Introduction

Astrometric Calibration

We begin the astrometric calibration by applying the CASU astrometric solution and radial distortion correction to each array in the catalogue to convert to equatorial coordinates. Note that the CASU astrometric solution is based on array coordinates determined by their source detection and aperture based centroiding. We don’t expect CASU centroids to agree exactly with the DoPhot centroids but they are sufficiently close that the astrometric solution is still valid. At this point we need only equatorial coordinates good enough to identify sources common to our astrometric reference catalogue.

As our astrometric reference catalogue we use the projected position of Gaia DR2 sources at the epoch of the VVV observation taking into account their proper motions and parallaxes (Gaia hereafter). Of the Gaia reference sources we require astrometric_gof_al 3, astrometric_excess_noise_sig 2 and a full 5-parameter astrometric solution. To produce a pool of astrometric reference sources we cross match the Gaia catalogue to the VVV catalogue with a 0.25 matching radius and require each match to be the closest in both directions. We also require that VVV detections of reference sources are ’perfect’ stars according to DoPhot, i.e. they are well fitted by the psf model.

The Gaia positions of the reference sources are projected onto the tangent plane using a tangent point at the center of the VIRCAM focal plane as given in the FITS header of the original VVV image. The resultant tangent plane coordinates are the Gaia astrometric reference frame.

For each VIRCAM array we generate a grid of array coordinates with S points per dimension, where the first and last points in both dimensions are at the extreme edges of the array. At each grid point we select sources from the reference source pool inside a radius R, requiring a minimum of M reference sources. Where R is insufficient to select M reference sources it is expanded until it is. With the selected reference sources we fit the 6 coefficients of a linear function necessary to transform the XY array coordinates onto the Gaia coordinates at each grid point. We reject outliers and repeat the process once. We also measure the RMS residual to the fit of all reference sources at each grid point. We interpolate the 6 coefficients and the RMS residuals to the fit between grid points to enable us to describe the transformation necessary to map XY array coordinates onto the Gaia reference frame and the relative quality of the calibration at any point on the array.

Preliminary testing indicated that S=10, R=200 pixels, and M=15 provided good calibration accuracy without significantly sacrificing compute efficiency. Average residuals to the calibration are 65 mas per dimension give the average across bright sources with seeing less than some value for bright sources. Interestingly, we found significantly diminished returns on increasing S past about 10. Were S infinitely large we would effectively have a unique local astrometric solution for every source (e.g. , ), but these results suggest that this is unnecessary.

Note that this process is unlikely to yield as accurate a calibration in surveys covering more sparse fields. It works in the VVV because we have a large number of astrometric reference sources available in every field. In principle one could produce an average astrometric correction based on this process that could be applied to all VIRCAM observations (see e.g. ), but this is outside the scope of this paper.

We apply our derived transformation to the Gaia astrometric reference system to all DoPhot detections and then reverse the projection to the tangent plane to provide accurate equatorial coordinates in the Gaia astrometric system.

Photometric Calibration

The method we use for photometric calibration is simpler than for the astrometric calibration described above but employs the same basic strategy: Measure a local transformation at different points across the array and interpolate between them.

We chose to use the DoPhot based VVV photometric catalogues of ( hereafter) as a photometric reference. These have the advantage that they are at essentially the same depth as the catalogues we wish to calibrate, and that have done much of the hard work necessary to anchor PSF based photometry to the original 2MASS based calibration of the aperture photometry done by ( hereafter). It’s unfortunate that we must add one more link to the chain of this photometric calibration, but

1. Calibrating high resolution photometry to the low-resolution photometry of 2MASS in such dense fields is a significant effort (see ), far beyond the scope of this paper.

2. We do not care a great deal that the photometry are calibrated perfectly to an absolute photometric system, only that the shape of the light curves are accurate.

Point (ii) highlights the an additional advantage of the catalogues: They are provide a singular reference point at any position in the survey, across arrays, pawprints and tiles. This means that even across pawprint overlaps (i.e. same patch of the sky observed in different parts of the focal plane) we are calibrating to a fixed reference, and hence systematic offsets between light curves of different pawprints and tiles are calibrated out.

We cross match catalogues to the original CASU astrometric solution based coordinates of each of our pawprint catalogues, since the CASU astrometric solution was applied by . We use a 02 matching radius, and require each match to the the closest in both directions. We again require our source are ’perfect’ stars as determined by DoPhot, these are our pool of reference sources.

As for the astrometric calibration, we place a grid of S2 points across the array and select at least M reference sources from a radius of R about each point. The inverse variance weighted mean difference between our raw DoPhot Ks band magnitudes and the Ks band magnitudes gives us our calibration value and error at each grid point. We then interpolate between grid points as before to give an offset to be applied and a calibration error at any position on the array. The calibration error is added in quadrature to the raw DoPhot magnitude error to provide the error on the calibrated photometry.

We were able to use a finer grid of samples and a smaller reference source selection radius due to fewer coefficients needing to be measured at each point and the larger number of available reference sources compared to the astrometric calibration. We found S=20, R=100 pixels, and M=15 improved the calibration noticeably but with minimal additional compute time.

WSDB Info

This data can currently only be used on a collaboratory basis since VIRAC v2 contains private VVV and VVVx data. If you’d like access to the below tables please email me with your wsdb username.

leigh_smith.virac_pm2_jhk

This table is identical in structure to leigh_smith.virac_pm2, but it contains only sources with J and H (and obviously Ks) detections. This is the most reliable version of the table and would be the one to use unless you’re really digging into the noise.

leigh_smith.virac_pm2

leigh_smith.virac_lc

leigh_smith.virac2_cat_index

leigh_smith.virac2_x_gdr2

Example Queries

Select all detections and non-detections of an object

with c as (
with a as (
select unnest(catid) as catid,
unnest(mjdobs) as mjdobs,
unnest(mag) as mag,
unnest(emag) as emag,
unnest(dp_chi) as chi
from leigh_smith.virac_lc
where sourceid=641242039174
)
select b.uq_ppid, b.filename, b.seeing, a.*
from a
inner join leigh_smith.virac2_cat_index as b
on b.id=a.catid
)
select filename, seeing, mjdobs, mag, emag, chi
from c
union
select d.filename, d.seeing, d.mjdobs, NULL, NULL, NULL
from leigh_smith.virac2_cat_index as d
left join c on d.uq_ppid=c.uq_ppid
where d.uq_ppid in (select uq_ppid from c)
and d.id not in (select catid from c)
order by mjdobs;

This selects filename, seeing, mjdobs, mag, emag and dophot chi for all detections or non-detections of source 641242039174. This identifies VVV pointings (pawprints, identified by ‘uq_ppid’) in which a source is detected at least once, then assumes it was covered by all observations at the same pointing. This could fail if a source is right at the edge of a pawprint, particularly in vvv tiles d015 and b390 where the pointing coordinates changed in the middle of the survey. It will also fail if a source is in the area covered by two pawprints but for whatever reason it is only detected in one set, in which case I’d question the validity of the source anyway.