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Adrianne Slyz

Lessons on ISM modelling from kiloparsec scale simulations. Adrianne Slyz. University of Oxford. Zurich, September 18 th 2007. What physical processes regulate …. Kennicutt (1998). starbursts.

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Adrianne Slyz

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

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

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

  4. Key insights from periodic box simulations in the 90’s: 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) 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) Zurich, September 18th 2007

  5. Initial conditions Homogeneous gas ρ= 1 at/cm3 1.28 kpc T = 105 K Turbulent velocity field imposed on large scales P(k) ∝ k-4 1.28 kpc 1.28 kpc Periodic boundary conditions Zurich, September 18th 2007

  6. Initial conditions Homogeneous gas ρ= 1 at/cm3 1.28 kpc T = 105 K Turbulent velocity field imposed on large scales P(k) ∝ k-4 1.28 kpc 1.28 kpc Periodic boundary conditions Zurich, September 18th 2007

  7. Radiative cooling -21 -22 -23 -24 -25 -26 log10(T) ergs cm3/s 3 4 5 6 7 8 T (Kelvin) White and Sarazin (1987), Rosen and Bregman (1995) Zurich, September 18th 2007

  8. PDF = 1___ (2 π)1/2σ - (lnρ- < lnρ>) 2 2σ2 exp with σ= ln 1 + (Mrms/2)2 log10(normalized PDF) log10gas - <log10gas> ( ) [ ] (Padoan & Nordlund 2002) Zurich, September 18th 2007

  9. PDF = 1___ (2 π)1/2σ - (lnρ- < lnρ>) 2 2σ2 exp with σ= ln 1 + (Mrms/2)2 log10(normalized PDF) log10gas - <log10gas> ( ) [ ] (Padoan & Nordlund 2002) Zurich, September 18th 2007

  10. PDF = 1___ (2 π)1/2σ - (lnρ- < lnρ>) 2 2σ2 exp with σ= ln 1 + (Mrms/2)2 log10(normalized PDF) log10gas - <log10gas> ( ) [ ] (Padoan & Nordlund 2002) Zurich, September 18th 2007

  11. PDF = 1___ (2 π)1/2σ - (lnρ- < lnρ>) 2 2σ2 exp with σ= ln 1 + (Mrms/2)2 log10(normalized PDF) log10gas - <log10gas> ( ) [ ] (Padoan & Nordlund 2002) Zurich, September 18th 2007

  12. PDF = 1___ (2 π)1/2σ - (lnρ- < lnρ>) 2 2σ2 exp with σ= ln 1 + (Mrms/2)2 log10(normalized PDF) log10gas - <log10gas> ( ) [ ] (Padoan & Nordlund 2002) Zurich, September 18th 2007

  13. fc =∫ ρPDF dρ ρth ∞ ∫ ρPDF dρ 0 Open questions Universal PDF? (Elmegreen 2002 Krumholz & McKee 2005 Wada & Norman 2007) ∞ Is there a clear density threshold for star formation? fraction of mass above th Zurich, September 18th 2007

  14. PDF = 1___ (2 π)1/2 σ - (ln ρ - < ln ρ >) 2 2σ2 exp Log-normal fit to high density end of run with stars, self-gravity, fbk ( ) log10(normalized PDF) < lnρ> = 3.9 ⇒ρpeak ≈ 50 at cm-3 σ= 1.22 ⇒Mrms= 3.1 log10gas (at/cm3) Zurich, September 18th 2007

  15. PDF for SN driven stratified segment of a disk 1 X 1 X 20 kpc density Probability Distribution Function (PDF) 10 8 6 4 2 1 0.5 0 -0.5 -1 -2 -4 -6 -8 -10 x-y plane PDF Z (kpc) n (cm3) Avillez & Breitschwerdt 2005 Zurich, September 18th 2007

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

  17. 3D isolated disks, 25-50 pc resolution New generation of ISM simulations density temperature pressure stars face-on view 7.5 PDF log Temp 2.5 0.001 1.0 1000  (Msol pc3) edge-on view Tasker & Bryan 2006 Zurich, September 18th 2007

  18. Different philosophies for adding supernovae explosions in ISM models A B Model observed supernovae rates & mimic their distribution (e.g. isolated, clustered) Model star formation m*=ρgasVcell ∆t/tdyn + Stellar Initial Mass Function 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: dNB ~ n*-2dn* (Kennicutt et al. 1989, McKee & Williams 1997) Calculate energy and mass returned to interstellar medium via supernovae and stellar winds Zurich, September 18th 2007

  19. B 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 Msun. Radius of this sphere Rexp ~ 7 pc to 50 pc Rexp Mexp = 60 Msun 3.) Redistribute mass in that sphere so that it has uniform density  = 3Mexp/(4  Rexp3) 4.) Inject thermal energy ESN = 1051 ergs evenly into the sphere NO mass ever removed to form a star Zurich, September 18th 2007

  20.  = 1 ~ 1 order of magnitude  = 0.3 predictions Compare estimated SFR to input SN rates SFRs derived from input SN rates Identify Jeans unstable boxes Mbox/MJ > 1 where MJ = <J3  = avg density in box J = (/G<)1/2tot tot = (<cs>2 + 1/3<2)1/2 (Chandrasekhar 1951) (2 input supernovae rates: assuming 130 and 200 Msol required per SN) SFR = Mbox/tff where  = 0.3 or 1 Joung & MacLow 2006 Zurich, September 18th 2007

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

  22. r > rthresh ->dense T < T thresh->cold A First make stars . . . Heyer et al. 1998 (FCRAO CO survey) m*= ερgasVcell ∆t/tdyn if the gas satifies: Cen & Ostriker 1992 v < 0->contracting t cool< t dyn->cooling rapidly Zurich, September 18th 2007

  23. 1.28 kpc  Then do stellar feedback . . . Cen & Ostriker 1992 Calculate a time dependent SFR: DmSF (t) =m*(t-t*)/т2 exp [-(t-t*)/τ] whereτ = max(tdyn, 10 Myr) Stellar winds: f ∆mSF returned to gas 100 pc @ 10 Myr if v=10 km/s Supernovae: ∆mSF c2 injected as thermal energy f, determined by IMF Zurich, September 18th 2007

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

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

  26. Is this the same old story. . . ? When put supernova thermal energy ESN = 1051 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) Zurich, September 18th 2007

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

  28. Time evolution of energy spectra s-g no fbk no s-g no fbk no s-g fbk s-g fbk compressible ∇✘vcom= 0 solenoidal ∇⋅vsol = 0 ratio Zurich, September 18th 2007

  29. Time evolution of energy spectra s-g no fbk Instantaneous feedback no s-g no fbk no s-g fbk s-g fbk compressible ∇✘vcom= 0 solenoidal ∇⋅vsol = 0 ratio Zurich, September 18th 2007

  30. Comparison of inputs intoSilk prescription Q = SFR G-1/2 ρgas-3/2(σgas / σf ) -2.72 0.8 0.6 0.4 0.2 0.0 SFR (Msun/yr) no fbk, no gravity 5 4 3 2 1 Porosity no fbk, with gravity -1.5 -2.0 -2.5 -3.0 Different physics withnon-instantaneous fbk, no gravity log10<ρ> (Msun/pc3) withnon-instantaneous fbk, with gravity 40 30 20 10 0 <σ>MW (km/s) withinstantaneous fbk, with gravity 0 100 200 300 time (Myr) Zurich, September 18th 2007

  31. Effect on star formation rate 4.5 Myr pressure temp density non-instantaneous feedback density 22 Myr pressure temp 0.8 0.6 41 Myr SFR (Msun/yr) 0.4 0.2 instantaneous feedback 0 100 200 300 time (Myr) Slyz, Devriendt, Bryan, Silk (2005) Zurich, September 18th 2007

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

  33. How to erase a thermal instability… 1 kpc2 box P(k) ∝ k-4 Large scale forcing log (number of cells) vs Small scale forcing > thresh v < 0 heat for 6 X 106 yrs to mimic log « photo- ionization » Vazquez-Semadeni, Gazol, Scalo 2000 Zurich, September 18th 2007

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

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

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

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

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

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

  40. Thermally unstable regime Zurich, September 18th 2007

  41. Lines of constant pressure (kB-1 cm-3 K) Zurich, September 18th 2007

  42. 1D cut Accretion shock! 2D pressure map x-velocity Density, pressure X (kpc) Zurich, September 18th 2007

  43. Different philosophies for adding supernovae explosions in ISM models A B Model observed supernovae rates & mimic their distribution (e.g. isolated, clustered) Model star formation m*=ρgasVcell ∆t/tdyn + Stellar Initial Mass Function 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: dNB ~ n*-2dn* (Kennicutt et al. 1989, McKee & Williams 1997) Calculate energy and mass returned to interstellar medium via supernovae and stellar winds Zurich, September 18th 2007

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