arXiv subjects

Eve J. Lee

Publications and source records attributed to Eve J. Lee.

At least 37 records · Page 2Linked to original sources

arXiv2024

Impacting Atmospheres: How Late-Stage Pollution Alters Exoplanet Composition

Atmospheric composition of exoplanets is often considered as a probe of the planet's formation condition. How exactly the initial chemical memory may be altered from the birth to the final state of the planet, however, remains unknown. Here, we develop a simple model of pollution of planetary atmosphere by the vaporization of infalling planetesimal of varying sizes and composition (SiO$_2$ inside 1 au and H$_2$O outside 1 au), following their trajectory and thermal evolution through the upper advective and radiative layers of a sub-Neptune class planet during the late stage of disk evolution. We vary the rate of pollution by changing the solid content of the disk and by dialing the level of disk gas depletion which in turn determines the rate of planetary migration. We find that pollution by silicate grains will always be limited by the saturation limit set by the thermal state of the atmosphere. By contrast, pollution by water ice can lead to $\sim$2--4 orders of magnitude variation in the atmospheric water mass fraction depending on the solid and gas content of the disk. Both cases suggest that post-formation pollution can erase the initial compositional memory of formation. Post-formation pollution can potentially transform sub-Neptunes with H/He-dominated envelope that initially formed beyond the iceline to waterworlds (water-enriched envelope) when the disk gas is depleted by $\gtrsim$2 orders of magnitude, allowing gentle migration. We additionally discuss the expected C/O ratio profile under pollution by water and refractory carbon species.

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arXiv2024

The First Evidence of a Host Star Metallicity Cut-off In The Formation of Super-Earth Planets

Planet formation is expected to be severely limited in disks of low metallicity, owing to both the small solid mass reservoir and the low opacity accelerating the disk gas dissipation. While previous studies have found a weak correlation between the occurrence rates of small planets ($\leq$4R$_\oplus$) and stellar metallicity, so far no studies have probed below the metallicity limit beyond which planet formation is predicted to be suppressed. Here, we constructed a large catalog of ~110,000 metal-poor stars observed by the TESS mission with spectroscopically-derived metallicities, and systematically probed planet formation within the metal-poor regime ([Fe/H] $\leq$ -0.5) for the first time. Extrapolating known higher-metallicity trends for small, short-period planets predicts the discovery of ~68 superEarths around these stars (~85,000 stars) after accounting for survey completeness; however, we detect none. As a result, we have placed the most stringent upper limit on super-Earth occurrence rates around metal-poor stars (-0.75 < [Fe/H] $\leq$ -0.5) to date, $\leq$ 1.67%, a statistically significant (p-value=0.000685) deviation from the prediction of metallicity trends derived with Kepler and K2. We find a clear host star metallicity cliff for super-Earths that could indicate the threshold below which planets are unable to grow beyond an Earth-mass at short orbital periods. This finding provides a crucial input to planet formation theories, and has implications for the small planet inventory of the Galaxy and the galactic epoch at which the formation of small planets started.

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arXiv2024

The Not-So Dramatic Effect of Advective Flows on Gas Accretion

Super-Earths and mini-Neptunes are the most common types of exoplanets discovered, yet the physics of their formation are still debated. Standard core accretion models in gas-rich environment find that typical mini-Neptune mass planets would blow up into Jupiters before the underlying disk gas dissipates away. The injection of entropy from the protoplanetary disk into forming gaseous envelopes has recently been put forward as a mechanism to delay this runaway accretion, specifically at short orbital distances. Here, we reevaluate this line of reasoning by incorporating recycling flows of gas into a numerical one-dimensional thermodynamic model with more realistic equation of state and opacities and the thermal state of the advective flow. At 0.1 AU, we find that advective flows are only able to produce mini-Neptunes if they can penetrate below ~0.25 of the planet's gravitational sphere of influence. Otherwise, the gas-to-core mass ratio (GCR) reaches above ~10% which is too large to explain the measured properties of mini-Neptunes, necessitating other gas-limiting processes such as late-time core assembly. The effect of entropy advection on gas accretion weakens even further beyond 0.1 AU. We present an updated scaling relation between GCR and the penetration depth of the advective flows which varies non-trivially with orbital distances, core masses and dusty vs. dust-free opacity. We further demonstrate how measurements of planet mass distribution beyond ~1 AU using future instruments such as the Nancy Grace Roman Space Telescope could be used to disambiguate between different formation conditions of gas-poor planets.

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arXiv2024

Probing Dust and Gas Properties Using Ringed Disks

How rapidly a planet grows in mass and how far they may park from the host star depend sensitively on two non-dimensional parameters: Stokes number St and turbulent $α$. Yet, these parameters remain highly uncertain being difficult or impossible to measure directly. Here, we demonstrate how the ringed disks can be leveraged to obtain St and $α$ separately by constructing a simple toy model that combines dust radial equation of motion under aerodynamic drag and coupling to gas motion with the measured distribution of dust masses in Class 0/I disks. Focusing on known systems with well-resolved dust rings, we find that the range of St and $α$ that are consistent with the measured properties of the rings are small: $10^{-4} \lesssim {\rm St} \lesssim 10^{-2}$ and $10^{-5} \lesssim α\lesssim 10^{-3}$. These low St and $α$ ensure the observed rings are stable against clumping. Even in one marginal case where the formation of bound clumps is possible, further mass growth by pebble accretion is inhibited. Furthermore, the derived low $α$ is consistent with the nearly inviscid regime where Type I migration can be prematurely halted. Our analysis predicts minimal planet population beyond $\sim$10s of au where we observe dust rings and significantly more vigorous planet formation inside $\sim$10 AU, consistent with current exo-giant statistics. We close with discussions on the implications of our results on small planet statistics at large orbital distances.

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arXiv2024

Friends not Foes: Strong Correlation between Inner Super-Earths and Outer Gas Giants

The connection between outer gas giants and inner super-Earths reflects their formation and evolutionary histories. Past work exploring this link has suggested a tentative positive correlation between these two populations, but these studies have been limited by small sample sizes and in some cases sample biases. Here we take a new look at this connection with a sample of 184 super-Earth systems with publicly available radial velocity data and resolved outer gas giants. We calculate the frequency of outer gas giants (GG) in super-Earth (SE) systems, dividing our sample into metal-rich ([Fe/H] $>$ 0) and metal-poor ([Fe/H]$\leq$0) hosts. We find P(GG$|$SE, [Fe/H]$>$0) = 28.0$^{+4.9}_{-4.6}\%$ and P(GG$|$SE, [Fe/H]$\leq$0) = 4.5$^{+2.6}_{-1.9}\%$. Comparing these conditional occurrence rates to field giant occurrence rates from Rosenthal et al 2021, we show that there is a distinct positive correlation between inner super-Earths and outer gas giants for metal-rich host stars at the 2.7$σ$ level, but this correlation disappears for metal-poor systems. We further find that, around metal-rich stars, the GG/SE correlation enhances slightly for systems with giants that are more distant (beyond 3 AU), more eccentric ($e > 0.2$), and/or in multi-gas giant systems. Such trends disappear around metal-poor stars with the exception of systems of multiple giants in which we observe a tentative anti-correlation. Our findings highlight the critical role metallicity (disk solid budget) plays in shaping the overall planetary architecture.

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arXiv2023

A Uniform Analysis of Debris Disks with the Gemini Planet Imager I: An Empirical Search for Perturbations from Planetary Companions in Polarized Light Images

The Gemini Planet Imager (GPI) has excelled in imaging debris disks in the near-infrared. The GPI Exoplanet Survey (GPIES) imaged twenty-four debris disks in polarized $H$-band light, while other programs observed half of these disks in polarized $J$- and/or $K1$-bands. Using these data, we present a uniform analysis of the morphology of each disk to find asymmetries suggestive of perturbations, particularly those due to planet-disk interactions. The multi-wavelength surface brightness, the disk color and geometry permit identification of any asymmetries such as warps or disk offsets from the central star. We find that nineteen of the disks in this sample exhibit asymmetries in surface brightness, disk color, disk geometry, or a combination of the three, suggesting that for this sample, perturbations, as seen in scattered light, are common. The relationship between these perturbations and potential planets in the system are discussed. We also explore correlations among stellar temperatures, ages, disk properties, and observed perturbations. We find significant trends between the vertical aspect ratio and the stellar temperature, disk radial extent, and the dust grain size distribution power-law, $q$. We also confirm a trend between the disk color and stellar effective temperature, where the disk becomes increasingly red/neutral with increasing temperature. Such results have important implications on the evolution of debris disk systems around stars of various spectral types.

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arXiv2023

Small Planets Around Cool Dwarfs: Enhanced Formation Efficiency of Super-Earths around M dwarfs

Current measurements of planet population as a function of stellar mass show three seemingly contradictory signatures: close-in super-Earths are more prevalent around M dwarfs than FGK dwarfs; inner super-Earths are correlated with outer giants; and outer giants are less common around M dwarfs than FGK dwarfs. Here, we build a simple framework that combines the theory of pebble accretion with the measurements of dust masses in protoplanetary disks to reconcile all three observations. First, we show that cooler stars are more efficient at converting pebbles into planetary cores at short orbital periods. Second, when disks are massive enough to nucleate a heavy core at 5 AU, more than enough dust can drift in to assemble inner planets, establishing the correlation between inner planets and outer giants. Finally, while stars of varying masses are similarly capable of converting pebbles into cores at long orbital periods, hotter stars are much more likely to harbor more massive dust disks so that the giant planet occurrence rate rises around hotter stars. Our results are valid over a wide range of parameter space for a disk accretion rate that follows $\dot{M}_\star \sim 10^{-8}\,M_\odot\,{\rm yr}^{-1}(M_\star/M_\odot)^2$. We predict a decline in mini-Neptune population (but not necessarily terrestrial planets) around stars lighter than $\sim 0.3-0.5 M_\odot$. Cold giants ($\gtrsim$5 AU), if they exist, should remain correlated with inner planets even around lower mass stars.

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arXiv2023

Removal of Hot Saturns in Mass-Radius Plane by Runaway Mass Loss

The hot Saturn population exhibits a boundary in mass-radius space, such that no planets are observed at a density less than $\sim$0.1 g cm$^{-3}$. Yet, planet interior structure models can readily construct such objects as the natural result of radius inflation. Here, we investigate the role XUV-driven mass-loss plays in sculpting the density boundary by constructing interior structure models that include radius inflation, photoevaporative mass loss and a simple prescription of Roche lobe overflow. We demonstrate that planets puffier than $\sim$0.1 g cm$^{-3}$ experience a runaway mass loss caused by adiabatic radius expansion as the gas layer is stripped away, providing a good explanation of the observed edge in mass-radius space. The process is also visible in the radius-period and mass-period spaces, though smaller, high-bulk-metallicity planets can still survive at short periods, preserving a partial record of the population distribution at formation.

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arXiv2022

Creating the Radius Gap without Mass Loss

The observed exoplanet population features a gap in the radius distribution that separates the smaller super-Earths ($\lesssim$1.7 Earth radii) from the larger sub-Neptunes ($\sim$1.7--4 Earth radii). While mass loss theories can explain many of the observed features of this radius valley, it is difficult to reconcile them with potentially rising population of terrestrials beyond orbital periods of $\sim$30 days. We investigate the ability of gas accretion during the gas-poor phase of disk evolution to reproduce both the location of the observed radius gap and the existence of long-period terrestrial planets. Updating the analytic scaling relations of gas accretion rate accounting for the shrinking of the bound radius by hydrodynamic effects and deriving a more realistic disk temperature profile, we find that the late-stage gas accretion alone is able to carve out the observed radius gap, with slopes $R_{\rm gap} \propto P^{-0.096}$ and $R_{\rm gap} \propto M_\star^{0.15}$ for top-heavy; and $R_{\rm gap} \propto P^{-0.089}$ and $R_{\rm gap} \propto M_\star^{0.22}$ for bottom-heavy core mass distributions, in good agreement with observations. The general morphology of the primordial radius gap is stable against a range of disk gas density and disk accretion rate with the latter affecting mostly the population of large planets ($\gtrsim$3--4$R_\oplus$). The peaks and valleys in the radius distribution were likely set in place primordially while post-formation mass loss further tunes the exoplanetary population. We provide potential observational tests that may be possible with TESS, PLATO and Roman Space Telescope.

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arXiv2022

Establishing Dust Rings and Forming Planets Within Them

Radio images of protoplanetary disks demonstrate that dust grains tend to organize themselves into rings. These rings may be a consequence of dust trapping within gas pressure maxima wherein the local high dust-to-gas ratio is expected to trigger the formation of planetesimals and eventually planets. We revisit the behavior of dust near gas pressure perturbations enforced by a planet in two-dimensional, shearing box simulations. While dust grains collect into generally long-lived rings, particles with small Stokes parameter $τ_s < 0.1$ tend to advect out of the ring within a few drift timescales. Scaled to the properties of ALMA disks, we find that rings composed of larger particles ($τ_s \geq 0.1$) can nucleate a dust clump massive enough to trigger pebble accretion which proceeds to ingest the entire dust ring well within $\sim$1 Myr. To ensure the survival of the dust rings, we favor a non-planetary origin and typical grain size $τ_s \lesssim 0.05$--0.1. Planet-driven rings may still be possible but if so we would expect the orbital distance of the dust rings to be larger for older systems.

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arXiv2021

Sculpting the sub-Saturn Occurrence Rate via Atmospheric Mass Loss

The sub-Saturn ($\sim$4--8$R_{\oplus}$) occurrence rate rises with orbital period out to at least $\sim$300 days. In this work we adopt and test the hypothesis that the decrease in their occurrence towards the star is a result of atmospheric mass loss, which can transform sub-Saturns into sub-Neptunes ($\lesssim$4$R_{\oplus}$) more efficiently at shorter periods. We show that under the mass loss hypothesis, the sub-Saturn occurrence rate can be leveraged to infer their underlying core mass function, and by extension that of gas giants. We determine that lognormal core mass functions peaked near $\sim$10--20$M_{\oplus}$ are compatible with the sub-Saturn period distribution, the distribution of observationally-inferred sub-Saturn cores, and gas accretion theories. Our theory predicts that close-in sub-Saturns should be $\sim$50\% less common and $\sim$30\% more massive around rapidly rotating stars; this should be directly testable for stars younger than $\lesssim$500 Myr. We also predict that the sub-Jovian desert becomes less pronounced and opens up at smaller orbital periods around M stars compared to solar-type stars ($\sim$0.7 days vs.~$\sim$3 days). We demonstrate that exceptionally low-density sub-Saturns, "Super-Puffs", can survive intense hydrodynamic escape to the present day if they are born with even larger atmospheres than they currently harbor; in this picture, Kepler 223 d began with an envelope $\sim$1.5$\times$ the mass of its core and is currently losing its envelope at a rate $\sim$2$\times 10^{-3}M_{\oplus}~\mathrm{Myr}^{-1}$. If the predictions from our theory are confirmed by observations, the core mass function we predict can also serve to constrain core formation theories of gas-rich planets.

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arXiv2021

Radial Gradients in Dust-to-Gas Ratio Lead to Preferred Region for Giant Planet Formation

The Rosseland mean opacity of dust in protoplanetary disks is often calculated assuming the interstellar medium (ISM) size distribution and a constant dust-to-gas ratio. However, the dust size distribution and the dust-to-gas ratio in protoplanetary disks are distinct from those of the ISM. Here, we use simple dust evolution models that incorporate grain growth and transport to calculate the time evolution of mean opacity of dust grains as a function of distance from the star. Dust dynamics and size distribution are sensitive to the assumed value of the turbulence strength $α_{\rm t}$ and the velocity at which grains fragment $v_{\rm frag}$. For moderate-to-low turbulence strengths of $α_{\rm t} \lesssim 10^{-3}$ and substantial differences in $v_{\rm frag}$ for icy and ice-free grains, we find a spatially non-uniform dust-to-gas ratio and grain size distribution that deviate significantly from the ISM values, in agreement with previous studies. The effect of a non-uniform dust-to-gas ratio on the Rosseland mean opacity dominates over that of the size distribution. This spatially varying -- that is non-monotonic -- dust-to-gas ratio creates a region in the protoplanetary disk that is optimal for producing hydrogen-rich planets, potentially explaining the apparent peak in gas giant planet occurrence rate at intermediate distances. The enhanced dust-to-gas ratio within the ice line also suppresses gas accretion rates onto sub-Neptune cores, thus stifling their tendency to undergo runaway gas accretion within disk lifetimes. Finally, our work corroborates the idea that low mass cores with large primordial gaseous envelopes (`super-puffs') originate beyond the ice line.

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arXiv2020

Primordial Radius Gap and Potentially Broad Core Mass Distributions of Super-Earths and Sub-Neptunes

The observed radii distribution of {\it Kepler} exoplanets reveals two distinct populations: those that are more likely to be terrestrials ($\lesssim1.7R_\oplus$) and those that are more likely to be gas-enveloped ($\gtrsim2R_\oplus$). There exists a clear gap in the distribution of radii that separates these two kinds of planets. Mass loss processes like photoevaporation by high energy photons from the host star have been proposed as natural mechanisms to carve out this radius valley. These models favor underlying core mass function of sub-Neptunes that is sharply peaked at $\sim$4--8$M_\oplus$ but the radial-velocity follow-up of these small planets hint at a more bottom-heavy mass function. By taking into account the initial gas accretion in gas-poor (but not gas-empty) nebula, we demonstrate that 1) the observed radius valley is a robust feature that is initially carved out at formation during late-time gas accretion; and 2) that it can be reconciled with core mass functions that are broad extending well into sub-Earth regime. The maximally cooled isothermal limit prohibits cores lighter than $\sim$1--2$M_\oplus$ from accreting enough mass to appear gas-enveloped. The rocky-to-enveloped transition established at formation produces a gap in the radius distribution that shifts to smaller radii farther from the star, similar to that observed. For the best agreement with the data, our late-time gas accretion model favors dust-free accretion in hotter disks with cores slightly less dense than the Earth ($\sim$0.8$ρ_\oplus$) drawn from a mass function that is as broad as $dN/dM_{\rm core} \propto M_{\rm core}^{-0.7}$.

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arXiv2020

WASP-107b's density is even lower: a case study for the physics of planetary gas envelope accretion and orbital migration

With a mass in the Neptune regime and a radius of Jupiter, WASP-107b presents a challenge to planet formation theories. Meanwhile, the planet's low surface gravity and the star's brightness also make it one of the most favorable targets for atmospheric characterization. Here, we present the results of an extensive 4-year Keck/HIRES radial-velocity (RV) follow-up program of the WASP-107 system and provide a detailed study of the physics governing the accretion of its gas envelope. We reveal that WASP-107b's mass is only 1.8 Neptune masses ($M_b = 30.5 \pm 1.7$ $M_\oplus$). The resulting extraordinarily low density suggests that WASP-107b has a H/He envelope mass fraction of $> 85$% unless it is substantially inflated. The corresponding core mass of $<4.6$ $M_\oplus$ at 3$σ$ is significantly lower than what is traditionally assumed to be necessary to trigger massive gas envelope accretion. We demonstrate that this large gas-to-core mass ratio most plausibly results from the onset of accretion at $\gtrsim 1$ AU onto a low-opacity, dust-free atmosphere and subsequent migration to the present-day $a_b = 0.0566 \pm 0.0017$ AU. Beyond WASP-107b, we also detect a second more massive planet ($M_c \sin i = 0.36 \pm 0.04$ $M_{J}$) on a wide eccentric orbit ($e_c = 0.28 \pm 0.07$) which may have influenced the orbital migration and spin-orbit misalignment of WASP-107b. Overall, our new RV observations and envelope accretion modeling provide crucial insights into the intriguing nature of WASP-107b and the system's formation history. Looking ahead, WASP-107b will be a keystone planet to understand the physics of gas envelope accretion.

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arXiv2020

A Featureless Infrared Transmission Spectrum for the Super-Puff Planet Kepler-79d

Extremely low density planets ('super-puffs') are a small but intriguing subset of the transiting planet population. With masses in the super-Earth range ($1-10$ M$_{\oplus}$) and radii akin to those of giant planets ($>4$ R$_{\oplus}$), their large envelopes may have been accreted beyond the water snow line and many appear to be susceptible to catastrophic mass loss. Both the presence of water and the importance of mass loss can be explored using transmission spectroscopy. Here, we present new HST WFC3 spectroscopy and updated Kepler transit depth measurements for the super-puff Kepler-79d. We do not detect any molecular absorption features in the $1.1-1.7$ $μ$m WFC3 bandpass and the combination of Kepler and WFC3 data are consistent with a flat line model, indicating the presence of aerosols in the atmosphere. We compare the shape of Kepler-79d's transmission spectrum to predictions from a microphysical haze model that incorporates an outward particle flux due to ongoing mass loss. We find that photochemical hazes offer an attractive explanation for the observed properties of super-puffs like Kepler-79d, as they simultaneously render the near-infrared spectrum featureless and reduce the inferred envelope mass loss rate by moving the measured radius (optical depth unity surface during transit) to lower pressures. We revisit the broader question of mass loss rates for super-puffs and find that the age estimates and mass loss rates for the majority of super-puffs can be reconciled if hazes move the photosphere from the typically assumed pressure of $\sim 10$ mbar to $\sim 10 \; μ$bar.

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arXiv2020

The First Habitable Zone Earth-sized Planet from TESS. I: Validation of the TOI-700 System

We present the discovery and validation of a three-planet system orbiting the nearby (31.1 pc) M2 dwarf star TOI-700 (TIC 150428135). TOI-700 lies in the TESS continuous viewing zone in the Southern Ecliptic Hemisphere; observations spanning 11 sectors reveal three planets with radii ranging from 1 R$_\oplus$ to 2.6 R$_\oplus$ and orbital periods ranging from 9.98 to 37.43 days. Ground-based follow-up combined with diagnostic vetting and validation tests enable us to rule out common astrophysical false-positive scenarios and validate the system of planets. The outermost planet, TOI-700 d, has a radius of $1.19\pm0.11$ R$_\oplus$ and resides in the conservative habitable zone of its host star, where it receives a flux from its star that is approximately 86% of the Earth's insolation. In contrast to some other low-mass stars that host Earth-sized planets in their habitable zones, TOI-700 exhibits low levels of stellar activity, presenting a valuable opportunity to study potentially-rocky planets over a wide range of conditions affecting atmospheric escape. While atmospheric characterization of TOI-700 d with the James Webb Space Telescope (JWST) will be challenging, the larger sub-Neptune, TOI-700 c (R = 2.63 R$_\oplus$), will be an excellent target for JWST and beyond. TESS is scheduled to return to the Southern Hemisphere and observe TOI-700 for an additional 11 sectors in its extended mission, which should provide further constraints on the known planet parameters and searches for additional planets and transit timing variations in the system.

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arXiv2020

The First Habitable Zone Earth-Sized Planet From TESS II: $Spitzer$ Confirms TOI-700 d

We present $Spitzer$ 4.5$μ$m observations of the transit of TOI-700 d, a habitable zone Earth-sized planet in a multiplanet system transiting a nearby M-dwarf star (TIC 150428135, 2MASS J06282325-6534456). TOI-700 d has a radius of $1.144^{+0.062}_{-0.061}R_\oplus$ and orbits within its host star's conservative habitable zone with a period of 37.42 days ($T_\mathrm{eq} \sim 269$K). TOI-700 also hosts two small inner planets (R$_b$=$1.037^{+0.065}_{-0.064}R_\oplus$ & R$_c$=$2.65^{+0.16}_{-0.15}R_\oplus$) with periods of 9.98 and 16.05 days, respectively. Our $Spitzer$ observations confirm the TESS detection of TOI-700 d and remove any remaining doubt that it is a genuine planet. We analyze the $Spitzer$ light curve combined with the 11 sectors of TESS observations and a transit of TOI-700 c from the LCOGT network to determine the full system parameters. Although studying the atmosphere of TOI-700 d is not likely feasible with upcoming facilities, it may be possible to measure the mass of TOI-700 d using state-of-the-art radial velocity instruments (expected RV semi-amplitude of $\sim$70 cm/s).

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arXiv2020

Most Stars (and Planets?) Are Born in Intense Radiation Fields

Protostars and young stars are strongly spatially "clustered" or "correlated" within their natal giant molecular clouds (GMCs). We demonstrate that such clustering leads to the conclusion that the incident bolometric radiative flux upon a random young star/disc is enhanced (relative to volume-averaged fluxes) by a factor which increases with the total stellar mass of the complex. Because the Galactic cloud mass function is top-heavy, the typical star in our Galaxy experienced a much stronger radiative environment than those forming in well-observed nearby (but relatively small) clouds, exceeding fluxes in the Orion Nebular Cluster by factors of $\gtrsim$30. Heating of the circumstellar disc around a median young star is dominated by this external radiation beyond $\sim 50\,$AU. And if discs are not well-shielded by ambient dust, external UV irradiation can dominate over the host star down to sub-AU scales. Another consequence of stellar clustering is an extremely broad Galaxy-wide distribution of incident flux (spanning $>10$ decades), with half the Galactic star formation in a substantial "tail" towards even more intense background radiation. We also show that the strength of external irradiation is amplified super-linearly in high-density environments such as the Galactic centre, starbursts, or high-redshift galaxies.

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