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)

orientation angles of SDSS images wrt North

I was happy using the position angles of galaxies relative to SDSS image's y axis, but people in the collaboration needed the absolute position angles with respect to the North. I used astroLib's astWCS.getRotationDeg() function, in this script. Didn't test yet, I don't know if that makes sense.

SDSS CASjobs -- looking for objects within a given radius of a coordinate pair

There's an inbuilt function for that:

select p.ra,p.dec,p.b,p.l,p.objID,p.run,p.rerun,p.camcol,p.field,p.obj,p.type,p.flags,p.fiberMag_r,p.petroMag_u,p.petroMag_g,p.petroMag_r,p.petroMag_i,p.petroMag_z,
       p.petroRad_r,p.petroR50_r,p.petroR90_r,p.isoA_g,p.isoB_g,p.isoA_r,p.isoB_r,p.isoPhi_r,p.specObjID into mydb.MiceB from PhotoObjAll as p,

dbo.fGetNearbyObjEq(191.5, 30.7, 1.0)

n 
WHERE p.objID = n.objID 

      and
      ( flags & (dbo.fPhotoFlags('NOPETRO') +
       dbo.fPhotoFlags('MANYPETRO')
       +dbo.fPhotoFlags('TOO_FEW_GOOD_DETECTIONS')) ) = 0

WCS to pixel values and vice versa in Python

It's often necessary to convert pixel coordinates within a binary image to physical(ra, dec) sky coordinates. For instance, one might need to find brightness at the central pixel of the galaxy, calculate flux, any photometry-related task would do, actually. I used astLib.astWCS for this purpose, though I think pywcs might work just as well.

 
from astLib import astWCS

WCS=astWCS.WCS("Galaxy.fits")

center = WCS.wcs2pix(ra, dec)
print center
print 'brightness at the galaxy center', img[center[1], center[0]] 

#thanks, numpy -- python indexes arrays ass-backward (or, rather, column-backward) for some reason. One have to be careful not to swap them.