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**Catalogues with membership and sub-membership (download)**

  * A2192: download here: {{budhies:optical:wht_spectroscopy:A2192_final_with_additional_HI.txt.tar.gz}}

  * A963: In prep.
 

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**The Dressler-Shectman test:**

__References__:

  - see original paper by Dressler & Shectman (1988) 
  - recent paper that explains it nicely: Hou et al. 2012 MNRAS 421 3594). See section 2

For A2192_1 I made the following bubble-plot. Colous correspond to the different structures defined by us (red=A2192_1a, black=1b, turquoise=1c, yellow=1d, and green=none). The size of the circles scales with exp(delta), where delta is defined for each galaxy by:

(delta_i)^2 = [(N_neighbours + 1)/ sigma_cluster^2] * [ (<v>local_i - <v>)^2 + (sigma_local_i - sigma_cluster)^2 ] (eq. 1 in Hou et al)

N_neighbours=10
and <v>local_i= mean velocity of the 10 galaxies in the neighborhood of galaxy i

{{budhies:optical:wht_spectroscopy:A2192_1_DS_plot.gif}}

__Things to notice:__ 

(i) A2192_1d couldn't be clearer!!! And A2192_1c is very clear to.!

(ii) A2192_1a and 1_b are also well separated (specially if you look at big black circles and big red circles), but the smaller circles in the middle are a bit mixed, so to check that they are separated in z, I made this plot:

{{budhies:optical:wht_spectroscopy:A2192_1_histogram_from_DS_plot.gif}}

Where you can see the little red doots (dashed red histogram) is well separated from the black little dots (black dashed histogram). The dotted histogram is the overall velocity distribution (A2192_1)

__Some numbers to quantify the degree of substructure in the cluster:__

**I. Basic method** 

I computed D_obs = SUM[delta_i] (see eq 2 in Hou et al.) and got that D_obs=220. 

If we divide D_obs by N_members (113 in this case) we get 1.947, which is > 1.

According to the threshold value method, having D_obs/N_members > 1 means that there IS substructure! (it was obvious from the bubble-plot anyway)

**II. More sofisticated method** 

A more robust method involves Monte Carlo simulations. I did such simulations to compute P, the probability that a value of D > Dobs would have been arrived by chance

In A2192_1 I get that P < 1/15000 !!!! 

CONCLUSION: we can be super-duper sure that there IS substructure in this cluster, and from the plots above, we can also be confident that our (visual) classification is good, and consistent with this DS method!