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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
Assumptions in Cole et al. Model
(A Partial List)
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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
Assumptions in Cole et al. Model
(A Partial List, continued)
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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
Assumptions in Cole et al. Model
(A Partial List, continued)
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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
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.
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.
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.
Flattening Predicted by
Mashchenko et al. 2006
Central Density Profile Flattening by
Random Bulk Motions - Implications
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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)