From its beginning DES was envisioned with SN Ia acting as a major probe for dark energy, with the knowledge that accurate calibration was paramount to making precise cosmological measurements. Thus, photometric calibration had always been a focus. The current method of calibration, the Forward Global Calibration Method (FGCM) (Burke et al., 2018), sets out to improve on existing calibration methods.
In recent years, photometric calibration of wide-field surveys has depended on calibrating a net- work of standard stars based on the CALSPEC network, consisting of a chain non-variable stars resting on the three HST DA white dwarfs, as described in Section 3.1.1.
Surveys which have used this approach included SDSS (Padmanabhan et al., 2008), SNLS (Regnault et al., 2009), and PS1 (Rest et al., 2014). The first iteration of the DES calibration, Drlica-Wagner et al. (Y1A1 Gold; 2018), followed this method; in the three-year data release (Y3A1) the PGCM (Photometric Global Calibrations Model) was used as a cross-check for FGCM.
The model-based approach in FGCM addresses limitations in the above calibration method, pri- marily the approximate nature of the spectral energy distributions (SEDs) of objects used to calculate them. A magnitude system is typically calibrated by a set of non-variable stars and extended to other objects. Then extrapolating thus calibrated magnitude systems to supernovae, which have significantly different SEDs, carries some uncertainty which must be corrected for or taken into account. In particular, FGCM eliminates the uncertainty associated with varying SEDs by including functions called ‘chromatic corrections’, which correct broadband magnitudes given an object’s SED.
In summary, the FGCM method fits a set of parameters nightly to predict zero points in the DES standard system, and additionally computes colour correction terms for an estimated or exact SED. For each exposure and CCD, the model forward computes (for a set of observed stars) the number of photons at top of the atmosphere, compared to photons predicted to be detected in the camera. The model parameters, consisting of eight atmospheric terms (for each night of observation) and two optical terms (for each time the mirrors are washed), are solved for to model the responses of the DECam passbands. Repeated observations of non-variable stars in the DES footprint are used to predict the number of photons at the top of the atmosphere are predicted iteratively, to determine these model parameters.
Thus, FGCM establishes a typical and representative DES standard (referred to as just ‘stan- dard’ for the remainder of this section), which comprises a set of filter passbands from the top of atmosphere to the detector, as well as a network of stars (acting as tertiary standards) which cover the DES footprint and are used to calibrate the science fields, determining observing conditions for
individual exposures. The FGCM calibration is tied to the HST system (for absolute magnitudes) via the CALSPEC standard star C26202. This process occurs outside of FGCM and has its own error contributions (Section 6.5.2). For each exposure and CCD the FGCM computes a zero point. An additional AB offset (determined from observations of C26202) is added to the FGCM zero point, to place magnitudes on an AB scale (Burke et al., 2018, equation 40).
Chromatic corrections are applied to give differential magnitudes in the DECam system, given ei- ther an object’s broadband colours (an approximation) or precise SED: the ‘full integrated chromatic correction’, necessary for supernovae. To first order, the chromatic correction integral (Burke et al., 2018, equations 6 and 14)is computed for each CCD and exposure.
Actual passband throughputs evolve with time and position, and the difference from the stan- dard system are measured. The calibration is adjusted in real time to account for deviations from DES standard for each exposure and CCD, comprising both the FGCM fit for the atmosphere and mirror model, and DECal: in situ monitoring, which measures the variation of optical properties of the survey system and atmospheric conditions in real time including both spatial and temporal variations of the instrument throughput, similar to other in situ systems such as SNDICE (Barrelet & Juramy, 2008; Regnault et al., 2016; Barrelet, 2016).
The release products of FGCM are the DES standard system, including instrument and atmo- sphere, in the form of transmission curves and zero points. The end goal of photometric calibration with FGCM is the ability to determine the magnitude zero points of any observation in standard passbands, given the SED (or an approximation of it in broadband colours), making use of atmospheric models and DECal data, as well as the FGCM model itself. This differs from previous broadband photometry methods, which have end products of magnitude zero points for the instrument passbands, which along with instrument transmissions allow transformations into other magnitude systems.
The most notable improvement from previous methods is the elimination (to a great extent) of the ambiguity associated with broadband photometry (from matrix transformations), by greatly improving SED estimates. Current performance is to a level of random residuals around 6 mmag and uniformity to withinσ= 7 mmag (Burke et al., 2018). The computation of associated systematic uncertainties is described in Section 6.5.2. Further details of FGCM are given in Burke et al. (2018), and details of application to differential photometry for SN Ia observations are presented in Lasker et al., (in prep.). Next, we detail uncertainties in both FGCM and the calibration transfer from the HST CALSPEC scale to FGCM, which go into our computations ofCcal.
FGCM calibration uncertainties
We describe the following sources of uncertainty in the FGCM calibration, and their contributions toCκ.
The two parts of this are the determination of the FGCM zero points, and the AB offsets. In addition, we consider the large scale spatial variations of FGCM. So far, these estimates neglect an uncertainty in the chromatic correction, which is not yet modelled well enough.
Unless otherwise specified, the following terms are added to diagonal elements of Cκ which corre-
spond to DECam zero points.
• Zero point uncertainty per exposure:
The accuracy of FGCM zero points (for a given CCD and exposure) depends on the number of stars used to measure the ZP in Scene Modelling Photometry (Section 6.4.2; used to then estimate SN Ia magnitudes), and the ZP accuracy of a single star’s measurement. The latter is informed by the scatter of tertiary stars in FGCM, 5–6 mmag (figure 11, Burke et al., 2018). There are sufficiently many stars used to determine the ZP in SMP that we can take the zero point uncertainty to be 1 mmag.
• AB offset uncertainty from filter curve:
§6.4 Methods 111
DES synthetic magnitudes of C26202 (using DES filters) and the DES standard magnitude of C26202 to transform. For DES instruments, these have errors of 5˚A. These uncertainties are also correlated with zero points, resulting in off-diagonal terms inCκ.
• AB offset uncertainty from C26202 magnitude:
The uncertainty in a single measurement of C26202 in the DECam standard system is given by the residual scatter of 5 mmag in FGCM (Burke et al., 2018), divided by the square root of the number of observations of C26202 in that passband.
• Large scale spatial variations of FGCM:
The uniformity of the FGCM calibration over the sky is assessed by comparison to GAIA observa- tions above the atmosphere, in Burke et al. (2018, section 5.3). In particular, correlated measure- ment error in observations that were made close in time can imprint on the large scale uniformity. The difference in observed GAIA DR1 G magnitudes and those predicted by transforming DES gri bands are binned in HEALPIX with NSIDE= 256.3 The binned residuals are distributed as found to resemble a gaussian distribution with σres = 6.6 mmag. This mean uncertainty applied to the calibration of DES SNe Ia is reduced by a factor√2 by the (assumed) equal contribution of GAIA and FGCM scatter to the residual, and by a further factor of√2 when considering that spatial uniformity applied to the calibration of DES SN fields is applied to the difference between two positions, of the SN Ia and the standard stars. Thus we add 1
2σres to diagonal DECam zero point errors inCκ, assuming that this scatter is uncorrelated between filters.
Calibration transfer uncertainties
The following uncertainties are associated with the transfer of the HST CALSPEC scale to the FGCM natural system, placing the FGCM standard stars on an absolute scale. These largely follow JLA, and are as described in Betoule et al. (2014, section 3.4). We compute these contributions to Cκ following
descriptions therein.
• Uncertainty in white dwarf colour: following Betoule et al. (2014, section 3.4.1), we estimate the uncertainty in the colour of the three DA white dwarfs that anchor the HST scale (are primary standards) as a 0.5% uncertainty in the slope of their spectra over the 3000–10000˚A range.
• Uncertainty of calibration transfer to CALSPEC standard C26202:the FGCM calibration (viewed as magnitudes of standard stars in science fields) is tied to the CALSPEC network via the standard star C26202, which is calibrated by the primary HST stars. In JLA, the uncertainty in this transfer was estimated by modelling the measurement error in individual spectra by monitoring the repeatability of the spectrum of AGK +81 266. For DES, we assume 0.3% uncertainties based on Bohlin (2000) in the absence of such spectral monitoring. In both cases, the uncertainty falls with the square root of number of observations of the CALSPEC standard with STIS; however C26202 only has a single STIS observation.