scholarly journals Sculpting the Sub-Saturn Occurrence Rate via Atmospheric Mass Loss

2022 ◽  
Vol 924 (1) ◽  
pp. 9
Author(s):  
Tim Hallatt ◽  
Eve J. Lee
Keyword(s):  
Mass Loss ◽  
Mass Function ◽  
Occurrence Rate ◽  
Rotating Stars ◽  
Core Mass ◽  
Orbital Periods ◽  
M Stars ◽  
Gas Accretion ◽  
Rapidly Rotating Stars ◽  
Atmospheric Mass

Abstract The sub-Saturn (∼4–8 R ⊕) occurrence rate rises with orbital period out to at least ∼300 days. In this work we adopt and test the hypothesis that the decrease in their occurrence toward the star is a result of atmospheric mass loss, which can transform sub-Saturns into sub-Neptunes (≲4 R ⊕) 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 ∼10–20 M ⊕ 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 ∼50% less common and ∼30% more massive around rapidly rotating stars; this should be directly testable for stars younger than ≲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 (∼0.7 days versus ∼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 ∼1.5× the mass of its core and is currently losing its envelope at a rate of ∼2 × 10−3 M ⊕ 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.

scholarly journals The nature of the radius valley

2020 ◽  
Vol 643 ◽  
pp. L1 ◽  
Author(s):  
Julia Venturini ◽  
Octavio M. Guilera ◽  
Jonas Haldemann ◽  
María P. Ronco ◽  
Christoph Mordasini
Keyword(s):  
Mass Loss ◽  
Size Distribution ◽  
Point Of View ◽  
Parameter Study ◽  
Type I ◽  
Water Ice ◽  
Wide Range ◽  
Orbital Periods ◽  
Gas Accretion ◽  
Second Peak

The existence of a radius valley in the Kepler size distribution stands as one of the most important observational constraints to understand the origin and composition of exoplanets with radii between those of Earth and Neptune. In this work we provide insights into the existence of the radius valley, first from a pure formation point of view and then from a combined formation-evolution model. We run global planet formation simulations including the evolution of dust by coagulation, drift, and fragmentation, and the evolution of the gaseous disc by viscous accretion and photoevaporation. A planet grows from a moon-mass embryo by either silicate or icy pebble accretion, depending on its position with respect to the water ice line. We include gas accretion, type I–II migration, and photoevaporation driven mass-loss after formation. We perform an extensive parameter study evaluating a wide range of disc properties and initial locations of the embryo. We find that due to the change in dust properties at the water ice line, rocky cores form typically with ∼3 M⊕ and have a maximum mass of ∼5 M⊕, while icy cores peak at ∼10 M⊕, with masses lower than 5 M⊕ being scarce. When neglecting the gaseous envelope, the formed rocky and icy cores account naturally for the two peaks of the Kepler size distribution. The presence of massive envelopes yields planets more massive than ∼10 M⊕ with radii above 4 R⊕. While the first peak of the Kepler size distribution is undoubtedly populated by bare rocky cores, as shown extensively in the past, the second peak can host half-rock–half-water planets with thin or non-existent H-He atmospheres, as suggested by a few previous studies. Some additional mechanisms inhibiting gas accretion or promoting envelope mass-loss should operate at short orbital periods to explain the presence of ∼10–40 M⊕ planets falling in the second peak of the size distribution.

scholarly journals Mass loss in 2D rotating stellar models

2010 ◽  
Vol 6 (S272) ◽  
pp. 93-94
Author(s):  
Catherine Lovekin ◽  
Robert G. Deupree
Keyword(s):  
Mass Loss ◽  
Stellar Evolution ◽  
Effective Temperature ◽  
Massive Stars ◽  
Surface Flux ◽  
Rotating Stars ◽  
Stellar Models ◽  
Rapidly Rotating Stars ◽  
Loss Rates

AbstractRadiatively driven mass loss is an important factor in the evolution of massive stars. The mass loss rates depend on a number of stellar parameters, including the effective temperature and luminosity. Massive stars are also often rapidly rotating, which affects their structure and evolution. In sufficiently rapidly rotating stars, both the effective temperature and surface flux vary significantly as a function of latitude, and hence mass loss rates can vary appreciably between the poles and the equator. In this work, we discuss the addition of mass loss to a 2D stellar evolution code (ROTORC) and compare evolution sequences with and without mass loss.

scholarly journals Occurrence rates of planets orbiting M Stars: applying ABC to Kepler DR25, Gaia DR2, and 2MASS data

2020 ◽  
Vol 498 (2) ◽  
pp. 2249-2262 ◽  
Author(s):  
Danley C Hsu ◽  
Eric B Ford ◽  
Ryan Terrien
Keyword(s):  
Small Sample ◽  
Occurrence Rate ◽  
Early Type ◽  
M Dwarfs ◽  
Orbital Periods ◽  
M Stars ◽  
Stellar Properties ◽  
Approximate Bayesian ◽  
M Dwarf ◽  
Gaia Dr2

ABSTRACT We present robust planet occurrence rates for Kepler planet candidates around M stars for planet radii Rp = 0.5–4 R⊕ and orbital periods P = 0.5–256 d using the approximate Bayesian computation technique. This work incorporates the final Kepler DR25 planet candidate catalogue and data products and augments them with updated stellar properties using Gaia DR2 and 2MASS point source catalogue. We apply a set of selection criteria to select a sample of 1746 Kepler M dwarf targets that host 89 associated planet candidates. These early-type M dwarfs and late K dwarfs were selected from cross-referenced targets using several photometric quality flags from Gaia DR2 and colour–magnitude cuts using 2MASS magnitudes. We estimate a habitable zone occurrence rate of $f_{\textrm {M,HZ}} = 0.33^{+0.10}_{-0.12}$ for planets with 0.75–1.5 R⊕ size. We caution that occurrence rate estimates for Kepler M stars are sensitive to the choice of prior due to the small sample of target stars and planet candidates. For example, we find an occurrence rate of $4.2^{+0.6}_{-0.6}$ or $8.4^{+1.2}_{-1.1}$ planets per M dwarf (integrating over Rp = 0.5–4 R⊕ and P = 0.5–256 d) for our two choices of prior. These occurrence rates are greater than those for FGK dwarf target when compared at the same range of orbital periods, but similar to occurrence rates when computed as a function of equivalent stellar insolation. Combining our result with recent studies of exoplanet architectures indicates that most, and potentially all, early-type M dwarfs harbour planetary systems.

scholarly journals Sculpting the valley in the radius distribution of small exoplanets as a by-product of planet formation: the core-powered mass-loss mechanism

2019 ◽  
Vol 487 (1) ◽  
pp. 24-33 ◽  
Author(s):  
Akash Gupta ◽  
Hilke E Schlichting
Keyword(s):  
Mass Loss ◽  
Thermal Evolution ◽  
Relative Magnitude ◽  
Occurrence Rate ◽  
Loss Mechanism ◽  
Water Ice ◽  
The Core ◽  
Planetary Cores ◽  
Short Period ◽  
Atmospheric Mass

ABSTRACT Recent observations revealed a bimodal radius distribution of small, short-period exoplanets with a paucity in their occurrence, a radius ‘valley’, around 1.5–2.0 R⊕. In this work, we investigate the effect of a planet’s own cooling luminosity on its thermal evolution and atmospheric mass loss (core-powered mass-loss) and determine its observational consequences for the radius distribution of small, close-in exoplanets. Using simple analytical descriptions and numerical simulations, we demonstrate that planetary evolution based on the core-powered mass-loss mechanism alone (i.e. without any photoevaporation) can produce the observed valley in the radius distribution. Our results match the valley’s location, shape and slope in planet radius–orbital period parameter space, and the relative magnitudes of the planet occurrence rate above and below the valley. We find that the slope of the valley is, to first order, dictated by the atmospheric mass-loss time-scale at the Bondi radius and given by d logRp/d logP ≃ 1/(3(1 − β)) that evaluates to −0.11 for β ≃ 4, where Mc/M⊕ = (Rc/R⊕)β(ρc∗/ρ⊕)β/3 is the mass–radius relation of the core. This choice for β yields good agreement with observations and attests to the significance of internal compression for massive planetary cores. We further find that the location of the valley scales as $\rho _{\rm c*}^{-4/9}$ and that the observed planet population must have predominantly rocky cores with typical water–ice fractions of less than ${\sim } 20{{\, \rm per\, cent}}$. Furthermore, we show that the relative magnitude of the planet occurrence rate above and below the valley is sensitive to the details of the planet-mass distribution but that the location of the valley is not.

scholarly journals Most super-Earths formed by dry pebble accretion are less massive than 5 Earth masses

2020 ◽  
Vol 644 ◽  
pp. A174
Author(s):  
Julia Venturini ◽  
Octavio Miguel Guilera ◽  
María Paula Ronco ◽  
Christoph Mordasini
Keyword(s):  
Mass Loss ◽  
Size Distribution ◽  
Growth Patterns ◽  
Parameter Study ◽  
Core Mass ◽  
Low Viscosity ◽  
Advection Diffusion Equation ◽  
Rocky Planets ◽  
Atmospheric Mass ◽  
Second Peak

Aims. The goal of this work is to study the formation of rocky planets by dry pebble accretion from self-consistent dust-growth models. In particular, we aim to compute the maximum core mass of a rocky planet that can sustain a thin H-He atmosphere to account for the second peak of the Kepler size distribution. Methods. We simulate planetary growth by pebble accretion inside the ice line. The pebble flux is computed self-consistently from dust growth by solving the advection–diffusion equation for a representative dust size. Dust coagulation, drift, fragmentation, and sublimation at the water ice line are included. The disc evolution is computed solving the vertical and radial structure for standard α-discs with photoevaporation from the central star. The planets grow from a moon-mass embryo by silicate pebble accretion and gas accretion. We perform a parameter study to analyse the effect of a different initial disc mass, α-viscosity, disc metallicity, and embryo location. We also test the effect of considering migration versus an in situ scenario. Finally, we compute atmospheric mass loss due to evaporation over 5 Gyr of evolution. Results. We find that inside the ice line, the fragmentation barrier determines the size of pebbles, which leads to different planetary growth patterns for different disc viscosities. We also find that in this inner disc region, the pebble isolation mass typically decays to values below 5 M⊕ within the first million years of disc evolution, limiting the core masses to that value. After computing atmospheric mass loss, we find that planets with cores below ~4 M⊕ become completely stripped of their atmospheres, and a few 4–5 M⊕ cores retain a thin atmosphere that places them in the “gap” or second peak of the Kepler size distribution. In addition, a few rare objects that form in extremely low-viscosity discs accrete a core of 7 M⊕ and equal envelope mass, which is reduced to 3–5 M⊕ after evaporation. These objects end up with radii of ~6–7 R⊕. Conclusions. Overall, we find that rocky planets form only in low-viscosity discs (α ≲ 10−4). When α ≥ 10−3, rocky objects do not grow beyond 1 Mars mass. For the successful low-viscosity cases, the most typical outcome of dry pebble accretion is terrestrial planets with masses spanning from that of Mars to ~4 M⊕.

scholarly journals Atmospheric mass loss by stellar wind from planets around main sequence M stars

Icarus ◽  
2010 ◽  
Vol 210 (2) ◽  
pp. 539-544 ◽  
Author(s):  
J. Zendejas ◽  
A. Segura ◽  
A.C. Raga
Keyword(s):  
Mass Loss ◽  
Stellar Wind ◽  
Main Sequence ◽  
M Stars ◽  
Atmospheric Mass

Energy Dissipation due to Mass Loss in a Rotating System

1992 ◽  
Vol 10 (1) ◽  
pp. 48-51
Author(s):  
D.B. Melrose
Keyword(s):  
Energy Dissipation ◽  
Mass Loss ◽  
Magnetic Energy ◽  
Angular Speed ◽  
Acceleration Of Particles ◽  
Stellar Systems ◽  
Rotating Stars ◽  
Rotating System ◽  
Energy Part ◽  
Rapidly Rotating Stars

AbstractWhen a rotating magnetised system (angular speed Ω), such as a planet or star, loses mass there is necessarily an energy dissipation associated with the mass loss. Consider mass loss at rate M, such that the matter is flung off with the orbital speed ΩR1, at a radius R1 ≫ R0, where R0 is the radius of the planet or star. The power released is approximately equal to the power Prot = 1/2MΩ2R2 carried off in rotational kinetic energy. Part of the energy released is carried off as magnetic energy in the escaping plasma, and the remainder is released through dissipation of currents. Such dissipation plausibly leads to the acceleration of particles. The power released should be important for Jupiter and for some rapidly rotating stars. For most stellar systems, the power released is small compared to that required to drive a wind.

scholarly journals Planet formation and migration near the silicate sublimation front in protoplanetary disks

2019 ◽  
Vol 630 ◽  
pp. A147 ◽  
Author(s):  
Mario Flock ◽  
Neal J. Turner ◽  
Gijs D. Mulders ◽  
Yasuhiro Hasegawa ◽  
Richard P. Nelson ◽  
...  
Keyword(s):  
Orbital Period ◽  
Planet Formation ◽  
Protoplanetary Disks ◽  
Occurrence Rate ◽  
Parameter Study ◽  
Sublimation Front ◽  
Small Grains ◽  
Orbital Periods ◽  
M Stars ◽  
And Migration

Context. The increasing number of newly detected exoplanets at short orbital periods raises questions about their formation and migration histories. Planet formation and migration depend heavily on the structure and dynamics of protoplanetary disks. A particular puzzle that requires explanation arises from one of the key results of the Kepler mission, namely the increase in the planetary occurrence rate with orbital period up to 10 days for F, G, K and M stars. Aims. We investigate the conditions for planet formation and migration near the dust sublimation front in protostellar disks around young Sun-like stars. We are especially interested in determining the positions where the drift of pebbles would be stopped, and where the migration of Earth-like planets and super-Earths would be halted. Methods. For this analysis we use iterative 2D radiation hydrostatic disk models which include irradiation by the star, and dust sublimation and deposition depending on the local temperature and vapor pressure. Results. Our results show the temperature and density structure of a gas and dust disk around a young Sun-like star. We perform a parameter study by varying the magnetized turbulence onset temperature, the accretion stress, the dust mass fraction, and the mass accretion rate. Our models feature a gas-only inner disk, a silicate sublimation front and dust rim starting at around 0.08 au, an ionization transition zone with a corresponding density jump, and a pressure maximum which acts as a pebble trap at around 0.12 au. Migration torque maps show Earth- and super-Earth-mass planets halt in our model disks at orbital periods ranging from 10 to 22 days. Conclusions. Such periods are in good agreement with both the inferred location of the innermost planets in multiplanetary systems, and the break in planet occurrence rates from the Kepler sample at 10 days. In particular, models with small grains depleted produce a trap located at a 10-day orbital period, while models with a higher abundance of small grains present a trap at around a 17-day orbital period. The snow line lies at 1.6 au, near where the occurrence rate of the giant planets peaks. We conclude that the dust sublimation zone is crucial for forming close-in planets, especially when considering tightly packed super-Earth systems.

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