Limiting Surface Brightness

Note, edited after bug fix. Slightly more optimistic values now

HI all. We have added a computation of the expected coadded limiting surface brightness magnitudes in each filter to the standard set of metrics we run on each simulated observing cadence. A full tech note doing the math can be found here:

The end result is that the median 3-sigma surface brightness limits for a 10x10 arcsec area in our current baseline survey strategy after 10 years is:

filter # 30s visits coadded 3-sigma depth mag/sq arcsec
u 54 29.4
g 69 30.3
r 179 30.3
i 182 29.7
z 159 28.9
y 166 28.1

Note that some recent cadence white papers claimed Rubin would get deeper than 30.5 mag/ sq arcsec in some filters. This value is overly optimistic, possibly assuming we would obtain 825 visits in each filter rather than summed over all filters.

Hi Peter+,

Thank you for your nice derivation.

The numbers you derive are for perfect flat-fielding, it seems to me.

My experience is typically with galaxies that have a much larger angular extent (arc minutes typically), and using data where the flat field is taken from twilight and/or dark sky flats.

In those situations the limiting surface brightness is set by how flat the flat field is. Since we were using sky flats the limit is how flat the sky appears to be. For that situation we measure the sky level in areas (squares each about 15 arcsec wide) away from the galaxy / objects of interest that appear to be free of sources, and then take the rms of the average level in each of those boxes to be the sky uncertainty.

The rule of thumb is that we can typically get to a few tenths of a percent of the sky surface brightness, as long as there is not much scattered light about (this typically comes from moonlight scattering around the dome, so images go deeper when the moon is down).

By fitting a surface to apparently object free areas, in principle you can subtract the local variation due to the glow of the moon and other bright sources. This appears to be the approach being adopted.

However you run the risk of subtracting real structure in the sky (i.e. very faint and distant sources, individually close to or below the detection limit), some of which may be scientifically interesting.


– Gerhardt

Yes, these are the depths one could reach in the theoretical limit where there is perfect flat fielding, perfect sky subtraction, no issues from scattered light, etc. Rubin will have a dome screen and tunable laser for flat fielding, so we don’t have to rely on sky flats, but these numbers are still a best-case scenario.

Just an update - after the bug fix, which came in with help from the surface brightness team in the galaxies collaboration, who helped set up the metric in the first place - the result is much closer to but still not quite the same as in the cadence note. However, it does match rough scaling estimates from other surveys such as Stripe 82.

Actual data processing is more complicated, of course, and may result in different values. More feedback and updates from the DM team are appreciated, to help guide the community working on low surface brightness work and for evaluating survey strategy (as described in the Cadence Note [1812.04897] LSST Cadence Optimization White Paper in Support of Observations of Unresolved Tidal Stellar Streams in Galaxies beyond the Local Group).