Wednesday, January 2, 2013

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
    • 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)

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