Plot richness vs. ngal for matched clusters in RM and WaZP

[chihway]

These two quantities should be correlated, but by how much?

[ajamsellem]

[ajamsellem]

[ajamsellem]

Although the reduced χ2 values for both of these fits are on the order of 1, the models seem to diverge at higher richness/galaxy numbers. Do we expect more spread about the fit at higher richness?

[chihway]

Can you maybe bin the points or plot it transparent? it's a little hard to tell when all the points are overlapped. Interesting that the high mass clusters are more different and RM has systematically more "counts" compared to WaZP. Naively I might expect the opposite since RM only counts red galaxies... but there are many many factors, so prob not a big deal.

This is a good start -- we can imagine making some equivalent richness selection in ngal, it will be noisy given the scatter, but it's something to start with.

[ajamsellem]

Maybe this is a better illustration of the data. The binning in each plot are labeled according to the tick marks on the axes. There were so few data points above 70 on the x-axis and 100 on the y-axis, that these parts of the data were not included (because you couldn't tell that those regions were non-trivial anyway). I also include a zoom-in of the dense region of Ngals = (5,10) and Richness = (5,15). Note that there are no richness or Ngal values below 5.

I think this plot bolsters your point that there will be quite a bit of scatter. If there was no scatter at all, we would see a nice diagonal line (of square bins) from the bottom left to the top right of the plot. There is noticeable departure from such an ideal.

[chihway]

In the first plot above, was the binning in log-space? I'm a little confused why there are relatively few galaxies in the area number count and richness 10-20?

Also, can you make the same plot for clusters with richness 20-100? This is the sample used for the Y1 splashback measurement.

In any case, let's ask Ricardo whether the lack of scatter is expected.

[ajamsellem]

Revised 2d histogram with log colorbar.