Star formation simulations -> Star formation simulations -> N=10000…….N=10000…….

Cathie Clarke, I.O.A.

cf special issue Phil. Trans. Roy. Soc. , ed. De Grijs,Ch.3,arXiv:0911.0780

Simulations useful iff:Simulations useful iff:• Agree on model Agree on model

ingredients:ingredients:

• Codes numerically reliableCodes numerically reliable

• Codes contain necessary Codes contain necessary physicsphysics

E_grav E_turb

E_mag E_therm

See Federrath et al 2010

Stellar feedback

LARGE SCALE SIMULATIONS TO LARGE SCALE SIMULATIONS TO DATEDATE

• 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,bBate 2009 a,b

Ionisation feedback Dale et al 2005,2007Gritschneder et al 2009

Stellar winds:Dale & Bonnell 2008

Magnetic fieldsPrice & Bate 2009

Radiative transfer Price & Bate 2009

“VANILLACALCS.”

““VANILLA” CALCS:VANILLA” CALCS:

GravityGravity

++

`turbulence’`turbulence’

++

Barotropic e.o.s:Barotropic e.o.s:

( approx. isothermal at ( approx. isothermal at < 10^{- < 10^{-13} g/cm^3)13} g/cm^3)

No stellar feedback B=0

The largest simulation yetThe largest simulation yetM = 10^4 M_sunM = 10^4 M_sun

Note total duration of simulation=Note total duration of simulation=

0.5 Myr0.5 Myr

Bonnell et al 2008

Hierarchical cluster Hierarchical cluster formationformation

Clusters identified with Clusters identified with

`minimum spanning tree’`minimum spanning tree’

Maschberger et al 2010

QuickTime™ and a decompressor

are needed to see this picture.

Cluster propertiesCluster properties

Mass spectrumMass spectrum

Cluster shapeCluster shapeMildly aspherical(set by interplay of mergers and relaxation)

Cluster PropertiesCluster PropertiesStrong segregation of most Strong segregation of most massive stars by age of 0.5 massive stars by age of 0.5

Myr 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 IMFStar Properties: the IMF

IMF with initial mean Jeans IMF with initial mean Jeans mass of 5 and Larson e.o.s.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)

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

The upper tail of the IMFThe upper tail of the IMF~ Salpeter overall but slightly flatter within clusters ~ 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 indexSalpeter

Virial state of clustersVirial state of clusters

Surprise! Clusters are in ~ virial equilibrium Surprise! Clusters are in ~ virial equilibrium when only consider the stellar potential when only consider the stellar potential little gas on scale of stellar clusters little gas on scale of stellar clusters loss loss of gas wouldn’t unbind clusters but would of gas wouldn’t unbind clusters but would

inhibit cluster merging thereafterinhibit cluster merging thereafter

Kruijssen et al in prep.

boundvirialised

`Vanilla summary’:`Vanilla summary’:

All stars form in (small N) clustersAll stars form in (small N) clusters

Some merge into successively larger Some merge into successively larger clustersclusters

Successive mergers mainly affect Successive mergers mainly affect upper end of IMF 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 (non-ionising) thermal feedbackfeedback

Forming protostars heat surrounding gas Forming protostars heat surrounding gas and inhibit excessive fragmentation in and inhibit excessive fragmentation in

vicinity (cf Krumholz et al 2007)vicinity (cf Krumholz et al 2007)

Bate 2009Price & Bate 2009

(radiative heating doesn’t disrupt cores or prevent accretion onto them)

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

Vanilla calcs over-predict bd:star ratio (3:2 cf 1:3 observationally (Andersen et al 2008): solved by feedback

SPH simulation of SPH simulation of embedded ionising sourceembedded ionising source

Feedback Feedback surprisingly surprisingly ineffective - ineffective - bulk of cloud bulk of cloud remains bound remains bound though energy though energy absorbed by absorbed by gas >> cloud gas >> cloud binding energy binding energy

QuickTime™ and a decompressor

are needed to see this picture.

Other feedback….

Dale et al 2005; see also Dale et al 2007

Stellar windsStellar windsMain effect on upper end of IMF. Ineffective at Main effect on upper end of IMF. Ineffective at

cloud disruption (momentum coupling cloud disruption (momentum coupling inefficient).inefficient).

Putting in feedback Dale & Bonnell 2008

No wind Isotropic winds Collimated winds

Unbound fraction changes from 8 - 14% when include winds

Note lack of classic wind bubbles in heavily embedded phase

Magnetic fieldsMagnetic fields

• Magnetic support reduces Magnetic support reduces efficiency (fraction of cloud -> efficiency (fraction of cloud -> stars per ff time)stars per ff time)

inc. field

Price & Bate 2009

…perhaps offers opportunity for effective feedback

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

Inc. field

Larger N still: single cluster with Larger N still: single cluster with N=3x10^4: Nbody6 +accretionN=3x10^4: Nbody6 +accretion

New result: get accretion New result: get accretion induced stellar collisions ! (cf induced stellar collisions ! (cf

BBZ 1998)BBZ 1998)

Need large N if core Need large N if core shrinkage by accretion is to shrinkage by accretion is to beat puffing up by two and beat puffing up by two and

three body interactionsthree body interactions

(Clarke & Bonnell 2008, Davis (Clarke & Bonnell 2008, Davis et al 2010)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….?