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Diversity of Planetary Systems in Low-Mass Disks Terrestrial-Type Planet Formation and Water Delivery M A&A 567, A54 (2014) Astronomy DOI: 10.1051/0004-6361/201323313 & c ESO 2014 Astrophysics Diversity of planetary systems in low-mass disks Terrestrial-type planet formation and water delivery M. P. Ronco and G. C. de Elía Facultad de Ciencias Astronómicas y Geofísicas, Universidad Nacional de La Plata and Instituto de Astrofísica de La Plata, CCT La Plata-CONICET-UNLP, Paseo del Bosque S/N, 1900 La Plata, Argentina e-mail: [email protected] Received 20 December 2013 / Accepted 5 May 2014 ABSTRACT Context. Several studies, observational and theoretical, suggest that planetary systems with only rocky planets are the most common in the Universe. Aims. We study the diversity of planetary systems that might form around Sun-like stars in low-mass disks without gas-giant planets. We focus especially on the formation process of terrestrial planets in the habitable zone (HZ) and analyze their water contents with the goal to determine systems of astrobiological interest. In addition, we study the formation of planets on wide orbits because they can be detected with the microlensing technique. Methods. N-body simulations of high resolution were developed for a wide range of surface density profiles. A bimodal distribution of planetesimals and planetary embryos with different physical and orbital configurations was used to simulate the planetary accretion process. The surface density profile combines a power law for the inside of the disk of the form r−γ, with an exponential decay to the outside. We performed simulations adopting a disk of 0.03 M and values of γ = 0.5, 1 and 1.5. Results. All our simulations form planets in the HZ with different masses and final water contents depending on the three different profiles. For γ = 0.5, our simulations produce three planets in the HZ with masses ranging from 0.03 M⊕ to 0.1 M⊕ and water −4 contents between 0.2 and 16 Earth oceans (1 Earth ocean = 2.8 × 10 M⊕). For γ = 1, three planets form in the HZ with masses between 0.18 M⊕ and 0.52 M⊕ and water contents from 34 to 167 Earth oceans. Finally, for γ = 1.5, we find four planets in the HZ with masses ranging from 0.66 M⊕ to 2.21 M⊕ and water contents between 192 and 2326 Earth oceans. This profile shows distinctive results because it is the only one of those studied here that leads to the formation of water worlds. Conclusions. Since planetary systems with γ = 1and1.5 present planets in the HZ with suitable masses to retain a long-lived atmosphere and to maintain plate tectonics, they seem to be the most promising candidates to be potentially habitable. Particularly, these systems form Earths and Super-Earths of at least 3 M⊕ around the snow line, which can be discovered by the microlensing technique. Key words. astrobiology – methods: numerical – protoplanetary disks 1. Introduction scenario. From this theoretical study, these authors indicated that the occurrence rate of planets with masses M > 100 M⊕ The accretion process that leads to the formation of terrestrial is 14.3%, which agrees with that obtained by Cumming et al. planets is strongly dependent on the mass distribution in the sys- (2008). More recently, Miguel et al. (2011) developed a semi- tem and on the presence of gas-giant planets. Therefore, it is analytical code for computing the planetary system formation, necessary to consider protoplanetary disks with different surface based on the core instability model for the gas accretion of the density profiles as well as several physical and orbital parameters embryos and the oligarchic growth regime for the accretion of for the gas giants to analyze the diversity of planetary systems solid cores. The most important result obtained by these authors that might form around solar-type stars. suggests that planetary systems with only small rocky planets During the past years, several observational works have sug- represent probably the vast majority in the Universe. gested that the planetary systems consisting only of rocky plan- The standard model of solar nebula (MSN) developed by ets are the most common in the Universe. In fact, using pre- Weidenschilling (1977)andHayashi (1981) predicts that the sur- cise radial velocity measurements from the Keck planet search, face densities of dust materials and gases vary approximately Cumming et al. (2008) inferred that 17%–19% of the solar-type as r−1.5,wherer is the distance from the Sun. This model is stars have giant planets with masses M > 100 M⊕ within 20 AU. constructed by adding the solar complement of light elements to More recently, Mayor & Queloz (2012) analyzed the results each planet and then by distributing this augmented mass uni- of an eight-year survey carried out at the La Silla Observatory formly across an annulus around the location of each planet. with the HARPS spectrograph and suggested that about 14% Davis (2005) reanalyzed the MSN nebula and predicted that the −0.5 of the solar-type stars have planets with masses M > 50 M⊕ surface density follows a decay rate of r in the inner re- within 5 AU. On the other hand, many theoretical works comple- gion and a subsequent exponential decay. Later, Desch (2007) ment these results. For example, Mordasini et al. (2009)devel- adopted the starting positions of the planets in the Nice model oped a great number of planet population synthesis calculations (Tsiganis et al. 2005) and suggested that the surface density of solar-like stars within the framework of the core-accretion of the solar nebula varies approximately as r−2.2. On the other Article published by EDP Sciences A54, page 1 of 13 A&A 567, A54 (2014) hand, detailed models of structure and evolution of protoplane- history of a planetary system. From this, it is possible to ana- tary disks (Dullemond et al. 2007; Garaud & Lin 2007) suggest lyze the water delivery to the resulting planets, primarily to those that the surface density falls off with radius much less steeply formed in the habitable zone (HZ), which is defined as the cir- (as r−1) than that assumed for the MSN. More recently, Andrews cumstellar region inside which a planet can retain liquid water et al. (2009, 2010) analyzed protoplanetary disk structures in on its surface. Therefore the criteria adopted in the present paper the Ophiuchus star-forming region. They inferred that the sur- to determine the potential habitability of a planet are based on face density profile follows a power law in the inner disk of the its location in the system and its final water content. form r−γ and an exponential taper at large radii, where γ ranges This paper is therefore structured as follows: in Sect. 2, we from 0.4 to 1.1 and shows a median value of 0.9. present the main properties of the protoplanetary disks used in Several authors have tried to build a minimum-mass extraso- our simulations. Then, we discuss the main characteristics of lar nebula (MMEN) using observational data of exoplanets. On the N-body code and outline our choice of initial conditions the one hand, Kuchner (2004) used 11 systems with Jupiter-mass in Sect. 3. In Sect. 4, we present the results of all simulations. planets detected by radial velocity to construct an MMEN. On Finally, we discuss these results within the framework of the cur- the other hand, Chiang & Laughlin (2013)usedKepler data of rent knowledge of planetary systems and present our conclusions planetary candidates with radii R < 5R to build an MMEN. Both in Sect. 6. analyses produced steep density profiles. In fact, Kuchner (2004) predicted that the surface density varies as r−2 for the gas giants, while Chiang & Laughlin (2013) suggested that the surface den- 2. Protoplanetary disk: properties −1.6 sity follows a decay rate of r for the super-Earths. Recently, Here we describe the model of the protoplanetary disk and then Raymond & Cossou (2014) suggested that it is inconsistent to define the parameters we need to develop our simulations. assume a universal disk profile. In fact, these authors predicted The surface density profile is one of the most relevant pa- that the minimum-mass disks calculated from multiple-planet rameters to determine the distribution of material in the disk. systems show a wide range of surface density slopes. In this model, the gas surface density profile that represents the ff Several previous studies have analyzed the e ects of the sur- structure of the protoplanetary disk is specifically given by face density profile on the terrestrial planet formation in a wide −γ range of scenarios. On the one hand, Chambers & Cassen (2002) −γ 0 r −( r )2 Σ (r) =Σ e rc , (1) and Raymond et al. (2005) examined the process of planetary ac- g g r cretion in disks with varying surface density profiles in presence c of giant planets. On the other hand, Kokubo et al. (2006)inves- Σ0 where g is a normalization constant, rc a characteristic radius, tigated the final assemblage of terrestrial planets from different and γ the exponent that represents the surface density gradient. surface density profiles considering gas-free cases without gas Σ0 By integrating Eq. (1) over the total area of the disk, g can be giants. While these authors assumed disks with different masses, expressed by they only included planetary embryos (no planetesimals) in a narrow radial range of the system between 0.5 AU–1.5 AU. Σ0 = − γ Md · g (2 ) 2 (2) Raymond et al. (2007b) simulated the terrestrial planet forma- 2πRc tion without gas giants for a wide range of stellar masses.
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