Numerical Modeling of Hierarchical Galaxy Formation

1. Numerical Modeling of Hierarchical Galaxy Formation Cole, S. et al. 2000, MNRAS 319, 168-204. Adam Trotter December 4, 2007 Astronomy 704, UNC-Chapel Hill, Prof. Jim Rose

2. Assumptions in Cole et al. Model (A Partial List) • Galaxies grow hierarchically from primordial Gaussian density fluctuations in CDM (bottom-up model) OK • Baryonic galaxy formation can be described semi-analytically to arbitrary resolution, using numerical modeling of CDM OK • Complicated processes such as star formation can be described via scaling laws containing free parameters, constrained by observations of local universe  Prob not OK • Can ignore baryonic mass in computing certain quantities, e.g., rotation curves (sometimes).  Prob OK • Monte-Carlo merger trees provide good match to N-body simulation results for CDM OK, if halo and SF feedback parameters are physical • Can limit cosmological parameters (convergence model) OK • Haloes retain original mass, mean density, angular momentum throughout lifetime  Prob not OK • Press-Schechter mass function accurately describes halo masses ? Unsure

3. Assumptions in Cole et al. Model (A Partial List, continued) • Angular momenta of merging haloes are uncorrelated  Prob OK • Halo density profile described by NFW model Not OK • Rotation velocity of baryonic gas in disk is constant with radius (gas and dark matter have same specific angular momentum within Virial radius)  Prob OK • Hot halo gas does not necessarily have same density profile as dark matter. Shock-heated gas is less centrally concentrated (beta parameter) ? Unsure • Cluster gas is in hydrostatic equilibrium -> temperature profiles vary slowly with radius ? Unsure • All diffuse gas is shock heated in formation of halo, settles into spherical distribution with core radius rcore=rNFW/3 Not OK • Cooling time assumes hot halo gas is in collisional ionization equilibrium ? Unsure • Gas density profile held fixed throughout halo lifetime Not OK • When gas cools, it settles into a disk at center of halo, conserving its angular momentum  Prob Not OK • Star Formation Rate in disk is proportional to mass of cold gas  Prob OK • Reheating/ejection of gas from disk directly proportional to SFR  OK

4. Assumptions in Cole et al. Model (A Partial List, continued) • Assume satellite galaxies have all hot gas stripped ? Unsure • At merger, most massive galaxy becomes sole central galaxy in halo ? Unsure • Disk instabilities not included in reference model  Not OK – redistributes angular momentum and affects SFR • Size of disk entirely determined by angular momentum of halo it forms from (no loss of angular momentum in disk formation)  Not OK. Many models predict loss of angular momentum. • Disks merge by dynamical friction, assuming circular orbits ? Unsure. • Assume Kennicutt IMF, universal in time and space ? Unsure. • Dust has same radial scale length as stars, dust mass per unit area scales with total mass of metals per unit area  Prob Not OK: Dust formation is complicated and metallicity and ISM environment is evolving • Disks with solar metallicity have same gas to dust ratio as local ISM  Prob Not OK (See Above) • Extinction due to dust is well-described by MW extinction curve  Prob Not OK • No clumping of dust, disk gas or stars; no starbursts Not OK

5. A Very Complex Modeling Problem “The galaxy formation model as a whole is a complex system, with the result that the dependence of a particular statistic on a given parameter can be complicated...One should therefore be careful not to over-interpret the trends...it is dangerous to assume that [the predicted trends presented here] can be used to assess the result of varying more than one parameter at a time.” Coles et al. 2000, p 185.

6. A Look at One Assumption: Density Profiles of Disks and Haloes • Cole et al. model assumes that density profiles of baryonic haloes and disks are constant in time, until a merger occurs • But...we observe galaxies, especially dwarfs like the Magellanic clouds, whose cores are less centrally concentrated than would be predicted by this model, or by NFW CDM halo profiles. • Reference model does not include disk instabilities, clumpiness, or the effects of random mass redistribution due to galactic winds due to starbursts, supermassive black hole jet-disk interaction and SNe.

7. Stellar Feedback in High-z Dwarf Galaxies Flattens Central Density Profile of Both Disk Gas and CDM Mashchenko, Couchman & Wadsley 2006, Nature 442, 539 “The removal of cusps from galaxy centres by stellar feedback in the early Universe” Mashchenko, Wadsley & Couchman 2007, Science (Nov 29), “Stellar Feedback in Dwarf Galaxy Formation” • Observations of nearby galaxies indicate a flat core in CDM distribution (Burkert 1995 ApJ 447, L25), but numerical models predict a “cusp” (NFW profile) • Simulations that include random bulk motion of clumpy material in small galaxies with active star formation and frequent SNe gravitationally smooths out the NFW profile on short (100 Myr) timescales, for both baryonic and CDM • Once the cusp is destroyed, it is not able to be recovered in subsequent mergers that produce larger galaxies • If all galaxies are built “bottom up” from these earliest dwarf galaxies, then we should not expect the NFW profile to apply to CDM or baryonic haloes in later epochs.

8. Flattening Predicted by Mashchenko et al. 2006

9. Central Density Profile Flattening by Random Bulk Motions - Implications • CDM cusp is flattened by resonant heating in a fluctuating central gravitational potential • All haloes produced by subsequent mergers will have similarly flattened central density distributions. • Does not invoke extreme events (e.g., total gas clearout by massive starburst) SNe occur in all star-forming galaxies, and reasonable SNe rates result in bulk motions necessary to produce the flattening. • Smooths out the cusp on a timescale of only ~100 Myr using only moderate (~10 km/s) random bulk motions induced by SNe • Requires recognition that gas distribution in progenitor galaxy disks is clumpy • Suggests that NFW density profile is not appropriate choice for Cole et al.’s CDM merger trees, at least at recent epochs. • Since Cole et al. model shows correlation between parameter aNFW and halo mass, results in a different mass spectrum at any given epoch; other parameters would have to be adjusted accordingly to match observed luminosity function. • Explains other observed features of present-epoch dwarf galaxies: low central densities, persistence of GC orbits, stellar population gradients (Mashchenko et al. 2007)