A Multiphase, Sticky Particle, Star
Formation Recipe for Cosmology
Craig Booth
Tom Theuns
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
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
From the
Astro-1
mission
Blitz, 04
Star Formation in Disk Galaxies
• Schmidt (1959):
N~1.4
Kennicutt, 1998
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 rules
2. Model the ISM statistically
Yepes et. al. 1997
Springel & Hernquist, 2003
2. Models of the ISM
• Need a simple ISM model:
McKee & Ostriker, 1977
CNM
T~100K
f~0.02
Stars
HIM
T~106
warm
cloud
corona
T~4000K
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
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
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
Springel & Hernquist, 2003
– assumes pressure
equilibrium
between hot & cold
phases
– carries no
information about
the properties of
the cold gas
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
• Clouds are treated as ballistic particles,
following a couple of very simple rules upon
collision:
– vapp < vm
Collision
– vapp> vm
Cooling
vm is a parameter in our simulations
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
Results From the One Zone Model
Observed cloud mass spectrum index -1.6 to
-1.9
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
Thank you for listening!
Thank you for listening!
Equations