1. Star Formation in Cosmological Simulations: the Molecular Gas Connection Kostas Tassis Jet Propulsion Laboratory California Institute of Technology

2. Co-starring Andrey Kravtsov Nick Gnedin Gnedin, Tassis & Kravtsov 2009 ApJ, 697, 55 /arXiv:0810.4148

3. Star Formation in cosmological simulations Cosmological Simulations: ISM physics not followed in detail Sub-grid SF modeling typically based on observed scaling relations, tied to cold gas (HI+H 2 ) Observations of high z galaxies: –Probe molecular content, star formation (ALMA,JWST) –Simulations must match this advance and increase fidelity of simulated galaxies Kennicutt 1998

4. Use ART (Adaptive Refinement Tree) N-body+gas+SF+RT: 6 Mpc comoving box 50 pc resolution in high-redshift galaxies Mass resolution m dm =10 6 Msun, m gas =10 5 Msun Starting Point

5. Use ART (Adaptive Refinement Tree) N-body+gas+SF+RT: 6 Mpc comoving box 50 pc resolution in high-redshift galaxies Mass resolution m dm =10 6 Msun, m gas =10 5 Msun

6. Starting Point Use ART (Adaptive Refinement Tree) N-body+gas+SF+RT: 6 Mpc comoving box 50 pc resolution in high-redshift galaxies Mass resolution m dm =10 6 Msun, m gas =10 5 Msun Optically Thin Variable Eddington Tensor Approximation (OTVET) for following time-dependent and spatially-variable RT Cooling rates and ionization/chemical balance are computed “on the fly”

7. More Details Optically Thin Variable Eddington Tensor (OTVET) Only ET is OT!

8. OTVET Approximation Eddington tensor from the optically thin regime: Collect 1/r 2 contribution from all sources –just like gravity! Fast (~Nlog(N)), no scaling with # of sources Energy density and flux are conserved exactly Sometimes flux advected in the wrong direction (shadowing)

9. How Molecular Clouds Form H 2 forms on the surface of dust grains. Self-shielding starts the process, dust shielding finishes it. Young stars Molecular gas Atomic gasDust

10. H 2 Formation Model: gas + dust “Primordial” hydrogen balance (gas-phase reactions) Adding dust heuristically

11. H 2 Formation Model: parameters Formation rate: Dust/Gas ~ Z Molecular gas is inhomogeneous, clumping factor ~ 10 for typical clumpy molecular cloud models (e.g.: Padoan et al. 1997; Ostriker et al. 2001) Shielding factors: a la Draine & Bertoldi (1996) see also Glover& Mac Low(2007) Parameters & to be calibrated Wolfire et al. (2008)

12. H 2 Formation Model: column density Column densities for shielding factors from Sobolev-like approximation

13. H 2 fractions in translucent clouds have been measured by Copernicus & FUSE space missions (Tumlinson et al 2002, Rachford et al 2002, Gillmon et al 2006, Wolfire et al 2008) Training the Model HINSA measurements of HI fractions (Goldsmith & Li 2005)

14. Star Formation (Krumholz & Tan 2006) Specific SFR per local free-fall time is not sensitive to the environment (both normal galaxies and starbursts), and is about 1-2% in molecular gas (star formation is slow).

15. Thermodynamics Automatically get 3+phases: Hot coronal gas Warm neutral and ionized medium Cold neutral and molecular gas

16. Atomic-to-molecular Transition Transition between atomic and molecular phases very sharp scales with metallicity Z=1.0Z=0.3Z=0.1

17. Atomic-to-molecular Transition Transition between atomic and molecular phases NOT very sensitive on UV field Draine field10 x Draine field

18. Simulation Kennicutt Plots Reality (THINGS) Bigiel et al. 2008

19. Kennicutt Plots SimulationReality (THINGS) Bigiel et al. 2008

20. Kennicutt Plots Simulation Reality (CO) Bigiel et al. 2008

21. Kennicutt Plots Simulation Reality (THINGS+CO) Bigiel et al. 2008

22. Metallicity Dependence  Text Z=1.0Z=0.1

23. UV Flux Matters Little  Text Draine field10 x Draine field

24. Traditional Interpretation of KS Scaling h ≈ const. Free-fall but not only

25. Complications Conceptual Star formation a local phenomenon only takes place at very dense cores at ~ 0.1 pc scales Mean density dependence of timescale assumed not necessarily meaningful

26. Complications In simulations Large-scale SF law reproduced in ART, Enzo sims assuming constant SF timescale (Kravtsov 2003; Tasker & Bryan 2006) Kravtsov (2003)

27. Complications Observational In dwarf galaxies e.g. : NGC 6822 de Blok & Walter (2006) M33 Heyer et al. (2004) IC10 Leroy et al. (2006) SF correlates linearly with dense gas Gao & Solomon (2004) Wu et al. (2005)

28. From Small to Large Non-linear correlation of total gas density and dense gas is implied

29. Multifractal ISM? Multifractal topology generic in systems where multiple nonlinear processes act in parallel, such as ISM Tassis 2007: Multifractal density field (generated using random-b model of fully developed turbulence) naturally produces scaling n~1.5 for large galaxies / wide density pdfs n>1.5 for dwarfs / narrow pdfs

30. How robust is this scaling? Slope saturates close to 1.5 for wide pdfs Not sensitive to  den def. Slope saturates to higher values for narrower pdfs appropriate for dwarfs Tassis et al. (2008) Wada & Norman (2007)

31. Summary SF in cosmological simulations needs to be tied to molecular hydrogen – just like in nature! Transition from atomic to molecular gas is very sharp – lack of dependence of SFR on HI surface density in Kennicutt-like correlations. In the zeroth order, the SF density threshold scales inversely with metallicity, n SF ≈ 30/Z cm -3. Since dust-to-gas ratio depends on the metallicity, it constitutes a feedback effect that needs to be accounted for in cosmological simulations and galaxy evolution models. Since dust-to-gas ratio depends on the metallicity, it constitutes a feedback effect that needs to be accounted for in cosmological simulations and galaxy evolution models.