Theories of Massive Star Theories of Massive Star FormationFormation

Ian A. BonnellIan A. BonnellUniversity of St AndrewsUniversity of St Andrews

Two IssuesTwo Issues• How do massive stars form?How do massive stars form?

• Problem of accretion versus radiation Problem of accretion versus radiation pressurepressure Once M > 10-40 MOnce M > 10-40 Moo

e.g. Wolfire & Casinelli 1986; Edgar & Clarke e.g. Wolfire & Casinelli 1986; Edgar & Clarke 20032003

c.f. Mark Krumholz’s talkc.f. Mark Krumholz’s talk

• Why do massive stars form?Why do massive stars form?• Why are some stars 100 x MWhy are some stars 100 x Mstar star ? ? • Where does the star’s mass come from ?Where does the star’s mass come from ?• Monolithic collapse versus competitive Monolithic collapse versus competitive

accretionaccretion

Radiation Pressure: Radiation Pressure: SolutionsSolutions

• I)I) Radiation beaming and disc Radiation beaming and disc accretionaccretion

• III)III) Stellar mergersStellar mergers n ~ 10 n ~ 1088 stars stars pcpc-3-3

• Binary mergersBinary mergers n ~ 10 n ~ 1066 stars pc stars pc-3-3 Many O stars in close binariesMany O stars in close binaries

Yorke & Sonnhalter 2002Yorke & Sonnhalter 2002

Krumholz et al 2005Krumholz et al 2005

Bonnell et al. 1998; Bonnell & Bate 2002; Bally & Zinnecker 2005Bonnell et al. 1998; Bonnell & Bate 2002; Bally & Zinnecker 2005

II)II) Rayleigh-Taylor instabilitiesRayleigh-Taylor instabilities accretion in high optical depth filamentsaccretion in high optical depth filaments

Bonnell & Bate 2005Bonnell & Bate 2005

Possible ModelsPossible Models• Monolithic CollapseMonolithic Collapse

• 1 core 1 massive star1 core 1 massive star• Pressure induced, in centre of clusterPressure induced, in centre of cluster• Slow, quasistaticSlow, quasistatic• Question: Do initial conditions exist? Fragment?Question: Do initial conditions exist? Fragment?

• Competitive AccretionCompetitive Accretion • Fragmentation: thermal Jeans mass : 1 MFragmentation: thermal Jeans mass : 1 Moo

• Multiple coresMultiple cores• Accretion from shared reservoirAccretion from shared reservoir• Dynamical, gravity drivenDynamical, gravity driven• Question: Does it work?Question: Does it work?

• Need predictions/testsNeed predictions/tests• Occam’s Razor: simplest solution bestOccam’s Razor: simplest solution best

McKee & Tan 2004

Zinnecker 1982;

Bonnell et al 1997, 2001, 2004

Massive Star formation: Massive Star formation: contextcontext

• Need to understand in context of Need to understand in context of low mass star formationlow mass star formation

• ~All massive stars form ~All massive stars form in clusters in clusters

Full IMFFull IMF• Mass segregatedMass segregated• Massive stars in centreMassive stars in centre• Too young for dynamical Too young for dynamical

2-body relaxation 2-body relaxation

• In BinariesIn Binaries With close massive companionsWith close massive companions

• Trapezium like systemsTrapezium like systems

M. McCaughrean

Stellar clusters and Stellar clusters and massive star formationmassive star formation

• Observed relation Observed relation of Mof Mmaxmax and M and Mclusclus, , stellar densitystellar density

• Causal ?Causal ?

• Not random Not random sampling of IMF?sampling of IMF?

Weidner & Kroupa 2005Weidner & Kroupa 2005

Testi et al. 1997

Stellar clusters and Stellar clusters and massive star formationmassive star formation

• Observed relation Observed relation of Mof Mmaxmax and M and Mclusclus, , stellar densitystellar density

• Causal ?Causal ?

• Not random Not random sampling of IMF?sampling of IMF?

Weidner & Kroupa 2005Weidner & Kroupa 2005

Weidner & Kroupa 2005

TurbulenceTurbulence• Clump formation in shock layers Clump formation in shock layers

• Structures part of larger scale flowStructures part of larger scale flow• Come and goCome and go

• Generate distGenerate distnn of of clump masses clump masses

• Higher massesHigher masses• Weaker shocksWeaker shocks

Padoan & Nordlund 2002

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• Density, width of shock:Density, width of shock: Clump massesClump masses

Ballesteros-Paredes et al 2006

• Inverse mass segregationInverse mass segregation• Higher-mass clumps most separatedHigher-mass clumps most separated

Elmegreen 1991; Padoan et al 1997

Turbulence and massive star Turbulence and massive star formationformation

• Upper-mass IMF too steep? Upper-mass IMF too steep? (Ballesteros-Paredes (Ballesteros-Paredes et.al. 2006)et.al. 2006)

• Worse with fragmentationWorse with fragmentation

• Star formation sets in at Star formation sets in at Jeans mass Jeans mass

• Turbulence crucial for structure Turbulence crucial for structure formationformation

• Seeds for gravitational fragmentationSeeds for gravitational fragmentation

Ballesteros-Paredes et al 2006Ballesteros-Paredes et al 2006Clark & Bonnell 2006Clark & Bonnell 2006

Turbulent cores Turbulent cores fragmentfragment

• Centrally Centrally condensed condensed turbulent coreturbulent core

• Fragments on Fragments on dynamical dynamical timescaletimescale

• How do such How do such cores form ?cores form ?

• Take many TTake many Tdyndyn

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Dobbs et al 2005

The Formation of a The Formation of a stellar clusterstellar cluster

Forms full IMF

Hierarchical :

Filaments fragment

Forms small-N clusters

Grow and merge

103 Msun in 1 pc

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MJeans = Msun

Stellar PropertiesStellar Properties• Forms 419 stars

• in 2.5 tff (5 x 105

years)

• ~ 10 final tdyn

• Mmax ~30 Mo

• MMaccacc ~ 10 ~ 10-4-4 M Moo/yr/yr

• Mmed ~ 0.5 Mo

Ste

llar

mas

s

Where does the mass Where does the mass come from?come from?1. Initial fragment

2. Envelope till next forming star

3. Outside : competitive accretion

Origin of stellar Origin of stellar masses masses

Fragmentation mass Fragmentation mass ~ Jeans Mass~ Jeans Mass

• Clump massClump mass • Accretion from Accretion from outside stellar clusteroutside stellar cluster

•Massive stars form due to accretion from large-scale reservoir

Bonnell, Vine & Bate (2004)

Competitive accretionCompetitive accretion• Accretion ratesAccretion rates

Cluster potential

Gas inflow

€

˙ M acc = πρvRacc2 ≈ πρ

GM*( )2

v 3

All local variables

Global Cloud

2 10-19 g/cm3

v 2 km/s

M* 0.1 Msun

10-9 Msun/yr

€

˙ M acc

Competitve accretion doesn’t work ?

Krumholz et al 2005

Competitive accretionCompetitive accretion

• Accretion ratesAccretion rates

Cluster potential

Gas inflow

€

˙ M acc = πρvRacc2 ≈ πρ

GM*( )2

v 3

All local variables

Global Cloud Local Cluster Core

2 10-19 g/cm3 10-17 g/cm3

v 2 km/s 0.5 km/s

M* 0.1 Msun 0.5 Msun

10-9 Msun/yr 10-4 Msun/yr

€

˙ M acc

Large range in possible

full IMF €

˙ M acc

Competitive accretionCompetitive accretion• Gas inflow due to cluster potentialGas inflow due to cluster potential

• to cluster centreto cluster centre• Higher gas densityHigher gas density

• Initially low relative velocitiesInitially low relative velocities• Turbulence locally smallTurbulence locally small• Small-N clustersSmall-N clusters

• Stars in centre accrete moreStars in centre accrete more Higher accretion ratesHigher accretion rates

massive stars massive stars Cluster potential

Gas inflow

All local variables

Massive star formation in a stellar cluster

Bonnell, Bate & Vine 2003 Bonnell, Vine & Bate 2004

Gas that forms most massive starFormation of a stellar cluster

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• Accretion starts in small-N clustersAccretion starts in small-N clusters• Low velocity dispersionLow velocity dispersion

• Short accretion timescale Short accretion timescale

• Attain ~higher masses before vAttain ~higher masses before vdispdisp highhigh

• Form massive stars in few 10Form massive stars in few 1055 years years

Bonnell & Bate 2006

€

tacc = M*˙ M acc

Observables: KinematicsObservables: Kinematics

• Line of sight velocities largeLine of sight velocities large due to due to projection effects projection effects

• Multiple clumps, extended gas structuresMultiple clumps, extended gas structures

Bonnell & Bate 2006

Accretion and Mass Accretion and Mass SegregationSegregation

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Stellar masses colour coded

Mass segregated clusters

Bonnell, Larson & Zinnecker 2006

103 Msun in 1 pc

Accretion forms massive star in centre of each sub-cluster

Link to Cluster Link to Cluster FormationFormation

• Massive star grows Massive star grows by accreting gas by accreting gas that falls into that falls into clustercluster

• Gas is accompanied Gas is accompanied by low-mass starsby low-mass stars

• Forms cluster Forms cluster around massive around massive star.star.

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Mmax ∝ Ncomp

Link to Cluster Link to Cluster FormationFormation

32

systemmax MM ∝

Accretion and massive Accretion and massive binariesbinaries

• Stars form with low-Stars form with low-mass and well mass and well separatedseparated

• Form binary system due Form binary system due to 3-body (and gas) to 3-body (and gas) capturecapture

• Accretion Accretion • Increases massesIncreases masses• Decreases separationDecreases separation

• Stellar interactions Stellar interactions harden binaryharden binary

• Forms close massive Forms close massive binariesbinaries

€

R ∝ M−2

Evolve

Bonnell & Bate 2005

Final Binary PropertiesFinal Binary Properties

• RRbinarybinary and M and Mbinarybinary

• < 1 to 1000 AU< 1 to 1000 AU

• RRperiperi and M and Mstarstar

• <0.01 to 100 AU<0.01 to 100 AU

• More massive stars in More massive stars in closer binariescloser binaries

• Periastron separation Periastron separation < R< R**

• Binary mergers likelyBinary mergers likelyRadius of star

Binary MergersBinary Mergers

Stellar mergers

Separation of binary system

Distance to next closest (3rd) star

Mass of most massive star

• Binary hardens due to accretion and interactions with 3rd star

•Interactions can force mergers

Bonnell & Bate 2002

Discs around massive Discs around massive starsstars

• Disc formation

• Due to angular momentum in accreting gas

•Scale ~ 1000s AU

• Disc is disturbed, semi-transient structure

• Forms/Reforms on Tdyn

Bonnell, & Bate 2005

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Discs and OutflowsDiscs and Outflows

Circumstellar Circumstellar structurestructure

Collimated Collimated windswinds

edge-on

Feedback Feedback from OB from OB starsstars

• Ionisation from massive Ionisation from massive starsstars

• Collimated by Collimated by circumstellar structurecircumstellar structure

• HII region one-sidedHII region one-sided

• Accretion continues Accretion continues relatively unimpededrelatively unimpeded

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Dale et al. 2005

Feedback and AccretionFeedback and Accretion• Accretion largely Accretion largely

unimpeded by unimpeded by feedbackfeedback

• Dale et al 2005; Krumholz etal Dale et al 2005; Krumholz etal 20052005

• Escapes along Escapes along preferential preferential directionsdirections

Dale et al 2005Dale et al 2005

Feedback and Cloud Feedback and Cloud SupportSupport

• Unlikely to support cluster over Unlikely to support cluster over many tmany tdyndyn

• ttfeedbackfeedback ≤ t ≤ tdyndyn

• Cluster cannot adapt to energy Cluster cannot adapt to energy sourcesource

• Feedback willFeedback will1.1. Do littleDo little2.2. Remove gas (destroy system)Remove gas (destroy system)

• e.g. Li & Nakamura feedback simulation e.g. Li & Nakamura feedback simulation ~ to our non feedback ~ to our non feedback runsruns

Triggering of star Triggering of star formationformation

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Model PredictionsModel Predictions• Competitive accretionCompetitive accretion

• Hierarchical fragmentationHierarchical fragmentation• Non-relaxed, structured systems Non-relaxed, structured systems

(early)(early)• MMmaxmax function of M function of Mtottot (IMF at all (IMF at all

times)times)

• Monolithic CollapseMonolithic Collapse• QuasistaticQuasistatic• Relaxed, no significant sub structureRelaxed, no significant sub structure• Truncated IMFs (early)Truncated IMFs (early)

Massive stars form lastMassive stars form last

ConclusionsConclusions

• Competitive accretion viable Competitive accretion viable mechanism to form massive starsmechanism to form massive stars

Gravity driven: simplest solutionGravity driven: simplest solution

• Massive star formation linked Massive star formation linked to formation of stellar clusterto formation of stellar cluster

• Full IMFsFull IMFs• Mass segregated clustersMass segregated clusters• Close binariesClose binaries

Observables: clump Observables: clump massesmasses

• 3-D ‘real’ clumps 2-D 3-D ‘real’ clumps 2-D projected clumpsprojected clumps

Radiative driven Radiative driven implosionimplosion

• Some SF triggeredSome SF triggered• 2x # of stars2x # of stars

• Some just revealedSome just revealed

• Can we tell which?Can we tell which?• Not from end-Not from end-

resultresult

• Need observable Need observable tests, predictionstests, predictions

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Formation of OB Formation of OB AssociationsAssociations

•Globally unbound GMCsGlobally unbound GMCs

•Local dissipation of turbulenceLocal dissipation of turbulence

•Star formation Star formation

• SF involves SF involves ~10%~10% of mass of mass

Clark et al 2005

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Need models in context of GMC

104 Msun in 10 pc

Clustered and distributed SF

Universal IMF

Gravity, turbulence and thermal pressure

External Collimation of External Collimation of winds from massive winds from massive

starsstars• Intrinsically Intrinsically spherical windspherical wind

• SPH Particle SPH Particle injectioninjection

• Collimated by Collimated by external density external density structurestructure

• From a previous From a previous simulation of simulation of massive star massive star formationformation

• Produces collimated outflowProduces collimated outflow

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High surface density simulation

= 1.0 Msun pc-2

(106 Msun)

Size ~ 500 pc

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FormingForming close binary close binary systemssystems• Calculate real Calculate real

separations from spec. separations from spec. angular momentum and angular momentum and energy of binaryenergy of binary

• Semi-major axis of 0.1 Semi-major axis of 0.1 to 10 AUto 10 AU

• Periastron separations Periastron separations of <0.01 to > 1 AUof <0.01 to > 1 AU

• But stellar radii are But stellar radii are ~0.03 AU~0.03 AU

• collisionscollisions

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Rsemi = J 2 GM

€

e = 1+ 2EJ 2 G2M2

Binary MergersBinary Mergers• Many binaries have rMany binaries have rperiperi < r < rstarstar

• Binary mergersBinary mergers

• Mergers > double Mergers > double star’s massstar’s mass

• Stellar density need Stellar density need not be so highnot be so high

• Require encounters Require encounters at at R= rR= rapastron apastron >> r>> rstarstar

• For R=10 AU, For R=10 AU, • need n ~ 10need n ~ 1066 stars/pc stars/pc33

Binary separationBinary separation

Red: M>8 Mo

Modeling stellar Modeling stellar mergersmergers• Little mass loss Little mass loss (Dale & Davies 2005, Davies et al 2005)(Dale & Davies 2005, Davies et al 2005)

• Rapid rotation Rapid rotation • Energies 10Energies 104848 to 10 to 105151 ergs ergs

1.1. Tidal capture Tidal capture from close from close flyby’sflyby’s

2.2. Tidal shredding of Tidal shredding of lower-mass star lower-mass star• Disc formation Disc formation from from debrisdebris

• Disc capture of Disc capture of next close passagenext close passage

Davies et al 2005

(Bally & Zinnecker 2005(Bally & Zinnecker 2005

Circumstellar structure Circumstellar structure and Outflowsand Outflows

• Circumstellar Circumstellar structurestructure

• Collimated Collimated windswinds

x-y

x-z

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Characteristic stellar Characteristic stellar massmass• What sets the characteristic What sets the characteristic

stellar mass?stellar mass?

• Simulations show Simulations show Masses ~ MMasses ~ MJ J

(Jeans Mass) (Jeans Mass)

• What sets MWhat sets MJJ??• Equation of stateEquation of state• line to dust coolingline to dust cooling

T TT T

Bonnell, Clarke & Bate 2006

(Larson 2005, Spaans & Silk 2000)(Larson 2005, Spaans & Silk 2000)

Formation of Molecular Formation of Molecular CloudsClouds

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Spiral shocks forms GMCs

10% of gas in molecular clouds

Forms spurs and feathering

Size ~ 4 kpc

Dobbs et al 2006

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Spiral Triggering of Spiral Triggering of star formationstar formation

• Follow gas flow through Follow gas flow through spiral armspiral arm

• Form dense cloudsForm dense clouds• GMCsGMCs

• Onset of gravitational Onset of gravitational collapse and SF collapse and SF

• Efficiencies ~10 %Efficiencies ~10 %

Bonnell et al 2006

Low surface density simulation

= 0.1 Msun pc-2

(105 Msun)

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GMC KinematicsGMC Kinematics• Convergent gas streamsConvergent gas streams

• Clumpy gasClumpy gas • Broadens shockBroadens shock

• Post-shock velocityPost-shock velocity• Mass loading in shockMass loading in shock• generates velocity dispersiongenerates velocity dispersion

5.0Rv ∝ΔVelocity dispersion in plane of galaxy

Velocity dispersion in clumpy Velocity dispersion in clumpy shocksshocks

- Gas through 1D sinusoidal potential.

- Velocity dispersion flat and subsonic for uniform shock (---)

- Clumpy shock Δv ~ r 0.5 for clumpy shock (---)

Dobbs & Bonnell 2006