A Decreased Probability of Habitable Planet Formation around Low‐Mass Stars

“The average distance of the HZ from the parent star depends primarily on the star’s luminosity, and is closer-in and narrower around lowermass stars (Kasting et al. 1993).”

“For a planet to remain habitable, it must control its surface temperature over long timescales, possibly via the CO2-carbonate cycle (Walker et al. 1981), which is enabled by a relatively thick atmosphere, a hydrological cycle, and active plate tectonics.”

“We integrated each simulation for 200 Myr using the hybrid integrator Mercury (Chambers 1999).”

“…M⋆, f is a scaling factor for the disk (f=1 for MMSN), Z is the stellar metallicity (1.0=solar), and α moderates the steepness of the density profile (α = 3/2 in the MMSN model; Hayashi 1981, but more recent reconstructions using an accretion disk model as a constraint gives α = 1/2; Davis 2005).”

“There also exists a factor of 3-5 range in metallicity for thin-disk stars (Nordstrom et al. 2004), which adjusts the effective gas-to-dust ratio.”

“…in situ from a very massive disk, with fZ ∼ 30− 50; or 2) our assumption of in situ formation failed in this case: the planets of Gl 581 formed farther from the star (probably in the icy regions of a relatively massive disk, with fZ of at least 5-10) and migrated inward (Goldreich & Tremaine 1980).”

“2004; Fischer & Valenti 2005) allow for 70-90% of stars to have planetary systems without Jovians, and an even larger fraction for lower-mass stars (Endl et al. 2006; Butler et al. 2006).”

“The most promising lead comes from estimates of outer disk masses using submm and mm techniques (Beckwith et al. 1990), which remain uncertain because of adopted dust temperatures, opacities, distances, and radiative transfer model.”

“…HZs of lower-mass stars – is inefficient dynamical stirring in the low-mass disks found around low-mass stars, because more massive embryos are needed to increase eccentricities enough for significant radial mixing and therefore water delivery (Morbidelli et al. 2000; Raymond et al. 2004, 2007).”

“…of the Gl 581 planets were to transit the parent star, then it would be possible to derive a rough composition (rocky vs. icy: Valencia et al. 2007; Fortney et al. 2007; Sotin et al. 2007), and to distinguish between these two formation scenarios (Gaidos et al. 2007; S. Raymond et al. 2007, in…”

“Present estimates of disk masses in nearby star-forming regions (see Andre & Montmerle 1994, Eisner & Carpenter 2003, Andrews & Williams 2005) give a large spread, with median or average masses usually somewhat below the MMSN value, but a significant fraction more massive, including a very massive…”

“In other words, models of embryo growth predict that there really are more embryos in these inner disks than in the more distant regions studied for higher-mass stars (e.g., Kokubo & Ida 1998).”

“…of debris disks and the metallicity of the parent star (Greaves et al. 2006; Beichman et al. 2006; Moro-Mart́ın et al. 2007), unlike the correlation known for exogiant planets (Gonzalez 1997, Santos et al. , Fischer & Valenti 2005), also supports the likelihood of gas-giant-free planetary systems.”

“It might therefore seem natural to assume that Mdisk ∝ M 2 ⋆ , i.e. h=2, assuming that the viscous timescale is independent of stellar mass (e.g., Ida & Lin 2005).”

“A system of three planets with minimum masses between 5 and 15 M⊕ was recently discovered orbiting the 0.31 M⊙ star Gliese 581 (Bonfils et al. 2005; Udry et al. 2007).”

“There are observational (Endl et al. 2006; Butler et al. 2006) and theoretical (Ward & Hahn 1995; Adams et al. 2004; Laughlin et al. 2004, Ida & Lin 2005) reasons to think that the fraction of M stars with Jovian planets is significantly smaller than for solar-mass stars.”

“There are observational (Endl et al. 2006; Butler et al. 2006) and theoretical (Ward & Hahn 1995; Adams et al. 2004; Laughlin et al. 2004, Ida & Lin 2005) reasons to think that the fraction of M stars with Jovian planets is significantly smaller than for solar-mass stars.”

“Second, for a given set of parameters, there still exists a range of potential outcomes because of the stochastic nature of the final stages of planetary growth (e.g., Wetherill 1996, Raymond et al. 2004; see Fig.”

“Present estimates of disk masses in nearby star-forming regions (see Andre & Montmerle 1994, Eisner & Carpenter 2003, Andrews & Williams 2005) give a large spread, with median or average masses usually somewhat below the MMSN value, but a significant fraction more massive, including a very massive…”

“However these latter two points should not affect decisions concerning M star planet searches, since they only apply to the very lowest-mass stars, ∼ 0.1 − 0.2 M⊙, whose apparent brightness and HZ angular separation are far too small for any planned search (Scalo et al. 2007).”

“Note that systems with close-in giant planets may also contain Earth-like planets, which should be very waterrich (Raymond et al. 2006b; Mandell et al. 2007).”

“We assume that the disk evolved following the standard model of terrestrial planet growth (e.g. Chambers 2004): grains coalesced to form kmsized planetesimals; and embryos formed from planetes- imals via runaway and oligarchic growth (e.g., Kokubo & Ida 1998), spaced by 5-10 mutual Hill radii (RH,m…”

“Additional clues come from the observed stellar accretion rate Ṁ , which scales as Ṁ ∝ M2⋆ , with a large dispersion (Muzerolle et al. 2003, 2005, Natta et al. 2006).”

“For instance, if we assume L⋆ ∝ M 4 ⋆ (a rough fit to Hillenbrand & White 2004), then the location of the HZ, rHZ , scales with the stellar mass as rHZ ∝ L 1/2 ⋆ ∝ M 2 ⋆ .”

“…by intense stellar activity coupled with their small distance to their parent stars, depending on the strength of the planetary magnetic field (Lammer et al. 2007), a snow line that takes perhaps a Gyr to get close enough to the HZ to give sufficient water (Kennedy et al. 2006), or loss of…”

“Additional clues come from the observed stellar accretion rate Ṁ , which scales as Ṁ ∝ M2⋆ , with a large dispersion (Muzerolle et al. 2003, 2005, Natta et al. 2006).”

“If any of the Gl 581 planets were to transit the parent star, then it would be possible to derive a rough composition (rocky vs. icy: Valencia et al. 2007; Fortney et al. 2007; Sotin et al. 2007), and to distinguish between these two formation scenarios (Gaidos et al. 2007; S. Raymond et al. 2007,…”

“Using the radioactive flux limit from Williams et al. (1997), the critical planetary mass scales like ρ−2e3λt, where ρ is the planet’s bulk density, λ = 1.5× 1010yr−1 for 238U, and t is the duration of tectonic activity.”

“Figure 2 shows the final outcome of ten simulations, with the Solar System included for scale (the Earth’s water content is ∼ 10−3bymass; Lécuyer et al. 1998).”

“A system of three planets with minimum masses between 5 and 15 M⊕ was recently discovered orbiting the 0.31 M⊙ star Gliese 581 (Bonfils et al. 2005; Udry et al. 2007).”

“This increases to 20-50 Myr for Sun-like stars, consistent with estimates from Hf/W isotopic measurements (e.g., Jacobsen 2005).”

“2004; Fischer & Valenti 2005) allow for 70-90% of stars to have planetary systems without Jovians, and an even larger fraction for lower-mass stars (Endl et al. 2006; Butler et al. 2006).”

“Additional clues come from the observed stellar accretion rate Ṁ , which scales as Ṁ ∝ M2⋆ , with a large dispersion (Muzerolle et al. 2003, 2005, Natta et al. 2006).”

“Indeed, the combined effects of embryo scattering and perturbations from Jupiter and Saturn are thought to be the cause of the depletion of the Solar System’s asteroid belt (Wetherill 1992; Chambers & Wetherill 2001; Petit et al. 2001).”

“Note that systems with close-in giant planets may also contain Earth-like planets, which should be very waterrich (Raymond et al. 2006b; Mandell et al. 2007).”

“Most disk models that include viscous and irradiation heating give α between about 1/2 and 1 for the inner disk (e.g. D’Alessio et al. 1998; Garaud & Lin 2007, Dullemond et al. 2007), and high-resolution submillimeter observations suggest α between 1/2 and 1 in the outer disk (Mundy et al. 2000,…”

“Many of the data points from Scholz et al. (2006) are only upper limits, but we think extreme cases h = 0 or h > 2 would be apparent in this data.”

“…& Duncan 2000; see Table 1), and so varied with each set of simulations, from 6 Note that the outer edge of 4 AU for the embryo disk is chosen based on previous simulations showing that the feeding zone of a terrestrial planet in the habitable zone does not extend beyond 4 AU (Raymond et al. 2007).”

“Note that systems with close-in giant planets may also contain Earth-like planets, which should be very waterrich (Raymond et al. 2006b; Mandell et al. 2007).”

“Indeed, the combined effects of embryo scattering and perturbations from Jupiter and Saturn are thought to be the cause of the depletion of the Solar System’s asteroid belt (Wetherill 1992; Chambers & Wetherill 2001; Petit et al. 2001).”

“The lack of a correlation between the presence of debris disks and the metallicity of the parent star (Greaves et al. 2006; Beichman et al. 2006; Moro-Mart́ın et al. 2007), unlike the correlation known for exogiant planets (Gonzalez 1997, Santos et al. , Fischer & Valenti 2005), also supports the…”

“Simulations have shown that giant planets play an important role in terrestrial planet formation (e.g., Wetherill 1996; Levison & Agnor 2003).”

“Indeed, the combined effects of embryo scattering and perturbations from Jupiter and Saturn are thought to be the cause of the depletion of the Solar System’s asteroid belt (Wetherill 1992; Chambers & Wetherill 2001; Petit et al. 2001).”

“The water line may actually be located somewhat interior to the snow line, as water-rich bodies can be shifted inward via either gas drag or by eccentricity pumping during embryo formation (e.g., Cyr et al. 1998; Kokubo & Ida 1998).”

“Kokubo et al. (2006) showed that the bulk properties of accreted planets are not particularly sensitive to such variations in N , so we are not concerned that our choice of embryo formation models will affect our results.”

“Giant planets on orbits exterior to the terrestrial region, such as Jupiter and Saturn, stir up the eccentricities of embryos from the outside in via secular and resonant perturbations, while mutual scattering of embryos excites eccentricities from the inside out (e.g., Raymond et al. 2005b).”

“Indeed, terrestrial planets in systems with giant planets on eccentric orbits are likely to be dry (Chambers & Cassen 2002; Raymond et al. 2004; Raymond 2006).”

“…on the strength of the planetary magnetic field (Lammer et al. 2007), a snow line that takes perhaps a Gyr to get close enough to the HZ to give sufficient water (Kennedy et al. 2006), or loss of volatiles due to larger impact speeds and faster formation times (Lissauer 2007; but see §3.2 and Fig.”

“This matter is still unresolved; several solutions have been proposed (see Padoan et al. 2006; Alexander and Armitage 2006; Dullemond et al. 2006; Hartmann et al. 2006; Gregory et al. 2007) including selection/detection limitations (Clarke & Pringle 2006).”

“Simulations have shown that giant planets play an important role in terrestrial planet formation (e.g., Wetherill 1996; Levison & Agnor 2003).”

“Note, however, that there exists a large uncertainty in tying a given f value to an absolute disk mass or surface density, because of both observational and theoretical uncertainties (e.g., Carpenter et al. 2005).”

“However, migrating giant planets (not modeled here) can stir up eccentricities and induce the formation of very water-rich planets in their wake (Raymond et al. 2006b; Fogg & Nelson 2007; Mandell et al. 2007).”

“Timesteps were chosen to sample the innermost body’s orbit at least twenty times (e.g., Rauch & Holman 1999; Levison & Duncan 2000; see Table 1), and so varied with each set of simulations, from 6 Note that the outer edge of 4 AU for the embryo disk is chosen based on previous simulations showing…”

“2004; Fischer & Valenti 2005) allow for 70-90% of stars to have planetary systems without Jovians, and an even larger fraction for lower-mass stars (Endl et al. 2006; Butler et al. 2006).”

“This matter is still unresolved; several solutions have been proposed (see Padoan et al. 2006; Alexander and Armitage 2006; Dullemond et al. 2006; Hartmann et al. 2006; Gregory et al. 2007) including selection/detection limitations (Clarke & Pringle 2006).”

“There exists a range of 3-5 in metallicity Z for thin-disk stars (Nordstrom et al. 2004), although the range for currently-forming stars may be much smaller, only ∼20% (see Cartledge et al. 2006).”

“Timesteps were chosen to sample the innermost body’s orbit at least twenty times (e.g., Rauch & Holman 1999; Levison & Duncan 2000; see Table 1), and so varied with each set of simulations, from 6 Note that the outer edge of 4 AU for the embryo disk is chosen based on previous simulations showing…”

“Giant planets on orbits exterior to the terrestrial region, such as Jupiter and Saturn, stir up the eccentricities of embryos from the outside in via secular and resonant perturbations, while mutual scattering of embryos excites eccentricities from the inside out (e.g., Raymond et al. 2005b).”

“…on the strength of the planetary magnetic field (Lammer et al. 2007), a snow line that takes perhaps a Gyr to get close enough to the HZ to give sufficient water (Kennedy et al. 2006), or loss of volatiles due to larger impact speeds and faster formation times (Lissauer 2007; but see §3.2 and Fig.”

“…heating give α between about 1/2 and 1 for the inner disk (e.g. D’Alessio et al. 1998; Garaud & Lin 2007, Dullemond et al. 2007), and high-resolution submillimeter observations suggest α between 1/2 and 1 in the outer disk (Mundy et al. 2000, Looney et al. 2003, Andrews and Williams 2006).”

“Indeed, terrestrial planets in systems with giant planets on eccentric orbits are likely to be dry (Chambers & Cassen 2002; Raymond et al. 2004; Raymond 2006).”

“This matter is still unresolved; several solutions have been proposed (see Padoan et al. 2006; Alexander and Armitage 2006; Dullemond et al. 2006; Hartmann et al. 2006; Gregory et al. 2007) including selection/detection limitations (Clarke & Pringle 2006).”

“…Eisner & Carpenter 2003, Andrews & Williams 2005) give a large spread, with median or average masses usually somewhat below the MMSN value, but a significant fraction more massive, including a very massive disks observed in both Orion and Taurus (e.g. Williams et al. 2005, Eisner & Carpenter 2006).”

“…M⋆, f is a scaling factor for the disk (f=1 for MMSN), Z is the stellar metallicity (1.0=solar), and α moderates the steepness of the density profile (α = 3/2 in the MMSN model; Hayashi 1981, but more recent reconstructions using an accretion disk model as a constraint gives α = 1/2; Davis 2005).”

“Indeed, terrestrial planets in systems with giant planets on eccentric orbits are likely to be dry (Chambers & Cassen 2002; Raymond et al. 2004; Raymond 2006).”

“This matter is still unresolved; several solutions have been proposed (see Padoan et al. 2006; Alexander and Armitage 2006; Dullemond et al. 2006; Hartmann et al. 2006; Gregory et al. 2007) including selection/detection limitations (Clarke & Pringle 2006).”

“The lack of a correlation between the presence of debris disks and the metallicity of the parent star (Greaves et al. 2006; Beichman et al. 2006; Moro-Mart́ın et al. 2007), unlike the correlation known for exogiant planets (Gonzalez 1997, Santos et al. , Fischer & Valenti 2005), also supports the…”

“Present estimates of disk masses in nearby star-forming regions (see Andre & Montmerle 1994, Eisner & Carpenter 2003, Andrews & Williams 2005) give a large spread, with median or average masses usually somewhat below the MMSN value, but a significant fraction more massive, including a very massive…”

“Significant mass is a necessary, but not sufficient, requirement for sustainable planetary habitability (e.g., Lissauer 1999).”

“There are observational (Endl et al. 2006; Butler et al. 2006) and theoretical (Ward & Hahn 1995; Adams et al. 2004; Laughlin et al. 2004, Ida & Lin 2005) reasons to think that the fraction of M stars with Jovian planets is significantly smaller than for solar-mass stars.”

“Studies by Raymond et al. (2007) and Lissauer (2007) suggest that planets forming in situ in the HZs of M dwarfs are likely to form quickly ( * 10 Myr after the formation of the star), to be relatively small ( ( 0.3 M 4 ), and to have water contents smaller than Earth’s.”

“Models of rocky planet formation around M dwarfs have found that those that accrete from primordial material are likely to be sub-Earth mass (Raymond et al. 2007) and volatilepoor (Lissauer 2007).”

“Given the recent results suggesting that habitable-zone M-dwarf planets may be dry—either due to low protostellar disk mass (Raymond et al., 2007), or extended XUV radiation input over as long as 1 Gyr (Luger & Barnes, 2015)—and land planets are both less likely to have saturated atmospheres prone…”