smoothly mask out very red galaxies

[aphearin]

As pointed out by @erykoff in #6, there is a ~5-10% sub-population of field galaxies that are significantly redder than the cluster red sequence at each redshift. Properly resolving this is not straightforward because we have limited information about the luminosity-dependence of the red sequence at each redshift, and so in the short term we prioritized having realistic color-magnitude scalings over having a perfect redMaPPer red sequence. For a short term workaround, we could conduct some additional masking on the Galacticus library to throw away such galaxies, as described below.

For example, suppose that at redshift z=0.5, the mean g-r color of the red sequence observed in DES is g-r=1.5. Well then the simplest masking would be to just throw away all Galacticus galaxies redder than this, and then repeat the search we are already doing. However, a possible side effect of this implementation would be that the entire 5-10% sub-population will crowd tightly at exactly g-r=1.5 at this redshift, creating a sharp discontinuity in color-redshift space.

Here is an alternative implementation that may resolve this. Rather than making a hard cut on g-r<1.5, we could instead increase the dimension of our KDTree search using a newly created fake galaxy property. Let's call the fake galaxy property y, and use a simple sigmoid function that relates y to observed g-r:

Here is how the matchup would proceed using the new property y. In this example, let's restrict attention to a single redshift, but this trick applies more generally to z-dependent g-r values. For every empirically modeled galaxy, we manually set its y value equal to 0. For every Galacticus galaxy, we use the sigmoid model demonstrated in the figure to create the property y from the observed g-r color of the Galacticus galaxy. Then we augment our KDTree search with the property y: for every empirical galaxy, we not only look for a matching Galacticus with matching restframe g-r and r-i, we additionally require a match on y. Effectively, this requires that the galaxy will be near the observed red sequence, but the enforcement of this requirement is "softened" by the finite slope of the sigmoid function. As a further detail, in order to protect against the observed red sequence being too tight with this technique, instead of setting y to be identically zero for all empirical galaxies, we could instead use a Gaussian tightly localized about zero.

Again, in the real case that we would implement, the behavior of the sigmoid function we use to map onto Galacticus will not just have constant sigmoid parameters, but it will instead have a midpoint that scales with the mean of the red sequence at the Galacticus galaxy's redshift. In the ideal case, we know this value of y not just as a function of redshift, but also as a function of luminosity. If we knew that, we could properly resolve #27. But without knowing that information, something along these lines is the best we can do.

@erykoff - This model patch is primarily important for redMaPPer; most of the proposed science papers for DC2 would not be significantly impacted by this one way or another. So if this proposed improvement seems trivial from your perspective since it does not resolve the root issue #27, then we will not bother implementing it at all, so please weigh in here whether you think this is worth bothering to take the time (and labor) to implement during this final calibration stage.

CC @evevkovacs @abensonca @yymao @j-dr

[erykoff]

This sounds interesting and useful, but I don't think it is mission-critical for redMaPPer on DC2.