## Appendix EFCFs 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.

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

 $\mathrm{Extinction\phantom{\rule{2.22198pt}{0ex}}}$ (E.1)

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:

 ${\tau }_{\nu }=a×\left({\tau }_{225,\mathrm{zen}}+b+c×\sqrt{{\tau }_{225,\mathrm{zen}}}\right),$ (E.2)

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.

%  hislist file | grep EXT.TAURELATION

This will return something like the following,

EXT.TAURELATION.450=(23.3,-0.018,0.05),
EXT.TAURELATION.850=(3.71,-0.040,0.202), EXT.TAUSRC=auto, FAKESCALE=1,

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.

 Date FCF – 450 $\mu$m FCF – 850 $\mu$m Jy/pW/beam Jy/pW/arcsec${}^{2}$ Jy/pW/beam Jy/pW/arcsec${}^{2}$ until 2011 April 30 383 4.9 1080 5.0 2011 May 1–2016 November 1 $531±93$ $4.61±0.60$ $525±37$ $2.25±0.13$ 2016 November 2–2018 June 29 $531±93$ $4.61±0.60$ $516±42$ $2.13±0.12$ 2018 June 30 onwards $472±76$ $3.87±0.53$ $495±32$ $2.07±0.12$

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

Date
Opacity Relationship

450 $\mu$m 850 $\mu$m

until 2011 April 30 32 $×$ (${\tau }_{225}$ - 0.02) 5.2 $×$ (${\tau }_{225}$ - 0.013)
2011 May 1 onwards
 $a$ = 23.3$±$1.5 $b$ = -0.018$±$0.006 $c$ = 0.05$±$0.04
 $a$ = 3.71$±$0.18 $b$ = -0.040$±$0.008 $c$ = 0.202$±$0.044

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

 Date FCF – 450 $\mu$m FCF – 850 $\mu$m Jy/pW/beam Jy/pW/arcsec${}^{2}$ Jy/pW/beam Jy/pW/arcsec${}^{2}$ until 2012 January 383 4.9 1080 5.0 2012 January–2012 July 606 6.06 556 2.42 2012 July onwards 491 4.71 537 2.34

 Date Opacity Relationship 450 $\mu$m 850 $\mu$m until 2012 January 32 $×$ (${\tau }_{225}$ - 0.02) 5.2 $×$ (${\tau }_{225}$ - 0.013) 2012 January–2012 July 26 $×$ (${\tau }_{225}$ - 0.01923) 4.6 $×$ (${\tau }_{225}$ - 0.00435) 2012 July onwards 26 $×$ (${\tau }_{225}$ - 0.01196) 4.6 $×$ (${\tau }_{225}$ - 0.00435)