Based on the NYU-VAGC DR4 (Blanton et al. 2005), we have extracted the galaxy catalogue
for our purpose. You may download our extracted galaxy catalogue
or directly go to NYU-VAGC to obtain the full version of galaxies. 

There are a few differences in the extracted catalogue with respect to NYU-VAGC:  

- We have ran our own K-corrections, both to z=0.0 and to z=0.1, using the
  latest version of Blanton's Kcorrect software (v_4).

- We now have Kcorrections to z=0.0 and z=0.1 for ALL GALAXIES and QSOs
  that have meaningful magnitudes and a meaningful redshift, including the
  galaxies that have been ASSIGNED a NEAREST redshift, as well as those
  galaxies that have a redshift from an alternative source (the ALTO systems).

- We have applied the latest zero-point corrections for the apparent magnitudes, 
  to convert the SDSS magnitudes to proper AB magnitudes.
  The corrections are: m_AB - m_SDSS = [-0.036, +0.012, +0.010, +0.028, +0.040]
  for [u,g,r,i,z]

- One can estimate the stellar mass using the fitting formula given by Bell et al. 2003
  log(M) = -0.306 + 1.097 *[^{0.0}(g-r)]-0.1-0.4*[^{0.0}M_r-5log h-4.64]

Anyway, in our group catalogue, the NYU_VAGC galaxy ID is used.

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Find the groups in SDSS.

I. Selections:

   1. 0.01 <= z <= 0.20
   2. completeness >= 0.7     (fgotmain)

   We adopt these selections in order to have a fair sample to search the
   groups. Note that we did not apply  (3. m < mmax @ r-band) cut.
   After these selections, we get 362356, 369447 and 408119 galaxies which covers
   an area of 4514 square degrees for Samples I, II and III, respectively. 

II. group catalogue: (We are using luminosity normalized to z=0.1)

   1. The galaxies are listed in `isdss4a_1' (Sample I), `isdss4b_1' (Sample II)
     and `isdss4c_1' (Sample III) with format:
     1. galaxy id; 
     2. galaxy id in NYU_VAGC (row-number in the VAGC DR4 files)
     3. group id; (0: not selected in any groups)
     4. brightest galaxy = 1; other galaxies in groups = 2
     5. most massive galaxy (M_stellar) = 1; other galaxies in groups = 2
   
   2. The group members are listed in `isdss4a_2' (Sample I), `isdss4b_2' (Sample II)
     and `isdss4c_2' (Sample III) with format:
     1. group id; 
     2. member galaxy id in NYU_VAGC
     3. member galaxy id in sdss4?

   3. group properties are stored in `sdss4a_group' (Sample I), `sdss4b_group' (Sample II)
     and `sdss4c_group' (Sample III) with format:
     1. group id;
     2. RA; 3. dec; 4. z; (they are luminosity weighted group center)
     5. group L_{-19.5} log L_{\odot}/h^2; (characteristic group luminosity)
     6. group stellar mass of galaxies brighter than M_r<-19.5   
     7. halo mass1 in log M_halo/ (M_{\odot}/h); (estimated using the ranking of group L_{-19.5})
     8. halo mass2 in log M_halo/ (M_{\odot}/h); (estimated using the ranking of M_stellar)
     9. f_{edge}; edge effect: See Yang et al. 2007 
     10. ID1: 1: mass estimated using the ranking of L_{-19.5}, -1: extrapolation
     11. ID2: 1: mass estimated using the ranking of M_stellar, -1: extrapolation 

   Note that the halo masses are estimated using the ranking of the groups
   according to their L_{-19.5} or M_stellar. At high redshift, 
   the small halos are not all resolved in our group catalogue, thus suffer 
   from the (mass) incompleteness. [Readers who are interested in the halo 
   mass assignment please refer to Yang et al. (2007) for more 
   details.] The first 3 lines in `sdss4?_group' contain such incompleteness
   information.   

   For very small groups, no masses are assigned (with log M_halo = 0).
   However one can obtain an estimation of the halo mass using the mean relation between the 
   stellar mass of the central galaxy and the halo mass obtained in Yang et al. (2008b).

   Note that M_halo is estimated according to the mass function of WMAP3 cosmology, 
   one can convert it to the cosmology which he/she is interested. 

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