An Analytic Approach to Assess Galaxy Projection Along A Line of Sight Anbo Chen University of Michigan

In Collaboration University of Michigan University of Chicago Gus Evrard, Jiangang Hao, Tim Mckay University of Chicago Matt Becker

Outline Building a halo model to assess the projection effect Tuning model parameters to SDSS Making predictions on expected projection effect Monte Carlo realizations and applications Future directions

Building the Analytic Model Initial power spectrum (Eisenstein & Hu) Halo-halo correlation (Seljak & Warren) HOD (Brown et al.) N(M,z,MB)~(M-Mmin)/Mscale Color Model (Hao et al.) G-R mean and sigma for Red and Blue galaxies Blue fraction in central and satellite galaxies

The Current Color Model

The Color Model (Ctd.) z~0.6 turn around is not currently well characterized Crucial on background projections from Red population

Mean Projection Effect Targeting on a dark matter halo (cluster) and calculate the expected projection of galaxies

Projection from Different Epoch

Sensitivity to Magnitude Limit

Comparison to SDSS M-N200 Relationship Johnston et al. (right panel) has slope = 1.28 +/- 0.04 Consistent only considering projection effect

Monte Carlo Simulation Method Calculate the probability of finding a halo within each volume in space and mass Calculate the probability of having a galaxy in each volume in N-dim space Application Distribution of contamination Velocity dispersion

Realization in Color Diagram

Application to Velocity Dispersion The analytic model can help interpret the non-Gaussianity in velocity dispersion and henceforth put corrections on the velocity dispersion

Conclusion An analytic model built to address the projection effect along line of sight Parameters tuned to the result from SDSS Expected projection predicted with cluster size and magnitude limit Application via Monte Carlo method Future directions high redshift M-N relation velocity dispersion