# An ultra-dense Neptune-sized planet
in the hot-Neptune desert

L. Naponiello,${}^{1,2,3\,\ast}$ L. Mancini,1,3,4 A. Sozzetti,3 A. S. Bonomo,3
A. Morbidelli,5
J. Dou,6 L. Zeng,7,8 Z. M. Leinhardt,6 K. Biazzo,9 P. Cubillos,3,10 M.
Pinamonti,3
D. Locci,11 A. Maggio,11 M. Damasso,3 A. F. Lanza,12 J. J. Lissauer,13,14
A. Bignamini,15 W. Boschin,16,17,18 L. G. Bouma,19,20 P. J. Carter,6 D. R.
Ciardi,20
K. A. Collins,7 R. Cosentino,16 I. Crossfield,21 S. Desidera,22 X. Dumusque,23
A. F. M. Fiorenzano,16 A. Fukui,35,17 P. Giacobbe,3 C. L. Gnilka,13,20 A.
Ghedina,16
E. Gonzales,24 G. Guilluy,3 A. Harutyunyan,16 S. B. Howell,13 J. M. Jenkins,13
M. B. Lund,20 E. L. N. Jensen,25 J. F. Kielkopf,26 K. V. Lester,13
L. Malavolta,22,27 A. W. Mann,28 R. A. Matson,29 E. C. Matthews,4
D. Nardiello,22 N. Narita,36,37,17 E. Pace,2 I. Pagano,12 E. Palle,17,18 M.
Pedani,16
S. Seager,8,30,31 J. E. Schlieder,32 R. P. Schwarz,7 A. Shporer,30
J. D. Twicken,13,33 J. N. Winn,34 C. Ziegler,35 T. Zingales22,27

1Department of Physics, University of Rome “Tor Vergata”, Rome, Italy. 2Department of Physics and Astronomy, University of Florence, Florence, Italy. 3INAF, Turin Astrophysical Observatory, Pino Torinese, Italy. 4Max Planck Institute for Astronomy, Heidelberg, Germany. 5Laboratoire Lagrange, Université Cote d’Azur, CNRS, Observatoire de la C$\hat{\rm o}$te d’Azur, France. 6University of Bristol, H. H. Wills Physics Laboratory, Bristol, UK. 7Center for Astrophysics | Harvard & Smithsonian, Cambridge, MA, USA. 8Department of Earth and Planetary Sciences, Harvard University, Cambridge, MA, USA. 9INAF – Rome Astronomical Observatory, Monte Porzio Catone, Italy. 10Space Research Institute, Austrian Academy of Sciences, Graz, Austria. 11INAF – Palermo Astronomical Observatory, Palermo, Italy. 12INAF – Catania Astrophysical Observatory, Catania, Italy. 13NASA Ames Research Center, Moffett Field, CA, USA. 14Department of Earth & Planetary Sciences, Stanford University, Stanford, CA, USA 15INAF – Trieste Astronomical Observatory, Trieste, Italy. 16Fundación Galileo Galilei - INAF, Tenerife, Spain 17Instituto de Astrofísica de Canarias (IAC), Tenerife, Spain. 18Departamento de Astrofísica, Universidad de La Laguna (ULL), Tenerife, Spain. 1951 Pegasi b Fellow 20NASA Exoplanet Science Institute-Caltech/IPAC, Pasadena, CA, USA. 21Department of Physics and Astronomy, University of Kansas, Lawrence, KS 66045, USA 22INAF - Padova Astronomical Observatory, Padova, Italy. 23Observatoire de Geneéve, Université de Geneéve, CH-1290 Versoix, Switzerland 24Department of Astronomy and Astrophysics, University of California, Santa Cruz, CA 95064, USA 25Department of Physics & Astronomy, Swarthmore College, PA, USA. 26Department of Physics and Astronomy, University of Louisville, KY, USA. 27Dipartimento di Fisica e Astronomia, Università degli Studi di Padova, PD, Italy 28Department of Physics and Astronomy, The University of North Carolina, NC, USA. 29U. S. Naval Observatory, Washington, D.C., USA. 30Department of Physics and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, MA, USA. 31Department of Aeronautics and Astronautics, MIT, Cambridge, MA, USA 32NASA Goddard Space Flight Center, Greenbelt, MD, USA. 33SETI Institute, Mountain View, CA, USA 34Department of Astrophysical Sciences, Princeton University, NJ, USA. 35Dep. of Physics, Engineering and Astronomy, Stephen F. Austin State University, TX, USA. 36Komaba Institute for Science, The University of Meguro, Japan 37Astrobiology Center, Osawa, Mitaka, Japan

∗Corresponding author: E-mail<EMAIL_ADDRESS>
> The paucity of Neptune-type planets at short orbital periods was recognised
> in the statistical studies of exoplanet populations and is known as ‘hot-
> Neptune desert’ (?). As many Neptune planets have been discovered with
> longer orbital periods, this dearth is not caused by observational biases
> (?, ?) but primarily by atmospheric photo-evaporation effects (?, ?). Since
> then, the desert has been increasingly populated with planets (?, ?) having
> a wide range of different and, in some cases, unusual characteristics (?,
> ?). The study of exoplanets that have experienced unconventional
> evolutionary processes offers a novel opportunity to enhance our current
> understanding of planetary formation and composition theories. Here we
> report the discovery of the transiting planet TOI-1853 b, which orbits a
> dwarf star every 1.24 days. This planet has a mass of $73.5^{+4.2}_{-4.0}$
> Earth masses, almost twice that of any other Neptune-sized planet known.
> These values place TOI-1853 b in the middle of the Neptunian desert and
> imply that its mass is dominated by heavy elements. The remarkable
> properties of TOI-1853 b could be the result of multiple proto-planets
> collisions or the final state of an initially high-eccentricity planet which
> migrated closer to its parent star.

##  1 Main text

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 TESS space telescope and the analysis of its light curve (?)
showed transit-like events compatible with a planet candidate, 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 (?). As part of the standard process for
validating transiting exoplanets and assessing the possible contamination of
companions on the derived planetary radii (?), 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 the High Resolution Imaging on the 4.1 m
Southern Astrophysical Research (SOAR) telescope. No nearby stars bright
enough to significantly dilute the transits were detected within
$0.5^{\prime\prime}$, $1^{\prime\prime}$ and $3^{\prime\prime}$ of TOI-1853 in
the Gemini, Keck and SOAR observations, respectively (?). Using Gaia DR3 data
(?) we also found that the astrometric solution is consistent with the star
being single (?).

We monitored TOI-1853 in the context of the Global Architecture of Planetary
Systems programme (?, ?), with the HARPS-N spectrograph (?) at the Telescopio
Nazionale Galileo in La Palma. The HARPS-N data reduction software pipeline
provided wavelength-calibrated spectra (?), which we used to determine the
stellar atmospheric properties. TOI-1853 is a K2 V star with effective
temperature $T_{\rm eff}=4985\pm 70$ K, surface gravity $\log{g}=4.49\pm 0.11$
dex, iron abundance [Fe/H] $=0.11\,\pm\,0.08$ dex, and solar Fe/Si - Mg/Si
ratios (?). Furthermore, we determined a mass of $M_{\star}=0.837\pm 0.036$
solar masses ($M_{\odot}$), a radius of $R_{\star}=0.808\pm 0.009$ solar radii
($R_{\odot}$), and an advanced, though uncertain, stellar age of
$7.0^{+4.6}_{-4.3}$ Gyr (Table 1). We computed the Generalised Lomb-Scargle
periodogram of the HARPS-N RVs and found a significant peak (with False Alarm
Probability - FAP $\ll$ 0.1%) at a frequency of $\approx 0.8$ d-1 that matches
the transit period and the phase of the planet candidate.

To determine the main physical and orbital parameters of the system, we
performed a transit and RV joint analysis (?). Fig. 1 displays the _TESS_
photometric light curve, together with the transits and the HARPS-N RV data
phase-folded to the best fit period of the candidate. We measured the radius
of the companion to be $3.45^{+0.13}_{-0.14}$ Earth radii $(R_{\oplus})$, with
a mass of $73.5^{+4.2}_{-4.0}\,M_{\oplus}$, thus confirming the planetary
nature of TOI-1853.01, hereafter TOI-1853 b. These values imply a bulk density
of $9.8^{+1.9}_{-1.5}$ g cm-3 ($\approx$ 6 times that of Neptune) and surface
gravity of $g_{\rm p}=60^{+14}_{-11}$ m s-2 ($\approx$ 5.5 times that of
Neptune), as detailed in Table 1. Despite its short orbital period, TOI-1853 b
may not be engulfed during the remaining main-sequence lifetime of its host
(?).

The exceptional properties of TOI-1853 b are clearly evident in comparison
with the currently known exoplanet population (Fig. 2). Objects with the same
density of TOI-1853 b are rare, typically super-Earths, while 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 desert (?). TOI-1853 b is twice as massive as the two runners-up with
similar radius in the radius-mass diagram (Fig. 2), i.e. the ultra-hot
($P=0.76$ days) Neptune-sized TOI-849 b (?) and the warm ($P=55$ days) Neptune
HD 95338 b (?).

While for HD 95338 b and TOI-849 b the atmospheric mass fraction is expected
to be at most $\sim 5-7\%$ (?) and $\sim 4\%$ (?), respectively, TOI-1853 b is
best described as a bare core of half water–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). The characteristic pressure of its
deep interior is estimated to reach $\sim 5000$ GPa (50 times the core-mantle
boundary pressure of Earth), where most elements and their compounds are
expected to metalize due to the reduced spacings of neighbouring atoms under
extreme compression. TOI-1853 b’s metallic core could be surrounded by a
mantle constituted by H2O in a high-pressure ice phase and, possibly, also in
liquid form (?), although the properties of matter at such high central
pressures are still quite uncertain and compositional mixing (?, ?, ?, ?)
might be present rather than distinct layers as postulated by standard models
(?, ?).

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 interior (?). While 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 might be telling. For instance, by combining at
least three transit observations with the NIRISS/SOSS instrument it should be
possible to detect the series of H2O absorption bands in the $0.9-2.8\,\mu$m
range, which might allow us to distinguish a thin, H2-dominated atmosphere
from an H2O-dominated atmosphere (?).

It is difficult to explain the formation of planets with such a large amount
of heavy elements. Pebble accretion, which is the most efficient growth
process for massive planets, shuts off when the core is massive enough to
disrupt the gas disk (?), and accreting solids beyond this mass requires a
different process. The planetesimal isolation mass for runaway growth (?) as
well post-isolation growth (?) 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 like TOI-1853 b by
planetesimal accretion alone appears 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
merging. Our simulations (?) show that the formation of a planet with a large
mass of heavy elements by merging of solid-rich planets is possible, even
though merging into a single planet is an unlikely event. Moreover, groups of
small planets carrying cumulatively $\sim 100\,M_{\oplus}$ in proto-planetary
disks might be rare, although the Kepler-mission results indicate this
scenario is not unrealistic (?).

Another possible formation scenario is based on the jumping-model (?), in
which at least three giant planets form at a few au 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 then can 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 most of it near perihelion. To test this possibility, we simulated an
eccentric Jupiter-mass planet with an initial budget of 20 to $40\,M_{\oplus}$
in heavy elements and found that it can accrete an additional
$30-40\,M_{\oplus}$ (?). An initially massive H/He dominated giant planet
TOI-1853 b could have lost the bulk of its envelope mass due to tidal
stripping (?, ?) 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 system’s history since the host star would
have shrunk to a size of less than 2 $R_{\odot}$ 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 atmosphere (?, ?, ?).

The anomalous density and location within the Neptunian desert of TOI-1853 b
present a fascinating puzzle for planet formation and evolution theories, thus
making it a remarkable addition to the growing catalogue of exoplanets. Since
the local merging of solid-rich proto-planets rarely develops into a single
planet, while the migration scenario would have removed all objects within
$\sim$1 au, we computed the sensitivity limits of HARPS-N RVs to additional
planetary companions (?), and found that we can only exclude, with a 90%
confidence level, the presence of companions of masses $>10\,M_{\oplus}$ up to
orbital periods of $\lesssim 10$ days and with masses $>30\,M_{\oplus}$ up to
$\lesssim 100$ days. Eventually, by searching for planetary companions and
investigating its possibly thin atmosphere, new data collection will help us
unveil both the formation and composition of the densest Neptune-sized planet
currently known.

Table 1: Table 1: Stellar and planetary properties. The errors represent the 68% confidence intervals (one standard deviation or $\sigma$) for each value. The equilibrium temperature is estimated for a zero Bond albedo, in the assumption of uniform heat redistribution to the night side. The eccentricity upper limit is also constrained at the confidence level of $1\sigma$. Parameters | Unit | Value
---|---|---
Stellar |  |
Right ascension (J2020) |  | 14:05:50.24
Declination (J2020) |  | +16:59:32.53
Spectral type |  | K2.5V
$V$-band magnitude | mag | 12.276 $\pm$ 0.092
Parallax | mas | 6.022 $\pm$ 0.016
Distance | pc | 166.8${}^{+0.9}_{-0.5}$
$v\sin{i}$ | km s-1 | 1.3 $\pm$ 0.9
$\log R^{\prime}_{\rm HK}$ | dex | $-4.73\pm 0.06$
Mass, $M_{\star}$ | $M_{\odot}$ | 0.837${}^{+0.038}_{-0.034}$
Radius, $R_{\star}$ | $R_{\odot}$ | 0.808 $\pm$ 0.009
Luminosity, $L_{\star}$ | $L_{\odot}$ | 0.3696 $\pm$ 0.0093
Effective temperature, $T_{\rm eff}$ | K | 4985 $\pm$ 70
Surface gravity, $\log{g}$ | dex | $4.49\pm 0.11$
Iron abundance, [Fe/H] | dex | $0.11\pm 0.08$
Magnesium abundance, [Mg/H] | dex | $0.09\pm 0.06$
Silicon abundance, [Si/H] | dex | $0.14\pm 0.06$
Planetary |  |
Orbital period, $P$ | days | 1.2436275${}^{+0.0000027}_{-0.0000031}$
Radial velocity semi-amplitude, $K$ | m s-1 | 49.0 $\pm$ 1.2
Eccentricity, $e$ |  | $<0.03$
Argument of periastron, $\omega$ | degrees | unconstrained
Impact parameter, $b$ |  | $0.51^{+0.06}_{-0.07}$
Reference epoch of mid-transit, $T_{0}$ | BJDTDB | 2 459 690.7419 $\pm$ 0.0008
Transit duration, $T_{14}$ | hours | $1.49\pm 0.09$
Orbital semi-major axis, $a$ | au | 0.021 $\pm$ 0.001
Mass, $M_{\rm p}$ | $M_{\oplus}$ | 73.5 ${}^{+4.2}_{-4.0}$
Radius, $R_{\rm p}$ | $R_{\oplus}$ | 3.45${}^{+0.13}_{-0.14}$
Inclination, $i$ | degrees | 84.9${}^{+0.7}_{-0.6}$
Density, $\rho_{\rm p}$ | g cm-3 | $9.8^{+1.9}_{-1.5}$
Surface gravity, $g$ | m s-2 | 60${}^{+14}_{-11}$
Equilibrium temperature, $T_{\rm eq}$ | K | 1478 $\pm$ 35

Figure 1: (a) TOI-1853 light curve, (b) Phase curve of all the transits, (c)
Phase curve of radial velocities. The light curves are binned at 30-minutes
cadence for clarity. Cadences marked with anomaly flags (i.e. Coarse Point,
Straylight, Impulsive Outliers and Desaturation events) were excluded from the
light curve. In panel (c), the average of $\approx 6$ radial velocity
measurements are indicated by red dots. In all panels, the error bars
represent one standard deviation, while the best-fitting model are shown in
black along with its residuals below.

Figure 2: Diagrams of known transiting exoplanets. The exoplanets properties
have been extracted from TEPCat (?) and displayed as diamonds, while their
colour is associated with the Equilibrium Temperature. Horizontal and vertical
error bars represent one standard deviation. TOI-1853 b, TOI-849 b and HD
95338 b are displayed as a circle, triangle and square respectively. (a)
Radius-mass diagram with blue lines representing different internal
compositions [dashed: 99% Earth-like rocky core + 1% H layer (at temperature
and pressure of 1000K, 1mbar); solid: 50% Earth-like + 50% water]. (b) Mass-
period diagram, where the blue dashed lines enclose the Neptunian desert (?).
(c) Density-mass diagram. (d) Density-radius diagram.

##  2 Methods

###  2.1 TESS photometric data

The star TIC 73540072, or TOI-1853, was observed by _TESS_ in Sector 23 at a
30-minute full-frame images (FFI) cadence in early 2020, and in Sector 50 at a
2-minute cadence in early 2022. The transit signal was first identified in the
Quick-Look Pipeline (QLP) (?), and later promoted to _TESS_ Object of
Interest, TOI-1853.01, planet candidate status by the TESS Science Office (?).
The Science Processing Operations Center (SPOC) (?, ?) pipeline retrieved the
2-minutes Simple Aperture Photometry (SAP) and Presearch Data Conditioning
Simple Aperture Photometry [PDC-SAP; (?, ?)] light curves. The transit signal
was identified through the Transiting Planet Search [TPS; (?, ?)] and passed
all diagnostic tests in the Data Validation [DV; (?, ?)] modules. All TIC
objects, other than the target star, were excluded as sources of the transit
signal through the difference image centroid offsets (?). Here, for the joint
transit-RV analysis of the system, we adopted the PDC-SAP light curve, from
which long-term trends were removed using the so-called Co-trending Basis
Vectors (CBVs). In particular, for Sector 23 we used the TESS-SPOC High-Level
Science Product (HLSP) (?) light curve.

###  2.2 Ground-based photometric follow-up

The _TESS_ pixel scale is $\sim 21$ arcsec pixel-1 and photometric apertures
extend out to multiple pixels, generally causing multiple 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 [TFOP; (?)].

We observed full transit windows of TOI-1853 b on May 25, 27 and June 27 2020
respectively with the MuSCAT2 imager (?) installed at the 1.52 m Telescopio
Carlos Sanchez in the Teide Observatory (in $g$, $r$, $i$, and
$z_{\mathrm{s}}$ bands), with the 0.61 m University of Louisville Manner
Telescope (ULMT) located at Steward Observatory (through a Sloan-$r^{\prime}$
filter) and with the Las Cumbres Observatory Global Telescope [LCOGT; (?)] 1.0
m network node at Siding Spring Observatory (through a Sloan-$g^{\prime}$ band
filter). We extracted the photometric data with AstroImageJ (?) and measured
transit-depths across multiple optical bands consistent with an achromatic
transit-like event and compatible with _TESS_. We ruled out an NEB blend as
the cause of the TOI-1853 b detection for all the surrounding stars. We
additionallyperformed a joint transit model fit using ULMT and LCOGT data
(Ext. Fig. 1), including an ephemeris prior from the global fit of this work
(Ext. Table 2). We derived $R_{\rm p}=3.35^{+0.40}_{-0.30}\,R_{\oplus}$, which
is well within $1\sigma$ consistent with the value from the global fit.

###  2.3 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 radii (?), we observed TOI-1853 with near-infrared adaptive optics
(AO) 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 AO system (?) on 2020-05-28 UT in the
standard 3-point dither pattern. The dither pattern step size was
$3^{\prime\prime}$ and was repeated twice, with each dither offset from the
previous dither by $0.5^{\prime\prime}$. NIRC2 was used in the narrow-angle
mode with a full field of view of $\sim 10^{\prime\prime}$ and a pixel scale
of approximately $0.0099442^{\prime\prime}$ per pixel. The Keck observations
were made in the narrowband Br-$\gamma$ filter $(\lambda_{\rm
O}=2.1686;\Delta\lambda=0.0326~{}\mu$m) with an integration time of 15 seconds
for a total of 135 seconds 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: $0.053^{\prime\prime}$. The sensitivities of the
final combined AO image (Ext. Fig. 2) were determined by injecting simulated
sources azimuthally around the primary target every $20^{\circ}$ at
separations of integer multiples of the central source’s FWHM (?).

We observed TOI-1835 with the ‵Alopeke speckle imaging camera at Gemini North
(?, ?), obtaining seven sets of 1000 frames (2020-06-10 UT), with each frame
having an integration time of 60 ms, in each of the instrument’s two bands
(centred at 562 nm and 832 nm) (?). The observations of the target reach a
sensitivity in the blue channel of 5.2 mag, while in the red channel of 6.3
mag at separations of 0.5 arcsec, and show no evidence of additional point
sources. We also searched for stellar companions to TOI-1853 with speckle
imaging on the 4.1-m SOAR telescope (?) on 2021-02-27 UT, observing in
Cousins-$I$ band, similar to the TESS bandpass. This observation was sensitive
to a 4.7-magnitude fainter star at an angular distance of 1 arcsec from the
target.

###  2.4 Gaia

Gaia DR3 astrometry (?) provides additional information on the possibility of
inner companions that may have gone undetected by high-resolution imaging. For
TOI-1853 Gaia found a Renormalised Unit Weight Error (RUWE) of $\approx 1$,
indicating that the Gaia astrometric solution is consistent with the star
being single (?). In addition, Gaia identified no widely separated companions
that have the same distance and proper motion as TOI-1853.

###  2.5 Spectroscopic data

We gathered 56 spectra of TOI-1853 with HARPS-N [High Accuracy Radial velocity
Planet Searcher for the Northern hemisphere; (?)] between February 2021 and
August 2022, within the GAPS programme, and reduced them using the updated
online Data Reduction Software (DRS) v2.3.5 (?).

We observed the star in $\rm OBJ\\_AB$ mode, with fiber A on the target and
fiber B on the sky to monitor possible contamination by moonlight, which we
deemed negligible (?). 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.

###  2.6 Stellar analysis

We derived spectroscopic atmospheric parameters exploiting the co-added
spectrum of TOI-1853. In particular, we measured effective temperature
($T_{\rm eff}$), surface gravity ($\log{g}$), microturbulence velocity
($\xi$), and iron abundance ([Fe/H]) through a standard method based on
measurements of equivalent widths (EWs) of iron lines [see (?, ?)]. We then
adopted the (?) grid of model atmospheres with new opacities and the spectral
analysis package MOOG (?) version 2017. $T_{\rm eff}$ was derived by imposing
that the abundance of Fe i is not dependent on the line excitation potentials,
$\xi$ by obtaining the independence between Fe I abundance and the reduced
iron line EWs, 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 Sun (?), 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 ($v\sin{i}$) was obtained through the
spectral-synthesis technique of three regions around 5400, 6200, and 6700 Å,
as done in (?). By assuming a macroturbolence velocity $v_{\rm macro}=1.8$ km
s-1 from the relationships by (?), we found $v\sin{i}=1.3\pm 0.9$ km s-1,
which is below the HARPS-N spectral resolution, thus suggesting a slow stellar
rotation unless the star is observed nearly pole-on.

Finally, we determined the stellar physical parameters with the EXOFASTv2 tool
(?), which simultaneously adjusts the stellar radius, mass and age in a
Bayesian differential evolution Markov chain Monte Carlo (DE-MCMC) framework
(?), through the modelling of the stellar Spectral Energy Distribution (SED)
and the use of the MESA Isochrones and Stellar Tracks (MIST) (?). To sample
the stellar SED we used the APASS Johnson $B$, $V$ and Sloan $g^{\prime}$,
$r^{\prime}$, $i^{\prime}$ magnitudes (?), the 2-MASS near-infrared $J$, $H$
and $K$ magnitudes (?), and the WISE W1, W2, W3 infrared magnitudes (?). We
imposed Gaussian priors on the $T_{\rm eff}$ and [Fe/H] as derived from the
analysis of the HARPS-N spectra, and on the Gaia DR3 parallax $6.0221\pm
0.0159$ mas (?). We used uninformative priors for all the other parameters,
including the $V$-band extinction $A_{V}$, for which we adopted an upper limit
of 0.085 from reddening maps (?). Ext. Fig. 3 displays the best fit of the
stellar SED.

###  2.7 RV and activity indicators periodograms

Simultaneously with the RVs, we extracted the time series of several stellar
activity indices (Ext. Fig. 4): the FWHM, contrast and bisector (BIS) span of
the CCF (Cross-Correlation Function) profile, as well as the Mount Wilson
index ($S_{MW}$) and the spectroscopic lines H$\alpha$, Na and Ca. We computed
the Generalized Lomb-Scargle (GLS) periodogram, with astropy v.4.3.1 (?, ?),
for both the RVs and the activity indexes, which can be inspected in Ext. Fig.
4. In the RVs, we found the most significant peak at 1.24 days (FAP $\ll$
0.1%), i.e. the expected transiting period of TOI-1853 b. This signal is not
attributable to stellar activity since none of the measured activity
indicators shows a similar periodicity or harmonics. Another strong peak
appears at the 1d alias frequency $f_{\rm alias}$ of the planetary period in
the form of $f_{\rm alias}=f_{1\,{\rm d}}-f_{1.24\,{\rm d}}$, giving rise to a
period of $P_{\rm alias}\approx 5.1$ days, which is no longer seen when the
signal of TOI-1853 b is subtracted, along with any other peak with
$\rm{FAP}\lesssim 5\%$. The activity indicators do not show signals with
$\rm{FAP}\gtrsim 0.1\%$.

###  2.8 Joint transit and RV analysis

For the joint transit-RV analysis of TOI-1853 b, we employed the modelling
tool juliet (?), which makes use of batman (?) for the modelling of transits,
RadVel (?) for the modelling of RVs and correlated variations which are
treated as GPs with the packages george (?) and celerite (?). We exploited the
dynamic nested sampling package, dynesty (?), to compute Bayesian posteriors
and evidence for the models.

Even though by default the PDC-SAP photometry is already corrected both for
dilution from other objects contained within the aperture using the Compute
Optimal Aperture (COA) module (?), and major 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) Matern
GP (Gaussian Process) kernel (?). We also analysed the SPOC SAP photometry (?,
?), which is not corrected for long trends and found no significant 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 $T_{0}$, eccentricity $e$
and argument of periastron $\omega$ via the parametrization
$(\sqrt{e}\sin{\omega},\sqrt{e}\cos{\omega})$ and the mean density of the
parent star $\rho_{\star}$ (?) from our stellar analysis. The _TESS_ data
parameters adopted in our model were the flux offset and jitter parameters,
$TESS_{\rm off}$ and $TESS_{\rm jitt}$, and the two hyper-parameters of the
Matern GP model: $\sigma_{\rm GP}$ and $\rho_{\rm GP}$, respectively the
amplitude in parts per million (ppm) and the length-scale of the GP. The
impact parameter [$b=(a_{\rm p}/R_{\star})\cos{i_{\rm p}}$ for a circular
orbit] and the planet-to-star radius ratio $k$ were parameterized as
$(r_{1},r_{2})$ (?). Moreover, here we make use of the limb-darkening
parametrizations described in (?) for the two-parameters limb-darkening law
($q_{1},q_{2}\to u_{1},u_{2}$), with Gaussian priors centred around the values
estimated from (?). Then, we include the RV model with the usual systemic
velocity $\overline{\gamma}_{\rm HARPS-N}$, jitter $\sigma_{\rm HARPS-N}$, and
the RV signal semi-amplitude $K_{\rm p}$.

The priors for all the parameters that are used in the joint analysis along
with the estimates of the parameters’ posteriors are summarized in Ext. Table
2, while the posterior distributions of the sampling parameters are shown as
corner plots in Ext. Fig. 5. The addition of linear slopes or RV GP models
(quasi-periodic, simple harmonic oscillator, Matern) did not increase the
Bayesian-log evidence. We also did not detect any trace of transit time
variations in a test done with juliet, where the orbital period of the transit
model was fixed at its best-fitting value while all the transit times were
allowed to vary. Furthermore, the inclusion of a second planetary RV signal
didn’t improve the Bayesian-log evidence, which is consistent with the lack of
a significant peak in the GLS of the RVs after the subtraction of TOI-1853 b
signal.

###  2.9 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 TOI-1853 b
signal. We simulated signals of additional companions in a logarithmic grid of
$30\times 40$ in the planetary mass, $M_{\rm p}$, orbital period, $P$,
parameter space respectively, covering the ranges $1-1000\,M_{\oplus}$ and
$0.5-5000$ d. For each location in the grid, we generated 200 synthetic
planetary signals, drawing $P$ and $M_{\rm p}$ from a log-uniform distribution
inside the cell, $T_{0}$ 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, i.e.
fitting the signals with either a circular-Keplerian orbit or a linear or
quadratic trend, to correctly take into account long-period signals which
would not be correctly identified as a Keplerian due to the short time-span of
the RV observations (500 d). We adopted the Bayesian Information Criterion
(BIC) to compare the fitted planetary model with a constant model: when
$\Delta\text{BIC}>10$ in favour of the planet-induced model, we considered the
planetary signal significantly detected. The detection function was then
computed as the fraction of detected signals for each element of the grid
(Ext. Fig. 6).

###  2.10 Orbital decay

According to the current tidal theory, tidal inertial waves are presently not
excited inside TOI-1853 by planet b because the rotation period of the star is
certainly longer than twice the planetary orbital period (?), while tidal
gravity waves are not capable of dissipating efficiently in the central region
of the star given the relatively low planetary mass (?). Even assuming a lower
limit for the modified tidal quality factor $Q^{\prime}_{\star}=10^{7}$, the
remaining lifetime of the planet is about 4 Gyr according to Eq. (1) of ref.
(?), or longer if we take into account equilibrium tides (?).

The situation is different if the planet’s orbital plane is inclined relative
to the stellar equator (?) 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, while it is not equally effective
in producing a decay of the orbit semi-major axis (?). Therefore, the
effective $Q^{\prime}_{*}$ ruling the orbital decay can be assumed to be
approximately unaffected by the stellar or planetary obliquities [see,
however, Sect. 2.2 of (?), for a quantification of how the obliquities affect
the evolution of the semimajor axis]. On the other hand, assuming
$Q^{\prime}_{\star}\sim 10^{6}$ for the dynamical obliquity tide, the
e-folding damping time of the stellar obliquity would be about 1.6 Gyr, which
is significantly shorter than the estimated age of the system. Therefore, any
initial stellar obliquity may have had time to be damped along the lifetime of
the system.

###  2.11 Formation simulations

We simulated systems of 2, 4 and 8 solid-rich planets with a total mass of
80$\,M_{\oplus}$, using the code swift symba5 (?). 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 5e-2 and the inclinations
between 0 and 1.4 degrees, to ensure that the system evolves in 3D and the
collision probability is not artificially enhanced. The systems with initially
2 and 4 proto-planets merged into a single planet with 80$\,M_{\oplus}$. The
system with 8 super-Earths merged into two planets of 50 and 30$\,M_{\oplus}$
respectively. We then did a fourth simulation starting from a system of 10
super-Earths of 10$\,M_{\oplus}$ each, which led to the formation of two
planets of 70$\,M_{\oplus}$ and 30$\,M_{\oplus}$.

For the second scenario, we simulated a Jupiter-mass planet on an orbit with a
semi-major axis at 1 au, perihelion distance at 0.02 au and inclination of 10
degrees. The planet is assumed to have a radius of 2 Jupiter radii, due 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. The
sharp decay of efficiency with the distance from the star is expected from the
increase in Savronov’s number (?).

###  2.12 Detailed impact simulations

A sequence of giant impacts should remove most of the gaseous envelopes that
might have been initially present around the original proto-planets. We
conducted a series of smoothed particle hydrodynamics impact simulations to
assess the effectiveness of atmosphere removal under different conditions,
using SWIFT (?, ?). Assuming the planets have three layers (H/He on top, rock
in the core and water in between) we explored three different compositions:
water-rich by mass (67.5 % water, 22.5 % rock, 10 % H/He), neutral (45 % rock,
45 % water, 10 % H/He), and rock-rich (67.5 % rock, 22.5 % water, 10 % H/He),
with the planets’ thermodynamic profiles generated using WoMa (?). The rocky
core, water, and atmosphere layers are modelled using the ANEOS forsterite
(?), AQUA water (?), and a mixture of hydrogen–helium (?) equation of states,
respectively. The ANEOS forsterite equation of state table was regenerated
using (?). The mass of the largest post-collision remnant ($M_{\rm lr}$) was
calculated using the method described in (?, ?). The maximum smoothing length
$h_{\rm max}$ was set to $5\,R_{\oplus}$ in these SWIFT simulations.

We tested various impact scenarios including head-on and oblique impacts with
pre-impact impactor to target mass ratio ranging from 0.5 to 1 (target masses
are 25, 45, 50 and 60 $M_{\oplus}$). We found that head-on (oblique) merging
collisions, where the target and impactor collide at a speed approximately
equal to their mutual escape velocity, would result in the removal of at most
10% (5%) of their atmospheres. Therefore, the system would have to go through
at least one high-speed impact ($\gtrsim 2$ mutual escape velocity) during its
final formation stage in order to remove most of the atmosphere. In Ext. Table
3, we list three impact simulation results that could lead to the formation of
TOI-1853 b.

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 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 setups,
confirming that rock is less likely to be lost due to the core being in the
centre and being less compressible than water and the atmosphere.

###  2.13 Photo-evaporation

At the present age, the Jeans escape parameter $\Lambda$ ($\propto M_{\rm
p}/R_{\rm p}T_{\rm eq}$) (?) indicates that the atmosphere of TOI-1853 b is in
hydrodynamic stability, thanks to the deep gravitational potential well of the
planet. To explore its evolution, we adapted a numerical code developed for
studying single systems (?, ?), considering the following three scenarios:
rocky core + an H2-dominated envelope (1% by mass), 49.95% rocky core + 49.95%
water mantle + 0.1% H2-dominated envelope, 50% rocky core + 50% water mantle
and no envelope. For each case, we created a synthetic population of young
planets (10 Myr old) with a large envelope and different atmospheric
fractions. At any age, the planet’s radius is the sum of a fixed core radius
plus a time-dependent envelope radius.

The planets passed through an evaporation phase in which the radius contracted
due to mass loss and gravitational shrinking. We followed their evolutionary
history up to 7 Gyr and found that none of the planets is either initially, or
later becomes, hydro-dynamically 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 $\sim
200$ Myr. This means that the current planet’s structure cannot be the result
of strong photo-evaporation processes.

###  2.14 Atmospheric transmission spectrum modeling

To estimate expected transmission spectral signals that could be observed by
the JWST (?), we generated synthetic spectra for TOI-1853 b using the open-
source Pyrat Bay modelling framework (?). We considered two extreme cases
based on the scenarios previously explored: 99% rocky core with 1% H2
atmosphere, and 50% rocky core, 40% H2O mantle with a 10% H2O supercritical
steam atmosphere. We assumed an atmosphere with an isothermal temperature
profile at the planet’s $T_{\rm eq}$ and, for simplicity, we only considered
the opacity from H2 and H2O. We then simulated with PandExo (?) a series of
transmission-spectrum data for the JWST NIRISS/SOSS, NIRSpec/G395H, and
MIRI/LRS to cover the $0.9-10.0\,\mu$m wavelength range.

Ext. Fig. 7 shows our model spectra of TOI-1853 b along with the simulated
JWST observations combining three transits with each instrument to enhance the
signal-to-noise ratios. The main difference between the H2\- and H2O-dominated
cases is the flattening of the H2O spectral features due to the larger mean
molecular mass of the latter. For the H2-dominated atmosphere we assumed a
solar H2O trace abundance, though there were no significant variations for a
range $0.01-50.0\times$ solar metallicities. Of the three instruments,
NIRISS/SOSS is the best suited to differentiate between H2\- and H2O-dominated
atmospheres, being able to trace the slope of increasing H2O absorption with
wavelength over the 0.9 and 2.8 $\mu$m range for the H2-dominated atmosphere,
as opposed to the flat transmission spectrum for the H2O-dominated atmosphere.

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##  3 Addendum

###  3.1 Author contributions

L. N. analyzed the transit, RV data and wrote the manuscript. A. S. and A. S.
B. performed the selection of TESS Neptunes for the HARPS-N follow-up and
scheduled the HARPS-N observations within the GAPS consortium. A. S. performed
a preliminary RV analysis. L. M., A. S. B., A. S. and M. D. supervised the
work and contributed to writing the manuscript. X. D. reduced HARPS-N spectra.
M. P. estimated the detection function of HARPS-N RVs. A. S. B. and K. B.
determined the stellar parameters. A. W. M. and C. Z. performed and analyzed
SOAR observations, while J. E. S., S. B. H., K. V. L. and R. M. obtained and
reduced the Gemini data. D. R. C and C. Z. contributed to writing the high-
resolution imaging section. E. G. is the Keck data collector. A. M. performed
the simulations and contributed to writing the formation scenario with the
help of J. J. L., while J. D., Z. L. and P. C. computed the body collision
simulations. L. Z. analyzed the planet’s composition. K. A. C. scheduled the
LCO observations, performed data reduction along with R. P. S., and
contributed to writing the light curve follow-up sections. J. F. K. performed
the ULMT observations and their data reduction. E. L. N. J. performed the
joint MCMC analysis of the LCO and ULMT light curves. E. Pal. obtained the
data of MuSCAT2. D. L. and A. Ma. analyzed the evolutionary history of the
atmosphere. P. C. estimated the transmission spectral signals observed by
JWST. A. L. computed the lifetime of the planet. D. S., A. B., D. N., I. P.,
L. Mal. and T. Z. are members of the Science Team of the GAPS (Global
Architecture of Planetary System) consortium, while A. G., R. C., W. B., A. F.
M. F., M. Pe. and A. H. are members of the TNG (Telescopio Nazionale Galileo)
which has conducted the RV observations. L. G. B. is a member of the _TESS_
Payload Operations Center (POC), while J. D. T. is a member of the _TESS_
Science Processing Operations Center (SPOC). A. Sh., M. B. L, S. S. and J. N.
W. are _TESS_ contributors. All authors have contributed to the interpretation
of the data and the results.

###  3.2 Acknowledgments

We acknowledge the use of public TESS data from pipelines at the TESS Science
Office and at the TESS Science Processing Operations Center. Resources
supporting this work were provided by the NASA High-End Computing (HEC)
Program through the NASA Advanced Supercomputing (NAS) Division at Ames
Research Center for the production of the SPOC data products. The work is
based on observations made with the Italian Telescopio Nazionale Galileo (TNG)
operated on the island of La Palma by the Fundacion Galileo Galilei of the
INAF (Istituto Nazionale di Astrofisica) at the Spanish Observatorio del Roque
de los Muchachos of the Instituto de Astrofisica de Canarias. This work has
also made use of data from the European Space Agency (ESA) mission Gaia
(https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and
Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). This work makes use of
observations from the LCOGT network. Part of the LCOGT telescope time was
granted by NOIRLab through the Mid-Scale Innovations Program (MSIP). MSIP is
funded by NSF. This research has made use of the Exoplanet Follow-up
Observation Program (ExoFOP; DOI: 10.26134/ExoFOP5) website, which is operated
by the California Institute of Technology, under contract with the National
Aeronautics and Space Administration under the Exoplanet Exploration Program.
This paper makes use of observations made with the MuSCAT2 instrument,
developed by the Astrobiology Center, at Telescopio Carlos Sánchez operated on
the island of Tenerife by the IAC in the Spanish Observatorio del Teide, and
is also based in part on observations obtained at the Southern Astrophysical
Research (SOAR) telescope, which is a joint project of the Ministério da
Ciência, Tecnologia e Inovações do Brasil (MCTI/LNA), the US National Science
Foundation’s NOIRLab, the University of North Carolina at Chapel Hill (UNC),
and Michigan State University (MSU). This work has been carried out within the
framework of the NCCR PlanetS supported by the Swiss National Science
Foundation under grants 51NF40-182901 and 51NF40-205606. This paper made use
of observation from the High-Resolution Imaging instrument ‘Alopeke and were
obtained under Gemini LLP Proposal Number: GN/S-2021A-LP-105. ‘Alopeke was
funded by the NASA Exoplanet Exploration Program and built at the NASA Ames
Research Center by Steve B. Howell, Nic Scott, Elliott P. Horch, and Emmett
Quigley. ‘Alopeke was mounted on the Gemini North telescope of the
international Gemini Observatory, a program of NSF’s OIR Lab, which is managed
by the Association of Universities for Research in Astronomy (AURA) under a
cooperative agreement with the National Science Foundation. On behalf of the
Gemini partnership: the National Science Foundation (United States), National
Research Council (Canada), Agencia Nacional de Investigación y Desarrollo
(Chile), Ministerio de Ciencia, Tecnología e Innovación (Argentina),
Ministério da Ciência, Tecnologia, Inovações e Comunicações (Brazil), and
Korea Astronomy and Space Science Institute (Republic of Korea). The giant
impact simulations were carried out using the computational facilities of the
Advanced Computing Research Centre, University of Bristol.

###  3.3 Funding

Funding for the DPAC has been provided by national institutions, in
particular, the institutions participating in the Gaia Multilateral Agreement.
L. N. and D. L. acknowledge the support of the ARIEL ASI-INAF agreement
2021-5-HH.0. L. M. acknowledges support from the “Fondi di Ricerca Scientifica
d’Ateneo 2021” of the University of Rome “Tor Vergata”. A. Ma. and A. S. B.
acknowledge support from the ASI-INAF agreement n.2018-16-HH.0 (THE StellaR
PAth project), and from PRIN INAF 2019. Funding for the TESS mission is
provided by NASA’s Science Mission Directorate. This project has received
funding from the European Research Council (ERC) under the European Union’s
Horizon 2020 research and innovation programme (grant agreement SCORE No
851555). S. B. H acknowledges funding from the NASA Exoplanet Program Office.
K. A. C acknowledges support from the TESS mission via sub-award s3449 from
MIT. TZi acknowledges support from CHEOPS ASI-INAF agreement n. 2019-29-HH.0.
J. D. acknowledges the funding support from the Chinese Scholarship Council
(No. 202008610218,). This work is partly supported by JSPS KAKENHI Grant
Numbers JP17H04574, JP18H05439, and JST CREST Grant Number JPMJCR1761.

###  3.4 Competing interests:

We declare no competing interests.

###  3.5 Data and materials availability

The juliet code is freely available at https://github.com/nespinoza/juliet.
astropy is a common core package for astronomy in Python, and EXOFASTV2 is a
public exoplanet fitting software. TESS photometric time series can be freely
obtained from the Mikulski Archive for Space Telescopes (MAST) archive at
https://exo.mast.stsci.edu/. All follow-up light curve data are available on
the EXOFOP-TESS website. Radial velocities are presented in Ext. Table 1.

##  4 Extended data

Table 2: Extended Data Table 1: HARPS-N Radial velocities. FWHM is the Full Width Half Maximum of the CCF profile, BIS is the Bisector Inverse Slope span, Contrast is referred to stellar line measurement of the spectral lines and $S_{MW}$ is the Mount Wilson index. BJDTDB | RV | $\sigma_{\rm RV}~{}~{}~{}$ | FWHM | BIS | Contrast | $S_{\rm MW}$ | $\sigma_{S_{\rm MW}}$
---|---|---|---|---|---|---|---
(2 459 000 + ) | (m s-1) | (m s-1) |  |  |  |  |
277.591475 | -26 221.79 | 4.97 | 6696 | -24 | 66.70484 | 0.3101 | 0.0059
286.743959 | -26 312.69 | 7.21 | 6658 | -37 | 67.19193 | 0.2436 | 0.0096
288.667942 | -26 223.50 | 4.32 | 6656 | -37 | 66.92455 | 0.2719 | 0.0048
289.698557 | -26 266.22 | 4.32 | 6646 | -53 | 66.86836 | 0.2740 | 0.0046
297.604184 | -26 219.81 | 8.57 | 6795 | -7 | 65.98741 | 0.1466 | 0.0102
298.627811 | -26 222.97 | 10.08 | 6720 | -28 | 66.33820 | 0.4311 | 0.0126
299.645873 | -26 264.59 | 7.65 | 6748 | -42 | 66.35285 | 0.3371 | 0.0086
305.749103 | -26 286.43 | 6.23 | 6697 | -22 | 66.60946 | 0.3230 | 0.0078
307.671216 | -26 246.47 | 4.47 | 6743 | -39 | 66.21211 | 0.3493 | 0.0041
325.603943 | -26 309.55 | 11.53 | 6667 | -68 | 66.49581 | 0.3380 | 0.0158
327.671492 | -26 281.97 | 4.65 | 6757 | -32 | 66.08518 | 0.2944 | 0.0045
360.503076 | -26 287.33 | 7.28 | 6789 | -10 | 65.92973 | 0.3035 | 0.0072
365.572246 | -26 253.24 | 6.43 | 6723 | -37 | 66.24472 | 0.3000 | 0.0075
366.609855 | -26 306.84 | 5.35 | 6734 | -47 | 66.30966 | 0.2581 | 0.0064
367.546558 | -26 299.87 | 4.04 | 6695 | -34 | 66.79568 | 0.2893 | 0.0046
377.551116 | -26 298.74 | 3.69 | 6712 | -39 | 66.35716 | 0.3009 | 0.0037
378.532182 | -26 245.68 | 4.70 | 6735 | -41 | 66.01514 | 0.2932 | 0.0047
379.507227 | -26 208.93 | 6.26 | 6748 | -29 | 66.11978 | 0.3012 | 0.0070
387.495223 | -26 304.60 | 4.86 | 6705 | -36 | 66.52209 | 0.2931 | 0.0058
391.502386 | -26 298.61 | 6.35 | 6721 | -24 | 66.32581 | 0.3742 | 0.0076
416.441714 | -26 287.90 | 5.64 | 6683 | -37 | 66.62051 | 0.2863 | 0.0069
565.753307 | -26 266.64 | 5.33 | 6711 | -46 | 66.64815 | 0.3154 | 0.0082
615.721992 | -26 217.35 | 5.88 | 6621 | -38 | 67.06423 | 0.2632 | 0.0093
617.727567 | -26 312.22 | 10.41 | 6700 | -65 | 66.12045 | 0.2601 | 0.0156
618.719631 | -26 293.86 | 8.97 | 6703 | -48 | 66.26545 | 0.2636 | 0.0138
624.713851 | -26 249.18 | 3.55 | 6638 | -39 | 67.17890 | 0.2693 | 0.0050
625.734802 | -26 232.57 | 4.89 | 6642 | -48 | 66.95316 | 0.3119 | 0.0075
627.729205 | -26 322.66 | 4.68 | 6675 | -44 | 66.86213 | 0.3163 | 0.0069
642.724298 | -26 301.89 | 8.37 | 6692 | -61 | 66.50986 | 0.3280 | 0.0139
646.687152 | -26 249.38 | 2.91 | 6697 | -45 | 66.83894 | 0.3069 | 0.0035

Extended Data Table 1. Continued

648.731285 | -26 318.04 | 3.59 | 6682 | -47 | 66.86892 | 0.2862 | 0.0049
---|---|---|---|---|---|---|---
649.716835 | -26 272.73 | 4.75 | 6695 | -41 | 66.83616 | 0.2651 | 0.0070
650.721339 | -26 223.27 | 3.14 | 6665 | -35 | 67.02990 | 0.3126 | 0.0042
656.721298 | -26 240.13 | 8.62 | 6685 | -43 | 66.52727 | 0.2212 | 0.0139
663.759353 | -26 313.20 | 4.18 | 6697 | -53 | 66.54938 | 0.3136 | 0.0057
678.681216 | -26 304.51 | 7.85 | 6664 | -14 | 66.59712 | 0.2085 | 0.0131
681.703784 | -26 220.95 | 4.43 | 6710 | -43 | 66.56025 | 0.3083 | 0.0063
682.627666 | -26 272.22 | 3.47 | 6673 | -31 | 66.80372 | 0.3234 | 0.0047
690.693058 | -26 253.74 | 6.26 | 6734 | -40 | 66.21964 | 0.3055 | 0.0085
705.597822 | -26 243.73 | 5.00 | 6706 | -38 | 66.47439 | 0.3220 | 0.0069
706.532481 | -26 222.90 | 4.93 | 6691 | -41 | 66.80752 | 0.3202 | 0.0074
708.602432 | -26 321.66 | 9.21 | 6705 | -84 | 66.49706 | 0.3678 | 0.0151
717.556786 | -26 253.74 | 2.63 | 6692 | -37 | 66.83179 | 0.3263 | 0.0029
718.552650 | -26 312.70 | 3.47 | 6707 | -46 | 66.61027 | 0.3156 | 0.0041
735.582824 | -26 291.38 | 13.70 | 6701 | -81 | 66.50634 | 0.3421 | 0.0226
737.473873 | -26 272.62 | 34.93 | 6692 | 24 | 65.65718 | 0.0604 | 0.0619
738.528763 | -26 290.10 | 8.60 | 6694 | -37 | 66.51006 | 0.3167 | 0.0134
748.535890 | -26 270.21 | 9.92 | 6700 | -51 | 66.38869 | 0.2286 | 0.0155
750.506612 | -26 279.02 | 5.85 | 6717 | -33 | 66.28337 | 0.2809 | 0.0075
751.517693 | -26 228.38 | 4.37 | 6731 | -39 | 66.26938 | 0.2608 | 0.0052
752.506892 | -26 228.51 | 4.88 | 6685 | -40 | 66.58633 | 0.2531 | 0.0070
773.458642 | -26 265.56 | 3.49 | 6693 | -48 | 66.6854 | 0.3202 | 0.0042
774.449876 | -26 320.37 | 2.72 | 6662 | -56 | 66.99418 | 0.3100 | 0.0033
775.457294 | -26 295.77 | 4.99 | 6689 | -42 | 66.72325 | 0.3196 | 0.0072
803.398361 | -26 245.88 | 3.47 | 6656 | -32 | 66.94536 | 0.2849 | 0.0047
807.396243 | -26 222.41 | 6.10 | 6705 | -38 | 66.42269 | 0.2925 | 0.0095

Table 3: Extended Data Table 2: Global joint fit priors and posteriors. The best-fitting values and uncertainties are extracted from the posterior probability distributions. $\mathcal{U}(a,\>b)$ indicates a uniform distribution between $a$ and $b$; $\mathcal{L}(a,\>b)$ a log-normal distribution, and $\mathcal{N}(a,\>b)$ a normal distribution with mean $a$ and standard deviation $b$. |  | Prior | Posterior
---|---|---|---
Parameters | Unit | distribution | Value ($\pm 1\sigma$)
Keplerian Parameters |  |  |
$P$ | days | $\mathcal{U}(1,\>100)$ | $1.2436275^{+0.0000027}_{-0.0000031}$
$T_{0}$ | BJDTDB | $\mathcal{U}(2459669.0,\>2459691.5)$ | $2\,459\,690.7419\pm 0.0008$
$\sqrt{e}\,\sin\omega$ |  | $\mathcal{U}(-1.0,\>1.0)$ | $-0.038\pm 0.11$
$\sqrt{e}\,\cos\omega$ |  | $\mathcal{U}(-1.0,\>1.0)$ | $0.043\pm 0.06$
$\rho_{\star}$ | kg m-3 | $\mathcal{N}(2240,\>130)$ | $2255^{+131}_{-128}$
Transit Parameters |  |  |
$r_{1}$ |  | $\mathcal{U}(0.0,\>1.0)$ | $0.670\pm^{+0.038}_{-0.045}$
$r_{2}$ |  | $\mathcal{U}(0.0,\>1.0)$ | $0.0391\pm^{+0.0010}_{-0.0011}$
$q_{1}$ |  | $\mathcal{N}(0.44,\>0.10)$ | $0.48^{+0.10}_{-0.09}$
$q_{2}$ |  | $\mathcal{N}(0.20,\>0.10)$ | $0.25^{+0.09}_{-0.10}$
$b$ |  | – | $0.51^{+0.06}_{-0.07}$
$i$ | deg | – | $84.9^{+0.7}_{-0.6}$
$TESS_{\textsf{off}}$ |  | $\mathcal{N}(1.0,\>0.001)$ | $0.0001\pm 0.0002$
$TESS_{\textsf{jitt}}$ | ppm | $\mathcal{L}(10^{-1},\>10^{3})$ | $0.27^{+2.77}_{-0.24}$
$\sigma_{\textsf{GP}}$ | ppm | $\mathcal{L}(10^{-5},\>10)$ | $0.00052^{+0.00016}_{-0.00010}$
$\rho_{\textsf{GP}}$ | days | $\mathcal{L}(0.1,\>100)$ | $3.0^{+1.0}_{-0.7}$
RV Parameters |  |  |
$K_{\rm p}$ | m s-1 | $\mathcal{U}(0.0,\>100.0)$ | $49.0\pm 1.2$
$\overline{\gamma}_{\textsf{HARPS-N}}$ | m s-1 | $\mathcal{U}(-26280,\>-26250)$ | $-26267.4\pm 0.8$
$\sigma_{\textsf{HARPS-N}}$ | m s-1 | $\mathcal{U}(0,\>10)$ | $4.5^{+0.8}_{-0.7}$

Table 4: Extended Data Table 3: Impact simulation results. Three scenarios of a $30\,M_{\oplus}$ impactor colliding onto a $60\,M_{\oplus}$ target with varying water/rock ratios. $M_{\rm lr}$ is the mass of the largest post-collision remnant. $f$ shows the mass ratio of each material in the largest post-collision remnant. $X^{\rm atmos}_{\rm loss}$ shows the total mass fraction of the atmosphere that is lost. All simulations shown are head-on impacts.  Component |  $V_{\rm imp}$ (km/s) | $M_{\rm lr}/M_{\oplus}$ | $f_{\rm H_{2}O}$ | $f_{\rm si}$ | $f_{\rm H\&He}$ | $X^{\rm atmos}_{\rm loss}$
---|---|---|---|---|---|---
Water Rich | 75.5 | 74.2 | 71.67% | 27.20% | 1.13% | 90.7%
Equal water and rock | 77.7 | 72.8 | 42.92% | 55.30% | 1.78% | 85.6%
Rock Rich | 80.2 | 73.5 | 16.13% | 81.11% | 2.76% | 77.4%

Extended Data Figure 1: Fit of phase-folded on-ground transits. The blue
symbols show the LCOGT data in Sloan $g^{\prime}$ band in 10-minute bins. The
red symbols show the ULMT data in Sloan $r^{\prime}$ band in 10-minute bins,
shifted on the Y-axis for clarity. Grey symbols show the unbinned data. The
error bars represent one standard deviation. A joint transit model fit to both
light curves, which included an ephemeris prior from the global fit in this
work, is over-plotted using solid lines.

Extended Data Figure 2: Keck Near-Infrared Adaptive Optics sensitivity curve.
The image reaches a contrast of $\sim 7.5$ magnitudes fainter than the host
star within $0.5^{\prime\prime}$ in the Br-$\gamma$ filter. Inset: Image of
the central portion of the data.

Extended Data Figure 3: TOI-1853 Spectral Energy Distribution. The error bars
represent one standard deviation. The best-fit model is displayed as a solid
black line.

Extended Data Figure 4: GLS periodograms of RVs and activity indexes. The main
peak of the RV GLS periodogram, at 1.24 days, and his 1-day alias are
highlighted by a red and green vertical bar, respectively. The horizontal
dashed lines remark the $10\%$ and $1\%$ confidence levels (evaluated with the
bootstrap method), respectively.

Extended Data Figure 5: Corner plot for the posterior distributions of the
global joint fit. The blue lines indicate the average value of every
parameter, while the dashed vertical lines are plotted at a distance of one
standard deviation.

Extended Data Figure 6: HARPS-N RV detection map. The colour scale expresses
the detection function (e.g. the detection probability), and the red circle
marks the position of TOI-1853 b.

Extended Data Figure 7: TOI-1853 b transmission spectra simulated for JWST.
The solid curves show two synthetic spectra for an H2-dominated atmosphere
(orange line) and an H2O-dominated atmosphere (grey line), with the respective
simulated JWST observations (top and bottom panel), shown as markers with
$1\sigma$ error bars, when combining 3 transits for each instrument (see
labels).