Diversity Of Extrasolar Planets And Diversity Of Molecular Cloud Cores

Extrasolar planets appear to be very diverse. Most of them are quite different from oursolar system. As the observations progress and the number of detected planets grows, animportant issue is the physical mechanism causing the diversity. Up to this point, among over900detected extrasolar planets surrounding solartype stars, most are gas giants (seehttp://exoplanet.eu/). There are two striking features of the distribution of the semimajor axes ofthese giant planets. First, there is a pile-up of planets at about0.04AU. Conventionally, thepopulation of planets with semimajor axes less than about0.1AU is defined as “hot Jupiters.”Second, a large fraction of planets are on orbits with semimajor axes larger than about0.1AU.Most of these planets have semimajor axes from0.1to2.7AU. Beyond this, the numberdecreases with heliocentric distance and very few gas giants have semimajor axes greater than7AU. It is important to note, however, that present observing techniques are biased towardplanets close to their stars. A hot Jupiter is thought to form in the outer region of a disk, then toquickly migrate to a short-period orbit and stop there by a final stopping mechanism. It has lostthe memory of its original formation location. In this paper, we focus on those gas giant planetswith semimajor axes larger than0.1AU. We believe that they preserve the information of theirformation location. Surprisingly, quite different from the solar system, a large number ofextrasolar planets have semimajor axes less than2.7AU and they are inside the snowline of theminimum mass solar nebula. In previous studies of planet formation, artificial initial conditions of disks or steady statedisks, such as the minimum mass nebulamodel, have often been used. Therefore, the linkbetween properties of a cloud core and properties of its planetary system is not often mentioned.The aim of this paper is to showhowthe diversity of extrasolar planets is related to thediversity of molecular cloud cores. According to the standard star formation theory, a star formsfrom the gravitational collapse of a molecular cloud core. Observations tell us that a core rotatesslowly. The existence of this angular momentum leads to the formation of a protostar+disksystem from the collapse. A planet forms in such a disk which is referred to as a protoplanetarydisk. The properties of a cloud core set up the initial conditions of the system and determine theproperties of the protoplanetary disk which provides the formation environment of planets.Therefore, besides stochastic processes such as solid collisions, the cloud core properties shoulddetermine the properties of the final planetary system.We use the disk model including the mass influx from the gravitational collapse of amolecular cloud core and calculate the dependence of disk surface density on cloud coreparameters. To be quantitative and specific, we study the diversity of semimajor axes ofextrasolar planets. Using the standard core accretion model of planet formation, the boundary ofthe planet formation region in a disk can be calculated as a function of cloud core properties.Our approach takes advantage of the fact that properties of molecular cloud cores can beunderstood reasonably well through observations.From amolecular cloud core to a planetary system, the system goes through many physicalprocesses, such as disk formation and evolution, solid collisions, planetesimal formation, solidcore formation of giant planet, and gas accretion, and some are still not understood. Some processes, such as solid collisions may be stochastic, and the formation location may not bedeterministic. However, we show that the boundary of the planet formation region in a disk canbe determined by initial conditions. The determined boundary could be related to the diversesemimajor axes of extrasolar planets and could be compared with the orbits of Jupiter andSaturn. Although there are uncertainties with theoretical understanding of these physicalprocesses, we choose the accepted treatment in order to demonstrate the link between aplanetary system and its progenitor molecular cloud core.We have investigated the relationships between the diversity of extrasolar planets and thediversity of molecular cloud cores by using the disk model including the mass influx from thegravitational collapse of a core and the core accretion model of planet formation. Specifically,we have studied the dependence of semimajor axes of planets on properties of cloud cores. Ourmain conclusions are as follows.(1) The core properties, angular velocity, temperature, andmass determine the total mass and angular momentum of the system, collapse time of the core,and mass influx rate, and therefore the structure and evolution of a protoplanetary disk.(2) Thestructure and evolution of a protoplanetary disk depend on its gravitational stability since theeffective viscosity is enhanced and the surface density is decreased more rapidly when a disk isunstable. In the literature, it is often mentioned that the disk instability is related to the mass.Our study confirms that the instability is related to not only the mass but also to the specificangular momentum. Whether or not a disk is stable depends on angular velocity, temperature,and mass of its progenitorial cloud core. A disk is gravitationally unstable when angular velocityis greater than a critical value, e.g.,1.31014s1for temperature to be15K and mass to be1M⊙, temperature is less than a critical value, e.g.,22K for angular velocity to be 2.81014s1and mass to be1M⊙, and the mass is greater than a critical value, e.g.,0.62M⊙for angular velocity to be2.81014s1and temperature to be15K.(3) For fixedtemperature and mass, the surface density in the planet formation region of a disk first increaseswith angular velocity and then decreases with angular velocity due to high instability viscositywhen the angular velocity is greater than the critical value. The variation of the surface density,with decreasing temperature, is similar to that with increasing angular velocity. The surfacedensity expands to large radius as the mass increases.(4) We have calculated the dependence ofthe boundary of planet formation region and the maximum radius of the snowline on angularvelocity, temperature, and mass. For fixed temperature and mass, the planet formation regionfirst expands with angular velocity and then shrinks with angular velocity, when the angularvelocity is greater than the critical value. The variation of the boundary with decreasingtemperature is similar to that with increasing angular velocity. The planet formation regionexpands as the mass increases and shrinks when the mass is greater than the critical value.(5)We also compare our calculations with observations of extrasolar planets. From theobservational data of cloud cores, our model could infer the range and most frequent values ofobserved semimajor axes of extrasolar planets.(6) For most observed values of angular velocityand temperature, the snowline is located at>10AU. Planet formation at the snowline alonecould not completely explain the observed semimajor axis distribution. If the currently observedrarity of semimajor axes>8AU is not due to observational bias, this will indicate alowefficiency of planet formation at the snowline.(7) Our formation region calculation could becompared with the orbits of Jupiter and Saturn.(8) We suggest that there will be more observedplanets with semimajor axis <9AU than>9AU, even with a longer duration of observations, if the planet formation at the snowline is inefficient.(9) If the highly populated region extendsbeyond12AU, Region I alone could not explain the whole populated region, and we could notinfer a low efficiency of planet formation at the snowline. The populated region could beexplained by the combination of planet formation in Region I and at the snowline.