K2-155: A Bright Metal-poor M Dwarf with Three Transiting Super-Earths

We performed high-resolution imaging on the night of UT 2017 September 5 with the WIYN 3.5 m telescope and the NASA Exoplanet Star and Speckle Imager (NESSI; Scott et al., in preparation). This instrument uses high-speed electron-multiplying CCDs (EMCCDs) to obtain 40 ms exposures simultaneously in two bands: a "blue" band centered at 562 nm with a width of 44 nm, and a "red" band centered at 832 nm with a width of 40 nm. The pixel scales of the 'blue' and "red" EMCCDs are 00175649 pix⁻¹ and 00181887 pix⁻¹, respectively. We observed K2-155 along with nearby point-source calibrator stars, spaced closely in time. Following the procedures described by Howell et al. (2011), we used the calibrator images to compute reconstructed 256 pix × 256 pix images in each band, corresponding to 46 × 46.

No additional light sources were detected in the reconstructed images of K2-155. We measured the background sensitivity of the reconstructed images using a series of concentric annuli centered on the target star, resulting in 5σ sensitivity limits (in delta-magnitudes) as a function of angular separation. The 5σ contrast curve as well as the reconstructed image in each band are displayed in Figure 2.

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We observed K2-155 with the Tull Coude Spectrograph (Tull et al. 1995) on the McDonald Observatory 2.7 m Harlan J. Smith Telescope on UT 2017 September 14 and 2017 October 14. The spectrograph is a cross-dispersed echelle instrument covering 375–1020 nm, with increasingly larger inter-order gaps longward of 570 nm. A 1.2 arc-second wide slit projects to 2 pixels on the CCD detector, resulting in a spectral resolving power of 60000. On each date, three successive short exposures were obtained in order to reject cosmic ray events. We used an exposure meter to obtain an accurate flux-weighted barycentric correction, and to establish an exposure time resulting in a signal-to-noise ratio (S/N) of about 30 per pixel. Bracketing exposures of a Th–Ar hollow cathode lamp were obtained in order to generate a wavelength calibration and to remove spectrograph drifts. The raw data were processed using IRAF routines to remove the bias level, inter-order scattered light, and pixel-to-pixel ("flat field") CCD sensitivity variations. We traced the apertures for each spectral order and used an optimal-extraction algorithm to obtain the detected stellar flux as a function of wavelength.

We obtained four high-resolution spectra with the FIbre-fed Echelle Spectrograph (FIES; Frandsen & Lindberg 1999; Telting et al. 2014) on the 2.56 m Nordic Optical Telescope (NOT) at the Observatorio del Roque de los Muchachos, La Palma (Spain). The observations were carried out on UT 2017 December 24, 25, 27, and 2018 January 10 as part of the observing programs 2017B/059 (OPTICON) and 56-209 (CAT). We used the 13 high-resolution fiber (λ/Δ λ = 67000) and set the exposure time to three times 20 minutes, following the same observing strategy as in Gandolfi et al. (2015). We traced the RV drift of the instrument by acquiring Th–Ar spectra immediately before and after each observation. The data were reduced using standard IRAF and IDL routines. The S/N of the extracted spectra is about 20 per pixel at 5500 Å.

We analyzed the high-resolution spectra taken by McDonald 2.7 m/Tull and estimated the stellar parameters. Following Hirano et al. (2017), we used SpecMatch-Emp (Yee et al. 2017) to derive the spectroscopic parameters for K2-155. SpecMatch-Emp tries to match the input observed spectrum to hundreds of library spectra covering a wide range of stellar parameters, and finds a subset of stellar spectra that best match the input spectrum. The stellar parameters (the effective temperature T_eff, radius R_⋆, and metallicity [Fe/H]) are then estimated by interpolating the parameters for the best-matched spectra. We analyzed each of the two Tull spectra separately with SpecMatch-Emp, finding that the results were consistent with each other to within 1σ.²³ To check for the accuracy of our analysis, we also applied the same technique to the FIES spectrum and obtained a fully consistent result.

To derive the stellar mass M_⋆, surface gravity $\mathrm{log}g$, density ρ_⋆, and luminosity L_⋆, we used a Monte Carlo technique based on the empirical relations for the stellar parameters of M dwarfs derived by Mann et al. (2015). Assuming that T_eff, R_⋆, and [Fe/H] returned by SpecMatch-Emp follow independent Gaussian distributions, we perturbed those parameters to estimate M_⋆, $\mathrm{log}g$, ρ_⋆, and L_⋆ through the absolute K_s-band magnitude, which we estimated as 5.52 ± 0.33 mag. The result is shown in Table 1, which also includes the distance of K2-155, estimated from the absolute and apparent K_s-band magnitudes.

Following the method described in Gandolfi et al. (2008), we derived the interstellar reddening along the line of sight (A_v) and obtained an independent estimate of T_eff and $\mathrm{log}g$ for K2-155. Briefly, we built the spectral energy distribution (SED) of the star using the APASS B, g', V, r', 2MASS J, H, K_s, and WISE W1, W2, W3 magnitudes listed in Table 1.

We retrieved the Johnson BV, Sloan g' and r', 2MASS JHK_s, WISE W1, W2, W3, and W4 transmission curves, and absolute flux calibration constants from the Asiago Database on Photometric Systems (Moro & Munari 2000; Fiorucci & Munari 2002) and from Wright et al. (2010). We simultaneously fitted the SED for T_eff and A_v using the BT-SETTL CIFIST synthetic spectra from Baraffe et al. (2015). We assumed a total-to-selective extinction of 3.1 (normal interstellar extinction) and adopted the reddening law from Cardelli et al. (1989). We found a reddening of A_v = 0.095 ±0.050 mag, effective temperature of T_eff = 4200  ±  200 K, and surface gravity of $\mathrm{log}g=5.5\pm 1.0$ (cgs). The result of the SED fit is shown in Figure 3. Both T_eff and $\mathrm{log}g$ are in good agreement with the spectroscopically derived values, corroborating our results. Note that A_v is explored in the positive range, and thus its estimate could be biased toward higher values.

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In order to estimate the absolute radial velocities (RVs) of the star and check for any secondary lines in the high-resolution spectra, we cross-correlated the Tull spectra against the M2 numerical mask (e.g., Bonfils et al. 2013), developed for the precise RV measurement for HARPS-like spectrographs. To take into account the possible wavelength drift of the spectrograph within the night, we also cross-correlated the spectral segment including strong telluric absorptions (6860–6930 Å) against a theoretical telluric template created by the line-by-line radiative transfer model (LBLRTM; Clough et al. 2005). The absolute RV of K2-155 was calculated by subtracting the telluric RV value (whose magnitude is ∼0.5 km s⁻¹) from the stellar RV value, both of which were estimated by inspecting the peaks of the cross-correlation functions (CCFs).

Table 2 lists the absolute RVs measured from the Tull spectra. The mean absolute RV (19.34 ± 0.16 km s⁻¹) by Tull is consistent with the value reported in the literature within 2σ (20.3 ± 0.5 km s⁻¹; Kharchenko et al. 2007), which also suggests that there has been no significant RV variation of the star over the course of ∼10 years.

For the FIES spectra, we measured relative RVs using multi-order cross-correlations. In doing so, we first derived the RVs by cross-correlating the spectra against the first spectrum. We then applied the RV shift and co-added the individual spectra to obtain the combined spectrum. Finally, the co-added spectrum is used to extract the final RVs. Thus, derived relative RVs are listed in Table 2.

To place an upper limit on the mass of any companion, we estimated the upper limit of the RV semi-amplitude K by fitting the data folded by the orbital periods of the planet candidates. In the fit, we introduced an RV offset parameter for each of the two data sets. This yielded K = −8±19 m s⁻¹, $K=-{38}_{-42}^{+39}$ m s⁻¹, and $K=-{26}_{-25}^{+23}$ m s⁻¹ for the inner, middle, and outer planet candidates, respectively, indicating that the observed RVs are consistent with K = 0 m s⁻¹ within ∼1-σ for all three periods (Figure 4). Thus, the eclipsing binary (EB) scenario for the three planet candidates is strongly constrained. The 2σ upper limits on K translate to the upper limits on the companion's mass of 60 M_⊕, 102 M_⊕, and 75 M_⊕, respectively, all of which fall on the planetary regime. As the RV data should be fitted for the three companions simultaneously, however, these cannot be interpreted as the mass upper limits of the planet candidates.

The absence of secondary lines in the CCF for Tull spectra also allows us to place an upper limit on the brightness of any close-orbiting companions. To do so, we fitted the observed CCFs by two components: (1) the observed CCF after flattening the continuum to its average value, and (2) the scaled and Doppler-shifted version of the same CCF to mimic a possible faint companion. Here, we implicitly assume that the spectrum of the hypothetical companion is similar to that of the primary (i.e., a late-type star). For a given Doppler shift for the secondary line (relative RV >15 km s⁻¹), we computed the possible contamination of a secondary peak, and looked for the maximum contamination flux from a hypothetical companion. We conclude that the contamination is no more than 2% of the primary star's flux in the visible band, which corresponds to the lowest mass stars ($\sim 0.1\,{M}_{\odot }$) for the case of K2-155. This is a good constraint on the presence of close-in companion(s), but when the companion has a long orbital distance, the relative RV between the primary and secondary stars becomes small (relative RV $\lesssim 10$ km s⁻¹), and we are not capable of constraining its flux by the present analysis.

The coordinates of K2-155 place it near the same line of sight as the Hyades open cluster. However, K2-155 does not share the same metallicity, proper motion, or radial velocity as typical Hyades stars. The metallicity and mean proper motion of the Hyades are reported to be [Fe/H] = 0.14 ± 0.05 (Perryman et al. 1998) and ${\mu }_{\alpha }\cos \delta =1.4\pm 3.7$ mas yr⁻¹ and μ_δ =  4.3 ± 4.4 mas yr⁻¹ (Dias et al. 2014), respectively. Together with the absolute RV,²⁴ we conclude that K2-155 is in the background of the Hyades.

Based on the coordinates, proper motion, distance, and RV of K2-155, we also computed the galactic space velocity (U, V, W) to the Local Standard of Rest (LSR) as in Table 1. The space velocity components are in agreement with those of both thick disk and thin disk stellar populations (e.g., Fuhrmann 2004), making it impossible to tell on this basis to which population K2-155 belongs. The low stellar metallicity is more consistent with the thick disk.

To determine the planetary parameters, we compared two available light curves: our own light curve as produced in Section 2 and the publicly available light curve provided by Vanderburg & Johnson (2014). The two light curves have almost the same noise level, although our light curve exhibits a slightly larger scatter at the beginning of the K2 observation. We decided to adopt the light curve of Vanderburg & Johnson (2014) for subsequent analysis.

The fitting procedure of the K2 light curve was described in detail by Hirano et al. (2015), which we summarize here. We first split the light curve into chunks each spanning approximately 5 days and fitted each chunk after removing transit signals with a fifth-order polynomial to detrend and obtain the normalized light curve. Then, based on the preliminary ephemerides obtained in Section 2, we extracted small segments of the normalized light curve, which cover the transits of each planet candidate as well as the flux baselines on both sides spanning 2.0 times the transit durations.

For each planet candidate, we simultaneously fitted all of the segments to estimate the global parameters common to all of the segments as well as segment-specific parameters. The global parameters are the scaled semimajor axis a/R_⋆, transit impact parameter b, limb-darkening parameters for the quadratic law (u₁+u₂ and u₁−u₂), orbital eccentricity and argument of periastron ($e\cos \omega$ and e sin ω), and planet-to-star radius ratio R_p/R_⋆. To take into account possible transit timing variations (TTVs), we allowed the mid-transit time T_c to float freely for each light curve segment. We also introduced additional parameters describing the baseline flux variation for each segment, which we assumed to be a linear function of time.

The goodness of fit was assessed with the χ² statistic:

$$\begin{eqnarray}&&{\chi }^{2}=\displaystyle \sum _{i}\displaystyle \frac{{({f}_{\mathrm{obs},i}-{f}_{\mathrm{calc},i})}^{2}}{{\sigma }_{i}^{2}},\end{eqnarray} \tag{ 1 }$$

where f_obs,i and f_calc,i are the observed and calculated flux, and σ_i is the flux uncertainty. For the transit model, we integrated the analytic light curve model of Ohta et al. (2009) over the 30-minute averaging interval of K2 observations. We sampled the posterior distributions of the parameters using our implementation of the Markov Chain Monte Carlo (MCMC) technique (Hirano et al. 2015). In the code, all of the free parameters are first optimized simultaneously by Powell's conjugate direction method (e.g., Press et al. 1992), and the flux baseline parameters are held fixed at the best-fitting values. We then took 10⁶ MCMC steps for each planet candidate with all of the parameters being allowed to adjust. We imposed prior distributions for u₁+u₂ and u₁−u₂ adopted from the table by Claret et al. (2013), assuming Gaussian functions with widths of 0.20. Because close-in planets in multi-planet systems are known to have low eccentricities (Van Eylen & Albrecht 2015), we also imposed Gaussian priors on $e\cos \omega$ and e sin ω with their centers and widths being 0 and 0.05, respectively. For the other parameters, we assumed uniform priors. The reported parameter values and ±1σ errors are based on the 50, 15.87, and 84.13 percentile levels of the marginalized posterior distributions. Table 3 gives the results.

Table 3.  Fitting and Planetary Parameters

Parameter	Value
K2-155b
P (days)	6.34365 ± 0.00028
Tc,0 (BJD−2454833)	2985.7153 ± 0.0021
a/R⋆	${20.3}_{-6.1}^{+3.2}$
b	${0.50}_{-0.33}^{+0.30}$
Rp/R⋆	${0.0271}_{-0.0012}^{+0.0023}$
u1	0.36 ± 0.13
u2	0.41 ± 0.14
Rp (R⊕)	${1.55}_{-0.17}^{+0.20}$
a (au)	0.0546 ± 0.0019
Sp (S⊕)	19.9 ± 4.5
K2-155c
P (days)	13.85402 ± 0.00088
Tc,0 (BJD−2454833)	2981.5643 ± 0.0025
a/R⋆	${30.0}_{-9.8}^{+6.2}$
b	${0.57}_{-0.39}^{+0.27}$
Rp/R⋆	${0.0339}_{-0.0016}^{+0.0031}$
u1	0.33 ± 0.13
u2	${0.40}_{-0.14}^{+0.13}$
Rp (R⊕)	${1.95}_{-0.22}^{+0.27}$
a (au)	0.0920 ± 0.0032
Sp (S⊕)	7.0 ± 1.6
K2-155d
P (days)	40.6835 ± 0.0031
Tc,0 (BJD−2454833)	2949.8324 ± 0.0048
a/R⋆	${73.5}_{-15.9}^{+8.4}$
b	${0.41}_{-0.28}^{+0.30}$
Rp/R⋆	${0.0286}_{-0.0010}^{+0.0015}$
u1	0.32 ± 0.12
u2	${0.38}_{-0.13}^{+0.14}$
Rp (R⊕)	${1.64}_{-0.17}^{+0.18}$
a (au)	0.1886 ± 0.0066
Sp (S⊕)	1.67 ± 0.38

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Based on the mid-transit times, we calculated the ephemerides (P and T_c,0) for each planet under the assumption of a constant period. Figure 5 shows the observed minus calculated (O − C) T_c plots for the three candidates. The period ratio between K2-155b and K2-155c is somewhat close to 1:2, but Figure 5 exhibits no clear sign of TTVs. In the bottom panels of Figure 1, we display the folded transits along with the model light curves (solid lines) based on the parameters given in Table 3.

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As K2-155 has three planet candidates, the probability that any of the candidates will turn out to be an FP is extremely low. Lissauer et al. (2012) calculated the odds that the systems of multiple transiting planet candidates are FPs. For three-planet systems, they found that fewer than one such system is expected to contain an FP among the entire Kepler sample. In this sense, the presence of three candidates is self-validating. Below, we investigate the constraints on FP scenarios based on direct follow-up observations rather than the statistical argument of Lissauer et al. (2012).

As shown in Section 4.2, the absence of a large RV variation ($\gtrsim 100$ m s⁻¹) as well as a secondary peak in the CCFs implied that the transit signals are not caused by a stellar companion orbiting and occulting K2-155 (i.e., EB). The remaining possible FP scenarios are background eclipsing binaries (BEB) and hierarchical-triple eclipsing binaries (HEB). However, these scenarios are also constrained by the lack of bright nearby sources in the reconstructed image from the speckle observations (Figure 2). In addition, checking the POSS1 archival images taken in 1950 (Figure 6), we found no bright star at the current position of K2-155, verifying that no background sources are hidden in the reconstructed image of K2-155 by chance alignment.

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As the speckle observations with WIYN/NESSI are only able to find companions in the proximity of the target, it is still possible that a fainter object at a large separation is blended in the K2 aperture, which could be responsible for the transit-like photometric signals. We thus searched for fainter objects within 20'' from K2-155 using the SDSS photometric catalog (Alam et al. 2015). As a consequence, we identified five stars within 12''–20'' from K2-155, but all of those stars have r-band magnitudes (similar to the Kepler magnitudes) fainter than 20 mag. The r-magnitude of K2-155 is 12.437 ± 0.002 mag, and thus the maximum magnitude that can produce an eclipse depth of 0.1% is r = 19.9 mag (100% occultation). Therefore, we conclude that K2-155 is the source of the transit signals.

Regarding the HEB scenario, the speckle observations achieved a 5σ contrast of 4.2 mag (562 nm) at 02, corresponding to the mass upper limit of ≈0.1 M_⊙ for a possible bound companion (e.g., Dotter et al. 2008) at the projected separation of ≈12 au and further. There is still a possibility, however, that a very late-type star is orbiting K2-155 at an orbital distance of 1–12 au; for instance, a 0.1 M_⊙ star with P = 2 year exerts an RV semi-amplitude of only ≈3 km s⁻¹, which could be overlooked in the RV data (Table 2). But even if this is the case and the bound later-type star is responsible for the transit signals, the depths of these candidates correspond to those of "planets."

The fact that K2-155 is transited by the three planet candidates is corroborated by comparing the mean stellar density inferred from spectroscopy (ρ_⋆ = 3.84 ± 0.79 ρ_⊙) with the mean stellar density implied by the transit modeling. The scaled semimajor axes a/R_⋆ in Table 3 are translated into the mean stellar densities of ${2.8}_{-1.8}^{+1.6}\,{\rho }_{\odot }$ for the inner, ${1.9}_{-1.3}^{+1.4}\,{\rho }_{\odot }$ for the middle, and ${3.2}_{-1.7}^{+1.2}\,{\rho }_{\odot }$ for the outer planet, respectively. Hence, the stellar densities estimated from transit modelings are consistent with the spectroscopic density for K2-155 within about 1σ, but would be inconsistent with later-type stars; according the observed mass–radius relation for M dwarfs (e.g., Mann et al. 2015), the mean density of mid-to-late M dwarfs with ${M}_{\star }\lt 0.4\,{M}_{\odot }$ is higher than ≈6 ρ_⊙.

To quantify the false positive probability (FPP) of each planet candidate, we used the statistical framework implemented in the vespa software package (Morton 2012, 2015). This code simulates FP scenarios using the TRILEGAL Galaxy model (Girardi et al. 2005) and assesses the likelihoods of EB, BEB, and HEB scenarios. The inputs to vespa are the phase-folded light curve, the size of the photometric aperture, contrast curves from high-resolution imaging, the maximum secondary eclipse depth allowed by the K2 light curve, as well as the broadband photometry and spectroscopic stellar parameters of the host star. The FPPs computed by vespa are below 10⁻⁵ for all three planet candidates of K2-155. However, because vespa considers each planet individually, it does not take into account the "multiplicity boost" suggested by Lissauer et al. (2012), who found that planet candidates belonging to stars with three or more candidates are a priori ∼100 times more likely to be valid planets than single candidates. This means that the FPPs computed by vespa are likely to be overestimated by two orders of magnitude. Each of K2-155's three planet candidates are therefore below the fiducial validation threshold of 1% FPP by some five orders of magnitude. Thus, all three candidates are quantitatively validated, in addition to our independent determination of the low likelihoods of FP scenarios. We conclude that the three candidates of K2-155 are indeed bona fide planets.

K2-155 is similar to K2-3 (Crossfield et al. 2015) in many aspects. Both stars are relatively bright early M dwarfs (V = 12.81 mag for K2-155 and V = 12.17 mag for K2-3) hosting three transiting super-Earths. Table 4 summarizes the planetary parameters for the two systems (Dai et al. 2016; Fukui et al. 2016; Hirano et al. 2017). In both systems, the outermost transiting planets receive stellar insolations that are slightly higher than the solar insolation on the Earth (1 S_⊕), but less than ≈2 S_⊕. One difference between the two systems is the size ordering of the planets. For K2-155 the middle planet is the largest, while for K2-3 the inner planet is the largest.

Table 4.  Comparison between the K2-155 System and K2-3 System

Planet	P (days)	Rp (R⊕)	Sp (S⊕)	Planet	P (days)	Rp (R⊕)	Sp (S⊕)
K2-155b	6.34365 ± 0.00028	${1.55}_{-0.17}^{+0.20}$	19.9 ± 4.5	K2-3b	${10.05403}_{-0.00025}^{+0.00026}$	1.90 ± 0.20	8.7 ± 2.0
K2-155c	13.85402 ± 0.00088	${1.95}_{-0.22}^{+0.27}$	7.0 ± 1.6	K2-3c	24.6454 ± 0.0013	1.52 ± 0.17	2.64 ± 0.59
K2-155d	40.6835 ± 0.0031	${1.64}_{-0.17}^{+0.18}$	1.67 ± 0.38	K2-3d	44.55612 ± 0.00021	1.35 ± 0.16	1.20 ± 0.27

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The outer planet (K2-155d) has a relatively long orbital period and receives a stellar insolation flux similar to that of Earth (S = 1.67 ± 0.38 S_⊕). This implies that K2-155d is located in or near the habitable zone around K2-155. Another factor affecting potential habitability is whether the planet has a solid surface or is smothered by a massive atmosphere. Rogers (2015) noted that planets larger than 1.6 R_⊕ are likely to possess volatile-rich atmospheres. The size of K2-155d (≈1.64 R_⊕) is very close to this boundary. It also falls within the observed "valley" in the planet radius distribution (Fulton et al. 2017), making it a particularly interesting target for characterizing its internal structure and atmosphere. Recently, Van Eylen et al. (2017) confirmed the presence of the radius gap with more precise measurements of stellar and thus planetary radii, and found that its dependence on the orbital period suggests that it is likely caused by photoevaporation.

At this point, it is unclear whether K2-155d is rocky or not, until we make a precise mass measurement by RV or TTV observations. We decided to investigate whether the planet would be habitable if it does turn out to have an Earth-like composition and atmosphere. Three-dimensional (3D) global climate simulations have shown that tidally locked planets can have a moderate surface temperature in a wide range of orbital distance due to the climate-stabilizing effects of dayside clouds (Yang et al. 2013; Kopparapu et al. 2016) but may undergo the classical moist greenhouse state at the higher end of the incident flux. Recent studies suggested that for an Earth-sized planet with a nitrogen-dominated atmosphere around an M1 star, this occurs when the total incident flux exceeds ≈1.4 S_⊕ (Fujii et al. 2017; Kopparapu et al. 2017).

In earlier studies, the planet was assumed to be an Earth-sized one (1.0 R_⊕) with the Earth's surface gravity. In order to find a possible climate specifically for K2-155d, we ran a series of global climate simulations using a 3D General Circulation Model ROCKE-3D (Way et al. 2017), fixing the planetary parameters at the values of K2-155d. The setup is equivalent to the model coupled with a dynamic ocean (900 m depth) used in Fujii et al. (2017), except that the planetary size and the rotation/orbital period are specified for K2-155d. Namely, the planetary radius is fixed at 1.6 R_⊕ and its mass is set to 4.2 M_⊕ based on the empirical relation of Weiss & Marcy (2014). Given the proximity to the star, the three planets around K2-155 are expected to be tidally locked (e.g., Kasting et al. 1993; Barnes 2017), and thus the rotation period is assumed to be equal to the orbital period (40.6835 days). For the input stellar spectrum, we adopted the PHOENIX atmosphere model (BT-SETTL; Allard et al. 2013) for which we adopted the stellar parameters of K2-155. We assumed the planet is covered with a thermodynamic ocean, and assumed a 1 bar N₂ atmosphere and 1 ppm of CO₂ as in Fujii et al. (2017). We increased the incident flux from 1.29 S_⊕ (the 1σ lower limit of S_p in Table 3) to 1.67 S_⊕ (the best-fit value) and checked the range that allows for the planet to have a moderate surface temperature. The upper panel of Figure 7 shows the water mixing ratio at 1 mbar for varying incident flux, while the lower panel presents the corresponding maximum, global average, and minimum surface temperatures.

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Similarly to previous works for an Earth analogue, equilibrium climates were secured up to S_p ≈ 1.5 S_⊕. Above this limit, the model surface temperature continues to increase until it enters the regime where the model is invalid and the simulation stops. When the insolation is close to or lower than 1.5 S_⊕, the surface temperature remains moderate, comparable to that of the Earth. The upper humidity increases gradually as incident flux increases and is about to cross the classical moist greenhouse state at about 1.5 S_⊕. Thus, K2-155d has a potential of being habitable if the incident flux turns out to be close to the lower end within the uncertainty range, though the actual habitability also depends on other factors including its atmosphere, water content, and initial stellar luminosity (e.g., Luger & Barnes 2015; Tian & Ida 2015). Another important factor that potentially affects the habitability is the presence of frequent flares of the host star (e.g., Vida et al. 2017). We inspected the K2 light curve of K2-155 but found no such event over the course of 80 days.

Given the brightness for an M dwarf, K2-155 is an attractive target for future follow-up studies, including Doppler mass measurements and transit photometry. Among M dwarfs (T_eff ≤ 4000 K) with transiting planets, K2-155 is the fourth brightest star in the V-band, after GJ 436, K2-3, and GJ 3470. It is also the second brightest M dwarf in optical passbands (after K2-3) having a possibly habitable transiting planet (${S}_{p}\lesssim 2.0\,{S}_{\oplus }$).

Based on the empirical mass estimates by Weiss & Marcy (2014), we estimate the RV semi-amplitudes of the planets to be K ≈ 2.1 m s⁻¹, 2.0 m s⁻¹, and 1.2 m s⁻¹ for the inner, middle, and outer planets, respectively, suggesting that the masses of at least inner two planets could be constrained by gathering a large number (∼50–100) data points with a precision of 2–3 m s⁻¹ (e.g., Guenther et al. 2017). Although challenging, observations of M dwarfs of similar magnitude (e.g., K2-3) have shown that RV precisions of 2–3 m s⁻¹ were achieved by TNG/HARPS-N and Magellan/PSF (e.g., Almenara et al. 2015; Dai et al. 2016), and thus these measurements seem feasible with high precision spectrographs on 8–10 m telescopes such as Keck/HIRES. Considering that the three planets straddle the rocky to volatile-rich boundary (Rogers 2015) and also the radius gap suggested by Fulton et al. (2017), the comparison between the mean densities of these planets may provide some insight into the origin of close-in super-Earths in multi-planet systems.

We note that the expected RV jitter for K2-155 is small. In order to estimate the rotation period of the star, we computed the Lomb–Scargle periodogram and auto-correlation function of the light curve (McQuillan et al. 2014), both of which are shown in Figure 8. Both methods yielded similar estimates for the rotation period (${P}_{\mathrm{rot}}={47.5}_{-9.0}^{+19.3}$ days and ${P}_{\mathrm{rot}}={46.2}_{-5.6}^{+8.1}$ days, respectively), although the detected period could be an alias given the short observing span of K2 (∼80 days). Using this tentative rotation period together with the stellar radius (R_⋆ = 0.526 R_⊙), we estimate the equatorial velocity of the star as ≈0.58 km s⁻¹, which is the maximum value for the projected stellar spin velocity (v sin i). The K2 light curve exhibits the photometric variation amplitude of ≈0.2%, and hence the maximum stellar jitter in the visible wavelengths should be no more than ≈1 m s⁻¹.

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Transiting planets with relatively long orbital periods (P > 30 days) detected by K2 sometimes suffer from the problem of "stale ephemerides" due to the small number of observed transits. Indeed, only two transits of K2-155d were observed by K2, leading to a large uncertainty in its orbital period. Follow-up transit observations are encouraged to enable accurate long-term predictions of transit times. K2-155 could be a good target for the upcoming CHEOPS space mission (CHaracterizing ExOPlanet Satellite; Broeg et al. 2013), which is specifically designed to observe low-amplitude transits around bright stars. The orbital periods of K2-155b and K2-155c appear to be close to a 2:1 mean-motion resonance and those of K2-155c and K2-155d are close to a 3:1 resonance, but no clear signs of TTVs were seen in the O–C diagrams (Figure 5). It will be interesting to see if future transit observations reveal any TTVs in this system.

The brightness of K2-155 also facilitates transit spectroscopy as a means of probing the atmospheres of the super-Earths. Following Niraula et al. (2017), we plot in Figure 9 the "relative S/N" of transmission spectroscopy for known transiting planets except hot Jupiters (R_p < 6.0 R_⊕) around M dwarfs, based on the stellar and planet radii, atmospheric scale height, V-band magnitude, and transit duration (see Equation 1(b)) and (b) of Niraula et al. 2017). We here plotted the S/N per transit rather than the S/N for a given period of time as in Niraula et al. (2017). The three planets around K2-155 are plotted with the colored circles. Many Neptune-class planets (R_p = 2.0–6.0 R_⊕ ; according to Kepler's classification) show a higher S/N, but among super-Earths and Earth-like planets (R_p < 2.0 R_⊕), K2-155c is one of the best targets for transmission spectroscopy. Figure 9 also shows that K2-155d is a good target in the sample as a possibly habitable super-Earth.

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The actual signal amplitudes of the three super-Earths depend on the (unknown) scale heights of their atmospheres. The atmospheric feature in transmission spectroscopy is of the order of 10H · R_p/R_⋆², where H is the atmospheric scale height (Miller-Ricci et al. 2009). When a cloud-free hydrogen-dominated atmosphere is assumed, the variation amplitude in transit depth is expected to be 60 ppm (K2-155d) to 120 ppm (K2-155c), which would be detectable by observations from the space (e.g., Hubble Space Telescope). But if the planets have an Earth-like atmosphere (i.e., mean molecular weight of μ ∼ 30), the expected signal would be 4–8 ppm and its detection would be challenging.