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).”

“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…”

“, 2013), it is not guaranteed, as water may not have been delivered to the planet during its formation (Lissauer, 2007; Raymond et al., 2007), or it may have been subsequently lost (Luger and Barnes, 2015; Airapetian et al.”

“…water contents, such as desiccation of constituent planetesimals by short-lived radionuclides (Grimm & McSween 1993), water loss during giant impacts between embryos (Genda & Abe 2005), and heating during the very rapid growth expected around low-mass stars (Lissauer 2007; Raymond et al. 2007).”

“Indeed, planet formation models find that the disk mass strongly impacts the frequency and location of planets that can form, from giants down to Earth-sized planets (e.g., Raymond et al. 2007; Alibert et al. 2011; Mordasini et al. 2012).”

“It is apparent at a glance that Proxima b is more vulnerable to the negative consequences of impacts than are Earth and Venus, a not surprising observation that has been anticipated (cf, Raymond et al. 2007; Lissauer 2007).”

“…between the dust mass and the stellar mass such that the typical protoplanetary disk contains a few percent of the stellar mass (Andrews & Williams 2007a), which has important implications for the planet frequency as a function of stellar mass (Ida & Lin 2005; Raymond et al. 2007; Greaves 2010).”

“The loss of hydrogen does not significantly change when considering different initial time of protoplanetary disk dispersion (3 or 10 Myr here).”

“This was either attributed to higher orbital speeds, leading to more energetic collisions with other bodies (Lissauer 2007), or they began dry because of inefficient radial mixing, and so fewer volatilerich planetesimals from larger distances would be accreted (Raymond et al. 2007).”

“However, planets orbiting in the habitable zones of M dwarf stars may be depleted in water due to M dwarfs’ prolonged, high-luminosity premain sequence phases (e.g., Luger and Barnes, 2015) or may have formed volatile-poor (Lissauer, 2007; Raymond et al., 2007).”

“However, if Proxima Cen b formed in situ, then planet formation models suggest that it may be water-poor (Lissauer et al., 2007; Raymond et al., 2007); but if it migrated in from 1http://www.jwst.nasa.gov 2http://wfirst.gsfc.nasa.gov 3http://www.jpl.nasa.gov/habex…”

“Several studies have argued that terrestrial planets within the HZs of M dwarfs may not be habitable, either because they could be deficient in volatiles (Lissauer 2007) or form dry as a result of inefficient water delivery (Raymond et al. 2007), if they formed in situ.”

“It may be an imprint of a different formation efficiency of planets around low-mass stars, for example, the formation of more numerous, but smaller planets (e.g., Kokubo et al. 2006; Raymond et al. 2007).”

“Water is also present in significant quantities in comets and protoplanetary bodies; delivery of the water reservoir of Earth is thought to have been via impact with similar, water-rich objects during the early, violent stages of planetary accretion (Raymond et al., 2007; Lammer et al., 2009).”

“Qualitatively, this does match the prediction of in-situ formation models, where more numerous, but smaller planets form in low-mass disks around lowmass stars (e.g. Wetherill 1996; Kokubo & Ida 2002; Raymond et al. 2007; Ciesla et al. 2015).”

“Giant planets are expected to form just outside the snow line, given the increase in solid material (Hayashi 1981; Stevenson & Lunine 1988; Ida & Lin 2004).”

“However, such proximity implies that terrestrial planets forming within the HZs of low-mass stars are likely to be small ( ( 0.3 M 4 ) and form dry (Lissauer, 2007; Raymond et al. , 2007).”

“heir “minimum mass ” model has z0,s = 0.047, α = 2.75, and ρ0,g = 1.4×10−9 gm/cm3. Theoretical arguments (Lissauer 1987) as well as accretion disk modelling and observational constraints (reviewed by Raymond et al 2007) suggest that the density profile was likely shallower and the overall density at 5 AU higher than su…”

“Stars of mass ∼1 M⊙ or higher, on the other hand, could easily have habitable-zone planets of similar or greater fractional mass of water than Earth (Raymond et al. 2007).”

“) (Williams et al. , 1997; Raymond et al., 2007b), which on Earth drives the carbonate-silicate cycle (Walker et al., 1981); and substantial water content ( e.g., Raymond et al., 2004) for life and plate tectonics (Regenauer-Lieb et al. , 2001).”

“, 2010), decreased initial volatile inventory (Raymond et al., 2007; Lissauer, 2007) or tidal effects (e.”

“To answer these questions, we rely on N-body simulations of interacting planetary embryos and planetesimals (e.g., Morbidelli et al. 2000; Chambers 2001; Raymond et al. 2004, 2006, 2007).”

“…is trapped near the ice line (Kretke & Lin 2007; Ida & Lin 2008b; Kretke et al. 2009), the final close-in terrestrial planets would be rocky due to the inefficient water delivery by the migration, because radial mixing of planetesimals is also inefficient around M dwarfs (Raymond et al. 2007).”

“Accretion times close to the star are extremely short, and simulations show that Earth-sized or larger planets grow within 0.1–1 Myr [Lissauer, 2007; Raymond et al., 2007; Bolmont et al., 2014; Ogihara et al., 2015a].”

“It is interesting to note that ∼ 0.2M⊕ is the minimum habitable mass for a planet or moon used by several other sources in the literature, including Raymond et al. (2007) (0.3M⊕) and Williams et al. (1997) (0.12M⊕).”

“anger surface life on Earth-like worlds may enable sub-surface life under an icy crust. Whether a planet as volatile-rich as Europa could actually form around an M star is speculative (Lissauer 2007; Raymond et al. 2007), but if they do form, the same processes that may make Europa habitable may also make these planet…”

“Planets significantly smaller than the Earth, which may be common around M stars (Raymond et al. 2007a), may be especially susceptible to insufficient heating (the radiogenic heat flux scales as the ratio of volume to area).”

“Furthermore, there is a tendency for low-mass stars to produce low-mass planets, and these planets are less likely to sustain substantial atmospheres and plate tectonic activity, which are probably required for complex life (Raymond et al. , 2007).”

“We therefore expect planets in such systems to have relatively circular orbits (Raymond et al. 2007).”

“…systems (Chambers et al. 2002; Quintana et al. 2002, 2007; Quintana & Lissauer 2006), around stars of various stellar types (Lissauer 2007; Raymond et al. 2007), in the presence of inward migration of disk material (Mandell et al. 2007) and in the presence of various giant planet…”

“For example, the planet could have formed with little or no water (Raymond et al. 2004, 2007), or lost that water in the first billion years of the star’s evolution (Ramirez and Kaltenegger 2014; Luger et al. 2015; Tian and Ida 2015).”

“However, more massive discs only tend to form more massive planets (e.g. Kokubo et al. 2006; Raymond et al. 2007b).”

“, [178,179] and see counterpoints in Section 9).”

“Additionally, as argued by Raymond et al. (2007), there is a decreased probability of habitable planet formation around those stars.”

“…(Howe & Burrows 2015) and giant planet core formation (Kennedy & Kenyon 2008; Morbidelli et al. 2015), the composition of giant planet atmospheres (Öberg et al. 2011; Madhusudhan et al. 2014) as well as the delivery of water to the surfaces of terrestrial planets (e.g. Raymond et al. 2007).”

“[32]).”

“On the other hand, other simulations concluded that planets forming around low mass stars should be less massive and very dry (e.g. Lissauer et al. 2007, Raymond et al. 2007, Ciesla et al. 2015).”

“The planet formation timescale is proportional to the orbital frequency (Safronov 1969; Raymond et al. 2007) and is thus far shorter than the disk lifetime for close-in orbits, but planet-disk interactions probably overwhelm planetstar tidal interactions during this time.”

“To compare the later stages of planet formation, we looked at the Hill sphere and feeding zone of a forming planet, to see how much mass is available for its formation, in a way similarto Raymond et al. (2007).”

“With very high densities in the inner disk the growth timescale for super-Earths is extremely fast [285, 430, 419, 210, 449, 378].”

“It is expected that the abundance of water on planetary surfaces varies greatly (Raymond et al. 2007), but we can consider a simple scaling to understand how the conditions for liquid water scale with planet mass and water complement.”

“For lower-mass M dwarf stars, N-body simulations indicated that terrestrial planets in the habitable zone would be dry (Raymond et al. 2007; Lissauer 2007), in contrast to planets that formed farther out in the disk and migrated to their current locations (Ogihara & Ida 2009).”

“Habitable Zone estimates taken from Raymond et al. (2007) Fig.”

“More massive disks tend to form fewer, more massive planets (Kokubo et al. 2006; Raymond et al. 2007; Hansen & Murray 2013), although the timescale problem for forming and ejecting Earth-mass planets still applies.”

“By spanning a wide range of stellar masses, we can hope to provide a long lever arm to probe how the birth, growth, and survival of planets depends on various environmental factors (see Raymond et al. 2007; Barnes et al. 2008; Montgomery & Laughlin 2009; Ogihara & Ida 2009).”

“M-star habitable zone planets may be very dry because of inefficient scattering of water-bearing planetesimals from beyond the ice line into the habitable zone during planetary formation (Lissauer 2007; Raymond et al. 2007).”

“Simulations of in situ formation by Raymond et al. (2007) suggest that habitable zone planets around M-dwarfs could form with as little as two orders of magnitude less bulk water than Earth, which would likely result in significantly reduced amounts of surface water as well.”

“…niche in the parameter space of BD and disk properties (BD mass, disk mass, surface density distribution, and lifetime) that allows for the formation of sizeable (∼ 0.1 Earth masses or larger) terrestrial planets near the habitable zone of BDs (see Raymond et al., 2007; Payne & Lodato, 2007).”

“These distributions are only known for solar-mass stars and may be different for M dwarfs (Raymond et al. 2007; Montgomery and Laughlin 2009).”

“Astrict In Situ formation model for sub-Neptunes, where planet mass is directly related to mass available in disk (e.g. Raymond et al. 2007; Ciesla et al. 2015), is not favored by stellar-mass dependencies as evident from Figure 7.”

“Using the radiogenic flux model provided by Williams et al. (1997), Raymond et al. (2007) established that planets with roughly M < 0.3M⊕ will lack this important geological activity.”

“The system provides a direct probe into the limiting conditions for planet formation at the bottom of the main sequence and is a benchmark for formation theory and modeling in very low mass disks (e.g., Payne & Lodato 2007; Raymond et al. 2007; Ogihara & Ida 2009; Ormel et al. 2017).”

“However, as expected, less material survives around 1 AU for the migrating multiple-super-Earth system, reducing the probability of forming terrestrial planets (or perhaps just producing lower-mass terrestrial planets; Raymond et al 2007b).”

“Given their rapid energetic accretion, water retention may in fact be a concern for planets orbiting low-mass stars (e.g., Lissauer 2007; Raymond et al. 2007b).”

“However, it must be recognized that the water inventory of planets and satellites has been predicted to vary considerably (Raymond et al., 2007; Mulders et al., 2015; Ciesla et al., 2015; Bergin et al., 2015), and hence the depth and existence of the subsurface ocean cannot be estimated a priori.”

“n Maanen, 1917) at a distance of only 4 pc. Owing to the numerous perils for habitability around M dwarf stars such as tidal locking (Dole, 1964), reduced formation of water-rich terrestrial planets (Raymond et al., 2007), weak quiescent ultraviolet radiation from the star (Guo et al., 2010), planetary atmospheric ero…”

“…the planets around M dwarfs; Traditional Solar System-based models predict that large numbers of low-mass planets would be found around such stars (Raymond et al. 2007; Ciesla et al. 2015) while surveys indicate that such systems contain much more massive planets, more so than around the higher…”

“Planet formation models typically adopt these scaling laws to predict the planets that may form around lowmass stars (e.g. Raymond et al. 2007; Mordasini et al. 2012).”

“Further, there may not be an exo-Earth around all Sun-like stars, or not within the Habitable Zone where water can be liquid on the surface; see Raymond et al. (2007) for a model prediction that stars of & 0.8M⊙ are the most suitable hosts.”

“• Effect of Disk Properties The accreted planet mass is slightly more than linearly proportional to the disk mass because the planetary feeding zone widens with disk mass due to stronger embryo-embryo scattering (Kokubo et al., 2006; Raymond et al., 2007a).”

“Recently, Lissauer (2007)and Raymond et al. (2007) discuss the potential of habitable M dwarf HZ planets in the context of their formation and in particular water delivery and find that these planets might be devoid of volatiles and thus less suitable for life.”

“…to gamble on ‘ultracool’ (i.e. later than M6) dwarf stars, at the bottom of the mainsequence, despite that most theoretical expectations presented such super-low-mass (≤ 0.1M ) stars as unlikely to form short-period rocky planets similar in size to Earth (e.g. Raymond, Scalo, and Meadows, 2007).”

“For example, Raymond et al. (2007) present a suite of accretion calculations which predict that Earth-sized terrestrial planets should be rare around M-type stars with M∗ .”

“The initial disk masses and surface density profiles are based on terrestrial planet formation around low-mass stars (Raymond et al. 2007).”

“…be anticipated because the properties of the protoplanetary disc affect the outcome both for the debris disc and the planets (Wyatt et al. 2007a), or because dynamical effects such as instabilities in the planetary system can also have a significant effect on the debris disc (Raymond et al. 2007).”

“On the other hand, in situ formation of volatile rich planets would be less likely (Lissauer 2007; Raymond et al. 2007, 2022), even when accounting for volatile delivery through the migration of icy planetesimals (Ciesla et al. 2015).”

“estions we can hope to answer in the coming years. It is interesting to note that ∼ 0.2M⊕ is the minimum habitable mass for a planet or moon used by several other sources in the literature, including Raymond et al. (2007) (0.3M⊕) and Williams et al. (1997) (0.12M⊕). It has also been proposed by Scharf (2006) that the…”

“The main reasons range from the possible deficiency of volatiles in the planetary atmosphere [33], to the scarce water delivery during the planet evolution [34], or the loss of planetary water during the pre-main sequence due to the higher luminosity of the protostar in that evolutionary phase [35].”

“This study is aimed at quantifying that effect, focusing on planets of ∼ 0.1–1.0 M⊕, which are expected to be abundant around M dwarfs (Raymond et al. 2007; Ida & Lin 2005; Alibert & Benz 2017; Miguel et al. 2019).”

“For other systems with terrestrial planets formed closer in, volatile delivery could be essential for the development of an atmosphere that could support life (e.g., Raymond et al. 2007; Lissauer 2007).”

“Raymond et al. (2007) studied the habitable planet formation around stars with masses between 0.2 and 1 M (cid:12) .”

“The low potential water inventory on M-dwarf planets, due to low planetary disk mass (Raymond et al. 2007) or ocean evaporation as the result of an extended pre-main sequence host star phase (Luger & Barnes 2015), could certainly impact the likelihood of hydrohalite formation in sea ice.”

“Of course, the exact outcome of the accretion process depends on the disk mass and mass distribution (Raymond et al. 2007; Payne & Lodato 2007), which probably scales roughly linearly with the primary mass (Andrews et al. 2010).”

“The simulations in Raymond et al. (2007) use between 75 and 190 embryos, but also spread them out over a wider range of semi-major axes.”

“Such a planet would likely have formed at larger distances and migrated in, as accumulation of local material is unlikely to form such a ‘‘large’’ planet around such a small star (Raymond et al., 2007).”

“Limitations to using planetary atmospheres to infer a magnetodynamo are that planets can conceivably accrete without atmospheres [Raymond and Meadows, 2007; Lissauer, 2007] or may have lost their atmospheres early in their evolution due to increased stellar activity and before any dynamo started.”

“Another important point is that all the simulations start at 10 Myr, which is the stellar age at which the protoplanetary disk has mostly dissipated and the planets are formed ( S. N. Raymond et al. 2007; M. Lambrechts et al. 2019; M. S. Clement et al. 2022 ) .”

“…that are commonly utilized in N -body studies of planet formation (e.g.: surface density profile, disk mass, orbital eccentricities and inclinations of the particles, and integration time-step as a fraction of the innermost particle’s orbital period: Chambers 2001; Raymond et al. 2007, 2009).”