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S/N versus magnitude for post-cryo as a function of galactic latitude | |
First it's important to note that our S/N estimation process does not account for confusion noise. That's because the noise-sigma was derived using a standard-deviation of the fluxes from repeated single-exposure photometry on each source. Hence, the magnitude limits in the table below are upper limits (lower limits in flux space). Alternatively, the inverse of a S/N estimate (the σmag axes in the figures below) can be used to assess the photometric stability at a specific magnitude.
These estimates also apply to difference-image photometry since the photometric noise in a properly differenced image of the same piece of sky will be immune to "static" source confusion. The only contribution is from instrumental and Poisson-noise. For example, for a single-exposure differenced with a 12-frame deep co-add, the σmag values below need to inflated by ~ √[1 + 1/12] ~ 1.04. This is small compared to the accuracy at which a magnitude-limit can be determined.
These single-exposure limits (and corresponding σmag) were used to generate plots of the W1 discovery space (from difference-imaging) for a variable source as a function of time-averaged magnitude and amplitude, at low and high galactic latitudes. The assumptions here are that (i) the time-averaged magnitude can be determined to relatively high precision (e.g., from a co-add, which may also serve as a reference image) and (ii) the peak-to-peak amplitude must be measured to > 4σmag.
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b [deg] W1 W2
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s/n: 5 10 20 s/n: 5 10 20
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0 12.5* 11.8* 10.7 12.6* 11.9 10.5
5 14.6* 14.3 12.9 14.0 13.1 11.9
15 15.8 15.0 13.8 14.4 13.5 12.5
30 15.8* 15.0* 14.0* 14.5* 13.6* 12.6*
45 15.9* 15.0* 14.0* 14.5* 13.7* 12.6*
70 15.9 15.1 14.1 14.5 13.7 12.5
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NOTES:
o Asterisked (*) values:
These are based exclusively on 3-band cryo multiframe repeatability metrics
using data acquired towards the end of the 3-band period. Here's why:
(i) some magnitude limits at low b from the L1-averaged post-cryo
analysis were speculative [due to biases from a higher L1 flux
detection threshold; see text].
(ii) for b=30 and 45 deg, no L1 post-cryo data was queried and used.
These latitudes were added later for completeness following
3-band cryo multiframe analyses.
o magnitude limits are accurate to about +/- 0.05-0.1 mag.
o estimates pertain to averages over several fields within a galactic
longitude range of ~ +/- 30 deg of the galactic center. For measurements
at a few other longitudes, see Roc's allsky (4-band cryo) results.
Given the multiframe production pipeline was not run on the Pass-2 Post-Cryo frames, we do not have access to the versatile single-exposure flux-repeatability metrics to perform this analysis. We therefore restorted to working with the Post-Cryo single-exposure source database directly. First, the All-sky Catalog was first queried for multiframe (L3) "seed" extractions at four different galactic longitudes within +/- 30 deg of the galactic bulge for each latitude of interest (b = 0, 5, 15, 30, 45, 70 deg). Each region was about 3 square degrees in size. These seed extractions were then cross-matched to the Pass-2 Post-Cryo single-exposure (L1) source database to obtain the L1 flux history for each source.
The L1 fluxes for each source were then trim-averaged and the standard-deviation also estimated. To avoid abnormally lo/hi L1 fluxes, outliers etc.. for each L3 input seed, the minimum and maximum L1 measurements were blindly tossed from each stack. The final L1 magnitudes were computed from the averaged L1 fluxes using the single-exposure zero-points appropriate to Pass-2 Post-Cryo reprocessing. A proxy for the flux repeatability (in 1-sigma mag units) was then computed using:
σmag = 1.0857 * StdDev(L1 fluxes; unbiased estimate of population sigma) / <L1 fluxes>.
The direct L1-averaging method has a major limitation. Given the L1 extractions correspond to a higher detection threshold in flux space than the deeper L3 extractions from multiframe (for a given detection S/N), the averaged L1 fluxes will be biased high at low flux levels (or as one approaches the detection limit). I.e., we are likely to catch the high tail of the L1 flux distribution for a source, comprising only those measurements that made it above the L1 detection limit. This explains the turnover at faint magnitudes in some of the plots below, but it is present at all galactic latitudes. The vertical red lines demarcate the magnitudes where this bias starts to become appreciable (determined from comparisons with the relatively less biased L3 photometry - our "pseudo truth"). Estimates to the right of these lines should not be trusted. Because of this faint L1-flux bias, we also show for comparison the flux-repeatibility sigma versus L3 magnitude from the multiframe pipeline at the same galactic latitudes using data from the end of the 3-band cryo period.
Furthermore, the faint L1-flux bias will occur at
progressively brighter magnitudes as source-confusion increases
(towards |b| ~ 0).
This is because the noise-sigma used for
source-detection in the pipeline
includes a confusion noise estimate.
A higher confusion noise contribution implies that brigher sources
will be predominately selected for a given S/N detection threshold.
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Note: red horizontal lines in figures below correspond to S/N levels of 5, 10, and 20 from top to bottom respectively. These are density-plots where the number of points per 2D mag,sigma bin is represented by the color bar.
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