Planet Population Synthesis Models Research Articles

Populating the Milky Way. Characterising planet demographics by combining galaxy formation simulations and planet population synthesis models

Stellar populations and their distribution differ widely across the Galaxy, which is likely to affect planet demographics. Our local neighbourhood is dominated by young, metal-rich stars in the galactic thin disc, while the stellar halo and galactic bulge host a large fraction of older, metal-poor stars. We study the impact of these variations on planet populations in different regions of the Galaxy by combining a high-resolution galaxy formation simulation with state-of-the-art planet population synthesis models. We constructed a population model to estimate occurrence rates of different planet types, based on the New Generation Planet Population Synthesis (NGPPS). We applied this model to a simulated Milky Way (MW)\ analogue in the HESTIA galaxy formation simulation. We studied the planet occurrence rate in the metal-rich regions of the inner Galaxy, namely, in the galactic bulge and thin disc. We compared these result with the frequencies in the more distant, metal-poor region such as the thick disc and stellar halo. We find that the planet demographics in the central, metal-rich regions of the MW analogue differ strongly from the planet populations in the more distant, metal-poor regions. The occurrence rate of giant planets ($>300 M_ is 10 to 20 times larger in the thin disc compared to the thick disc, driven by the low amounts of solid material available for planet formation around metal-poor stars. Similarly, low-mass Earth-like planets around Sun-like stars are most abundant in the thick disc, being 1.5 times more frequent than in the thin disc. Moreover, low-mass planets are expected to be abundant throughout the galaxy, from the central regions to the outer halo, due to their formation processes being less dependent on stellar metallicity. The planet populations differ more strongly around Sun-like stars compared to dwarfs with masses 0.3 -- 0.5 $M_ caused by a weaker correlation between Fe/H metallicity and planet mass. However, it is important to note that the occurrence rates of low-mass planets are still uncertain, making our findings strongly model-dependent. Massive planets are more comprehensively understood and our findings are more robust. Nonetheless, other systematic effects have the potential to alter the giant planet population that we have not addressed in this study. We discuss some of these limitations and offer further directions for future research.

Secular evolution of MHD wind-driven discs: analytical solutions in the expanded α-framework

ABSTRACT The evolution of protoplanetary discs and the related process of planet formation is regulated by angular momentum transport and mass-loss processes. Over the past decade, the paradigm of viscosity has been challenged and MHD disc winds appear as a compelling scenario to account for disc accretion. In this work, we aim to construct the equivalent of the widely used analytical description of viscous evolution for the MHD wind case. The transport of angular momentum and mass induced by the wind is parametrized by an α-like parameter and by the magnetic lever arm parameter λ. Extensions of the paradigmatic Lynden-Bell and Pringle similarity solutions to the wind case are presented. We show that wind-driven accretion leads to a steeper decrease in the disc mass and accretion rate than in viscous models due to the absence of disc spreading. If the decline of the magnetic field strength is slower than that of the gas surface density, the disc is dispersed after a finite time. The evolution of the disc in the $\dot{M}_*-M_{D}$ plane is sensitive to the wind and turbulence parameters. A disc population evolving under the action of winds can exhibit a correlation between $\dot{M}_*$ and MD depending on the initial conditions. The simplified framework proposed in this work opens to a new avenue to test the effectiveness of wind-driven accretion from the observed disc demographics and constitutes an important step to include wind-driven accretion in planet population synthesis models.

The dispersal of protoplanetary discs – III. Influence of stellar mass on disc photoevaporation

ABSTRACT The strong X-ray irradiation from young solar-type stars may play a crucial role in the thermodynamics and chemistry of circumstellar discs, driving their evolution in the last stages of disc dispersal as well as shaping the atmospheres of newborn planets. In this paper, we study the influence of stellar mass on circumstellar disc mass-loss rates due to X-ray irradiation, extending our previous study of the mass-loss rate’s dependence on the X-ray luminosity and spectrum hardness. We focus on stars with masses between 0.1 and 1 M⊙, which are the main target of current and future missions to find potentially habitable planets. We find a linear relationship between the mass-loss rates and the stellar masses when changing the X-ray luminosity accordingly with the stellar mass. This linear increase is observed also when the X-ray luminosity is kept fixed because of the lower disc aspect ratio which allows the X-ray irradiation to reach larger radii. We provide new analytical relations for the mass-loss rates and profiles of photoevaporative winds as a function of the stellar mass that can be used in disc and planet population synthesis models. Our photoevaporative models correctly predict the observed trend of inner-disc lifetime as a function of stellar mass with an increased steepness for stars smaller than 0.3 M⊙, indicating that X-ray photoevaporation is a good candidate to explain the observed disc dispersal process.

The dispersal of protoplanetary discs – II: photoevaporation models with observationally derived irradiating spectra

ABSTRACT Young solar-type stars are known to be strong X-ray emitters and their X-ray spectra have been widely studied. X-rays from the central star may play a crucial role in the thermodynamics and chemistry of the circumstellar material as well as in the atmospheric evolution of young planets. In this paper, we present model spectra based on spectral parameters derived from the observations of young stars in the Orion nebula cluster from the Chandra Orion Ultradeep Project (COUP). The spectra are then used to calculate new photoevaporation prescriptions that can be used in disc and planet population synthesis models. Our models clearly show that disc wind mass loss rates are controlled by the stellar luminosity in the soft ($100\, \mathrm{eV}$ to $1\, \mathrm{keV}$) X-ray band. New analytical relations are provided for the mass loss rates and profiles of photoevaporative winds as a function of the luminosity in the soft X-ray band. The agreement between observed and predicted transition disc statistics moderately improved using the new spectra, but the observed population of strongly accreting large cavity discs can still not be reproduced by these models. Furthermore, our models predict a population of non-accreting transition discs that are not observed. This highlights the importance of considering the depletion of millimetre-sized dust grains from the outer disc, which is a likely reason why such discs have not been detected yet.

The imprint of X-ray photoevaporation of planet-forming discs on the orbital distribution of giant planets

Context. Numerical models have shown that disc dispersal via internal photoevaporation driven by the host star can successfully reproduce the observed pile-up of warm Jupiters near 1–2 au. However, since a range of different mechanisms have been proposed to cause the same feature, clear observational diagnostics of disc dispersal leaving an imprint in the observed distribution of giant planets could help in constraining the dominant mechanisms. Aims. We aim to assess the impact of disc dispersal via X-ray-driven photoevaporation (XPE) on giant planet separations in order to provide theoretical constraints on the location and size of any possible features related to this process within the observed semi-major axis distribution of giant planets. Methods. For this purpose, we perform a set of 1D planet population syntheses with varying initial conditions and correlate the gas giants’ final parking locations with the X-ray luminosities of their host stars in order to quantify observables of this process within the semi-major axis versus host star X-ray luminosity plane of these systems. Results. We find that XPE does create an under-density of gas giants near the gravitational radius, with corresponding pile-ups inside and/or outside this location. However, the size and location of these features are strongly dependent on the choice of initial conditions in our model, such as the assumed formation location of the planets. Conclusions. XPE can strongly affect the migration process of giant planets and leave potentially observable signatures within the observed orbital separations of giant planets. However, due to the simplistic approach employed in our model, which lacks a self-consistent treatment of planet formation within an evolving disc, a quantitative analysis of the final planet population orbits is not possible. Our results, however, should strongly motivate future studies to include realistic disc dispersal mechanisms in global planet population synthesis models with self-consistent planet formation modules.

Giant planet migration during the disc dispersal phase

Context. Transition discs are expected to be a natural outcome of the interplay between photoevaporation and giant planet formation. Massive planets reduce the inflow of material from the outer to the inner disc, therefore triggering an earlier onset of disc dispersal due to photoevaporation through a process known as Planet-Induced PhotoEvaporation. In this case, a cavity is formed as material inside the planetary orbit is removed by photoevaporation, leaving only the outer disc to drive the migration of the giant planet. Aims. We investigate the impact of photoevaporation on giant planet migration and focus specifically on the case of transition discs with an evacuated cavity inside the planet location. This is important for determining under what circumstances photoevaporation is efficient at halting the migration of giant planets, thus affecting the final orbital distribution of a population of planets. Methods. For this purpose, we use 2D FARGO simulations to model the migration of giant planets in a range of primordial and transition discs subject to photoevaporation. The results are then compared to the standard prescriptions used to calculate the migration tracks of planets in 1D planet population synthesis models. Results. The FARGO simulations show that once the disc inside the planet location is depleted of gas, planet migration ceases. This contradicts the results obtained by the impulse approximation, which predicts the accelerated inward migration of planets in discs that have been cleared inside the planetary orbit. Conclusions. These results suggest that the impulse approximation may not be suitable for planets embedded in transition discs. A better approximation that could be used in 1D models would involve halting planet migration once the material inside the planetary orbit is depleted of gas and the surface density at the 3:2 mean motion resonance location in the outer disc reaches a threshold value of 0.01 g cm‒2.

Planetesimal formation at the gas pressure bump following a migrating planet

Context. Many scenarios have been proposed to avoid known difficulties in planetesimal formation such as drift or fragmentation barriers. However, in these scenarios planetesimals in general only form at some specific locations in protoplanetary discs. On the other hand, it is generally assumed in planet formation models and population synthesis models that planetesimals are broadly distributed in the protoplanetary disc. Aims. We propose a new scenario in which planetesimals can form in broad areas of these discs. Planetesimals form at the gas pressure bump formed by a first-generation planet (e.g. formed by pebble accretion) and the formation region spreads inward in the disc as the planet migrates. Methods. We used a simple 1D Lagrangian particle model to calculate the radial distribution of pebbles in the gas disc perturbed by a migrating embedded planet. We consider that planetesimals form by streaming instability at the points where the pebble-to-gas density ratio on the mid-plane becomes larger than unity. In this work, we fixed the Stokes number of pebbles and the mass of the planet to study the basic characteristics of this new scenario. We also studied the effect of some key parameters, such as the gas disc model, the pebble mass flux, the migration speed of the planet, and the strength of turbulence. Results. We find that planetesimals form in wide areas of protoplanetary discs provided the flux of pebbles is typical and the turbulence is not too strong. The planetesimal surface density depends on the pebble mass flux and the migration speed of the planet. The total mass of the planetesimals and the orbital position of the formation area strongly depend on the pebble mass flux. We also find that the profile of the planetesimal surface density and its slope can be estimated by very simple equations. Conclusions. We show that our new scenario can explain the formation of planetesimals in broad areas. The simple estimates we provide for the planetesimal surface density profile can be used as initial conditions for population synthesis models.

Formation of planetary populations – III. Core composition and atmospheric evaporation

ABSTRACT The exoplanet mass–radius diagram reveals that super-Earths display a wide range of radii, and therefore mean densities, at a given mass. Using planet population synthesis models, we explore the key physical factors that shape this distribution: planets’ solid core compositions, and their atmospheric structure. For the former, we use equilibrium disc chemistry models to track accreted minerals on to planetary cores throughout the formation. For the latter, we track gas accretion during the formation and consider photoevaporation-driven atmospheric mass-loss to determine what portion of accreted gas escapes after the disc phase. We find that atmospheric stripping of Neptunes and sub-Saturns at small orbital radii (≲0.1 au) plays a key role in the formation of short-period super-Earths. Core compositions are strongly influenced by the trap in which they formed. We also find a separation between Earth-like planet compositions at small orbital radii ≲0.5 au and ice-rich planets (up to 50 per cent by mass) at larger orbits ∼1 au. This corresponds well with the Earth-like mean densities inferred from the observed position of the low-mass planet radius valley at small orbital periods. Our model produces planet radii comparable to observations at masses ∼1–3 M⊕. At larger masses, planets’ accreted gas significantly increases their radii to be larger than most of the observed data. While photoevaporation, affecting planets at small orbital radii ≲0.1 au, reduces a subset of these planets’ radii and improves our comparison, most planets in our computed populations are unaffected due to low-far ultraviolet fluxes as they form at larger separations.

Formation of planetary populations − II. Effects of initial disc size and radial dust drift

ABSTRACT Recent ALMA observations indicate that while a range of disc sizes exist, typical disc radii are small, and that radial dust drift affects the distribution of solids in discs. Here, we explore the consequences of these features in planet population synthesis models. A key feature of our model is planet traps – barriers to otherwise rapid type-I migration of forming planets – for which we include the ice line, heat transition, and outer edge of the dead zone. We find that the ice line plays a fundamental role in the formation of warm Jupiters. In particular, the ratio of super Earths to warm Jupiters formed at the ice line depends sensitively on the initial disc radius. Initial gas disc radii of ∼50 au results in the largest super Earth populations, while both larger and smaller disc sizes result in the ice line producing more gas giants near 1 au. This transition between typical planet class formed at the ice line at various disc radii confirms that planet formation is fundamentally linked to disc properties (in this case, disc size), and is a result that is only seen when dust evolution effects are included in our models. Additionally, we find that including radial dust drift results in the formation of more super Earths between 0.1 and 1 au, having shorter orbital radii than those produced in models where dust evolution effects are not included.

The Exoplanet Population Observation Simulator. II. Population Synthesis in the Era of Kepler

Abstract The collection of planetary system properties derived from large surveys such as Kepler provides critical constraints on planet formation and evolution. These constraints can only be applied to planet formation models, however, if the observational biases and selection effects are properly accounted for. Here we show how epos, the Exoplanet Population Observation Simulator, can be used to constrain planet formation models by comparing the Bern planet population synthesis models to the Kepler exoplanetary systems. We compile a series of diagnostics, based on occurrence rates of different classes of planets and the architectures of multiplanet systems within 1 au, that can be used as benchmarks for future and current modeling efforts. Overall, we find that a model with 100-seed planetary cores per protoplanetary disk provides a reasonable match to most diagnostics. Based on these diagnostics we identify physical properties and processes that would result in the Bern model more closely matching the known planetary systems. These are as follows: moving the planet trap at the inner disk edge outward; increasing the formation efficiency of mini-Neptunes; and reducing the fraction of stars that form observable planets. We conclude with an outlook on the composition of planets in the habitable zone, and highlight that the majority of simulated planets smaller than 1.7 Earth radii in this zone are predicted to have substantial hydrogen atmospheres. The software used in this paper is available online for public scrutiny at https://github.com/GijsMulders/epos.

Constraining disk evolution prescriptions of planet population synthesis models with observed disk masses and accretion rates

While planets are commonly discovered around main-sequence stars, the processes leading to their formation are still far from being understood. Current planet population synthesis models, which aim to describe the planet formation process from the protoplanetary disk phase to the time exoplanets are observed, rely on prescriptions for the underlying properties of protoplanetary disks where planets form and evolve. The recent development in measuring disk masses and disk-star interaction properties, i.e., mass accretion rates, in large samples of young stellar objects demand a more careful comparison between the models and the data. We performed an initial critical assessment of the assumptions made by planet synthesis population models by looking at the relation between mass accretion rates and disk masses in the models and in the currently available data. We find that the currently used disk models predict mass accretion rate in line with what is measured, but with a much lower spread of values than observed. This difference is mainly because the models have a smaller spread of viscous timescales than what is needed to reproduce the observations. We also find an overabundance of weakly accreting disks in the models where giant planets have formed with respect to observations of typical disks. We suggest that either fewer giant planets have formed in reality or that the prescription for planet accretion predicts accretion on the planets that is too high. Finally, the comparison of the properties of transition disks with large cavities confirms that in many of these objects the observed accretion rates are higher than those predicted by the models. On the other hand, PDS70, a transition disk with two detected giant planets in the cavity, shows mass accretion rates well in line with model predictions.

ROME/REA: A Gravitational Microlensing Search for Exoplanets Beyond the Snow Line on a Global Network of Robotic Telescopes

Planet population synthesis models predict an abundance of planets with semimajor axes between 1 and 10 au, yet they lie at the edge of the detection limits of most planet finding techniques. Discovering these planets and studying their distribution is critical to understanding the physical processes that drive planet formation. ROME/REA is a gravitational microlensing project whose main science driver is to discover exoplanets in the cold outer regions of planetary systems. To achieve this, it uses a novel approach combining a multiband survey with reactive follow-up observations, exploiting the unique capabilities of the Las Cumbres Observatory global network of robotic telescopes combined with a Target and Observation Manager system. We present the main science objectives and a technical overview of the project, including initial results.

Hints for a Turnover at the Snow Line in the Giant Planet Occurrence Rate

Abstract The orbital distribution of giant planets is crucial for understanding how terrestrial planets form and predicting yields of exoplanet surveys. Here, we derive giant planets occurrence rates as a function of orbital period by taking into account the detection efficiency of the Kepler and radial velocity (RV) surveys. The giant planet occurrence rates for Kepler and RV show the same rising trend with increasing distance from the star. We identify a break in the RV giant planet distribution between ∼2 and 3 au—close to the location of the snow line in the solar system—after which the occurrence rate decreases with distance from the star. Extrapolating a broken power-law distribution to larger semimajor axes, we find good agreement with the ∼1% planet occurrence rates from direct imaging surveys. Assuming a symmetric power law, we also estimate that the occurrence of giant planets between 0.1 and 100 au is for planets with masses 0.1–20 M J and decreases to for planets more massive than Jupiter. This implies that only a fraction of the structures detected in disks around young stars can be attributed to giant planets. Various planet population synthesis models show good agreement with the observed distribution, and we show how a quantitative comparison between model and data can be used to constrain planet formation and migration mechanisms.

Cometary ices in forming protoplanetary disc midplanes

Low-mass protostars are the extrasolar analogues of the natal Solar System. Sophisticated physicochemical models are used to simulate the formation of two protoplanetary discs from the initial prestellar phase, one dominated by viscous spreading and the other by pure infall. The results show that the volatile prestellar fingerprint is modified by the chemistry en route into the disc. This holds relatively independent of initial abundances and chemical parameters: physical conditions are more important. The amount of CO2 increases via the grain-surface reaction of OH with CO, which is enhanced by photodissociation of H2O ice. Complex organic molecules are produced during transport through the envelope at the expense of CH3OH ice. Their abundances can be comparable to that of methanol ice (few % of water ice) at large disc radii (R > 30 AU). Current Class II disc models may be underestimating the complex organic content. Planet population synthesis models may underestimate the amount of CO2 and overestimate CH3OH ices in planetesimals by disregarding chemical processing between the cloud and disc phases. The overall C/O and C/N ratios differ between the gas and solid phases. The two ice ratios show little variation beyond the inner 10 AU and both are nearly solar in the case of pure infall, but both are sub-solar when viscous spreading dominates. Chemistry in the protostellar envelope en route to the protoplanetary disc sets the initial volatile and prebiotically-significant content of icy planetesimals and cometary bodies. Comets are thus potentially reflecting the provenances of the midplane ices in the Solar Nebula.

A survey of young, nearby, and dusty stars conducted to understand the formation of wide-orbit giant planets

Direct imaging has confirmed the existence of substellar companions on wide orbits. To understand the formation and evolution mechanisms of these companions, the full population properties must be characterized. We aim at detecting giant planet and/or brown dwarf companions around young, nearby, and dusty stars. Our goal is also to provide statistics on the population of giant planets at wide-orbits and discuss planet formation models. We report a deep survey of 59 stars, members of young stellar associations. The observations were conducted with VLT/NaCo at L'-band (3.8 micron). We used angular differential imaging to reach optimal detection performance. A statistical analysis of about 60 % of the young and southern A-F stars closer than 65 pc allows us to derive the fraction of giant planets on wide orbits. We use gravitational instability models and planet population synthesis models following the core-accretion scenario to discuss the occurrence of these companions. We resolve and characterize new visual binaries and do not detect any new substellar companion. The survey's median detection performance reaches contrasts of 10 mag at 0.5as and 11.5 mag at 1as. We find the occurrence of planets to be between 10.8-24.8 % at 68 % confidence level assuming a uniform distribution of planets in the interval 1-13 Mj and 1-1000 AU. Considering the predictions of formation models, we set important constraints on the occurrence of massive planets and brown dwarf companions that would have formed by GI. We show that this mechanism favors the formation of rather massive clump (Mclump > 30 Mj) at wide (a > 40 AU) orbits which might evolve dynamically and/or fragment. For the population of close-in giant planets that would have formed by CA, our survey marginally explore physical separations (<20 AU) and cannot constrain this population.

The occurrence and the distribution of masses and radii of exoplanets

AbstractWe analyze the statistics of Doppler-detected planets and Keplere-detected planet candidates of high integrity. We determine the number of planets per star as a function of planet mass, radius, and orbital period, and the occurrence of planets as a function of stellar mass. We consider only orbital periods less than 50 days around Solar-type (GK) stars, for which both Doppler and Kepler offer good completeness. We account for observational detection effects to determine the actual number of planets per star. From Doppler-detected planets discovered in a survey of 166 nearby G and K main sequence stars we find a planet occurrence of 15+5−4% for planets with M sin i = 3–30 ME and P &lt; 50 d, as described in Howard et al. (2010). From Keplere, the planet occurrence is 0.130 ± 0.008, 0.023 ± 0.003, and 0.013 ± 0.002 planets per star for planets with radii 2–4, 4–8, and 8–32 RE, consistent with Doppler-detected planets. From Keplere, the number of planets per star as a function of planet radius is given by a power law, df/dlog R = kRRα with kR = 2.9+0.5−0.4, α = −1.92 ± 0.11, and R = RP/RE. Neither the Doppler-detected planets nor the Keplere-detected planets exhibit a “desert” at super-Earth and Neptune sizes for close-in orbits, as suggested by some planet population synthesis models. The distribution of planets with orbital period, P, shows a gentle increase in occurrence with orbital period in the range 2–50 d. The occurrence of small, 2–4 RE planets increases with decreasing stellar mass, with seven times more planets around low mass dwarfs (3600–4100 K) than around massive stars (6600–7100 K).

ORBITAL MIGRATION OF LOW-MASS PLANETS IN EVOLUTIONARY RADIATIVE MODELS: AVOIDING CATASTROPHIC INFALL

Outward migration of low-mass planets has recently been shown to be a possibility in non-barotropic disks. We examine the consequences of this result in evolutionary models of protoplanetary disks. Planet migration occurs towards equilibrium radii with zero torque. These radii themselves migrate inwards because of viscous accretion and photoevaporation. We show that as the surface density and temperature fall, the planet orbital migration and disk depletion timescales eventually become comparable, with the precise timing depending on the mass of the planet. When this occurs, the planet decouples from the equilibrium radius. At this time, however, the gas surface density is already too low to drive substantial further migration. A higher mass planet, of 10 Earth masses, can open a gap during the late evolution of the disk, and stops migrating. Low mass planets, with 1 or 0.1 Earth masses, released beyond 1 AU in our models, avoid migrating into the star. Our results provide support for the reduced migration rates adopted in recent planet population synthesis models.

Gas- and dust evolution in protoplanetary disks

Context. Current models of the size- and radial evolution of dust in protoplanetary disks generally oversimplify either the radial evolution of the disk (by focussing at one single radius or by using steady state disk models) or they assume particle growth to proceed monodispersely or without fragmentation. Further studies of protoplanetary disks - such as observations, disk chemistry and structure calculations or planet population synthesis models - depend on the distribution of dust as a function of grain size and radial position in the disk. Aims. We attempt to improve upon current models to be able to investigate how the initial conditions, the build-up phase, and the evolution of the protoplanetary disk influence growth and transport of dust. Methods. We introduce a new version of the model of Brauer et al. (2008) in which we now include the time-dependent viscous evolution of the gas disk, and in which more advanced input physics and numerical integration methods are implemented. Results. We show that grain properties, the gas pressure gradient, and the amount of turbulence are much more influencing the evolution of dust than the initial conditions or the build-up phase of the protoplanetary disk. We quantify which conditions or environments are favorable for growth beyond the meter size barrier. High gas surface densities or zonal flows may help to overcome the problem of radial drift, however already a small amount of turbulence poses a much stronger obstacle for grain growth.