The amount of elapsed time required to map a certain field size, to a certain depth, at a given atmospheric transmission is described in the equations below. For users who simply want a quick time estimate we advise using the ITC gui which is explained here.
Contents
Elapsed time
The elapsed telescope time (seconds) to map a given field size to a given 1-sigma depth (mJy) is described in the relations below.
| Mapping Mode | Time elapsed 450 microns (s) | Time elapsed 850 microns (s) |
|---|---|---|
| Daisy | \frac{1}{\sigma_{450}}\bigg]^{2}) |
\frac{1}{\sigma_{850}}\bigg]^{2}) |
| 900″ | \frac{1}{\sigma_{450}}\bigg]^{2}) |
\frac{1}{\sigma_{850}}\bigg]^{2}) |
| 1800″ | \frac{1}{\sigma_{450}}\bigg]^{2}) |
\frac{1}{\sigma_{850}}\bigg]^{2}) |
| 3600″ | \frac{1}{\sigma_{450}}\bigg]^{2}) |
\frac{1}{\sigma_{850}}\bigg]^{2}) |
| 7200″ | \frac{1}{\sigma_{450}}\bigg]^{2}) |
\frac{1}{\sigma_{850}}\bigg]^{2}) |
The 450 and 850 transmission factors (Τ450, Τ850) and the sampling factor (f) in the above equations are described below:
Atmospheric transmission
For a given air mass (AM) and opacity (classically defined at 225GHz, τ225GHz), the transmission can be calculated using the following relations:
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The opacity (τ225GHz) ranges for various weather Grades are given below:
- Grade 1: Less than 0.83mm PWV. (τ225GHz < 0.05)
- Grade 2: 0.83 – 1.58 mm PWV. (0.05 < τ225GHz < 0.08)
- Grade 3: 1.58 – 2.58 mm PWV. (0.08 < τ225GHz < 0.012)
- Grade 4: 2.58 – 4.58 mm PWV. (0.12 < τ225GHz < 0.2)
- Grade 5: More than 4.58 mm PWV. (τ225GHz > 0.2)
For a source at a given declination (δ, measured in degrees), a representative air mass near transit can be derived using:
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Sampling factor f
Elapsed times are derived using the basic reduction parameters in SMURF and use default map pixels of 2″ and 4″ at 450 and 850 microns, respectively. A change to this default pixel size is taken into account by the sampling factor (f) when estimating the elapsed time. The sampling factor f is simply defined as:
f = ( pixel size requested / default pixel size )2
At 450 and 850 this becomes:
f450 = ( pixel size requested / 2 )2 and f850 = ( pixel size requested / 4 )2
For Point-source detections the S/N can be dramatically improved by applying a matched-beam filter which utilizes the full flux in the beam rather than just the peak value at the position of a source. This will shorten required observing times to reach a certain S/N typically by factors of f = 8 (450μm) and f = 5 (850μm).
SCUBA-2 Confusion limit
The confusion limit depends on a number of factors including Galactic cirrus emission, the extra galactic background as well as the beam size. While dependent on assumptions and location the derived values are close to
- 850 microns = 0.7 mJy/beam
- 450 microns = 0.5 mJy/beam
The sensitivity of a SCUBA-2 blank field will be limited by a un-reduceable noise level of this order.
The implies that going below a detection limit of ~ 2 mJy in a blank field will give a high risk of false detections. See for instance Chen et.al Ap.J. 762, 81 (2011) “Faint Submillimeter Galaxy Counts at 450 micron”. The situation is better for detection of a source at a known position. The lower probability that a random peak coincide with your know source increases the chance it is a real detection. However, the confusion limit still needs to be taken into account when estimating the position and flux error.
Overheads
The SCUBA-2 ITC currently takes into account the 90 seconds required for set ups and fast flats
If you are calculating an integration time for a proposal it should be noted that there is no need to provide an overhead estimate for calibrations (pointing, focus, flux). The time used for calibration is absorbed by the observatory.