### 5 Calibrating SCUBA-2 Data

#### 5.1 Extinction Correction

Analysis of the SCUBA-2 skydips and heater-tracking data from the S2SRO data has allowed calculation of the opacity factors for the SCUBA-2 450 $\mu$m and 850 $\mu$m filters to be determined. Full details of the analysis and on-sky calibration methods of SCUBA-2 can be found in Dempsey et al. (2010) [6].

Archibald et al. (2002) [7] describes how the Caltech Submillimeter Observatory (CSO) 225 GHz opacity, ${\tau }_{225}$, relates to SCUBA opacity terms in each band, ${\tau }_{450}$ and ${\tau }_{850}$. It was assumed for commissioning and S2SRO that the new SCUBA-2 filters are sufficiently similar to the wide-band SCUBA filters that these terms could be used for extinction correction. In the form ${\tau }_{\lambda }=a×\left({\tau }_{225}-b\right)$, the original SCUBA corrections were:

 ${\tau }_{450}=26.2×\left({\tau }_{225}-0.014\right);$ (1)

and

 ${\tau }_{850}=4.02×\left({\tau }_{225}-0.001\right).$ (2)

The JCMT water-vapour radiometer (WVM) is now calibrated to provide a higher-frequency opacity value which has been scaled to ${\tau }_{225}$. The WVM (not the CSO 225 GHz tipper) data were used for this analysis.

The new filter opacities as determined from skydip data are as follows:

 ${\tau }_{450}=19.04×\left({\tau }_{225}-0.018\right);$ (3)

and

 ${\tau }_{850}=5.36×\left({\tau }_{225}-0.006\right).$ (4)

The SCUBA-2 filters are different from the SCUBA filters, with the 450 $\mu$m filter, in particular, significantly narrower than its SCUBA counterpart. The SCUBA-2 filter characteristics are described in detail on the JCMT website6.

The extinction correction parameters that scale from ${\tau }_{225}$ to the relevant filter have been added to the map-maker code. You can override these values by setting ext.taurelation.filtname in your map-maker config files to the two coefficients ‘(a,b)’ that you want to use (where ‘filtname’ is the name of the filter). The defaults are listed in \$SMURF_DIR/smurf_extinction.def. We have also added a slight calibration tweak to WVM-derived values to correct them to the CSO scale. It is worth noting that if an individual science map and corresponding calibrator observation has already been reduced with the old factors (and your source and calibrator are at about the same airmass and if the tau did not change appreciably), any errors in extinction correction should cancel out in the calibration.

#### 5.2 Flux conversion factors

Primary and secondary calibrator observations have been reduced using the specifically designed dimmconfig_bright_compact.lis. The maps produced from this are then analysed using tailor-made Picard recipes. Picard is a post-processing and data combination tool that uses the same infrastructure as ORAC-DR, but is designed to be used after the initial reduction with the DIMM is complete. Details of the Picard recipes and how to use them can be found on the ORAC-DR web page7.

A map reduced by the mapmaker has units of pW. To calibrate the data into units of janskys (Jy), a set of bright, point-source objects with well known flux densities are observed regularly to provide a flux conversion factor (FCF). The data (pW) can be multiplied by this FCF to obtain a calibrated map, and the FCF can also be used to assess the relative performance of the instrument from night to night. The noise equivalent flux density (NEFD) is a measure of the instrument sensitivity, and while not discussed here, is also produced by the Picard recipe shown here. For calibration of primary and secondary calibrators, the FCFs and NEFDs have been calculated as follows:

(1)
The Picard recipe SCUBA2_FCFNEFD takes the reduced map, crops it, and runs background removal. Surface fitting parameters are changeable in the Picard parameter file.
(2)
It then runs the Kappa beamfit task on the specified point source. The beamfit task will estimate the peak (uncalibrated) flux density and the FWHM. The integrated flux density within a given aperture (30 arcsec radius default) is calculated using Photom autophotom. Flux densities for calibrators such as Uranus, Mars, CRL 618, CRL 2688 and HL Tau are already known to Picard. To derive an FCF for other sources of known flux densities, the fluxes can be added to the parameter file with the source name (in upper case, spaces removed): FLUX_450.MYSRC = 0.050 and FLUX_850.MYSRC = 0.005 (where the values are in Jy), for example.

An example of a Picard parameter file (used for reduction of the 850 $\mu$m calibrators) is shown here:

[SCUBA2_FCFNEFD]
AUTOPHOTOM=1
BACKGROUND_FITMETHOD=fitsurface
FITSURFACE_FITTYPE=spline
FITSURFACE_FITPAR=4
USEFCF=1
FLUX_850.ARP220=0.688
FLUX_850.ALPHAORI=0.629
FLUX_850.TWHYDRAE=1.37
FLUX_850.V883ORI=1.34
LOGFILE=1
(3)
It then uses the above procedure to calculate the three alternative FCF values described below.
• $FC{F}_{arcsec}$ (surface brightness calibration)
$FC{F}_{arcsec}=\frac{{S}_{}}{}$ tot${P}_{}$

int $×{A}_{}$

pix, (5) 

where ${S}_{}$

tot$isthetotalfluxdensityofthecalibrator,$P_int$istheintegratedsumofthesourceinthemap\left(inpW\right)and$A_pix$isthepixelareainarcsec$^2$,producinganFCFinJy/arcsec$^2$/pW.This$FCF_arcsec$\phantom{\rule{1em}{0ex}}isthenumbertomultiplyyourmapbywhenyouwishtohavesurfacebrightnessunits,andtobeabletocarryoutaperturephotometry.$ $FC{F}_{beam}$ (point source calibration)

$FC{F}_{beam}=\frac{{S}_{}}{}$ peak${P}_{}$

peak (6) 

producing an FCF in units of Jy/beam/pW.

The measured peak signal here is derived from the Gaussian fit of beamfit. The peak value is susceptible to pointing and focus errors, and we have found this number to be somewhat unreliable, particularly at 450 $\mu$m. $FC{F}_{beam}$ is the number to multiply your map by when you wish to measure absolute peak flux densities of discrete unresolved point sources. The peak value in the map is then the total flux density of the point source. You should not integrate over the source after calibrating in this fashion, as this will give an overestimate of the flux density. $FC{F}_{beamequiv}$ (improved point source calibration)

To overcome the problems encountered as a result of the peak errors, a third FCF method has been derived, where the $FC{F}_{arcsec}$ is modeled with a Gaussian beam, with a FWHM equivalent to that of the theoretical JCMT diffraction-limited beam at each wavelength. In effect, the resulting FCF gives an ‘equivalent peak’ FCF from the integrated value, assuming that the point source is a perfect Gaussian.

$FC{F}_{beamequiv}=\frac{{S}_{}}{}$ tot $×1.133×{FWH{M}_{beam}}^{2}$${P}_{}$

int $×{A}_{}$

pix, (7) 

or more conveniently:

 $FC{F}_{beamequiv}=FC{F}_{arcsec}×1.133×{FWH{M}_{beam}}^{2},$ (8)

where FWHM is 7.5 arcsec and 14.0 arcsec at 450 $\mu$m and 850 $\mu$m, respectively. This produces an FCF in units of Jy/beam/pW.

The $FC{F}_{beamequiv}$ and $FC{F}_{beam}$ should agree with each other. However, this is often not the case when the source is distorted, for the reasons mentioned above. $FC{F}_{beamequiv}$ has been found to provide more consistent results and it is advisable to use this value when available, instead of $FC{F}_{beam}$. It is also advisable, when running the matched filter on data (see Section 6.1), to use the $FC{F}_{beamequiv}$ for calibration.

6http://www.eaobservatory.org/jcmt/instrumentation/continuum/scuba-2/filters/

7http://www.oracdr.org/oracdr/PICARD