Prestellar core formation simulations in turbulent molecular clouds with large scale anisotropy Nicolas Petitclerc, James Wadsley and Alison Sills McMaster University; petitcn, wadsley, The early stages of star formation have been getting lots of attention recently, with the observations being able to resolve the dense cores within molecular clouds. There is many unanswered questions about the way they form and how they evolve. We are tackling some of the issues via SPH simulations. We deliberately chose to not use “sink particles” (Bate et al., 1995) in order to avoid any possible numerical side effect. To avoid the issue of the very high density regions, slowing down the simulation, we limited our resolution to 50 AU. Which still enables us to resolve dense cores ranging in sizes generally ≥5000 AU. We simulated typical 5000 solar mass molecular clouds (36 million particles each) to get good statistics for cores. We investigated the effects of different initial large scale anisotropic turbulent velocity fields, that lead to spherical, filament, ribbon or even sheet structured collapses. To generate those initial velocity fields, we took a subset (1/8) of our initial turbulence box, this way we get larger scale modes of turbulence to dictate the overall collapse of the cloud. To be able to predict the outcome, we made measurements of the shear vectors, a positive value translates in a expansion and a negative in a contraction. Our statistical study (figure 1) of randomly generated anisotropic velocity fields shows a strong preference for the ribbon shaped collapse i.e. the shear vectors indicate a collapse in one direction, an expansion in an orthogonal direction and very little movement in the other. Figure 1 - Column density maps to perform direct comparisons with observations, using Clumpfind. The dense core identified by the black contour lines is shown in the zoom in section (top-left) References: - Bate et al., 1995, MNRAS, 277, 362- Padoan et al., 2007, ApJ, 661, Johnstone et al., 2000, ApJ, 559, Reid, 2005, PhD thesis - Motte, André and Neri, ApJ, 336, Tilley & Pudritz, 2004, MNRAS, 353, Nakamura & Li, 2007, ApJ, 662, 395- Ward-Thompson et al., PrPl V, 3 We identified all the primary 3D (spatial) density peaks with at least 200 particles (>0.03 solar mass) as dense cores. We then study the core mass functions (CMF) shape and evolution. We will compare our 3D results to what we find using the column density map shown on figure 1 in the near future. Figure 2 – Statistical study of the randomly generated initial velocity fields shear vectors, where λ 1 >λ 2 >λ 3 and λ 1 +λ 2 +λ 3 =0. The square represent the ribbon case (by far the most likely), the triangle the sheet case, the upside down triangle the filament case and the circles are the spherical cases. We choose the 4σ open circle (very unlikely) as a reference to most isotropic simulations, the other cases are taken at a more probable 2σ. Figure 3 – Turbulence energy evolution (spherical case) shows a significant increase in the RMS mach number, even though our turbulence is not explicitly driven. Figure 4 – Probability distribution function (PDF) evolution (spherical case), showing from grey to black the time steps: 100, 200, 400, 600, 800, 1000, 1120, 1200 and 1350 kyrs. It shows that our turbulence is not decaying, it’s rather building up in time as the log-normal distribution widens. This is the opposite of what happens in turbulent simulations without gravity with turbulence decay (Padoan et al., 2007). Figure 3 and 4 leads us the very interesting conclusion: Gravity can be a dominant turbulence driver within molecular clouds. As the cloud collapse gravity provides an ongoing source of energy as it tries to virialize. Some of the energy will be radiated away by the optically thin gas, but a significant fraction remain as kinetic energy. The lack of such evidence in periodic gravitational turbulent simulations, could be explained by our difference in dynamical range, only parts of their box can collapse and let gravity pump in energy the way our whole cloud does. They are rather showing decay of the large scale turbulence dominating the overall kinetic energy (Tilley & Pudritz, 2004). The kinetic energy increase shown on figure 3, is very similar in magnitude to what was found with explicit stellar feedback (Nakamura & Li, 2007) and it is very likely to increase as the collapse proceed further. We are currently testing this idea further with a initially subsonic turbulent velocity field simulation. Figure 5 – CMF of the 4 simulations with an approximated double power law fit. The Salpeter power law is also shown as reference. The dashed line represent the mass break point (m B = 0.16 solar mass) between the 2 power law, Γ= -1.7 for the high mass end and Γ= -0.6 at the lower mass end. These estimates are in very good agreement with observations (see figure 6). Figure 6 – Normalized CMF for the molecular clouds ρ Oph (left; Johnstone et al., 2000) and Orion (right; Motte et al., 1998). Tthis figure was adapted by Ward- Thompson et al., 2007 from Reid, Figure 7 – CMF evolution (spherical case) of the double power law fit parameters. We did systematic maximum likelihood fit at different time steps (same as figure 4). The dashed lines represent the 1σ uncertainty and the dotted lines the mean value over time. No normalization is applied, the mass are in solar mass. No trend is observed in the mass break point and the low mass end slope (S1). We however see a significant increase at the high mass end slope (S2), it tends to get less steep with time. Note that these measurements were done for only one simulation and for a limited range in time, we will improve on both aspects. Figure 8 – Distribution of the cores mass over their own jeans mass (spherical case). We found 110 bounded (M≥M J ) cores and a large majority 3271 of unbound cores. Figure 9 – Mass distribution of the bounded (left; dashed line) cores and the unbounded (right; dashed line). Compared to the complete CMF (full lines) and the mass break (dashed lines). Figures 8 and 9 suggest that the vast majority of dense cores are unbound (M<M J ) transient objects following a log normal distribution similar to the density distribution (see figure 9 right side dashed line). Which is reasonable since: So the distribution of cores remains log normal, but scaled relative to density distribution. The distribution of the bounded (M≥MJ) cores (figure 9 left side dashed line), is mostly above the breaking mass. This suggest that a departure from the log normal distribution at this point could be related to the accumulation of the bounded objects. They get form at a rate dictated by the turbulent flow, but don’t get disrupted as easily as the transient objects. They could possibly form a second log normal population at the higher mass. The lower statistics at the high mass end (also true for observations) doesn’t enable us to observe a clear bump, but the flattening of the power law (S2 on figure 7) with time is in good agreement with this picture. Looking at later stages of the collapse will definitely help test further this idea. SPH simulations also give us the advantage of being able to follow the cores in time, and give us the opportunity to directly measure the rates of formation, destruction and merge of cores.