et al. 2016a).

Using the Gemini/DSSI speckle results, we can constrain the contamination from nearby sources. The DSSI data in the 880 nm band provide the best constraints to bound and background companions at very close separations. At a separation of $0\buildrel{\prime\prime}\over{.} 1$, our sensitivity to companions is ${\rm{\Delta }}\mathrm{mag}(880\,\mathrm{nm})\,\approx$ 3.5 mag.

Our Keck/NIRC2 AO imaging provides deeper constraints on close background and bound companions at larger separations. At separations of 02 and 05, we estimate sensitivity to companions with ΔK ≈ 5 mag and ΔK ≈ 8 mag, respectively. This effectively rules out all background sources within these separations that could contribute significant flux to the light curve. We use the relations of Pecaut & Mamajek (2013) to estimate that our combined Keck and Gemini imaging rule out all bound companions at the same distance down to the hydrogen burning limit at separations of 01 (17 au) and well into the brown dwarf regime at ≳05 (86 au). We use both our Keck/NIRC2 and Gemini/DSSI contrast curves as constraints in the FPP analysis.

K2-95 was first identified as a candidate member of Praesepe by Williams et al. (1994) and was subsequently included in the proposed member lists of several works including Hambly et al. (1995) and Adams et al. (2002). Kraus & Hillenbrand (2007) combined photometry, astrometry, and the kinematics of well defined cluster members in a maximum likelihood analysis to estimate that K2-95 has a >99% probability of cluster membership. To further investigate its Praesepe membership, we use the star's partial kinematics and the methods described in Lépine & Simon (2009) to estimate a kinematic distance (d_kin) and predicted radial velocity (RV_p). In the analysis we adopt the UVW Galactic velocities of Praesepe from van Leeuwen (2009) and estimate errors using Monte Carlo sampling. We find ${d}_{\mathrm{kin}}=172\pm 14\,\mathrm{pc}$, consistent with our SED-based estimate of the star's distance and the average cluster distance, and ${\mathrm{RV}}_{{\rm{p}}}=34.1\pm 0.9\,\mathrm{km}\ {{\rm{s}}}^{-1}$, consistent with our measured RV from Keck/HIRES spectroscopy. The consistency of these predictions and measurements, along with the spectroscopic indications of activity in our HIRES data, confirm the membership of K2-95 in the low-mass population of Praesepe which places a conservative constraint on its age of 600–800 Myr. We also use the kinematic distance and K-band magnitude of the star to determine its luminosity using the conversions of Pecaut & Mamajek (2013). We estimate ${L}_{* }=0.021\pm 0.003\,{L}_{\odot }$. At the age of Praesepe, an M3 dwarf is expected to be on the main sequence and has stopped radial contraction. We can therefore combine our measured effective temperature and luminosity through the Stefan–Boltzmann law to estimate the star's radius, ${R}_{* }=0.40\pm 0.01\,{R}_{\odot }$. These alternative estimates of the star's fundamental parameters are consistent with those from our SpeX spectroscopy and SED fitting.

For a transiting planet-signal, there are five common sources of false-positive identification or transit mischaracterization, most of which are created by EBs:

• 1.  
  Background star.
• 2.  
  Blended EB system.
• 3.  
  Unblended EB system.
• 4.  
  Double-period EB system.
• 5.  
  Hierarchical EB companion.

Our collected data in form of photometry, spectroscopy, and high-resolution imaging can be used to place a number of constraints on the data to limit or even completely rule out all of the above scenarios. In the K2 data, we detected no secondary eclipse that would be indicative of an EB. Based on archival and high-resolution imaging and high-resolution spectra, a background source is strongly constrained to less than 3% of flux dilution and can be ruled out completely for a separation of more than 0.2 arcsec. This makes any kind of background blend or triple system highly improbable. In a case where it did exist, it would not impact the planet parameters significantly.

For a more quantitative assessment, we utilize the FPP calculator vespa (Morton 2012, 2015) which is open source and freely available online.²⁶ This program compares the light curve to transit shapes created by false-positive sources and combines this with priors about stellar population, multiplicity frequencies and the planet occurrence rate for the corresponding fitted parameters. We supply the algorithm with all of our determined constraints, including stellar photometry from 2MASS and WISE, contrast curves from high-angular resolution imaging and the light curve from K2. Furthermore, we also extract the photometric light curve from Vanderburg & Johnson (2014), remove the periodic modulations, recover the signal with the Pan-Planets signal detection pipeline (Obermeier et al. 2016) and then perform the same analysis. This way, we end up with an independent confirmation based on a different data reduction and signal detection routine. Based on all of the above constraints, the results from vespa rule out all false-positive scenarios to a FPP of less than 0.02% for both analyses. While vespa does not fit blended planetary systems, there are strong constraints on this scenario based on high-resolution imaging and the upper limit of 3% in flux dilution for background sources which makes this scenario highly unlikely. As an additional layer of security, we furthermore obtained three RV points based on high-resolution spectroscopy in order to constrain any EB or double-period EB scenario.

4.1.1. Unblended EB System

The unblended EB scenario consists of very shallow eclipses of both stars which may emulate a planet's transit light curve. There are many constraints to this scenario in the case of K2-95: the signal of a secondary eclipse is absent in the light curve data and the high-resolution spectroscopy excludes the presence of a second star down to 10 km s⁻¹ and 3% flux. Based on both our own observation with HIRES and the two additional data points from J. Pepper et al. (2016, in preparation), we cover a time baseline of  six days that we use to construct a 5σ upper limit for the maximum RV amplitude that could still fit to the data and is shown in Figure 7 in the top panel. The result is an amplitude $941\,{\rm{m}}\,{{\rm{s}}}^{-1}$ which equates to 5.25 ${M}_{{\rm{J}}}$, a giant planet. These limitations mean that this signal cannot be modeled as an unblended EB system.

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4.1.2. Double-period EB System

We analyze the light curve of K2-95 with a approach similar to the one described in more detail by Crossfield et al. (2015).²⁷ In brief: relying on the emcee package (Foreman-Mackey et al. 2013), we use the open-source BATMAN light curve code (Kreidberg 2015) which we optimize for long-cadence data. Utilizing the free and open-source LDTk/pyLDTk package from Parviainen & Aigrain (2015)²⁸ , we propagate our measured T_eff, surface gravity, metallicity and their respective uncertainties into limb-darkening coefficients for use as priors in our fit. The overall fitted parameters in our analysis are the candidate's orbital period P, initial transit time T₀, inclination i, eccentricity e, longitude ω, scaled semimajor axis $a/{R}_{\star }$ and the fractional candidate radius ${R}_{p}/{R}_{\star }$. The starting parameters for the fit are taken from our TERRA output. In the fit, we assume a linear ephemeris for the transits which should be a valid simplification since there is no evidence for any kind of TTV in the light curve. The best-fitting properties and their uncertainties are shown in Table 2. We estimate the planet's mass using the mass–radius relation²⁹ provided by Wolfgang & Lopez (2015) and Wolfgang et al. (2015), $M/{M}_{\oplus }=2.7{(R/{R}_{\oplus })}^{1.3}$ to ${M}_{{\rm{P}}}=13.71\pm 3.62\,{M}_{\oplus }$.³⁰ However, using the relation provided by Weiss & Marcy (2014), $M/{M}_{\oplus }=2.69{(R/{R}_{\oplus })}^{0.93}$, we get ${M}_{{\rm{P}}}={8.77}_{-0.53}^{+1.88}\,{M}_{\oplus }$. A third mass–radius relation, published by Chen & Kipping (2016)^{31 ,32} , yields ${M}_{{\rm{P}}}={8.26}_{-0.50}^{+1.77}\,{M}_{\oplus }$ based on the relation $M/{M}_{\oplus }={(R/{R}_{\oplus })}^{1.70}$. The mass–radius models lead to different estimates of the planet's mass. While the results from Wolfgang & Lopez (2015) are higher than the other two, the difference is still small enough for the masses to be marginally consistent with each other. The absence of TTVs in the system means that the mass cannot be determined through other means as of now. We estimate the RV amplitude of this planet to be $6.8\pm 1.8\,{\rm{m}}\,{{\rm{s}}}^{-1}$, based on the Wolfgang & Lopez (2015) results.

Table 2.  Best-fitting Properties of K2-95 and Its Planet Based on the BATMAN Code

Parameter	Units	K2-95
${T}_{0}$	${\mathrm{BJD}}_{\mathrm{TDB}}$—2454833	${2338.1477}_{-0.0019}^{+0.0018}$
P	day	${10.13389}_{-0.00077}^{+0.00068}$
i	deg	${88.77}_{-1.59}^{+0.86}$
${R}_{P}/{R}_{\star }$	%	${7.86}_{-0.93}^{+1.69}$
${R}_{\star }\ /a\$	⋯	${0.0400}_{-0.0068}^{+0.0187}$
T14	hr	${2.84}_{-0.26}^{+0.36}$
T23	hr	${2.18}_{-0.72}^{+0.26}$
a	au	${0.0653}_{-0.0045}^{+0.0039}$
RP	RE	${3.47}_{-0.53}^{+0.78}$
${R}_{\star }$	${R}_{\odot }$	${0.402}_{-0.050}^{+0.050}$
${M}_{\star }$	${M}_{\odot }$	${0.361}_{-0.069}^{+0.069}$

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