The TESS-Keck Survey. XII. A Dense 1.8 R ⊕ Ultra-short-period Planet Possibly Clinging to a High-mean-molecular-weight Atmosphere after the First Gigayear

The extreme environments of ultra-short-period planets (USPs) make excellent laboratories to study how exoplanets obtain, lose, retain, and/or regain gaseous atmospheres. We present the confirmation and characterization of the USP TOI-1347 b, a 1.8 ± 0.1 R ⊕ planet on a 0.85 day orbit that was detected with photometry from the TESS mission. We measured radial velocities of the TOI-1347 system using Keck/HIRES and HARPS-N and found the USP to be unusually massive at 11.1 ± 1.2 M ⊕. The measured mass and radius of TOI-1347 b imply an Earth-like bulk composition. A thin H/He envelope (>0.01% by mass) can be ruled out at high confidence. The system is between 1 and 1.8 Gyr old; therefore, intensive photoevaporation should have concluded. We detected a tentative phase-curve variation (3σ) and a secondary eclipse (2σ) in TESS photometry, which, if confirmed, could indicate the presence of a high-mean-molecular-weight atmosphere. We recommend additional optical and infrared observations to confirm the presence of an atmosphere and investigate its composition.


Introduction
Ultra-short-period planets, or USPs, are exoplanets that orbit their stars with short orbital period (<1 day).USPs tend to not exceed 2 R ⊕ in size, save for the closest of the hot Jupiter (HJ) population.This "hot-Neptune desert" (Mazeh et al. 2016) has been hypothesized to be sculpted by mass-loss mechanisms, such as photoevaporation (Owen & Wu 2017) or core-powered mass loss (Gupta & Schlichting 2019).Such mechanisms destroy the atmospheres of smaller planets, whereas giant Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
planets can better resist mass loss (in fact, HJ atmospheres can become inflated; Batygin et al. 2011;Grunblatt et al. 2017).The Kepler mission (Borucki et al. 2010) took the first steps to map out the demographics of close-in transiting planets and revealed that USPs exist around ∼0.5%-0.8% of GK stars (Sanchis-Ojeda et al. 2014).Another key discovery from Kepler was the "radius gap" around 1.7-1.9R ⊕ , which separated the bimodal peaks corresponding to the smaller super-Earth population (no atmosphere) and the larger sub-Neptunes (1% H/He atmosphere; Fulton et al. 2017;Fulton & Petigura 2018).
To date, only two nongiant USPs have been discovered with radii larger than 2 R ⊕ .TESS Object of Interest (TOI) 849 b (Armstrong et al. 2020) is a massive (∼40 M ⊕ ), rocky world that is likely the stripped core of a giant planet (perhaps via giant collisions).LTT-9779 b (29 M ⊕ , 0.79 day; Jenkins et al. 2020) defies its environment with a substantial (9% by mass) H/He atmosphere and a 4.6 R ⊕ radius.This suggests some USPs can retain atmospheres.If so, where is the boundary between bare rocky cores and those with residual (or secondary) atmospheres?
A close-in orbiting planet will reflect starlight and emit thermal radiation, causing the observed brightness of the system to vary with the planet's orbital position.This variation, called the phase curve, depends on the planet's albedo and day-night temperature contrast.Phase-curve variations have been used to directly probe the surfaces of several USPs, finding some to be bare rock (LHS 3844b; Kreidberg et al. 2019;Kane et al. 2020) and others to perhaps possess highmean-molecular-weight atmospheres (55 Cnc e; Demory et al. 2016).
Unlike Kepler, which observed a single patch of sky for 4 yr, the Transiting Exoplanet Survey Satellite (TESS; Ricker et al. 2015) is an all-sky transit survey that has discovered thousands of close-in planets around nearby bright stars that are amenable to radial velocity (RV) follow-up measurements.RVs provide key insight into the existence of exoplanetary atmospheres by measuring the planet's mass, thereby constraining the bulk density, planet surface gravity (which is related to atmospheric scale height), and its ability to resist photoevaporation.Our collaboration, the TESS-Keck Survey (TKS; Chontos et al. 2022), has been monitoring 86 TESS systems with RV followup using the HIgh Resolution Echelle Spectrometer (HIRES; Vogt et al. 1994) at the Keck I Telescope.As part of TKS, we have measured the masses of several USPs, such as TOI-561 b (Weiss et al. 2021) and TOI-1444 b (Dai et al. 2021), both of which have rocky compositions.In this paper, we present the discovery and mass measurement of the USP TOI-1347 b.The heaviest of the nongiant USPs31 to date, TOI-1347 b shows hints of phase-curve variability and a secondary eclipse in its TESS photometry, which may indicate the presence of a highmean-molecular-weight atmosphere.We also detected a second transiting planet in the system at 4.84 d, TOI-1347 c, in line with the common trend for USPs to have nearby outer companions that can shepherd the migrations of their USPs into their present sub-day orbits (Millholland & Spalding 2020).
This paper is structured as follows.In Section 2 we characterize the host star using spectroscopy.We rule out stellar companions using speckle imaging in Section 3. In Section 4 we analyze the TESS light curve to measure the stellar rotation period, planetary transits, and tentative phasecurve variability and secondary eclipse.In Section 5 we present our RV measurements and the resulting mass constraints for both planets.Finally, we discuss the implications of our observations for the TOI-1347 system in Section 6.

HK
), showing strong variability in both photometry (see Section 4) and RVs (see Section 5).
We obtained high-resolution spectra of TOI-1347 with HIRES (with the B3 decker, R = 67,000) and the High Accuracy Radial Velocity Planet Searcher-North (HARPS-N; R = 115,000); see Section 5 for details.We applied the SpecMatch-Synthetic (Petigura 2015) algorithm to the HIRES spectrum to measure T eff , M å , Fe/H, and g log .These parameters, as well as the J and K magnitudes from the TICv8 catalog (Paegert et al. 2021) and the Gaia parallax (Gaia Collaboration et al. 2023), were input into isoclassify (Huber et al. 2017;Berger et al. 2020) to constrain R å .We also used KeckSpec (A.Polanski 2024, in preparation) to compute alpha elemental abundances.Stellar parameters for TOI-1347 are included in the catalog of MacDougall et al. (2023).We verified that our values agree with the values therein to within 1σ.
We similarly derived spectroscopic parameters from the coadded HARPS-N spectra of TOI-1347 using the FASMA spectral synthesis package (Tsantaki et al. 2018(Tsantaki et al. , 2020)).We verified that all derived quantities were in agreement with the HIRES values.In particular, the HARPS-N data are of sufficient resolution to detect  v i sin , whereas with HIRES we only obtain an upper limit.Table 1 lists our adopted stellar parameters.

Age
We constrained the age of the host star using several methods.Using a stellar rotation period of 16.1 ± 0.3 days (see Section 4.1 for details), we estimated the gyrochronological age of the star.The scaling relation of Mamajek & Hillenbrand (2008) gives an age of 1.33 ± 0.06 Gyr.Using the latest empirical relations of Bouma et al. (2023), the age is 1.7 ± 0.1 Gyr.We also obtained an age estimate using chromospheric activity in the Ca II H and K lines from our HIRES spectra.We measured ¢ = - R log 4.66 0.05 HK using the method of Isaacson & Fischer (2010).Combining with the calibration of Mamajek & Hillenbrand (2008), the corresponding age is 1.6 ± 0.4 Gyr.We also looked for the lithium doublet in our HIRES spectra but were unable to detect the lithium doublet above the noise floor in the continuum (see Figure 1).We placed an upper limit of 2 m Å (95% confidence) on the equivalent width.According to Berger et al. (2018), the star is consistent with field stars and is most likely older than the Hyades cluster (∼650 Myr).Lastly, MacDougall et al. (2023) derived an age of -+ 0.8 0.6 1.1 Gyr from isochronal fitting.The age uncertainties above do not account for systematic errors.Therefore, we combined age indicators with an unweighted mean.We adopted a wide age uncertainty of 0.4 Gyr to reflect the systematic uncertainties between the different age estimators.Our best age estimate for TOI-1347 is thus 1.4 ± 0.4 Gyr.Importantly, this age is longer than the timescale on which photoevaporation operates, which is typically confined to the first few hundred megayears when the star is active in X-rays and extreme UV (Ribas et al. 2005;Tu et al. 2015).

High-resolution Imaging
To help validate the transiting planets, we observed TOI-1347 with the 'Alopeke (Scott et al. 2021) dual-channel speckle imaging instrument on Gemini-N (PI: Crossfield) with a pixel scale of 0 01 pixel −1 and a full width at half maximum resolution of 0 02.With 'Alopeke we obtained simultaneous speckle imaging at 562 and 832 nm, with a total of seven observing blocks each consisting of one thousand 60 ms exposures.e Petigura (2015), using an HIRES spectrum taken at R ∼ 67,000 with no iodine.f A. Polanski (2024, in preparation), using a HIRES spectrum taken at R ∼ 67,000 with no iodine.g Tsantaki et al. (2018Tsantaki et al. ( , 2020)), using the coadded HARPS-N spectra.We processed these images with the speckle pipeline of Howell et al. (2011), which yielded the 5σ sensitivity curves and reconstructed image shown in Figure 2. The curves do not show companions at angular separations of 0 5 or greater at a contrast of 4.12 mag at 562 nm and 6.52 mag at 832 nm (Figure 2).
We downloaded the 20 and 120 s cadence SPOC light curves using lightkurve (Lightkurve Collaboration et al. 2018).We removed all data points with a nonzero quality flag, i.e., those suffering from cosmic rays or other known systematic issues.We then stitched and normalized the multisector data using lightkurve and applied a 5σ clipping.lightkurve also provides the correction for scattered light (2% contamination reported by ExoFOP).The resulting light curve, shown in Figure 3, exhibits significant but coherent periodic variability corresponding to rotationally modulated surface inhomogeneities on the stellar disk.

Stellar Rotation Period
The effect of a starspot on photometry is to reduce the observed (integrated) intensity when on the visible hemisphere.The net effect of many spots is quasiperiodic variability that can be treated as time-correlated noise (Haywood et al. 2014;Rajpaul et al. 2015;Aigrain & Foreman-Mackey 2023).The TESS photometry of TOI-1347 shows strong rotational variability with maxima/minima occurring roughly every ∼8 days (see the top panel in Figure 3).A Lomb-Scargle periodogram of the photometry shows a strong peak at 8 days (Figure 4).However, a closer examination of the light curve reveals that the depths of adjacent maxima/minima are dissimilar.In fact, the depths of alternating maxima/minima tend to have similar amplitudes.This can be explained if the star has a 16 day rotation period and multiple spot groups concentrated on opposite hemispheres of the star, an effect noted for a number of other stars (Holcomb et al. 2022).In fact, a periodogram analysis of the RV data set shows a strong peak at 16 days (Figure 4).Spots affect RVs in much the same way as photometry by breaking the flux balance across star's rotational velocity profile (Saar & Donahue 1997), in addition to suppressing the convective blueshift (Haywood et al. 2016).
While the periodogram is essentially a Fourier decomposition showing the amplitude of the best-fitting sine wave at all possible periods, the autocorrelation function (ACF) measures the self-similarity of a time series as a function of time delay.Thus, if the variability in a time series is not sinusoidal (asymmetric, more complex shape), then the ACF will give a better estimate of the periodicity than the periodogram.The ACF of the TESS photometry has its highest peak at ∼16 days (Figure 3) with adjacent ACF peaks alternating between high and low amplitude.An analysis of the ACF using spinspotter (Holcomb et al. 2022) successfully identified the half-period effect by checking that the odd peaks are less than 10% the height of the even peaks.spinspotter returns a rotation period of P rot = 16.1 ± 0.3 days by averaging the locations of the even-numbered peaks only.We also measured the stellar rotation period using the TESS Systematics Insensitive Periodogram (TESS-SIP) algorithm (Hedges et al. 2020).TESS-SIP simultaneously corrects for instrument systematics while performing the periodogram search on the TESS Simple Aperture Photometry.Using TESS-SIP for sectors 14-26 for TOI-1347, we measured a stellar rotation period of 16.34 ± 0.57 days.
With all of this considered, we adopt the ∼16 day solution as the rotation period of TOI-1347 and explain the Lomb-Scargle periodogram peak at P rot /2 as arising from antipodal spot groups.The persistence of repeated peaks every 8 days in the ACF, even out to beyond 100 days, can be explained if the starspots on TOI-1347 live for many rotation periods.Following the prescription of Giles et al. (2017), we fit the observed ACF with an underdamped simple harmonic oscillator, including a second component with power at P/2: In Equation (1), y is the ACF strength, and the coefficients A and B give the relative strengths of the antipodal spot groups.We used scipy.optimize(Virtanen et al. 2020) to find the maximum a posteriori (MAP) solution, then used that as a seed for a Markov Chain Monte Carlo (MCMC) analysis using emcee (Foreman-Mackey et al. 2013).The fit recovered P = 16.0 days, and the best-fit exponential decay timescale was τ = 45 days, roughly 3 times the rotation period.Both coefficients A = 0.05 and B = 0.18 were constrained to nonzero values, again supporting the multiple spot group hypothesis.Lastly, our SpecMatch-Synthetic analysis of the HIRES spectrum in Section 2.1 yielded only an upper limit corresponding to the line spread function of HIRES (roughly 2.2 km s −1 ).Masuda et al. (2022) recently showed that on the population level, such nondetections of are most consistent with a <3 km s −1 upper limit.Combining P rot = 16.1 days with the stellar radius from Section 2.1, we get an equatorial rotational velocity of v eq = 2.6 ± 0.1 km s −1 .This is consistent with a <3 km s −1 upper bound for HIRES though it is slightly smaller than the measured HARPS-N value.Were the rotation period 8 days, we would instead have v eq ∼ 5 km s −1 , which (barring a misaligned stellar inclination of 30°) would be detectable in the HIRES spectrum and inconsistent with the HARPS-N measurement.If astrophysical, the slightly larger

Additional Transiting Planets?
We searched the TESS light curve for planetary transits with a Box-fitting Least Squares (BLS; Kovács et al. 2002) algorithm as described in Dai et al. (2021).We recovered the two planet candidates reported by ExoFOP at 0.84 and 4.84 days.We did not find any other transit signals with signal-to-noise ratio (S/N) > 6.5.

Transit Modeling
Our transit analysis closely follows that described in Dai et al. (2021).Briefly, we generated transit signals using the Python package Batman (Kreidberg 2015), parameterized with the stellar density (ρ * ) to break the degeneracy between the scaled semimajor axes (a/R * ) and impact parameters (b) of the transiting planets (Seager & Mallén-Ornelas 2003).We imposed a prior using the best-fit stellar density from our adopted M * and R * of ρ * = 2.25 ± 0.26 g cm −3 .For the limb darkening coefficients, we used the prior and parameterization scheme of Kipping (2013) for a quadratic limb darkening law (q 1 and q 2 ).The other transit parameters included the orbital period (P orb ), time of conjunction (T c ), planet-to-star radius ratios (R p /R å ), scaled orbital distances (a/R å , computed from stellar density and orbital period), orbital inclinations (cosi), orbital eccentricities (e), and the arguments of pericenter (ω).We initially allowed nonzero eccentricities for both TOI-1347 b and c; however, the posterior distributions are fully consistent with circular orbits.Neither the existing transit nor RV data (Section 5) support the detection of nonzero eccentricities.In our final fits, we chose to restrict both planets to circular orbits to reduce model complexity.
Our transit fitting pipeline takes the following steps: 1. Fit a global model of all transit epochs, assuming no transit timing variations (TTVs).This model is found by maximizing the likelihood with the Levenberg-Marquardt method implemented in Python package lmfit (Newville et al. 2014).2. Search for TTVs.We held the transit shape parameters fixed and fit for the mid-transit times of each transit epoch.We removed out-of-transit variations with a quadratic model.We did not detect significant TTVs for either planet, so we continued with fixed orbital periods.
3. Full model.We sampled the posterior distributions of both planets jointly using the MCMC framework implemented in emcee (Foreman-Mackey et al. 2013) with 128 walkers initialized near the MAP solution.We ran emcee for 50,000 steps, ensuring that this was many times longer than the autocorrelation of various parameters (typically 100 s of steps).1.68 0.07 0.09 ).

Phase Curve
We searched the TESS light curve for phase-curve variations and secondary eclipses of TOI-1347 b.First, we masked the intransit data and removed long-term variability (stellar and/or instrumental) using the method of Sanchis-Ojeda et al. (2013).This involves fitting a linear function of time to the out-of-  transit data points within a window of 2× the orbital period, then dividing the best-fit function within that window, repeating for every data point in the light curve.This detrended light curve is then phase folded to the orbital period of TOI-1347 b.
The resultant phase curve is shown in Figure 6.We were able to detect a tentative phase-curve variation (3σ) and a secondary eclipse (2σ) using a joint model.To model the secondary eclipse, we simply modified the best-fit transit model by shifting the mid-transit times by half the orbital period (i.e., assuming e = 0) and turning off limb darkening (q 1 = q 2 = 0).The secondary eclipse depth (d sec ) is allowed to vary freely to account for a combined effect of reflected stellar light and thermal emission from the planet's nightside.For the phase curve, we used a Lambertian disk model (see, e.g., Demory et al. 2016) parameterized by an amplitude A and phase offset of the peak θ.We sampled the posterior distribution with an MCMC analysis similar to that described in Section 4.3.We found a secondary eclipse depth of d =  26 12 ppm sec and a phase-curve amplitude of A = 28 ± 9 ppm.The peak of the phase-curve variation is shifted by 33°± 14°to the west of the planet.
The lower panel of Figure 6 compares the amount of thermal emission versus reflected light as a function of the planet's Bond albedo (A B ).At high albedo, the planet is more reflective, and the equilibrium temperature will be lower.In this case, the phase curve will be dominated by reflected stellar light rather than thermal emission.This is necessary to explain the large secondary eclipse depth measured in the TESS band.Moreover, we marginally detected a phase offset of 33°± 14°to the west of the planet.Both of these effects can be explained if TOI-1347 b is retaining a high-mean-molecular-weight atmosphere.Silicate clouds in this atmosphere could produce a high albedo, while partial cloud coverage may produce the observed phase offset to the West (see, e.g., Kepler-7 b, Demory et al. 2013).However, the data in hand are insufficient to definitively confirm the presence of an atmosphere on TOI-1347 b.Higher S/N follow-up observations with JWST are required.

Radial Velocities
We collected 120 high-resolution optical spectra of TOI-1347 between UT 2019 November 28 and UT 2022 July 26 with HIRES on the Keck I telescope as part of TKS (Chontos et al. 2022).We took exposures using the "C2" decker (R = 45,000) and integrated until the exposure meter reached 60,000 counts (S/N ∼100 per reduced pixel), which resulted in a typical exposure time of 648 s.We used the standard procedures of the California Planet Search (Howard et al. 2010) to reduce the HIRES spectra and extract precise RVs using the iodine cell for wavelength calibration (Butler et al. 1996).The average Doppler precision per measurement was 1.83 m s −1 .
We also obtained 14 spectra with the HARPS-N , installed at the Telescopio Nazionale Galileo (Cosentino et al. 2012).Observations were taken with 1800 s exposure times (average S/N is 42.3 in order 50) with simultaneous wavelength calibration provided by the Fabry-Perot etalon.Cross-correlation functions (CCFs) were created using the ESPRESSO G2 mask, and RVs were extracted by fitting for the CCF centroid (Dumusque et al. 2021).Before jointly fitting with the HIRES RVs, we subtracted the median RV from the HARPS-N data set.
See Table 3 for the full RV data set, which includes Mount Wilson S-Index values derived from the Ca II H and K lines (Duncan et al. 1991) for the HIRES data.The S HK index shows a weaker power excess around P rot in a Lomb-Scargle periodogram than the RVs (Figure 4) but are primarily dominated by a 1 day sampling alias.The S HK indices are correlated with the RVs at the 3.5σ level with a Pearson correlation coefficient of 0.31 (p-value of 0.0005).This weak correlation is likely why our models in Section 5.1 that were trained on the S-Index time series did not improve the overall fit.

RV Model
We chose to adopt the same two-component simple harmonic oscillator (SHO) model for our RV model that we used to model stellar variability in photometry.We used the exoplanet (Foreman-Mackey et al. 2021) package to construct a Gaussian process (GP) stellar activity model with a kernel defined by the built-in RotationTerm parameterization.This kernel is a mixture of two SHOs analogous to the first and second cosine terms in Equation (1).We also tried a GP with the quasiperiodic kernel implemented in radvel (Fulton et al. 2018), both untrained and trained on the S-Indices.We found that the quasiperiodic kernel struggled to identify a single primary period, often jumping between 8 and 16 days.In order for the MCMC to converge, a reasonably strong prior (±0.5 day or less) had to be placed on one of these period solutions.We found this undesirable compared to the SHO kernel in exoplanet, which was able to lock onto the 16 day period even with wide priors of >10 days.We also found the final fit to be statistically indistinguishable whether the GP was trained on the S-Indices or not, so for our final model we opted for an untrained SHO GP.
For the full mathematical definition of the SHO GP kernel, the interested reader is directed to Foreman-Mackey et al. (2017).In brief, the kernel is parameterized by the GP amplitude (A GP ), the primary period of variability (P GP ), the quality factor of the primary mode Q 0 , the difference in quality factors between the period and half-period modes (ΔQ 0 ), and lastly the fractional amplitude between the two modes ( f ).We followed the guidance of the exoplanet tutorials to choose the appropriate priors on these parameters, which are tabulated in Table 2.
In practice, the Keplerian models are only parameterized by the RV semiamplitude K, which we place a wide, uninformative Gaussian prior on.We do not restrict K to positive values only, as such a prior can bias mass estimates to higher values, especially in the case of nondetections (Weiss & Marcy 2014).We imposed Gaussian priors on the periods and times of conjunction using the best-fit mean and standard deviation derived from our transit fits (Table 2), effectively fixing them to the tight transit constraints.Like the transit model, we fixed the eccentricity (e) and argument of periastron (ω) to zero.We included separate jitter terms for HIRES (s HIRES ) and HARPS-N (σ HARPS ) and likewise separate RV offsets (g HIRES ) and HARPS-N (γ HARPS ).
We initialized our model at the best-fit values from photometry, where applicable, and determined initial guesses for the RV semiamplitudes using exoplanet.estimate_-semi_amplitude. We then solved for the MAP solution  et al. 1953;Hastings 1970), resulting in well-mixed MCMC chains in far fewer samples.We sampled with NUTS in four parallel chains for 5000 "tuning" steps, which are discarded.The number of tuning steps was chosen to obtain an acceptance fraction near the target of 0.9, which balances the number of retained samples and efficient exploration of the posterior space.Each chain then collects 5000 samples for a total of 20,000 posterior samples.We ensured adequate statistical independence among these samples by requiring that the per-parameter R statistic (Vehtari et al. 2021) be <1.001.
Our best-fitting RV model is shown in Figure 7.The GP robustly recovers a primary period of 16.2 ± 0.3 days, even with a wide prior, independently verifying our assessment of the stellar rotation period from photometry.The USP TOI-1347 b is also robustly detected at consistent semiamplitudes, regardless of the activity model used (trained/untrained, quasiperiodic/SHO).The resulting mass of TOI-1347 b is 11.1 ± 1.2 M ⊕ .The second planet, TOI-1347 c, is not detected in the RVs.We adopt an upper limit of <6.4 M ⊕ at 95% confidence.The residual rms to the combined Keplerian + GP model is 4.9 m s −1 for HIRES and 7.5 m s −1 for HARPS-N, which is (expectedly) similar to the fitted stellar jitter values (4.0 ± 0.7 m s −1 and - + 8.2 2.0 2.7 m s −1 respectively), but larger than the per-measurement uncertainty of each instrument (2.5 and 1.9 m s −1 ).
Of note is the large jitter for the HARPS-N RVs.We suspect this is due to the GP being primarily conditioned on the HIRES RVs, resulting in poor predictive accuracy for activity during the timespan of the HARPS-N data, which occur about 1-2 rotation cycles before the HIRES data.As a result, the jitter term for HARPS-N is inflated to compensate.We tried to separate GPs for both data sets, sharing all hyperparameters except for the GP amplitude (A GP ).We found a nearly identical result (in fact, the best-fit HARPS-N jitter was higher) with statistically indistinguishable planet parameters, likely due to the relatively few HARPS-N data points.As a result, we adopt the single GP model but encourage further investigation into the nature of stellar activity on TOI-1347.As it stands, there are too few HARPS-N data points to condition independent GPs, but the single GP model is potentially overfitted to the HIRES points, reducing its out-of-sample predictive accuracy (Blunt et al. 2023).

A Heavy Core Pushing the Limit of Photoevaporation
TOI-1347 b is the largest (in both mass and radius) of the super-Earth USPs to date.It seems to be rocky in composition and similar in iron core mass fraction to the Earth.Figure 8 shows the two planets in the context of known exoplanets on the mass-radius diagram. 32We modeled the core composition of TOI-1347 b assuming a simple two-layer model with an iron core and a silicate ("rock") mantle (Zeng et al. 2016).Our mass and radius measurements suggest an iron core mass fraction of 41% ± 27%, not far from Earth's 33% core mass fraction.TOI-1347 b joins a group of well-characterized USPs (Dai et al. 2019) that are consistent with an Earth-like composition.
With a core mass larger than 10 M ⊕ , TOI-1347 b, along with the USPs TOI-1075 b (Essack et al. 2023) and HD 20329 b (Murgas et al. 2022), are close to the theoretical limit for runaway accretion (see, e.g., Rafikov 2006).How did these planets evade runaway accretion and not become gas giants? Lee (2019) and Chachan et al. (2021) both noted that the local hydrodynamic conditions, the envelope opacity, and the timescale of core assembly relative to disk dissipation could all contribute to quenching runaway accretion.As more of these systems are discovered, population-level analyses may shed light on which planets are able to evade runaway and which grow into gas giants.
TOI-1347 b also pushes the efficacy of photoevaporation to its limit.At >10 M ⊕ , the outflowing atmosphere has to overcome a deep gravitational potential well.On the other hand, the temperature of atmospheric outflows is likely capped below 10 4 K due to strong radiative cooling at higher temperatures (see, e.g., Murray-Clay et al. 2009).An orderof-magnitude comparison reveals that the thermal sound speed (∼10 km s −1 at 10 4 K) may not overcome the escape velocity of the planet (∼25 km s −1 at 10 M ⊕ and 1.9 R ⊕ ), preventing bulk hydrodynamic outflow (i.e., photoevaporation).Previous models showed that photoevaporation is significantly quenched on planets with heavier cores (6 M ⊕ ; see, e.g., Owen & Wu 2017;Wang & Dai 2018).Planets like TOI-1347 b are therefore important test cases to understand the limit of both photoevaporation and core-powered mass loss (Ginzburg et al. 2018;Gupta & Schlichting 2019).Our mass and radius measurements disfavor the presence of a thick H/He envelope (Figure 8).Did TOI-1347 b have, and then lose, a primordial H/He envelope?Or, could TOI-1347 b have formed near to its present-day scorching orbit without ever acquiring a substantial atmosphere?We encourage further investigation on this question.

A Heavy-mean-molecular-weight Atmosphere?
Even though TOI-1347 b has a mass and radius that suggest an Earth-like bulk composition, we cannot rule out the presence of a heavy-mean-molecular-weight atmosphere.Lopez (2017) showed that the largest of the nongiant USPs (such as 55 Cnc e) can hold onto high-metallicity atmospheres even in the presence of strong stellar radiation.Such an atmosphere would only marginally inflate the planet's radius (the scale height of a CO 2 -based atmosphere is about 11 km, while planetary radii are ∼10,000 km).
In fact, our tentative phase curve (3σ) and secondary eclipse (2σ) detections of TOI-1347 b point to a nonzero albedo and a possible phase offset to the west.These features could indicate the presence of an atmosphere at least partially covered by reflective silicate clouds.It may be the case that the deep gravitational wells of the most massive super-Earth USPs are sufficient to cling to such an atmosphere and resist atmospheric loss mechanisms.R. Hu et al. (2024, in preparation) show that their JWST NIRCam and MIRI observations of 55 Cnc e, a similar massive USP (0.73 day orbit; 9M ⊕ ), can only be explained if the planet still has a CO-or CO 2 -based atmosphere.Future observations with JWST might uncover a similar story for TOI-1347 b (TSM =19, ESM =5.6, using the equations of Kempton et al. 2018).
Alternatively, the high-amplitude TESS phase curve of TOI-1347 b may be a consequence of outgassed Na emission on the hot dayside of the planet.Zieba et al. (2022) showed that this emission can explain the phase curve of the lava world K2-141 b, which has been observed in both the Kepler passband and Spitzer-4.5 μm passband (Malavolta et al. 2018).In their analysis, they found that the two phase curves are inconsistent with a blackbody model, with the visible-light phase curve having a higher amplitude than expected.Similarly high visible-light phase-curve amplitudes have been reported for the lava worlds 55 Cnc e (Kipping & Jansen 2020) and Kepler-10 b (Batalha et al. 2011;Rouan et al. 2011) although the latter has not yet been observed in the infrared, which would test blackbody emission.If Na emission is responsible for the observations of TOI-1347 b reported here, it may more easily explain the tentative phase-curve offset than reflective clouds, which would need to be nonuniformly distributed across the planet.

Summary
We have characterized two transiting planets in the TOI-1347 system, TOI-1347 b, a USP (0.85 day), and its outer small companion TOI-1347 c (4.84 days).Using TESS photometry and an independent transit fitting pipeline, we measured a radius of 1.8 ± 0.1 R ⊕ for the USP and 1.6 ± 0.1 R ⊕ for its companion.We conducted an RV campaign of the TOI-1347 system with HIRES (as part of TKS) and with HARPS-N.We measured a mass of 11.1 ± 1.2 M ⊕ for the USP, consistent with a bulk Earth-like composition and inconsistent with a H/He envelope (see Figure 8).This composition is perhaps unsurprising given the system age of 1.4 ± 0.4 Gyr, the short timescale on which intensive photoevaporation operates (few hundred megayears), and the high insolation flux at TOI-1347 b's orbit; any primordial H/He envelope should have been destroyed by now.We were unable to detect the companion TOI-1347 c with RVs.We placed a 95% upper limit of <6.4 M ⊕ .Of note is the minimum mutual inclination between planets b and c implied by our measured orbital inclinations: ∼7°.This is unusually large compared to typical  Zeng et al. (2016) are drawn for pure-iron, Earth-like (30% iron, 70% rock), pure-rock, and pure-water compositions.Contours from Chen & Rogers (2016) are also drawn for 0.5%, 0.1%, and 0.01% H/He envelopes surrounding rocky-composition cores, at an age of 1.4 Gyr old and at the maximum insolation flux of 400 S ⊕ for their model grids; it is worth noting that TOI-1347 b (1400 K, A = 0.7) receives an insolation flux of around 3000 S ⊕ .Our mass-radius constraints for TOI-1347 b and c (95% upper limit in mass) are plotted and labeled in red.The size of each point is proportional to M/σ M .TOI-1347 b is the most massive super-Earth USP to date, while TOI-1347 c is smaller but likely also rocky.
Kepler multis (Fabrycky et al. 2014), which may be another indicator of the migration dynamics that produce USPs.TOI-1347 b is the most massive of the <2 R ⊕ (i.e., primarily solid by volume) USPs to date.Its mass sets an upper limit on runaway accretion processes and places TOI-1347 b in a region of the mass-radius diagram in which the pressures and temperatures reached inside the planet have not been well characterized either by experiments or theoretical modeling.
Intriguingly, we measured a tentative (3σ) phase-curve variability, as well as a secondary eclipse (2σ) for the USP TOI-1347 b.The phase curve asymmetry strongly suggests an optically thick atmosphere.However, our mass and radius measurements of TOI-1347 b are highly inconsistent with any significant H/He envelope.As a result, any such atmosphere must have a high-mean molecular weight.It could be comprised of reflective silicate clouds, or may be the result of the outgassing of Na from the molten surface.Future observations (e.g., with JWST) would help confirm such an atmosphere and reveal its composition.

Figure 1 .
Figure 1.HIRES spectrum of TOI-1347 in the neighborhood of the lithium doublet.Nearby Fe I lines are labeled.No absorption attributed to lithium was detected.

Figure 2 .
Figure 2. Contrast curves around TOI-1347 from Gemini/'Alopeke; the inset shows the reconstructed image at 832 nm.No companions are detected.

Figure 3 .
Figure 3. Top: the full 120 s cadence SPOC TESS light curve, binned to 30 minutes.Rotationally modulated variability is strong and evolves over time; the three shaded regions highlight example 16 day windows in which different numbers of maxima/minima are observed.Middle: the 30 minute light curve phased to the 16.1 day rotation period.The red points further bin the folded data to ∼8 hr bins.The inset zooms in on these binned phased data and highlights the tendency for every other set of maximum/minimum to repeat in amplitude.Bottom: the ACF of the photometry, showing regular peaks at all multiples of 8 days (dashed line) with the highest peak at 16 days (dark line).The red dashed line shows the best-fit SHO model described in Section 4.1.

Figure 5
Figure 5 shows the phase-folded and binned transits of TOI-1347 b and c with the MAP model.Using the stellar radius derived in Section 2, we derived R p,b = 1.8 ± 0.1 R ⊕ and R p,c = 1.6 ± 0.1 R ⊕ , in agreement with the radii measured by MacDougall et al. (2023; = -+ Å R R 1.81 p b , 0.06 0.09

Figure 4 .
Figure 4. Lomb-Scargle periodograms of, from top to bottom, the TESS photometry, S-Indices, RVs and RVs with the GP model (Section 5.1) removed, the GP-corrected RVs with the Keplerian model for the USP subtracted, the GP-corrected RVs with both planets subtracted, and the window function (Dawson & Fabrycky 2010) of the RV time series.The periodograms are computed using astropy.timeseries.LombScargle (Astropy Collaboration et al. 2022).The blue lines correspond to the orbital periods of TOI-1347 b and c, and the two dark red lines are drawn at 8 days (thin) and 16 days (thick).The horizontal yellow line is the 1% false alarm probability.

Figure 5 .
Figure 5.The 2 minute TESS light curves phase folded and binned using the orbital periods of TOI-1347 b (top) and c (bottom).The best-fit transit models are shown with red solid lines.

Figure 6 .
Figure 6.Upper: the phase curve and secondary eclipse of TOI-1347 b as observed by TESS.The best-fit model is shown by the red curve.The green dotted line gives the model with no eclipse.The phase curve is detected at the 2σ level.It is likely a combination of thermal emission and reflected light in the TESS band (600-1000 nm).Lower: the thermal emission (red dotted line) and reflected light (orange solid line) from TOI-1347 b as a function of the Bond albedo.The blue dashed line and shaded area are the measured secondary eclipse depth (F p /F * ) and its 1σ central interval.

Figure 7 .
Figure 7.The adopted RV model.Panel (a) shows the HARPS-N and HIRES RV data sets, with the MAP RV model (Keplerian + GP and 1σ uncertainty) overplotted in blue.Panel (b) shows the residuals between the data and the MAP RV model.Panels (c) and (d) show the data phase folded to the orbital period of planets b and c, respectively, with contributions from the other planet and the GP removed.The red points are equal RV bins spanning 0.1 in phase.The median and central 68% credible interval of each Keplerian model is plotted in blue.The MCMC posteriors for the recovered semiamplitude and derived Mi sin are also summarized in the lower left annotations.Note that we do not include the MAP stellar jitter in the plotted error bars; error bars are drawn only as the measurement uncertainties to highlight the degree of unexplained scatter (i.e., jitter), given by the annotated residual rms, to which the stellar jitter fits.

Figure 8 .
Figure 8. Mass-radius diagram of known super-Earths (R p < 2 R ⊕ , filled circles) and sub-Neptunes (4 R ⊕ > R p 2 R ⊕ , empty circles) with 5σ or better mass measurements, obtained from the NASA Exoplanet Archive (NASA Exoplanet Archive 2023).Solid black points denote USPs.Contours from Zeng et al. (2016) are drawn for pure-iron, Earth-like (30% iron, 70% rock), pure-rock, and pure-water compositions.Contours fromChen & Rogers (2016) are also drawn for 0.5%, 0.1%, and 0.01% H/He envelopes surrounding rocky-composition cores, at an age of 1.4 Gyr old and at the maximum insolation flux of 400 S ⊕ for their model grids; it is worth noting that TOI-1347 b (1400 K, A = 0.7) receives an insolation flux of around 3000 S ⊕ .Our mass-radius constraints for TOI-1347 b and c (95% upper limit in mass) are plotted and labeled in red.The size of each point is proportional to M/σ M .TOI-1347 b is the most massive super-Earth USP to date, while TOI-1347 c is smaller but likely also rocky.

Table 2
Duane et al. 1987;Neal 2011) the TOI-1347 System using scipy.optimize.minimize.The MAP parameters were then used as a seed for an MCMC exploration of the posterior.We employed a Hamiltonian Monte Carlo (HMC;Duane et al. 1987;Neal 2011)implemented in PyMC3 (Salvatier et al. 2016), specifically the No-U-Turn Sampler (NUTS; Hoffman & Gelman 2014).HMC and NUTS are generally more efficient than the traditional Metropolis-Hastings algorithm (Metropolis