A Multiphase, Sticky Particle, Star Formation Recipe for Cosmology

A Multiphase, Sticky Particle, Star Formation Recipe for

Cosmology

Craig BoothTom Theuns & Takashi Okamoto

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

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

Results From the One Zone Model

Results From the One Zone Model

Results From the One Zone Model

Results From the One Zone Model

Results From the One Zone Model

Results From the One Zone Model

Results From the One Zone Model

Good match with Milky Way properties

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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