TOI-4860 b, a short-period giant planet transiting an M3.5 dwarf

We report the discovery and characterisation of a giant transiting planet orbiting a nearby M3.5V dwarf ( d = 80 . 4pc, G = 15.1mag, K =11.2mag, R ⋆ = 0 . 358 ± 0 . 015 R ⊙ , M ⋆ = 0 . 340 ± 0 . 009 M ⊙ ). Using the photometric time series from TESS sectors 10, 36, 46, and 63 and near-infrared spectrophotometry from ExTrA, we measured a planetary radius of 0 . 77 ± 0 . 03 R J and an orbital period of 1.52 days. With high-resolution spectroscopy taken by the CFHT/SPIRou and ESO/ESPRESSO spectrographs, we refined the host star parameters ([Fe / H] = 0 . 27 ± 0 . 12) and measured the mass of the planet (0 . 273 ± 0 . 006 M J ). Based on these measurements, TOI-4860b joins the small set of massive planets ( > 80 M E ) found around mid to late M dwarfs ( < 0 . 4 R ⊙ ), providing both an interesting challenge to planet formation theory and a favourable target for further atmospheric studies with transmission spectroscopy. We identified an additional signal in the radial velocity data that we attribute to an eccentric planet candidate ( e = 0 . 66 ± 0 . 09) with an orbital period of 427 ± 7 days and a minimum mass of 1 . 66 ± 0 . 26 M J , but additional data would be needed to confirm this.


Introduction
Twenty-five years ago, the discovery of GJ 876 b, a planet with twice the mass of Jupiter, marked an important milestone in exoplanet research (Marcy et al. 1998;Delfosse et al. 1998).It was the first planet detected around an M dwarf, and only the ninth exoplanet found around a main-sequence star at that time.The discovery of GJ 876 b soon after the detection of 51 Pegasi b around a solar-type star (Mayor & Queloz 1995) suggested that giant planets could form just as easily around late-type stars.The pace of planet detections around M dwarfs, however, remained much behind that around FGK stars, and giant planets appear to have a decreasing occurrence rate with decreasing stellar mass (Endl et al. 2006;Johnson et al. 2007;Bonfils et al. 2005).
Probing the whole sky for transiting planets, the Transiting Exoplanet Survey Satellite (TESS; Ricker et al. 2015) survey vastly expanded the target list and therefore was better able to detect rare outcomes of planet formation.A new planet population emerged: giant planets around very low-mass stars (e.g.TOI-519 b, Kagetani et al. 2023;TOI-3714 b, Cañas et al. 2022;TOI-3757 b, Kanodia et al. 2022;TOI-5205 b, Kanodia et al. 2023;and TOI-3235 b, Hobson et al. 2023).These planets are massive in comparison to expectations for protoplanetary disk masses around M dwarfs (Andrews et al. 2013;Gaidos 2017) and therefore are interesting for the investigation of planetary formation.
Recently, Bryant et al. (2023) performed a systematic search in the TESS photometry for giant planets transiting M dwarfs and measured an occurrence rate of 0.194 ± 0.072% giant plan-ets with periods below 10 days per M dwarf (0.08−0.71 M ⊙ ), and 0.134 ± 0.069% for stellar masses between 0.088 and 0.4 M ⊙ .Gan et al. (2023), also using the TESS data, measured a hot Jupiter occurrence rate around early-type M dwarfs (0.45−0.65 M ⊙ ) of 0.27±0.09%.For comparison, the hot Jupiter occurrence rate around G-type stars is 0.55 ± 0.14% (Beleznay & Kunimoto 2022).Further characterisation of these planets' masses, orbits, and general architecture is now key to understanding how they form.
We report here the confirmation and mass measurement of TOI-4860 b1 .Ground-based photometry confirms that the transits around TOI-4860, initially identified by TESS photometry, are produced by a giant planet.Doppler spectroscopy measures its mass and helps characterise the host star.This new planet detection adds to a small set of giant planets detected around stars with M ⋆ < 0.4 M ⊙ , a stellar mass regime where standard core accretion models are not able to form giants (e.g.Burn et al. 2021), and therefore provides a challenge to the hypothesis underlying these models.Additionally, TOI-4860 b is an interesting target for atmospheric characterisation with transmission spectroscopy.
In Sect. 2 we describe the data used to detect and characterise TOI-4860 b.In Sect. 3 we characterise its host star, and in Sect. 4

Observations
2.1.TESS photometry TOI-4860 was observed in four TESS sectors: one sector during the primary mission (sector 10, March and April 2019), two sectors during the first extended mission (sector 36, March and April 2021; sector 46, December 2021), and one sector in the second extended mission (sector 63, March and April 2023).Only full frame image (FFI) data were collected for sectors 10, 36, and 46, at respectively 30 min, 10 min, and 10 min cadence.For sector 63, data were obtained as both postage stamps at a 2-minute cadence and 200-second FFIs.
A transit signature with a 1.52-day period and 6% depth was first identified from the FFIs by the Faint Star Search (Kunimoto et al. 2022) using data products from the Quick-Look Pipeline (QLP; Huang et al. 2020a,b;Kunimoto et al. 2021).The TESS Science Processing Operations Center (SPOC; Jenkins et al. 2016;Caldwell et al. 2020) at NASA Ames Research Center conducted a transit search of Sector 36 on 5 May 2021 on an FFI 10-minute cadence observation with an adaptive, noisecompensating matched filter (Jenkins 2002;Jenkins et al. 2010Jenkins et al. , 2020)), producing a threshold crossing event for which an initial limb-darkened transit model was fitted (Li et al. 2019) and a suite of diagnostic tests were conducted to help make or break the planetary nature of the signal (Twicken et al. 2018).The signature and associated diagnostics were reviewed by the TESS Science Office and TOI-4860.01was alerted as a TESS Object of Interest (TOI) on 21 December 2021 (Guerrero et al. 2021).The signal was repeatedly recovered as additional observations were made in Sectors 46 and 63, and the transit signature passed all the diagnostic tests presented in the data validation reports.The difference image centroiding analyses constrain the location of the host star to within 3.5 ± 2.5 ′′ of the source of the transit signal.
For the analysis in Sect.4, we used the Presearch Data Conditioning Simple Aperture Photometry (PDCSAP; Smith et al. 2012, Stumpe et al. 2012, 2014, Caldwell et al. 2020) light curve of TOI-4860 (Fig. 1), produced by the SPOC, which is corrected for dilution in the TESS aperture by known contaminating sources.This is critical to ensure that no visually close-by targets that could affect the depth of the transit are present in the 21 ′′ TESS pixel and to check for a contaminating eclipsing binary.Figure 2 shows a plot of the target pixel file (TPF) from sector 10 and the aperture mask that is used for the simple aperture photometry (SAP).We can see that no star overlaps the TESS aperture down to six magnitudes fainter than TOI-4860.

Proper motion
TOI-4860 has a proper motion of 177 mas/yr (Gaia Collaboration et al. 2023), and therefore has moved by 12 ′′ from its position on the Palomar Observatory Sky Survey (POSS; Minkowski & Abell 1963;Lasker et al. 1996) I red plate taken in 1954.This offset is large enough to check for background stars at the current position of TOI-4860, and we see none (Fig. 3).

Gaia assessment
In addition to proper motion, we used Gaia (Gaia Collaboration et al. 2016Collaboration et al. , 2023) ) to identify any wide stellar companions that may be bound members of the system.Typically, these stars are already in the TESS Input Catalog (Stassun et al. 2019) and their flux dilution to the transit has already been accounted for in the transit fits and associated derived parameters.There are no additional widely separated companions identified by Gaia that have the same distance and proper motion as TOI-4860 (see also Mugrauer & Michel 2020, 2021).
The Gaia Data Release 3 (DR3) astrometry provides additional information on the possibility of inner companions that may have gone undetected by either Gaia or high-resolution imaging.The Gaia re-normalised unit weight error (RUWE) is a metric similar to a reduced chi-square, and values ≲ 1.4 indicate that the Gaia astrometric solution is consistent with the star being single, whereas RUWE values ≳ 1.4 indicate excess astrometric noise, which is often caused by an unseen companion (e.g.Ziegler et al. 2020).TOI-4860 has a Gaia DR3 RUWE value of 1.04 and therefore appears single.Additionally, TOI-4860 does not appear in the Gaia DR3 non-single stars table (Gaia Collaboration 2022); as such, the Gaia astrometric fit is fully consistent with a single-star model.

High-resolution imaging
As part of our standard process for validating transiting exoplanets to assess the possible contamination of bound or unbound companions on the derived planetary radii (Ciardi et al. 2015), we also observed TOI-4860 with high-resolution near-infrared adaptive optics (AO) imaging at Keck Observatory.The observations were made with the Near Infra Red Camera 2 (NIRC2) instrument on Keck-II behind the natural guide star AO system (Wizinowich et al. 2000) on 10 June 2023 UT in the standard three-point dither pattern that is used with NIRC2 to avoid the left-lower quadrant of the detector, which is typically noisier than the other three quadrants.The dither pattern step size was 3 ′′ and was repeated twice, with each dither offset from the previous dither by 0.5 ′′ .NIRC2 was used in the narrow-angle mode with a full field of view of ∼ 10 ′′ and a pixel scale of approximately 0.0099442 ′′ per pixel.The Keck observations were made in both the K s filter (λ o = 2.146; ∆λ = 0.311 µm) and J (λ o = 1.248; ∆λ = 0.163 µm) with an integration time in each filter of 20 and 40 seconds for a total of 180 and 360 seconds, respectively.Flat fields were generated from a median average of dark subtracted dome flats.Sky frames were generated from the median average of the nine dithered science frames; each science image was then sky-subtracted and flat-fielded.The reduced science frames were combined into a single combined image using a intra-pixel interpolation that conserves flux, shifts the individual dithered frames by the appropriate fractional pixels; the final resolution of the combined dithers was determined from the fullwidth half-maximum of the point spread function; 0.101 ′′ and 0.114 ′′ for the two filters, respectively.To within the limits of the AO observations, no stellar companions were detected.The final 5σ limit at each separation was determined from the average of all of the determined limits at that separation and the uncertainty on the limit was set by the root mean square (RMS) dispersion of the azimuthal slices at a given radial distance (Figure 4).

Ground-based photometry with ExTrA
Exoplanets in Transits and their Atmospheres (ExTrA; Bonfils et al. 2015) is a near-infrared (0.85 to 1.55 µm) multi-object lowresolution spectrograph fed by three 60 cm telescopes located at La Silla Observatory in Chile.One partial and six full transits were observed using two or three of the ExTrA telescopes.The first of those transits happened to be partial due to the then uncertain ephemeris, and helped refine the ephemeris for the following observations.We used 8 ′′ aperture fibres and the lowest-resolution mode (R∼20) of the spectrograph, a combination that is optimal for the target's magnitude, with an exposure time of 60 seconds.Five fibres are positioned in the focal plane of each telescope to select light from the target and four comparison stars.We chose comparison stars 2 with 2-Micron All-Sky Survey (2MASS) J magnitudes (Skrutskie et al. 2006a) and effective temperatures (Gaia Collaboration et al. 2018) similar to the target.The resulting Ex-TrA data were analysed using a custom data reduction software, described in more detail in Cointepas et al. (2021).

SPIRou
The SPectropolarimètre InfraROUge (SPIRou) instrument is a near-infrared high-resolution (980-2450 nm; R = 70, 000) highstability (∼1 m s −1 ) velocimeter and spectropolarimeter installed at the Cassegrain focus of the 3.6 m Canada-France-Hawaii Telescope (CFHT) at Mauna Kea (Donati et al. 2020).TOI-4860 was observed between March 2022 and July 2023 with SPIRou as part of the large programme SPIRou Legacy Survey (SLS; ID P42, PI: Jean-François Donati).It was observed at 28 observing epochs with four polarimetric exposures per epoch, except on 4 July 2023 when the sequence was interrupted after the first exposure.In total, 109 spectra were acquired with integration time changing from 184 s for the first 8 exposures to 602 s for the rest of the sequence.The median signal-to-noise ratio (S/N) per pixel measured in the middle of the H band for the two exposure times were 9 and 28, respectively.
To process the raw data obtained with SPIRou, we employed A PipelinE to Reduce Observations (APERO; Cook et al. 2022) version 0.7.275.The APERO software initially corrects detector effects, removes constant background thermal components, and detects bad pixels and cosmic-ray impacts.Subsequently, it calculates the position of echelle spectral orders and optimally extracts spectra from fibres A, B, A+B, and C into 2D orderseparated e2ds3 and 1D order-merged s1d spectra.For the RV analysis, we use the A+B extraction (i.e. the combined extraction of the A and B science channels).A blaze function is derived from flat-field exposures.The wavelengths of the spectra are determined from a set of nightly calibrations following Hobson et al. (2021).An absolute calibration of wavelengths with respect to the Solar System barycentric rest frame is also performed using the current barycentric Earth radial velocity (BERV) and the barycentric Julian date (BJD) of each exposure with the barycorrpy code (Kanodia & Wright 2018;Wright & Eastman 2014).Finally, APERO applies a three-step telluric correction that we summarise here with a complete description to come (Artigau et al. in prep.).First, the extracted spectrum is pre-cleaned by fitting a TAPAS atmospheric model (Bertaux et al. 2014).Second, an empirical removal of residuals left after step one is performed using observations of fast-rotating hot stars observed with SPIRou at varying conditions (e.g.airmass and water column).Third, finite resolution artefacts from telluric modelling (Wang et al. 2022) are mitigated, leaving final residuals at the level of the Artigau et al. (2014) principal component analysis method.The TOI-4860 SPIRou observations were performed in circular polarisation mode (Stokes V), where each visit consists of a set of four exposures that provide a polarimetric spectrum.We used previously described methods (Donati et al. 1997;Martioli et al. 2020Martioli et al. , 2022;;Cook et al. 2022), implemented in the APERO pipeline, to calculate the polarimetric spectra of TOI-4860 and analyse the Stokes V spectra using least squares deconvolution technique as in Donati et al. (1997).With a typical S/N of only 30 to 40, and even using least squares deconvolution analysis, we obtained a mean polarimetric RMS per visit of σ V = 0.2 ± 0.1%.Such precision is sensitive to a disk-integrated longitudinal magnetic field on the stellar surface of the order of B ℓ > 20 G. Non-detections suggest that TOI-4860 is not extremely active, but moderate magnetic activity cannot be completely ruled out.We observed TOI-4860 in the single Unit Telescope (UT), high-resolution (HR) mode (1 ′′ fibre, R∼140,000) over a spectral range from ∼380 to ∼780 nm.The spectrograph is contained in a temperature-and pressure-controlled vacuum vessel to avoid spectral drifts, and records cross-dispersed echelle spectra on two detectors.They were read out in the 2x1 binned mode, which presents a reduced level of continuum noise as compared to the unbinned readout mode.The calibration fibre (fibre B) was placed on sky in order to monitor and remove any possible contamination from the moon, as well as any sky emission lines.
The recorded spectra have a median S/N value of ∼ 8 at 550 nm, with this value rising to ∼ 25 towards the red end of the spectrum.The spectra were reduced with the updated version of the dedicated Data Reduction Software (DRS; v. 3.0.0),which, among other improvements, mitigates the bug in the exposure-meter data tables that affects the flux-weighted mid-exposure time calculation.The reduction includes all the standard steps, whereby the pipeline provides RV measurements by fitting a Gaussian function to the measured cross-correlation function (CCF; Baranne et al. 1996;Pepe et al. 2002).This CCF is calculated using a stellar template matching closest the spectral type of the star (M4 in this case).The measured RVs are given in Table A.2.

Stellar parameters
TOI-4860 is an M-type star located at a distance of 80.42 ± 0.22 pc (Gaia Collaboration et al. 2016Collaboration et al. , 2023;;Lindegren et al. 2021).The astrometry, photometry, and stellar parameters are reported in Table 1.
We derived the mass and radius of TOI-4860 from empirical relations based on luminosity.We used the Gaia-corrected (Gaia Collaboration et al. 2016Collaboration et al. , 2023;;Lindegren et al. 2021) parallax determination (12.43 ± 0.03 mas) to compute the distance and an absolute magnitude of M K s = 6.648 ± 0.027.We then used the empirical relations of Mann et al. (2019) and Mann et al. (2015) with the metallicity dependence to derive a mass of M ⋆ = 0.340 ± 0.009 M ⊙ and a radius of R ⋆ = 0.358 ± 0.015 R ⊙ , respectively.For the stellar radius, we used a systematic uncertainty floor of 4% following Tayar et al. (2022).We derived an alternate stellar radius from the spectral energy distribution (SED) that we constructed using the magnitudes from Gaia (Riello et al. 2021), 2MASS (Skrutskie et al. 2006b;Cutri et al. 2003), and the Wide-field Infrared Survey Explorer (WISE; Wright et al. 2010;Cutri & et al. 2013).Those measurements are listed in Table 1.We modelled these magnitude measurements using the procedure described in Díaz et al. (2014), with the PHOENIX/BT-Settl (Allard et al. 2012) stellar atmosphere models.We used informative priors for the effective temperature (T eff = 3190 ± 70 K), and metallicity ([Fe/H] = 0.27 ± 0.12 dex) derived from the co-added ESPRESSO spectra (which we analysed with SpecMatch-Emp; Yee et al. 2017), and for the distance from Gaia.We used uniform priors for the rest of the parameters.We used a jitter (Gregory 2005) for each set of photometric bands (Gaia, 2MASS, and WISE).The parameters, priors, and posteriors are listed in Table A.1.The maximum a posteriori (MAP) model is shown in Fig 5 .The derived SED radius (R ⋆ = 0.371 ± 0.010 R ⊙ ) is compatible (0.7σ) with the radius computed above using an empirical radius-luminosity relation.The derived SED T eff = 3260 ± 50 K, which corresponds to an M3.5V spectral type (Pecaut & Mamajek 2013), is our adopted value.
The flux around the calcium lines is low but using the coadded ESPRESSO spectra, we were able to measure the value of log R ′ HK = −5.65 ± 0.12, derived from the calcium doublet.This translates to an estimated stellar rotation period of P rot = 114 ± 22 days using the activity-rotation relation of Astudillo-Defru et al. (2017).Such a rotation period falls within the distribution of the 'slow-rotator' population of mid-M-type dwarfs in the field (Newton et al. 2017;Kiman et al. 2021;Popinchalk et al. 2021); thus, the star is likely in the Skumanich-like spin-down phase, in which the braking law is strongly rotationdependent and the period is a predictor of age.The effective temperature of TOI-4860 (3260 K) is at the poorly constrained cool end of the 4 Gyr gyrochronology calibration based on rotation periods of M67 M dwarf cluster members (Dungee et al. 2022;Gaidos et al. 2023), but adopting this yields an age of ∼2.2 Gyr.The star could be older if it has gained angular momentum from 0.27 ± 0.12 7,10 log R ′ HK −5.65 ± 0.12 7 the close-in planet via tides and is more rapidly rotating and active as a result (Ilic et al. 2022).

Analysis and modelling
We used the software package juliet (Espinoza et al. 2019) to model the photometric and RV data.The algorithm is built on many publicly available tools for the modelling of transits (batman, Kreidberg 2015), RVs (radvel, Fulton et al. 2018), and Gaussian processes (GPs) (george, Ambikasaran et al. 2015;celerite, Foreman-Mackey et al. 2017).In order to compare different models, juliet efficiently computes the Bayesian evidence (Z) using dynesty (Speagle 2020), a python package to estimate Bayesian posteriors and evidence using nested sampling methods.Instead of starting with an initial parameter vector centred on a likelihood maximum discovered through optimisation techniques, nested sampling algorithms sample directly from the given priors.

Transit chromaticity with TESS and ExTrA photometry
A wavelength-dependent transit depth would suggest a false positive scenario involving an eclipsing binary.We therefore performed a joint fit of both TESS and ExTrA photometry.To   (Koornneef et al. 1986), prior, posterior median, and 68.3% CI.U(a, b): A uniform distribution defined between a lower a and an upper b limit.
push further the chromatic analysis, in addition to ExTrA's full wavelength range (0.85 to 1.55 µm) light curve, we synthesised from the ExTrA spectrophotometry photometry in the UKIRT-WFCAM filters,4 to produce four additional light curves: a truncated Z band (Z * ), a Y, a J, and a truncated H band (H * ), shown in Fig.
A.1.The analysis is similar to that presented in Sect.4.4 except that RVs are not used and the eccentricity is fixed to zero.All planetary parameters except for the planet-to-star radius ratio (R p /R ⋆ ) are common to all datasets, to allow for a different transit depth at each band, whose posteriors' median and 68.3% credible interval (CI) are listed in Table 2.As shown in Fig. 6 the photometry for all of these bandpasses is consistently modelled with a similar R p /R ⋆ .No chromaticity is seen, lending confidence in the planet detection rather than a scenario with a blended binary 5 .(Kass & Raftery 1995) the model with a linear ephemeris (P, T 0 ) over the one with TTVs (log-Bayes factor Z P,T 0 /Z TTVs of 92.5 ± 0.8).

Radial velocity
The RVs are listed in  (Rossiter 1924;McLaughlin 1924) semi-amplitude of just ∼5 m s −1 (based on P rot , estimated from the log R ′ HK , we computed a v sin i ⋆ of ∼160 m s −1 , assuming i ⋆ = 90 • ).Except for in regards to the discussion on a potential system misalignment (Sect.5,Fig. A.4), we excluded the ESPRESSO measurement taken during the transit from our analyses.However, we included the SPIRou measurements taken during the transit in all our analyses, as the expected amplitude of the Rossiter-McLaughlin effect is smaller than their accuracy.For the SPIRou data, we used the nightly weighted average (we excluded the spectra on BJD 2460096.806090because it is an outlier, and BJD 2460064.896367 and 2460064.903591because of a low S/N of about 2.5 in the middle of the H band).We first analysed the RV data alone to choose the model for the RVs in the global fit.
Figure A.3 shows the periodogram of SPIRou RVs, whose highest peak corresponds to the period of TOI-4860 b.The residuals, after the signal from TOI-4860 b has been removed, exhibit additional signals over a longer timescale.This finding is also supported by the ESPRESSO data, for which a model with a circular planet (with priors on ephemeris from the transit observations) and a drift in RV are strongly favoured relative to the same model without drift (log-Bayes factor of 3.9 ± 0.3).We conducted a joint modelling of the SPIRou and ESPRESSO data to search for a second planet.We assumed a circular orbit for the transiting planet, and added a Keplerian with a period range between 10 and 1000 days.The marginal posterior distribution of the trial period shows a peak at 427 days (see Fig. A.3).The log-Bayes factor for this model with respect to the one-planet model is 12.3 ± 0.4, which can be interpreted as very strong evidence in favour of a second planet in the system (planet c candidate).We therefore used a model with two Keplerians for the joint fit of transit photometry and RVs.To confirm whether the additional signal in the RVs corresponds to a second planet in the system, more data are needed.The current time-span of 480 days is too close to the proposed period, and there is poor phase coverage.
The posterior of the SPIRou jitter in the two-planet modelling is 27±6 m s −1 , doubling the SPIRou uncertainties.This jitter is probably inherent to the SPIRou data since the ESPRESSO data do not support it.

Joint fit of all data
We conducted an analysis of the transit photometry from TESS (data were extracted around three transit durations at the centre of each transit) and ExTrA (spanning the full wavelength range from 0.85 to 1.55 µm), as well as the RVs from SPIRou and ESPRESSO.A GP with an approximate Matern kernel was utilised to model the residuals in the transit photometry.Each transit observation had distinct kernel hyperparameters, except for the TESS data, where common kernel hyperparameters were used within each sector.For TESS sectors 10, 36, and 46, we over-sampled the model in time and adjusted for the observation's integration time through binning (Kipping 2010).The RV model comprised two Keplerians.We sampled from the posterior using dynesty (Speagle 2020).Table 3 presents the prior, median, and 68% CI of the marginal distributions of the inferred system parameters.The stellar mass and radius, as determined in Sect.3, were used to calculate the planetary mass and radius of TOI-4860 b.Figures 7 and 8 display the datasets and the model derived from this analysis.The posterior of the stellar density (11.7 ± 0.8 g cm −3 ) is consistent with the value derived from the stellar mass and radius in Sect. 3 (10.4± 1.5 g cm −3 ).
We examined the transit windows of the candidate planet c over the span of available observations, and all of them fall at least 2σ away from a TESS sector.Additionally, we used REBOUND (Rein & Liu 2012) to estimate the TTVs of TOI-4860 b, due to the presence of the candidate planet c, for the median values of the posterior.The semi-amplitude of the TTVs is 1.6 seconds with a period corresponding to the candidate planet c, and is dominated by the light-time effect (Irwin 1952).This signal is well below the precision (18 or 56 seconds at best for a transit observed with ExTrA or TESS, respectively) and dispersion of the measured TTVs (Fig. A.2).

Results and discussion
In this paper we present the discovery and characterisation of a giant planet, TOI-4860 b, transiting an M3.5 dwarf with a period of 1.52 days.The exoplanet was detected by the TESS mission, then characterised from ground-based photometric follow-up using ExTrA and from precise RV measurements by both SPIRou and ESPRESSO.
The giant planet is close to its host star, at only 1.8 times the Roche limit (see Chandrasekhar 1987).Therefore, we expect that the system undergoes strong tidal interactions, which distort the planet and lead to orbital decay.Adopting a radial fluid Love number identical to that of Jupiter, h f = 1.5, we estimate a difference between the longest and the shortest radius of the planet of about 3% (Correia 2014).In addition, since the planet's mean radius is about 22% of the stellar radius, we expect ∼ 60 ppm discrepancies with respect to a spherical planet during transit ingress and egress (see Fig. 9).These variations are similar to those observed for WASP-103 b (Akinsanmi et al. 2019;Barros et al. 2022) and can thus be used to probe the interior structure of the planet using the transit light curves (Ragozzine & Wolf 2009;Correia 2014).The tidal dissipation of M-dwarf stars is unknown, but often believed to be similar to that of other convective stars (e.g.Mathis 2015).Assuming a tidal quality factor of Q ′ * = 10 5 , we estimate a variation in the orbital period of about Ṗ ∼ 10 −9 day/yr (Maciejewski et al. 2018).This rate is not detectable with current instrumentation, but a direct estimation of Ṗ can still be used to put a lower limit on the tidal Q factor of the star (e.g.Barros et al. 2022).
A long-standing prediction from core accretion planet formation is that giant planets do not form around low-mass stars (Laughlin et al. 2004).In particular, the models of Burn et al. (2021) are unable to form giant planets around stars with masses M * ≲ 0.4M ⊙ .The lack of such systems from the first groundbased transit surveys, such as WASP (Pollacco et al. 2006;Gaidos et al. 2014) and HATNet (Bakos et al. 2004), seemed to confirm this prediction, although the magnitude range of these surveys meant very few low-mass stars were monitored to the precision needed to find transiting exoplanets.A new generation of ground-based transit surveys, with increased telescope apertures (e.g.HAT-South and NGTS; Bakos et al. 2013;Bayliss et al. 2018), began to find transiting gas giant planets around lowermass stars (Hartman et al. 2015;Bayliss et al. 2018;Bakos et al. 2020;Jordán et al. 2022) but still not below the mass where core-accretion models have trouble forming giants.The TESS mission, with its near all-sky coverage and red wavelength sensitivity, is very well placed to detect giant planets transiting lowmass stars.This has allowed the discovery of transiting giants hosted by stars with masses M ⋆ ≲ 0.4 M ⊙ (TOI-5205, Kanodia et al. 2023;TOI-3235, Hobson et al. 2023;and TOI-519, Parviainen et al. 2021;Kagetani et al. 2023).The TOI-4860 system, an M3.5V star that hosts a giant planet with a radius of 0.77 ± 0.03 R J and a mass of 0.273 ± 0.006 M J (see Fig. 10) at the border of the hot Neptune desert (e.g.Lecavelier Des Etangs 2007), joins this short list of discoveries.With a mass of 0.340 ± 0.009 M ⊙ and a radius of 0.358 ± 0.015 R ⊙ , its host star is well within the mass range that challenges core accretion.
These recent discoveries have allowed for the occurrence rates of giant planets around low-mass stars to be calculated, at least for short orbital period systems.The results from Gan et al. (2023) and Bryant et al. (2023) suggest that short-period giant planets occur around early-type M dwarfs at approximately half the frequency they do around solar-mass stars, and about a quarter the frequency when comparing mid to late M-dwarf hosts (0.088−0.4 M ⊙ ), such as TOI-4860, to solar-mass stars.These results will become more concrete as more systems similar to TOI-4680 are confirmed.
TOI-4860 appears to be metal-rich ([Fe/H] = 0.27 ± 0.12), like other M dwarfs that host giant planets (see Fig. 3 of Kagetani et al. 2023).This suggests, as for FGK stars (Fischer & Valenti 2005), a correlation between the metallicity of a star and the likelihood of its hosting giant planets.
TOI-4860 b has a high transmission spectroscopy metric (Kempton et al. 2018) of 183 ± 15, among the highest for its planet size.Moreover, based on the host star's log R ′ HK (−5.65 ± 0.12), the lack of flares in the TESS light curve, and the small ESPRESSO RV jitter (< 1.9 m s −1 at 95% CI), we conclude that TOI-4860 currently exhibits low levels of activity.The planet's atmospheric composition can reveal insights into its formation and evolution history and is a key constraint for models of the planetary interior.Another constraint that can be  Notes.The table lists: prior, posterior median, and 68.3% CI.Parameters without prior are derived parameters. (a) Upper limit, 95% confidence. (b) The parameters listed for the photometry are different for each TESS sector and for each individual transit observed with each of the telescopes of ExTrA.The parameters q 1 and q 2 are the quadratic limb-darkening coefficients parameterised using Kipping (2013).The parameters r 1 and r 2 are the impact parameter and transit depth parameterised using Espinoza (2018).The planetary equilibrium temperature is computed for zero albedo and full day/night heat redistribution.IAU 2012: au = 149 597 870 700 m .IAU 2015: R N ⊙ = 6.957 ×10 8 m, R N eE = 6.378 1 ×10 6 m, (GM placed upon the formation history could be the spin-orbit angle.The expected semi-amplitude of the Rossiter-McLaughlin effect (Rossiter 1924;McLaughlin 1924) for TOI-4860 b is ∼5 m s −1 , well above ESPRESSO capabilities (e.g.Bourrier et al. 2022).The one ESPRESSO observation obtained during transit does not seem compatible with an aligned orbit (Fig. A.4), but this will have to be confirmed with further observations.TOI-4860 is located precisely at the fully convective boundary (Chabrier & Baraffe 1997), which can influence the star's angular momentum evolution (Irwin et al. 2011).Furthermore, due to the high levels of stellar activity, it can lead to increased stellar wind pressures that can strip away planetary atmospheres, particularly for close-in planets.
The RVs show evidence of an eccentric planet candidate (e = 0.66 ± 0.09) with a period of 427 ± 7 days and a minimum mass of 1.66 ± 0.26 M J .More data are needed to confirm this second planet, but this raises the possibility that TOI-4860 b ended up in its small-periapsis orbit through planet-planet scattering or Kozai resonance with the outer planet, and then became circularised by tides.scope were performed with care and respect from the summit of Maunakea which is a significant cultural and historic site.Based on observations obtained with SPIRou, an international project led by Institut de Recherche en Astrophysique et Planétologie, Toulouse, France.We thank the Swiss National Science Foundation (SNSF) and the Geneva University for their continuous support to our planet search programs.This work has been carried out within the framework of the National Centre of Competence in Research PlanetS supported by the Swiss National Science Foundation under grants 51NF40_182901 and 51NF40_205606.

Fig. 2 .
Fig. 2. TESS TPF image of TOI-4860 in Sector 10 (created with tpfplotter; Aller et al. 2020).The electron counts are colour-coded.The red-bordered pixels are used in the SAP.The size of the red circles indicates the Gaia Data Release 2 magnitudes of all nearby stars (Gaia Collaboration et al. 2018).

Fig. 3 .
Fig. 3. Images extracted from the Digitized Sky Survey (DSS; retrieved from https://archive.stsci.edu/cgi-bin/dss_form)and the Pan-STARRS survey (Chambers et al. 2016).From left to right, the epochs are years 1954, 1991, and 2011.The open red circle marks the position of the star as determined by Gaia (Gaia Collaboration et al. 2023).There is no background star at the current position of TOI-4860.

Fig. 4 .
Fig. 4. Companion sensitivity for the near-infrared AO imaging.The black points represent the 5σ limits and are separated in steps of one full width at half maximum; the purple represents the azimuthal dispersion (1σ) of the contrast determinations (see the main text).The inset image is of the primary target and shows no additional close-in companions.
2.4.2.ESPRESSOWe obtained seven spectra of TOI-4860 with the Echelle SPectrograph for Rocky Exoplanets and Stable Spectroscopic Observations (ESPRESSO;Pepe et al. 2021) at the 8.2 m ESO Very Large Telescope (VLT) array, at the Paranal Observatory in Chile.The observations were obtained from January to February 2023 in Programme ID: 0110.C-4069 (PI: Jordán) as part of a long-running campaign to obtain mass measurements for giant planets transiting low-mass host stars.Initially, candidates for this campaign were drawn from the HAT-South survey(Bakos et al. 2013), and more recently from the TOI list(Guerrero et al. 2021) and our own dedicated search of the TESS FFI data(Bryant et al. 2023).

Fig. 5 .
Fig. 5. SED of TOI-4860.The solid line is the MAP PHOENIX/BT-Settl-interpolated synthetic spectrum, red circles are the absolute photometric observations (the jitter has been added quadratically to the data error bars), and grey open circles are the result of integrating the synthetic spectrum into the observed bandpasses.

Fig. 7 .
Fig. 7. Modelling of transit photometry and RVs of TOI-4860.Top panel: ExTrA transit photometry observations of TOI-4860 b.Each column corresponds to a night (labelled with format YYYY-MM-DD) and each line to an ExTrA telescope (labelled T1, T2, and T3) that is offset vertically for clarity.For each transit, the median model (black line) and the 68% CI (grey band, barely visible) computed from 1000 random posterior samples are shown.Middle panel: TESS (separated by sector) and ExTrA transits detrended with the MAP model (whose transit component is shown as a grey line) and phase-folded.TESS sector 10 looks more V-shaped to the 30-minute sampling.Bottom-left panel: SPIRou RVs (red error bars), median model (black line), and 68% (grey band).Residuals from the median model are shown.Bottom-right panel: Same as the bottom-left panel but for ESPRESSO RVs (blue error bars).The time span of the ESPRESSO panel is highlighted a blue band in the SPIRou panel.

Fig. 8 .Fig. 9 .
Fig. 8. Phased Top panel: SPIRou (red error bars) and ESPRESSO (blue error bars) RVs corrected for the MAP Keplerian orbit of planet c and phase-folded to the period of planet b (the MAP jitter has been added quadratically to the data error bars).The black line is the best-fit Keplerian model from the joint fit.Bottom panel: Idem for the planet c candidate.

Fig. 10 .Fig. A. 1 .
Fig. 10.Comparison of TOI-4860 b with known exoplanets.Left: Mass-radius diagram of known exoplanets.Grey dots are transiting planets listed in the NASA Exoplanet Archive (https://exoplanetarchive.ipac.caltech.edu/)with planetary radius and mass uncertainties below 20%.TOI-519, TOI-3235, and TOI-5205 are shown (from left to right) as red dots.The blue open circle with error bars marks the position of TOI-4860 b.Centre: Idem for planetary versus stellar radii (restricted to planets with planetary radius uncertainties below 20%).Right: Idem for planetary radii versus orbital period.

Table 2 .
Inferred R p /R ⋆ in different bands.
Notes.The table lists: band, λ pivot Posterior distribution comparison for R p /R ⋆ (error bars) computed for different bands (shown and labelled with different colours).TESS, ExTrA (0.85 to 1.55 µm), Z * , Y, J, and H * data are fitted jointly with a different R p /R ⋆ parameter for each of the datasets.The horizontal solid and dotted grey lines represent the posterior median and 68.3% CI of R p /R ⋆ inferred in Sect.4.4.ExTrA transit photometry with two models: one with a linear ephemeris and a second that allows for the time of individual transits to vary (with uniform priors of ±10 minutes width around the linear ephemeris of the first model).The resulting TTVs are shown in Fig. A.2.A model comparison strongly favours