The SOPHIE search for northern extrasolar planets XV. A Warm Neptune around the M-dwarf Gl378

We present the detection of a Warm Neptune orbiting the M-dwarf Gl378, using radial velocity measurements obtained with the SOPHIE spectrograph at the Observatoire de Haute-Provence. The star was observed in the context of the SOPHIE exoplanets consortium's subprogramme dedicated to finding planets around M-dwarfs. Gl378 is an M1 star, of solar metallicity, at a distance of 14.96 pc. The single planet detected, Gl378 b, has a minimum mass of 13.02 $\rm M_{Earth}$ and an orbital period of 3.82 days, which place it at the lower boundary of the Hot Neptune desert. As one of only a few such planets around M-dwarfs, Gl378 b provides important clues to the evolutionary history of these close-in planets. In particular, the eccentricity of 0.1 may point to a high-eccentricity migration. The planet may also have lost part of its envelope due to irradiation.


Introduction
The mass-period diagram is an important diagnostic of the formation and evolution of planetary systems. There is a known dearth of Neptune-size exoplanets at short orbital periods compared to both Jupiter-size and Earth-size planets, which is generally referred to as the Neptune or sub-Jovian desert (Lecavelier Des Etangs 2007;Davis & Wheatley 2009;Szabó & Kiss 2011;Beaugé & Nesvorný 2013;Helled et al. 2016;Mazeh et al. 2016). It is unlikely to be an observational bias, but is more probably due to photoevaporation and/or high-eccentricity migration (Owen & Lai 2018;Ionov et al. 2018).
Statistics on M-dwarf planets remain less certain than those on planets around Sun-type stars, due to the comparatively small number of detections, though these detections are expected to increase thanks to several current or upcoming projects such as SPIRou (Artigau et al. 2014), CARMENES (e.g. Quirrenbach et al. 2014Quirrenbach et al. , 2016, HADES (e.g. Affer et al. 2016), and NIRPS (Bouchy et al. 2017) in radial velocity;or TESS (NASA mission, launched in April 2018, Ricker 2016, TRAPPIST (e.g. Gillon et al. 2017), SPECULOOS (Delrez et al. 2018), and ExTrA  in transits. Nevertheless, it is clear that while hot Jupiters are rare around M dwarfs, short-period Earths and superEarths are numerous; however, hot Neptunes remain unusual, making up only about 3% of the sample of known exoplanets around M dwarfs (e.g. Bonfils et al. 2013;Dressing & Charbonneau 2015;Hirano et al. 2018).
The SOPHIE exoplanet consortium has led several ongoing exoplanet-hunting programmes on the SOPHIE spectrograph at the Observatoire de Haute Provence since 2006 (Bouchy et al. 2009). Sub-programme 3, also known as SP3, is dedicated to the hunt for exoplanets around M-dwarf stars. Via a systematic survey of a volume-limited sample of M dwarfs within 12 parsecs of the Sun, it seeks to detect superEarths and Neptunes, constrain the statistics of planets around M dwarfs, and find potentially transiting companions. With a general radial velocity precision of 1-2 m s −1 on solar-type stars, SOPHIE has proved to be a successful planet hunter. For the SP3 in particular, we recently published the first two exoplanets from this sub-programme: the detection of Gl 96 b and the independent confirmation of Gl 617A b (Hobson et al. 2018).
In this work, we report the detection of a warm Neptune on the lower boundary of the hot Neptune desert, orbiting the M dwarf Gl 378, which was observed as part of this survey. We describe the data and its analysis in Sects. 2 and 3, respectively. The results are presented in Sect. 4 and discussed in Sect. 5. Finally, we conclude in Sect. 6.

Observations
Observations for Gl 378 were gathered between 2015 and 2018 with the SOPHIE+ spectrograph (Perruchot et al. 2011;Bouchy et al. 2013). A total of 62 spectra were obtained. All the observations were performed with simultaneous sky measurement in order to check for potential moonlight contamination. Additionally, a ThAr or FP calibration spectrum was obtained immediately prior to each observation in order to measure the instrumental drift (average value: 1 m s −1 ). For the observations where the velocity difference between the moon and the star was less than 20 km s −1 , a merit function was applied, computed from the velocity difference and the S/N and CCF contrast in fibre B, in order to identify possible contamination. In this way, 18 observations were found to be contaminated by the moon and were discarded, leaving a total of 44 spectra. We note that retaining these observations does not change the final planetary parameters within the uncertainties, but it does increase the noise. With an exposure time of 1800 s, the spectra have a median S/N of 83 (at 650 nm), resulting in a photon noise of ≈3 m s −1 . For this star the photon noise is a little higher than that of instrument systematics (1-2 m s −1 ).

Data analysis
The data were reduced using the SOPHIE Data Reduction Software (DRS, Bouchy et al. 2009), which computes the radial velocity (RV) by cross-correlation functions (CCF). For M dwarfs this approach does not use all the Doppler content, so we extracted RVs through a template-matching algorithm. We shifted all the spectra to a common reference frame using the DRS RVs, and co-added them to build a high S/N stellar template. This template was Doppler shifted over a series of guess RVs, producing a Chi-square profile whose minimum corresponds to the maximum likelihood RV (Astudillo-Defru et al. 2015, 2017b. SOPHIE shows long-term variations in the zero-point, an effect first described in Courcol et al. (2015). We constructed an up-to-date correction from the SP3 stars, plus the four solar-type "super-constant" stars of the SOPHIE high-precision programmes as defined by Courcol et al. (2015), in the same way as in Hobson et al. (2018). Our updated constant correction uses ten stars: the four super-constants HD185144, HD 221354, HD 89269A, and HD 9407; the three SP3 constants Gl 411, Gl 514, and Gl 686; and the additional SP3 stars Gl 521, Gl 15A, and Gl 694, selected because they have a corrected rms after the first iteration lower than 3 m s −1 (as defined by Courcol et al. 2015). Figure 1 shows the correction and the data used to derive it 1 .
The final radial velocities, which have a mean error bar of 3 m s −1 (including photon noise and instrumental error, following Astudillo-Defru et al. 2015), are reported in Appendix A, and were analysed with the Data and Analysis Center for Exoplanets (DACE) web platform 2 . We employed the Keplerian fitting tools (which follow Delisle et al. 2016) and the Markov chain Monte Carlo (MCMC) analysis facilities (described in Díaz et al. 2014Díaz et al. , 2016.

Activity indicators
The main spectral activity indicators are the Hα index, the log(R HK ) index, and the CCF bisector. We followed Boisse et al. (2009) to compute the Hα index; Astudillo-Defru et al. (2017a) to determine the log(R HK ) index from the Ca II H and K lines measured in the spectrum; and obtained the CCF bisector from the SOPHIE DRS. Since the Na I D lines have been shown to be good activity indicators for M dwarfs (Díaz et al. 2007; Gomes da Silva et al. 2011), we also calculated the Na index as defined by Gomes da Silva et al. (2011) from our SOPHIE spectra. The values obtained are given in Appendix A.

Stellar parameters
The stellar parameters are listed in Table 1. Gl 378 was characterised in Gaidos et al. (2014), where we obtained spectral type, magnitudes and colour indices (except for the K magnitude, which was taken from Cutri et al. 2003), effective temperature, and luminosity. The coordinates, parallax, and distance were taken from the Gaia DR2 (Gaia Collaboration 2016, 2018). We

Results
The time series of the radial velocities is shown in Fig. 2, and its periodogram in Fig. 3. The periodogram shows a clear peak at 3.82 d, which by bootstrap resampling we place below a 0.01% false alarm probability (FAP). The other notable peaks, at 0.79 d and 1.35d, are 1-day aliases of the 3.82 d period; they are systematically weaker than the 3.82 d peak, and attempted Keplerian fits have higher σ (O−C) . We also computed the l1-periodogram as in Hara et al. (2017), which is shown in Fig. 4, and confirms the 3.82 d signal as the most significant. The periodograms of the four activity indicators described in Sect. 3.1 are shown in Fig. 5. None of them shows any peaks below 10% FAP, or any peak whatsoever at the 3.82 d period found in the RVs. Likewise, there is no anti-correlation in evidence between the RVs and the CCF bisector. Additionally, for an M dwarf, a rotation period of 3.82 d would lead to an extremely high activity level, with saturated chromospheric emission of Hα (Delfosse et al. 1998) and Ca (Astudillo-Defru et al. 2017a), which is clearly not the case for Gl 378. Finally, Houdebine (2010) found Gl 378 to be a slow rotator, with v sin i = 2.25 km s −1 . Therefore, we conclude that the 3.82 d peak cannot be of stellar origin, and that Gl 378 shows no evidence of clear stellar activity (at the estimated rotation period of P Rot = 40.5 ± 4 d, indicated by the shaded grey regions in Fig. 5, or any other period) in the SOPHIE spectra.   We employed the DACE platform to fit a Keplerian signal to the 3.82 d period. The highest peak in the periodogram of the residuals has a FAP of 17%, and is therefore not significant (Fig. 6). In order to sample the joint posterior distribution of the model parameters, we carried out an MCMC analysis. We used a model with a single Keplerian and an additive stellar jitter. The resulting parameters are summarised in Table 2, with the full outputs available in Appendix B. The phase-folded data and fitted Keplerian are shown in Fig. 7.

Discussion
With a minimum mass of 13.63 M Earth and an orbital period of 3.82 d, Gl 378 b is a warm Neptune-like exoplanet. Depending on the heat redistribution factor and albedo assumed, we obtain equilibrium temperatures in the range of T eq ≈ 630 K (for a heat redistribution factor of 1 and an albedo of 0.3, close to that of Neptune) to T eq ≈ 830 K (for a redistribution factor of 2 and an albedo of 0, as a lower limit). Its orbital parameters place it on the lower boundary of the Neptune desert as defined by Mazeh et al. (2016), as shown in Fig. 8, although they note that the lower boundary is somewhat blurry, and other authors (e.g. Owen & Lai 2018) have placed the external limit in period at P ≈ 3 d rather than P ≈ 5 d. This location on the lower boundary rather than within the desert, and its range of probable equilibrium temperature well below the methane condensation temperature of 1200 K, lead us to classify it as a warm rather than a hot Neptune. Notes. For each parameter the median of the posterior is given, with error bars computed from the MCMC analysis using a 68.3% confidence interval. σ O−C corresponds to the weighted standard deviation of the residuals around the best solutions. All the parameters probed by the MCMC can be found in Table B.1. The lower boundary is believed to have its origin in photoevaporation (Owen & Lai 2018). Therefore, Gl 378 b may have lost at least part of its gaseous envelope due to the X-ray and EUV irradiation from its host star. We note that the young active phase is long for M dwarfs compared to Sun-type stars, giving more time for evaporation to work. If we assume that the mass of Gl 378 b is close to its M sin i, it is likely similar to GJ 436 b Lavie et al. 2017) and GJ 3470 b (Bourrier et al. 2018a). These planets are warm Neptunes, in the same region of the mass-period diagram as Gl 378 b (Fig. 8), and orbit M-dwarf stars. Both are surrounded by giant hydrogen exospheres; GJ 436b possibly became a warm Neptune recently due to a late high-eccentricity migration and is thus currently not losing much mass (Bourrier et al. , 2016(Bourrier et al. , 2018b, while GJ 3470b is much more irradiated by its younger and earlier-type star and could have lost up to 35% of its mass already (Bourrier et al. 2018a). This suggests that the warm Neptune population at the border of the desert is particularly sensitive to atmospheric escape, and supports this mechanism as the reason why hot Neptunes are missing. The three planets also have similar non-zero eccentricities (Deming et al. 2007;Kosiarek et al. 2019), which may point to high-eccentricity rather than disk-driven migrations. Therefore, objects like Gl 378 b are crucial to understanding the evolution of close-in planets, providing we can characterise them.
A fuller characterisation of the planet would require knowledge of its density, and therefore of its radius. The transit probability of a planet detected by radial velocity can be approximated by P(transit) ≈ R /a, with R the stellar radius and a the semi-major axis of the planetary orbit (Borucki & Summers 1984). For Gl 378 b, we obtain a transit probability of P(transit) = 6.5 ± 0.5%. As Gl 378 b is most likely a Neptunemass exoplanet, the analysis of Stevens & Gaudi (2013) suggests this transit probability is likely underestimated: they derive the posterior transit probability from the prior distributions of planetary masses and inclinations, finding that physically motivated distributions from planet formation models yield increased posterior transit probabilities for Neptune-mass planets. The transit depth is given by ∆F = (R p /R ) 2 . Using the mass-radius relation of Chen & Kipping (2017), we estimate the radius of Gl 378 b as R p ≈ 4.67 R ⊕ ; when combined with the stellar radius, this value gives a transit depth of ∆F ≈ 0.58%. This could be observed by ground-based surveys, and should be easily detectable by spacebased missions such as TESS (Barclay et al. 2018) or CHEOPS (Rando et al. 2018).
The metallicity estimated for the host star, Gl 378, from our SOPHIE spectra is [Fe/H] = 0.06 ± 0.09. This solar metallicity is in line with the tendency for M dwarfs hosting planets to be comparatively more metal rich (e.g. Courcol et al. 2016, Hirano et al. 2018, who find [Fe/H] 0 for planet hosts) with respect to the sub-solar average metallicity of nearby M dwarfs (e.g. Schlaufman & Laughlin 2010, who report [Fe/H] = −0.17 ± 0.07, and Passegger et al. 2018, who find mainly subsolar values for the CARMENES target sample) and also with findings that hot Neptunes are more common with increasing metallicity (Petigura et al. 2018, although it is a study on the Kepler survey where the planets are thus categorised by radius rather than mass).
The activity indicators analysed show no evidence for quasiperiodic stellar activity signals. Likewise, the residuals of the Keplerian fit to the 3.82 d planet show no significant periodicity, although statistics on M dwarfs indicate that most of their planets are found in multi-planet systems (e.g. Bonfils et al. 2013;Dressing & Charbonneau 2015). However, the σ O−C (weighted standard deviation of the residuals around the best solution) is high compared to the mean error bar of the observations, suggesting that there are further effects in the data, i.e. additional planets, stellar activity signals, and/or systematics. As an M dwarf, Gl 378 is faint in the visible, emitting most of its radiation in the infrared; consequently, high-precision infrared spectroscopy could help to detect further planets or place limits on their existence.

Conclusions
We have presented the detection of a Neptune-mass planet orbiting the M dwarf Gl 378 at a period of 3.82 d. Its orbital parameters place it at the edge of the hot Neptune desert, though with a sin(i) degeneracy on the mass. Transit observations could help to break this degeneracy: if the planet transits the inclination can be measured, while a non-detection can place limits on it. Transit measurements would also provide the radius and therefore the density, permitting a characterisation of its probable composition. Finally, if the planet transits, we should be able to characterise its atmosphere in the UV/Ly-α line, given the brightness and close distance of its host star to us, and because the planet is a warm Neptune and therefore likely surrounded by a giant hydrogen exosphere. This exosphere can extend beyond the Roche lobe, resulting in an effective planet radius in UV an order of magnitude larger than the optical radius, and hence a slightly increased transit probability. Therefore, UV/Ly-α observations at the expected transit times would be interesting even if the planet does not transit in the optical.
Although we do not detect any other periodic signals in our data, it is statistically likely that more planets are present. Monitoring this star with infrared spectroscopy should help to resolve this question, and to refine the ephemeris of Gl 378b for transit searches. We hope to observe Gl 378 with SPIRou in the near future.

Appendix A: Radial velocities
In this appendix, we present the radial velocities obtained for Gl 378 from SOPHIE+ using template-matching, corrected for the nightly drift and the long-term variations of the zero-point.