Joop Schaye (Leiden) (Yope Shea)

Transcription

1 Overview of sub-grid models in cosmological simulations Joop Schaye (Leiden) (Yope Shea)

2 Length Scales (cm) Subgrid models Cosmological simulations interparticle distance in stars interparticle distance in ISM interparticle distance in IGM stellar radii interstar distance star clusters galaxies clusters of galaxies observable universe

3 Length Scales (cm) Subgrid models Cosmological simulations interparticle distance in stars interparticle distance in ISM interparticle distance in IGM stellar radii interstar distance star clusters galaxies clusters of galaxies observable universe

4 Where to put the gap? Transition from warm (T ~ 4 K) to cold, molecular (T << 4 K) ISM expected at Σ H ~ M pc -2 (n H ~ -2-1 cm -3 in warm phase). Determined by dust column needed to shield UV Associated with sharp reduction in Jeans scale star formation Threshold decreases with metallicity and increases with UV (JS 04, Krumholz+ 11, Glover & Clark 12, Clark & Glover 13, ) Well-posed challenge: Resolve the Jeans scales down to the warm ISM

5 Basic resolution requirements Convergence requires resolving the Jeans scales: Resolving the warm phase requires: - Particle mass << 7 M - Spatial resolution << 1 kpc Resolving gas with n H ~ 1 cm -3 and T ~ 2 K requires : - particle mass << 3 M - spatial resolution << pc - Radiative transfer - Complex chemistry

6 The cold phase is still too demanding for cosmological simulations

7 Subgrid models for cosmological hydro simulations Radiative cooling/heating Star formation Chemodynamics/stellar evolution Black holes and AGN feedback Galactic winds driven by feedback from SF Less conventional things. E.g.: Turbulence (incl. mixing) Cosmic rays Dust

8 Radiative cooling Standard assumptions: H & He in photo-ionisation equilibrium (optically thin, UV background only) Metals in collisional ionisation equilibrium (though many studies still assume primordial abundances!) Recent developments (e.g. Wiersma, JS & Smith 09; Shen+ ; Vogelsberger+ 13, Aumer+ 13): Metals also in photo-ionisation equilibrium Relative abundance variations Cutting edge/future: Non-equilibrium ionization Radiative transfer Local radiation sources Molecules Dust

9 Cooling: effect of non-equil. and photo-ionisation n H = -4 cm -3, z=1, Z=Z Oppenheimer & JS (2013a)

10 AGN proximity zone fossils n H = -4 cm -3, T = 4 K, z=1, Z=Z Oppenheimer & JS (2013b)

11 AGN proximity zone fossils Most intergalactic metals may reside in out-of-equilibrium AGN fossil zones! n H = -4 cm -3, T = 4 K, z=1, Z=Z Oppenheimer & JS (2013b)

12 Standard approach: Star formation Schmidt volume density law with threshold Parameters tuned to match observed Kennicutt-Schmidt surface density law Stochastic implementation Power-law EoS for gas above SF threshold Recent developments: Pressure laws allow direct implementation of observed surface density laws w/o tuning (JS & Dalla Vecchia 08) Metallicity-dependent or only molecular gas (JS 04, Gnedin+ 09, Krumholz+ 09, JS+, Feldmann+ 11, Kuhlen+ 12, Christensen+ 12) Zoomed simulations: Higher thresholds Cold ISM physics ( * n g ) ( m * )

13 Kennicutt SF law = pressure law JS & Dalla Vecchia (2008)

14 Kennicutt SF law = pressure law JS & Dalla Vecchia (2008)

15 Kennicutt SF law = pressure law Pressure law reproduces observed surface density law independent of the EoS (which sets scale height) This it not the case for a volume density law! JS & Dalla Vecchia (2008)

16 Galactic winds driven by SF Winds may be: Energy-driven Momentum-driven Both Sources of energy/momentum: Supernovae Radiation pressure: On dust From photo-ionisation From trapping of Lyα Stellar winds Cosmic rays Combination of the above

17 Galactic winds driven by SF: WARNINGS Efficient feedback is required to match observations Feedback is often inefficient due to the numerical implementation but inefficient feedback is sometimes interpreted as a need for different physical processes Nearly all implementations are extremely crude (e.g. radiation pressure w/o radiative transfer) At the current resolution, the different feedback processes are hardly distinguishable Many hydro simulations use tricks that make them more like SAMs than you may think. E.g.: Wind velocity depends on halo mass or dark matter velocity dispersion (e.g. Okamoto+, Davé/Oppenheimer+, Viel+, Vogelsberger+) Temporarily turn off hydro for winds (e.g. Springel/Hernquist, Davé/Oppenheimer, Viel, Vogelsberger)

18 Implementing FB: recognized problems Simplest recipe: star particles inject thermal energy into surroundings (e.g. Katz et al. 1996) Recognized problems: Much of the mass in the ISM is in the cold phase (T << 4 K ) Simulations do not model cold phase intercloud density too high cooling rate too high feedback too inefficient SF insufficiently clustered feedback too inefficient

19 Driving winds: brute force solution Allow for a cold phase Increase SF threshold (only sensible for cold phase) Still require subgrid recipe, but on smaller scale Problem: need very high resolution Can only model a small number of galaxies (zoomed simulations) Need to pick initial conditions (e.g. merger history) (e.g. Ceverino & Klypin 07, Hopkins+ 12, Ceverino+ 13)

20 Driving winds: subgrid recipes Multiphase particles (e.g. Marri & White 93, Scannapieco, Murante, Aumer/White) Suppress cooling by hand (e.g. Gerritsen 97, Thacker, Stinson/Brook/Gibson/Governato/Maccio/Mayer/Wadsley/ ) Inject momentum (i.e. kinetic feedback) (e.g. Navarro & White 93, Springel/Hernquist, Davé/Oppenheimer, Teyssier, OWLS/GIMIC, Vogelsberger, ) Most relevant advantage: can decrease initial mass loading Temporarily decouple winds from the hydrodynamics (e.g. Springel/Hernquist 03, Davé/Oppenheimer, Viel, Vogelsberger, ) Multiple feedback processes (e.g. Stinson+ 13, )

21 Implementing FB: less recognized problems Reality: SNe (or BHs) inject lots of energy in very little mass High temperatures Long cooling times Efficient feedback Simulations: inject energy in large gas mass Low heating temperatures Short cooling times Inefficient feedback e.g. Kay+ 03; Booth & JS 09; Creasey+ 11; Dalla Vecchia & JS 12

22 Implementing FB: less recognized problems The SNII of an SSP of mass m * can heat a mass m g,heat by ΔT = 4x 7 K (m * / m g,heat ) Reality: m * >> m g,heat initially ΔT >> 8 K t c >> 8 yr (n H /1 cm -3 ) In simulations: m * ~ m g,heat ΔT ~ 6 K t c ~ 5 yr (n H /1 cm -3 ) overcooling Note that in simulations (m * / m g,heat ) is independent of resolution! Dalla Vecchia & JS (2012)

23 Implementing thermal FB: requirements FB only efficient if heated resolution elements expand faster than they cool radiatively: t c >> t s = h/c s where h is the spatial resolution Adiabatic expansion does not change t c / t s (assuming Brehmsstrahlung) Required T depends on density and resolution Dalla Vecchia & JS (2012)

24 Implementing efficient thermal FB: ΔT determined by resolution Stochastic FB (see also Kay+ 03) given ΔT, fraction of available energy that is injected, f th, determines heating probability f th not predicted, unresolved thermal losses need to be calibrated Dalla Vecchia & JS (2012)

25 Mass outflow rate: M halo Particle mass 7x 2 M t t c s 2/3 2 nh T cm K Max n H ~ 2 cm -3 insensitive to ΔT for ΔT 6.5 K Dalla Vecchia & JS (2012)

26 M halo, edge-on, gas density ΔT = 6.5 K ΔT = 7.5 K 17.5 kpc/h Dalla Vecchia & JS (2012)

27 Mass outflow rate: 12 M halo Particle mass 7x 4 M t t c s 2/3 2 nh T cm K Max n H ~ 3 cm -3 insensitive to ΔT for ΔT 7.5 K Dalla Vecchia & JS (2012)

28 12 M halo, edge-on, gas density ΔT = 6.5 K ΔT = 7.5 K 45 kpc/h Dalla Vecchia & JS (2012)

29 EAGLE: Evolution and Assembly of GaLaxies and their Environments Planck cosmology; 50, 0 Mpc boxes Jeans scale marginally resolved in warm ISM Gadget with Anarchy (pressure-entropy SPH, time step limiter,, Dalla Vecchia in prep) Improved OWLS subgrid physics Thermal feedback from SF, cooling not turned off Feedback efficiency function of metallicity (accounts for unresolved thermal losses) Naturally more efficient at lower mass and higher redshift Calibrated to observed z=0 galaxy mass function Virgo collaboration project Most active members: Booth, Bower, Crain, Dalla Vecchia, Frenk, Furlong, Jenkins, McCarthy, Rosas-Guevara, Schaller, Schaye (PI), Theuns

30 Hydro solvers vs subgrid variations Recently lots of good work on differences between AMR, moving mesh, standard SPH, fancy SPH Effect of hydro solver difficult to isolate because Different effective resolution Subgrid physics cannot be implemented identically Turning off feedback not a good solution as results unrealistic and hypersensitive to resolution At the current resolution, choice of hydro solver is generally much less important than choice of subgrid physics (e.g. Scannapieco+ 12) This should not be an excuse to do the hydro poorly

31 Different hydro solvers vs different subgrid physics Vogelsberger+ (2012) Vogelsberger+ (2013)

32 Cosmological hydro: Final thoughts Predictions for stellar properties and for ISM/CGM are currently limited by subgrid physics, particularly galactic winds Need to be careful about what questions to ask SPH vs AMR secondary issue Much to be gained from observations of gas around galaxies Predictions for intergalactic gas are more robust and limited by real physics, e.g. radiative transfer, non-equilibrium ionisation Large-scale simulations have become much better are reproducing observations thanks to: Better (more efficient) recipes for feedback from star formation AGN feedback Increased resolution The gap is starting to be closed from above using zoomed simulations (many talks this week)