IV. Chemo-dynamical Modeling of Galaxy Evolution

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1 IV. Chemo-dynamical Modeling of Galaxy Evolution Peter Berczik, Heidelberg, Beijing Andi Burkert, Munich Stefan Harfst, Berlin Joachim Köppen, Strasbourg Lei Liu, Heidelberg, Beijing Nigel Mitchell, Vienna Mikola Petrov, Vienna Sylvia Ploeckinger, Leiden Simone Recchi, Vienna Andreas Rieschick, Kiel Markus Samland, Basel Rainer Spurzem, Heidelberg, Beijing Christian Theis, Mannheim Gerhard Hensler (University of Vienna) 1. Requirements for Modeling Galaxy Evolution Highest self-consistency: lowest # of free parameters represent kinematics and energetics of ISM components most realisticly: single phase vs. 2-3 components? include most actual astrophysical processes (stellar evol., gravitation, yields, etc.) treat dynamical, energetic and materialistic plasma physical processes properly and inherently: coupling of components large-scale dynamics heating different cooling timescales gas-phase mixing processes star-gas interactions trace chemical enrichment by processes and timescales! Initial conditions (from cosmol. models and/or observations) include environmental effects! chemo-dynamical treatment 1

2 gas stars Gas dynamical Models of Disk Formation+Evolution Analytical models (inconsistent) 2d HD grid (single gas, general Z): Larson 1974, 75, 76 Burkert & Hensler 1987, 88 General results: o Gas clumps are condensing and assembling in the gravitational field of Dark Matter o a gaseous disk forms o halo stars develop vel. anisotropy o Central concentration forms early Request to the treatment of the ISM Small scales (subgrid): Clumpy structure (mol. Clouds) Star formation Energetic and matter feedback + SF self-regulation Cooling vs. heating: stellar radiation + winds Gas phase transitions: heat conduct., dynam. Instab., turbulent mixing Chemical abundances Intermediate scale: WNM/WIM diffuse intercloud medium Supernova explosions Dynamical gas interactions Large scale: Radial gas streaming by non-axisymmetric perturbations Superbubbles galactic winds Gas infall 2

3 2. Dynamical schemes for gal. evol. different numerical strategies (SPH vs. grid) possible. Lagrangian treatment: Eulerian description: Follow gas packages motion Simple gas dynamics Fluid through a fixed (or moving) grid Comparison of HD codes Agertz et al

4 2.2. Numerical modelling of galaxy formation and evol. (in a cosmological context) 1. Step: Purely gravitational N-body simulations are applied to the Cold Dark Matter mass assembly on cosmological scales. 2. Step: Inserting gas physics into DM halos; different numerical codes (SPH vs. grid): star formation recipes, heating and cooling prescriptions 4

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6 2.3. Hydrodynamical treatment of gas with SPH For reasons of ease a particle description is most suitable. smoothing length h, sphere with radius 2h, containing N=32 neighboring particles j. = mass density of particle i. = divergence of the velocity field (at pos. of part. i): SPH system of equations 6

7 Briggs 2012, MSc thesis Christensen et al. 2010, ApJ, 717 Gravitational softening Larger grav. softening length decreases early SFR and delays the SF. DM part. number affects SFR. For 1000 DM part.s softening length affects the SFR Grid system of equations advection terms important! 2D: 7

8 Numerical grid method allowing for substructure resolution Adaptive-mesh refinement with FLASH of an IS cloud in streaming hot plasma in 2D projection of the block structure of levels 1-4. Each is subdivided into 8x8x8 grid cells. Density colour code in units of g cm -3 (from S. Ploeckinger, 2009, master thesis, Univ. of Vienna) 3. SF criteria in numerical models: ~ subgrid physics because the star formation cannot be spatially resolved!!! SF crit no global value! Dep. on cloud mass T SF T crit no global value! Dep. on cl mass M cl M J M J to some extent not fulfilled div v 0 sometimes dropped; not in multi-phase cool < dyn (self-gravity) 8

9 Parameters controlling Star-formation Star-formation dependence KS law: ( ) 10 g SF efficiency * εsf ff Dependence on mol. fraction: SF Stellar feedback Stellar radiation and wind energy Supernova energy efficiency SF k * g g t t 4 Ms pc g 2, SN 1.5 g f (f fb H 2 for ) M s yr g 1 kpc 2 crit Effects of SF criteria on SFR Hopkins et al. (2013) MN, 432 t/gyrs log n(cm -3 ) 23 9

10 3.1. (Cosmological) Models with SPH Gas particle masses: few 10 8 M ; i.e. M J not resolved, always fulfilled! Problem I: SF criteria Kay et al. 2002, MN, 330 Higher overdensity threshold decreases the baryonic star fraction only slightly, but delays the SF. Higher crit leads to higher gas fraction. Kay et al. 2002, MN,

11 3.2. SF application to galaxy scales with SPH Stinson et al. (2006) = K : SPH particles as IS clouds Larson 1981 n(h 2 )(cm -3 ) = 3400 L(pc) M L 2 Rivolo & Solomon (1988): R cl (pc) = 50 [M/ (10 6 M )] ½ 11

12 Problem II: mass refinement: High mass resolution leads to low-mass gas particles: Jeans criterion hardly fulfilled crit should fulfill Larson s laws stellar IMF hardly filled E E E+8 Consequences for energy release (e.g. SNeII) and for chemical yields Stinson et al. (2006) MN, 373 total baryonic mass: M b = M larger N larger SFR higher crit smaller SFR lower T max smaller SFR SFR oscillates if M J resolved 12

13 3.4. High-resolution numerical simulations of the evolution with star-gas interactions Problems III-VII: III. Star-formation efficiency: varied between 1-10% and chosen in agreement with plausible model SFRs IV. Overcooling, because surrounding gas density too high cooling too fast V. Supernova energy distribution: How many neighbouring part.s or grid cells? VI. SN energy amount: SN efficiency! VII. Importance of immediate SF self-regulation by SW, Ly c? The effect of starformation efficiency on the disk evolution The change of the SFE by one o.o.m. ( = ) drives an extraordinary galactic wind and destroys the gas disk. Figs. after 377 Myrs. 60 kpc gas T P stars Tasker & Bryant, 2008, ApJ, 673,

14 Massive stars affect ISM + galactic evolution most dominantly Energy: enormous luminosities in all evolutionary stages Feedback: energy input vs. cooling negative star-formation feedback Dynamics: energy release stirs-up the ISM gas compression, turbulence, mixing, galactic winds star-formation feedback positive + negative Chemistry: rapid release of mainly elements thru supernovae type II, but also CNO by winds during their lifes consequences for early enrichment of the Universe 3.5. Stellar Feedback Supernovae typeii Superbubbles ISM Galaxies energetic (~10 51 ergs) dynamic chemical heating by E kin +E th turbulence, compression yields (st.evol.) + SF regulation star formation metal enrichment galactic wind metal reduction 14

15 Numerical Conditions for Galactic Winds Variations of the thermal SN feedback: Extreme T s let drive strong winds, but unreal. Dalla Veccia & Schaye (2008) Can strong Galactic Winds solve the CDM cusp/core problem? Loss of low-ang.mom. gas! (2010) Nature, 463 (2012) MNRAS, 422 Too large SNE ~100% + kin. Energy! NO solution; also metall. mismatch! 15

16 SF feedback lost by overcooling Cosmological models: SPH, single-phase ISM, simple SF treatment issues: on average, Kennicutt-S. law is fulfilled over a sample of models; However: no-feedback (NF) models produce the same! Big surprise? Kennicutt-S. law general? Overcooling problem!! Kravtzov (2003) ApJ, 590 SN mass factor (β) recipe cooling is disabled for gas particles surrounding a star particle within a sphere of mass βm SNII. cooling is deactivated for a fixed amount of time τ CS contains the mass β M SNII 16

17 SN feedback mass factor (β) β model for higher values of β: more gas particles have their radiative cooling disabled fewer stars form! contains the mass β M SN II Stinson et al. (2006) MN, 373 lower SFE smaller SFR For M b = M and part.s: M SPH = M longer CST smaller SFR 17

18 Blastwave recipe R E Feedback Type II Supernovae Problems: Energy distributed beyond the blast radius gets quickly radiated off: therefore, only gas particles inside the blast sphere get heated up. Metals and masses are distributed over the whole smoothing sphere (would lead to spurious allocations otherwise). Kernel function applying energy only to gas particles which have their cooling disabled. However, not a totally free para.: Range of mass distribution must be limited to expans./diffus. length! 18

19 SN energy efficiency: E SN blastwave model E SN has no huge impact on the SFR. Feedback works more efficient for SN energy only applied to the gas particles which have their cooling disabled. High SFR due to delayed SNII regulation! Therefore: 4. Heating of the ISM by massive stars during their lifetime Same idea, see: Murray et al. (2010) ApJ, 709 Hopkins et al. (2011) MN, 417 with: Already done in cd models!! See: Hensler (1987) Mitt. AG, 70, 141 Theis, Burkert & Hensler (1992) A&A, 280 Samland, Hensler & Theis (1997) ApJ, stellar wind + radiation 19

20 ENZO (gas) + PM (stars): Slyz et al. (2005) MN, 356 feedback enhances porosity and T, contrasts Energy feedback comparison studies of ISM structure of 2 schemes: MUGS vs. MaGICC (but diff. parameters!) M gal M M SPH M crit /cm SF.05 IMF Kroupa Chabrier SN R e /pc 100 CS /Myr 10 Stellar rad. no 1% 20

21 SFR dependence of a 10 9 M DG Briggs 2012, MSc thesis 5. Drawbacks of single-phase cd models Models up to now: Playing with free parameters If parameters fixed, then for isolated galaxy models SFR = f(infall)? Metal mixing + energy deposit to 1 gas phase Gas dynamics according to averaged force terms 21

22 Single-phase cd DG models Drawbacks: low SFR distributed over the disk fractions of IMF, less energy feedb. released abund.s mix locally; low metal. loss, high Z; physical state of the ISM? Valcke et al. (2008) MN, 389 Caution: single-gas phase collapse of a ge 1D, single gas phase with SF, stellar dm/dt + Z Exercise: mix 10 4 K gas with hot gas refilled by stars of Salp. IMF and SFE of 1%; same for released metals gas collapse cont.s until hot gas energy dominates 22

23 Disk formation with chemical abundances: details question. spatial resol. and 1-phase mixing are insuff. for derived conclus. Brook et al. (2012) MN, 426 Disk models with IMF + FB variations Pilkington et al. (2012) MNRAS,

24 Disk models with infall/outflow Brook et al. (2014) MNRAS, phase treatm. produces low-z outflows 6. 2-phase Chemo-dynamical Treatment Clouds: formation collisions CNM M<10 4 M o T100 K. M. E cooling cooling HIM T10 5 K dissipation WNM, WIM M M o T K evaporation condensation C,N star formation O,Si...Fe Fe planetary nebulae SNeII SNeIa low-mass stars M o intermediate-mass stars 1-10 M o WD massive stars, M o NS BH remnants Gerhard Hensler, Univ. Vienna 24

25 Chemodynamical Models 1d: vertical gal. disk structure Burkert, Truran, G.H. (1992) ApJ, 391, 651 giant ellipticals Theis, Burkert, G.H. (1992) A&A, 265, 465 dwarf ellipticals G.H., Theis, Gallagher (2004) A&A, 426, 25 2d: disk galaxies Samland, G.H. (1996) Rev. Mod. Astron. 9, 277 Samland, G.H., Theis (1997) ApJ. 476, 544 dwarf irregular gal.s G.H., Rieschick (1998) ASP, 147, 246 G.H., Rieschick, Köppen (1999) ASP, 187, 214 Rieschick, G.H. (2000) ASP, 215, 130 G.H. (2001) ASP, 245, 401 G.H., Rieschick (2002) ASP, 245, 381 Recchi & G.H. ((2006) A&A, 445, L39 Recchi, G.H., et al. (2006) A&A, 445, 875 Recchi & G.H. (2007) A&A, 476, 841 3d: dirrs Berczik, G.H., Theis, Spurzem (2003) Ap&SS, 284, 465 (cdsph) Harfst, G.H., Theis (2006) A&A, 339, 509 Liu, Petrov, G.H.,, Spurzem, Berczik (2014) A&A, subm. Mitchell, Vorobyov, G.H. (2013) MNRAS, 428, 2674 (cdflash) 25

26 Chemodynamical Ingredients cooling function Boehringer & G.H. (1989) A&A, 215, 147 self-regulated star formation Köppen, Theis, G.H. (1995) A&A, 296, 99 Köppen, Theis, G.H. (1998) A&A, 328, 121 energy release by massive stars Freyer, G.H., Yorke (2003) ApJ, 594, 888 Freyer, G.H., Yorke (2006) ApJ, 638, 262 Kroeger, G.H., Freyer (2006) A&A, 450, L5 G.H. (2007) EAS Publ. Ser., 7, 113 Recchi & G.H. (2006) Recchi & G.H. (2007) A&A, 477 cloud coagulation Theis & G.H. (1993) A&A, 280, 85 gas-phase interactions Vieser & G.H. (2007) A&A, 472, 141 Vieser & G.H. (2007) A&A, 475, 251 Arnold & Hensler (2014) in prep. most cd processes are self-regulated!! 6.1. cdsph model Z DM halo Vrot hot gas Y Harfst, Theis, G.H. (2006) A&A, 339 X Berczik, G.H., Theis, Spurzem (2004) Ap&SS, 284 Liu, Petrov, G.H., Spurzem, Berczik (2014) A&A, in subm. cold gas clumps 26

27 SPH/sticky-particle scheme HOT: SPH COLD: sticky part. + Visc STAR: N-body + SSP Harfst, Theis, Hensler (2006) A&A, 339, 509 (2002) 2 gas-phases with self-regul. But: upper temp. limit at 10 5 K, i.e. no hot gas, too rapid cool. no metallicity trace no gas-phase interactions: dynamical, energetic SF criteria: crit, converg.flow 27

28 6.2. The Multi-Phase interactions in SPH condensation/evaporation (Cowie et al., 1981) drag (ram pressure) (Shu et al., 1972) v cloud-cloud collisions (Theis & Hensler, 1993) Berczik, G.H. et al. (2004) 28

29 Star formation SF t 0 gas, Tgas M cl M low SF t 1 v(e SNII ) r(e SNII ) M cl gas, T gas M str,emb (M M cl,p cl ISM ) M cl gas, T gas t 0 t 1 t 2 Harfst, Theis, G.H. (2006) A&A, 339, 509 Elmegreen & Efremov (1997) cdsph applied to dirrs Liu et al. (2014) A&A subm. hot SPH particles cool cloudy particles stellar particles 29

30 Liu et al. (2014) A&A, subm. The effect of supernova efficiency The galactic wind mass loss depends on the SNII efficiency: DG of 10 9 M

31 Present-day observations cannot account for the historical galactic-wind mass loss, but chemical signatures can tell the story. The SF recipe alters the SFR. SN =1. = numerical grid treatment of cd cylindrical symmetry staggered grid, logarithmically stretched explicit/implicit code operator splitting, van Leer scheme 5 components (3 stellar, 2 gaseous) 7 variables/component (hot gas: 5) + R cl, f CM 22 transition rates: death rates for 16 stellar mass intervals 6 gas trans.: cond./evap., SFR, 2 cooling rates, drag force spatial resolution ~ pc Further numerical studies of involved problems: energy deposit of massive stars into the ISM clouds in a hot plasma mixing processes 31

32 6.4. Solving for the Moments of the Collisionless Boltzmann Equation Collisionless Boltzmann equation describes the distribution of a collection of collisionless particles in velocity phase space. f t v i f x i x i f v i 0 n f x, v, tdv Moments of the collisionless Boltzmann equation can be obtained by integrating over velocity space and making a few assumptions: Adopts a Schwarzschild velocity ellipsoid (1979) agrees with local system observations v v i j vk f x, v, t Aexp i j k Zero heat flux approximation applied to close the set of equations. The collisionless equations (right) compare closely with the Euler equations (left) for a collisionally dominated gas: Euler Equations v 0 t vi viv j P g t E i t E Pv v g The velocity dispersion tensor acts like the thermal pressure force in a standard collisional gas except that it allows anisotropy and shear. Stellar Hydrodynamics Equations v 0 t vi viv j ij g t Eii ii ii i t 2 2 E xx ij 2 E 2 v v g xy yy ii ii xz yz zz v i 32

33 6.5. Stars and Clouds continuity equation: Sources and sinks: star formation, stellar death, cloud formation, condensation momentum equations: energy equations (also for rr, ff ) : tilt of vel. ellipsoid: cloud collision rate: 6.6. Hot Gas continuity equation: Sources and sinks: supernovae, evap./condens. momentum equations: energy equations: Poisson equation for all components + static Dark Matter halo 33

34 6.7. ingredients cloud coagulation: energetic SF feedback massive stars: supernovae: ergs/sn (5% for CM accel., 95% thermal en. further data Star formation: see before Initial Mass Function: see before Stellar energy release: see before Stellar lifetime: Yields: Drag force: see before see before Heat conduction:see before 34

35 The matter cycle in multi-phase cd Samland, G.H., Theis (1997) ApJ 476, MWG cd model ICM CM after 3 Gyrs Samland, G.H., Theis (1997) ApJ 476, 544 stars form at first in an ellipsoidal halo the cloudy gas collapses dissipatively the central density enhancement forms the bulge hot SNII gas expands still infalling clouds are polluted with metal-rich SNII gas due to condensation a gaseous disk forms further infall of environmental gas 35

36 Star Formation Rates 2 kpc 2 kpc 2 kpc Samland, G.H., Theis (1997) ApJ 476, 544 Metallicity gradients outflow of hot metal-rich SNII gas condensation of metal-rich gas on infalling clouds leads to inwards moving enhancement rim temporarily constant radial O abundance (see Edvardsson et al. 1993) formation of a radial O gradient after ~10 Myrs caused by central gas consumption and further gas infall at larger radii, but flat at small and large radii (see e.g. Vilchez & Esteban 1996, Rudolph et al. 1997) rim Samland, Hensler, Theis (1997) ApJ 476,

37 gas mixing processes Samland (1994) PhD thesis SN enrichment metall.decrease by infall or unprocessed stellar ejecta evaporation CM ICM condensation ICMCM Metallicity Distributions One global chemodynamical model fits the observed MDs of different regions in the MWG self-consistently and can account for: different effective yields metallicity variations the G dwarf problem Samland, Hensler, Theis (1997) ApJ 476,

38 abundance ratios Samland, Hensler, Theis (1997) ApJ 476, 544 the observed stellar O/Fe-O distribution is well reproduced by the chemodynamical model the temporal evolution of O/Fe in different regions of the MWG can be predicted Samland (1994) PhD thesis initial conditions: starting from the recombination time mass: M g = 10 9 M M s=0 r ini = 20 kpc DM: M (Burkert 1995) (r), L/M(r) d cd models of dirrs with stellar HD on a grid questions: Mass and element loss? SF self-regulation? Local gas mixing? 2 kpc evolution: collapse sets in due to dissip. + cooling ISM phases approach equlibrium different evolutionary phases G.H., Rieschick (1998) G.H., Rieschick, Köppen (1999) Rieschick, G.H. (2000) G.H. (2001) G.H., Rieschick (2008) 38

39 Brightness of Stellar Components massive stars low-mass stars Local Gas Mixing vs. Large-scale Circulation problems: Abundances determined from HII regions Abundances of which component? SNII explosions have released What is the mixing time? additional metals. No DGs with pristine gas visible. Universal lower abundance threshold? or: No DG with first SF event? cond - evap parameter = cond + evap collapse phase (left), wind phase (half left); (for red =1, blue = -1.) wind phase: CM (half rigth), O CM (right) distributions 39

40 Gas mixing and cycles: metal self-enrichment star formation and resulting SNII explos.s: evaporation of local CM, mass-loaded flows condensation and sweep up of local gas in superbubble shells: local self-enrichment of star-forming regions by 25% outflow of hot SN-enriched gas: gradual mixing by condensation on slowly infalling (primordial) clouds enrichment timescales: for instantaneous recycling (locally 25%) = few 10 Myrs; for fall back (from above 3 kpc) > 1 Gyr Large-scale streaming + gas-phase mixing (2006) A&A, 445 In reality: blowaway almost impossible: gas halo, infalling clouds, turbulence metals retained Timescales of gas return cooling of blow-out hot gas and fall back: ~ Gyrs turbulent mixing: ~ 20 Myrs evaporative mixing: Myrs (Rieschick & G.H. 2002) 40

41 The dirr test case: NGC 1569 Cloud evaporation leads to mass-loaded flows (with N) and outflow; Condensation of expanding + cooling hot gas on infalling clouds leads to cloud enrichment; ISM is homogenized on scales up to 1 kpc (Kobulnicki & Skillman 97) Slow fall back of metal-enriched clouds; Remaining part: blowout, blowaway, stripping: What metal fraction goes to ICM? Best model with 3 SF epochs. Recchi, G.H., et al. (2006) A&A Galactic outflows and infalling clouds Suppression of galactic outflows? What happens to the freshly produced metals? Z of the galaxy increases or decreases? 41

42 Recchi & Hensler (2007) A&A, 477 Although clouds hamper the outflow by evaporated mass-loading, by this, reducing the metal loss, over-running clouds pierce holes into the superbubble shell: nozzle-like outflows are facilitated. In NGC 1569 and I Zw 18 the high star formation is fed by gas infall Infalling gas can hamper the outflow by drag and evaporation. Superbubbles interact with embedded clouds! see Recchi & Hensler (2007) A&A, 476 Recchi & Hensler (2007) A&A,