Signal-to-noise Analysis for NGC253 at 450μm - December 2006 run

I have used the data for 13 HWP cycles in NGC253. This includes file numbers 034373 - 378, 034387 - 388, and 034390 - 394. In these files the parallactic and zenith angles vary by 36 and 10 degrees, respectively; the airmass varies from 1.36 to 1.81; and τ₂₂₅ varies from 0.045 to 0.058.

Using the Uranus 450μm SHARP data I estimate a scale factor of 464 Jy per SHARP data unit. (Uranus has a flux of 153 Jy into a 10'' beam.) This scale factor yields a flux of 20 Jy/beam at the peak of NGC253 and 430 Jy/beam at the peak of Orion/BNKL. Note that SCUBA measured a peak 450 μm flux in NGC253 of only ~8 Jy per 10'' beam (Alton, Davies, & Bianchi 1999, A+A, 343, 51). SHARC-II measures ~1390 Jy/beam in Orion at 350 μm; our 450 μm measurement implies a spectral index of ~2.7, a bit on the steep side.

From this data I created a map of σ_P by propagating the errors on the q and u reduced Stokes parameters. To ensure that these errors were reasonable I ran sharp_combine on two subsets of the 13 files (the subsets contained 6 and 7 HWP cycles) and compared the variation in polarization between the 2 subsets with the errors. The resulting χ² are shown in the histogram below. The large number of results with χ² < 1 may suggest that the errors have been overestimated. For the χ² < 6 values shown below the median occurs at ~0.8, the mean ~ 1.5, and a standard deviation of ~ 1.6.

The SHARP specification table in the 2007 NSF proposal states that at 450 μm we should achieve σ_P < 1% in 5 hours of integation for a source with a total intensity of I = 0.28 Jy per 4.6'' x 4.6'' pixel. This can be written as
0.01 = σ_P (I / 0.28) (t_obs / 5)^1/2
where t_obs is the total observing time in hours. This is for weather conditions given by τ₂₂₅ = 0.05 and an airmass of 1.3 (ZA ~ 40 degrees).

Following our previous analysis on DR21 we compare the actual uncertainties achieved to this estimate by calculating the "degradation factor" DF:
DF = (σ_P / 0.01) (I / 0.28) (t_obs / 5)^1/2 exp[-25 (τ₂₂₅ sec z - 0.05*1.3)]
To determine this factor for NGC253 we use the σ_P and relative intensity (scaled to Jy/pixel using the number above) calculated from the 13 HWP cycles and an integration time of 90 seconds per file (90*4*13 = 1.3 hours). I used an average atmospheric attenuation of opacity τ₂₂₅ sec z ~ 0.077. The DF factor is shown in the map and histogram below. Left: Degradation factor map. Grayscale ranges from 0.1 (black) to 5 (white). Right: Degradation factor histogram. The peak occurs at ~ 0.7; the distribution has a median of 1.2 for all values of DF; for values of DF < 2.5 the standard deviation of the distribution is ~ 0.4.