Appendix E
FCFs by Reduction Date

Ongoing development of the SCUBA-2 analysis has resulted in ongoing changes to the atmospheric opacity relationships and the FCFs. Depending on when your data were reduced you will need to apply different calibration values. orac-dr will automatically apply the appropriate values.

Note: As of the 2021A Starlink release, the opacity relationships and FCF values have been updated following the results presented by Mairs et al. 2021 [16]. Historical values derived by Dempsey et al. 2013 [8] are presented below the updated values for comparison.

Explanation of parameters (see also Appendix B):

Starlink currently applies the following multiplicative extinction correction to SCUBA-2 data:

where ${\tau }_{\nu }$ is the atmospheric opacity at the given frequency, $\nu$. “Opacity relationships” relate the measured ${\tau }_{225}$ to the atmospheric opacity at the operating frequencies of SCUBA-2, ${\tau }_{666}$ (450 $\mu$m) and ${\tau }_{345}$ (850 $\mu$m). Their form is:

where $a$, $b$, and $c$ are empirically derived coefficients (see Mairs et al. 2021 [16]). You can find out what opacity relationship was applied by using the Kappa command hislist.

This will return something like the following,

indicating, for example, that at 850 $\mu$m, $a$=3.71, $b$=-0.040, and $c$=0.202.

There are two commonly used FCF types:

• Peak FCF (Jy/pW/beam)—multiply your map by this when you wish to measure absolute peak fluxes of discrete sources.
• Arcsec FCF (Jy/pW/arcsec${}^2$)—multiply your map by this if you wish to use the calibrated map to do aperture photometry/extended source flux recovery.

Note: The FCFs are applied after the extinction correction, so the values are intrinsically related to one another. The proper extinction correction must be applied before using the FCF values presented below.

Results from Mairs et al. 2021 [16]. These are employed by default from Starlink Version 2021A. Dates are inclusive. See Figure E.1.

From 2011 May 1 onwards, the $a$, $b$, and $c$ coefficients presented in the table below correspond to those in Equation E.2.

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Figure E.1: From Mairs et al. (2021) [16]. FCFs derived using flux measurements of the primary calibrator Uranus during the stable part of the night (07:00-17:00 UTC) as a function of date. The grey shaded regions indicate epochs that are not included in the FCF determinations. The horizontal, shaded regions indicate the median FCF value over each span of time and the associated median absolute deviation added in quadrature with the 5% uncertainty in the Uranus flux model. The black (dotted) lines indicate the original FCF value derived by Dempsey et al. (2013) [8], adjusted for the newly derived opacity relationships, assuming the most-common atmospheric transmissions during observations (see Figure 2 of Mairs et al. (2021). Left: Peak (Top) and Arcsecond (Bottom) FCFs derived at 450 $\mu$m. The solid, vertical line at the right edge of the latest grey region marks 2018 June 30 when the secondary-mirror-unit maintenance was completed. Data wherein the atmospheric transmission are less than 10% are excluded. Right: Peak (Top) and Arcsecond (Bottom) FCFs derived at 850 $\mu$m. The solid, vertical line marks 2016 November, when the SCUBA-2 thermal-filter stack was updated. Data wherein the atmospheric transmission are less than 25% are excluded.

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Results from Dempsey et al. 2013 [8]: employed by default in Starlink Version 2018A and previous releases.