Observational Test of Halo Model: an empirical approach Mehri Torki Bob Nichol
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Observational Test of Halo Model: an empirical approachMehri TorkiBob Nichol
Two types of pairs: both particles in same halo, or particles in different halos
dm(r) = 1h(r) + 2h(r) All physics can be decomposed similarly: influences from within halo, versus from outside (Sheth 1996)(lahmu.phyast.pitt.edu/~sheth/courses/allahabad/halomodel.ppt) The Halo-model of clustering
Halo Model as a tool to extract CosmologyGalaxies n(M),Mass & SizeCosmology ()
Largest spectroscopic cluster catalogue ever made.Contains galaxy clusters found in the SDSS DR3 spectroscopic database.1106 clusters.Clusters are found in a sevendimensional space.Galaxies within clusters are co-evolving.Thus, galaxies will not only cluster in position but also in colour.http://www.ctio.noao.edu/~chrism/current/research/C4/dr3The SDSS-C4 Galaxy Cluster Catalogue
We examine 94795 galaxies.Redshift range of 0.03 < z < 0.13Using all the galaxies projected within And of the cluster centres.Absolute magnitude range of -24 < < -21.2Colour-cut: we look at the radial profile of all the galaxies within of the red sequence for each cluster.Group membershipZ=0.07
Mass comes from the scaling relationship determined from the simulation presented in Miller et al. 2005 (summed optical r-band luminosity ) is a powerful tool -superior to the galaxy line-of-sight velocity dispersion -or the richness Mass estimation
It is not possible to measure directly the radius at which cluster has a mass over density of measure space over density of is radius where mean number density of galaxies = 200 critical densityCalculate for 1106 clusters in C4 by building the radial density profile of a certain mass and a certain r-band.Stack all the galaxies in 4 bins of mass.Determine for each bin of mass.Determination
Check value of the mean space density of field Check the effect of misidentifying the cluster centreCheck values by using only `good centres (von der Linden et al. in prep)Check for X-ray detectionCheck the colour constraint Check the fit to NFW profileTests of
Sheldon et al. (in prep.) have derived lensing profiles for clusters of galaxies in SDSS.Compare results
Finn et al. (in prep.) have determined as:
Total galaxy occupancy of `C4`Halo Occupation Distribution(HOD)
0Collister & Lahav 2004, Berlind & Weinberg 2002 Red galaxies All galaxies )Halo Occupation Distribution
Red All Faint Bright Investigating HOD as a function of galaxy properties
Motivated by halo model, we use `C4 to make a direct and empirical determination of HOD from the known halos (clusters).Compared to recent lensing work by Sheldon et al. (in prep.) & found remarkable agreement in size of radii.Summary & ConclusionFound a good fit to our galaxy radial distribution provided by NFW.We have a stable HOD with respect to the colour & luminosity.
Try to find an analytic equation for our mass function.Combine our HOD parameters with galaxy clustering measurements to better constrain cosmological parameters as and .Study HOD as a function of local environment.Compare HOD with other measurements of a cluster and group mass like X-ray parameters.Compare our results with the mock SDSS catalogue to ensure that the catalogues are a fair representation of the SDSS.Improve our results with latest SDSS and C4 catalogues.Compare properties of galaxies as colour, luminosity, morphology for different HODs to see which properties of galaxies in a halo change?Future work
The Holy GrailHalo model provides natural framework within which to discuss, interpret most measures of clustering; it is the natural language of galaxy biasThe Halo Grail(phrase coined by Jasjeet Bagla!)
The model come up recently is the best used for the statistical analysis and understanding the large datasets as SDSS survey.All the mass in the universe is assumed to be allocated in individual units called haloes.Specifically provides the `Halo Occupation Distribution (HOD) which is a function telling us how dark matter halos populate with galaxies.In contrast with the previous work which used the galaxy correlation functions to constrain HOD, we use known halos; clusters of galaxies to determine HOD. Matter distribution can be studied in two steps: the distribution of the mass within every halo and the spatial distribution of the haloesHalo Model as a tool to extract cosmology: an empirical approach
Testing Luminosity FunctionWe used the r-band LF of Blanton et al. (2003a) in order to derive the mean space density of field.We test if we get the same distribution in that band pass for our sample.We make this distribution for the absolute magnitude range of of the whole SDSS database.We find that for the galaxies in the absolute magnitude between -21 and -18 (as we go toward fainter galaxies), the number density of galaxies decrease.which is exactly where we are not complete!Our data is in redshift and Having considered -21.2 as our limit of completeness, there is no disagreement in the distribution we have achieved.
Testing value of the mean space density of fieldWe determine simply the value for N (number of galaxies in DR3 in spectroscopic area of 4188 sq. deg in the ) divided by the volume of our chosen sample.N = 94795S = Total sky area = F = Fraction of sky covered = 0.1V1 = Volume of the sphere in redshift 0.13V2 = Volume of the sphere in redshift 0.03V = (V1-V2). F N / V = 0.0042
Test the effect of misidentifying the cluster centreCheck if we are in the right centre, otherwise it cause different radial profile and hence different value for . There are three methods for finding the cluster centre; BCG, MEAN and GEOM cluster centroid measurements. BCG: position of the brightest galaxy in the cluster, we think is best to use because this method is relied on observations that clusters host a population of early type galaxies with small dispersion in colour.MEAN: coordinates of the galaxy with the highest density.GEOM: `luminosity weighted mean centroids, theses are cluster centres using all galaxies within 1 calculating a luminosity weighted average (in r-band) for RA and DEC of them. We find that by using other measurements of the cluster centroid there is no significant change in values of .
We also recalculate our estimates using the clusters with only `good centres.
For good centres we use the list of `C4 clusters with corrected BCG centres (von der Linden et al. in prep), they claimed that SDSS photometry of BCGs underestimates the flux and they correct for it.
We use this list to remove the `bad BCGs from `C4.
We find that there is no significant difference in our estimates of
Test the colour constraintIn the algorithm used to identify the galaxies around each cluster, we add this constraint in the sense that galaxies are clustered in colour & space.We looked at the radial profile of all galaxies within of the red sequence for each cluster.We may miss some galaxies.By relaxing this colour-cut to and we evaluate the impact on the value of We also vary -21.2 (limit of completeness) to brighter & fainter galaxies.
for X-ray detectionsCalculating the virial radius is crucial for our work.The X-ray detection is very accurate to measure the radii.We match `NORAS to `C4 in order to find which cluster has X-ray detection, the X-ray selected clusters are taken from Bohringer et al. (2000). We find 40 overlapped clusters. With the same formalism explained before we derive
Radial distribution of galaxies in groupsWe determine the projected galaxy density profile given mass from stacking groups scaled by their virial radius.Calculate the distance from cluster centre to each galaxy.Express them in units of (divide each distance to virial radius of each cluster).Stack them once in 4 bins of mass and then for the whole sample.Calculate the number of galaxies in radial bins divided by surface of each bin.Correct for the effect of fibre collision.
Profile fitting NFW profile is described as the universal density profile expressed in terms of by the formula:
Best-fitting NFW concentration parameters are:
This means that the criteria used in C4 clusters provides a good definition for the member galaxies and the clusters have the same shape with and without the colour-cut.
2.9 0.12.6 0.1 All galaxiesRed
0.38 0.44 0.46 0.49 0.55 0.56 0.61 0.71 0.73 0.79 0.94 0.96 0.42 0.46 0.47 0.54 0.59