1. A Multiphase, Sticky Particle, Star Formation Recipe for Cosmology
Craig Booth
Tom Theuns

2. Overview Star Formation in Disk Galaxies & Properties of the ISM
Simulating Star Formation & Feedback
The Sticky Particle Model
Results from a One Zone Simulation
Summary

3. 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

4. Star Formation in Disk Galaxies
From the Astro-1 mission
Blitz, 04

5. Star Formation in Disk Galaxies
Schmidt (1959):
N~1.4
Kennicutt, 1998

6. Supernova Feedback

7. 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

8. 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:
Empirical rules
Model the ISM statistically
Yepes et. al Springel & Hernquist, 2003

9. 2. Models of the ISM Need a simple ISM model: CNM T~100K f~0.02
McKee & Ostriker, 1977
Stars
warm
cloud corona
T~4000K
HIM
T~106
Three physical processes are important describing self-regulating star formation...

10. Models of the ISM
Clouds form by the radiative cooling of the hot phase

11. Models of the ISM
Clouds collapse into stars

12. Models of the ISM Stars go supernova and destroy clouds
Now treat each one in turn...

13. The Formation of Clouds
Sutherland & Dopita, 1993
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

14. 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

15. 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

16. 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

17. The Formation of Clouds
In our simulations 'cloud particles' form as in Yepes et. al (thermal instability)
Store the mass function for every cloud. Evolve the 'clouds' and 'cloudlets' differently
Unresolved clouds are called 'cloudlets' N M

18. The Coagulation of Clouds
Clouds are treated as ballistic particles, following a couple of very simple rules upon collision:
vapp < vm
vapp> vm
Collision
Cooling
vm is a parameter in our simulations

19. 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

20. 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

21. 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

22. Results From the One Zone Model
pure cloudlet run

23. Results From the One Zone Model
Observed cloud mass spectrum index -1.6 to -1.9

24. Results From the One Zone Model
delay, SFR

25. Results From the One Zone Model
SFR Shows little dependence on particle number
Cloudlets behave exactly like clouds
Higher resolution gives better spatial resolution

26. Schmidt Law

27. 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

28. Thank you for listening!

29. Equations