Non-isothermal Gravoturbulent Fragmentation: Effects on the IMF A.-K. Jappsen¹, R.S. Klessen¹, R.B. Larson²,Y. Li 3, M.-M. Mac Low 3 ¹Astrophysikalisches Institut Potsdam, Germany 2 Yale University, New Haven 3 American Museum of Natural History, New York Piecewise Polytropic Equation of State:  Discontinuity at critical density n c  P=K 1 n  1 n < n c  P=K 2 n  2 n > n c   1 =0.7,  2 =1.1 Jeans Mass:  M J ~  3/2 n (3/2)(-4/3) Initial setup:  M=120 M sun, cube size: 0.29 pc  n 0 =8.8 · 10 4 cm -3, N J =M/M J =171 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  ff ) (Klessen, Heitsch, Mac Low 2000)  Number of SPH particles: 200,000 1,000,000 and 5,000,000 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  show that the fragmentation depends on the value of  (Li et al. 2003) Why do we choose  1 =0.7 and  2 =1.1?:  below g/cm -3 : atomic and molecular cooling control temperature  temperature decreases with increasing density with a  of about 0.7  above g/cm -3 : gas becomes thermally coupled to the dust  temperature rises slowly with density, and  increases to about 1.1 (Larson 1985, Masanuga & Inutsuka 2000) Open Questions:  Is there a connection between the change of  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? n c =4.3 · 10 5 cm -3 n c =4.3 · 10 7 cm -3 Density Distribution of the Gas Results and Implications  Simulations show that change in  influences median mass of the clump mass spectrum: a higher critical density n c results in a lower median mass characteristic mass M ch scales with n c -0.4+/-0.2  Number of collapsed cores increases with increasing critical density n c  Influence of different realizations of the turbulent driving field: we find a similar trend of decreasing median mass with increasing n c 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 NAG and NAG , and by NSF grants AST and AST 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 Comparison of Number of Cores and Accretion RateMedian Mass vs Critical Density Temperature vs Critical Density Clump Mass Spectrum Different Turbulent Driving Fields k =7..8 n c =4.3 ·10 5 cm -3 n c =4.3 ·10 6 cm -3 n c =4.3 ·10 7 cm -3 n c =4.3 ·10 4 cm -3   = 0.7  = 1.1 M ~ n c -0.4+/-0.2 M ~ n c -0.3+/-0.1 M ~ n c -0.3+/