Report

Lessons on ISM modelling from kiloparsec scale simulations Adrianne Slyz University of Oxford Zurich, September 18th 2007 What physical processes regulate … log Σ SFR (Msol yr-1 kpc-2) Kennicutt (1998) starbursts centers of normal disks normal disks SFR Area ~ ∑gas1.4 log Σ gas(Msol pc-2) the rate at which gas turns into stars? Zurich, September 18th 2007 Link between density structure & star formation ? Zurich, September 18th 2007 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 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 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 Radiative cooling log10(T) ergs cm3/s -21 -22 -23 -24 -25 -26 3 4 5 6 7 T (Kelvin) 8 White and Sarazin (1987), Rosen and Bregman (1995) Zurich, September 18th 2007 log10(normalized PDF) log10gas - <log10gas> PDF = with σ = ln 1___ (2 π)1/2 σ [ 1 + (M rms exp /2)2 ] ( - (ln ρ - < ln ρ >) 2 2σ 2 (Padoan & 2002) ) Nordlund Zurich, September 18th 2007 log10(normalized PDF) log10gas - <log10gas> PDF = with σ = ln 1___ (2 π)1/2 σ [ 1 + (M rms exp /2)2 ] ( - (ln ρ - < ln ρ >) 2 2σ 2 (Padoan & 2002) ) Nordlund Zurich, September 18th 2007 log10(normalized PDF) log10gas - <log10gas> PDF = with σ = ln 1___ (2 π)1/2 σ [ 1 + (M rms exp /2)2 ] ( - (ln ρ - < ln ρ >) 2 2σ 2 (Padoan & 2002) ) Nordlund Zurich, September 18th 2007 log10(normalized PDF) log10gas - <log10gas> PDF = with σ = ln 1___ (2 π)1/2 σ [ 1 + (M rms exp /2)2 ] ( - (ln ρ - < ln ρ >) 2 2σ 2 (Padoan & 2002) ) Nordlund Zurich, September 18th 2007 log10(normalized PDF) log10gas - <log10gas> PDF = with σ = ln 1___ (2 π)1/2 σ [ 1 + (M rms exp /2)2 ] ( - (ln ρ - < ln ρ >) 2 2σ 2 (Padoan & 2002) ) Nordlund Zurich, September 18th 2007 Open questions fc = ∫ Universal PDF? ∞ ρ PDF d ρ ρth fraction of mass above th ∞ ∫0 ρ PDF d ρ (Elmegreen 2002 Krumholz & McKee 2005 Wada & Norman 2007) Is there a clear density threshold for star formation? Zurich, September 18th 2007 log10(normalized PDF) Log-normal fit to high density end of run with stars, self-gravity, fbk PDF = 2 1___ (ln ρ < ln ρ >) ( ) exp 1/2 (2 π) σ 2σ 2 < ln ρ > = 3.9 ⇒ ρpeak ≈ 50 at cm-3 σ = 1.22 log10gas (at/cm3) ⇒M rms = 3.1 Zurich, September 18th 2007 PDF for SN driven stratified segment of a disk 1 X 1 X 20 kpc density Probability Distribution Function (PDF) 10 8 6 4 x-y plane 2 1 0 -0.5 -1 -2 PDF Z (kpc) 0.5 -4 -6 -8 -10 Avillez & Breitschwerdt 2005 n (cm3) Zurich, September 18th 2007 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 3D isolated disks, 25-50 pc resolution stars New generation of ISM simulations temperature pressure face-on view density log Temp edge-on view 2.5 PDF 7.5 Tasker & Bryan 2006 0.001 1.0 1000 (Msol pc3) Zurich, September 18th 2007 Different philosophies for adding supernovae explosions in ISM models A Model star formation m* = ρgasVcell ∆t/tdyn + Stellar Initial Mass Function B 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 Calculate energy and mass returned to interstellar medium via supernovae and stellar winds Power law distribution of superbubbles: dNB ~ n*-2dn* (Kennicutt et al. 1989, McKee & Williams 1997) Zurich, September 18th 2007 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 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 =1 = 0.3 ~ 1 order of magnitude predictions J = (/G<)1/2 tot tot = (<cs>2 + 1/3<2)1/2 (Chandrasekhar 1951) SFR = Mbox/tff where = 0.3 or 1 (2 input supernovae rates: assuming 130 and 200 Msol required per SN) Joung & MacLow 2006 Zurich, September 18th 2007 Is that because they ignore self-gravity in their model? no fbk, with s-g Gotoh & Kraichnan (1993) found power law PDFs for 1D sims of Burgers flows ⇒ infinitely compressible flows Mrms=11.8 Mrms=5.1 Mrms=5.2 Mrms=5.8 (Slyz et al. 2005) Zurich, September 18th 2007 Heyer et al. 1998 A First make stars . . . (FCRAO CO survey) m = ε ρgasVcell ∆t/tdyn if the gas satifies: Cen & Ostriker 1992 * > thresh -> dense T < T thresh -> cold v < 0 -> contracting t cool < t dyn -> cooling rapidly Zurich, September 18th 2007 Then do stellar feedback . . . Cen & Ostriker 1992 DmSF (t) = m*(t-t*)/т2 exp [-(t-t*)/τ] 1.28 kpc Calculate a time dependent SFR: where τ = max(tdyn, 10 Myr) Stellar winds: f ∆mSF returned to gas Supernovae: ∆mSF c2 injected as thermal energy 100 pc @ 10 Myr if v=10 km/s f, determined by IMF Zurich, September 18th 2007 Non-instantaneous feedback 4.5 Myr density temp pressure 22 Myr 41 Myr Slyz, Devriendt, Bryan, Silk (2005) Zurich, September 18th 2007 Instantaneous feedback 4.5 Myr density temp pressure 22 Myr 41 Myr Slyz, Devriendt, Bryan, Silk (2005) Zurich, September 18th 2007 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 Time evolution of density PDF green: inst fbk, black: non-inst fbk Zurich, September 18th 2007 Time evolution of energy spectra no s-g no fbk s-g no fbk no s-g fbk s-g fbk compressible ∇ ✘ vcom= 0 solenoidal ∇ ⋅ vsol = 0 ratio Zurich, September 18th 2007 Time evolution of energy spectra no s-g no fbk Instantaneous s-g no s-g feedback no fbk fbk s-g fbk compressible ∇ ✘ vcom= 0 solenoidal ∇ ⋅ vsol = 0 ratio Zurich, September 18th 2007 Comparison of inputs into Silk prescription Q = SFR G-1/2 ρgas-3/2 (σgas / σf ) -2.72 0.2 0.0 5 4 3 2 1 Porosity (km/s) with instantaneous fbk, with gravity 0.4 -1.5 -2.0 (Msun/pc3) with non-instantaneous fbk, with gravity log10<ρ> with non-instantaneous fbk, no gravity 0.6 (Msun/yr) SFR no fbk, with gravity <σ>MW Different physics no fbk, no gravity 0.8 -2.5 -3.0 40 30 20 10 0 0 100 200 300 time (Myr) Zurich, September 18th 2007 Effect on star formation rate 4.5 Myr density temp pressure non-instantaneous feedback density 22 Myr 41 Myr 0.6 0.4 instantaneous feedback SFR (Msun/yr) 0.8 temp pressure 0.2 0 100 200 300 time (Myr) Slyz, Devriendt, Bryan, Silk (2005) Zurich, September 18th 2007 Time evolution of density PDF green: inst fbk, black: non-inst fbk Zurich, September 18th 2007 How to erase a thermal instability… log (number of cells) 1 kpc2 box P(k) ∝ k-4 Large scale forcing vs Small scale forcing > thresh v < 0 log Vazquez-Semadeni, Gazol, Scalo 2000 heat for 6 X 106 yrs to mimic « photoionization » Zurich, September 18th 2007 Time evolution of density PDF non-instantaneous feedback run Zurich, September 18th 2007 Time evolution of density PDF non-instantaneous feedback run ~85 Myr Time → Zurich, September 18th 2007 Time evolution of density PDF non-instantaneous feedback run Zurich, September 18th 2007 Time evolution of density PDF green: inst fbk, black: non-inst fbk Zurich, September 18th 2007 Time evolution of thermal phase diagrams Initial conditions Zurich, September 18th 2007 Time evolution of thermal phase diagrams Initial conditions Zurich, September 18th 2007 Thermally unstable regime Zurich, September 18th 2007 Lines of constant pressure (kB-1 cm-3 K) Zurich, September 18th 2007 1D cut Accretion shock! Density, pressure 2D pressure map X (kpc) Zurich, September 18th 2007 Different philosophies for adding supernovae explosions in ISM models A Model star formation m* = ρgasVcell ∆t/tdyn + Stellar Initial Mass Function B 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 Calculate energy and mass returned to interstellar medium via supernovae and stellar winds Power law distribution of superbubbles: dNB ~ n*-2dn* (Kennicutt et al. 1989, McKee & Williams 1997) Zurich, September 18th 2007 HORIZON Marenostrum Simulation ~ 1 billion DM particles ~1 billion cell root grid (3 -6 AMR levels) 50h-1 Mpc How can we begin to capture the complicated gas physics in a cosmological simulation? ~ 1.5 kpc physical resolution Zurich, September 18th 2007 How to make progress? 1 Run many local models at high resolution and use them to construct subgrid-models 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. Zurich, September 18th 2007 128 root grid, 3 nested grids 11-15 AMR refinement levels 3 h-1 Mpc spatial resolution ~ 1 pc (physical) on finest level Slyz & Devriendt (in prep) 9 h-1 Mpc 2 AMR « resimulations » … Zurich, September 18th 2007 No single density threshold th for gravitational collapse? large subbox ~ 32 pc small subbox ~ 4 pc th depends on scale on which collapse occurs Joung & Maclow 2006 Zurich, September 18th 2007 Zurich, September 18th 2007