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

2. Overview 1.Star Formation in Disk Galaxies & Properties of the ISM 2.Simulating Star Formation & Feedback 3.The Sticky Particle Model 4.Results from a One Zone Simulation 5.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 Blitz, 04 From the Astro-1 mission

5. Supernova Feedback

6. 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

7. 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 rules 2.Model the ISM statistically Yepes et. al. 1997 Springel & Hernquist, 2003

8. 2. Models of the ISM Need a simple ISM model: Stars HIM T~10 6 CNM T~100K f~0.02 warm cloud corona T~4000K McKee & Ostriker, 1977 Three physical processes are important describing self-regulating star formatio n...

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

10. Models of the ISM Clouds collapse into stars

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

12. 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

13. 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

14. 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

15. 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

16. 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

17. The Coagulation of Clouds v m is a parameter in our simulations Clouds are treated as ballistic particles, following a couple of very simple rules upon collision: –v app < v m –v app > v m Collision Cooling

18. 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

19. GMC Collapse & Star Formation Giant Molecular Clouds are defined to be 10 6 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

20. Results From the One Zone Model Set up 1kpc 3 region Density comparable to that in a MW spiral arm Evolve for 200Myr Both as 'pure cloudlet' and hybrid sticky particle/cloudlet

21. Results From the One Zone Model

28. Good match with Milky Way properties

29. Results From the One Zone Model delay, SFR

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

31. Schmidt Law

32. 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

33. Thank you for listening!

34. Equations