A Multiphase, Sticky Particle, Star Formation Recipe for Cosmology

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. 1997 Springel & Hernquist, 2003

9. 2. Models of the ISM CNM T~100K f~0.02 • Need a simple ISM model: 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 N M • 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'

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! Thank you for listening!

29. Equations