1. Zurich, September 18 th 2007 Adrianne SlyzUniversity of Oxford Lessons on ISM modelling from kiloparsec scale simulations

2. Zurich, September 18 th 2007 What physical processes regulate … the rate at which gas turns into stars? starbursts centers of normal disks Kennicutt (1998) SFR Area ~ ∑ gas log Σ SFR (M sol yr -1 kpc -2 ) log Σ gas (M sol pc -2 ) 1.4

10. Zurich, September 18 th 2007 Link between density structure & star formation ?

11. Zurich, September 18 th 2007 Key insights from periodic box simulations in the 90 ’ s: 2. Isothermal and adiabatic turbulence decays quickly (within a sound crossing time) whether the medium is magnetized or not (Stone et al. 1998, Maclow et al. 1998, Padoan & Nordlund 1999) 1. Density structure of isothermal medium structured by supersonic, compressible turbulence is well described by a log-normal distribution whose dispersion reflects the Mach number of the medium (Vazquez-Semadeni 1994, Padoan, Nordlund & Jones 1997, Nordlund & Padoan 1999)

12. Zurich, September 18 th 2007 1.28 kpc Initial conditions ρ  = 1 at/cm 3 T = 10 5 K Turbulent velocity field imposed on large scales P(k) ∝ k -4 Homogeneous gas Periodic boundary conditions 1.28 kpc

13. Zurich, September 18 th 2007 1.28 kpc Initial conditions ρ  = 1 at/cm 3 T = 10 5 K Turbulent velocity field imposed on large scales P(k) ∝ k -4 Homogeneous gas Periodic boundary conditions 1.28 kpc

14. Zurich, September 18 th 2007 Radiative cooling White and Sarazin (1987), Rosen and Bregman (1995) 3 4 5 6 7 8 T (Kelvin) -21 -22 -23 -24 -25 -26 log 10  (T) ergs cm 3 /s

15. Zurich, September 18 th 2007 PDF = 1 ___ (2 π ) 1/2 σ exp - (ln ρ  - ) 2 2 σ  2 with σ = ln 1 + (M rms /2) 2 (Padoan & Nordlund 2002) [] () log 10 (normalized PDF) log 10  gas -

16. Zurich, September 18 th 2007 PDF = 1 ___ (2 π ) 1/2 σ exp - (ln ρ  - ) 2 2 σ  2 with σ = ln 1 + (M rms /2) 2 (Padoan & Nordlund 2002) [] () log 10 (normalized PDF) log 10  gas -

17. Zurich, September 18 th 2007 PDF = 1 ___ (2 π ) 1/2 σ exp - (ln ρ  - ) 2 2 σ  2 with σ = ln 1 + (M rms /2) 2 (Padoan & Nordlund 2002) [] () log 10 (normalized PDF) log 10  gas -

18. Zurich, September 18 th 2007 PDF = 1 ___ (2 π ) 1/2 σ exp - (ln ρ  - ) 2 2 σ  2 with σ = ln 1 + (M rms /2) 2 (Padoan & Nordlund 2002) [] () log 10 (normalized PDF) log 10  gas -

19. Zurich, September 18 th 2007 PDF = 1 ___ (2 π ) 1/2 σ exp - (ln ρ  - ) 2 2 σ  2 with σ = ln 1 + (M rms /2) 2 (Padoan & Nordlund 2002) [] () log 10 (normalized PDF) log 10  gas -

20. Zurich, September 18 th 2007 ∞ f c =  ∫ ρ PDF d ρ ∫ ρ th 0 ∞ fraction of mass above  th Universal PDF? Is there a clear density threshold for star formation? (Elmegreen 2002 Krumholz & McKee 2005 Wada & Norman 2007) Open questions

21. Zurich, September 18 th 2007 Log-normal fit to high density end of run with stars, self-gravity, fbk ⇒ ρ peak ≈ 50 at cm -3 = 3.9 σ  = 1.22 ⇒ M rms = 3.1 PDF = 1___ (2 π ) 1/2 σ exp - (ln ρ - ) 2 2 σ 2 ( ) log 10  gas (at/cm 3 ) log 10 (normalized PDF)

22. Zurich, September 18 th 2007 Avillez & Breitschwerdt 2005 PDF for SN driven stratified segment of a disk 1 X 1 X 20 kpc x-y plane density P robability D istribution F unction ( PDF ) n (cm 3 ) PDF 10 8 6 4 2 1 0.5 0 -0.5 -2 -4 -6 -8 -10 Z (kpc)

23. Zurich, September 18 th 2007 Joung & MacLow 2006 PDFs for gas near midplane 4 pc subbox 125 pc subbox PDFs in different subbox sizes for SN driven stratified segment of a disk 0.5 X 0.5 X 10 kpc disk segment

24. Zurich, September 18 th 2007 New generation of ISM simulations density temperaturepressure stars 0.001 1.0 1000  (M sol pc 3 ) PDF 7.5 2.5 log Temp edge-on view face-on view 3D isolated disks, 25-50 pc resolution Tasker & Bryan 2006

25. Zurich, September 18 th 2007 Different philosophies for adding supernovae explosions in ISM models m * =  ρ gas V cell ∆ t/t dyn + Stellar Initial Mass Function Calculate energy and mass returned to interstellar medium via supernovae and stellar winds Model star formation Model observed supernovae rates & mimic their distribution (e.g. isolated, clustered) e.g. SN frequency Milky Way Galaxy:1/330 yr -1 for Type I and 1/44 yr -1 for Type II (Tammann et al. 1994) Scale heights: Type I :325 pc (Heiles 1987) Type II :90 pc Power law distribution of superbubbles: dN B ~ n * -2 dn * (Kennicutt et al. 1989, McKee & Williams 1997) A B

26. Zurich, September 18 th 2007 Supernovae feedback in Joung & Maclow 2006 1.) Identify supernovae site (stick to the observations) 2.) Grow a sphere at that site until it encloses 60 M sun. Radius of this sphere R exp ~ 7 pc to 50 pc 3.) Redistribute mass in that sphere so that it has uniform density  = 3M exp /(4  R exp 3 ) 4.) Inject thermal energy E SN = 10 51 ergs evenly into the sphere M exp = 60 M sun R exp NO mass ever removed to form a star B

27. Zurich, September 18 th 2007 Identify Jeans unstable boxes M box /M J > 1 where M J = <  J 3  = avg density in box J = (  /G<  ) 1/2  tot  tot = ( 2 + 1/3<  2 ) 1/2 (Chandrasekhar 1951) SFR =  M box /t ff where  = 0.3 or 1  = 1  = 0.3 ~ 1 order of magnitude predictions SFRs derived from input SN rates Compare estimated SFR to input SN rates Joung & MacLow 2006 (2 input supernovae rates: assuming 130 and 200 M sol required per SN)

28. Zurich, September 18 th 2007 Gotoh & Kraichnan (1993) found power law PDFs for 1D sims of Burgers flows ⇒ infinitely compressible flows no fbk, with s-g M rms =11.8 M rms =5.1 M rms =5.2 M rms =5.8 Is that because they ignore self-gravity in their model? (Slyz et al. 2005)

29. Zurich, September 18 th 2007  v contracting t cool cooling rapidly  >  thresh -> dense T cold m * = ε ρ gas V cell ∆ t/t dyn Heyer et al. 1998 if the gas satifies: (FCRAO CO survey) Cen & Ostriker 1992 First make stars... A

30. Zurich, September 18 th 2007 Then do stellar feedback... Calculate a time dependent SFR: Stellar winds: f ∆ m SF returned to gas Supernovae:  ∆ m SF c 2 injected as thermal energy  m SF (t) = m * (t-t * )/ т 2 exp [-(t-t * )/ τ ] where τ = max(t dyn, 10 Myr) Cen & Ostriker 1992  1.28 kpc  100 pc @ 10 Myr if v=10 km/s f,  determined by IMF

31. Zurich, September 18 th 2007 4.5 Myr 22 Myr 41 Myr Slyz, Devriendt, Bryan, Silk (2005) Non-instantaneous feedback pressuretemp density

32. Zurich, September 18 th 2007 4.5 Myr 22 Myr 41 Myr Slyz, Devriendt, Bryan, Silk (2005) Instantaneous feedback pressuretemp density

33. Zurich, September 18 th 2007 When put supernova thermal energy E SN = 10 51 ergs in dense regions most of the energy is quickly radiated away? Get neither thermal or dynamical heating (Katz 1992) Fixes: 1)artificial time delay in cooling (Gerritsen 1997; Thacker & Couchman 2001; Governato et al. 2006) 2)assign explosion energy to fluid parcels as pure kinetic energy (Navarro & White 1993) 3)introduce a thermalization efficiency whereby assign some fraction of supernova energy as kinetic and some as thermal (Navarro & White 1993, Hernquist & Mihos 1995) 4)sub-grid models of multi-phase ISM (Yepes et al. 1999, Springel & Hernquist 2003) Is this the same old story... ?

34. Zurich, September 18 th 2007 Time evolution of density PDF green: inst fbk, black: non-inst fbk

35. Zurich, September 18 th 2007 Time evolution of energy spectra compressible solenoidal ratio ∇ ⋅ v sol = 0 ∇ ✘ v com = 0 no s-g no fbk s-g no fbk no s-g fbk s-g fbk

36. Zurich, September 18 th 2007 Time evolution of energy spectra compressible solenoidal ratio ∇ ⋅ v sol = 0 ∇ ✘ v com = 0 no s-g no fbk s-g no fbk no s-g fbk s-g fbk Instantaneous feedback

37. Zurich, September 18 th 2007 Comparison of inputs into Silk prescription with non-instantaneous fbk, with gravity with non-instantaneous fbk, no gravity Different physics no fbk, no gravity no fbk, with gravity 0.8 0.6 0.4 0.2 0.0 SFR (M sun /yr) Porosity log 10 (M sun /pc 3 ) MW (km/s) 0 100 200 300 time (Myr) 5432154321 -1.5 -2.0 -2.5 -3.0 40 30 20 10 0 with instantaneous fbk, with gravity Q = SFR G -1/2 ρ gas -3/2 ( σ gas / σ f ) - 2.72

38. density temp pressure temp pressure Slyz, Devriendt, Bryan, Silk (2005) 4.5 Myr 22 Myr 41 Myr 0 100 time (Myr) 0.2 0.4 0.6 0.8 200300 non-instantaneous feedback instantaneous feedback SFR (M sun /yr) Zurich, September 18 th 2007 Effect on star formation rate

39. Zurich, September 18 th 2007 Time evolution of density PDF green: inst fbk, black: non-inst fbk

40. Zurich, September 18 th 2007 Vazquez-Semadeni, Gazol, Scalo 2000 log  log (number of cells) How to erase a thermal instability… 1 kpc 2 box  >  thresh   v < 0 heat for 6 X 10 6 yrs to mimic « photo- ionization » P(k) ∝ k -4 vs Small scale forcing Large scale forcing

41. Zurich, September 18 th 2007 Time evolution of density PDF non-instantaneous feedback run

42. Zurich, September 18 th 2007 Time evolution of density PDF non-instantaneous feedback run SFR ~85 Myr Time →

43. Zurich, September 18 th 2007 Time evolution of density PDF non-instantaneous feedback run

44. Zurich, September 18 th 2007 Time evolution of density PDF green: inst fbk, black: non-inst fbk

45. Zurich, September 18 th 2007 Time evolution of thermal phase diagrams Initial conditions

46. Zurich, September 18 th 2007 Time evolution of thermal phase diagrams Initial conditions

47. Zurich, September 18 th 2007 Thermally unstable regime

48. Zurich, September 18 th 2007 Lines of constant pressure (k B -1 cm -3 K)

49. Zurich, September 18 th 2007 1D cut Density, pressure x-velocity 2D pressure map Accretion shock! X (kpc)

50. Zurich, September 18 th 2007 Different philosophies for adding supernovae explosions in ISM models m * =  ρ gas V cell ∆ t/t dyn + Stellar Initial Mass Function Calculate energy and mass returned to interstellar medium via supernovae and stellar winds Model star formation Model observed supernovae rates & mimic their distribution (e.g. isolated, clustered) e.g. SN frequency Milky Way Galaxy:1/330 yr -1 for Type I and 1/44 yr -1 for Type II (Tammann et al. 1994) Scale heights: Type I :325 pc (Heiles 1987) Type II :90 pc Power law distribution of superbubbles: dN B ~ n * -2 dn * (Kennicutt et al. 1989, McKee & Williams 1997) A B

51. Zurich, September 18 th 2007 How can we begin to capture the complicated gas physics in a cosmological simulation? HORIZON Marenostrum Simulation ~ 1 billion DM particles ~1 billion cell root grid (3 -6 AMR levels) 50h -1 Mpc ~ 1.5 kpc physical resolution

52. Zurich, September 18 th 2007 e.g. For a given star formation rate do a high res simulation of a stratified disk to measure the efficiency of the energy transfer of a superwind, then use result as a subgrid model in a cosmological simulation. Enourmous parameter space! How many boxes do you have to simulate to capture conditions of ISM in different environments, at different redshifts, with different IMFs etc. How to make progress? Run many local models at high resolution and use them to construct subgrid-models 1

53. 9 h -1 Mpc spatial resolution ~ 1 pc (physical) on finest level 3 h -1 Mpc 128 root grid, 3 nested grids 11-15 AMR refinement levels AMR « resimulations » … Zurich, September 18 th 2007 Slyz & Devriendt (in prep) 2

54. Zurich, September 18 th 2007 No single density threshold  th for gravitational collapse? small subbox ~ 4 pc large subbox ~ 32 pc  th depends on scale on which collapse occurs Joung & Maclow 2006

55. Zurich, September 18 th 2007