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

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

3. 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

4. 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

5. The Current Color Model

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

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

8. Projection from Different Epoch

9. Sensitivity to Magnitude Limit

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

12. 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

13. Realization in Color Diagram

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

17. 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