Planet Formation Theories Research Articles

Chemical fingerprints of formation in rocky super-Earths’ data

ABSTRACT The composition of rocky exoplanets in the context of stars’ composition provides important constraints to formation theories. In this study, we select a sample of exoplanets with mass and radius measurements with an uncertainty $\lt 25{{\ \rm per\ cent}}$ and obtain their interior structure. We calculate compositional markers, ratios of iron to magnesium and silicon, as well as core mass fractions (CMFs) that fit the planetary parameters, and compare them to the stars. We find four key results that successful planet formation theories need to predict: (1) In a population sense, the composition of rocky planets spans a wider range than stars. The stars’ Fe/Si distribution is close to a Gaussian distribution $1.63^{+0.91}_{-0.85}$, while the planets’ distribution peaks at lower values and has a longer tail, $1.15^{+1.43}_{-0.76}$. It is easier to see the discrepancy in CMF space, where primordial stellar composition is $0.32^{+0.14}_{-0.12}$, while rocky planets follow a broader distribution $0.24^{+0.33}_{-0.18}$. (2) We introduce uncompressed density ($\overline{\rho _0}$ at reference pressure/temperature) as a metric to compare compositions. With this, we find what seems to be the maximum iron enrichment that rocky planets attain during formation ($\overline{\rho _0}\sim 6$ and CMF ∼0.8). (3) Highly irradiated planets exhibit a large range of compositions. If these planets are the result of atmospheric evaporation, iron enrichment and perhaps depletion must happen before gas dispersal. And, (4) We identify a group of highly irradiated planets that, if rocky, would be twofold depleted in Fe/Si with respect to the stars. Without a reliable theory for forming iron-depleted planets, these are interesting targets for follow-up.

An Astrometric Planetary Companion Candidate to the M9 Dwarf TVLM 513–46546

Abstract Astrometric observations of the M9 dwarf TVLM 513–46546 taken with the VLBA reveal an astrometric signature consistent with a period of 221 ± 5 days. The orbital fit implies that the companion has a mass m p = 0.35−0.42 M J, a circular orbit (e ≃ 0), a semimajor axis a = 0.28−0.31 au, and an inclination angle i = 71°−88°. The detected companion, TVLM 513b, is one of the few giant-mass planets found associated with ultracool dwarfs. The presence of a Saturn-like planet on a circular orbit 0.3 au from a 0.06−0.08 M ⊙ star represents a challenge to planet formation theory. This is the first astrometric detection of a planet at radio wavelengths.

How Flow Isolation May Set the Mass Scale for Super-Earth Planets

Abstract Much recent work on planet formation has focused on the growth of planets by accretion of grains whose aerodynamic properties make them marginally coupled to the nebular gas, a theory commonly referred to as “pebble accretion.” While the rapid growth rates of pebble accretion can ameliorate some problems in planet formation theory, they raise new concerns as well. A particular issue is the preponderance of observed planets that end their growth as “super-Earths” or “sub-Neptunes,” with masses in the range 2–10 M ⊕. Once planets reach this mass scale, growth by pebble accretion is so rapid that ubiquitously ending growth at super-Earth masses is difficult unless growth rates drop at this mass scale. In this work, we highlight this issue in detail using our previously published model of pebble accretion, and also propose a reason for this change in growth rate: feedback between the growing planet’s atmosphere and the gas disk inhibits accretion of smaller particle sizes by forcing them to flow around the growing planet instead of being accreted. For reasonable fiducial disk parameters, this “flow isolation” will inhibit accretion of all available particle sizes once the planet reaches super-Earth masses. We also demonstrate that the characteristics of this “flow isolation mass” agree with previously published trends identified in the Kepler planets.

Planetary mass–radius relations across the galaxy

Context. Planet formation theory suggests that planet bulk compositions are likely to reflect the chemical abundance ratios of their host star’s photosphere. Variations in the abundance of particular chemical species in stellar photospheres between different galactic stellar populations demonstrate that there are differences among the expected solid planet bulk compositions. Aims. We aim to present planetary mass-radius relations of solid planets for kinematically differentiated stellar populations, namely, the thin disc, thick disc, and halo. Methods. Using two separate internal structure models, we generated synthetic planets using bulk composition inputs derived from stellar abundances. We explored two scenarios, specifically iron-silicate planets at 0.1 AU and silicate-iron-water planets at 4 AU. Results. We show that there is a persistent statistical difference in the expected mass-radius relations of solid planets among the different galactic stellar populations. At 0.1 AU for silicate-iron planets, there is a 1.51–2.04% mean planetary radius difference between the thick and thin disc stellar populations, whilst for silicate-iron-water planets past the ice line at 4 AU, we calculate a 2.93–3.26% difference depending on the models. Between the halo and thick disc, we retrieve at 0.1 AU a 0.53–0.69% mean planetary radius difference, and at 4 AU we find a 1.24–1.49% difference depending on the model. Conclusions. Future telescopes (such as PLATO) will be able to precisely characterize solid exoplanets and demonstrate the possible existence of planetary mass-radius relationship variability between galactic stellar populations.

Planetary architectures in interacting stellar environments

ABSTRACT The discovery of exoplanetary systems has challenged some of the theories of planet formation, which assume unperturbed evolution of the host star and its planets. However, in star clusters the interactions with fly-by stars and binaries may be relatively common during the lifetime of a planetary system. Here, via high-resolution N-body simulations of star–planet systems perturbed by interlopers (stars and binaries), we explore the reconfiguration to the planetary system due to the encounters. In particular, via an exploration focused on the strong scattering regime, we derive the fraction of encounters that result in planet ejections, planet transfers, and collisions by the interloper star/binary, as a function of the characteristics of the environment (density, velocity dispersion), and for different masses of the fly-by star/binary. We find that binary interlopers can significantly increase the cross-section of planet ejections and collisions, while they only slightly change the cross-section for planet transfers. Therefore, in environments with high binary fractions, floating planets are expected to be relatively common, while in environments with low binary fractions, where the cross-sections of planet ejection and transfer are comparable, the rate of planet exchanges between two stars will be comparable to the rate of production of free-floating planets.

Requirements for Gravitational Collapse in Planetesimal Formation—The Impact of Scales Set by Kelvin–Helmholtz and Nonlinear Streaming Instability

Abstract The formation of planetesimals is a challenging problem in planet formation theory. A prominent scenario for overcoming dust growth barriers is the gravitational collapse of locally over-dense regions, shown to robustly produce ∼100 km–sized objects. Still, the conditions under which planetesimal formation occurs remain unclear. For collapse to proceed, the self-gravity of an over-density must overcome stellar tidal disruption on large scales and turbulent diffusion on small scales. Here, we relate the scales of streaming and Kelvin–Helmholtz instability (KHI), which both regulate particle densities on the scales of gravitational collapse, directly to planetesimal formation. We support our analytic findings by performing 3D hydrodynamical simulations of streaming and KHI and planetesimal formation. We find that the vertical extent of the particle mid-plane layer and the radial width of streaming instability filaments are set by the same characteristic length scale, thus governing the strength of turbulent diffusion on the scales of planetesimal formation. We present and successfully test a collapse criterion, 0.1Q β ϵ −1 Z −1 ≲ 1, and show that even for solar metallicities, planetesimals can form in dead zones of sufficiently massive disks. For a given gas Toomre parameter Q, pressure gradient β, metallicity Z, and local particle enhancement ϵ, the collapse criterion also provides a range of unstable scales, instituting a promising path for studying initial planetesimal mass distributions. Streaming instability is not required for planetesimal collapse but, by increasing ϵ, can evolve a system to instability.

Solid accretion onto planetary cores in radiative disks

The solid accretion rate, which is necessary to grow gas giant planetary cores within the disk lifetime, has been a major constraint for theories of planet formation. We tested the solid accretion rate efficiency on planetary cores of different masses embedded in their birth disk by means of 3D radiation-hydrodynamics, where we followed the evolution of a swarm of embedded solids of different sizes. We found that by using a realistic equation of state and radiative cooling, the disk at 5 au is able to efficiently cool and reduce its aspect ratio. As a result, the pebble isolation mass is reached before the core grows to 10 M⊕, thus fully stopping the pebble flux and creating a transition disk. Moreover, the reduced isolation mass halts the solid accretion before the core reaches the critical mass, leading to a barrier to giant planet formation, and this explains the large abundance of super-Earth planets in the observed population.

Strong Hα emission and signs of accretion in a circumbinary planetary mass companion from MUSE

Context. Intrinsic Hα emission can be advantageously used to detect substellar companions because it improves contrasts in direct imaging. Characterising this emission from accreting exoplanets allows for the testing of planet formation theories. Aims. We characterise the young circumbinary planetary mass companion 2MASS J01033563-5515561 (AB)b (Delorme 1 (AB)b) through medium-resolution spectroscopy. Methods. We used the new narrow-field mode for the MUSE integral-field spectrograph, located on the ESO Very Large Telescope, during science verification time to obtain optical spectra of Delorme 1 (AB)b. Results. We report the discovery of very strong Hα and Hβ emission, accompanied by He I emission. This is consistent with an active accretion scenario. We provide accretion rate estimates obtained from several independent methods and find a likely mass of 12−15 MJup for Delorme 1 (AB)b. This is also consistent with previous estimates. Conclusions. Signs of active accretion in the Delorme 1 system might indicate a younger age than the ∼30−40 Myr expected from a likely membership in Tucana-Horologium (THA). Previous works have also shown the central binary to be overluminous, which gives further indication of a younger age. However, recent discoveries of active discs in relatively old (∼40 Myr), very low-mass systems suggests that ongoing accretion in Delorme 1 (AB)b might not require in and of itself that the system is younger than the age implied by its THA membership.

Circumbinary planets -- the next steps

The Kepler mission opened the door to a small but bonafide sample of circumbinary planets. Some initial trends have been identified and used to challenge our theories of planet and binary formation. However, the Kepler sample is not only small but contains biases. I will present a circumbinary plan for the future. Specifically, I will cover the BEBOP radial velocity survey, the latest TESS transit mission and a new technique for digging out small circumbinary planets in archival Kepler photometry.

Unified Simulations of Planetary Formation and Atmospheric Evolution: Effects of Pebble Accretion, Giant Impacts, and Stellar Irradiation on Super-Earth Formation

Abstract A substantial number of super-Earths have been discovered, and atmospheres of transiting super-Earths have also been observed by transmission spectroscopy. Several lines of observational evidence indicate that most super-Earths do not possess massive H2/He atmospheres. However, accretion and retention of less massive atmospheres on super-Earths challenge planet formation theory. We consider the following three mechanisms: (i) envelope heating by pebble accretion, (ii) mass loss during giant impacts, and (iii) atmospheric loss by stellar X-ray and EUV photoevaporation. We investigate whether these mechanisms influence the amount of the atmospheres that form around super-Earths. We develop a code combining an N-body simulation of pebble-driven planetary formation and an atmospheric evolution simulation. We demonstrate that the observed orbital properties of super-Earths are well reproduced by the results of our simulations. However, (i) heating by pebble accretion ceases prior to disk dispersal, (ii) the frequency of giant impact events is too low to sculpt massive atmospheres, and (iii) many super-Earths having H2/He atmospheres of ≳10 wt% survive against stellar irradiation for 1 Gyr. Therefore, it is likely that other mechanisms, such as suppression of gas accretion, are required to explain less massive atmospheres (≲10 wt%) of super-Earths.

The Discovery of the First Exoplanet Orbiting a Solar-Type Star

Didier Queloz is Professor of Physics at the Cavendish Laboratory (University of Cambridge) and Geneva University. He was jointly awarded the 2019 Nobel Prize in Physics for “the discovery of an exoplanet orbiting a solar-type star”. In the first part of his conversation with Mejd Alsari he discusses the impact of his 1995 discovery on the theory of planetary systems formation.

TESS Spots a Hot Jupiter with an Inner Transiting Neptune

Abstract Hot Jupiters are rarely accompanied by other planets within a factor of a few in orbital distance. Previously, only two such systems have been found. Here, we report the discovery of a third system using data from the Transiting Exoplanet Survey Satellite (TESS). The host star, TOI-1130, is an eleventh magnitude K-dwarf in Gaia G-band. It has two transiting planets: a Neptune-sized planet (3.65 ± 0.10 ) with a 4.1 days period, and a hot Jupiter ( ) with an 8.4 days period. Precise radial-velocity observations show that the mass of the hot Jupiter is . For the inner Neptune, the data provide only an upper limit on the mass of 0.17 (3σ). Nevertheless, we are confident that the inner planet is real, based on follow-up ground-based photometry and adaptive-optics imaging that rule out other plausible sources of the TESS transit signal. The unusual planetary architecture of and the brightness of the host star make TOI-1130 a good test case for planet formation theories, and an attractive target for future spectroscopic observations.

Giant Planet Swaps during Close Stellar Encounters

Abstract The discovery of planetary systems outside of the solar system has challenged some of the tenets of planetary formation. Among the difficult-to-explain observations are systems with a giant planet orbiting a very low mass star, such as the recently discovered GJ 3512b planetary system, where a Jupiter-like planet orbits an M star in a tight and eccentric orbit. Systems such as this one are not predicted by the core accretion theory of planet formation. Here we suggest a novel mechanism, in which the giant planet is born around a more typical Sun-like star ( ), but is subsequently exchanged during a dynamical interaction with a flyby low-mass star ( ). We perform state-of-the-art N-body simulations with and to study the statistical outcomes of this interaction, and show that exchanges result in high eccentricities for the new orbit around the low-mass star, while about half of the outcomes result in tighter orbits than the planet had around its birth star. We numerically compute the cross section for planet exchange, and show that an upper limit for the probability per planetary system to have undergone such an event is Gyr−1, where a p is the planet semimajor axis around the birth star, σ the velocity dispersion of the star cluster, and M c the total mass of the star cluster. Hence these planet exchanges could be relatively common for stars born in open clusters and groups, should already be observed in the exoplanet database, and provide new avenues to create unexpected planetary architectures.

Realistic On-the-fly Outcomes of Planetary Collisions. II. Bringing Machine Learning to N-body Simulations

Abstract Terrestrial planet formation theory is at a bottleneck, with the growing realization that pairwise collisions are treated far too simply. Here, and in our companion paper that introduces the training methodology, we demonstrate the first application of machine learning to more realistically model the late stage of planet formation by giant impacts. We present surrogate models that give fast, reliable answers for the masses and velocities of the two largest remnants of a giant impact, as a function of the colliding masses and their impact velocity and angle, with the caveat that our training data do not yet include pre-impact rotation or variable thermal conditions. We compare canonical N-body scenarios of terrestrial planet formation assuming perfect merger with our more realistic treatment that includes inefficient accretions and hit-and-run collisions. The result is a protracted tail of final events lasting ∼200 Myr, and the conversion of about half the mass of the initial population to debris. We obtain profoundly different solar system architectures, featuring a much wider range of terrestrial planet masses and enhanced compositional diversity.

Deflating Super-puffs: Impact of Photochemical Hazes on the Observed Mass–Radius Relationship of Low-mass Planets

Abstract The observed mass–radius relationship of low-mass planets informs our understanding of their composition and evolution. Recent discoveries of low-mass, large-radius objects (“super-puffs”) have challenged theories of planet formation and atmospheric loss, as their high inferred gas masses make them vulnerable to runaway accretion and hydrodynamic escape. Here we propose that high-altitude photochemical hazes could enhance the observed radii of low-mass planets and explain the nature of super-puffs. We construct model atmospheres in radiative-convective equilibrium and compute rates of atmospheric escape and haze distributions, taking into account haze coagulation, sedimentation, diffusion, and advection by an outflow wind. We develop mass–radius diagrams that include atmospheric lifetimes and haze opacity, which is enhanced by the outflow, such that young (∼0.1–1 Gyr), warm (T eq ≥ 500 K), low-mass objects (M c < 4 M ⊕) should experience the most apparent radius enhancement due to hazes, reaching factors of three. This reconciles the densities and ages of the most extreme super-puffs. For Kepler-51b, the inclusion of hazes reduces its inferred gas mass fraction to <10%, similar to that of planets on the large-radius side of the sub-Neptune radius gap. This suggests that Kepler-51b may be evolving toward that population and that some warm sub-Neptunes may have evolved from super-puffs. Hazes also render transmission spectra of super-puffs and sub-Neptunes featureless, consistent with recent measurements. Our hypothesis can be tested by future observations of super-puffs’ transmission spectra at mid-infrared wavelengths, where we predict that the planet radius will be half of that observed in the near-infrared.

Constraining planet formation around 6–8 M⊙ stars

ABSTRACT Identifying planets around O-type and B-type stars is inherently difficult; the most massive known planet host has a mass of only about $3\, \mathrm{M}_{\odot }$. However, planetary systems which survive the transformation of their host stars into white dwarfs can be detected via photospheric trace metals, circumstellar dusty and gaseous discs, and transits of planetary debris crossing our line of sight. These signatures offer the potential to explore the efficiency of planet formation for host stars with masses up to the core-collapse boundary at $\approx 8\, \mathrm{M}_{\odot }$, a mass regime rarely investigated in planet formation theory. Here, we establish limits on where both major and minor planets must reside around $\approx 6\rm {-}8\, \mathrm{M}_{\odot }$ stars in order to survive into the white dwarf phase. For this mass range, we find that intact terrestrial or giant planets need to leave the main sequence beyond approximate minimum star–planet separations of, respectively, about 3 and 6 au. In these systems, rubble pile minor planets of radii 10, 1.0, and 0.1 km would have been shorn apart by giant branch radiative YORP spin-up if they formed and remained within, respectively, tens, hundreds, and thousands of au. These boundary values would help distinguish the nature of the progenitor of metal pollution in white dwarf atmospheres. We find that planet formation around the highest mass white dwarf progenitors may be feasible, and hence encourage both dedicated planet formation investigations for these systems and spectroscopic analyses of the highest mass white dwarfs.

The paradox of youth for ALMA planet candidates

ABSTRACT Recent ALMA observations indicate that the majority of bright protoplanetary discs show signatures of young moderately massive planets. I show that this result is paradoxical. The planets should evolve away from their observed states by radial migration and gas accretion in about 1 per cent of the system age. These systems should then hatch tens of giant planets in their lifetime, and there should exist a very large population of bright planet-less discs; none of this is observationally supported. An alternative scenario, in which the population of bright ALMA discs is dominated by secondary discs recently rejuvenated by deposition of new gas, is proposed. The data are well explained if the gaseous mass of the discs is comparable to a Jovian planet mass, and they last a small fraction of a Million years. Self-disruptions of dusty gas giant protoplanets, previously predicted in the context of the Tidal Downsizing theory of planet formation, provide a suitable mechanism for such injections of new fuel, and yield disc and planet properties commensurate with ALMA observations. If this scenario is correct, then the secondary discs have gas-to-dust ratios considerably smaller than 100, and long look ALMA and NIR/optical observations of dimmer targets should uncover dusty, not yet disrupted, gas clumps with sizes of order an au. Alternatively, secondary discs could originate from late external deposition of gas into the system, in which case we expect widespread signatures of warped outer discs that have not yet come into alignment with the planets.

Midplane temperature and outer edge of the protoplanetary disk around HD 163296

Knowledge of the midplane temperature of protoplanetary disks is one of the key ingredients in theories of dust growth and planet formation. However, direct measurement of this quantity is complicated, and often depends on the fitting of complex models to data. In this paper we demonstrate a method to directly measure the midplane gas temperature from an optically thick molecular line if the disk is moderately inclined. The only model assumption that enters is that the line is very optically thick, specifically in the midplane region where we wish to measure the temperature. Freeze-out of the molecule onto dust grains could thwart this. However, in regions that are expected to be warm enough to avoid freeze-out, this method should work. We apply the method to the CO 2–1 line channel maps of the disk around HD 163296. We find that the midplane temperature between 100 and 400 au drops only mildly from 25 K down to 18 K. While we see no direct evidence of the midplane being optically thin due to strong CO depletion by freeze-out, we cannot rule it out either. The fact that the inferred temperatures are close to the expected CO freeze-out temperature could be an indication of this. Incidently, for the disk around HD 163296 we also find dynamic evidence for a rather abrupt outer edge of the disk, suggestive of outside-in photoevaporation or truncation by an unseen companion.

Exoplanet characterisation in the longest known resonant chain: the K2-138 system seen by HARPS

The detection of low-mass transiting exoplanets in multiple systems brings new constraints to planetary formation and evolution processes and challenges the current planet formation theories. Nevertheless, only a mere fraction of the small planets detected byKeplerand K2 have precise mass measurements, which are mandatory to constrain their composition. We aim to characterise the planets that orbit the relatively bright star K2-138. This system is dynamically particular as it presents the longest chain known to date of planets close to the 3:2 resonance. We obtained 215 HARPS spectra from which we derived the radial-velocity variations of K2-138. Via a joint Bayesian analysis of both the K2 photometry and HARPS radial-velocities (RVs), we constrained the parameters of the six planets in orbit. The masses of the four inner planets, from b to e, are 3.1, 6.3, 7.9, and 13.0M⊕with a precision of 34, 20, 18, and 15%, respectively. The bulk densities are 4.9, 2.8, 3.2, and 1.8 g cm−3, ranging from Earth to Neptune-like values. For planets f and g, we report upper limits. Finally, we predict transit timing variations of the order two to six minutes from the masses derived. Given its peculiar dynamics, K2-138 is an ideal target for transit timing variation (TTV) measurements from space with the upcoming CHaracterizing ExOPlanet Satellite (CHEOPS) to study this highly-packed system and compare TTV and RV masses.

Bright C2H emission in protoplanetary discs in Lupus: high volatile C/O > 1 ratios

Context. Recent ALMA surveys in different star-forming regions have shown that CO emission in protoplanetary discs is much fainter than expected. Accordingly, CO-based gas masses and gas to dust ratios are orders of magnitude lower than previously thought. This may be explained either as fast gas dispersal, or as chemical evolution and locking up of volatiles in larger bodies leading to the low observed CO fluxes. The latter processes lead to enhanced C/O ratios in the gas, which may be reflected in enhanced abundances of carbon-bearing molecules like C2H. Aims. The goal of this work is to use C2H observations to understand whether low CO fluxes are caused by volatile depletion or by fast gas dissipation. Methods. We present ALMA Cycle 4 C2H (N = 3–2, J = 7∕2–5∕2, F = 4–3 and F = 3–2) observations of a subsample of nine sources in the Lupus star-forming region. The integrated C2H emission is determined and compared to previous CO isotopologue observations and physical-chemical model predictions. Results. Seven out of nine discs are detected in C2H, whose line emission is almost as bright as 13CO. All detections are significantly brighter than the typical sensitivity of the observations, hinting at a bimodal distribution of the C2H line intensities. This conclusion is strengthened when our observations are compared with additional C2H observations of other discs. When compared with physical-chemical models, the observed C2H fluxes can be reproduced only if some level of volatile carbon and oxygen depletion is allowed and [C]/[O] > 1 in the gas. Models with reduced gas-to-dust ratios near unity however fail to reproduce the observed C2H line luminosity. A steeper than linear correlation between C2H and CN emission line is found for the Lupus discs. This is linked to the fact that C2H emission lines are affected more strongly by [C]/[O] variations than CN lines. Ring-like structures are detected both in C2H and in continuum emission but, as for CN, they do not seem to be connected. The source Sz 71 shows ring-shaped emission in both C2H and CN with the location of the peak intensity coinciding, within our 30 au resolution. Conclusions. Our new ALMA C2H observations favour volatile carbon and oxygen depletion rather than fast gas dispersal to explain the faint CO observations for most of the discs. This result has implications for disc-evolution and planet-formation theories, as disc gas masses may be larger than expected if CO is considered to be the main carbon carrier in the gas phase.