Spiral Triggering of Star Formation Ian Bonnell, Clare Dobbs Tom Robitaille, University of St Andrews Jim Pringle IoA, Cambridge

Dynamical Models of Star Formation Local regions of GMCsLocal regions of GMCs Models for the origin ofModels for the origin of –Stellar clusters –Massive stars –Brown dwarfs –Initial Mass Function –But not the initial conditions for star formation

Giant Molecular Clouds Stars form in molecular cloudsStars form in molecular clouds Molecular cloud propertiesMolecular cloud properties –Mass: 1000’s to >10 5 M sun –Sizes: ~ 10 pc –Densities: to g cm -3 –Cold: T ~ 10 K –Located in spiral arms –Lots of structure –Supersonic ‘turbulence’ »Larson relation:

Spiral Shocks and Star Formation Do spiral shocks control star formation?Do spiral shocks control star formation? »Roberts 1971 Gas dynamics in 2 (4) armed spiral potentialGas dynamics in 2 (4) armed spiral potential »External potential –SPH simulations (4 x 10 5 to 4 x 10 6 particles) –Isothermal (100 K) –Clumpy : average M sun /pc 3 ; max M sun /pc 3 –Self gravity –Star formation modeled with sink-particles

Initial Conditions Test particle simulation in spiral potentialTest particle simulation in spiral potential –Inside co-rotation Region of over-density of 100 pc chosenRegion of over-density of 100 pc chosen Proto-GMC traced backwardsProto-GMC traced backwards Replace by self-gravitating SPH particlesReplace by self-gravitating SPH particles Surface density 0.1 to 1 M sun pc -2Surface density 0.1 to 1 M sun pc -2

Spiral 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 –GMCs Onset of gravitational collapse and SFOnset of gravitational collapse and SF Forms stellar clustersForms stellar clusters –At  > 10 3 M sun pc -3 Masses 10 2 to 10 4 M sunMasses 10 2 to 10 4 M sun

Low surface density simulation  = 0.1 M sun pc -2 (10 5 M sun )

Low surface density simulation  = 0.1 M sun pc -2 (10 5 M sun )

High surface density simulation  = 1.0 M sun pc -2 (10 6 M sun ) Size ~ 500 pc

Formation of Giant Molecular Clouds Convergent gas streamsConvergent gas streams –Due to spiral potential –Clumpy shock forms substructure (GMCs?) –Dissipate kinetic energy in shock –Forms bound substructure Star Formation –Structures due to instabilities »Self-gravity ? Probably not »Kelvin-Helmholtz ? – Edges sharper on upwind side Size ~ 50 pc

GMC Kinematics Convergent gas streamsConvergent gas streams –Clumpy gas –Broadens shock Post-shock velocity depends onPost-shock velocity depends on –Density of incoming clump –Mass loading in shock –generates velocity dispersion Velocity dispersion in plane of galaxy

Star Formation and Efficiencies Star formation requires :Star formation requires : –Orbit crowding –shock –Enough gas mass GMC lifetimes ~ 10 7 years (few dynamical times)GMC lifetimes ~ 10 7 years (few dynamical times) Star Formation Efficiencies LowStar Formation Efficiencies Low –5 to 30 % of gas mass formed into stars »Without any feedback Why?Why? –Clouds globally unbound –Majority of mass escapes –Clouds disperse leaving spiral arms

Unbound Clouds and SF Efficiency Globally unbound GMCsGlobally unbound GMCs Local dissipation of turbulenceLocal dissipation of turbulence Star formationStar formation SF involves ~10% of mass SF involves ~10% of mass Clark et al 2004

Global disk simulations Clare Dobbs poster (no. 18)Clare Dobbs poster (no. 18) Goal: explore gas dynamics through multiple spiral arm passagesGoal: explore gas dynamics through multiple spiral arm passages –Non self-gravitating –4 armed spiral –Gas ring: 5 to 10 kpc (co-rotation 10 kpc) –Mass: 5 x 10 8 M sun –Isothermal (100 to 10 4 K) –Distribution: globally uniform, locally clumpy –Post-processed H 2 formation Bergin et al (2004)Bergin et al (2004)

T=100 K

Size scale: 22kpc, 11kpc, 6kpc, 3kpc Location of H 2 gas

Formation of Molecular Clouds Size ~ 4 kpc

Formation of H 2 Molecular gas formed in spiral armsMolecular gas formed in spiral arms –Higher density –Higher extinction Giant Molecular Clouds:Giant Molecular Clouds: –Almost completely in spiral arms Mass components:Mass components: 10 % over full disk10 % over full disk % in spiral arms30-50 % in spiral arms Azimuthal distribution of gas and H 2

Spiral shocks and structure generation Molecular cloud spacing~ 500 pcMolecular cloud spacing~ 500 pc –Not due to self-gravity Simulation produces spurs and featheringSimulation produces spurs and feathering –Due to clumps in arms –Sheared in the inter-arm region –Disappears at higher gas temperatures

Velocity dispersion Velocity dispersion driven by spiral shocksVelocity dispersion driven by spiral shocks Due to clumpy shocksDue to clumpy shocks Velocity dispersion increases in each spiral arm passageVelocity dispersion increases in each spiral arm passage Lower in interarm regionsLower in interarm regions Azimuthal distribution of velocity dispersion

A local viewpoint of spiral shocks 1kpc region centred on gas particle Spot: motion of one gas particle

Conclusions Spiral shocks can trigger star formationSpiral shocks can trigger star formation Produce realistic GMCsProduce realistic GMCs –Structures –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) –Produce GMCs in spiral arms 10% of gas in H 2 –Observable signatures »as gas passes through shocks

Modelling Spiral Galaxies Pass gas through Galactic potential, consisting of 3 components: Disc: Logarithmic potential (Binney & Tremaine) - Flat rotation curve, v 0 =220km/s Spiral: Cox & Gomez (2002) (sum of 3 perturbations) - Milky Way parameters with 4 arms - Pattern speed of 2  rad/yr -1 Halo: Caldwell & Ostriker (1981) No self-gravity/ magnetic fields

Velocity 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 (-)