Gas Cloud Collisions and Stellar Cluster Formation J. Klapp 1, G. Arreaga-Garcia 2 1 Instituto Nacional de Investigaciones Nucleares, Km 36.5 Carretera México-Toluca, Ocoyoacac, 52750 Estado de México, México. Email: jaime.klapp@inin.gob.mx. 2 Centro de Investigación en Física, Universidad de Sonora, Blvd. Rosales y Blvd. Encinas, s/n, Col. Centro, Hermosillo 83000, Sonora, México. E-mail: garreaga@cajeme.cifus.uson.mx Abstract In this paper we present computer simulations of interstellar cloud collisions that for a given range of initial conditions could favor stellar cluster formation. We first construct a single spherical molecular hydrogen cloud with the Plummer (1911) radial density distribution with rigid rotation and an m=2 density perturbation. The isolated cloud collapses into a filament with no sign of fragmentation. We then place two clouds for a head-on collision, and for an oblique collision characterized by an impact parameter that depends on the initial radius of the cloud. The approaching velocity of the clouds is changed from zero up to thirty times the gas sound speed. We have found that for certain values of our parameter space fragmentation into a stellar cluster is possible. 1 Introduction A key feature observed by astronomers is that newborn stars are clustered in well defined regions of the galaxy. These clusters are embedded in the remaining of giant gas clouds. It has also been noted that both clouds and stellar clusters acquire irregular spatial forms. Giant molecular hydrogen clouds begin the star formation process by the action of several forces: gravitational, pressure, magnetic and centrifugal. The prominent attractive force of gravity is due to the weight of the cloud itself; when it exceeds the other forces the cloud collapses reducing its size and reaching higher densities and temperatures. The pressure force, due to the gas temperature, the centrifugal force caused by rotation, and in many cases the magnetic force, oppose the gravitational collapse. In addition to the mechanical forces mentioned above, the cooling and heating mechanisms play an important role as the clouds exchange energy with their environment. A successful theoretical model should contain the fragmentation of the progenitor gas cloud during the star formation process, in such a way that the result of the gravitational collapse of the cloud will be a group of stars rather than a single
204 J. Klapp, G. Arreaga-Garcia newborn star in isolation. A model containing this type of fragmentation would then be closer to reproducing the results of astronomical observations. An important question of a model is then to try to understand what physical mechanisms may promote the occurrence of fragmentation and how to capture the essence of such mechanisms in our theoretical models. We present here the result of a set of simulations aimed to study the collision between two identical molecular gas clouds. We are interested in studying the implications of collisions on the star formation process. We have found that the presence of fragmentation in a system can be a consequence of the occurrence of a collision. 2 The collision model It should be emphasized that cloud collisions may be common in the interstellar medium of a typical galaxy. For example, we know that there are a large number of these progenitor clouds located in the galaxy spiral arms. There are systems of two or more spiral galaxies forming compact groups such that they experience significant tidal forces that can make that the clouds in the same neighborhood of the spiral arm get too close or even collide. Astrophysicists have tried to construct theoretical models describing the most important aspects of the star formation process and in particular showing fragmentation. During the last two decades, models have relied increasingly on numerical simulations, despite that it is very difficult to incorporate all observed physical elements of the actual star formation process. Then we have to resign ourselves to work with models that are not strictly realistic but rather idealized. However, due to the increasing processing power of supercomputers today, there are good chances that a theoretical model based on numerical simulations can capture some key elements of the star formation process, as we hope to show in this work. To construct our collision models, let us consider two spherical molecular hydrogen gas clouds, which are face to face with an initial velocity which will make them to collide, as it is illustrated in Fig. 1. It should be noted that each separate cloud rotate as a rigid body around its own vertical axis in the opposite clockwise direction. Certainly, it is a highly idealized initial condition, given the complexity of the interstellar medium, but the advantage of this simple model is that it allows us to capture important dynamic elements such as the occurrence of turbulence in colliding gas clouds and above all, the occurrence of certain types of fragmentation, as we shall see later. However, to better understand the nature of fragmentation that we observed in the collision models, it is necessary first to study the evolution of the cloud as an isolated system, and then to discuss the result of the two clouds collision model. The individual spherical molecular hydrogen cloud is constructed so that the radial density follows the Plummer (1911) profile which is given by
Gas Cloud Collisions and Stellar Cluster Formation 205!!! =!!!!!!!!!!, (1) where R c = 3.0 x 10 18 cm is the radius of the cloud, ρ c =1.3025 x 10-21 gr/cm 3 its central density, and η is a constant. For the models of this paper the clouds are nearly uniform. In addition we introduce the density perturbation ρ 1 (r)= ρ (r) (1+ amp cos mφ), where amp is the amplitude that we take to be 0.5 and φ the azimutal angle. 3 The collapse of the isolated cloud Consider a spherical gas cloud, rotating around its vertical axis with a constant angular velocity, as illustrated in Fig. 2. As we indicated, the force of gravity pulls all matter in the cloud toward the center while the pressure force pushes the gas out. The rotation of the cloud causes the appearance of a centrifugal force toward the surface at any latitude plane (any plane in the area parallel to the equatorial plane). Thus, the acceleration of every gas element is composed of two contributions: the first due to the gravitational acceleration directed towards the center of the cloud, and the second one due to the pressure of the gas and the centrifugal acceleration toward the surface. Fig. 1. The initial configuration for the two cloud collision model
206 J. Klapp, G. Arreaga-Garcia Fig. 2. The isolated cloud model (left panel) and accretion disk that forms in the equatorial plane of the cloud (right panel) These accelerations are co-linear only in the equatorial plane while at the poles are perpendicular. For this reason, the total acceleration is greater at the equator than in regions near the polar circles. Moreover, because there are no external forces or torques acting on the cloud, the angular momentum is conserved. Then as a consequence of the initial rotation of the cloud and the angular momentum conservation, the cloud begins to flatten at the poles toward the equator, so that it forms a flattened disk that spins faster than the rest of the gas that is still in the spherical cloud. This region is called an accretion disk because it keeps falling under the influence of the gravity force. We use the Gadget2 computer program (Springel 2005) for solving the Navier- Stokes equations including the self gravitational interaction of the gas cloud. The Gadget2 code is based on the Smoothed Particle Hydrodynamics technique (SPH). To display the results of the simulations we use a color scale to show the density distribution of a slice of cloud parallel to the equatorial plane as seen from a high position on the axis of rotation. For example, according to this color density scale, yellow indicates high density regions, green and red intermediate densities and finally the blue correspond to low-density regions in the cloud. It should be noted that the length scale that appear in the axes of each panel are normalized with the initial radius of the cloud. For the isolated cloud in Fig. 3 we show isodensity contour curves for a time near the beginning of the simulation and after 5.7τ ffc, where the free fall time unit is τ ffc =1.84 Myr. The dense gas is contained in about 10% of the initial radius of the cloud and is concentrated in the central region of the accretion disk. We can see that the denser gas forms a continuous elongated filament that shows no signs of being next to fragment into any part of the filament. This tendency to form needle-like thin filaments has previously been observed in simulations of gravitational collapse of clouds with a uniform radial density profile.
Gas Cloud Collisions and Stellar Cluster Formation 207 4 Results of the collision In a collision between two gas clouds the most important parameters are the impact velocity and the impact arm. The magnitude of these parameters strongly determines the collision outcome. For example, with a high impact velocity, the system ends dispersing the entire mass of the cloud because gas jets flow in directions parallel to the collision zone. On the other hand, a zero-impact arm would correspond to a purely frontal collision while a nonzero value for this parameter indicates an oblique collision. We have explored a range of values for the magnitude of the impact velocity and the impact arm which are appropriated to avoid the total dispersion of the system, and in this way favor that the collapse occurs further and eventually lead to proto star formation. This is the kind of collision models in which we are primarily interested in this research. The approaching velocities of our collision models vary from 2.46 to 30.78 Mach and the clouds are initially almost in contact, see Fig. 1. Then just after the start of the simulations, the clouds suffer a collision and the first effect is that they are compressed and a shock front is formed that propagates to the two clouds. The artificial viscosity transforms kinetic energy into heat that is radiated away in a very short timescale and we can assume that the shock and the clouds remain isothermal. During the collision process a slab of material is formed along the shock front. The clouds then expands but eventually collapses as will be later described. The shocked slab which is formed as a result of the supersonic collision is susceptible of having various instabilities which has been studied by Vishniac (1983) for the linear regime and by Vishniac (1994) for the non-linear case. For the present work the relevant ones are the shearing and gravitational instabilities. The shearing instability dominates at low density while the gravitational one takes over for densities above a critical density of about!!!!"# 7.86132! 10!!!!!"!!"#$!"!! gr cm!!, where η is the amplitude of the perturbation,!!"#$ is the length of the unstable mode and T the temperature (Heitsch et al. 2008). Of the shearing instabilities the main ones are the non-linear thin shell instabilities (NTSI) and the Kelvin- Helmholtz (KH) instability. The NTSI instability is expected to occur in the shocked slab just after the cloud collision, and the non-linear bending and breathing modes could also be present. When the initial contact occurs between particles of different clouds, there is a density increase in the interface region, in which particles form knots and vortices, see Fig. 4. The magnitude of the density increase obviously depends on the impact velocity and we must mention that it is a transient behavior, because the density decreases after passing the initial impact stage. The effect of gravity is again evi-
208 J. Klapp, G. Arreaga-Garcia dent by causing the clouds to begin its collapse separately in its central regions, see Fig. 5. At this time, the temporal evolution of the peak density detected in the cloud shows an increasing trend, as can be seen in Fig. 4, where we have plot the peak density against another free fall time scale, given by τ ffc =5.22 Myr. It is interesting to note that one effect of the collision is to promote the occurrence of fragmentation in the central strand of each of the clouds, as seen in the Fig. 6. This observation should be contrasted with the result of the collision of the cloud as an isolated system (see Fig. 3), which never shows any tendency of fragmentation in the central filamentary region. The result just enunciated above, that the collision favors fragmentation is very important in the area of star formation, because each of the dense knots forming along filaments during cloud collisions could eventually form proto-stars. Since it is possible that more gas condensations are formed in the bridge connecting the clouds, the numerical simulation will produce a complex distribution of proto stars clustered in a binary group formed in the filaments, in addition to those proto stars formed in the bridge. Fig. 3. Isodensity colored curves for the isolated cloud in the first and last stages of evolution, shown in the left and right panels, respectively
Gas Cloud Collisions and Stellar Cluster Formation 209 Fig. 4. Velocity field of particles located in the interface region of the two colliding clouds (left panel) and its transient increases of the peak density (right panel) Fig. 5. Isodensity curves showing the result of one of the oblique collision model in the first (left panel) and last (right panel) states of evolution observed in the simulation
210 J. Klapp, G. Arreaga-Garcia Fig. 6. Zoom in of the central region of the clouds in the collision model of Fig. 5 5 Conclusions Studies using numerical simulations of gravitational collapse of clouds as isolated and colliding clouds have a long a history of nearly three decades. The early simulations predicted that the accretion of gas in the galactic disk (a collision between a gas cloud and a slab of gas) could have an enormous influence on the star formation process, and at the same time, will inherit a very peculiar physical structure for the interstellar gas. In fact, recent astronomical observations have shown some elongated gas structures in the Orion Molecular Cloud, a type of structure that appears to be common throughout the Galaxy interstellar medium. In this paper we have considered collisions between clouds as an alternative physical mechanism for promoting the formation of complex stellar systems. Today, we are in a position to follow the collapse of the cloud to densities in a range from 10-18 to 10-10 gr/cm 3, a peak density in which we can identify the clumps of denser gas as proto-stars. We know that some of the dynamic characteristics of a proto-star will be inherited by the real star to be formed once the process of gravitational collapse will continue further until peak densities of the order of 10-1 g/cm 3 are reached. Although we have been limited to consider only very idealized collision systems, we were able to capture and display some of the essential features of the collision process. For example, we must mention that we have observed some kind of fragmentation in the filaments, which is a direct consequence of the occurrence of the collision. This result can be considered as evidence that collisions can have a major influence on the process of star formation as was thought before.
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