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.

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

Piecewise Polytropic Equation of State:

Discontinuity at critical density nc

P=K1n1 n < nc

P=K2n2 n > nc

1=0.7, 2=1.1

Jeans Mass:

MJ ~ 3/2n(3/2)(-4/3)

Initial setup:

M=120 Msun, cube size: 0.29 pc

n0=8.8 · 104 cm-3, NJ=M/MJ=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 10-18 g/cm-3: atomic and molecular cooling control temperature temperature decreases

with increasing density with a of about 0.7

above 10-18 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?

nc=4.3 · 105 cm-3

nc=4.3 · 107 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 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.

ReferenceBate, Bonell & Price, 1995, MNRAS, 277, 362Klessen, 1997, MNRAS, 292, 11Klessen, Heitsch, Mac Low, 2000, ApJ, 535, 887Larson, 1985, MNRAS, 214, 379 Mac Low, 1999, ApJ, 524, 169Masunaga & Inutsuka, 2000, ApJ, 531, 350Li, Klessen, Mac Low, 2003, ApJ, 592, 975Springel, Yoshida, White, 2001, New Astronomy, 6, 79

Comparison of Number of Cores and Accretion Rate Median Mass vs Critical Density

Temperature vs Critical Density

Clump Mass Spectrum Different Turbulent Driving Fields

k =7..8

nc=4.3 ·105 cm-3

nc=4.3 ·106 cm-3

nc=4.3 ·107 cm-3

nc=4.3 ·104 cm-3

= 0.7

= 1.1

M ~ nc-0.4+/-0.2

M ~ nc-0.3+/-0.1 M ~ nc

-0.3+/-0.2

E-mail: [email protected]