Comparing the Photometric Calibration of DESI Imaging and Gaia Synthetic Photometry

We assess the relative calibration of the DESI Legacy Imaging Surveys (Zou et al. 2017; Dey et al. 2019; D. Schlegel et al. 2023, in preparation) by comparing with Gaia DR3 synthetic photometry (De Angeli et al. 2022; Gaia Collaboration et al. 2022). We analyze two LS data releases (DR9 and DR10). Here, we present the maps for DR9; additional figures and data for both DR9 and DR10 are included on zenodo. ⁷

To synthesize Gaia photometry in the DECam passbands, we use the Gaia XP Continuous Mean Spectra ⁸ and the GaiaXPy ⁹ packages. Gaia spectra are only available for stars with G ≤ 17.65, and there are significant spatial gaps in the coverage (see the additional figures on zenodo). We cross-match Gaia spectroscopic sources to LS sources with a search radius of 01. We only include stars with 0.6 < BP − RP < 2.5, G ≥ 13.5, and with valid flux measurements in g-, r- and z-bands. We remove blended sources by requiring FRACFLUX < 0.1 in grz. ¹⁰ We remove saturated sources in LS in each filter by using ANYMASK = 0. ¹¹ The saturation limit is fainter for decl. ≥32° (especially in z-band), and as a result, we have fewer (and typically fainter) stars available in the north.

The Gaia-DECam synthetic photometry is not "standardized" (see Section 2.2 of Gaia Collaboration et al. 2022) compared to the observed LS photometry, and it has systematic offsets (of up to 8 mmag) which depend on (BP − RP) and G. We correct for these offsets by fitting them with polynomials of BP − RP and G separately for the northern and southern LS. We obtain the polynomial coefficients using stars in −10° < decl. < +10° for DR9 South and DR10 and in all of DR9 North. In the regions where the fits are performed, the average photometric offset is zero by definition, i.e., we do not measure the absolute calibration offset.

To assess the spatial variation of the photometric offsets, we divide the cross-matched sample into HEALPix (Górski et al. 2005) pixels with Nside = 128 and compute the median magnitude difference in each pixel. We remove pixels with <20 stars in each pixel (which removes 4%–7% of the pixels in DR9 South). Figure 1 shows the maps of the median magnitude difference in grz-bands between LS DR9 and Gaia synthetic photometry. The relative calibration errors (i.e., the pixel-to-pixel rms) in grz are 4.7, 3.7, 4.4 mmag in DR9 South; 4.6, 4.5, 5.9 mmag in DR9 North; and 5.0, 3.9, 4.3, 5.5 mmag in DR10 griz bands. These estimates include calibration errors in both LS and Gaia, and represent the upper limit on the LS calibration error. The increase in DR10 calibration errors is due to its larger area coverage—restricting to stars in both DR9 and DR10, their calibration rms agrees within 0.02 mmag. These rms calculations exclude the region at decl. < −29° (see below).

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While photometric errors of individual stars contribute to the pixel-to-pixel rms, they are mostly negligible. For smaller spatial pixels (i.e., Nside = 256) with ≥20 stars/pixel (removing 26%–48% pixels), we get relative calibration rms of 5.0, 3.9, 4.9 mmag in grz in DR9 South. The higher rms compared to Nside = 128 is due to having fewer stars per pixel and thus larger per-pixel error, and to smaller-scale variations in the calibration systematics only probed at higher resolution.

A few patterns are visible: (1) Gaia scan patterns, which are most significant in the g band. (2) Honeycomb patterns (especially in r and i bands), likely due to calibration errors in Pan-STARRS1 (Chambers et al. 2016) to which LS photometry is tied at decl. > −2925. (3) Gradients at large angular scales, e.g., positive offsets toward the Galactic Plane at R.A. ≃ 300°. It is unclear if these variations are due to calibration systematics in LS or Gaia or both. (4) Large overall offsets at decl. < −2925  in r- and z-bands in DR9. At decl. = −2925  the LS photometric calibration switches from PS1 to internal calibration ¹² (the "ubercalibration" method; Padmanabhan et al. 2008; Schlafly et al. 2012). The r-band offset has a median value of −13 mmag with a slight gradient varying from −16 to −9 mmag. The z-band offset has a median value of 8 mmag with a stronger gradient varying from 1 to 19 mmag. These offsets are due to an absolute calibration error in DR9 (fixed in DR10). At decl. < −30°, the DR9 calibration rms errors in grz are 3.7, 3.3, 6.6 mmag; after removing the smoothly varying components (the monopole and dipole), the r and z band calibration rms errors are reduced to 2.8 and 4.1 mmag.

We have assessed the calibration precision of LS DR9 and DR10 photometry by comparing with Gaia synthetic photometry. Due to systematics in the Gaia synthetic photometry (which we cannot separate from the LS calibration systematics), we only obtain upper limits on the LS calibration error. We find spatial variations in the photometric offsets due to LS calibration systematics (i.e., the "honeycomb" patterns) as well as variations at larger angular scales. We also find large systematic offsets at decl. < −2925  in r- and z-bands in DR9, which do not affect DESI as it only observes at decl. > −2925. But for samples selected with the full DR9 imaging data, the offsets could cause a systematic shift in the surface density or in the photometric redshifts.

We thank Michele Bellazzini and Francesca De Angeli for useful suggestions and comments. This research is supported by the Director, Office of Science, Office of High Energy Physics of the U.S. Department of Energy under Contract No. DEAC0205CH11231, and used the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility under the same contract. This research made use of data from the DESI Legacy Imaging Surveys (https://www.legacysurvey.org/acknowledgment/ for the complete acknowledgments) and from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC,https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement.