Spiral Triggering of Star FormationSpiral Triggering of Star Formation

Ian Bonnell, Clare Dobbs Tom Robitaille, Ian Bonnell, Clare Dobbs Tom Robitaille, University of St AndrewsUniversity of St Andrews

Jim PringleJim PringleIoA, CambridgeIoA, Cambridge

Dynamical Models of Star FormationDynamical Models of Star Formation

• Local regions of GMCsLocal regions of GMCs

• Models for the origin ofModels for the origin of– Stellar clustersStellar clusters

– Massive starsMassive stars

– Brown dwarfsBrown dwarfs

– Initial Mass FunctionInitial Mass Function

– But not the initial conditions But not the initial conditions for star formationfor star formation

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Giant Molecular CloudsGiant Molecular Clouds

• Stars form in molecular cloudsStars form in molecular clouds

• Molecular cloud propertiesMolecular cloud properties– Mass: 1000’s to >10Mass: 1000’s to >1055 M Msunsun

– Sizes: ~ 10 pc Sizes: ~ 10 pc

– Densities: 10Densities: 10-19-19 to 10 to 10-22-22 g cm g cm-3-3

– Cold: T ~ 10 KCold: T ~ 10 K

– Located in spiral armsLocated in spiral arms

– Lots of structureLots of structure

– Supersonic ‘turbulence’Supersonic ‘turbulence’» Larson relation: Larson relation:

5.0Rv ∝Δ

Spiral Shocks and Star FormationSpiral Shocks and Star Formation

• Do spiral shocks Do spiral shocks control star formation?control star formation?

» Roberts 1971Roberts 1971

• Gas dynamics in Gas dynamics in 2 (4) armed spiral potential 2 (4) armed spiral potential

» External potential External potential

– SPH simulations (4 x 10SPH simulations (4 x 1055 to 4 x 10 to 4 x 1066 particles) particles)

– Isothermal (100 K)Isothermal (100 K)

– Clumpy : average 10Clumpy : average 10-3-3 MMsun sun /pc/pc3 3 ; max 10 ; max 10-1-1 MMsun sun /pc/pc33

– Self gravitySelf gravity

– Star formation modeled with sink-particlesStar formation modeled with sink-particles

Initial ConditionsInitial Conditions• Test particle simulation in Test particle simulation in

spiral potentialspiral potential– Inside co-rotation Inside co-rotation

• Region of over-density of Region of over-density of 100 pc chosen100 pc chosen

• Proto-GMC traced Proto-GMC traced backwardsbackwards

• Replace by self-gravitating Replace by self-gravitating SPH particlesSPH particles

• Surface density 0.1 to 1 Surface density 0.1 to 1 MMsun sun

pcpc-2-2

Spiral Triggering of star formationSpiral Triggering of star formation• Follow gas flow through spiral armFollow gas flow through spiral arm

• Shocks leaving pot. minimumShocks leaving pot. minimum

• Form dense cloudsForm dense clouds– GMCsGMCs

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

• Forms stellar clustersForms stellar clusters– At At > > 101033 MMsun sun pcpc-3-3

• Masses 10Masses 1022 to 10 to 1044 M Msunsun

Low surface density simulation

= 0.1 Msun pc-2

(105 Msun)

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Low surface density simulation

= 0.1 Msun pc-2

(105 Msun)

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High surface density simulation

= 1.0 Msun pc-2

(106 Msun)

Size ~ 500 pc

Formation of Giant Molecular CloudsFormation of Giant Molecular Clouds• Convergent gas streamsConvergent gas streams

– Due to spiral potentialDue to spiral potential

– Clumpy shockClumpy shock forms substructure (GMCs?) forms substructure (GMCs?)

– Dissipate kinetic energy in shockDissipate kinetic energy in shock

– Forms bound substructure Forms bound substructure Star FormationStar Formation

– Structures due to instabilities Structures due to instabilities

» Self-gravity ? Probably notSelf-gravity ? Probably not

» Kelvin-Helmholtz ?Kelvin-Helmholtz ?

– Edges sharper on Edges sharper on upwind sideupwind side

Size ~ 50 pc

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GMC KinematicsGMC Kinematics• Convergent gas streamsConvergent gas streams

– Clumpy gasClumpy gas

– Broadens shockBroadens shock

• Post-shock velocity Post-shock velocity depends ondepends on

– Density of incoming clumpDensity of incoming clump

– Mass loading in shockMass loading in shock

– generates velocity dispersiongenerates velocity dispersion

5.0Rv ∝ΔVelocity dispersion in plane of galaxy

Star Formation and EfficienciesStar Formation and Efficiencies• Star formation requiresStar formation requires::

– Orbit crowdingOrbit crowding– shockshock– Enough gas massEnough gas mass

• GMC lifetimes ~ 10GMC lifetimes ~ 1077 years (few dynamical times) years (few dynamical times)

• Star Formation Efficiencies LowStar Formation Efficiencies Low– 5 to 30 % of gas mass formed into stars5 to 30 % of gas mass formed into stars

» Without any feedbackWithout any feedback

• Why?Why?– Clouds globally unbound Clouds globally unbound – Majority of mass escapesMajority of mass escapes– Clouds disperse leaving spiral armsClouds disperse leaving spiral arms

Unbound Clouds and SF EfficiencyUnbound Clouds and SF Efficiency

•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 2004

Global disk simulationsGlobal disk simulations• Clare Dobbs poster (no. 18)Clare Dobbs poster (no. 18)

• Goal: explore gas dynamics through multiple spiral Goal: explore gas dynamics through multiple spiral arm passagesarm passages

– Non self-gravitatingNon self-gravitating

– 4 armed spiral4 armed spiral

– Gas ring: 5 to 10 kpc (co-rotation 10 kpc)Gas ring: 5 to 10 kpc (co-rotation 10 kpc)

– Mass: 5 x 10Mass: 5 x 1088 M Msunsun

– Isothermal (100 to 10Isothermal (100 to 1044 K) K)

– Distribution: globally uniform, locally clumpy Distribution: globally uniform, locally clumpy

– Post-processed HPost-processed H22 formation formation• Bergin et al (2004)Bergin et al (2004)

T=100 K

Size scale:

22kpc, 11kpc, 6kpc, 3kpc

Location of H2 gas

Formation of Molecular CloudsFormation of Molecular Clouds

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Size ~ 4 kpc

Formation of HFormation of H22

• Molecular gas formed in Molecular gas formed in spiral armsspiral arms– Higher densityHigher density

– Higher extinctionHigher extinction

• Giant Molecular Clouds:Giant Molecular Clouds:

– Almost completely in spiral Almost completely in spiral armsarms

• Mass components:Mass components:

• 10 % over full disk10 % over full disk

• 30-50 % in spiral arms30-50 % in spiral arms Azimuthal distribution of gas and H2

Spiral shocks and structure Spiral shocks and structure generationgeneration

• Molecular cloud spacing~ 500 pcMolecular cloud spacing~ 500 pc– Not due to self-gravityNot due to self-gravity

• Simulation produces spurs and Simulation produces spurs and feathering feathering

– Due to clumps in armsDue to clumps in arms– Sheared in the inter-arm regionSheared in the inter-arm region

– Disappears at higher gas temperaturesDisappears at higher gas temperatures

Velocity dispersionVelocity dispersion• Velocity dispersion driven Velocity dispersion driven

by spiral shocksby spiral shocks

• Due to clumpy shocksDue to clumpy shocks

• Velocity dispersion Velocity dispersion increases in each spiral arm increases in each spiral arm passagepassage

• Lower in interarm regionsLower in interarm regions

Azimuthal distribution of velocity dispersion

A local viewpoint of spiral shocksA local viewpoint of spiral shocks

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1kpc region centred on gas particleSpot: motion of one gas particle

ConclusionsConclusions• Spiral shocks can trigger star formationSpiral shocks can trigger star formation

• Produce realistic GMCs Produce realistic GMCs – StructuresStructures– Kinematics (not turbulence)Kinematics (not turbulence)

• Low star formation efficiencies (clouds unbound)Low star formation efficiencies (clouds unbound)

• Global disk simulationsGlobal disk simulations– Generates Spurs and feathering (when cold)Generates Spurs and feathering (when cold)– Produce GMCs in spiral arms 10% of gas in HProduce GMCs in spiral arms 10% of gas in H22

– Observable signatures Observable signatures » as gas passes through shocksas gas passes through shocks

Modelling Spiral GalaxiesModelling Spiral Galaxies

Pass gas through Galactic potential, consisting of 3 components:

Disc: Logarithmic potential (Binney & Tremaine)

- Flat rotation curve, v0=220km/s Spiral: Cox & Gomez (2002) (sum of 3 perturbations)

- Milky Way parameters with 4 arms

- Pattern speed of 210 -8 rad/yr

-1

( )21 c

c

rr+=

ρρ Halo: Caldwell & Ostriker

(1981)

No self-gravity/ magnetic fields

Velocity dispersion in clumpy shocksVelocity dispersion in clumpy shocks

- Gas through 1D sinusoidal potential.

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

- Velocity size-scale relation (v) r 0.5 for clumpy shock (-)