Jerusalem WS lecture notes: 08. Extended Press-Schechter formalism formalism

by F. van den Bosch, slides here.

• Press - Schechter theory:
  • filters of density fields: Gaussian, top-hat, sharp k-space filter (same, as top-hat, except we end up having a nice box in Fourier space)
  • mass variance
  • halo mass function: how can we assign halo mass to a collapsed region?
  • PS: only half of the mass of the Universe can become collapsed (overdense), but due to smoothing, this is not entirely correct. fudge factor of 2
  • halo mass function: many more small haloes than higher, exponential suppression
• Excursion set (EPS) formalism (Bond et al, ~1991, statistics of peak heights):
  • excursion: locations of space
  • sharp k-space filter: Markovian trajectory
  • http://ned.ipac.caltech.edu/level5/Sept06/Loeb/Loeb4.html
  • all mass elements will eventually sit in a halo of arbitrarily low mass
  • works in a statistical sense, not necessarily correct on a per-halo basis
  • the sharp k-space filter looks ugly in real space (sinc-like)
  • the Spherical Cow
  • simulations: underpredicts number of high-mass haloes, over-predicts low-mass haloes
  • halo finding: how we define the haloes? It changes the halo mass function!
• Ellipsoidal collapse EPS theory:
  • moving barrier up-crossing, mcmc simulations
  • much better agreement w/ simulations
• Halo merger trees:
  • accurately sampling progenitor mass f-n
  • mass conservation
  • impossible to do properly: conditional probabilities, many ways to draw from the distribution
  • tests on the accuracy of merger trees: consistency test, comparison w/ numerical simulation
  mass assembly history:
  • main central galaxy accretes lower mass haloes (subhaloes, which may survive or not)
  • satellite
  • assembly time: main progenitor reaches 1/2 the final mass (more massive haloes assemble later)