I am pulling together a bunch of information about the Mark IV Engineering Database, as I try to prepare a paper for eventual publication. I thought it would help to post occasional results here, as I derive them, so that others can see and provide helpful feedback.
The first thing is to look at the overall quality of the photometry which is sitting in the Mark IV database. There are several ways one can imagine correcting this data, but let's concentrate on the existing data, as-is.
I created two sets of standard stars against which we can compare the Mark IV photometry. There are
The Landolt stars are concentrated on the celestial equator, so only one of Tom's Mark IV units measured them frequently.
These are scattered all over the sky, at a range of Declinations, so that all three of the Mark IV units observed at least some of these stars.
For each one of the stars in this group, I used Michael Sallman's Mark IV Engineering Database interface to grab all the Mark IV measurements. I then compared the Mark IV measurements to the standard magnitudes of these stars, one by one. I report the differences in the sense
difference = (standard mag) - (Mark IV mag)
So, if you see differences which are positive, it means that the
Mark IV measurements are brighter than the standard values.
Okay. Let's look at an overall view of differences in magnitude as a function of magnitude. We expect to see an envelope which opens up to the right: fainter stars should have larger differences. However, if all goes well, the average differences should be zero.
Here are the differences for the Landolt standards. The heavy points on the graph show the mean and standard deviation (after one round of 3-sigma clipping) of all stars within bins one magnitude wide: from V=7.0 to V=8.0, for example. I've offset the I-band differences by +1.0 magnitudes for clarity.
You can see that the brightest stars have TASS magnitudes which are brighter than they ought to be; that's not surprising, as those stars are saturated on the Mark IV images. There's also a hint that the TASS V-band values are too faint for V > 13.5 or so; that, too, is not surprising, as the relatively large, fixed aperture we used to measure all stars will underestimate the brightness of very faint sources. Finally, I see a small, but significant, fixed offset in the I-band values: it looks like the TASS I-band magnitudes should be shifted by about +0.06 magnitudes to match the Landolt values.
Okay, now let's look at the comparison between Henden and TASS magnitudes. The Henden values are in some sense less primary than the Landolt ones -- they have been calibrated against the Landolt stars -- but they are the best I can find at high Declinations. In addition, Arne Henden is known to be a very careful photometrist, so I put a high weight on his work. In this case, I do not draw the errorbars because the graph becomes too dense and complicated.
This looks consistent with the earlier results: the V-band values are, on average, equal to the standard magnitudes, but the I-band values are, on average, a bit brighter than they ought to be. The very large scatter in the measurements of the faintest stars hides any bias.
The next check to make is to look for differences between the standard and TASS magnitudes as a function of stellar color. The TASS passbands don't match the standard passbands exactly, so we used a correction based on the Tycho-2 stars observed each night to make corrections. Did we do a good job? Let's see. I will use the standard (V-I) color along the horizontal axis in the graphs below.
Let's begin with the Landolt stars. Remember that only one of the Mark IV units observed these stars regularly, so the "Landolt" comparison reveals any color terms in the TOM1 camera alone. The "Henden" comparisons include measurements from all three Mark IV units. I may run separate comparisons for each camera unit soon.
Here are the V-band differences as a function of stellar color.
Hmmmm. There are only a few red Landolt stars, with (V-I) > 1.5, but they appear to show a significant offset: the Mark IV measurements are brighter than they ought to be for these red stars. The Henden stars have a somewhat larger scatter, but don't seem to show this effect.
Now, the the I-band differences as a function of stellar color.
I see no significant trends here.
There is good evidence that the standard Mark IV reduction pipeline produces magnitudes which suffer from some type of large-scale photometric errors as a function of position across the field of a single image. That is, stars in one corner are consistently fainter than stars in the middle, and so on. This is probably due to scattered light contaminating the flatfields. It is not easy to do flatfielding properly for very wide-field telescopes, and the Mark IV has a field of view more than 4 degrees on a side.
One way that these large-scale errors can be ameliorated -- but not removed completely! -- is to break up the sky into small "patches", each patch being considerably smaller than the full field. I have chosen patches which are about 1x1 degree. Now, if these patches are smaller than the scale over which photometric errors occur, then the relative magnitudes of all stars within a patch ought to be relatively free of that systematic error. Of course, if the stars within this patch happened to fall in the upper-left corner of the field on one night, but near the center of the field another night, there could still be big jumps in reported magnitude from one night to the next.
So, we collect all measurements of the stars within a patch, from all the nights available. Let's call this big collection of measurements an "ensemble". We then assume that there may be a single zero-point shift in the magnitudes from one night to the next (or from one image on a single night to the next), so that the measurements from each image can be written like so:
mag of star A on image 1 = true mag of star A + offset_1
mag of star B on image 1 = true mag of star B + offset_1
mag of star C on image 1 = true mag of star C + offset_1
mag of star A on image 2 = true mag of star A + offset_2
mag of star B on image 2 = true mag of star B + offset_2
mag of star C on image 2 = true mag of star C + offset_2
etc.
If we can find these "offsets" for each image, then we can remove them, leaving only the relative magnitudes -- which, if our assumption is correct, are pretty accurate. The result will be a set of relative magnitudes which may have smaller scatter than the originals, since we have removed one source of error.
This idea of "ensemble photometry" is described more fully in a paper by R. Kent Honetcytt, CCD ensemble photometry on an inhomogeneous set of exposures", in Publications of the Astronomical Society of the Pacific, volume 104, page 435 (1992). I've written code to do the job:
I have grabbed data for all the patches from Michael Sallman's Mark IV database, and am running a script which performs an ensemble solution on each patch. It takes about 3-10 hours on my machine to crunch through all the stars in a band of Dec about 0.75 degrees wide. At the moment, the bands from Dec = -5 to Dec = +8 degrees have been processed, which is about 15 percent of the total. I figure that the job will finish near the end of October ...
Does it really help? I think so. I'll try to put together a more detailed explanation soon, but for a quick demonstration, see the figure below. It contains data for stars in a region with (1 < RA < 6) and (0 < Dec < 7).
On the horizontal axis is the mean magnitude of a star, and on the vertical axis, the scatter of its measured magnitudes from the mean value. Green crosses represent V-band measurements taken from the Mark IV database, and red crosses I-band measurements. I plotted the I-band values upside-down so that they wouldn't overlap with the V-band values.
You can see two populations of both green and red symbols. The group with larger scatter represents stars which were measured at least twice; their scatter is based on the standard deviation of all catalog measurements from the mean value. The group with smaller scatter and a tighter locus are stars which were measured only once; since it is impossible to define a scatter given just a single value, the database contains the uncertainty estimate produced by the Mark IV reduction pipeline. That estimate is always a poor one, being much too small. The problem is that the software used to reduce the images did not compute the statistics of counts in the background and in the synthetic aperture for each star properly. Pay attention to the first population -- that's the one which represents the real measurements.
Now, the ensemble solution produces a value of the scatter from the mean magnitude for each star which was included in the solution. I set the software to reject stars which appeared in fewer than 20 percent of all images covering a particular patch; most of these are the very faint ones. For each star which was included, I plot a small black dot showing the mean magnitude and scatter from the mean in the ensemble solution. You can see that the ensemble solution produces a smaller scatter than the catalog contains, especially for bright stars, and most especially for the V-band.
This is no panacea, but it will improve the Mark IV dataset for some purposes. I plan to continue the ensemble reductions until they are finished. I'll try to create some more quantitative demonstration of the improvement and the final quality of the output.
Last modified 10/1/2005 by MWR.