A Multiphase, Sticky Particle, Star Formation Recipe for

Cosmology

Craig BoothTom Theuns

Overview

1. Star Formation in Disk Galaxies & Properties of the ISM

2. Simulating Star Formation & Feedback

3. The Sticky Particle Model4. Results from a One Zone

Simulation5. Summary

Star Formation in Disk Galaxies

• Most stars form in Giant Molecular clouds

• Cloud dynamics are very complex and not very well understood

• The mechanism by which clouds form is unclear

Star Formation in Disk Galaxies

Blitz, 04

From the Astro-1 mission

• Schmidt (1959):

Kennicutt, 1998N~1.4

Star Formation in Disk Galaxies

Supernova Feedback

Model Overview

• The Physics we need to implement:– GMCs form in spiral arms

– Stars form from GMC collapse– Stellar winds destroy GMCs– Feedback drives superwinds &

regulates star formation

Simulating Star Formation

• Difficult problem for two reasons:– Scales of cosmological interest are

vastly different to those on which star formation takes place

– Simulation codes do not contain enough physics to accurately track star formation

• Take one of two approaches:1. Empirical rules2. Model the ISM statistically

Yepes et. al. 1997 Springel & Hernquist, 2003

2. Models of the ISM

• Need a simple ISM model:

Stars

HIMT~106

CNMT~100Kf~0.02

warmcloud coronaT~4000K

McKee & Ostriker, 1977

Three physical processes are important describing self-regulating star formation...

Models of the ISM

• Clouds form by the radiative cooling of the hot phase

Models of the ISM

• Clouds collapse into stars

Models of the ISM

• Stars go supernova and destroy clouds

Now treat each one in turn...

The Formation of Clouds

• Cooling Instability (Yepes et. al., 1997)

• if density > X and temperature allows for thermal instability then rather than cooling, hot gas is assumed to collapse into clouds

Sutherland & Dopita, 1993

The Multiphase Model

• Yepes et. al. formulated differential equations that describe:– the rate of formation of clouds– the rate of collapse of clouds to stars– the rate of supernova energy injection

cold

hot

The Multiphase Model

• Drawbacks:– coupling between

hot and cold gas– assumes pressure

equilibrium between hot & cold phases

– carries no information about the properties of the cold gas

Springel & Hernquist, 2003

The Sticky Particle Model

• Follow the same format with our model.

• Treat each process separately:– formation of clouds– coagulation of clouds into GMCs– collapse of GMCs– star formation

The Formation of Clouds

• In our simulations 'cloud particles' form as in Yepes et. al. 1997 (thermal instability)

• Store the mass function for every cloud. Evolve the 'clouds' and 'cloudlets' differently

• Unresolved clouds are called 'cloudlets'N

M

The Coagulation of Clouds

vm is a parameter in our simulations

• Clouds are treated as ballistic particles, following a couple of very simple rules upon collision:

– vapp < vm

– vapp> vm

Collision

Cooling

The Coagulation of Cloudlets

• We want the cloudlets to behave in exactly the same way as the clouds

• Integrate coagulation equation (and similar equations for energy evolution) to evolve system

Smoluchowski, 1916

GMC Collapse & Star Formation

• Giant Molecular Clouds are defined to be 106 solar masses

• When we form a GMC it lives for one dynamical time (~10Myr) then collapses.

• Some fraction of its mass becomes stars, the rest is fragmented into tiny clouds.

• This represents formation & coagulation of clouds and destruction of clouds by star formation

Results From the One Zone Model

• Set up 1kpc3 region• Density comparable to that in a MW

spiral arm• Evolve for 200Myr• Both as 'pure cloudlet' and hybrid sticky

particle/cloudlet

Results From the One Zone Model

pure cloudlet run

Observed cloud mass spectrum index -1.6 to -1.9

Results From the One Zone Model

Results From the One Zone Model

delay, SFR

Results From the One Zone Model

• SFR Shows little dependence on particle number• Cloudlets behave exactly like clouds• Higher resolution gives better spatial resolution

Schmidt Law

Summary

• Statistical star formation model• One zone simulation:

– reproduces cloud mass spectrum, velocity dispersion & SFR in Milky Way conditions

– Schmidt law as an output– Resolution independence

• Avoids some problems of the Multiphase model

• Provides a natural mechanism for delay

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Thank you for listening!

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