In this work we have developed a new way to estimate the mass of galaxy clusters. We present templates of spatial profiles of total galaxy luminosity and number from a low-redshift (z < 0.2) cluster sample, using data from the
Millennium Run. After binning clusters in different mass ranges, we produce luminosity and number density profiles for each of the cluster subsamples, using a statistical background subtraction method. This method is inspected and the result shows that the profiles are quite different for different mass bins. We then apply the same procedure to 20 real clusters (also z < 0.2) using data from the Sloan Digital Sky Survey. The mass of these real clusters has been measured to high precision using deep Chandra observations. It also produces different template profiles with different mass bins. Thus these profiles can be used to estimate the mass of an unknown cluster. It will be very useful for large optical/infrared extragalactic surveys.

Abstract i
1 Introduction 1
1.1 Importance of Cluster Mass 1
1.2 Existing ways to estimate cluster mass 2
1.2.1 Masses of Clusters from X-ray Gas 2
1.2.2 S􀀀Z effect 3
1.2.3 Velocity Dispersion of Member Galaxies 5
1.2.4 Weak-Lensing Effect 6
1.2.5 Large􀀀Scale Bias 6
1.2.6 Number Count of Member Galaxies 7
1.3 Era of Large Imaging Surveys 8
2 the Method 11
2.1 Querying the Millennium Simulation Data 11
2.2 K-correction 13
2.3 Statistical Background Subtraction Method 14
2.4 Luminosity Function 14
2.5 Characteristic Magnitude 18
2.6 Construction of Templates 21
2.7 SDSS Cluster Sample 26
2.8 SDSS Footprint 29
2.9 Query SDSS data 30
2.10 Finding BCGs 32
2.11 Templates of SDSS Data 34
3 Results 37
3.1 Templates - Mass Relation 37
3.2 2 fitting 38
3.3 Spline Interpolation 40
3.4 Selection of Radial Bins 41
3.5 Mass Estimation 42
4 Dscussion and Prospects 45
4.1 The Combination of Radial Bins 45
4.2 Millennium Run v.s. SDSS data 47
4.3 Prospects 49
Bibliography 51

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