2.1. Observing strategy and cadence

The observing strategy in the Shallow Survey is very simple: any time a field is targeted, it is observed with a full colour sequence of six filters that is completed within 4 min, if there are no interruptions. The Main Survey, in contrast, has several components that are completed over different visits to a field:

1. 1. For the first long visit, we take a colour sequence that includes three exposures for the filters u and v and one exposure for the remaining filters griz, using the order uvgruvizuv. The sequence is executed as a block and typically completed in 20 min.

2. 2. Additional exposure pairs in the filters g and r are added during dark and grey time; since March 2017 we restricted the gr pairs to dark time, because g-band is our most sensitive filter to moonlight.^{Footnote b} Two gr blocks are collected on different nights and typically executed in 4 min each.

3. 3. Additional iz pairs are executed as 4-min blocks and observed during astronomical twilight (between $-12^{\circ}$ and $-18^{\circ}$ Sun altitudes) or in bright time, regardless of other progress on the field. Up to three iz pairs are added over the course of the survey.

4. 4. The final step is a second colour sequence that is identical to the first.

Owing to this strategy, we obtain near-instantaneous six-filter spectral energy distributions (SEDs) via the colour sequences, and we gain more depth by adding further data when the observing conditions are most suitable. As a result of this strategy, DR2 contains a mix of completion statistics across the hemisphere. Since 2014 November 14, the astronomical twilight time at SkyMapper has been used exclusively for Main Survey iz pairs, which explains why these filters already provide nearly hemispheric coverage with at least one visit. Nearly 33% of the Southern sky is covered with all six filters in the Main Survey, typically including one colour sequence, two gr pairs and some iz pairs, i.e., three exposures per filter. The full data set brings the exposure numbers up to (6,6,4,4,5,5) for the (u,v,g,r,i,z) filters but is only complete for 1% of the hemisphere in DR2.

The resulting cadence of repeat observations also depends on the filter: the colour sequences provide a short-cadence lightcurve in uv consisting of three pairs separated by typically 8 min. Repeat observations of gr pairs and iz pairs take place on separate nights, hence they could be as close as $\sim\! 20$ h, or separated by years. The final colour sequence is typically at least a year after the first colour sequence, so the full spectral energy distribution of faint sources is probed only for long-term variability.

Main Survey exposures have a median separation of 14 d in the filters g and r, and 1 yr in the filters i and z. The distribution of time difference between the first and the second colour sequence has two peaks, at 1 yr and at 1 month (owing to the Lunar period).

While the cadence described above holds for a given SkyMapper field, it does not necessarily apply to every object within the field. Because of the gaps between CCDs within the mosaic (0.5 and 3.2 arcmin between rows, 0.8 arcmin between columns), a dither pattern is been applied for the observations of each visit. For the Main Survey observations in each filter, the nominal pattern of (RA, Dec) offsets from the field centre, in arcmin, is $(-5, -1.7), (-1.7, +5), (+1.7, -5), (+5, +1.7), (-8.6, -8.6), (+8.6, +8.6)$ . The malfunction of various detector controller electronics since October 2017 has led to modifications of the pattern, with step sizes as large as $12\ \text{arcmin}$ , but only 1% of DR2 data entails such a large offset. For the Shallow Survey, the dither pattern of the first three visits ranges up to $5\ \text{arcmin}$ from the field centre, but the subsequent visits apply roughly half-field ( $1^{\circ}_{\cdot} 1$ ) offsets in each of RA and Dec, in order to yield more homogeneous photometry from the complete data set.

2.2. Image selection

We started from $\sim160\,000$ images that were observed between 2014 March 15 and 2018 March 14 and processed with our Science Data Pipeline (SDP; Luvaul et al. Reference Luvaul, Onken, Wolf, Smillie, Sebo, Lorente and Shortridge2015; Wolf et al. Reference Wolf, Luvaul, Onken, Smillie, White, Lorente and Shortridge2015). We then selected 121 494 images using the following quality control criteria:

1. 1. While the median number of calibrator stars for zero-point determination is over 1 600 per frame, we require at least 6 calibrator stars; only 0.6% of frames have less than 100 stars.

2. 2. We fit linear throughput gradients across our wide field of view to the calibrator stars and reject images with strong gradients. Our mean ensemble gradients are consistent with zero; we require that their slopes do not exceed 0.05 mag per $2^{\circ}_{\cdot} 3$ width of the field of view in griz filters and no more than 0.1 mag in the uv filters.

3. 3. We measure the root mean square (RMS) scatter of zero points among the calibrator stars to identify frames with uneven throughput due to structured cloud or other reasons, and reject frames where the RMS exceeds 0.05 mag in griz filters and 0.12 mag in the uv filters.

4. 4. We determine typical zero points per filter, which drift in time as the telescope optics accumulate dust and reject frames with low throughput, when the loss is on the order of 1 mag or more.

5. 5. We reject frames where the mean point spread function (PSF) has a full-width at half maximum (FWHM) above $5\ \text{arcsec}$ or elongation (the ratio of semi-major to semi-minor axis lengths) above 1.4.

6. 6. We tighten the constraints on the World Coordinate System solutions compared to DR1, such that both corner-to-corner lengths of each CCD are required to be within $1\ \text{arcsec}$ of the median values for that particular CCD and filter.

7. 7. We reject frames with high background and use thresholds ranging from 500 counts for uv filters, irrespective of exposure time, to thresholds of 3 000 counts for Main Survey frames in iz filters.

2.3. Data processing differences

The major improvement in the image processing compared to DR1 is the treatment of fringing in the iz filters. Each filter was investigated with a principal component (PC) analysis to determine the main modes of fringing behaviour [similar procedures have been described by Brooks, Fisher-Levine, & Nomerotski (Reference Brooks, Fisher-Levine and Nomerotski2017) and Bernstein et al. (Reference Bernstein, Abbott and Desai2017)]. We expect the fringes to be a linear combination of patterns, each of which is created by groups of night-sky emission lines that vary separately in intensity. The fringe pattern caused by each independently varying group would thus be represented by a PC. We find that this approach of multiple, independent fringe frames suppresses fringe residuals in SkyMapper images better than using only a mean fringe pattern, i.e. the first PC.

Taking about 5 000 bias- and flat-field-corrected Main Survey images for each filter, the astrophysical objects in each image were removed and a large-spatial-scale background map was created and subtracted. For the final analysis, we chose a subsample of images that were not excessively dense with objects, were free of large numbers of saturated pixels, and had background levels (prior to subtraction) between 250 and 2 500 counts. About 3 000 images per filter, selected independently for each CCD, were run through a PC analysis routine (using the scikit-learn Python module; Pedregosa et al. Reference Pedregosa2011) to produce the top 20 PCs. For each CCD, the PC creation required $1\!-\!2$ h of processing time and $400\!-\!500$ GB of RAM on the raijin supercomputer at the National Computational Infrastructure.^{Footnote c}

We employed 3 PCs for i-band images and 10 PCs for z-band images. The choice of the number of PCs to use for each filter was guided by experimentation with fitting different numbers of PCs to a set of test images. This by-eye estimation as to when the fringing pattern was no longer visible against the sky noise turned out to be when the last included PC accounted for about 6% of the variance explained by the first PC. An example of the method’sPlease spell out ‘PCA’ if needed. effectiveness is shown in Figure 3 for a z-band Main Survey image. The fitting process mirrored that of the PC generation: astrophysical objects were removed, a large-spatial-scale background map was created and subtracted, and the PCs were fit using the linear algebra least-squares fitter in NumPy (linalg.lstsq; Oliphant Reference Oliphant2006). While the primary goal of fitting the fringes was to clean the Main Survey images, about 4 200 Shallow Survey images in each of i- and z-band were also corrected (about 1 000 new Shallow Survey images in each filter were not corrected). Any Shallow Survey images that were included in DR1 were not reprocessed (and therefore, not defringed), although new photometric zero points were determined (see Section 2.5). Not defringing Shallow Survey images has a limited effect, as the fringe amplitude is below the read noise of the CCDs. In the future, however, all Shallow Survey images will be re-reduced and defringed.

Figure 3. Example Main Survey z-band image before (left) and after (right) defringing with 10 PCs. The peak-to-peak amplitude of the fringes is up to 30 counts in this particular image, with a background level of $\sim400$ counts.

2.4. Masking of electronic noise

Following a period of observatory downtime in 2015, a new source of electronic noise became apparent in the raw images. With correlated fluctuations across all amplifiers, amplitudes of tens to hundreds of counts, typically spanning three pixels in the x direction, and small positional differences between the four quadrants of the mosaic related to timing offsets during the readout process, the source of this noise was subsequently identified as due to ground loops being introduced to the electronics. The problem was rectified by cabling modifications on 2018 July 25.

For DR2 images obtained after November 2015, the following procedure was applied to identify and flag the affected pixels in the associated mask file: after flat-field correction and immediately prior to the flagging of cosmic rays, and taking each mosaic quadrant in turn, the astrophysical sources were masked, based on a 2 $\sigma$ detection threshold in SOURCE EXTRACTOR. We also masked the pixels previously flagged by the SDP (bad pixels, saturated pixels, pixels affected by cross-talk, etc.). The data from the 16 amplifiers (eight CCDs) of the quadrant were appropriately flipped to align pixels read out at the same instant, and the minimum unmasked value at each pixel location was used to construct a source-free image. After subtracting the overall median count value of the source-free image to remove the background, pixels with values exceeding 7 $\sigma$ in either direction were flagged, as was one pixel to the left and one to the right of the outlying pixel. The flagged pixels were assigned values of 64 in the image mask (see Figure 4 for an example).

Figure 4. Example of electronic noise near the centre of a CCD, showing the near-symmetric behaviour in the two amplifiers used to read out each detector (left), and the resulting image mask (right) with the affected pixels flagged by the procedure described in Section 2.4.

2.5. Photometric zero-point calibration

For DR1, we used the American Association of Variable Star Observers (AAVSO) Photometric All Sky Survey (APASS DR9; Henden et al. Reference Henden, Templeton, Terrell, Smith, Levine and Welch2016) and 2MASS catalogues as the external reference points for photometric calibration, after training a transformation from APASS to Pan-STARRS1 (PS1) bandpasses using stars in a common area and then applying a theoretical colour transformation from PS1 to SkyMapper bandpasses based on stellar templates. We subsequently noted significant inhomogeneities in the APASS zero points across the sky, but now that Gaia DR2 provides all-sky homogeneity, we anchor the SkyMapper DR2 zero points to that.

In the Asteroid Terrestrial-impact Last Alert System (ATLAS) Reference Catalog 2 (Refcat2), Tonry et al. (Reference Tonry, Denneau and Flewelling2018) present a transformation from the Gaia filters Bp and Rp to PS1 griz, including a correction based on the flux density of neighbouring stars. This was capable of predicting PS1 griz magnitudes all over the sky to within less than 0.01 mag RMS. We then apply an updated PS1-to-SkyMapper bandpass transformation, using a restricted set of calibrator stars and an updated dust term. The bandpass transformation is derived from synthetic photometry using the stellar spectral library of Pickles (Reference Pickles1998).

In the case of the uv filters, this process involves extrapolation from the PS1 g-band, which has a strong colour term (see below) and is thus prone to significant error propagation. Since we do not have prior knowledge of the metallicity of our zero-point stars, we ignore the significant metallicity dependence in this transformation, which increases zero-point scatter due to metallicity scatter among the calibrator stars, and potentially introduces a subtle calibration drift due to stellar-population gradients across the sky.

Stars are only used as calibrator stars when (i) Gaia DR2 reports a parallax of $>\!1$ milliarcsec, meaning the stars are closer than 1 kpc, to limit the potential impact of dust extinction, (ii) Gaia photometry is considered reliable and not a blend of sources, and (iii) the star is in a suitable colour range for linear colour terms; for details, see Tonry et al. (Reference Tonry, Denneau and Flewelling2018). We further require that either the integrated $E(B-V)$ reddening in the all-sky map of Schlegel, Finkbeiner, & Davis (Reference Schlegel, Finkbeiner and Davis1998), hereafter SFD is below 0.3 mag or the star has a meaningful (i.e., non-zero) value for the $A_G$ extinction estimated in Gaia DR2.

We estimate extinction levels for sight lines with $E(B-V)_{\rm SFD}<0.3$ using $A_V = 0.86 \times 3.1 E(B-V)$ (Schlafly & Finkbeiner Reference Schlafly and Finkbeiner2011), while reducing the estimated $A_V$ further at higher SFD dust levels to take into account that the stars are most likely not reddened by the full dust column. To this end, we use the Gaia reddening estimate $A_G$ , but we do not simply adopt it owing to its large noise. Instead, we determine a weighted average between the SFD estimate and the Gaia estimate, whereby the fractional SFD weight declines from 1 at $E(B-V)_{\rm SFD}=0.3$ towards zero for extremely high $E(B-V)_{\rm SFD}$ values. Our final bandpass transformations are then (subscript to u-band denotes airmass, over which we interpolate when applying to a given image) as follows:

$$ \begin{align*} u_2 & = g_{\rm PS} + 0.783 + 1.127(g-i) - 0.313\times A_V, \\[2pt] u_1 & = g_{\rm PS} + 0.778 + 1.350(g-i) - 0.354\times A_V, \\[2pt] v & = g_{\rm PS} + 0.333 + 1.495(g-i) - 0.459\times A_V, \\[2pt] g & = g_{\rm PS} - 0.012 - 0.174(g-i) + 0.022\times A_V, \\[2pt] r & = r_{\rm PS} + 0.000 + 0.022(g-i) - 0.004\times A_V, \\[2pt] i & = i_{\rm PS} + 0.011 - 0.043(g-i) - 0.007\times A_V, \\[2pt] z & = z_{\rm PS} + 0.016 - 0.043(g-i) - 0.019\times A_V ~. \end{align*} $$

For each SkyMapper image, we match as many stars to the zero-point catalogue as possible, and fit a two-dimensional plane to the zero-point values across the mosaic. The resulting zero-point plane is then applied to all photometry across the image.

Currently, the flat-field process includes no correction for scattered light in the twilight flats, which will be introduced in the future. Heavily dithered observations of the SkyMapper standard star fields indicate that corrections are mostly less than 2% in sensitivity, but in the 1% area of the mosaic that is closest to the corners the calibration offsets can reach locally up to 5%. This means that an object measured once in a very corner of the mosaic and another time in the inner bulk area could show apparent variability up to a 5% level in extreme cases.

2.6. Distil process for master table

The final step in the production of the data release is a distil process. It uses the photometry table that has one row per detection and creates a master table with one row per unique astrophysical object. When objects have multiple detections in the same filter, these may be from both the Shallow Survey and the Main Survey, and they are combined into best-estimate values assuming the object is not variable. Variable sources are of course better characterised by their individual detections in the photometry table, as sampled by the observed cadence. (The timescales for and between visits were described in Section 2.1.)

3.1. Image data set

Data Release 2 contains a total of 121 494 exposures, comprised of 84 946 exposures from the Shallow Survey that provide nearly full hemispheric coverage in all filters with multiple visits, and 36 548 exposures from the Main Survey providing partial coverage in terms of fields, filters, and depth (Table 1). A total of $\sim\!3.7$ millionPlease spell out at ‘FITS’ first use, if needed. individual CCDs passed the quality cuts. The median airmass is 1.11, but a tail to airmass 2 is unavoidable given that the survey footprint includes the South Celestial Pole.

Table 1. DR2 image numbers by filter and survey segment. The row All refers to the sum for the Images, CCDs, and Detections columns, but for the Fields column refers to the distinct number that have coverage in all filters. PSF represents the median FWHM in arcsec. The saturation limit in the last column is the median value, but ranges over more than $\pm 1$ mag within each filter due to variable observing conditions.

As in DR1, the median FWHM of the PSF among all DR2 images ranges from 2.3 arcsec in z-band to 3.1 arcsec in u-band (see Figure 5). Although the median is similar in the two survey components, the distribution is broader in the Shallow Survey: it benefits from occasional short ( $<\!20$ s) periods of good seeing, but it also includes observations in bad seeing, when the image scheduling software (‘the scheduler’) avoids the Main Survey and defaults to the Shallow Survey. The median elongation is independent of filter, with values of 1.12 and 1.14 in the Shallow and Main Survey, respectively.

Figure 5. Distribution of PSF FWHM in DR2 images: u-band images (solid lines) have a median seeing of 3.1 arcsec seeing compared to 2.3 arcsec in z-band (dotted lines). The Main Survey (black lines) has a tighter distribution than the Shallow Survey (grey lines).

Most images of the Shallow Survey are read-noise limited, as the median sky background is less than 100 counts, except for the z-band images that are mostly background-limited. Median count levels in the Shallow Survey have slightly increased in DR2 as most of the frames added since DR1 were taken in full-moon conditions. In the Main Survey, 98% of uv frames are read-noise limited because the Main Survey colour sequence is not observed in bright time, and so the median background is 11 counts. The griz frames, in contrast, are all background-limited in the Main Survey, with sky levels always above 100 counts and median levels range from 227 in g-band to 646 in z-band.

The photometric zero points show long-term drifts towards lower efficiencies across all filters due to dust settling on the telescope optics over time (see Figure 6). A cleaning of the telescope optics on 2015 May 5 (Modified Julian Date, MJD, 57147) improved the zero points by $\sim\!0.3$ mag, as did another cleaning on 2018 February 1 (MJD 58150). We observe an average trend in the loss of system throughput on the order of 1% per month, which might motivate an annual cleaning in the future. Most zero points for a given filter scatter within 0.1 mag RMS at a given calendar epoch, but some nights with bad weather produce tails with higher atmospheric extinction.

Figure 6. Time evolution of magnitude zero points per filter for Main Survey exposures: the gradient shows gradual deterioration of optical reflectivity at a mean rate of $-0.33$ mmag d-1. Cleaning of the telescope optics on 2015 May 5 (MJD 57147) and 2018 February 1 (MJD 58150) improved the zero points by $\sim\!0.3$ mag each time.

An important influence on zero points is airmass-dependent atmospheric extinction. The SkyMapper scheduler attempts to observe any field close to meridian, but for fields with near-polar declination that still means high airmass. This effect translates into a declination-dependent upper envelope for the zero points, where fields around $-30^\circ$ enjoy best transparency, while zero points deteriorate towards the South Celestial pole (see Figure 7). The effect is most pronounced in u-band (which even changes its filter curve due to the atmospheric cut-off), where we lose over 0.7 mag between zenithal declinations and the pole.

Figure 7. Declination dependence of Main Survey zero points: the upper envelope results from airmass-dependent atmospheric throughput. The u-band suffers $>\!0.75$ mag loss from zenith to the Celestial pole. While the SkyMapper scheduler attempts to observe at minimal airmass, near-polar fields never rise to low airmass.

3.2. Sky coverage

The mixture of Shallow Survey and Main Survey data and their sky coverage can be seen from Figure 8, which shows, for each filter, the deepest photometric zero point for each SkyMapper field. While the zero-point maps distinguish between the areas with Shallow Survey (light) and Main Survey (dark) images, the FWHM and background levels for each observation serve to further modify the true point source sensitivity across the sky.

Figure 8. Maximum photometric zero points for each field, separated by filter. Darker colours indicate deeper data, with white fields having no images. The nominal zero-point difference between Shallow Survey and Main Survey is roughly given by the ratio of exposure times, amounting to (1.0, 1.75, 3.25, 3.25, 2.5, 1.75) mag in (u,v,g,r,i,z), respectively.

The sky coverage of the Main Survey falls into two filter groups owing to the observing strategy: uvgr coverage is driven by the colour sequences that are available for 40% of the hemisphere, and slight differences in image availability stem from the application of hard quality thresholds to individual images. In contrast, the iz filters cover nearly the whole hemisphere because of twilight observations that are dedicated to this filter pair.

DR2 has tighter limits on image quality than DR1, in particular for zero-point homogeneity within exposures; this means that users could find data missing in DR2 that was previously part of DR1. Since better data are not always available, some DR1 objects will be absent.

3.3. Photometric table data set

The data set comprises tables with observing information (images, ccds, and mosaic), tables of on-sky photometry, (master and photometry), and copies of external catalogues pre-matched to SkyMapper sources, so that users can quickly generate multi-wavelength table joins.

DR2 provides instantaneous photometry, i.e. measurements made on individual images, as well as averages distilled from repeat measurements, which will be meaningful for non-variable objects. Since objects are only searched on individual images and not on image stacks, the object catalogue is less deep than the data set would allow in principle.

However, the distilled photometry in the master table reduces errors by combining all individual measurements that are flagged as reliable, and the distilled errors reflect variations beyond photon noise, such as resulting from uneven throughput variations. A planned addition for the next release is searching for objects on deeper co-added frames and performing forced-position photometry, which will create a deeper catalogue and more precise photometry for extended sources.

Most science applications will be served well with data from the master table alone, which contains astrometry and six-filter PSF and Petrosian photometry, as well as flags and cross-link IDs to multi-wavelength tables from external sources. Each row in the master table represents one astrophysically unique object.

The more detailed photometry table contains one row per unique detection in any SkyMapper image. A single object from the master table may thus appear in several dozen rows in the photometry table, depending on the number of visits to the field and the number of filters in which the object is visible. Objects can be identified or joined to the master table with the OBJECT_ID column (described further in the next section).

3.3.1. Master table

The DR2 master table contains about half a billion (505 176 667) unique astrophysical objects. Their photometric measurement can have good flags (SOURCE EXTRACTOR FLAGS 0 to 3, no other issues) or bad flags (SOURCE EXTRACTOR FLAGS $\geq$ 4 or other issues).

Among the half billion objects, about 2.75 million (0.55%) do not have a single good measurement in any filter, either because they are saturated in all filters or because they are too close to a very bright star and thus flagged to have possibly bad photometry or be bogus detections due to scattered light.

A further $\sim82.3$ million (16%) have at least one filter with only one good measurement. The remaining 422 839 424 objects (83%) have more than one good measurement in all filters in which they are detected at all. Filters without any detections do not count towards this consideration.

The astrometric calibration of DR2 is done as in DR1 and astrometric precision has not changed overall. The median offset between our positions and those in Gaia DR2 is 0.16 arcsec for all objects and 0.12 arcsec for bright, well-measured objects. In the next release, we plan to switch the astrometric reference frame to Gaia DR2.

The change in calibration procedure from DR1 to DR2 implies that every object in common between the two releases will have new photometry (and a new OBJECT_ID).^{Footnote e} In the ugri filters, the average change among bright stars is less than 1%, while the average v-band magnitude has dimmed by 2.5%; that is, it moved by the opposite of what was suggested in Casagrande et al. (Reference Casagrande, Wolf and Mackey2019), and the average z-band magnitude has brightened by 1.5%.

Figure 9 shows a map of the magnitude differences between our two data releases, which are almost entirely a result of changing the calibration reference; the change from APASS DR9 in our DR1 to Gaia DR2 in our DR2 imports the all-sky homogeneity of Gaia into the SkyMapper calibration and removes the substructure we had imported previously from APASS DR9.

Figure 9. Comparison of DR2 photometry with DR1 photometry in all filters: plotted are the median magnitude differences per deg $^2$ , restricted to objects with PSF magnitudes brighter than 16. These differences are expected to result primarily from the improved calibration procedure in DR2.

When we compare our measured photometry with that predicted from Gaia for the sample of our zero-point stars, we find on average no offset in any filter, as expected by design of our calibration procedure. We find, however, RMS dispersions among magnitude differences that range from 1.5% for g and r filters to 5% for the u-band. This is a result of true physical dispersion, presumably due to the distribution of metallicity values and their effect on measured u-band magnitudes, where the predicted magnitudes ignore metallicity and involve just a mean transformation for the overall sky population.

Figure 10 compares our measured photometry with that of Pan-STARRS1 DR1, assuming bandpass transformations by Tonry et al. (Reference Tonry, Denneau and Flewelling2018). We restrict the comparison to the magnitude range $[14.5,17.5]$ for all four filters, where both surveys should be complete and free from saturation effects. The predominant differences are close to the Galactic plane and follow Galactic structure, and so are likely due to the treatment of reddening and/or issues of source density in crowded fields (cf. Tonry et al. Reference Tonry, Denneau and Flewelling2018). The mottled effect in the ( $g-r$ ) map (which is shown at higher contrast than the others) is primarily due to residual flat-fielding imperfections in the SkyMapper images.

Figure 10. Comparison of SkyMapper DR2 photometry with Pan-STARRS1 DR1 photometry in g,r,i,z after applying bandpass transformations by Tonry et al. (Reference Tonry, Denneau and Flewelling2018): plotted are the median magnitude differences per deg $^2$ , restricted to objects with PSF magnitudes between 14.5 and 17.5. The large offsets at the Southern edge of the PS1 coverage are where PS1 becomes unreliable. The bottom panel compares the median $g-r$ colours in a high-contrast map and shows that the most extreme differences reach $\pm 0.03$ mag.

We also see small-scale structure away from the plane, where star densities should be generally low. Focusing on a small halo region around RA $\,=180$ , we find RMS differences in the map of less than 0.01 mag in gr filters and also in the $g-r$ colour map, although peak-to-peak the $g-r$ colour can range by 0.035 mag in the halo fields at Northern Galactic latitudes.

We estimate the internal reproducibility of DR2 photometry from repeat measurements of bright stars with good flags and find RMS values in the PSF magnitude of 10 mmag in u and v filter, and 7 mmag in griz.

We also show a map of the median colours of stars as measured by SkyMapper and PS1 ( $g-r$ ) as well as Gaia ( $B_p-R_p$ ) in Figure 11. We note that the visible structures are extremely similar. Overall, we see the well-known trend with Galactic latitude: halo fields are dominated by red stars seen through little reddening by interstellar dust, while intermediate-latitude fields are populated increasingly by younger and bluer stars; closer to the Galactic plane dust reddening makes the population appear strongly redder, while some special regions on the plane show only unreddened foreground stars, as the most highly reddened stars are invisible.

Figure 11. Median colour of the stellar population as seen in Gaia $B_p-R_p$ , Pan-STARRS1 $g-r$ and SkyMapper $g-r$ : plotted are the median colours per deg $^2$ , restricted to objects with magnitudes 14.5 to 17.5. The bottom panel shows the median $E(B-V)$ reddening value from Schlegel et al. (Reference Schlegel, Finkbeiner and Davis1998).

Finally, Figure 12 shows the number counts from the master table in all six passbands using only objects with PSF magnitude errors of less than 5%, corresponding to $>\!20\sigma$ -detections. The curve for each filter shows a double-peaked structure as a result of combining two contributions: the Shallow Survey peaks around 17–18 mag and covers nearly the whole hemisphere, while the deeper Main Survey peaks around 19–20 mag depending on filter but covers a smaller area. In the i and z filters, the double peak is not pronounced because the exposure advantage of the Main Survey translates only into a square-root gain in depth with the sky-limited background in these two filters. Generally, the peaks are softened by a range in sky transparencies and seeing levels mixed in the overall data set.

Figure 12. Number of counts per filter, restricted to objects with $<\!5$ % error in PSF magnitude. All filters show the sum of two contributions: a large area covered by the Shallow Survey that is complete to nearly 18 mag, and a smaller area covered by the Main Survey that provides deeper data and creates a second maximum.

3.3.2. Photometry table

The photometry table serves three purposes that go beyond the role of the master table:

1. 1. It lists photometry in 10 nested apertures ranging from 2 to 30 arcsec diameter. Since aperture magnitudes are seeing-dependent, and seeing changes between exposures, we do not distil these quantities.

2. 2. It lists astrometry and photometry for individual exposures of the object. This can be used to study variability in brightness as well as motions (for examples, see Sections 3.6 and 3.7).

3. 3. It lists photometry that is flagged as potentially (but not necessarily) bad and thus excluded from the results in the master table. Users may find the measurements useful, and the measurements may at times be correct.

Nested-aperture photometry is illustrated in Figure 13 for an extended galaxy as well as for a point source. Crucially, we report the aperture data for counts and magnitudes differently: aperture counts are listed as measured and thus represent a raw growth curve; aperture magnitudes, in contrast, are estimates of total magnitude corrected with the local growth curve (MAG_APCnn, ‘C’ indicating corrected values for an aperture diameter of nn arcsec) for all apertures smaller than 15 arcsec. The growth curve is determined by comparing the ratio of the smaller aperture flux to the 15 arcsec-aperture flux. We do this on a CCD-by-CCD basis, and the fit is allowed to vary linearly in (x, y) position on the CCD. We choose the 15 arcsec aperture as a total-magnitude reference for point source calibration; this magnitude, as well as that from the two larger apertures with diameters of 20 and 30 arcsec, is listed as measured without correction (MAG_APRnn, ‘R’ indicating raw values). PSF magnitudes are estimated as a constant-value fit to the inverse variance-weighted sequence of corrected aperture magnitudes. Formally, these fits produce estimates of PSF magnitude that appear precise to a milli-mag-level, while residual calibration errors can be much larger. Figure 13 also describes the wings of the SkyMapper PSF and shows that point sources still have a few percentage of their flux outside a 15 arcsec aperture in median seeing.

Figure 13. Growth curves of aperture measurements in the photometry table for the double source NGC 1321 (OBJECT_ID 21671053, a galaxy with a foreground star) and for a star (OBJECT_ID 21670913) in the same image (z-band, FWHM 2.7 arcsec). Left: Count rates measured in apertures with diameters of 2, 3, 4, 5, 6, 8, 10, 15, 20, and 30 arcsec (table columns FLUX_AP02 to FLUX_AP30). Overplotted are measured Petrosian and estimated 1D-PSF fluxes, which are identical within 0.5% for the star, while (unsurprisingly) the PSF flux of the galaxy is just a fraction of the total flux. Centre: Aperture magnitudes for apertures from 2 to 10 arcsec (MAG_APC02 to MAG_APC10) are corrected for the growth curve of the expected PSF at the object location assuming that a 15 arcsec aperture represents total magnitude. Aperture magnitudes for 15 arcsec (MAG_APR15) to 30 arcsec (MAG_APR30) are as measured. For the star, the various nested apertures predict nearly identical PSF magnitudes after correction, and the scatter among them is $\sim\!2$ mmag; however, the uncorrected magnitudes in the larger apertures show that there is an additional $\sim3.5$ % of flux in the wings of the PSF between the 15 arcsec and the 30 arcsec aperture. Right: Image cut-outs of the two objects, size $1 \times 1$ arcmin.

3.4. Limitations of PSF magnitudes

Our PSF magnitudes are based on one-dimensional (1D) growth curves of point-source light profiles over a 15 arcsec diameter, as in DR1. We estimate the precision of these growth curves from the internal reproducibility of the PSF photometry among repeat visits of the same bright objects, and find RMS variations of the PSF flux of 0.7%. However, our 1D PSF magnitudes are affected by close neighbours as a function of separation d and magnitude difference $\Delta m$ ; see Figure 14. As a rule of thumb, the PSF magnitudes can be biased brighter by $>\!1$ % when $d (\text{arcsec}) < 5 + 2 \times \Delta m$ . Binary stars of equal brightness only affect each other by $>\!1$ % if they are closer than 5 arcsec. Faint sources with bright neighbours, however, can be more strongly affected, even at 15 arcsec separation when the neighbour is over 5 mag brighter.

Figure 14. Effect of close neighbours on the 1D PSF magnitude of stars: flux from neighbouring stars contributes to the aperture magnitudes of nearby objects and biases their measurement up relative to isolated stars. The effect is $>\!1$ % for neighbours of equal brightness, when they are closer than 5 arcsec. Brighter neighbours (positive $\Delta m_{12}$ ) have an effect already at larger separations, while fainter neighbours can be ignored.

We have expressed this rule of thumb in the column FLAGS_PSF, where bits 0 to 5 (values 1 to 32) are set when the filters z to u are estimated to be affected by $>\!1$ %. This rule assumes that both sources are PSF-shaped, and it may be wrong when applied to extended objects. Also, saturated neighbours and those with other bad flags in the master table are assumed to have bad effects out to 15 arcsec. We did not record neighbours with separations of $>\!15$ arcsec. If they are sufficiently bright, they might still have an effect, but they would also inhibit the detection of faint neighbours in their PSF wings.

3.5. Missing table entries

Users of our data services may encounter situations where image cut-outs at the position of a known target show images with a source on them, while the cone search and a full catalogue search reveals an object entry at the position in question, for which the photometry in the relevant filter is missing. How can that be? There are several possible reasons:

• 1. The most common reason will be the bright-star flag that is set for all detections in the vicinity of very bright (−1 to 8 mag) stars. These flags are set for all objects within a radius around the bright stars that depends on the magnitude of the star and filter. Objects in this zone have all measurements flagged within one filter, or some of them if the object is on the edge of the flagging radius. When no unflagged data survives for a filter, the photometry columns in the master table will be empty, and its FLAGS column will reveal the reason. If no filter provides any good measurements, the object’s entire SED will be lost from the master table, but it will be visible in the photometry table.

• 2. Another reason may be that all detections of an object in the relevant filter were flagged as bad due to other causes, such as large numbers of bad pixels that are counted in NIMAFLAGS, which have a threshold of 4 for inclusion in the master table, or all detections are saturated (FLAGS $=4$ bit being set).

• 3. Finally, the parent object identified by the merge algorithm at the location in question might have more than one child in the filter in question, which suppresses the listing of distilled photometry; in this case, the column {F}_NCH ({F} being the filter) contains a value $>\!1$ and the photometry table contains more information.

It is also possible that the photometry table does not reveal entries for an object in an image, which is clearly visible in the image in question. Unless Source Extractor overlooked the object, given the parameters we chose, this should only happen when Source Extractor extracted two objects in this image while they are considered children of a single parent object for this filter. If all images within one filter show multiple children for what is taken to be a single merged object, all measurements for this object will be missing from the photometry table and hence no distilled summary photometry for this filter can appear in the master table.

3.6. Variable objects

The observing strategy involves multiple exposures per filter on each sky field, with a range of cadences explained in Section 2.1. This allows us to identify variable objects, although the distribution of cadences over filters and survey components means that the selection function will be generally complex and depend on sky position, filter, and object brightness. The master table contains a variability index {F}_RCHI2VAR for each filter {F}, which is calculated as the reduced $\chi^2$ among the repeat measurements for the hypothesis of an object being constant in brightness. This measure is driven by both true brightness variations as well as calibration uncertainties and erroneous measurements.

Figure 15 shows a random sample of objects from a small sky area of $2^\circ \times 2^\circ$ in comparison with known variable objects, for which we use a random 1% subset of the objects from the AAVSO International Variable Star Index (VSX; Watson, Henden, & Price Reference Watson, Henden and Price2006; Watson et al. Reference Watson, Henden and Price2017). Most of the known variable stars are clearly distinguished by a high variability index. New variables can be identified using suitable thresholds, but any analysis of their SEDs for classification purposes would ideally consider the individual detections in the photometry table.

Figure 15. Significance of variability detected among DR2 repeat measurements: we compare a random sample (grey) taken from a small sky area with 1% of the variable source catalogue VSX (large black dots); the plotted variability index is the reduced $\chi^2$ for the set of DR2 photometry being consistent with a constant source, assuming formal flux errors.

The six-filter SED of variable objects in the master table can be entirely wrong, because filters are observed at different times and clipped for outliers from a median estimate in the distil process. In Figure 16, we compare a known variable star of type RR Lyrae to a random star seen as not varying. The SED of the variable star is plotted from the photometry table for two epochs with Shallow Survey photometry that captures all six filters within a few minutes, while the non-varying star is represented with three to four (depending on filter) epochs. Error bars on magnitudes are mostly too small to be visible, and horizontal error bars represent the filter FWHM.

Table 2. Example of a moving object: multiple appearances of the dwarf planet Pluto in the master table.

Figure 16. Example SEDs of two stars. Top: a known RR Lyrae star (OBJECT_ID 533362) easily recognisable as variable already in the Shallow Survey photometry (two epochs shown). Bottom: a star (OBJECT_ID 97057927) seen as not varying even with the better precision of the Main Survey (3 to 4 epochs per filter shown).

3.7. Moving and transient objects

Some objects in the master table have only one detection, although that region has been visited multiple times. This includes asteroids and dwarf planets that will be seen at different times in different sky locations, as well as transients that are stable in location but have such high variability amplitudes that they exceed the detection threshold of our imaging only on one occasion. The latter category includes flares on M dwarf stars that are too faint in quiescent state, as well as novae and supernovae.

Here, we note two examples: first, the 14th magnitude dwarf planet Pluto appears five times in the master table between July 2014 and April 2017 (see Table 2). A second, noteworthy, case was identified while selecting M dwarf flares from DR1 (Chang et al. in preparation): an apparent super-flare was seen in an M giant (OBJECT_ID 282264432 in DR2) on 2014 June 18, that seemed to brighten the star to $g\approx 10.7$ mag relative to the other detections around 15 mag. This event turned out to be a chance blend of the star with the $V=10.6$ mag Inner Main Belt asteroid (230) Athamantis, which was moving about half an arcsec min^–1.^{Footnote f} Figure 17 shows the time/filter sequence of the Shallow Survey visit to the target location on 2014 June 18 around 16:40 UT, where the middle of the first and last exposures are separated by 3 min. Due to the motion, the u and v centroids differ from the star’s own location such that blended uv magnitudes appear in a separate entry in the master table with OBJECT_ID 282264433.

Figure 17. Time/filter sequence of the Shallow Survey visit from 18 June 2014 to the $g\approx 15$ M star with object ID 282264432. Pixel scale is the usual $\sim 0.5$ arcsec. In these images, the dominant source here is actually the $V=10.6$ mag asteroid (230) Athamantis, which was moving with $\sim 0.5$ arcsec per minute. From left to right the filters run along the usual Shallow Survey sequence uvgriz, and the middle of the first and last exposure are separated by 177 s.

3.8. Images and CCDs tables

The image table lists dates, positions, exposure times, and quality indicators of each individual telescope exposure. It can be used to differentiate between Shallow Survey and Main Survey images, based on the column IMAGE_TYPE, which is ‘fs’ for the Shallow Survey^{Footnote g} and ‘ms’ for the Main Survey, or based on EXP_TIME, which is 100 s for the Main Survey but shorter for the Shallow Survey. Images are identified by a unique IMAGE_ID, which encodes roughly the UT date and time of the shutter opening for the exposure in the format YYYYMMDDhhmmss. While the value is rounded to 1 s, it is not actually the time stamp for the exposure start: it is on average 2 s earlier than the exposure start and extreme values in DR2 range from $-11$ to $+9$ s. (The DATE column contains the actual MJD at the start of the exposure.) Image IDs are listed for every object detection in the photometry table.

The ccds table contains every valid CCD of every exposure, and thus nearly 32 times as many rows as the images table. Occasionally, CCDs will be missing for some exposures, either because an adequate World Coordinate System (WCS) solution could not be determined or because the read-out amplifiers failed. The COVERAGE column defines the polygon of a CCD’s footprint, and could be used to check whether a known target location has fallen on a CCD that is part of the data release. This information can be used to investigate non-detections of known targets. An alternative approach for a small number of targets is to visually inspect small images served by the cut-out service, which will return all release images at the target location.