Add a notebook for cluster mass-richness relation in cosmoDC2

[shenmingfu]

This notebook studies the mass-richness relation of galaxy clusters in cosmoDC2 extragalatic catalog as a validation test.

[evevkovacs]

@shenmingfu @cavestruz Thanks, this looks very nice. I cannot see the plot in the notebook and I tried to look at the notebook with nbviewer but it didn't work for some reason. I assume that it looks like the plot in the slack channel.
I think the next step is to add some data to this plot. Can you please add some of the curves from Fig 14 in https://arxiv.org/pdf/1805.00039.pdf. That paper is for redmapper clusters. Camille, can you point us to any other measurements of mass-richness that you think should be included on this plot? Thanks

[evevkovacs]

@shenmingfu @cavestruz There is a cosmoDC2 composite (add-on) catalog available with redmapper selected clusters and member galaxies. It is called cosmoDC2_v1.1.4_redmapper_v0.2.1py and should be accessible through GCR Catalogs. Could you could make a plot of the cosmoDC2 redmapper selected clusters versus the DES fit? Thanks!

[cavestruz]

@shenmingfu @evevkovacs - it might be easiest to overplot some of the work from Table 5/Fig 15 since there are the best fit scaling relations provided (e.g. add bands for Simet+17, Farahi+16)

[shenmingfu]

@evevkovacs @cavestruz Thank you. I was running the notebook on Nersc with desc-python. Could you try it on Nersc? I added plots to the updated notebook (though the instruction asks to clear all output before commit...) Yes the plot is the same as the one in the slack. The new notebook includes the results from DES Y1 redmapper clusters (McClintock et al. 2018), which also includes comparison with DES SV (Melchior et al. 2017) and SDSS (Simet et al. 2017). I will check the cosmoDC2 redmapper catalog.

[evevkovacs]

Thanks Shenming, this is very nice. The units of 'halo_mass' from the GCR are indeed Msun. The catalog native halo mass is in units of Msun/h but the GCR reader converts this to Msun, so your units should be ok. However, Katrin and I were just having a discussion about mass definitions. The McClintock paper/DES use M200m, whereas cosmoDC2 uses FOF mass, and they are different. The FOF mass is much lower than M200m. So you will need to convert M200m to M_FOF. As a first step, you can convert M200m to M200c. It turns out that M200c is not too different from M_FOF, for the FOF definition used in cosmoDC2. (A proper conversion between M200c and M_FOF requires an estimate for halo concentration, which we can get you, but for now, let's just go from M200m to M200c). The difference between M200m and M200c is that the former uses the background density and the latter uses the critical density. So the two definitions differ by a factor of Omega_m(z). (At z=0, the factor is about .265 and you would be multiplying M200m by this factor.) We think this will help a lot. (I am sot sure what mass definition was used in the SDSS work, but I assume that McClintock et al took this into account) Could you also please add the magnitude and radius cuts to the title of the plot, (along with the redshift range) and add the mass definition in parentheses to the legend: eg cosmoDC2 (M_FOF), DES Y1 (M_200c). We want to make clear that the mass definitions are not identical. Thanks

[evevkovacs]

@sfu @cavestruz I think that the conversion between M200m and M200c is not quite as simple as multiplying by the matter-density factor because you cannot assume that the radius of the halo is fixed. (ie it's not just a ratio of densities). You need to assume an NFW profile and a mass-concentration relation . This is discussed in https://arxiv.org/abs/1910.04121 in Sec . 6.1.2. They also give a reference to the Colussus code: https://bitbucket.org/bdiemer/colossus/src/master/colossus/ (They also fit M_500c in Eq. 11 and Table 4, which could go onto your plot, but again you would have to convert the mass. ) Take a look at Appendix C of https://arxiv.org/pdf/astro-ph/0203169.pdf. They give a formula for converting masses in the case where the density is the mean matter density, but would also work if you were using the critical density. The formulae would apply for converting M_500c to M_200c, for example, but I would use the updated fits to the concentration given in Child et al. (https://arxiv.org/pdf/1804.10199.pdf) Table 2. Extension to the case where the mean density is used in one mass definition and the critical density in the other should be feasible. Please let me know if you have any questions.

[shenmingfu]

@evevkovacs @cavestruz Thank you. Based on Child et al. 2018 Table 2, the clusters in 0.3<z<0.4, 4e13<halo_mass<1e15 Msun have 3<c<4.5. If we assume NFW profile, then R200m/R200c is about 1.2, this gives M200m/M200c about 1.1. This ratio is smaller than our earlier calculation (i.e. on the figure the mass-richness relation in DES Y1 still has larger mass than cosmoDC2). Marina made figures for redmapper richness versus halo mass (the two catalogs were geometrically matched) and that is very helpful for comparing the mass-richness relation in cosmoDC2 with observations. We can also try matching galaxies in the two catalogs with galaxyID, but it might be possible that a halo could be detected as multiple clusters or multiple halos could be detected as one cluster.

[katrinheitmann]

If your last statement is true (one halo = several clusters or several halos = one cluster) that would be indeed an interesting result, no? In cosmoDC2 every halo should have exactly on central galaxy (which is marked as such) so the identification of one halo=several clusters would mean that those clusters don't all have a well-defined central and vice-versa. Not difficult to imagine this happening, but I think interesting to study how often and why.

[shenmingfu]

Hi Katrin @katrinheitmann , Marina Ricci studied this earlier. I will ping you on the desc-dc2-validation slack channel and point you to her slides.

[reneehlozek]

hi @shenmingfu, just wanted to check how this was proceeding - did you post the link to the slides and/or do the changes proposed seem doable?

[shenmingfu]

Hi @reneehlozek , thanks for asking. I updated the notebook with new conversion between 200m and 200c. We are still working on the association criteria for the matching between cosmoDC2 extragalactic and redmapper catalog.

[reneehlozek]

Are these changes acceptable @cavestruz? Can this PR be merged?

[reneehlozek]

hi @evevkovacs, just wanted to check that this can be closed?