Diverse outcomes of planet formation and composition around low-mass stars and brown dwarfs (original) (raw)

Abstract

The detection of Earth-size exoplanets around low-mass stars –in stars such as Proxima Centauri and TRAPPIST-1– provide an exceptional chance to improve our understanding of the formation of planets around M stars and brown dwarfs. We explore the formation of such planets with a population synthesis code based on a planetesimal-driven model previously used to study the formation of the Jovian satellites. Because the discs have low mass and the stars are cool, the formation is an inefficient process that happens at short periods, generating compact planetary systems. Planets can be trapped in resonances and we follow the evolution of the planets after the gas has dissipated and they undergo orbit crossings and possible mergers. We find that formation of planets above Mars mass and in the planetesimal accretion scenario, is only possible around stars with masses M⋆ ≥ 0.07Msun and discs of Mdisc ≥ 10−2 Msun. We find that planets above Earth-mass form around stars with masses larger tha...

Figures (13)

Figure 1. Mass ratio of the planets/satellites in different systems compared to that of the central star/planet. The dashed area marks the approximate mass of gas in the giant planets in the Solar system. Data by Berta-Thompson et al. (2015) for GJ1132, Charbonneau et al. (2009) for GJ1214, Astudillo-Defru et al. (2017) for GJ3323, Dittmann et al. (2017) and Ment et al. (2019) for LHS1140, Bonfils et al. (2018) for Ross128, Anglada-Escudé et al. (2016) for Proxima Centauri, Gillon et al. (2016) for TRAPPIST-1, Astudillo-Defru et al. (2017) for YZ Cet and Zechmeister et al. (2019) for Teegarden’s star system.

Figure 1. Mass ratio of the planets/satellites in different systems compared to that of the central star/planet. The dashed area marks the approximate mass of gas in the giant planets in the Solar system. Data by Berta-Thompson et al. (2015) for GJ1132, Charbonneau et al. (2009) for GJ1214, Astudillo-Defru et al. (2017) for GJ3323, Dittmann et al. (2017) and Ment et al. (2019) for LHS1140, Bonfils et al. (2018) for Ross128, Anglada-Escudé et al. (2016) for Proxima Centauri, Gillon et al. (2016) for TRAPPIST-1, Astudillo-Defru et al. (2017) for YZ Cet and Zechmeister et al. (2019) for Teegarden’s star system.

where M, is the stellar mass, a is the parameter that characterizes the viscosity and M, is the accretion rate into the star, which has a typical value of 10~!° Mo yr! for small stars (Manara & Testi 2014). The irradiation temperature profile is given by: an inner disc dominated by viscous heating, and an outer disc where the temperature is determined by the irradiation from the central star (Hueso & Guillot 2005; Oka, Nakamoto & Ida 2011; Ida, Guillot & Morbidelli 2016). We follow Ida et al. (2016) and adopt the following expression for the temperature of the disc in the viscous heating dominated region:

where M, is the stellar mass, a is the parameter that characterizes the viscosity and M, is the accretion rate into the star, which has a typical value of 10~!° Mo yr! for small stars (Manara & Testi 2014). The irradiation temperature profile is given by: an inner disc dominated by viscous heating, and an outer disc where the temperature is determined by the irradiation from the central star (Hueso & Guillot 2005; Oka, Nakamoto & Ida 2011; Ida, Guillot & Morbidelli 2016). We follow Ida et al. (2016) and adopt the following expression for the temperature of the disc in the viscous heating dominated region:

Figure 2. Temperature profile of 100 planetary systems (orange lines). In each system, the stellar mass was chosen randomly between 0.05 and 0.25 Mgun. The extreme profiles with the largest and smallest stellar masses are shown with grey thick lines. The temperature where water condenses is shown with the horizontal grey dotted line. The dashed vertical area covers all the possible snow lines.

Figure 2. Temperature profile of 100 planetary systems (orange lines). In each system, the stellar mass was chosen randomly between 0.05 and 0.25 Mgun. The extreme profiles with the largest and smallest stellar masses are shown with grey thick lines. The temperature where water condenses is shown with the horizontal grey dotted line. The dashed vertical area covers all the possible snow lines.

Figure 3. Gas surface density versus semimajor axis of 100 planetary systems (blue lines). Similarly as in Fig. 2, these 100 systems are chosen randomly as examples of the discs used in the calculations. The full range of surface densities considered in this work is shown with the grey area.

Figure 3. Gas surface density versus semimajor axis of 100 planetary systems (blue lines). Similarly as in Fig. 2, these 100 systems are chosen randomly as examples of the discs used in the calculations. The full range of surface densities considered in this work is shown with the grey area.

where p, is the planetesimals’ typical density and r, their radius, assumed as 30 km in the calculations, close to the typical size distri- bution in the asteroid and Kuiper belt objects (Sheppard & Trujillo 2010) and that can also be reproduced by detailed simulations of streaming instability (Johansen et al. 2015; Abod et al. 2019). The disc of solids is also depleted globally because of the gas drag effect. Planetesimals orbit the star at a Keplerian speed and suffer a headwind caused by the gas that orbits at a slightly sub-Keplerian velocity. As a consequence, the planetesimals drift towards the star at a time-scale given by (Mosqueira & Estrada 2003; Miguel & Ida 2016):

where p, is the planetesimals’ typical density and r, their radius, assumed as 30 km in the calculations, close to the typical size distri- bution in the asteroid and Kuiper belt objects (Sheppard & Trujillo 2010) and that can also be reproduced by detailed simulations of streaming instability (Johansen et al. 2015; Abod et al. 2019). The disc of solids is also depleted globally because of the gas drag effect. Planetesimals orbit the star at a Keplerian speed and suffer a headwind caused by the gas that orbits at a slightly sub-Keplerian velocity. As a consequence, the planetesimals drift towards the star at a time-scale given by (Mosqueira & Estrada 2003; Miguel & Ida 2016):

Figure 4. Solids surface density versus semimajor axis of 100 planetary sys- tems (red lines). All possible snow lines are shown within the vertical dashed area. The Solar system snow line is shown as a comparison (dotted line).

Figure 4. Solids surface density versus semimajor axis of 100 planetary sys- tems (red lines). All possible snow lines are shown within the vertical dashed area. The Solar system snow line is shown as a comparison (dotted line).

Figure 5. Mass versus semimajor axis and torque in different colours, for the three cases considered: low mass star and disc (a), intermediate case (b) and massive star and disc (c) (see the text for details). Migration is inwards in the red areas, it is outwards in the blue areas and the planets are trapped in the white region. The transition between the viscous and irradiated regime is shown with the dashed black line.

Figure 5. Mass versus semimajor axis and torque in different colours, for the three cases considered: low mass star and disc (a), intermediate case (b) and massive star and disc (c) (see the text for details). Migration is inwards in the red areas, it is outwards in the blue areas and the planets are trapped in the white region. The transition between the viscous and irradiated regime is shown with the dashed black line.

Figure 6. Mass versus semimajor axis of the population of synthetic planets formed (grey dots). Observed systems with masses detected with radial velocities are shown as a comparison. Different panels show the populations formed when using different migration scenarios, with Cmigi = 10 representing a slow migration and Cyigt = | the fastest one. Data for GJ 3512b is from Morales et al. (2019).

Figure 6. Mass versus semimajor axis of the population of synthetic planets formed (grey dots). Observed systems with masses detected with radial velocities are shown as a comparison. Different panels show the populations formed when using different migration scenarios, with Cmigi = 10 representing a slow migration and Cyigt = | the fastest one. Data for GJ 3512b is from Morales et al. (2019).

Figure 7. Mass and semimajor axis of all the bodies formed in the simulations and their dependence with the stellar (top panel) and disc masses (bottom panel).

Figure 7. Mass and semimajor axis of all the bodies formed in the simulations and their dependence with the stellar (top panel) and disc masses (bottom panel).

Figure 8. Mass versus semimajor axis of the synthetic planets formed (all migration scenarios included). The water content is shown by the colour code.

Figure 8. Mass versus semimajor axis of the synthetic planets formed (all migration scenarios included). The water content is shown by the colour code.

Figure 9. Pie charts showing the percentage of planets by their water fractions depending on their mass and semimajor axis. Planets with M, > 1Mg are in the top panels, those on the left have a < ayjs — irr and the ones on the right have avis — irr < @ < snow. The bottom panels are planets with 0.1 < M, < 1Mg and a < dyjs — irr (bottom left) and avis — irr < @ < Asnow (bottom right). Exoplanets are located next to the corresponding pie chart depending on their mass and semimajor axis. * Water fraction for the TRAPPIST-1 planets are from Unterborn et al. (2018). The authors found that any value could be possible for TRAPPIST-1d and TRAPPIST-le. **TRAPPIST-1b could also be in the category <1M@ due to errors in the mass determination. ***TRAPPIST-If can have >1Mg, if we account for the error in mass. **** YZ Cet c has a large error in mass and could have > 1Mg.

Figure 9. Pie charts showing the percentage of planets by their water fractions depending on their mass and semimajor axis. Planets with M, > 1Mg are in the top panels, those on the left have a < ayjs — irr and the ones on the right have avis — irr < @ < snow. The bottom panels are planets with 0.1 < M, < 1Mg and a < dyjs — irr (bottom left) and avis — irr < @ < Asnow (bottom right). Exoplanets are located next to the corresponding pie chart depending on their mass and semimajor axis. * Water fraction for the TRAPPIST-1 planets are from Unterborn et al. (2018). The authors found that any value could be possible for TRAPPIST-1d and TRAPPIST-le. **TRAPPIST-1b could also be in the category <1M@ due to errors in the mass determination. ***TRAPPIST-If can have >1Mg, if we account for the error in mass. **** YZ Cet c has a large error in mass and could have > 1Mg.

Figure 10. Histogram showing the number of planets per system (top panel) for the 2883 systems that have objects with M, > 0.1Mg@. The bottom panel shows the number of planetary systems that have only small planets (with masses 0.1 < M, < 1Mg) and the ones that have at least one planet with My > 1Mo.

Figure 10. Histogram showing the number of planets per system (top panel) for the 2883 systems that have objects with M, > 0.1Mg@. The bottom panel shows the number of planetary systems that have only small planets (with masses 0.1 < M, < 1Mg) and the ones that have at least one planet with My > 1Mo.

Figure 11. Examples of architectures of planetary systems found with three (top panel) and six or seven planets (bottom panel). TRAPPIST- 1 and YZ Cet systems are shown as a comparison. Planets are in different size according to their mass.

Figure 11. Examples of architectures of planetary systems found with three (top panel) and six or seven planets (bottom panel). TRAPPIST- 1 and YZ Cet systems are shown as a comparison. Planets are in different size according to their mass.

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