Star formation simulations -> N=10000……. Cathie Clarke, I.O.A. cf special issue Phil. Trans. Roy. Soc., ed. De Grijs,Ch.3,arXiv:

Simulations useful iff: Agree on model ingredients: Agree on model ingredients: Codes numerically reliable Codes numerically reliable Codes contain necessary physics Codes contain necessary physics  E_grav E_turb E_mag E_therm See Federrath et al 2010 Stellar feedback 

LARGE SCALE SIMULATIONS TO DATE Klessen 2001, Schmeja & Klessen 2004, 2006, Klessen 2001, Schmeja & Klessen 2004, 2006, Bate et al 2002,2003, Bonnell et al 2003,2004, 2006,2008, Clark & Bonnell 2004, Clark et al 2008, Bate et al 2002,2003, Bonnell et al 2003,2004, 2006,2008, Clark & Bonnell 2004, Clark et al 2008, Bate 2009 a,b Bate 2009 a,b Ionisation feedback Dale et al 2005,2007 Gritschneder et al 2009 Stellar winds:Dale & Bonnell 2008 Magnetic fields Price & Bate 2009 Radiative transfer Price & Bate 2009     “VANILLA CALCS.” 

“VANILLA” CALCS: Gravity+`turbulence’+ Barotropic e.o.s: ( approx. isothermal at  < 10^{-13} g/cm^3) No stellar feedbackB=0 

The largest simulation yet M = 10^4 M_sun Note total duration of simulation= 0.5 Myr Bonnell et al 2008

Hierarchical cluster formation Clusters identified with `minimum spanning tree’ Maschberger et al 2010

Cluster properties Mass spectrum Cluster shape Mildly aspherical (set by interplay of mergers and relaxation)

Cluster Properties Strong segregation of most massive stars by age of 0.5 Myr Histogram of fractional radial ranking of most massive star in cluster - strong preference for inner quartile for clusters with N > 50 …….though mergers temporarily disarrange mass ordering Technically not primordial - result of relaxation and mergers

Star Properties: the IMF IMF with initial mean Jeans mass of 5 and Larson e.o.s. Can characterise by piecewise power laws - steeper at high mass  For isothermal e.o.s, IMF `knee’ set by mean Jeans mass of initial cloud  Break dependence on cloud properties by introducing mild departures from isothermal e.o.s. (Larson 2005, Bonnell et al 2006) 

The upper tail of the IMF ~ Salpeter overall but slightly flatter within clusters Two reasons: a) mass segregation (lower mass stars in field) b) truncation of IMF within individual clusters * * = IGIMF effect cf Weidner & Kroupa 2006  All stars  All stars in clusters  Individual clusters IMF index Salpeter 

Virial state of clusters Surprise! Clusters are in ~ virial equilibrium when only consider the stellar potential  little gas on scale of stellar clusters  loss of gas wouldn’t unbind clusters but would inhibit cluster merging thereafter Kruijssen et al in prep.  bound  virialised

`Vanilla summary’: All stars form in (small N) clusters Some merge into successively larger clusters Successive mergers mainly affect upper end of IMF Bottom-up cluster formation: ( depending on cloud mass/ whether clouds are bound/efficacy of feedback) (maximum mass, slope of upper tail) HOW IS ALL THIS AFFECTED AS ADD EXTRA PHYSICS?

(non-ionising) thermal feedback (non-ionising) thermal feedback Forming protostars heat surrounding gas and inhibit excessive fragmentation in vicinity (cf Krumholz et al 2007) Bate 2009 Price & Bate 2009 (radiative heating doesn’t disrupt cores or prevent accretion onto them) Vanilla calcs over-predict bd:star ratio (3:2 cf 1:3 observationally (Andersen et al 2008): solved by feedback

SPH simulation of embedded ionising source Feedback surprisingly ineffective - bulk of cloud remains bound though energy absorbed by gas >> cloud binding energy Feedback surprisingly ineffective - bulk of cloud remains bound though energy absorbed by gas >> cloud binding energy Other feedback…. Dale et al 2005; see also Dale et al 2007

Stellar winds Stellar winds Main effect on upper end of IMF. Ineffective at cloud disruption (momentum coupling inefficient). Putting in feedbackDale & Bonnell 2008 No windIsotropic windsCollimated winds Unbound fraction changes from % when include winds Note lack of classic wind bubbles in heavily embedded phase

Magnetic fields Magnetic support reduces efficiency (fraction of cloud -> stars per ff time) Magnetic support reduces efficiency (fraction of cloud -> stars per ff time)  inc. field Price & Bate 2009 …perhaps offers opportunity for effective feedback  Inc. field

Larger N still: single cluster with N=3x10^4: Nbody6 +accretion New result: get accretion induced stellar collisions ! (cf BBZ 1998) New result: get accretion induced stellar collisions ! (cf BBZ 1998) Need large N if core shrinkage by accretion is to beat puffing up by two and three body interactions (Clarke & Bonnell 2008, Davis et al 2010) analytic Monte Carlo Model for Arches (cf Chatterjee 2010)? Moeckel & Clarke in prep. Doesn’t work at small N e.g. in ONC (Bonnell & Bate 2002) IMBHs in globular clusters….?