Protoplanetary disks and stars interaction in young open clusters: study of gas migration and chemical mixing with an SPH treatment.
Authors: Pinto Luis Diego , Capaccioni Fabrizio , Magni Gianfranco 
Published: July 2021

&#8211; IntroductionThe early dynamical evolution of the Solar System is nowadays clear to be likely occurred in an non isolated context, like many studies of Sun evolution inside an Open Cluster suggest (see Pfalzner, 2015 for istance). Such a framework indicates us that even protoplanetary matter around young stars may evolve in complex environments, which is further proved by some recent observations of protoplanetary disks around stars in Open Clusters (Mann et al., 2015).An important role in the evolution of a disk in a non isolated system may be played by secular perturbations due to the far field stars, and, on the other hand, by the strong perturbations induced, on a shorter time-scale, by the close fly-bys. Occasional encounters with passing-by stars may considerably affect the dynamical evolution of the gas and change the balance of distribution of matter around each star.We aim to investigate such a framework by means of 3D numerical hydrodynamical simulations, schematizing a solar-like star+disk system perturbed by close encountering stars.By means of a Lagrangian Smoothed Particles Hydrodynamics (SPH) scheme, we calculate the evolution of the gas by including also the thermal effects induced by both the propagation of the radiation through the optically thick disk and the effects of the radiation coming from the stars. The temperature profile of a disk, which is substantially dependent on the thermal scheme assumed, may determine the turbulent viscous evolution of the disk itself and its susceptibility to the strong macroscopical perturbations induced by fly-by events.2 &#8211; gas mixing and gas migrationIt is worth to consider some recent formation models according which the time scale of giant planet formation inside the disks may be less than 105 yr (Magni &amp; Coradini, 2004; Brennecka et al., 2020), far shorter than the previous classical results which amount of the order of 106 yr . Such a framework changes considerably the action of the cluster in altering the disk evolution.&#160; As a matter of fact, on one hand, the role of far field star becames less prominent in influencing the destiny of a gaseous disk since the secular perturbations has a small interval of time to act. On the other hand, the early stages of an Open Cluster are typically characterized by a chaotic non-relaxed state, in which the close interactions have a substantially high probability to occur. Thus, if the key processes inside the disk happen in a relatively short time, the disks itself have good chances to undergo strong perturbations by close approaching stars during its crucial evolutionary phases close to the planet formation stage.We are interested to investigate two peculiar phenomena connected to the transport of matter induced by fly-by perturbation. One is represented by the macroscopical transport of matter from the inner to the outer layers of the disk, which may explain a still opened question about the Solar System consisting in unexpected observation of crystalline sylicates in comets (Brownlee et al. 2006). Despite sylicate compounds in comets are expected to be amorphous, they present a crystalline structure which need to be generated in the hot inner regions, hence incompatible with the current cometary distances from the sun.On the other hand, we focus our attention to gas swapping among stars consisting in substantial capture and migration of matter towards another star during a close encounter. The simplest case that may happen is characterized by a star, previously lacking of any gas distribution around, that acquires a new disk. But a rather more complex situation occurs when gas migrates towards another disk during its phases of gaseous planet formation, altering the planetary cores feeding process.The figure 1 shows an interesting example of gas migrated and captured by an approaching star, the sequence illustrates the main phases of truncation of a protoplanetary revolving around a single solar-like star, and further formation of a secondary tiny disk around the second star.3 &#8211; Numerical methodWe implemented an SPH based code to integrate the hydrodynamical evolution of disks, with a tree code based algorithm to account for their selfgravity. SPH algorithms represent a class of lagrangian schemes commonly employed to face a wide range of astronomical problems ( see for example Monaghan, 2005 or Price &amp; Monaghan, 2007) involving self-grativating fluids. They employ a set of free moving particles which automatically mimic the gas density distribution into the 3D space without the need of any regular mesh-grid. This is an essential feature in problems where rather irregular distributions of gas are involved, like our investigation where the close interactions between 2 or more stars and a disk may substantially alter the original morphology of the disks and cause violent matter migration.To perform the work, we developed an SPH algorithm (Pinto et al., 2019) to which we further added a radiative transfer scheme (according to the schematization of Viau et al., 2006) implemented with a careful study of the boundary conditions, due to the complex geometry and thermal exchange during a close encounter star&#8211;disk. This approach allows to describe a physically reasonable propagation of radiation through matter.References:- Brennecka et al. 2020, Science 370, 837&#8211;840- Brownlee, D. et al. 2006, Science 314 , 1711 DOI: 10.1126/science.1135840- Mann, R. K., Andrews, S. M., Eisner, J. A., et al. 2015, ApJ, 802, 77- Magni, G. and Coradini, A. 2004, Planetary and Space Science 52, 343- Monaghan, J. J. 2005, Reports on Progress in Physics, 68:1703&#8211;1759- Pfalzner, S., Davies, M. B., Gounelle, M., et al. 2015, Physica Scripta, 90, 068001- Price, D. J. and Monaghan, J. J. 2007, MNRAS, 374:1347&#8211;1358- Pinto, L. D., Capuzzo-Dolcetta, R., and Magni, G. 2019, A&amp;A 628, A82- Viau, S. , Bastien, P. &amp; Cha, S.H. 2006, ApJ, 639:559&#8211;57