The ATLAS All-Sky Stellar Reference Catalog

The 2MASS (Skrutskie et al. 2006) covered the entire sky in the infrared JHK_s bandpasses. The systematic errors in astrometry are no larger than 005 and in photometry no larger than 0.02 mag, but the infrared magnitudes are not directly convertible to gri at the level required here. These magnitudes are very useful in combination with the Gaia photometry to distinguish stellar color from reddening, however. We downloaded the 2MASS data from IPAC.⁵

The AAVSO has released a catalog of stellar photometry for about 50 million stars over the entire sky from APASS DR9 (Henden et al. 2016). The astrometry is tied to UCAC3 (Zacharias et al. 2010) with an accuracy better than 01, and its photometry includes BVgri across the range 7 < m < 17. Their cameras are an Apogee U16m with a 4k KAF16803 detector and Astrodon u', g', r', i', z', B, and V filters. The KAF16803 detector has lower quantum efficiency than our ATLAS Pathfinder CCID20 CCDs (see Section 3.1), but APASS used 180/90/90 s exposures in gri, so the depths are comparable.

As described below, we corrected for substantial systematic photometric offsets in this published DR9 data set. Because APASS carried out a flattening correction, photometry, and detection combination for DR9 that is independent of the work performed here, we consider it to be a quasi-independent source of photometry, and we added it into the sources of gri magnitudes once these offsets were corrected on a square-degree basis.

The Pan-STARRS1 Telescope (Chambers et al. 2016) surveyed the sky north of decl. −30° many times in grizy filters between 2010 and 2014. The Pan-STARRS bandpasses have been well characterized (Tonry et al. 2012). These data have been homogenized using an "ubercal" procedure (Padmanabhan et al. 2008; Schlafly et al. 2012) and tied to the Space Telescope Science Institute's "Calspec" stars (Bohlin et al. 2001; Bohlin 2007, 2014). The Pan-STARRS1 data processing (Magnier et al. 2016a, 2016b; Waters et al. 2016) and calibration (Magnier et al. 2016c) provide accurate grizy photometry (<0.005 mag) and astrometry (<20 mas), but only for stars fainter than m ∼ 14; brighter stars are saturated.

We used the Pan-STARRS DR1 catalog database (Flewelling et al. 2016) by running a query that checks that the object has a stack magnitude less than 19 in any of g, r, i, or z and that bestDetection=1 and primaryDetection=1 in the StackObjectThin tables and reports back the mean positions (R.A./decl.) and mean point-spread function (PSF) magnitudes in grizy from the ObjectThin and MeanObject tables. This query was chosen to restrict the objects to those that are bright enough for ATLAS, as well as to select objects that have been seen multiple times by Pan-STARRS and for which the Pan-STARRS stack photometry (measurement from the coadd of all images) succeeded. We use the Pan-STARRS mean photometry (mean of measurements from all images) because it has had ubercal corrections applied (see Schlafly et al. 2012; Magnier et al. 2016c), whereas the corresponding stack photometry has not. However, to maximize the probability that an object is a real star (and not a spurious detection, transient source, or moving object), it is useful to check that it exists and that certain flags are set in the stack table. In Appendix B, we provide an example of the query, should others wish to select a similar set of Pan-STARRS1 data from the MAST archive.⁶

In 2017 December, SkyMapper published a slight revision to their first data release, DR1.1,⁷ comprising 285 million sources (Wolf et al. 2018). The DR1.1 employs 2MASS and a selection of APASS stars to set observation zero-points (the number that converts flux reported by photometry routines to calibrated magnitude) and determine magnitudes. We found that photometric errors in APASS DR9 had left a substantial imprint on the SkyMapper photometry, so we corrected the SkyMapper photometry on each square degree, as described below. We caution that the point-source photometry in DR1.1 is derived from 1D growth curves and thus is only reliable for isolated sources that have no neighbors within 10''.

The ESA Hipparcos satellite (van Leeuwen 2007) surveyed the entire sky to determine the parallaxes of bright stars, and it included the Tycho photometry instrument. The Tycho-2 catalog it produced contains almost all of the stars in the sky brighter than m ∼ 12 (Høg et al. 2000). Its astrometry is superb, and its photometry is quite homogeneous over the entire sky, albeit subject to crowding problems in the Galactic plane. Tycho had two filters, B_T and V_T, similar to Johnson B and V, so it cannot be compared directly with gri photometry without significant color transformations.

The 2MASS team performed a match between Tycho-2 and 2MASS, providing ${B}_{T}{V}_{T}{JHK}$ photometry for about 2.5 million stars. Pickles & Depagne (2010) then used this 2MASS match to determine a best-fitting stellar spectral energy distribution (SED) from their compendium of SEDs and published synthetic gri photometry for each of the Tycho-2 stars.

The Tycho-2 catalog becomes quite incomplete for m < 3, so we augmented it with the Yale BSC (Hoffleit 1964). The griz magnitudes were estimated from the B, V, and (U − B) and (R − I) colors when available. These estimates are not particularly accurate, but they ensure the completeness of the final Refcat2. We shifted the Tycho-2 and BSC coordinates to epoch 2015.5 according to the Tycho-2 proper motions and merged the two, with a preference for Tycho-2 for stars listed by both.

The Gaia Collaboration published a first data release in 2016 (DR1; Gaia Collaboration et al. 2016) and issued a greatly improved second data release (DR2) on 2018 April 25 (Gaia Collaboration et al. 2018). The DR2 has three substantial improvements relative to DR1: it closes holes in the sky, provides Gaia "G_BP" and "G_RP" magnitudes for stars brighter than G ∼ 19, and provides proper motions and parallaxes for many stars. The star coordinates in DR2 are all epoch 2015.5. This is a revolutionary data set, not only because of the unprecedented depth and accuracy of the astrometry but also because of the accuracy of the photometry. Comparison of DR1 G magnitudes against Pan-STARRS clearly showed the Gaia scan patterns, indicating photometry errors at the ∼0.02 mag level. The DR2 does not show Gaia scan patterns relative to Pan-STARRS at the 0.005 mag level or better, and of course, there is every expectation that the Gaia photometry can be homogeneous over the entire sky. As we discuss later (Section 4.2), we do observe a small difference between Gaia DR2 photometry and ground-based photometry that correlates with star density.

The ATLAS Pathfinder Telescope is a Takahashi Epsilon-180 astrograph that has a 5° diameter field of view, an aperture of 180 mm, and a focal length of 500 mm. It is equipped with an FLI PDF focuser and an FLI filter changer. The filter changer has Astrodon⁸ 50 mm SDSS Gen-2 g-, r-, and i-band filters inserted. These filters have very square bandpasses with half-transmission points of 401–550 (g filter), 562–695 (r filter), and 695–844 nm (i filter). This is followed by a Uniblitz 45 mm shutter and a custom CCD camera. The CCD camera has two 2k × 4k Lincoln Lab CCID20 CCDs with 15 μm pixels for a plate scale of 62 arcsec pixel^–1. The Takahashi illuminates a circle of diameter 3000 pixels, so the field of view is about 19 deg². These CCDs are back-illuminated and 45 μm thick, so their quantum efficiency and uniformity are excellent.

The telescope was used on Mauna Loa in the ATLAS Ash dome at the NOAA observatory at an elevation of 11,000 feet for approximately 2 yr prior to the installation of the ATLAS 0.5 m telescope. We observed between MJD 57,396 (2016 January 9) and 57,782 (2017 January 29), initially collecting images in a single filter on a given night, applying dithers, and letting some time elapse between observations. In 2016 March (MJD 57,449), we switched to a mode of collecting three consecutive images in gri at each pointing, covering about one-fifth of the visible sky on a given night. We normally observed in five decl. bands between −45 and +90. All exposure times were 30 s, and the Takahashi vignettes about 40% of the light at the edge of the field of view.

The Takahashi telescope produces a focal surface that curls up at the edge of the field of view, and at f/2.8, there is a distinct nonuniformity of focus. In addition, the detectors are slightly tilted with respect to the focal surface. At its best, the Takahashi makes images of about 1.2 pixels, but we deliberately chose a focus that produces images of about 1.7 pixels full width at half maximum (FWHM) over the entire field of view. There is a distinct variation in the shape of the images as a function of position, but the overall FWHM is reasonably constant for all filters over the entire field of view. However, prior to running DoPhot, we elected to convolve images with a Gaussian of 2 pixels FWHM. This costs about a half magnitude in sensitivity but significantly improves the photometric accuracy over the field.

Among the Pathfinder data, "good nights" were identified as those with a scatter in zero-point (magnitude that provides 1 count s^–1) less than 0.03 mag (4/3 the quartile range) as a function of airmass over the majority of the night, and "good observations" were selected. A total of 362 nights and 232,558 exposures in gri yielded 213 nights that were at least partly photometric, with a total of 165,294 exposures. After fairly stringent cuts on quality-control metrics, 159,397 exposures survived to provide stellar photometry. Our sky coverage of these exposures is displayed in Figure 1. Each image produces a table of about 30,000 stars with an astrometric accuracy of about 02 relative to Gaia DR1 and a photometric accuracy of about 0.05 mag relative to Pan-STARRS at g ∼ 16.5, r ∼ 16, and i ∼ 15.5. The Pathfinder observations saturate at approximately m < 9.

Zoom In Zoom Out Reset image size

The basic ATLAS pipeline (Tonry et al. 2018) was used to reduce the ATLAS Pathfinder data. The stages involve bias subtraction, division by a flat field, and identifying many stars to determine pixel positions and fluxes. A subset of these stars is matched to sky positions using code from astrometry.net (Lang et al. 2010) to obtain an initial astrometric solution. All stars are then matched to the first-generation ATLAS reference catalog⁹ to derive an accurate astrometric solution expressed as WCS coefficients and a photometric zero-point. Refcat1 has estimates of star magnitudes on the Pan-STARRS g_P1, r_P1, and i_P1 filter system (Tonry et al. 2012), and these magnitudes are converted to the Pathfinder gri observational bandpasses (see Table 2 below).

The flat field is initially a nighttime sky-flat image derived from the median of all images in a given filter for a night, but then the stars from images that overlap the Pan-STARRS catalog are compared with Pan-STARRS magnitudes, a low-order 8 × 8 spline fit to the differences is multiplied into the flat field to make a "photo flat" or "star flat," and the data from the night are rereduced with this new flat field. As described below, the purpose of the photo flat is to correct intra-exposure photometric variations, not to get the final zero-point for the exposure correct; the zero-point evaluation follows a completely different procedure. This photo flat serves for a lunation.

Finally, we run a version of DoPhot (Schechter et al. 1993) that was modified by Alonso-Garcia (Alonso-Garcia et al. 2012) to accept floating point data and cope with a varying PSF. We also had to make a number of modifications to DoPhot as well to get the variable PSF to work properly and be able to introduce an external variance image. DoPhot processes an image iteratively. At any point, it maintains a catalog of all stars it has detected, and it subtracts its model of those stars from the image before detecting and measuring new stars or remeasuring old stars in the catalog. In this way, DoPhot does a very creditable job of dealing with high star densities and blended images.

DoPhot calculates two different fluxes for most stars: an "aperture magnitude," which is the sum of the flux within a large-aperture (∼30'') radius, and a "fit magnitude," which is the flux derived from the integral of the DoPhot PSF function. The former includes almost all the light from a star but is noisy; the latter has systematic errors when the DoPhot PSF model does not match the actual star profile. All stars have a "fit magnitude," but only bright stars have an "aperture magnitude." By examining the difference between the aperture and fit magnitudes for bright stars, the fit magnitudes for faint stars can be converted to aperture magnitudes. The result is that we can produce low-noise instrumental magnitudes for each star that are referred to large-aperture fluxes.

The APASS project kindly provided ATLAS with 258,312 images of the southern sky on a 3 TB external drive. They were taken at the APASS facility at the Cerro Tololo Inter-American Observatory in Chile, primarily (237,498 images) in the g, r, i, B, and V filters over a span of MJD 55,507 (2010 November 7) to 56,725 (2014 March 9). They cover nearly the entire sky with decl. < +20°, with few gaps (the southern "crack in the sky" that stretches between α, δ 260°, −60° and 270°, −77° is not covered by these images). The APASS system has a 29 × 29 field of view with 26 pixels, and exposure times were varied so as to extend the dynamic range to brighter stars.

We reduced all APASS exposures through the ATLAS pipeline, including the match with ATLAS reference catalog Refcat1. Because the APASS observing strategy on each night brought the telescope well north of decl. −30°, virtually every night overlapped the Pan-STARRS catalog well enough to provide a photo-flat correction to the APASS flat field. This was not a trivial modification, amounting to a peak-to-peak of 0.2 mag over a typical image and an rms of about 0.05 mag. There was also a dramatic, steady decrease in zero-point by 0.7 mag in all filters over this 3.3 yr span. We found that the Pan-STARRS flat-field comparison was very consistent in a given filter from night to night, and on the few nights when APASS did not venture north of −30°, we used the photo-flat correction from the closest night that did. The astrometric errors are typically 007 in each coordinate at m ∼ 15, and the typical photometric errors in the long exposures are 0.05 mag at g ∼ 17.5, r ∼ 16.5, i ∼ 15, B ∼ 17.5, and V ∼ 16.5.

As with the Pathfinder data, "good nights" and "good observations" were identified from the scatter in zero-point as a function of airmass and quality-control metrics. A total of 692 nights yielded 542 nights that we deem photometric, with a total of 178,094 exposures, of which 154,406 in g, r, i, B, and V provided stellar photometry. The APASS sky coverage is displayed in the right panel of Figure 1. (There is also an APASS-north survey, which we did not use.)

It is important that readers and users note the following. Hereafter, the "APASS" catalog will be used to mean the APASS data that have been reprocessed by ATLAS, and the "APASS DR9" catalog will refer to the magnitudes published by the APASS project. These share many of the same data files, but the processing is completely different. As detailed below, this rereduction of APASS made the intra-CCD photometry about a factor of 3 better than what was published in APASS DR9, the reprocessed photometry is about 2 mag deeper, and, even after we correct APASS DR9 into agreement with Gaia and Pan-STARRS, this rereduced APASS catalog is distinctly more homogeneous across the sky.

Initial attempts to assemble the Pathfinder and APASS detections into a consistent set of photometry over the sky were only successful at the 10 mmag level—not good enough for our purposes. The reference catalog, photo flats, and dithers did a good job of making the photometry consistent (∼10 mmag) within a given exposure, and averaging many detections could then, in principle, bring the photometry to the accuracy we need.

However, determination of zero-points for the exposures to make a combination whose systematic error was below 10 mmag proved to be difficult. We used a combination of three methods to determine zero-points for exposures: (1) set the zero-point directly by comparison with external authority, (2) set the zero-point by regression against airmass on photometric nights, and (3) set the zero-point by intercomparison of overlapping exposures (the ubercal approach; Padmanabhan et al. 2008; Schlafly et al. 2012).

Although Pan-STARRS is an excellent external authority and the basis for the photo flats, it does not exist south of decl. −30°. Gaia is available all-sky but provides only very broad bands, and it is a priori not clear how well they constrain the narrower Pan-STARRS passbands. It turned out to be challenging to determine zero-points from airmass regression for two reasons. We were simply reluctant to severely restrict the list of workable nights in search of truly photometric nights; we did not feel that we would have enough exposures remaining to cover the sky. The second reason is that the zero-point for an exposure actually depends on more than airmass. Since the zero-point is the conversion between summed flux and magnitude, it depends on the details of the photometry algorithm, not just the aperture and detector quantum efficiency and gain. In particular, the pixel size of 62 (Pathfinder) or 26 (APASS) means that variations in star density cause very substantial shifts in the zero-point, and PSF size and shape are additional factors. The zero-point for images derived by comparison with Pan-STARRS (026 pixels) during a night depends markedly on galactic latitude, photometry algorithm, and parameters, as well as the expected dependency on airmass.

We wrote an elaborate program to simultaneously solve for as many as 10⁵ zero-points based on inter-exposure differences (the third method) in addition to absolute zero-points provided by an external authority (first method) and airmass regression (second method). This procedure worked very well. With external zero-points weighted lightly, the resulting errors in star magnitudes (judged by comparison with Pan-STARRS in the belt with −30° < decl. < + 20°) are very smooth but have large-scale variations, as might be expected from the differential constraint. When the zero-points from airmass regression and external authority were heavily weighted, the small-scale variation became much rougher on the scale of an observation footprint in the south, where we did not have external zero-points, but the rms improved slightly.

The rms values of the reflattened APASS images were 17–12 mmag when we let the inter-exposure differences dominate the fit weights (labeled "diff" in the second column of Table 1) and 13–11 mmag when zero-points from airmass regression dominated (labeled "secz" in Table 1). Optimizing the weights between differences and external zero-points made things slightly better, but we could not find a combination that made the rms values substantially better than 10 mmag. Since this is the rms between square-degree tiles, it represents an unacceptable systematic error.

The release of Gaia DR2 created a new opportunity to set zero-points. The Gaia bandpasses are very broad and very different from griz. Here, G is approximately 410–840 nm, G_BP is approximately 335–660 nm, and G_RP is approximately 640–900 nm, but G and G_RP have extensive red tails and G_BP a substantial dip between 365 and 400 nm.¹⁰ However, comparison between Gaia magnitudes synthesized from Pan-STARRS griz revealed little spatial variation across the sky. It therefore appeared to be possible to pick a subset of Gaia stars that match with 2MASS and have low reddening and use the Gaia and 2MASS magnitudes to make accurate estimates of griz magnitudes over the entire sky. Since our goal is to set the overall zero-point for exposures with photometry for many stars and good internal photometric consistency, a small subset of stars can serve to set the zero-point for all stars in that exposure.

Experiments revealed that the most fruitful comparison was griz with Gaia magnitudes in the (G_BP − G_RP), (J − H) plane. The stellar locus has a tight regression for unreddened, nonred stars, and the reddening vector is distinctly nonparallel to the stellar locus, so (J − H) can serve to deredden as well as distinguish giant from dwarf stars. Comparing the Gaia and 2MASS data with the Pan-STARRS DR1 catalog revealed an appropriate subset of stars and regressions for Pan-STARRS griz from the Gaia and 2MASS magnitudes (abbreviated GMP).

The stars that are chosen for the GMP subset have

• 1.  
  neither a Gaia VARIABLE nor a DUPLICATE flag set;
• 2.  
  uncertainties in G_BP and G_RP less than 0.03 mag;
• 3.  
  uncertainties in J and H less than 0.05 mag;
• 4.  
  0.7 ≤ (G_BP − G_RP) ≤ 1.4, 0.2 ≤ (J − H)) ≤ 0.5, AG < 1; and
• 5.  
  (G − G_RP) − (G − R)_SSL < 0.05,

where

$$\begin{eqnarray}\begin{array}{rcl}{(G-R)}_{{SSL}} & = & +0.0175+0.642({G}_{{BP}}-{G}_{{RP}})\\ & & -0.0784{({G}_{{BP}}-{G}_{{RP}})}^{2}+0.002{({G}_{{BP}}-{G}_{{RP}})}^{3}\end{array}\end{eqnarray} \tag{ 1 }$$

is the Gaia stellar locus. Evidently, the color cuts are removing very blue and very red stars, regardless of whether the color is intrinsic or caused by reddening. We are also removing stars with AG ≥ 1 that Gaia believes are extremely reddened (AG is the Gaia extinction estimate in the Gaia broadband G bandpass), and the last cut is removing stars that deviate from the stellar locus in Gaia colors.

We found that the residuals of Pan-STARRS magnitudes with respect to a regression based on the GMP subset of Gaia and 2MASS magnitudes still had rather large errors (∼0.1 mag) near the Galactic plane, but these correlated well with star density. These deviations are minimal below a threshold star density but then increase roughly proportionally to the square root of star density (inverse of mean star separation) in more crowded regions. We use the count of Gaia stars with 15 < G < 16 in each angular square degree (N_15–16) to create a star proximity variable we term ng = (N_15–16)^1/2. In the i band, for example, the threshold for disagreement is ng ∼ 50 (2500 stars deg^_–2), and the disagreement rises to ∼100 mmag at ng ∼ 100.

We do not understand the origin of these deviations. They do not depend directly on galactic latitude (extremely obscured areas right on the plane have small ng and small deviation). They do not appear to depend on star brightness, are still present when 2MASS is removed from the Gaia–Pan-STARRS comparison, and do not appear to correlate well with reddening, either Gaia estimates or the total column reddening from Schlegel et al. (1998). Star density correlates with extinction and giant/dwarf ratio, of course, but neither of these variables correlates as well as star density. Our best guess is that Gaia incurs some sort of photometry offset as it scans areas with very high star densities that creates a small error.

Our predictions for Pan-STARRS griz from Gaia and 2MASS for the GMP subset are

$$\begin{eqnarray}\begin{array}{rcl}({g}_{P1}-{G}_{{BP}}) & = & -0.0321-0.0520\,X+0.1314\,{X}^{2}\\ & & +0.0084\,Y+\,0.00189\,n\\ & & +0.01326\,{n}^{2}-0.00243\,{n}^{3},\end{array}\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}\begin{array}{rcl}({r}_{P1}-G) & = & +0.1940-0.4013\,X\\ & & +0.2022\,{X}^{2}-0.0974\,Y+\,0.02234\,n\\ & & +0.00352\,{n}^{2}-0.00124\,{n}^{3},\end{array}\end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray}\begin{array}{rcl}({i}_{P1}-{G}_{{RP}}) & = & +0.3564-0.0268\,X\\ & & +0.0429\,{X}^{2}-0.0537\,Y-\,0.01324\,n\\ & & +0.03023\,{n}^{2}-0.00484\,{n}^{3},\end{array}\end{eqnarray} \tag{ 4 }$$

$$\begin{eqnarray}\begin{array}{r}\begin{array}{rcl}({z}_{P1}-{G}_{RP}) & = & +0.4706-0.1733\,X\\ & & -0.0362\,{X}^{2}+0.0714\,Y-\,0.02992\,n\\ & & +0.03099\,{n}^{2}-0.00509\,{n}^{3},\end{array}\end{array}\end{eqnarray} \tag{ 5 }$$

where X = (G_BP − G_RP) is the Gaia color, Y = (J − H) is the 2MASS color, and n = ng/50 = (N₁₅₋₁₆)^1/2/50 is the scaled, square root star density.

The advantage of using GMP to set zero-points is its uniformity over the entire sky. The cost of such an approach is that errors in the Gaia and 2MASS source catalogs are impressed on all the results, and the risk is that systematic changes in reddening, metallicity, dwarf/giant population ratio, and crowding will also create systematic biases. Our judgment is that the Gaia systematic errors are less than 0.01 mag (although we are not certain about crowded regions) and that the coefficients multiplying (J − H) are small enough to ensure that the 2MASS systematic errors will not contribute at the 0.01 mag level either. We examine the final results for systematic errors below and find that they are small. Using GMP to set the photometric basis for our reference catalog appears to be the best we can do for photometry south of −30° decl., at least until the release of Gaia DR3, which will presumably synthesize griz from the BP/RP spectra.

We created a GMP catalog of stars for the entire sky using the regressions of Equations (2)–(5) and used them to set zero-points for all our APASS rereductions and Pathfinder observations. Since GMP is a regression that produces Pan-STARRS bandpass magnitudes from Gaia and 2MASS, we must first convert the Pan-STARRS g_P1, r_P1, i_P1, and z_P1 to each individual catalog's bandpass before comparison. To our knowledge, only Pan-STARRS has published bandpasses measured in situ, so we did not trust any estimates of color terms derived from integration of SEDs against bandpass estimates but worked entirely empirically. Regressions for catalog magnitude as a function of Pan-STARRS magnitude and vice versa over the usual decl. band are given in Table 2.

The relations in Table 2 are not inverses. The calculation of catalog magnitude as a function of Pan-STARRS was derived from the GMP subset of stars in order to set zero-points (the same relation is applicable to both the APASS rereduction and APASS DR9.) The relations that predict Pan-STARRS magnitude as a function of catalog magnitude are, conversely, calculated from all stars, regardless of color or reddening. In order to derive these, we matched all stars from each catalog to Pan-STARRS, sorted the independent variable (g − r) or (r − i) from the catalog into bins of size 0.1 mag, and then took the median of all magnitude differences in that bin. We fitted a line to a selected range in abscissa and verified that it matched trends visible in these medians, as well as the cloud of all points. The results for the APASS rereduction and APASS DR9 are quite independent of each other, because the APASS rereduction includes much fainter and redder stars than APASS DR9. As with all simple, empirical, linear color-term transformations, these do not pretend to high accuracy for stars with extremely red or blue SEDs. Therefore, individual Refcat2 magnitudes for very red or blue stars without direct Pan-STARRS photometry (south of decl. −30° or brighter than m ∼ 14) should be treated with care.

The APASS rereduction and Pathfinder detections were then grouped by matching against the list of all Gaia stars, and weighted median magnitudes were calculated for each star. (The "weighted median" occurs at the 50% quantile of the cumulative inverse variance weights for all detection magnitudes.) An uncertainty was estimated from the weighted quartiles and the number of contributing observations. When this uncertainty is significantly discrepant from the individual uncertainties, we flag the star as a potential variable.

There are real stars in the APASS and Pathfinder observations for which the closest Gaia star is more than 108 distant. For these, we assembled a median magnitude by grouping among themselves, and we include them in the Refcat2 output. We endeavored to avoid galaxies in the DoPhot output for APASS and Pathfinder, but these images do not have a lot of spatial resolution, so a few bright galaxies have crept into Refcat2 (about 0.02% of the total). These non-Gaia objects can be distinguished because the Gaia magnitude and uncertainty are zero. Appendix A provides details.

The photometry of the final APASS and Pathfinder objects is compared against Pan-STARRS in Table 1, with GMP listed as the source of the zero-point. The scatter for APASS and Pathfinder is now only a few mmag.

We also used the GMP set of stars to correct the photometry of APASS DR9. Because the reduction, photometric analysis, and detection combination used by the APASS project for DR9 is completely different from our rereduction, there is merit in treating it as an independent set of photometry. We cannot reflatten the APASS DR9 observations and recombine them, but we can correct on a square-degree basis using the GMP subset; as noted above, much of the variation of APASS DR9 with respect to Pan-STARRS occurs on scales of many degrees, so a square-degree correction should not create serious discontinuities.

Similarly, we created a new version of SkyMapper DR1.1 where the magnitudes for griz in each square degree are shifted to agree with the GMP estimates. SkyMapper DR1.1 flags some stars as having uncertain photometry because of crowding. For these, we added 0.2 mag in quadrature to the uncertainties. This 0.2 mag is really an operational choice rather than an estimate of true uncertainty. The effect causes the contribution to the final magnitude to be minimal if another catalog has data and serves to flag uncertain photometry when only SkyMapper contributes.

For both APASS DR9 and SkyMapper, the magnitudes in each filter and square degree are shifted by a constant value, so the relative photometry between stars of different brightness in a given square degree is not changed. The regressions to convert these revised APASS DR9 and SkyMapper magnitudes to the Pan-STARRS bandpasses are given in Table 2.

Finally, we list in Table 3 a crude set of regressions to get Pan-STARRS magnitude estimates from Gaia magnitudes alone in order to provide some sort of magnitude estimate when no other catalog is available. (These are given large systematic errors, which deweights their contribution if some other catalog provides real griz photometry.) There is a large scatter, of course, and these are not available for stars too faint to have G_BP and G_RP. There is a prominent set of red stars (M giants) that diverge significantly from this relationship, but for magnitudes fainter than m > 14, the M dwarfs will dominate.

Figure 2 shows the star counts in all contributing surveys as a function of star brightness. The assembled Refcat2 looks no different than the Gaia counts because it includes all Gaia stars, as well as a tiny fraction more. Many features are apparent, such as the progressive failure of Pathfinder to be able to discern crowded stars fainter than r > 15, the dramatically lower density of stars in the GMP resulting from the severe selection filters applied, the tiny "crack in the sky" in the APASS counts, and, of course, the markedly different appearance of the Galactic plane in the 2MASS J band.

Zoom In Zoom Out Reset image size

Note that the APASS DR9 counts also show the APASS DR8 stars in the northern hemisphere, although these were not used in the production of Refcat2. Pan-STARRS loses stars in the r band relative to the redder Gaia G band due to extinction, but the correspondence between the star lists is nearly perfect at these bright magnitudes. The APASS counts are also very similar to Gaia for r < 16, although the completeness for 16 < g < 17 begins to fall off.

Figures 3 and 4 show the difference between the star magnitudes in each of eight catalogs relative to the final Refcat2. These are computed as the median difference between the catalog's star magnitudes (converted to Pan-STARRS bandpasses using the color terms of Table 2) and Refcat2, evaluated on each square degree of the sky. Pathfinder and APASS have g, r, and i comparisons, and GMP, Pan-STARRS, and SkyMapper also have z comparisons. The color palette stretches between −0.015 and +0.015 mag.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Close inspection of the GMP–Refcat2 comparison does not show any obvious Gaia scan pattern (although it is obvious if the DUPLICATE stars are not eliminated), but it is possible to discern tiny errors in Pan-STARRS: the 3° honeycomb pattern and 10° square chunk pattern can be seen at the 5 mmag level. Because of the heavy weighting given to Pan-STARRS, these artifacts are not seen in the Pan-STARRS–Refcat2 comparison, indicating that these features have been carried into Refcat2.

The third row of Figure 3 shows the DR1.1 SkyMapper magnitudes, spatially corrected on a degree scale to GMP. The roughness in the −30 < decl. < +0 overlap region with Pan-STARRS is relatively large because its zero-point is corrected by GMP, not Pan-STARRS. Some minor offsets from crowding are visible in the Large Magellanic Cloud. The fourth row shows the uncorrected SkyMapper DR1.1 comparison as a reference (but we do not use uncorrected magnitudes). The flaws that SkyMapper inherited by using zero-points from APASS DR9 photometry are visible in this panel.

Figure 4 shows the comparison with Pathfinder, APASS as rereduced for this work, and APASS DR9 published by the APASS project. The Pathfinder comparison looks a bit better than the GMP where it overlaps with Pan-STARRS, presumably because the bandpasses are more closely matched (compare the top rows of Figures 3 and 4). The mild discontinuity at decl. −30° shows the onset of a southern systematic error in Refcat2. Pathfinder also reveals a honeycomb pattern on 5° scales at the 5 mmag rms level arising from the Takahashi telescope vignetting and imperfect flattening.

The APASS comparison reveals the APASS footprint and the imperfections in the reflattening we imposed. The APASS DR9 comparison is based on the magnitudes published by the APASS project corrected on a square-degree basis by GMP, and the comparison looks somewhat different than the rereduction of APASS above. Apart from the effects of our rereduction of the images, APASS DR9 is more than 1 mag shallower than the APASS rereduction, so different stars are being compared. Some of the degree-by-degree roughness in these images stems from fluctuations in degrees with few matching stars. The fourth row in Figure 4 shows the APASS DR9 (and DR8 for decl. north of +20°) before correction by GMP. Not only are there large differences in degree and much larger scales, the mean offsets listed in the upper left corner are significant.

The SkyMapper project integrated the Calspec set of HST standard-star SEDs against the Pan-STARRS bandpasses to make predictions for magnitudes in the g_P1, r_P1, i_P1, and z_P1 bands.¹¹ We do not expect great accuracy for Refcat2 magnitudes brighter than m < 10 because the only contributions are from Tycho-2, BSC, or Gaia, with rather gross color transformations to griz.

The differences between Refcat2 magnitudes and HST Calspec magnitudes are shown in Figure 5 as a function of g magnitude and (g − r) color.

Zoom In Zoom Out Reset image size

Restricting to stars fainter than g > 10, we find the difference between Refcat2 and 36 HST standards to be Δg = +0.014 ± 0.013, Δr = +0.000 ± 0.016, Δi = −0.001 ± 0.017, and Δz = +0.000 ± 0.025. Restricting to stars fainter than g > 13, the differences with respect to 17 HST standards are Δg = +0.003 ± 0.013, Δr = −0.007 ± 0.015, Δi = −0.003 ± 0.015, and Δz = +0.008 ± 0.021. We do not regard any of these differences as significant enough to compel us to adjust the absolute zero-point that has been set by GMP and its calibration against Pan-STARRS. There are eight HST standards south of decl. −30°, but only one is fainter than g > 10. These scatter evenly among the northern stars and do not show any offset in any of these bandpasses, confirming that Refcat2 maintains all-sky accuracy even where Pan-STARRS makes no contribution.

The griz photometry in Refcat2 has both statistical and systematic errors. The statistical errors listed for each star's magnitude in Refcat2 are derived from the errors of extant catalogs and photometry augmented by judicious systematic allowances according to the trustworthiness of zero-point adjustments we have applied, as well as the degree of color correction from catalog to standard Pan-STARRS bandpasses. The combination process of photometry from different catalogs appears to obey Gaussian statistics for most stars, which gives us confidence that the individual star magnitudes have reasonable error estimates. The distribution of χ²/dof and the frequency of outlier rejection provided in the catalog are consistent with a Gaussian distribution with a few percent tail from variable stars and other outliers. However, Refcat2 remains a heterogeneous compilation at some level, and examination of magnitude error as a function of magnitude will reveal disjoint clumps according to the dominant contributor during the catalog combination.

It is difficult to be certain about systematic error and fidelity to absolute photometry. The comparison with the STScI Calspec standards affirms the absolute photometry heritage of Refcat2 through Pan-STARRS. Comparing Gaia with Pan-STARRS, two completely different sets of photometry with completely different processes to achieve internal consistency, is a means to understand the systematic errors that may be present in each.

The top two rows in Figure 3 illustrate the difference between GMP versus Refcat2 and Pan-STARRS versus Refcat2. The difference between Pan-STARRS and Refcat2 in the second row is virtually nonexistent, as expected because Pan-STARRS observations have lower errors than any other contributor to Refcat2 and therefore strongly dominate the weighted average magnitudes for stars.

However, GMP is also fundamental to Refcat2 because it provides the normalization for the Pathfinder and APASS exposures that were rereduced, as well as the renormalization of APASS DR9 and SkyMapper DR1.1. Therefore, by construction, the difference between GMP and Refcat2 south of decl. −30° is also very small.

We can therefore get a sense of the systematic inaccuracy of Refcat2 by looking at the discontinuity in the GMP–Refcat2 comparison north and south of decl. −30°. Figure 6 shows the GMP–Refcat2 comparison evaluated on square degrees in a pair of 4° wide strips immediately above and below the discontinuity.

Zoom In Zoom Out Reset image size

The northern strip shows marked deviations from zero, exceeding ±20 mmag at particular locations, although the rms is much less than 10 mmag. The r band has the worst residuals: 5119 (coordinate) deg² deviate by more than 5 mmag, 771 deg² deviate by more than 10 mmag, and 23 deg² deviate by more than 20 mmag. The g band never deviates by as much as 20 mmag, the i band deviates by at least 20 mmag on 5 deg², and the z band on 1 deg². Formally, the difference between GMP and Pan-STARRS evaluated on each square degree over the entire sky north of decl. −28° has an rms of about 2 mmag, but of course it is the excursions that are of concern. Because the Pan-STARRS–Refcat2 comparison has no such deviations, we can conclude that these reflect error in the GMP predictions for Pan-STARRS magnitudes. We presume that GMP is continuous and actually has errors akin to the ones visible in the north strip, and so Refcat2 has such errors south of decl. −30°. As noted above, the GMP–Refcat2 comparison north of decl. −30° reveals hints of the Pan-STARRS footprint and chunks, so the northern part of Refcat2 surely also has systematic errors of at least 2 mmag.

Although the all-sky rms is about 2 mmag, there are obvious coherent patches, particularly in r and z near the galactic anticenter where the GMP–Refcat2 difference is consistently around ±5 mmag. These patches remain from the density-correction terms of Equation (2) that erased much bigger errors near the Galactic plane. Although we have a suspicion that this has to do with Gaia–Pan-STARRS filter mismatch and gradients in stellar population or metallicity, we were unable to find an all-sky correlate with these features. It is also conceivable that the ubercal procedure that sets the internal consistency of the Pan-STARRS photometry has wandered because of poor constraints on large-scale error. However, for our purposes, this level of error is not important, and we do not have an all-sky method to correct for it.

Therefore, our summary assessment of the accuracy of Refcat2 is that, by construction, it matches Pan-STARRS north of decl. −30° with an rms systematic error of at least 2 mmag, and south of decl. −30°, it has an rms systematic error of at least 3 mmag, except near the galactic center, where systematic errors can occasionally grow to more than 20 mmag. However, note that these excursions are more correlated with stellar density than galactic latitude; the differences are small right on the plane because the extinction is so high that the star density is lower.