# Testing Completeness with Shallow SN Field Coadds¶

Using the SVA1 SN Field Shallow Coadds, we can test completeness

-Eli.

## Completeness as a function of Limiting Magnitude (mag_auto_i)¶

I take the combined masked catalogs from above, and split according to limiting magnitude. Using the mangledepth systematics maps, we can approximately recreate the mag_auto_i limiting magnitude map using the same depth reconstruction technique as for SVA1 Gold. However, it seems that due to the pixelization and the different dither strategy, the reconstruction is not working as well as it appears to do for SVA1 gold. Therefore, in any region of "constant depth" there is actually a range of depths (though the majority of galaxies in any thus selected region will have the same depth.)

A sample completeness plot looks like this:

The erf model fit is:

c = (e/2) [ 1-erf((m-m50)/sqrt(2w))) ]

where c is the completeness, e is the efficiency, m50 is 50% completeness magnitude, and w is the width.

The erf model looks good. The vertical line shows the 10sigma i band limiting magnitude.

Next, we can look at how m50, the 50% completeness magnitude, varies with limiting magnitude:

There is a nice relation here, with some scatter:

m50 = 23.81 + 0.78*(lim-23)

I have not yet compared this to Balrog or UFIG, but this is a more direct estimate, and I think it's what I'm going to use for redMaPPer at least.

Finally, we can look at the width parameter, which is surprisingly constant with depth (w=0.193):

## Completeness as a function of limiting magnitude and surface brightness¶

We can also look at the completeness as a function of surface brightness, for different bins in depth.

First, let's look at the measured magnitude and surface brightness (mu_max_i) values. White points are the deep "all" catalog, and red points are from the shallow T1000 catalog.

Left: shallower limiting magnitude | Right: Deeper limiting magnitude |

In the left panel, at all magnitudes there is a bias such that the mu_max_i value is biased brighter. Interestingly, there isn't this bias at the bright end in the deeper regions. I'm not sure why this is, but it may be related to different seeing...

At the faint end, you can see in all cases that we're only detecting the galaxies at any given magnitude with the highest surface brightness, as expected.

We can map out the completeness as a function of magnitude and surface brightness:

Left: shallower limiting magnitude | Right: Deeper limiting magnitude |

The red lines show the m50 parameter from the completeness plots above.

Things look reasonable, and I'd like to model this, but I don't know the obvious functional form.

It would also be nice to look at this (and the completeness) as a function of galaxy type, but we don't have an obvious handle on this at the moment.