Planet Formation around Stars of Various Masses: The Snow Line and the Frequency of Giant Planets

By G. Kennedy, S. Kenyon. 2007

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We use a semianalytic circumstellar disk model that considers movement of the snow line through evolution of accretion and the central star to investigate how gas giant frequency changes with stellar mass. The snow line distance changes weakly with stellar mass; thus, giant planets form over a wide range of spectral types. The probability that a given star has at least one gas giant increases linearly with stellar mass from 0.4 to 3 M☉. Stars more massive than 3 M☉ evolve quickly to the main sequence, which pushes the snow line to 10-15 AU before protoplanets form and limits the range of disk masses that form giant planet cores. If the frequency of gas giants around solar mass stars is 6%, we predict occurrence rates of 1% for 0.4 M☉ stars and 10% for 1.5 M☉ stars. This result is largely insensitive to our assumed model parameters. Finally, the movement of the snow line as stars ≳2.5 M☉ move to the main sequence may allow the ocean planets suggested by Léger et al. to form without migration.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/009e1ede307ea4afb006449a27d7d3a0311a204b

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An ALMA Survey of Protoplanetary Disks in the σ Orionis Cluster (2017, background): “…host star mass (Endl et al. 2006; Johnson et al. 2007; Bowler et al. 2010; Bonfils et al. 2013), as the cores of giant planets theoretically form more efficiently both in higher-mass disks (e.g., Thommes et al. 2008; Mordasini et al. 2012) and around higher-mass stars (e.g., Kennedy & Kenyon 2008).”
NEW DEBRIS DISKS AROUND YOUNG, LOW-MASS STARS DISCOVERED WITH THE SPITZER SPACE TELESCOPE (2009, neutral): “Theoretical modeling indicates that the orbital distance for the formation of Jovian planets at the “snow line” has a weak dependence on stellar mass (Kennedy & Kenyon 2008; Kennedy et al. 2007, 2006).”
A Low-Mass Planet with a Possible Sub-Stellar-Mass Host in Microlensing Event MOA-2007-BLG-192 (2008, background): “In the context of planet formation theory (Ida & Lin 2004; Lecar et al. 2006; Kennedy et al. 2006; Kennedy & Kenyon 2008), the “snow-line” is the region in the proto-planetary disk where it is just cold enough for water-ice to form.”
Stable-isotopic anomalies and the accretionary assemblage of the Earth and Mars: A subordinate role for carbonaceous chondrites (2011, background): “It has long been customary to assume that ureilite traits such as high bulk carbon contents and diverse, (16)O-rich oxygen isotopic compositions imply a link with the carbonaceous chondrites (e.g., Berkley et al., 1980; Goodrich et al., 2007; Kita et al., 2004; Singletary and Grove, 2006; Takeda, 19”
Microlensing Surveys for Exoplanets (2012, methodology): “Figure 6 shows the estimated masses and semimajor axes scaled to the location of the snow line for the detected microlensing planets, where we have assumed a snow line location as l = 2.7 AU (M /M⊙) (Kennedy & Kenyon 2008).”
Gaps and Rings in an ALMA Survey of Disks in the Taurus Star-forming Region (2018, background): “For more massive stars, the formation of the cores of giant planets is expected to be more efficient (Kennedy & Kenyon 2008).”
CHARACTERIZING THE COOL KOIs. IV. KEPLER-32 AS A PROTOTYPE FOR THE FORMATION OF COMPACT PLANETARY SYSTEMS THROUGHOUT THE GALAXY (2012, background): “For these calculated rates, the timescale for these planets to have migrated from beyond the snow line at ∼ 1AU (Kennedy & Kenyon 2008) to their present day locations is short, τmig ∼ 104 years, in comparison to typical disk lifetimes.”
THE OCCURRENCE RATE OF SMALL PLANETS AROUND SMALL STARS (2013, background): “…in the 1.4 − 4R⊕ planet occurrence rate at cooler temperatures might be due to the decreased surface density in the circumstellar disks of very low-mass stars and the longer orbital timescales at a given separation (Laughlin et al. 2004; Adams et al. 2005; Ida & Lin 2005; Kennedy & Kenyon 2008).”
Extrasolar planets and brown dwarfs around A-F type stars. VI. High precision RV survey of early type dwarfs with HARPS (2008, background): “…the mass of the parent star, at least for low-mass stars (Ida & Lin 2005) and that the frequency of giant planets increases linearly with the parent-star mass for stars between 0.4 and 3 M (Kennedy & Kenyon 2008), with e.g., 6% frequency of giant planets around 1 M and 10% frequency around 1.5 M .”
ON THE METAL RICHNESS OF M DWARFS WITH PLANETS (2009, background): “Similarly, the disks around massive stars also have enhanced surface densities, as well as expansive radial regions in which protoplanetary cores grow most efficiently (Laughlin et al. 2004; Ida & Lin 2005; Kennedy & Kenyon 2008).”
The habitability of Proxima Centauri b. I. Irradiation, rotation and volatile inventory from formation to the present (2016, background): “The snow line therefore moves inward in time, (e.g., Lecar et al. 2006; Kennedy & Kenyon 2008; Podolak 2010; Martin & Livio 2012).”
PLANETS AROUND LOW-MASS STARS (PALMS). IV. THE OUTER ARCHITECTURE OF M DWARF PLANETARY SYSTEMS (2014, background): “Since orbital period scales as M −1/2 ∗ , the timescale associated with planetesimal coagulation (a few Myr) is faster for high-mass stars so more cores are able to form and accrete gaseous envelopes before protoplanetary disks disperse (e.g., Laughlin et al. 2004; Kennedy & Kenyon 2008).”
Variations on Debris Disks: Icy Planet Formation at 30-150 AU for 1-3 M☉ Main-Sequence Stars (2008, background): “If the cores of gas giant planets form before their parent stars reach the main sequence, we expect gas giants at 20Y30 AU around 2Y 3 M stars (e.g., Kennedy & Kenyon 2008).”
THE FORMATION MECHANISM OF GAS GIANTS ON WIDE ORBITS (2009, positive): “Our work confirms the finding of Kennedy & Kenyon (2008) that A stars have wider planet formation zones than lower-mass stars.”
Origin of water in the inner Solar System: Planetesimals scattered inward during Jupiter and Saturn's rapid gas accretion (2017, background): “However, the snow line is not fixed but moves inward in time as the disk cools (Lecar et al., 2006; Kennedy and Kenyon, 2008; Martin and Livio, 2012).”
THE MASS DEPENDENCE BETWEEN PROTOPLANETARY DISKS AND THEIR STELLAR HOSTS (2013, background): “…core growth is accelerated for disks with higher densities (∝ Md; e.g., Ikoma et al. 2000; Hubickyj et al. 2005; Thommes et al. 2008), and sees modest benefits from shorter orbital periods (∝ √ M∗ at a fixed semimajor axis) and larger potential formation zones (∼ M∗; e.g., Kennedy & Kenyon 2008).”
FREQUENCY OF SOLAR-LIKE SYSTEMS AND OF ICE AND GAS GIANTS BEYOND THE SNOW LINE FROM HIGH-MAGNIFICATION MICROLENSING EVENTS IN 2005–2008 (2010, background): “While there is observational evidence from the asteroid belt that the Solar-System snow line is near Rsnow,⊙ = 2.7 AU (Morbidelli et al. 2000), there is considerable uncertainty on how this scales with stellar mass (Sasselov & Lecar 2000; Kennedy & Kenyon 2008).”
Precise Radial Velocities of Giant Stars VII. Occurrence Rate of Giant Extrasolar Planets as a Function of Mass and Metallicity (2014, background): “The details of the models differ significantly, yet both predict an increase in the giant planet formation rate with mass over the range from about 0.5 to 1.5 M (Ida & Lin 2005) and from about 0.5 to 3.0 M (Kennedy & Kenyon 2008b), respectively (see Fig.”
MOA-2009-BLG-387Lb: a massive planet orbiting an M dwarf (2011, background): “…theory of giant planet formation predicts that giant planets should be less common around lowmass stars (Laughlin et al. 2004; Ida & Lin 2005; Kennedy & Kenyon 2008; D’Angelo et al. 2010), whereas the gravitational instability model predicts that giant planets can form around M dwarfs with…”