# SCUBA-2 Integration Time and Sensitivity

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.

### 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
900″
1800″
3600″
7200″

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:

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:

### 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 )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.