Color Transformations of Photometric Measurements of Galaxies in Optical and Near-infrared Wide-field Imaging Surveys^*

Before starting data homogenization, it is necessary to reduce all the magnitudes to common zero-points and aperture radii, as well as clear the sample from obviously incorrect values that will clog up the statistics. In the beginning, magnitudes with NaN values such as −9999, 999, etc. (the exact value depends on the survey) were removed from the sample. Surveys that are not originally in the AB system are converted to AB using published zero-point differences: Hewett et al. (2006) for the UKIRT surveys UKIDSS and UHS (+0.634, +0.938, +1.379, +1.9 for YJHK respectively) and González-Fernández et al. (2018) for the VISTA surveys VHS and VIKING (+0.6, +0.916, +1.366, +1.827 for YJHK respectively). Also, to fit the data we use measurements only for galaxies with small angular sizes having radii containing 50% of Petrosian flux smaller than 25 to minimize the effects of potentially poor sky subtraction for very extended targets.

After preprocessing we convert all magnitudes to some "standard" photometric system: this is a crucial step when one needs to use photometric measurements originating from different sources. Despite the same name, e.g., "SDSS g," the actual implementations of a given photometric systems by different survey have significantly different filter throughput curves. Therefore, one needs to adopt one reference photometric system and convert all the available measurements into it. We adopted the filter sets from SDSS in the optical and UKIDSS in the near-infrared as our internal reference. One has to pay special attention to the fact that "integrated" photometry from different surveys may have different magnitude types, e.g., Petrosian in SDSS vs Kron (Kron 1980) in PanSTARRS. Also, Petrosian radii depend on the survey depth, therefore they are not the same for, e.g., SDSS and DES, leading to inconsistent integrated flux measurements. Nevertheless, for the computation of color transformations we used total magnitudes because the main goal of our work was to be able to build integrated spectral energy distributions of galaxies using data from different surveys, which would be consistent among them. We also discuss the applicability of our transformations to aperture magnitudes, which do not depend on the survey depth, but do depend on the image quality.

We approximate a relation between the magnitude difference of the survey being converted and the reference survey and an observed color of a galaxy. A simple χ² fitting of a 2D scattered data set with the weights of each point corresponding to the uncertainties of original measurements will not produce satisfactory results because densely populated regions of the color–magnitude space will dominate the statistics and the solution will "ignore" sparsely populated "edges." Chilingarian & Zolotukhin (2012) proposed a weighted approach to fit 2D and 3D scattered data sets from SDSS and GALEX to infer the parameterisation of the color–color–magnitude relation for non-active galaxies: a weight assigned to each measurement depends on the local density of data points in the parameter space inferred from 2D or 3D histograms. Here we use a variant of this approach, which includes 2 steps.

The first step is to compute a 2D color–magnitude histogram in the survey we are converting, e.g., g vs (g − r) if we correct DES g into SDSS g using DES g − r color. We keep 98% of data along each dimension by first computing 1D distributions of all data points along color and magnitude and then rejecting 1% of the strongest outliers on each side of the distribution. Then the remaining color–magnitude space is split into 50 × 50 bins to compute a 2D histogram. Then the 1st-step weight is computed as the inverse of a count in the 2D histogram to account for the non-uniform distribution of galaxies in the observed color–magnitude space. For the subsequent analysis we reject the measurements, which fall into the bins of a 2D histogram containing fewer than 15 data points.

On the second step we compute a set of 1D distributions of magnitude difference between the survey being converted (e.g., DES g) and the reference (e.g., SDSS g) in 17 bins on the observed color (e.g., DES g − r) assigned as follows: (i) the 80%-ile of the data is split into 11 equally sized bins; (ii) the 80%–98%-ile is split into 3 bins on each side of the 90%-ile distribution; (iii) the remaining 1% of outliers by color on either side are rejected. Then in each of the 17 bins we compute a 1D histogram on the magnitude difference (e.g., g_DES − g_SDSS) in 150 bins rejecting 10% of the strongest outliers on each side, i.e., keeping 80%-ile of the data. This apparently high number is needed to properly handle the central very dense part of the distribution. Then, each of these 1D histograms is normalized by its maximum and the 2nd-step weights for each photometric measurement is computed as the inverse of the counts in the 1D distributions.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

At the end, we multiply 1st- and 2nd-step weights to assign a final weight to each measurement and use a linear regression to compute the color transformation in the form:

$$\begin{eqnarray*}&&{\mathrm{mag}}_{\mathrm{target}}={\mathrm{mag}}_{\mathrm{ref}}+a+b\cdot {\mathrm{color}}_{\mathrm{ref}}\end{eqnarray*}$$

In most cases, a linear regression cannot properly describe the photometric transformation in the entire range of observed colors. In such cases, we use a piece-wise linear regression with up-to three color sub-ranges (see Figure 4). We preferred a piece-wise linear fit to a nonlinear (e.g., 2nd or 3rd degree polynomial) solution because the latter case could lead to very high residuals in the tails of the color distribution. We do not impose any constraints on magnitude range and compute the regression for the color dependence only, because the result does not show any magnitude dependent effects (see Figure 5).

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

To calculate the quality of the derived transformation, we could not use a standard r.m.s. because some of the photometric measurements used in the fitting have rather large uncertainties of up-to 0.3 mag (see the previous section). Therefore, when we compute a histogram of the fitting residuals, we see a "background" level looking like a large Gaussian with a sharp peak on top of it: if we compute an r.m.s. value without taking this into account, we will severely overestimate the r.m.s. of the residuals. Therefore, the values of residuals presented in the next section of the paper correspond to the moments of the peak on top of the background distribution shown in Figure 6.

Zoom In Zoom Out Reset image size

We used a piece-wise linear regression of 2 or 3 segments to compute the transformations between DES and SDSS measurements. Overall, the fitting quality is very high with the residuals at a few-% level for Petrosian magnitudes. The DELVE survey despite being shallower than DES was conducted with the same instrument using the same (physical) filters, and all the data reduction, processing, and analysis algorithms were identical (DES Data Management system pipeline; Morganson et al. 2018). We applied the color transformations obtained for DES to DELVE data and they demonstrated full consistency (see the discussion about the reconstruction of the red sequence below).

DES → SDSS:

g − r < 0.656: gsdss = gdes + 0.072(gdes − rdes) + 0.033

0.656 < g − r < 1.187: gsdss = gdes + 0.198(gdes − rdes) − 0.049

g − r > 1.187: gsdss = gdes − 0.005(gdes − rdes) + 0.193

${\sigma }_{{{\rm{g}}}_{\mathrm{sdss}}}=0.048\,\mathrm{mag}$

g − r < 0.792: rsdss = rdes + 0.052(gdes − rdes) + 0.074

0.792 < g − r < 1.148: rsdss = rdes + 0.098(gdes − rdes) + 0.037

g − r > 1.148: rsdss = rdes + 0.208(gdes − rdes) − 0.088

${\sigma }_{{{\rm{r}}}_{\mathrm{sdss}}}=0.041\,\mathrm{mag}$

r − z < 0.621: rsdss = rdes + 0.034(rdes − zdes) + 0.089

0.621 < r − z < 1.284: rsdss = rdes + 0.381(rdes − zdes) − 0.126

r − z > 1.284: rsdss = rdes − 0.058(rdes − zdes) + 0.438

${\sigma }_{{{\rm{r}}}_{\mathrm{sdss}}}=0.042\,\mathrm{mag}$

i − z < 0.237: isdss = ides + 0.122(ides − zdes) + 0.048

0.237 < i − z < 0.400: isdss = ides + 0.407(ides − zdes) − 0.019

i − z > 0.400: isdss = ides + 0.174(ides − zdes) + 0.074

${\sigma }_{{{\rm{i}}}_{\mathrm{sdss}}}=0.046\,\mathrm{mag}$

r − z < 0.803: zsdss = zdes + 0.060(rdes − zdes) + 0.031

r − z > 0.803: zsdss = zdes − 0.099(rdes − zdes) + 0.159

${\sigma }_{{{\rm{z}}}_{\mathrm{sdss}}}=0.061\,\mathrm{mag}$

SDSS → DES:

g − r < 0.797: gdes = gsdss − 0.132(gsdss − rsdss) − 0.001

0.797 < g − r < 1.043: gdes = gsdss − 0.238(gsdss − rsdss) + 0.083

g − r > 1.181: gdes = gsdss − 0.165(gsdss − rsdss) + 0.007

${\sigma }_{{{\rm{g}}}_{\mathrm{des}}}=0.045\,\mathrm{mag}$

g − r < 0.600: rdes = rsdss + 0.027(gsdss − rsdss) − 0.117

g − r > 0.600: rdes = rsdss − 0.093(gsdss − rsdss) − 0.044

${\sigma }_{{{\rm{r}}}_{\mathrm{des}}}=0.040\,\mathrm{mag}$

r − z < 0.659: rdes = rsdss − 0.040(rsdss − zsdss) − 0.083

0.659 < r − z < 1.783: rdes = rsdss − 0.276(rsdss − zsdss) + 0.072

r − z > 1.783: rdes = rsdss − 0.235(rsdss − zsdss) − 0.0003

${\sigma }_{{{\rm{r}}}_{\mathrm{des}}}=0.036\,\mathrm{mag}$

i − z < 0.216: ides = isdss − 0.162(isdss − zsdss) − 0.040

0.216 < i − z < 0.583: ides = isdss − 0.237(isdss − zsdss) − 0.024

i − z > 0.583: ides = isdss​​​​ − 0.102(isdss − zsdss) − 0.102

${\sigma }_{{{\rm{i}}}_{des}}=0.038\,\mathrm{mag}$

r − z < 0.336: zdes = zsdss + 0.421(rsdss − zsdss) − 0.231

0.336 < r − z < 0.868: zdes = zsdss + 0.035(rsdss − zsdss) − 0.101

r − z > 0.909: zdes = zsdss + 0.123(rsdss − zsdss) − 0.177

${\sigma }_{{{\rm{z}}}_{\mathrm{des}}}=0.063\,\mathrm{mag}$

Download table as:  ASCIITypeset images: 1 2

The DESI Legacy Surveys (Dey et al. 2019) include the two parts, Northern and Southern, carried out using three different telescopes and instruments: the Northern part consists of the Beijing–Arizona Sky Survey (BASS; g and r-band observations collected at the 2.3 m telescope using the 90Prime camera) and the Mayall z-band Sky Survey (MzLS; z-band observations collected at the 4 m Mayall telescope using the Mosaic-3 camera); the Southern part includes the data collected with the DECam instrument at the 4 m Blanco telescope (same as DES/DELVE). Therefore, one needs to derive separate sets of photometric transformations for the Northern and Southern parts of DESI Legacy Surveys data. It turns out that the DES/DELVE color transformations cannot be applied to the LS-South measurements despite being collected with the same telescope and instrument and even sometimes being derived from the same raw data, because of the differences the original observations were reduced and analyzed (see details in the next section). Therefore, we derived specific transformations for LS-South to/from SDSS photometry. The LS-South transformations yield higher residuals than those for DES/DELVE data because of higher systematic errors in the DECaLS photometry: (e.g., ${\sigma }_{{r}_{\mathrm{decals}}}=0.087\,\mathrm{mag}$ versus ${\sigma }_{{r}_{\mathrm{des}}}=0.044\,\mathrm{mag}$ and ${\sigma }_{{r}_{\mathrm{vst}}}=0.041\,\mathrm{mag}$). Transformations for LS-South (DECaLS) and LS-North (MzLS+BASS) yield similar r.m.s. of the fitting residuals.

DECaLS → SDSS:

g − r < 0.712: gsdss = gdecals + 0.014(gdecals − rdecals) + 0.055

0.712 < g − r < 0.984: gsdss = gdecals + 0.404(gdecals − rdecals) − 0.223

g − r > 0.984: gsdss = gdecals + 0.049(gdecals − rdecals) + 0.126

${\sigma }_{{{\rm{g}}}_{\mathrm{sdss}}}=0.072\,\mathrm{mag}$

g − r < 0.732: rsdss = rdecals + 0.038(gdecals − rdecals) + 0.084

0.732 < g − r < 0.951: rsdss = rdecals + 0.252(gdecals − rdecals) − 0.073

g − r > 0.951: rsdss = rdecals + 0.082(gdecals − rdecals) + 0.089

${\sigma }_{{{\rm{r}}}_{\mathrm{sdss}}}=0.087\,\mathrm{mag}$

r − z < 0.629: rsdss = rdecals + 0.061(rdecals − zdecals) + 0.099

0.629 < r − z < 1.280: rsdss = rdecals + 0.359(rdecals − zdecals) − 0.088

r − z > 1.280: rsdss = rdecals + 0.054(rdecals − zdecals) + 0.302

${\sigma }_{{{\rm{r}}}_{\mathrm{sdss}}}=0.073\,\mathrm{mag}$

r − z > 0.779: zsdss = zdecals + 0.191(rdecals − zdecals) − 0.023

r − z < 0.779: zsdss = zdecals − 0.066(rdecals − zdecals) + 0.177

${\sigma }_{{{\rm{z}}}_{\mathrm{sdss}}}=0.079\,\mathrm{mag}$

SDSS → DECaLS:

g − r < 0.657: gdecals = gsdss − 0.034(gsdss − rsdss) − 0.035

0.657 < g − r < 0.973: gdecals = gsdss − 0.356(gsdss − rsdss) + 0.176

g − r > 0.973: gdecals = gsdss − 0.113(gsdss − rsdss) − 0.060

${\sigma }_{{{\rm{g}}}_{\mathrm{decals}}}=0.071\,\mathrm{mag}$

g − r < 0.662: rdecals = rsdss + 0.007(gsdss − rsdss) − 0.112

0.662 < g − r < 0.968: rdecals = rsdss − 0.214(gsdss − rsdss) + 0.034

g − r > 0.968: rdecals = rsdss − 0.057(gsdss − rsdss) − 0.117

${\sigma }_{{{\rm{r}}}_{\mathrm{decals}}}=0.065\,\mathrm{mag}$

r − z < 0.619: rdecals = rsdss − 0.036(rsdss − zsdss) − 0.107

0.619 < r − z < 1.787: rdecals = rsdss − 0.247(rsdss − zsdss) + 0.022

r − z > 1.787: rdecals = rsdss − 0.202(rsdss − zsdss) − 0.056

${\sigma }_{{{\rm{r}}}_{\mathrm{decals}}}=0.068\,\mathrm{mag}$

r − z > 0.787: zdecals = zsdss − 0.093(rsdss − zsdss) − 0.041

0.787 > r − z > 0.893: zdecals = zsdss + 0.050(rsdss − zsdss) − 0.154

r − z < 0.893: zdecals = zsdss + 0.2356(rsdss − zsdss) − 0.320

${\sigma }_{{{\rm{z}}}_{\mathrm{decals}}}=0.144\,\mathrm{mag}$

MzLS + BASS → SDSS:

g − r < 0.664: gsdss = gbass − 0.072(gbass − rbass) + 0.071

0.664 < g − r < 1.102: gsdss = gbass + 0.241(gbass − rbass) − 0.137

g − r > 1.102: gsdss = g bass + 0.017(g bass − rbass) + 0.110

${\sigma }_{{{\rm{g}}}_{\mathrm{sdss}}}=0.066\,\mathrm{mag}$

g − r < 0.732: rsdss = rbass − 0.053(gbass − rbass) + 0.120

0.732 < g − r < 0.951: rsdss = rbass + 0.265(gbass − rbass) − 0.099

g − r > 0.951: rsdss = rbass + 0.048(gbass − rbass) + 0.108

${\sigma }_{{{\rm{r}}}_{\mathrm{sdss}}}=0.061\,\mathrm{mag}$

r − z < 0.619: rsdss = rbass + 0.040(rbass − zmzls) + 0.102

0.619 < r − z < 1.302: rsdss = rbass + 0.262(rbass − zmzls) − 0.035

r − z > 1.302: rsdss = rbass + 0.081(rbass − zmzls) + 0.201

${\sigma }_{{{\rm{r}}}_{\mathrm{sdss}}}=0.072\,\mathrm{mag}$

r − z < 0.692: zsdss = zmzls + 0.235(rbass − zmzls) − 0.053

0.692 < r − z < 0.797: zsdss = zmzls + 0.047(rbass − zmzls) + 0.078

r − z < 0.797: zsdss = zmzls − 0.076(rbass − zmzls) + 0.175

${\sigma }_{{{\rm{z}}}_{\mathrm{sdss}}}=0.081\,\mathrm{mag}$

SDSS → MzLS + BASS:

g − r < 0.689: gbass = gsdss + 0.007(gsdss − rsdss) − 0.025

0.689 < g − r < 0.845: gbass = gsdss − 0.455(gsdss − rsdss) + 0.293

g − r > 0.845: gbass = gsdss − 0.107(gsdss − rsdss) − 0.001

${\sigma }_{{{\rm{g}}}_{\mathrm{bass}}}=0.067\,\mathrm{mag}$

g − r < 0.603: rbass = rsdss + 0.007(gsdss − rsdss) − 0.106

0.603 < g − r < 0.930: rbass = rsdss − 0.188(gsdss − rsdss) + 0.011

g − r > 0.930: rbass = rsdss − 0.030(gsdss − rsdss) − 0.135

${\sigma }_{{{\rm{r}}}_{\mathrm{bass}}}=0.060\,\mathrm{mag}$

r − z < 0.592: rbass = rsdss − 0.045(rsdss − zsdss) − 0.091

0.592 < r − z < 1.240: rbass = rsdss − 0.198(rsdss − zsdss) − 0.001

r − z > 1.240: rbass = rsdss − 0.218(rsdss − zsdss) + 0.023

${\sigma }_{{{\rm{r}}}_{\mathrm{bass}}}=0.068\,\mathrm{mag}$

r − z < 0.309: zmzls = zsdss − 0.349(rsdss − zsdss) + 0.036

0.309 < r − z < 1.015: zmzls = zsdss − 0.077(rsdss − zsdss) − 0.047

r − z < 1.015: zmzls = zsdss + 0.247(rsdss − zsdss) − 0.377

${\sigma }_{{{\rm{z}}}_{\mathrm{mzls}}}=0.078\,\mathrm{mag}$

Download table as:  ASCIITypeset images: 1 2

VST ATLAS is a wide-field survey of the Southern hemisphere of the sky; KiDS covers a smaller area, but at a higher depth. Both surveys were conducted with the 2.6 m ESO VST telescope and include the u band in addition to griz even though the u band images are very shallow, especially in VST ATLAS. Both surveys have a small overlap with SDSS, what makes the analysis more difficult because of a much smaller number of measurements, which we can use to fit color transformations. Nevertheless, it was still possible to calculate the transformations to/from SDSS. We use VST ATLAS DR3 data because it is accessible via Virtual Observatory protocols through CDS Vizier. However, we compared DR3 versus DR4 photometric measurements and found no statistically significant differences between them, therefore the color transformations presented here can be used for VST ATLAS DR4. The VST ATLAS catalog contains Petrosian magnitudes, while only Kron magnitudes are provided by KiDS, which introduces additional systematic uncertainties to the transformations of KiDS to/from SDSS. The fitting residuals are rather small for the griz bands (0.039 to 0.065 mag; similar to DES) and much larger for the u band in the KiDS survey (0.13 mag). We do not provide u-band transformations between VST ATLAS and SDSS because of the limited depth of both surveys in the u band for galaxies as compared to stars. The VST ATLAS color transformations published in Shanks et al. (2015) provide a very good quality of the converted color. We find a very small difference about 0.02 mag in the mean r-band magnitudes. Nevertheless, here we provide color transformations obtained using our approach for consistency with other surveys.

VST ATLAS → SDSS:

g − r < 0.309: gsdss = gvst − 0.051(gvst − rvst) + 0.040

0.309 < g − r < 1.059: gsdss = gvst + 0.010(gvst − rvst) + 0.021

g − r > 1.059: gsdss = gvst − 0.128(gvst − rvst) + 0.169

${\sigma }_{{{\rm{g}}}_{\mathrm{sdss}}}=0.052\,\mathrm{mag}$

g − r < 0.248: rsdss = rvst + 1.206(gvst − rvst) − 0.284

0.248 < g − r < 0.821: rsdss = rvst + 0.080(gvst − rvst) − 0.005

g − r > 0.821: rsdss = rvst + 0.021(gvst − rvst) + 0.042

${\sigma }_{{{\rm{r}}}_{\mathrm{sdss}}}=0.041\,\mathrm{mag}$

r − i < 0.024: isdss = ivst + 0.636(rvst − ivst) − 0.138

0.024 < r − i < 0.310: isdss = ivst + 0.547(rvst − ivst) − 0.136

r − i > 0.310: isdss = ivst − 0.004(rvst − ivst) + 0.035

${\sigma }_{{{\rm{i}}}_{\mathrm{sdss}}}=0.047\,\mathrm{mag}$

i − z < − 0.297: zsdss = zvst + 1.011(ivst − zvst) + 0.071

−0.297 < i − z < 0.356: zsdss = zvst + 0.504(ivst − zvst) − 0.079

i − z > 0.356: zsdss = zvst + 0.079(ivst − zvst) + 0.072

${\sigma }_{{{\rm{z}}}_{\mathrm{sdss}}}=0.067\,\mathrm{mag}$

SDSS → VST ATLAS:

g − r < 1.056: gvst = gsdss − 0.079(gsdss − rsdss) + 0.038

g − r > 1.056: gvst = gsdss + 0.051(gsdss − rsdss) − 0.099

${\sigma }_{{{\rm{g}}}_{\mathrm{vst}}}=0.041\,\mathrm{mag}$

g − r < 0.544: rvst = rsdss + 0.044(gsdss − rsdss) − 0.058

g − r > 0.544: rvst = rsdss − 0.043(gsdss − rsdss) − 0.010

${\sigma }_{{{\rm{r}}}_{\mathrm{vst}}}=0.036\,\mathrm{mag}$

ivst = isdss + 0.128(rsdss − isdss) − 0.071

${\sigma }_{{{\rm{i}}}_{\mathrm{vst}}}=0.041\,\mathrm{mag}$

i − z < 0.089: zvst = zsdss + 0.492(isdss − zsdss) − 0.194

0.089 < i − z < 0.399: zvst = zsdss + 0.413(isdss − zsdss) − 0.187

i − z > 0.399: zvst = zsdss + 0.561(isdss − zsdss) − 0.246

${\sigma }_{{{\rm{z}}}_{\mathrm{vst}}}=0.061\,\mathrm{mag}$

KiDS → SDSS:

u − g < 1.809: usdss = uKiDS + 0.037(uKiDS − gKiDS) − 0.105

u − g > 1.809: usdss = uKiDS − 0.460(uKiDS − gKiDS) + 0.795

${\sigma }_{{{\rm{u}}}_{\mathrm{sdss}}}=0.130\,\mathrm{mag}$

gsdss = gKiDS − 0.005(gKiDS − rKiDS) + 0.030

${\sigma }_{{{\rm{g}}}_{\mathrm{sdss}}}=0.052\,\mathrm{mag}$

rsdss = rKiDS − 0.002(gKiDS − rKiDS) + 0.035

${\sigma }_{{{\rm{r}}}_{\mathrm{sdss}}}=0.039\,\mathrm{mag}$

r − i < 0.477: isdss = iKiDS + 0.129(rKiDS − iKiDS) − 0.020

r − i > 0.477: isdss = iKiDS − 0.231(rKiDS − iKiDS) + 0.152

${\sigma }_{{{\rm{i}}}_{\mathrm{sdss}}}=0.046\,\mathrm{mag}$

SDSS → KiDS:

u − g < 1.253: uKiDS = usdss − 0.549(usdss − gsdss) + 0.679

1.253 < u − g < 1.579: uKiDS = usdss + 0.444(usdss − gsdss) − 0.565

u − g > 1.579: $\left.{u}_{\mathrm{KiDS}}={u}_{\mathrm{sdss}}-0.622({u}_{\mathrm{sdss}}-{g}_{\mathrm{sdss}})+1.118\right)$

${\sigma }_{{{\rm{u}}}_{\mathrm{KiDS}}}=0.131\,\mathrm{mag}$

g − r < 0.872: gKiDS = gsdss − 0.142(gsdss − rsdss) + 0.083

0.872 < g − r < 1.452: gKiDS = gsdss − 0.019(gsdss − rsdss) − 0.023

g − r > 1.452: gKiDS = gsdss − 0.175(gsdss − rsdss) + 0.201)

${\sigma }_{{{\rm{g}}}_{\mathrm{KiDS}}}=0.049\,\mathrm{mag}$

g − r < 1.153: rKiDS = rsdss − 0.005(gsdss − rsdss) − 0.026

g − r > 1.153: rKiDS = rsdss + 0.022(gsdss − rsdss) − 0.058

${\sigma }_{{{\rm{r}}}_{\mathrm{KiDS}}}=0.037\,\mathrm{mag}$

r − i < 0.335: iKiDS = isdss + 0.147(rsdss − isdss) − 0.096

r − i > 0.335: iKiDS = isdss + 0.193(rsdss − isdss) − 0.111

${\sigma }_{{{\rm{i}}}_{\mathrm{KiDS}}}=0.045\,\mathrm{mag}$

Download table as:  ASCIITypeset images: 1 2

PanSTARRS data demonstrate a highly nonlinear structure of magnitude differences from SDSS magnitudes as a function of color. Therefore, the method of piecewise linear regression described above could not be applied to the PanSTARRS data with a reasonable number of segments, and we used color transformations based on PSF measurements from the literature Finkbeiner et al. (2016). These transformations yield high systematic differences for the corrected values of Kron magnitudes compared to SDSS Petrosian magnitudes (see Figure 9), much higher than those we observed in the case of VST KiDS. We notice that the differences with SDSS increase with the size of galaxy. PanSTARRS also contains Petrosian magnitudes, which can be better for comparison with SDSS data, but we do not consider them because they are not available through Virtual Observatory services which we used to access the data.

Zoom In Zoom Out Reset image size

The wide-field infrared surveys VHS and VIKING conducted at the 4 m ESO VISTA telescope were translated to the UKIRT system using the same method as for the optical surveys. Both surveys use identical prescriptions for data reduction, processing and analysis and, hence, were treated as a single data set in our study. For the approximation, we used a piecewise linear regression with 2 segments over the entire color range. The fitting residuals are somewhat higher than for optical surveys (0.07–0.1 mag) but the residuals do not show any trends with the color.

VISTA → UKIRT:

Yukirt = Yvista − 0.342(Yvista − Jvista) − 0.226

${\sigma }_{{{\rm{Y}}}_{\mathrm{ukirt}}}=0.077\,\mathrm{mag}$

Jukirt = Jvista − 0.288(Jvista − Yvista) − 0.372

${\sigma }_{{{\rm{J}}}_{\mathrm{ukirt}}}=0.102\,\mathrm{mag}$

Hukirt = Hvista − 0.239(Hvista − Ksvista) − 0.358

${\sigma }_{{{\rm{H}}}_{\mathrm{ukirt}}}=0.099\,\mathrm{mag}$

Kukirt = Ksvista − 0.091(Ksvista − Hvista) − 0.320

${\sigma }_{{\mathrm{Ks}}_{\mathrm{ukirt}}}=0.103\,\mathrm{mag}$

UKIRT → VISTA:

Y − J < 0.216: Yvista = Yukirt + 0.078(Yukirt − Jukirt) + 0.260

Y − J > 0.216: Yvista = Yukirt − 0.109(Yukirt − Jukirt) + 0.300

${\sigma }_{{{\rm{Y}}}_{\mathrm{vista}}}=0.074\,\mathrm{mag}$

Jvista = Jukirt + 0.713(Jukirt − Yukirt) + 0.122

${\sigma }_{{{\rm{J}}}_{\mathrm{vista}}}=0.086\,\mathrm{mag}$

H − K < 0.200: Hvista = Hukirt − 0.069(Hukirt − Ksukirt) + 0.354

H − K > 0.200: Hvista = Hukirt − 0.332(Hukirt − Ksukirt) + 0.407

${\sigma }_{{{\rm{H}}}_{\mathrm{vista}}}=0.098\,\mathrm{mag}$

H − K < − 0.218: Kvista = Ksukirt + 0.490(Ksukirt − Hukirt) + 0.375

H − K > − 0.218: Kvista = Ksukirt + 0.210(Ksukirt − Hukirt) + 0.314

${\sigma }_{{\mathrm{Ks}}_{\mathrm{vista}}}=0.101\,\mathrm{mag}$

Download table as:  ASCIITypeset image

We implemented the derived transformations on the project web-site https://colors.voxastro.org/ in the form of a simple calculator that can convert individual measurements. We also provide the conversion formulae in the form of code snippets in idl and python available from the same website. Both implementations yield identical results provided the same input data. The input parameters for the function calc_color_transf are: (i) a name of a filter added to the name of a survey for the input data, e.g., for magnitudes in DES g band this argument is "g_des"; (ii) the same as (i) for an output values; (iii) a list of input total magnitude measurements; (iv) a list of input color values. The size of an output array equals to the size of input lists in (i)—(ii), which should also be equal to each other.

While our main goal was to correct integrated photometric measurements to build galaxy SEDs consistent among different surveys, it is also important to be able to correct aperture photometric measurements, e.g., to compute the photometry in the apertures matching fiber sizes in spectroscopic surveys.

We applied the transformations derived for total magnitudes in Section 4 to magnitudes extracted from circular apertures with the diameters 15 (Hectospec fibers), 2'', 3'' (SDSS fibers) and 57, the largest aperture in VST ATLAS and WFCAM/VIRCAM infrared surveys. For photometric surveys that do not include measurements in these apertures, the magnitudes were calculated using quadratic interpolation from the available aperture magnitudes. In Table 1 we list the available aperture diameters for each of the surveys. Because the extrapolation beyond the maximum available aperture is subject to biases, we use the converted optical photometry in the 15, 2'' and 3'' apertures (estimating 15 aperture magnitudes also requires an extrapolation "inwards," however it is done into a smaller aperture than the original measurements and therefore is only affected the shape of the inner part of a galaxy light profile convolved with the atmospheric seeing). Then, we compare the converted aperture measurements from each survey to those in either SDSS or UKIDSS/UHS. Because we do not have SDSS magnitudes in the 57 aperture, we compare the VST and DES surveys where such measurements are available with each other (see Figure 12).

The aperture values calculated using transformations for total magnitudes demonstrate different offsets from the reference survey depending on the size of the aperture without noticeable color trends in most color/survey/aperture combinations. At the same time, the offset values vary a lot for different surveys even for the same aperture size and reference photometric band, e.g., 3'' DES photometry in the z-band is offset with respect to the SDSS by 0.187 mag, and the 3'' VST magnitudes are offset by 0.312 mag. The offset values were taken into account to correctly translate the aperture photometry and are presented in Table 2. These offsets are caused primarily by the difference in the mean seeing quality of the imaging surveys we consider, and also by the difference in depth between the surveys, which are absorbed by our color transformations of integrated magnitudes and have to be taken back from the transformations when dealing with aperture fluxes, which should not be seriously affected by the depth.

Table 2. Mean Offset values in Different Apertures used for Correction of Aperture Magnitudes into SDSS Bands (Survey value—SDSS value)

Aperture	g	r	i	z
	mag	mag	mag	mag
DES 15 a	−0.051	−0.239	−0.317	−0.308
DES 2'' a	−0.193	−0.334	−0.393	−0.379
DES 3'' a	−0.100	−0.168	−0.200	−0.187
VST 15 a	−0.187	−0.233	−0.330	−0.359
VST 2''	−0.209	−0.239	−0.312	−0.330
VST 3'' a	−0.115	−0.123	−0.158	−0.159
DECaLS 15	−0.055	−0.124		−0.197
DECaLS 2''	−0.190	−0.241		−0.284
DECaLS 3''	−0.078	−0.110		−0.112
MzLS+BASS 15	0.133	−0.038		−0.261
MzLS+BASS 2''	−0.040	−0.168		−0.325
MzLS+BASS 3''	0.023	−0.052		−0.127
Aperture	Y	J	H	K
	mag	mag	mag	mag
VISTA 15 a	0.015	0.048	0.033	0.059
VISTA 2''	0.012	0.044	0.023	0.050
VISTA 3'' a	0.011	0.040	0.009	0.035

Note.

^a Magnitudes were calculated using quadratic interpolation from the available aperture magnitudes (see Table 1).

Download table as:  ASCIITypeset image

The VST Atlas survey includes two types of an aperture magnitude, "Default point source aperture corrected magnitude" and "Default extended source aperture magnitude." We provide offsets only for "Default extended source aperture magnitude" since this is more correct for extended objects.

Zoom In Zoom Out Reset image size

As one can see in Figures 11, 13, 19, 20, 21, the aperture magnitude differences for small-sized apertures (15 and 2'') have substantial dispersion about a mean value, it is higher for 15 than for 2'', and the dispersion drops significantly for 3'' values getting close to that of total magnitudes. This effect is trivially explained by the mean image quality difference among the considered surveys when measuring aperture fluxes of extended sources having a great variety of intrinsic light profiles. For SDSS the average seeing FWHM is 17 (Abazajian et al. 2009), while it is close to 1'' for DECaLS (Dey et al. 2019) and is subarcsecond for VST ATLAS (Shanks et al. 2015). Therefore, the smaller the aperture size, the larger fraction of light will be lost for a compact object in a survey with a worse delivered image quality. On the other hand, for extended galaxies without much central light concentration, the seeing quality will have a much lesser effect, dropping to zero in the limiting case of a constant surface brightness object. If we look at non-variable stars, which are constant point sources, they will form very tight sequences without color dependence having the mean value, which can be calculated by integrating two-dimensional Gaussians corresponding to the typical values of seeing quality in the two surveys inside the apertures and then converting the flux ratio into a magnitude difference. Larger aperture sizes, which significantly exceed the seeing FWHM (e.g., 3''), enclose a higher fraction of the central light concentration of a galaxy, therefore the mean offset becomes smaller and the dispersion of points around the mean values also decreases. This explanation is consistent with the results shown in Figure 12, which demonstrates a zero difference between the VST and DES in 57 apertures computed using the transformations for total magnitudes. This is because (i) 57 is a relatively large aperture to being affected, and (ii) the VST and DES surveys have similar seeing FWHM (sub-arcsecond and arcsecond), while the SDSS has a FWHM of 17.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

In Figure 11 we see a clump that consists of a large number of data points in the g and r bands residuals between DES and SDSS in the 3'' aperture at the mean color g − r = 1.8 mag, which lies substantially off the principal sequence formed by the rest of the galaxies in the sample. This clump includes exclusively intermediate-redshift (z > 0.4) luminous red galaxies (LRGs) and it disappears in the residuals in the i and z bands. The most prominent difference is seen in the r band and we attribute it to difference among the filter throughput curves: the DES r extends sufficiently further into the red (λ_r,cutoff,DES = 720 nm versus λ_{r,cutoff,SDSS} = 670 nm). The difference in the g band has an opposite sign and a similar mean absolute offset but larger spread because the SDSS g-band photometry has very poor quality for LRGs because they are red and therefore faint in g band. As a result, the color difference Δ(g − r) in the converted colors remains very close to zero. The clump originates from the sharp increase of the number of objects in the sample at z > 0.4 because of the LRG selection in eBOSS. They present at colors (g − r) < 1.8 mag but in relatively small quantities, however the LRG selection kicks in at around z = 0.4. LRGs have a very strong redshift dependence of g − r and it is very sensitive to the difference between the exact filter throughput curves in SDSS and DES, and one needs a redder color, e.g., r − z to properly describe the trend. For luminous red galaxies at redshifts z > 0.4, the g − r color saturates at ∼1.7 mag and therefore it cannot be used for parameterization of the color transformation. Therefore, for very red galaxies we recommend using the r − z-based transformations (see color differences for the r − z parameterization in Figure 13).

Zoom In Zoom Out Reset image size

As we mentioned in the Introduction, the optical color–magnitude diagram constructed from integrated extinction and k-corrected photometric measurements represents the ultimate test of the quality of the obtained photometric relations: early-type galaxies form a very narrow "red sequence"—its position and tightness reflects the quality of the input photometric data. It is also important to know the red sequence shape in different colors for practical astrophysical purposes, such as selecting early-type candidate members in galaxy clusters using photometric data. Chilingarian et al. (2017) published the red sequence shape derived for different filter combinations in the SDSS DR7.

In Figure 14 we present the (g − r) versus M_r color–magnitude plots the 5 surveys we used in our combined catalog transformed into the SDSS photometric system using our results and the PanSTARRS survey converted using the literature transformations. We restricted the redshift range to 0.02 < z < 0.2. We applied k-corrections to the converted measurements according to Chilingarian et al. (2010), Chilingarian & Zolotukhin (2012) and corrections for the Galactic extinction (Schlafly & Finkbeiner 2011). We overplot the polynomial approximation for the red sequence presented in Chilingarian et al. (2017). It turns out that the red sequence has the same slope and location in all surveys except PanSTARRS, which validates the photometric transformations we derived in this work. The red sequence in DES, DELVE, and KiDS has a similar or smaller scatter compared to SDSS, and also a very small number of very red outliers (> + 2σ from the mean red sequence position). The distributions of galaxies in the (g − z) versus M_z and (g − i) versus M_i color spaces behave similarly: DES, DELVE, and KiDS show fully consistent results with the SDSS as presented in the RCSED catalog paper (Chilingarian et al. 2017).

Zoom In Zoom Out Reset image size

The red sequence based on the DESI Legacy Surveys data, both from DECaLS and MzLS demonstrates a larger scatter than those from DES and DELVE despite being based on the data from the same facility, however, for the most luminous late-type galaxies, the scatter value is similar or even smaller compared to DES likely because of the better number statistics. There is also a substantial number of very red objects above +2σ off the red sequence in the intermediate-luminosity range—we see a similar behavior in the VST ATLAS data. We have inspected some of the objects off from the red sequence by >4σ and they all settle within 1σ of the DES red sequence (see Figure 15). The first object (marked by red star) probably has a segmentation problem related to the presence of the dust lane. The second galaxy (marked by yellow star) is the central galaxy in a cluster and it has issues with deblending caused by the presence of numerous satellites in its vicinity. These examples illustrate that compared to other surveys, total magnitudes in the DESI Legacy Surveys have a higher intrinsic scatter, which we investigate in the next subsection.

Zoom In Zoom Out Reset image size

The red sequence based on PanSTARRS total magnitudes converted into SDSS using the transformations from the literature is wider than that in SDSS and has the same tilt as SDSS only for small and spatially unresolved objects. It "bends up" for spatially extended galaxies, which is probably caused by imperfect sky subtraction for extended targets. The red sequence is also substantially thicker and there is a large number of red outliers.

While computing photometric transformation for different imaging surveys carried out with the DECam instrument we noted that while DES-based transformations yielded excellent results for DELVE, they do not work properly for DESI Legacy Surveys: the residuals displayed strong systematics with a nonlinear color dependence. This was the reason why we used other transformations for DESI Legacy Surveys, which work well for it as shown at Figures 7 and 8. DELVE and DES used the same data processing and photometric calibration tools while DESI Legacy Surveys used totally different solutions.

There are two possible reasons for this behavior: (i) difference in the pipeline processing of raw images, e.g., a sky subtraction algorithm clipping outer parts of extended targets in one of the pipelines; (ii) difference in the source extraction and deblending algorithms. To identify the primary source of inconsistencies, we decided first to test the source extraction. DES and DELVE used Source Extractor (Bertin & Arnouts 1996) while DECaLS used tractor (Lang et al. 2016) implemented in python. To perform the test, we downloaded a 16' × 16' region of the sky in the r-band centered on the galaxy cluster A168 from DECaLS using Astro Data Lab. Galaxy clusters are convenient for such a comparison because they include a large number of galaxies at the same redshift, many of which reside on the red sequence and have regular elliptical morphology, which simplifies source extraction and measurement. Then we ran Source Extractor with a default configuration on this image and compared the results with those presented in DES for about 100 sources. In Figure 16 we present the comparsion of Source Extractor-based DECaLS photometry and the published values derived by tractor against DES. It turns out that using Source Extractor on DECaLS images yields fully consistent results with DES with a zero mean deviation and an r.m.s of 0.044 mag compared to 0.075 mag for DECaLS photometry. We also see fewer "catastrophic outliers" especially among extended galaxies. In the insets of Figure 16 we present two examples of such outliers. Both seem to have problems with deblending: one galaxy has a red star projected on its outer part, which was not separated from it by tractor and caused the unphysically red color of this object in DECaLS; the second galaxy was not separated from a satellite in DECaLS. The increased r.m.s. is probably due to a less stable algorithm used in tractor to define a surface brightness threshold for extended sources.

Zoom In Zoom Out Reset image size

This test provides an explanation why the color–magnitude plot from DESI Legacy Surveys shows a puffed-up red sequence and a high number of red outliers (see the discussion in Section 5.2). We also see a way to improve extended object photometry in DECaLS: the images from DECaLS should be analyzed using Source Extractor to bring the photometry to the consistency with DES and DELVE.

As an example use case for our color transformation, we compiled integrated photometric measurements in the optical and NIR bands for the galaxy samples from the two CfA public archives for FAST (73,849 spectra for 42,694 objects) and Hectospec (211,075 spectra for 164,439 objects). Both data sets originate from data archives and cover a very wide area that extends beyond the SDSS footprint, so that a combination of SDSS, DELVE, DES, and BASS/MzLS was needed to compile an optical photometric catalog.

The CfA FAST archive (Mink et al. 2021) contains 141,531 spectra for 72,247 objects and include observations of nearby galaxies, supernovae, various types of stars, and planetary nebulae collected between 1994 and 2021 using the FAST spectrograph operated at the 1.5 m Tillinghast telescope at the Fred Lawrence Whipple Observatory. The spectra were automatically processed with the FAST data reduction pipeline. We kept 42,694 objects which we identified as extragalactic targets using either their redshifts or a cross-identification in Hyperleda and for which we could find photometric measurements in wide-field surveys.

The CfA Hectospec archive includes the results of spectroscopic observations from the multi-fiber spectrograph Hectospec operated at the 6.5 m MMT (Fabricant et al. 2005). These are the results of publicly released programs typically older than 5 yr processed with the Hectospec pipeline. The sample includes observations of low-to-intermediate redshift galaxies, extragalactic star clusters, bright stars, H ii regions, and planetary nebulae in nearby galaxies as well as some distant quasars. We kept 164,439 distinct objects, which we identified as galaxies with available photometric measurements and excluded extragalactic star clusters and planetary nebulae as well as Galactic and Local group stars.

To compile a photometric catalog, we converted the Petrosian magnitudes from DES, DELVE, and BASS/MzLS, VHS, and VIKING into the SDSS and UKIDSS photometric systems, and corrected them for the foreground extinction. We complemented these measurements with extinction-corrected GALEX and unWISE photometry. Some examples of multi-wavelength SEDs for Hectospec galaxies are shown in Figure 17: we demonstrate the differences of the magnitudes from the original SDSS measurements before (red) and after (black) applying our color transformations. The converted DES measurements show excellent agreement with SDSS. Our photometric catalog will be included into the CfA data archive in the form of additional properties for each extragalactic object.

Zoom In Zoom Out Reset image size

As an additional quality check, we computed k-corrections for the converted optical magnitudes using prescriptions from Chilingarian & Zolotukhin (2012) and built fully corrected color–magnitude diagrams for FAST and Hectospec galaxies, which we show in Figure 18. The red sequence position and tightness based on DES and DELVE data perfectly match those from SDSS published by the RCSED project (Chilingarian et al. 2017).

Zoom In Zoom Out Reset image size

By applying photometric transformations derived in this work to the data originating from various surveys and comparing them against SDSS and each other, and also quantifying the properties of the color–magnitude diagrams (e.g., red sequence location and tightness), we can make the following assessment of the quality of integrated photometric measurements of galaxies:

• 1.  
  DES provides the highest quality of optical photometry of galaxies compared to all other wide-field surveys and can be used as a "gold standard" for many scientific applications and future projects, e.g., to check the quality of photometric calibration from the forthcoming Rubin Legacy Survey of Space and Time. It also allows for refined photometric tasks, e.g., color-based search for rare galaxies (Chilingarian & Zolotukhin 2015; Grishin et al. 2021) or simultaneous fitting of spectral and photometric information (Chilingarian & Katkov 2012) to infer detailed star formation histories of galaxies using complex parametric stellar population models (see e.g., Grishin et al. 2019).
• 2.  
  DELVE is a shallower equivalent of DES with similar photometric quality and low systematic errors even though higher statistical uncertainties because of the lower depth. Its main advantage is a very wide sky coverage of 17,000 deg² versus 5000 deg² in DES.
• 3.  
  VST ATLAS and KiDS conducted at the 2.6 m ESO VST also have minimal systematic photometric errors and are complementary to DES and DELVE. In addition, they supply u-band photometry not available in the surveys done with DECam providing a Southern hemisphere to SDSS.
• 4.  
  Both parts of the DESI Legacy Surveys, DECaLS and BASS/MzLS exhibit significant systematics in the extended source photometry, which exceeds statistical uncertainties by a factor of a few. Nevertheless, the photometric measurements can be adequately transformed into the SDSS photometric system and can be used for certain applications of the photometric/SED-based selection even though the photometric uncertainties in any type of an SED fitting using DESI Legacy Surveys data should be artificially increased to account for the systematics. We attribute it mostly to the source extraction algorithm, so that a complete re-processing of DECaLS data using a different software package (e.g., Source Extractor) should drastically improve the quality of photometry of galaxies.
• 5.  
  PanSTARRS photometry deviates from SDSS nonlinearly with color, and the deviations in all bands show significant trends with the galaxy size. This is noticeable not only by the dependence between residuals and sizes, but also by the red sequence—it has a correct slope and is tight only for spatially unresolved objects. Further investigations are needed to fully understand the sources of this systematics, but it will likely be improved when using a different source extraction software (see e.g., Makarov et al. 2022, for an application of Source Extractor to PanSTARRS data).