1. A Prescription for High-Redshift star formation
Alexander (Sasha) Muratov
University of Michigan Advisor: Oleg Gnedin L

2. Star Formation History of The Universe
Dwarf Galaxies and Globular Clusters represent some of the oldest objects known in the universe. As we all know, much observational and theoretical effort these days is going into understanding the process of star formation. Even in the local universe, it is hard for us to tell exactly what is going on. At high redshifts the problem becomes even worse and more open ended.
Of course, over the last 10 years or so, strides have been made at modeling high redshift star formation.
Ideally we'd just observe and/or simulate everything properly, but thus far, as Brian O'shea alluded to yesterday, it's not quite possible and semi-analytical modelling could be useful
Using some observed relations, can we figure out a simple prescription for star formation through cosmic time that would naturally produce a galaxy like the one we live in today?
Madau et al

3. State of Simulations
As you can see, this N-body simulation from 2004 has excellent resolution of substructure in Milky Way-like halo .
What are the stars and gas doing here though?
This is where we need to use Semi-analytical modelling comes in handy.
Kravtsov et al. (2004)
Collisionless dark matter simulations can be run with great resolution down to zero redshift, but what are the stars and gas doing?

4. Prescriptive Model: Advantages
All quantities available at all times
Made to be consistent with observations and simulations
Can provide insight into global processes on different scales: Star Formation.
Makes testable predictions.
Disadvantages: makes testable predictions – need to match many data sets. Sometimes difficult to constrain.
Perscriptive (or semi-analytical) modelling is an exercise that can help us understand some of the important physical processes involved in astrophysics.
As Brian O'shea alluded to yesterday, it is important

5. Observed fits
M*-Mh relation (Woo et al. 2008) logVc = logM* , M* ~ Vc3.8 Vc = Vmax * 2½ Mh ~ Vmax3.3
M*-Mgas relation (McGaugh 2005)
Mass metallicity relation: Woo et al. (2008)
We start out with dark matter subhalos. How can we assign gas mass, stellar mass, and metallicity to them? We start out with stellar mass. Woo et al found scaling relations between the circular velocity and the total stellar mass.
Now is a good time to point out that while this analysis is being done on Andrey's simulation results, the actual methodology for assigning masses to halos is different. Andrey used a selective matching technique. We employ this relation from woo et al, which points out a total stellar mass to v_circ relation that is nearly linear for the classical dwarfs.
The subhalos we were considering were largely in this mass range.
To go from Vcirc to M_h we note that in the case of dark matter halos, we always measure
Ms(z=0) = MꙨ

6. Observed fits 2 – time evolution
Dave & Oppenheimer (2007) .3 dex lower over 10 Gyr
Conroy & Wechsler (2008) Well fit by M* ~ (1+z)-2
We also have to understand what the difference is between star formation at high redshift and the current epoch. The relations I showed you before were based on observations of dwarfs and galaxies now. When they formed and went through their main phase of star formation. Conditions were different.
Several different simulations have recently determined
What is conroy & Wechsler
Dave & Oppenheimer: use ga

7. Equations again Mass MW = 5.5 * 10^10 Solar (M*)
MW = 1 * 10^10 Solar (Mgas)
Metallicity: extra constraints:
Here are all the equations again.
It ultimately boils down to these three relations for mass and two relations for metallicity. That's it. No need to think about M300 or half light radius/mass. As I have pointed out below, the milky way stellar mass according to this is approximately 5.5 * 10^9
The gas mas is:

8. fgas(z, M)
And this is what the model looks like. This is how much gas mass and/or stellar mass we predict for different values of the halo mass. You can see different lines for diff redshifts that range from 0 to 3
The trends are as you expect: higher redshift implies lower stellar mass, and higher gas mass. Note that this gas refers to mass in the “cold” phase – HI and H_2. Therefore .

9. Anchored by GC's DM halos from Kravtsov et al. (2004)
Hydro constraints from Kravtsov & Gnedin (2005)
Bimodal metallicity distribution! (Muratov & Gnedin, in prep)
KS Probablity: 51%
I should mention that this model was mainly developed to model the formation of globular clusters in hierarchical cosmology. Using only a few adjustable parameters, we applied our resjults to Andrey's DM and got a bimodal dsistribution

10. prediction for stellar fraction in dwarf galaxies
M* = *Mh
RMS: 0.212
Red Line : Andrey Kravtsov's relation (2009)
Different techniques used: instead of matching brightest to most massive, we apply direct relations.
Which is right?

11. Summary
We present a prescriptive model for baryonic mass and metallicity as a function of time and halo mass.
Applying this prescription to DM simulations, we have studied GC formation.
We also obtain a fit for MW Dwarfs. Produces a different result from Kravtsov 2009, Busha 2009.