The Formation And Dynamical Evolution Of Terrestrial Planets Around M Dwarfs

With the launch of space telescopes,such as Kepler,TESS and JWST,and the enhancement of ground-based telescopes,the number of exoplanets observed recently has grown exponentially.As of March 24 2022.5005 exoplanets have been discovered orbiting around main sequence stars.The mass,radius,as well as the orbital distribution of planets are closely related to their host stars.The planetary masses and distance between planets and their hosts generally increase with stellar masses,and the occurrence rate of giant planets increases with stellar metallicity.In Morgan-Keenan system,stars are typically classified by their spectrum and temperature into O,B,A,F,G,K,and M.M dwarfs are low-mass cold stars,while they account for about 75%of the stars in the Milky Way.Statistical analysis shows that about 80%of the planets discovered around red dwarfs are short-period rocky planets with 1-10 Earth masses（M⊕）and only 0.010.3 AU away from their host stars.The lower effective temperature of red dwarf leads to closer habitable zone.Studies have shown that the occurrence rate of terrestrial planets around red dwarfs is about 3.5 times of that of F,G,and K type stars.On average,there are 2.5 terrestrial planets orbiting each red dwarf.Therefore,it would be easier to find terrestrial planets and even habitable planets around red dwarfs,compared with other types of stars.To explain the formation of terrestrial planets and the tightly-compacted planetary systems around red dwarfs,we take the Minimum-Mass Solar Nebula model.The solid disks are assumed to be 0.01%of the masses of host stars and spread from 0.01 to 0.5 AU.N-body simulations of the accretion of planetary embryos and planetesimals are extensively performed with three models of in-situ,inward migration and convergent migration.Different stellar masses and slopes of protoplanetary disks are also simulated.Results show that the in-situ model produces the largest number of planets(average 7.77_-3.77^+3.23),but the average masses of planets are smaller(average 1.23_-0.93^+4.01 M⊕).More planets and more compact systems would be formed around high-mass stars.The planet formation rates of the inward migration and convergent migration models are similar,which produce 2.55_-1.55^+1.45 and 2.85_-0.85^+1.15,respectively,with masses of 3.76_-3.46^+8.77 M⊕ and 3.01_-2.71^+13.77 M⊕.The number of planets tends to increase with a larger stellar mass,and the semi-major axes of planets decrease as the steeper of the disk slope.The insitu formation model probably provide a suitable scenario to elucidate the formation of planetary system composed of a vast number of comparable planets,for instance TRAPPIST-1 planetary system,however,this model cannot explain the formation of habitable planets.If the migration of planets is unsuppressed,only close-in terrestrial planets and hot Neptunes might be well explained by inward migration model.Convergent migration model could provide water-rich planets in habitable zone,who hold the fraction of water up to 10%.Meanwhile,the simulation outcomes of convergent migration model produce the best matching with observations in the distribution of planetary mass,semi-major axis,eccentricity and orbital period ratio,indicating the convergent migration scenario may act as an effective mechanism to throw light on the formation of terrestrial planet and habitable planets around red dwarfs.Gas giant planets are also discovered in a fraction of planetary systems around red dwarfs,which are usually formed when massive cores accrete vast amounts of gas.We investigate the formation of terrestrial planets under the effect of the runaway accretion of giant,and the dynamical evolution of terrestrial planets influenced by a distant gas-giant.The results show that planetary systems tends to have a wider spread after scattering.The formation rate of terrestrial planets could be significantly reduced under the perturbation of gas-giant.After inward migration,terrestrial planets tend to accumulate near mean motion resonance（MMR）,which is relevant to the speed of Type Ⅰmigration,the mass of planets,and the existence of giant planet.The mass and eccentricity of the giant planet may play a crucial role in shaping the final configuration of the sy stem.With the increase of the gravitational perturbation of giant.the MMR configuration varies.Taking Kepler-68 system as an example,terrestrial planets can be trapped in 5:3 or 7:4 MMRs other than first order MMRs if the giant planet revolves the central star with an eccentric orbit,which gives an explanation to the formation of the configuration of Kepler-68.Moreover,we find that the eccentricity of the middle planet can be excited to roughly 0.2 if the giant planet is more massive than 5 MJ,otherwise the terrestrial planets are inclined to remain near-circular orbits.Our study may provide a likely formation scenario for the planetary systems that harbor several terrestrial planets near MMRs inside and one gas-giant exterior to them.The formation and evolution of terrestrial planets around red dwarfs is a crucial topic in the field of planetary science.This paper optimizes the parameters of theoretical model with observational statistics,and systematically analyze the characteristics of multiple planet formation models from the perspectives of planetary distribution,gas accretion,formation rate,and habitability.We propose that the convergent migration model may be suggestive of a likely mechanism for planetary formation around red dwarfs.These will provide the theoretical guidance for future observations of planets around red dwarfs.