Non-isothermal Gravoturbulent Fragmentation: Effects on the IMF

1. Non-isothermal Gravoturbulent Fragmentation: Effects on the IMF A.-K. Jappsen¹, R.S. Klessen¹, R.B. Larson²,Y. Li3, M.-M. Mac Low3 ¹Astrophysikalisches Institut Potsdam, Germany 2Yale University, New Haven 3American Museum of Natural History, New York SPH Simulations: • parallel code GADGET (Springel et al. 2001) • Collapsed cores (protostars) repre- sented by sink particles (Bate et al. 95) • Uniform turbulent driving field on large scales (k=1..2) (Mac Low 99) • Periodic, uniform density cube (Klessen 97) • Self-gravity turned on after turbulence is established (after 2 tff) (Klessen, Heitsch, Mac Low 2000) • Number of SPH particles: 200,000 1,000,000 and 5,000,000 • Piecewise Polytropic Equation of State: • Discontinuity at critical density nc • P=K1ng1 n < nc • P=K2ng2 n > nc • g1=0.7, g2=1.1 Jeans Mass: • MJ ~ g3/2n(3/2)(g-4/3) Initial setup: • M=120 Msun, cube size: 0.29 pc • n0=8.8 · 104 cm-3, NJ=M/MJ=171 Why a Piecewise Polytropic Equation of State?: • isothermal treatment neglects influence of thermal physics on fragmentation • calculations with polytropic equation of state but with constant g show that the fragmentation depends on the value of g (Li et al. 2003) Why do we choose g1=0.7 and g2=1.1?: • below 10-18 g/cm-3: atomic and molecular cooling control temperature  temperature decreases with increasing density with a g of about 0.7 • above 10-18 g/cm-3: gas becomes thermally coupled to the dust  temperature rises slowly with density, and g increases to about 1.1 (Larson 1985, Masanuga & Inutsuka 2000) Open Questions: • Is there a connection between the change of g and a characteristic stellar mass? • Is the stellar mass spectrum (IMF) universal? • Can we find an explanation for the IMF based on fundamental atomic and molecular physics? • How appropriate is an isothermal EOS for star-forming gas? Temperature vs Critical Density g1= 0.7 g2= 1.1 Density Distribution of the Gas Different Turbulent Driving Fields Clump Mass Spectrum k =7..8 nc=4.3 · 105cm-3 M ~ nc-0.3+/-0.1 M ~ nc-0.3+/-0.2 nc=4.3 ·104 cm-3 nc=4.3 ·105 cm-3 • Results and Implications • Simulations show that change in g influences median mass of the clump mass spectrum: • a higher critical density nc results in a lower median mass • characteristic mass Mch scales with nc-0.4+/-0.2 • Number of collapsed cores increases with increasing critical density nc • Influence of different realizations of the turbulent driving field: • we find a similar trend of decreasing median mass with increasing nc but variations due to stochastic nature of turbulent flows • Dependency on the scale of turbulence: • small-scale turbulence leads to less fragmentation (see also Li et al. 2003) • More simulations needed to determine influence of: • realistic chemical network, radiation transfer processes and varying abundances Visits by AKJ and YL were supported by Kade fellowships. RSK and AKJ acknowledge support by the Deutsche Forschungsgemeinschaft grant KL1385/1. YL and M-MML were supported by NASA grants NAG5-10103 and NAG5-13028, and by NSF grants AST99-85392 and AST03-07793. • Reference • Bate, Bonell & Price, 1995, MNRAS, 277, 362 • Klessen, 1997, MNRAS, 292, 11 • Klessen, Heitsch, Mac Low, 2000, ApJ, 535, 887 • Larson, 1985, MNRAS, 214, 379 • Mac Low, 1999, ApJ, 524, 169 • Masunaga & Inutsuka, 2000, ApJ, 531, 350 • Li, Klessen, Mac Low, 2003, ApJ, 592, 975 • Springel, Yoshida, White, 2001, New Astronomy, 6, 79 nc=4.3 ·106 cm-3 nc=4.3 · 107cm-3 nc=4.3 ·107 cm-3 Comparison of Number of Cores and Accretion Rate Median Mass vs Critical Density M ~ nc-0.4+/-0.2 E-mail: akjappsen@aip.de