Main

TOI-1853 is a dwarf star with a V-band optical brightness of 12.3 magnitudes, located 167 pc from the Sun. It was photometrically monitored by the Transiting Exoplanet Survey Satellite (TESS) space telescope and the analysis of its light curve showed transit-like events compatible with a planet candidate (see Methods section ‘TESS photometric data’), designated as TOI-1853.01, having a short orbital period of 1.24 days and a Neptune-like radius. We ruled out a nearby eclipsing binary (NEB) blend as the potential source of the TOI-1853.01 detection in the wide TESS pixels by monitoring extra transit events with the higher angular resolution of three ground-based telescopes: MuSCAT2, ULMT and LCOGT (see Methods section ‘Ground-based photometric follow-up’). As part of the standard process for validating transiting exoplanets and assessing the possible contamination of companions on the derived planetary radii7, we observed TOI-1853 with near-infrared adaptive optics imaging, using the NIRC2 instrument on the Keck II telescope, and with optical speckle imaging, using the ‘Alopeke speckle imaging camera at Gemini North and high-resolution imaging on the 4.1-m Southern Astrophysical Research (SOAR) telescope. No nearby stars bright enough to markedly dilute the transits were detected within 0.5″, 1″ and 3″ of TOI-1853 in the Gemini, Keck and SOAR observations, respectively (see Methods section ‘High-resolution imaging’). Using Gaia DR3 data8, we also found that the astrometric solution is consistent with the star being single (see Methods section ‘Gaia’).

In the context of the Global Architecture of Planetary Systems programme9,10, we monitored TOI-1853 with the High Accuracy Radial velocity Planet Searcher for the Northern hemisphere (HARPS-N) spectrograph11, at the Telescopio Nazionale Galileo on the island of La Palma, with the aim of measuring variations of its radial velocity (RV), that is, its velocity projected along the line of sight. The HARPS-N data-reduction software pipeline provided wavelength-calibrated spectra (see Methods section ‘Spectroscopic data’), which we used to determine the stellar atmospheric properties. TOI-1853 is a quiet K2 V star with effective temperature Teff = 4,985 ± 70 K, surface gravity log g = 4.49 ± 0.11 dex, iron abundance [Fe/H] = 0.11 ± 0.08 dex and solar Fe/Si and Mg/Si ratios (see Methods section ‘Stellar analysis’). Furthermore, we determined a mass of M⋆ = 0.837 ± 0.039 solar masses (M⊙), a radius of R⋆ = 0.808 ± 0.013 solar radii (R⊙) and an advanced, although uncertain, stellar age of \({7.0}_{-4.3}^{+4.6}\,{\rm{Gyr}}\) (Table 1). We computed the generalized Lomb–Scargle (GLS) periodogram of the HARPS-N RVs and found a substantial peak (with false alarm probability (FAP) ≪ 0.1%) at a frequency of about 0.8 per day that matches the transit period and the phase of the planet candidate (see Methods section ‘RV and activity indicators periodograms’). To determine the main physical and orbital parameters of the system, we performed a global transit and RV joint analysis (see Methods section ‘Joint transit and RV analysis’). Figure 1 shows both the TESS photometric light curve and the HARPS-N RV data, as a function of time and orbital phase. We measured the radius of the companion to be 3.46 ± 0.08 Earth radii (R⊕), with a mass of 73.2 ± 2.7 Earth masses (M⊕), thus confirming the planetary nature of TOI-1853.01, hereafter TOI-1853 b. These values imply a bulk density of \(9.7{4}_{-0.76}^{+0.82}\,{\rm{g}}\,{{\rm{cm}}}^{-3}\) (roughly six times that of Neptune) and surface gravity of \({g}_{{\rm{p}}}={60.1}_{-3.6}^{+3.8}\,{\rm{m}}\,{{\rm{s}}}^{-2}\) (about 5.5 times that of Neptune), as detailed in Table 1. Despite its short orbital period, TOI-1853 b may survive during the remaining main-sequence lifetime of its host star (see Methods section ‘Orbital decay’).

Table 1 Stellar and planetary properties
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Fig. 1: Light curve and RVs.
figure 1

a, TESS light curve of TOI-1853. b, Phase curve of all TESS transits fitted separately. c, Phase curve of all the RVs. d, HARPS-N RVs. The light curves are binned at a 30-min cadence for clarity. Data points marked with anomaly flags (that is, Coarse Point, Straylight, Impulsive Outliers and Desaturation Events) were excluded from the light curve. In c, the average of approximately six RV measurements are indicated by red dots. In all panels, the error bars represent one standard deviation and in a–c, the best-fitting model is shown in black along with its residuals underneath. ppm, parts per million; ppt, parts per thousand.

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The exceptional properties of TOI-1853 b are clearly evident in comparison with the known exoplanet population at present (Fig. 2). Objects with the same density as TOI-1853 b are rare, typically super-Earths, whereas planets with the same mass usually have radii more than twice as large. Furthermore, it occupies a region of the mass–orbital period space of hot planets that was previously devoid of objects, corresponding to the driest area of the hot-Neptune desert12. TOI-1853 b is twice as massive as the two runners -up with similar radius in the radius–mass diagram (Fig. 2), that is, the ultrahot (P = 0.76 days) Neptune-sized TOI-849 b (ref. 4) and the warm (P = 55 days) Neptune HD 95338 b (ref. 3). Although for HD 95338 b and TOI-849 b the atmospheric mass fraction is expected to be at most about 5–7% (ref. 13) and about 4% (ref. 4), respectively, TOI-1853 b is best described as a bare core of half water and half rock with no or negligible envelope, or as having at most 1% atmospheric H/He mass fraction on top of a 99% Earth-like rocky interior (Fig. 2) (see Methods section ‘Composition’).

Fig. 2: Diagrams of known transiting exoplanets.
figure 2

The properties of known exoplanets have been extracted from TEPCat29 and shown as diamonds, their colour being associated with their equilibrium temperature. Horizontal and vertical error bars represent one standard deviation. TOI-1853 b, TOI-849 b and HD 95338 b are shown as circles, triangles and squares, respectively. a, Radius–mass diagram with blue lines representing different internal compositions (dashed line, 99% Earth-like rocky interior + 1% H layer (at temperature and pressure of 1,000 K and 1 mbar, respectively); solid line, 50% Earth-like + 50% water). b, Period–mass diagram, in which the dashed blue line encloses the Neptunian desert6 (Porb ≈ 55 days for HD 95338 b). c, Mass–density diagram. d, Radius–density diagram.

Source data

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The characteristic pressure of its deep interior is estimated to reach around 5,000 GPa (50 times the core–mantle boundary pressure of Earth), at which most elements and their compounds are expected to metalize owing to the reduced spacings of neighbouring atoms under extreme compression. The metallic core of TOI-1853 b could be surrounded by a mantle of H2O in a high-pressure ice phase and, possibly, in the supercritical fluid form14. However, the properties of matter at such high central pressures are still uncertain and compositional mixing15,16,17,18 might be present rather than distinct layers, as postulated by standard models19,20. If TOI-1853 b is a water-rich world, its upper structure could be described in terms of a hydrosphere with variable mass fractions of supercritical water on top of a mantle-like interior21. Although existing structural models of Neptunes addressing this possibility do not encompass objects with a mass similar to that of TOI-1853 b, atmospheric characterization measurements with the James Webb Space Telescope (JWST) might be telling. For instance, by combining three secondary-eclipse observations with the NIRSpec/G395H instrument, we could constrain the CO2 absorption feature at 4.5 μm, whose strength is a tracer of atmospheric metallicity. Transmission observations are more challenging; however, NIRISS/SOSS might be able to detect the series of H2O absorption bands in the 0.9–2.8-μm range, which would distinguish a thin H2-dominated atmosphere from an H2O-dominated atmosphere (see Methods section ‘Spectral atmospheric characterization prospects’).

Explaining the formation of such a planet is challenging because of the substantial abundance of heavy elements involved. Pebble accretion, which is the most efficient growth process for massive planets, shuts off when the core is massive enough to disrupt the gas disk22, and accreting solids beyond this mass requires a different process. The planetesimal isolation mass for runaway growth23 as well as post-isolation growth24 would require exceedingly and unrealistically high surface densities to grow a planet composed almost entirely of condensable material in situ. Thus, the growth of a planet such as TOI-1853 b by planetesimal accretion alone seems unrealistic as well. One possibility is that a system of small planets migrated from the distant regions of the disk towards its inner edge, which could have loaded the inner disk of solid mass. After the disappearance of gas from the disk, the system became unstable, leading to several mutual collisions among the small planets and eventually forming a planet with a large mass of heavy elements, by growth-dominated collisions (Fig. 3). A preliminary, indicative simulation (see Methods section ‘Formation simulations’) shows that the formation of a planet with a large mass of heavy elements by accreting several solid-rich planets is possible, even though growth into a single planet in the system is an unlikely event. More detailed hydrodynamic simulations also suggest that a final high-speed giant impact between two massive proto-planets is needed to account for the atmosphere-poor structure of TOI-1853 b (see Methods section ‘Detail impact simulations’). Moreover, groups of small planets carrying cumulatively about 100 M⊕ in proto-planetary disks might be rare, although the Kepler Mission results indicate that this scenario is not unrealistic25.

Fig. 3: Formation scenarios.
figure 3

Two possible pathways for the formation of TOI-1853 b are shown. a, The merging of super-Earth-sized proto-planets ends up in a giant collision, generating with high probability a planetary companion within about 1 au. b, Distant giant planets undergo mutual scattering after the disk dissipation and the surviving one eventually settles into a highly elliptical orbit. Over time, tidal stripping causes the planet to lose its atmosphere and tidal damping at periastron circularizes its orbit. c, Both pathways eventually lead to TOI-1853 b, for which three probable compositions are shown.

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Another possible formation scenario is based on the jumping model26, in which at least three giant planets form at a few astronomical units from their parent star. After the disappearance of the disk, this system becomes unstable and suffers mutual scattering, leading to high-eccentricity orbits for the surviving planets, which can then be circularized by tidal damping at perihelion passages. If the inner disk initially contained a lot of solid mass, in the form of planetesimals or small proto-planets, the innermost planet would have engulfed a large fraction of it near perihelion (Fig. 3). To test this possibility, we simulated an eccentric Jupiter-mass planet with an initial budget of 20 to 40 M⊕ in heavy elements and found that it can accrete an extra 30–40 M⊕ (see Methods section ‘Formation simulations’). Then, we investigated the evolutionary history of the atmosphere and concluded that the structure of the current planet cannot be the result of photoevaporation processes owing to the high surface gravity, but might be the result of Roche lobe overflow (RLO)12 (see Methods section ‘Atmospheric evaporation’). Thus, an initially massive H/He-dominated giant planet TOI-1853 b could have lost the bulk of its envelope mass because of tidal stripping27 near periastron passage during the high-eccentricity migration. The planet that we see now may have survived very close passages to its parent star from early in the history of the system, as the host star would have shrunk to a size of less than 2 R⊙ well before reaching the main sequence. Tidal heating of a young giant planet still hot from accretion would have further expanded its envelope, facilitating the escape of light gases from the original atmosphere12,27,28.

In any case, the anomalous mass–radius and mass–period combinations of TOI-1853 b are challenging to explain with conventional models of planet formation and evolution. The local merging of solid-rich proto-planets rarely develops into a single planet, whereas the migration scenario would have removed all objects within about 1 au, so we computed the sensitivity limits of HARPS-N RVs to other planetary companions (see Methods section ‘RV detection function’) and found that we can only exclude, with a 90% confidence level, the presence of companions of masses >10 M⊕ up to orbital periods of ≲10 days and with masses >30 M⊕ up to ≲100 days (or about 0.4 au). Further RV monitoring is thus needed to firmly exclude the presence of other planets within about 1 au to constrain TOI-1853 b formation, whereas future atmospheric characterization attempts could decipher its composition, allowing us to unveil the history of the densest Neptune-sized planet known at present.

Methods

TESS photometric data

The star TIC 73540072, or TOI-1853, was observed by TESS in Sector 23 at 30-min full-frame images cadence in early 2020 and in Sector 50 at a 2-min cadence in early 2022. The transit signal was first identified in the Quick-Look Pipeline (QLP)30 and later promoted to TESS Object of Interest, TOI-1853.01, planet candidate status by the TESS Science Office31. The Science Processing Operations Center (SPOC)32,33 pipeline retrieved the 2-min Simple Aperture Photometry (SAP) and Presearch Data Conditioning Simple Aperture Photometry (PDC-SAP34,35) light curves. The transit signal was identified through the Transiting Planet Search (TPS36,37) and passed all diagnostic tests in the data validation38,39 modules. All TIC objects, other than the target star, were excluded as sources of the transit signal through the difference image centroid offsets38. Here, for the global joint transit–RV analysis of the system, we adopted the PDC-SAP light curves: SPOC for Sector 23 and TESS-SPOC High-Level Science Product (HLSP)33 for Sector 50, for which, unlike SAP or QLP light curves, long-term trends were already removed using the so-called co-trending basis vectors. The light curve of Sector 23 was supersampled40 at 2 min for the global analysis to properly account for the longer cadence compared with Sector 50 and the ground-based follow-up light curves. The transit depths are found to be consistent within different TESS extraction pipelines, including PATHOS41, and with ground-based photometry.

Ground-based photometric follow-up

The TESS pixel scale is about 21 arcsec per pixel and photometric apertures extend out to several pixels, generally causing several stars to blend in the TESS aperture. To rule out the NEB-blend scenario and attempt to detect the signal on-target, we observed the field as part of the TESS Follow-up Observing Program Sub Group 1 (TFOP42). We observed full transit windows of TOI-1853 b on 25 and 27 May and 27 June 2020, respectively, with the MuSCAT2 imager43 installed at the 1.52-m Telescopio Carlos Sánchez in the Teide Observatory (in g, r, i and zs bands), with the 0.61-m University of Louisville Manner Telescope (ULMT) located at Steward Observatory (through a Sloan-r′ filter) and with the Las Cumbres Observatory Global Telescope (LCOGT44) 1.0-m network node at Siding Spring Observatory (through a Sloan-g′ band filter). We extracted the photometric data with AstroImageJ (ref. 45) and measured transit depths across several optical bands consistent with an achromatic transit-like event and compatible with TESS well within 1σ. We ruled out an NEB blend as the cause of the TOI-1853 b detection for all the surrounding stars and included the detrended ground-based observations in the global fit (Extended Data Fig. 1).

High-resolution imaging

As part of the standard process for validating transiting exoplanets to assess the possible contamination of bound or unbound companions on the derived planetary radii7, we observed TOI-1853 with near-infrared adaptive optics imaging at Keck and with optical speckle imaging at Gemini and SOAR.

We performed observations at the Keck Observatory with the NIRC2 instrument on Keck II behind the natural guide star adaptive optics system46 on 28 May 2020 UT in the standard three-point dither pattern. 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 about 10″ and a pixel scale of approximately 0.0099442″ per pixel. The Keck observations were made in the narrowband Br-γ filter (λO = 2.1686; Δλ = 0.0326 μm) with an integration time of 15 s for a total of 135 s on the target. The final resolutions of the combined dithers were determined from the full width at half maximum (FWHM) of the point spread functions: 0.053″. The sensitivities of the final combined adaptive optics image (Extended Data Fig. 2) were determined by injecting simulated sources azimuthally around the primary target every 20° at separations of integer multiples of the central source’s FWHM47.

We observed TOI-1835 with the ‘Alopeke speckle imaging camera at Gemini North48,49, obtaining seven sets of 1,000 frames (10 June 2020 UT), with each frame having an integration time of 60 ms, in each of the instrument’s two bands50 (centred at 562 nm and 832 nm). The observations of the target reach a sensitivity in the blue channel of 5.2 mag and in the red channel of 6.3 mag at separations of 0.5 arcsec and show no evidence of further point sources. We also searched for stellar companions to TOI-1853 with speckle imaging on the 4.1-m SOAR telescope51 on 27 February 2021 UT, observing in Cousins-I band, similar to the TESS bandpass. This observation was sensitive to a 4.7-mag fainter star at an angular distance of 1 arcsec from the target (Extended Data Fig. 2).

Gaia

Gaia DR3 astrometry8 provides extra information about the possibility of inner companions that may have gone undetected by high-resolution imaging. For TOI-1853, Gaia found a renormalized unit weight error of 1.08, indicating that the Gaia astrometric solution is consistent with the star being single48. Also, in the Gaia archive, we identified no sources within 40 arcsec from the target (approximately 7,000 au at the distance of TOI-1853) and, therefore, no potentially widely separated companions with the same distance and proper motion.

Spectroscopic data

We gathered 56 spectra of TOI-1853 with HARPS-N11 between February 2021 and August 2022 (Extended Data Table 1), within the GAPS programme, and reduced them using the updated online Data Reduction Software v2.3.5 (ref. 52). A different pipeline based on the template-matching technique, TERRA v1.8 (ref. 53), gave comparable errors and resulted in a fully consistent mass determination.

We observed the star in OBJ_AB mode, with fibre A on the target and fibre B on the sky to monitor possible contamination by moonlight, which we deemed negligible54. We extracted the RVs by cross-correlating the HARPS-N spectra with a stellar template close to the stellar spectral type. The median (mean) of the formal uncertainties of the HARPS-N RVs is 3.8(4.6) m s−1; the RV scatter of 34 m s−1 reduces to 4.5 m s−1 after removing the planetary signal. Our observations had average air mass, signal-to-noise ratio and exposure time of 1.25, 18 and 1,200 s, respectively.

Stellar analysis

We derived spectroscopic atmospheric parameters exploiting the co-added spectrum of TOI-1853. In particular, we measured effective temperature (Teff), surface gravity (log g), microturbulence velocity (ξ) and iron abundance ([Fe/H]) through a standard method based on measurements of equivalent widths of iron lines55,56. We then adopted the grid of model atmospheres57 with new opacities and the spectral analysis package MOOG58 version 2017. Teff was derived by imposing that the abundance of Fe I is not dependent on the line excitation potentials, ξ by obtaining the independence between Fe I abundance and the reduced iron line equivalent widths and log g by the ionization equilibrium condition between Fe I and Fe II.

We also computed the elemental abundance of magnesium and silicon, with respect to the Sun56, using the same code and grid of models. The elemental ratios [Mg/Fe] and [Si/Fe] have solar values within the errors, with no evident enrichment in none of these elements with respect to the others. The stellar projected rotational velocity (vsin i) was obtained through the spectral-synthesis technique of three regions around 5,400, 6,200 and 6,700 Å (ref. 56). By assuming a macroturbolence velocity59 vmacro = 1.8 km s−1, we found vsin i = 1.3 ± 0.9 km s−1, which is below the HARPS-N spectral resolution, thus suggesting an inactive, slowly rotating star, unless it is observed nearly pole-on.

Finally, we determined the stellar physical parameters with the EXOFASTv2 tool60, which simultaneously adjusts the stellar radius, mass and age in a Bayesian differential evolution Markov chain Monte Carlo framework61, through the modelling of the stellar spectral energy distribution (SED) and the use of the MESA Isochrones and Stellar Tracks (MIST)62. To sample the stellar SED, we used the APASS Johnson B, V and Sloan g′, r′, i′ magnitudes63, the 2-MASS near-infrared J, H and K magnitudes64 and the WISE W1, W2, W3 infrared magnitudes65. We imposed Gaussian priors on the Teff and [Fe/H] as derived from the analysis of the HARPS-N spectra and on the Gaia DR3 parallax 6.0221 ± 0.0159 mas (ref. 66). We used uninformative priors for all of the other parameters, including the V-band extinction AV, for which we adopted an upper limit of 0.085 from reddening maps67. Extended Data Fig. 3 shows the best fit of the stellar SED. In doing so, we derived a mass of M⋆ = 0.837 ± 0.038 M⊙, a radius of R⋆ = 0.808 ± 0.009 R⊙ and an age of \(\tau ={7.0}_{-4.3}^{+4.6}\,{\rm{Gyr}}\). To evaluate the uncertainties inherent in stellar models, we determined the stellar parameters with two further stellar evolutionary tracks, namely, Yonsie-Yale68 (Y2) and Dartmouth69, finding M⋆ = 0.835 ± 0.029 M⊙, R⋆ = 0.807 ± 0.009 R⊙, \(\tau ={8.0}_{-4.4}^{+3.8}\,{\rm{Gyr}}\) and M⋆ = 0.849 ± 0.025 M⊙, \({R}_{\star }=0.79{2}_{-0.004}^{+0.005}\,{R}_{\odot }\), τ = 4.6 ± 2.8 Gyr, respectively. We then summed in quadrature to the EXOFASTv2 uncertainties on M⋆ and R⋆ the standard deviations of 0.009 M⊙ and 0.009 R⊙ from the MIST, Y2, and Dartmouth stellar models, to obtain the adopted mass and radius of M⋆ = 0.837 ± 0.039 M⊙ and R⋆ = 0.808 ± 0.013 R⊙.

RV and activity indicators periodograms

Simultaneously with the RVs, we extracted the time series of several stellar activity indices (Extended Data Fig. 4): the FWHM, contrast and bisector span of the cross-correlation function profile, as well as the Mount Wilson index (SMW) and the spectroscopic lines Hα, Na and Ca. We computed the GLS periodogram, with astropy v.4.3.1 (refs. 70,71), for both the RVs and the activity indexes, which can be seen in Extended Data Fig. 4. In the RVs, we found the most notable peak at 1.24 days (FAP ≪ 0.1%), that is, the expected transiting period of TOI-1853 b. This signal is not attributable to stellar activity because none of the measured activity indicators shows a similar periodicity or harmonics. Two strong peaks appear at the frequencies of the 1d aliases of the planetary period (for example, falias = f1d − f1.24d, giving rise to a period of Palias ≈ 5.1 days), which are no longer seen when the signal of TOI-1853 b is subtracted, along with any other peak with FAP ≲ 5%. The activity indicators do not show signals with FAP ≳ 0.1%.

Joint transit and RV analysis

For the joint transit–RV analysis of TOI-1853 b, we used the modelling tool juliet72, which makes use of batman73 for the modelling of transits, RadVel74 for the modelling of RVs and correlated variations, which are treated as Gaussian processes with the packages george75 and celerite76. We exploited the dynamic nested sampling package, dynesty77, to compute Bayesian posteriors and evidence (\({\mathcal{Z}}\)) for the models.

Even though by default the TESS PDC-SAP photometry is already corrected for both dilution from other objects contained within the aperture using the Compute Optimal Apertures module78 and substantial systematic errors, we corrected it for minor fluctuations that were still observable in the light curve (Fig. 1). In particular, we normalized it by fitting a simple (approximate) Matérn GP kernel72. We also analysed the SPOC SAP photometry79,80, which is not corrected for long trends, and found no substantial change in the transit depths or any conclusive evidence of the stellar rotation period over the brief time coverage of both sectors.

We constructed a transit-light-curve model with the usual planetary orbital parameters: period P, time of inferior conjunction T0, eccentricity e and argument of periastron ω through the parametrization \((\sqrt{e}\sin \omega ,\sqrt{e}\cos \omega )\) and the mean density of the parent star ρ⋆ (ref. 72) from our stellar analysis. For the flux of TESS and the on-ground light curves, we included in the global model both offsets and jitter parameters, along with two hyperparameters of the Matérn GP model: σGP and ρGP, which are the amplitude and the length scale, respectively, of the GP used to correct TESS light curves. The impact parameter (b = (ap/R⋆)cos ip for a circular orbit) and the planet-to-star radius ratio k were parameterized as (r1, r2) (ref. 81). Moreover, here we make use of a limb-darkening parametrization82 for the quadratic limb-darkening coefficients (q1, q2 → u1, u2), with Gaussian priors83. Then we include the RV model with the usual systemic velocity \({\overline{\gamma }}_{{\rm{HARPS-N}}}\), jitter σHARPS-N and the RV signal semi-amplitude Kp.

The priors for all the parameters that are used in the joint analysis along with the estimates of the parameters’ posteriors are summarized in Extended Data Table 2 and the posterior distributions of the most relevant sampling parameters are shown as corner plots in Extended Data Fig. 5. The addition of an RV linear term (for example, RV intercept and slope) or RV GP models72 with the simple harmonic oscillator, Matérn and quasi-periodic (which had the best result of the three) kernels84 did not substantially increase the Bayesian-log evidence or even worsened it (\(\Delta {{\mathcal{Z}}}_{{\rm{base}}}^{{\rm{quasi}}\,{\rm{per}}}\approx 2\), \(\Delta {{\mathcal{Z}}}_{{\rm{base}}}^{{\rm{linear}}}\approx -3\)), and resulted in an unconstrained value for the GP evolution timescale. The inclusion of a second planet in the model, with a uniform orbital period prior between 2 and 500 days, did not improve the Bayesian-log evidence either (\(\Delta {{\mathcal{Z}}}_{{\rm{base}}}^{2{\rm{pl}}}\approx 0\)), also resulting in an unconstrained value for the period, which is consistent with the observed lack of features in the GLS of the RV residuals after the subtraction of the TOI-1853 b signal. Furthermore, to check for transit-time variations, we ran a simple test in which the orbital period of the transit model was fixed at its best-fitting value, whereas all the transit times were allowed to vary, finding no clear evidence of transit-time variations as all the transit times are compatible with their expected value within roughly 1σ (see Supplementary Materials).

RV detection function

We estimated the detection function of the HARPS-N RV time series by performing injection-recovery simulations, in which synthetic planetary signals were injected in the RV residuals after the subtraction of the TOI-1853 b signal. We simulated signals of further companions in a logarithmic grid of 30 × 40 in the planetary mass, Mp, orbital period, P, and parameter space respectively covering the ranges 1–1,000 M⊕ and 0.5–5,000 days. For each location in the grid, we generated 200 synthetic planetary signals, drawing P and Mp from a log-uniform distribution inside the cell, T0 from a uniform distribution in [0, P] and assuming circular orbits. Each synthetic signal was then added to the RV residuals. We computed the detection function as the recovery rate of these signals, that is, fitting the signals with either a circular-Keplerian orbit or a linear or quadratic trend, to correctly take into account long-period signals that would not be correctly identified as a Keplerian owing to the short time span of the RV observations (500 days). We adopted the Bayesian information criterion (BIC) to compare the fitted planetary model with a constant model: we considered the planetary signal to be notably detected when ΔBIC > 10 in favour of the planet-induced model. The detection function was then computed as the fraction of detected signals for each element of the grid (Extended Data Fig. 6).

Orbital decay

According to the current tidal theory, tidal inertial waves are at present not excited inside TOI-1853 by planet b because the rotation period of the star is certainly longer than twice the planetary orbital period85, whereas tidal gravity waves are not capable of dissipating efficiently in the central region of the star given the relatively low planetary mass86. Even assuming a lower limit for the modified tidal quality factor \({Q}_{\star }^{{\prime} }=1{0}^{7}\), the remaining lifetime of the planet is about 4 Gyr according to equation (1) of ref. 87, or longer if we take into account equilibrium tides88.

The situation is different if the orbital plane of the planet is inclined relative to the stellar equator89 because a dynamical obliquity tide is expected to be excited independently of the star rotation period. Such a dynamical tide would produce a fast decay of the obliquity, whereas it is not equally effective in producing a decay of the orbit semimajor axis89. Therefore, the effective \({Q}_{* }^{{\prime} }\), which rules the orbital decay, can be assumed to be approximately unaffected by the stellar or planetary obliquities (see, however, section 2.2 of ref. 90 for quantification of how the obliquities affect the evolution of the semimajor axis). On the other hand, assuming \({Q}_{\star }^{{\prime} }\approx 1{0}^{6}\) for the dynamical obliquity tide, the e-folding damping time of the stellar obliquity would be about 1.6 Gyr, which is much shorter than the estimated age of the system. Therefore, any initial stellar obliquity may have had time to be damped during the lifetime of the system.

Composition

The planet bulk composition was constrained on the basis of mass–radius relations derived in refs. 14,20. For the calculation, we adopted a second-order adapted polynomial equation of state from ref. 91, using equation of state coefficients from ref. 14. This is a robust estimate because any density of a condensed phase (solid or liquid) in the interior of the planet is mostly determined by pressure, which—in this case—is generated by strong self-gravitation and weakly depends on the temperature. We assumed a completely differentiated planet with an iron (Fe) core and a mantle consisting of silicate (MgSiO3) rock. The rocky interior (Fig. 2) was assumed to be 32.5% Fe plus 67.5% silicates, broadly consistent with cosmic element abundance ratios and those derived from the host-star abundances taken as a proxy for the proto-planetary disk composition (Table 1), which point to Mg:Si:Fe being close to 1:1:1. The H2–He gaseous envelope above the rocky interior was assumed to be a cosmic mixture of 75% H2 and 25% He by mass. Instead, the 50% H2O curve in Fig. 2 corresponds to an Earth-like composition with exactly equal mass of H2O on top. The latter component approximates the mixture of (C,N,O,H)-bearing material that condensed beyond the iceline of the proto-planetary disk in a water-dominated mixture of H2O, NH3 and CH4. Slightly different compositions are compatible with TOI-1853 b as well, for example, a thin H2 envelope, 0.1% by mass, might be present along with a rocky interior (49.95%) and the H2O mantle (49.95%). We neglected both the role of miscibility and chemical reactions at the interface between rock and icy material16,17 and that of any phase transition between high-pressure ice and supercritical water21. Finally, neither of the possible compositions producing the mass–radius curves in Fig. 2 is expected to be primordial for a planet with the mass and radius of TOI-1853 b. Catastrophic events such as the ones we discuss here, that is, several proto-planet collisions at the onset of dynamical instabilities on disk disappearance or tidal disruption in a high-eccentricity migration scenario, must be invoked.

Formation simulations

We simulated systems of two, four and eight solid-rich planets with a total mass of 80 M⊕, using the code swift symba5 (ref. 92). For the first scenario of merging proto-planets, we placed the innermost planet at 0.02 au from the star, similar to TOI-1853 b, and the other planets separated by 1.5 mutual Hill radii, to ensure that the system is violently unstable. The initial eccentricities were assumed to be between 0 and 5 × 10−2 and the inclinations between 0 and 1.4°, to ensure that the system evolves in 3D and the collision probability is not artificially enhanced (see Supplementary Materials). The systems with initially two and four proto-planets merged into a single planet with 80 M⊕. The system with eight super-Earths merged into two planets of 50 and 30 M⊕, respectively. We then performed a fourth simulation starting from a system of ten super-Earths of 10 M⊕ each, which led to the formation of two planets of 70 M⊕ and 30 M⊕.

For the second scenario, we simulated a Jupiter-mass planet on an orbit with a semimajor axis at 1 au, perihelion distance at 0.02 au and inclination of 10°. The planet is assumed to have a radius of two Jupiter radii, owing to tidal heating at perihelion. We placed test particles in three rings at 0.02–0.06 au, 0.1–0.3 au and 0.5–1.5 au. In a million years, the planet engulfed 30%, 6% and 2% of the particles in the three rings, respectively (see Supplementary Materials). The sharp decay of efficiency with the distance from the star is expected because the planetesimals are spread over a larger area. However, this means that the planet can accrete an extra 30–40 M⊕ if there is enough mass in the disk to begin with.

Detailed impact simulations

TOI-1853 b is too massive to have been formed in situ, but a single large impact, or several smaller ones, might have removed its atmosphere and crust during the final stages of formation, thus boosting its density. Here we consider giant impacts between super-Earths (or mini-Neptunes) as a possible explanation for the internal compositions depicted in Fig. 3. If all the pre-impact super-Earths in the system originally had thin atmospheres like Earth, it would be straightforward to form TOI-1853 b with 1% atmosphere on top of a 99% Earth-like rocky interior. However, for pre-impact super-Earths with thick atmospheres, the required impact velocity to remove most of the atmosphere could be as high as three times the mutual escape velocity of the two colliding bodies93,94. A series of high-speed impacts (≳2 mutual escape velocity) or one last catastrophic high-speed impact (≳3 mutual escape velocity) could expel most of the gaseous envelope. N-body simulations show that the impact speeds of similar-sized objects are normally within two times the mutual escape velocity95,96, but given the close distance of TOI-1853 b to its star, high-speed impacts are not impossible. If TOI-1853 b is a half water–half rock planet, the pre-impact mini-Neptunes composition could be very different. A layer of water on top of a planet could greatly enhance the loss efficiency of the atmosphere97, but few studies have examined the problem in three dimensions.

To better understand the loss process of volatiles during these collisions, we conducted a series of smoothed particle hydrodynamics impact simulations under different conditions using SWIFT98. Assuming that the initial planets have three layers (H/He on top, a water mantle and a rocky interior), we explored three different compositions: water-rich by mass (67.5% water, 22.5% rock, 10% H/He), equal rock and water (45% rock, 45% water, 10% H/He) and rock-rich (67.5% rock, 22.5% water, 10% H/He), with the thermodynamic profiles of the planets generated using WoMa99. These conditions were chosen to give a range of reasonable Neptune-like compositions for the precursor planets. The rocky interior, water and atmosphere layers are modelled using the ANEOS forsterite100, AQUA water101 and a mixture of hydrogen–helium102 equation of states, respectively. The ANEOS forsterite equation-of-state table was regenerated using ref. 103 with a more dense grid (1,560 grid points for density, 744 grid points for temperature) and higher maximum density (80 g cm−3) to better model the high-pressure and high-density rocky interior. Each initial target contained approximately 106 particles and the atmosphere layers were resolved with at least ten particle layers. The most promising impacts were repeated with higher resolution (107 particles) to ensure that the post-collision results converged. The mass of the largest post-collision remnant (Mlr) was calculated using a known methodology104,105, whereas the maximum smoothing length hmax was set to 5 R⊕.

We tested various impact scenarios including head-on and oblique impacts with a pre-impact impactor to target mass ratios ranging from 0.5 to 1 and target masses of 25, 45, 50 and 60 M⊕. In Extended Data Table 3, we provide selected results from impact simulations. We found that head-on (oblique) merging collisions, in which a target and an impactor collide at a speed approximately equal to their mutual escape velocity (simulations 1–3, 5–7 and 9–11 in Extended Data Table 3), would result in the removal of at most 10% (5%) of their atmospheres. Although giant impacts at approximately mutual escape velocity are the most common, they have low atmosphere-removal efficiency and even a series of impacts may not be enough to remove the gaseous envelope completely. Therefore, the system would need to experience a sequence of mid-speed impacts (≳1.5 mutual escape velocity, simulations 4, 8 and 12 in Extended Data Table 3) or at least one high-speed impact (≳2 mutual escape velocity) during its final formation stage to remove most of the atmosphere. Simulations 16, 17 and 18 in Extended Data Table 3 represent the potential final giant impact leading to the formation of TOI-1853 b, assuming that the target planet with a mass of 60 M⊕ was formed by several previous merging collisions that resulted in little or no compositional change.

A high percentage of water on the initial planets would make the removal of the atmosphere more efficient, as water-rich impacts require the lowest impact velocity and have the highest atmosphere loss fraction. Although there is always some loss of water during impacts, the water-loss efficiency is reduced if more water is present on the planet initially. The mass fractions of the rock in the post-collision remnant tend to increase in all three impact composition setups, confirming that rock is less likely to be lost owing to the core being in the centre and being less compressible than water and the atmosphere.

Considering the results shown in Extended Data Table 3, we expect that the post-collision remnant could have half water and half rock (with a very thin or negligible atmosphere) if the initial planets contained more water than in the equal rock and water case (simulation 17 Extended Data Table 3) but not as much as the water-rich planet (simulation 16). If TOI-1853 b is a half-rock and half-water planet, these impact simulations can be used to infer the composition of either the planets before the final impact or the primordial disk that supplied the material from which TOI-1853 b accreted.

Generating a pure-rock post-collision remnant requires a higher impact speed, as the atmosphere-removal efficiency for rock-rich planets is relatively low. Scaling laws93, applied in the mass regime of TOI-1853 b, suggest that the impact energies required to remove a large fraction of the atmosphere will be in the super-catastrophic regime, and the initial planet would need roughly ten times the final mass to produce a rocky planet with a thin atmosphere. Therefore, if TOI-1853 b is mainly composed of rock, then there would need to have been a greater mass budget in the disk initially, as a higher velocity impact would have ejected much more mass. A water-rich composition for TOI-1853 b is probably easier to produce through impacts than a water-free super-Earth composition.

Atmospheric evaporation

We have considered two possible evaporation mechanisms: photoevaporation induced by high-energy irradiation or RLO. At the present age, the Jeans escape parameter (∝Mp/RpTeq)106 resulted in Λ ≳ 100, adopting the planetary parameters in Table 1. Such a high value indicates that the atmosphere of TOI-1853 b is in hydrodynamic stability against photoevaporation, thanks to the deep gravitational potential well of the planet. To explore its evolution, we adapted a numerical code developed for studying single systems107,108, considering the following three scenarios: rocky interior + an H2-dominated envelope (1% by mass); 49.95% rocky interior + 49.95% water mantle + 0.1% H2-dominated envelope; 50% rocky interior + 50% water mantle and no envelope. For each case, we created a synthetic population of young planets (10 Myr old) with different atmospheric mass fractions, ranging from 0, 0.1% or 1% (depending on the case) to around 75% of the current planetary mass. At any age, the radius of the planet is the sum of a fixed core radius plus a time-dependent envelope radius.

During the evolutionary history, which we followed up to 7 Gyr, planet contraction occurs as a result of gravitational shrinking and to the possible mass loss through atmospheric evaporation. Assuming a Jupiter-like albedo, A = 0.5, we found that none of the planets is either initially, or later becomes, hydrodynamically unstable. Larger radii imply lower values of the Jeans escape parameter, but this is compensated by the lower equilibrium temperatures until the host star reaches the main sequence at an age of approximately 200 Myr.

In the extreme case of zero Bond albedo, planets with initial mass ≤180 M⊕ and ≥75 M⊕ can be hydrodynamically unstable (Λ < 80). We explored the cases near the lowest initial mass (about 75 M⊕) or the lowest initial value of the Jeans parameter (Λ ≈ 60), but we found that—in all these cases—the total mass loss and the radius contraction are not sufficient to recover the assumed planetary structure at the current age.

To investigate the possible mass loss owing to RLO, we computed the volume-averaged Roche radius RL (ref. 109) during the different evolutionary histories of the planet described above. It always resulted in being larger than 1.8Rp at the start of the evolution (t = 10 Myr), for any value of the assumed initial mass. At later ages, the Roche radius tends to increase owing to any possible mechanism of mass loss. For comparison, we evaluated the outer limit of the atmosphere, that is, the so-called exobase (pb ≈ 10−12 bar), by scaling the thermal escape parameter110 Γ = GMpμmH/kT1r, in which μ = 2.3 is the mean molecular weight and T1 = Teq, assuming an isothermal atmosphere in hydrostatic equilibrium and r1 = Rp at p = 1 bar. We found that the exobase is located at rb = 1.1 Rp and, hence, always below the Roche radius. Finally, we computed the orbital period at which a planetary companion would begin losing mass as a result of RLO, given by PRL = 0.4ρ−1/2 days (refs. 111,112), in which ρ is the mean planet density. This critical period always resulted in being shorter than 0.5 days. Assuming that the planet is not migrating during the evolution, the critical period also remains shorter than the orbital period, and hence no RLO should occur. This result is because of the very large density of the planet, with respect to standard models. As a countercheck, we verified that the critical period would become equal to or larger than the orbital period if the past density of the planet was lower than about 0.1 g cm−3. In our grid of models, the planetary radius remains in the range 4–12 R⊕ for envelope mass fractions up to 75% of the current planetary mass, whereas the critical density would require radii from 16 to 25 R⊕. We conclude that RLO processes could have contributed to the loss of TOI-1853 b envelope only if the planet was closer to the star in the past, which—for a circular orbit—corresponds to Porb ≈ 0.5 days, almost half of the current one. For this to be true, the planet should have later migrated to its current position in agreement with the high-eccentricity formation scenario, for which planets roughly circularize at twice the periastron distance of the initial eccentric orbit.

Spectral atmospheric characterization prospects

We explored whether the JWST is able to detect spectroscopic signatures of a TOI-1853 b-like planet. According to the transit and emission spectroscopic metrics113,114, TOI-1853 b is at the lower end distribution of targets selected for transmission. For emission instead, TOI-1853 b is comparable with the bulk of the selected JWST secondary-eclipse observations (Extended Data Fig. 7).

We generated synthetic spectra for TOI-1853 b using the open-source PYRAT BAY modelling framework115. We considered two extreme cases based on the scenarios previously explored: (1) a planet with a rocky interior and a 1% H2 atmosphere and (2) a planet with a 50% rocky interior, 40% H2O mantle and a 10% H2O supercritical steam atmosphere. Given the lack of atmospheric composition constraints other than the bulk density of the planet, we adopted a generic solar composition with scaled heavy-element metallicities such that we match the atmospheric mass fraction of the H2-dominated and the heavy-element-dominated atmosphere. On the basis of the planet’s equilibrium temperature, we assumed an isothermal temperature profile for transmission and a radiative-equilibrium profile for emission. We computed the molecular composition assuming thermochemical equilibrium. We considered the main opacity sources expected for exoplanets in the infrared, that is, from molecular line lists116,117 (pre-processed with the repack package118), collision-induced absorption119,120 and Rayleigh scattering121. We then simulated JWST transmission and emission observations with PandExo122 for all instruments on board.

Extended Data Fig. 7 shows our model spectra of TOI-1853 b along with the simulated JWST observations combining three visits with each instrument to enhance the signal-to-noise ratios. Either transmission or emission spectroscopic characterization efforts will be challenging. According to the adopted synthetic models, NIRISS/SOSS and NIRSpec/G395H are the most favourable instruments to detect spectral features based on their spectral coverage and signal-to-noise ratios. Furthermore, NIRSpec/G235H provides the best signal-to-noise ratio at approximately 2–3 μm. The transmission spectra present the largest spectral features for metallicities ranging from 0.01 to 50.0 times solar. For larger metallicities, the amplitude of the features starts to flatten as the mean molecular mass of the atmosphere increases. Notable spectral features are the H2O bands at 1.0–2.5 μm and a strong CO2 band at 4.5 μm for super-solar metallicities. Certainly, the presence of clouds and hazes would complicate the interpretation of these observations, as they can also flatten the spectral features, although they tend to be more prevalent for lower-temperature atmospheres123. The emission spectra seem to provide more identifiable features than in transmission (as confirmed by the relatively better spectroscopic metric). Under the assumption of equilibrium chemistry, the CO2 absorption feature at 4.5 μm is the clearer tracer of metallicity, as the abundance of CO2 increases more steeply with metallicity than other dominant species, such as H2O.