Like Technical Note 97 , this Tech Note discusses measurements of magnitudes taken from Tom Droege's Mark IV unit "TOM1" during the period Julian Date 2,452,605 to 2,452,656 (Nov 26, 2002 to Jan 16, 2003). However, this document describes the results of applying conventional "all-sky" techniques to a subset of this dataset. As a result, I include only those measurements made on "good" nights, which showed uniform properties throughout (nearly) their entire lengths.
The measurements were processed through the Mark IV pipeline version 0.3. Tom distributed these (and other data) on a set of 5 CD-Roms labelled "TR1" to "TR5". This note concentrates on the contents of the first CD-Rom, "TR1".
The Mark IV unit TOM1 pointed near the celestial equator, covering an area between -5 and +15 degrees Declination. I ignored the area between Right Ascension 300 and 360 degrees, considering only RA between 0 and 160 degrees.
Following the methods described in Technical Note 97, I evaluated the quality of each night stored on the TR1 disk. I decided that there were only six nights which appeared to be good enough to allow for a single zero-point all night long: their JD limits are
2452609.52 - 2452609.82 aka "night 609" 2452616.48 - 2452616.99 aka "night 616" 2452618.73 - 2452618.99 aka "night 618" 2452619.57 - 2452619.99 aka "night 619" 2452647.82 - 2452647.97 aka "night 647" 2452654.79 - 2452654.99 aka "night 654"
As I check the data again, I see that a few measurements with JD values between 2452618.00 and 2452618.01 have snuck into these reductions. Ooops.
In order to pin down the color term for each camera, I wanted to reduce simultaneously measurements made on different nights. However, Tom had already run all the data through the Mark IV pipeline, which creates a photometric solution for each image individually and applies it to the data. As they appeared on the CDs, the data was already calibrated.
Therefore, my first step was to un-calibrate the magnitudes, turning them back into the original instrumental values.
Actually, after un-calibration, the magnitudes weren't quite the original ones: they still included a normalization to an exposure time of 1 second.
I used the solutions listed in the .cal files on the CDs to remove the original calibration. I then discarded all measurements falling outside the bounds of the six "good" nights. The end result: "raw" instrumental magnitudes for stars.
To these "raw" magnitudes, I applied the spatial correction terms to the V-band measurements, as described in Technical Note 97. This may not help a great deal to reduce the scatter in V-band measurements, as you will see below.
Now, since the Mark IV has a limited range of movement in RA, all these measurements were made over a small range of airmass. For the fields in the TR1 set, near the celestial equator, the range of airmass was only from about 1.30 to 1.40; that's too small a range to derive a good extinction coefficient. I did some experiments, and found that while I could tell the difference between reductions with first-order extinction coefficients of, say, kV = 0.00 and kV = 0.40, I couldn't see the difference between reductions with a difference of only 0.10 in kV. I choose to fix the first-order extinction at these values:
kV = 0.20 mag/airmass
kI = 0.06 mag/airmass
I chose the Landolt equatorial standards as my photometric reference catalog, restricting the set to those which satisfied these conditions:
8 < V < 12
8 < I < 12
In addition, I discarded several of these Landolt stars
which didn't work well with the Mark IV data (due to
crowding, mostly).
So, we have two sets of measurements:
I ran a version of the photom program
with several modifications which have not yet been copied into the version on the WWW page; namely, options to fix the color term and to discard outliers iteratively during the solutionto derive a connection between the standard and instrumental magnitudes. The model I used was
V = v + aV(j) + bV*(v-i) + kV*airmass
I = i + aI(j) + bI*(i-v) + kI*airmass
where
The extinction coefficients were fixed, but the other parameters -- the zeropoints for each night and the color term for each camera -- were solved via linear least squares. Here are the results:
V-band solution aV +/- bV +/- k V=V,(V-I) N 226 a 0 -8.402 0.030 b -0.021 0.018 k 0.200 RMS 0.040 V=V,(V-I) N 226 a 1 -8.399 0.010 b -0.021 0.018 k 0.200 RMS 0.040 V=V,(V-I) N 226 a 2 -8.471 0.011 b -0.021 0.018 k 0.200 RMS 0.040 V=V,(V-I) N 226 a 3 -8.377 0.008 b -0.021 0.018 k 0.200 RMS 0.040 V=V,(V-I) N 226 a 4 -8.439 0.019 b -0.021 0.018 k 0.200 RMS 0.040 V=V,(V-I) N 226 a 5 -8.353 0.014 b -0.021 0.018 k 0.200 RMS 0.040 I-band solution aI +/- bI +/- k I=I,(I-V) N 226 a 0 -8.040 0.023 b 0.158 0.012 k 0.060 RMS 0.035 I=I,(I-V) N 226 a 1 -8.150 0.008 b 0.158 0.012 k 0.060 RMS 0.035 I=I,(I-V) N 226 a 2 -8.179 0.008 b 0.158 0.012 k 0.060 RMS 0.035 I=I,(I-V) N 226 a 3 -8.164 0.006 b 0.158 0.012 k 0.060 RMS 0.035 I=I,(I-V) N 226 a 4 -8.135 0.015 b 0.158 0.012 k 0.060 RMS 0.035 I=I,(I-V) N 226 a 5 -8.087 0.012 b 0.158 0.012 k 0.060 RMS 0.035
The V-band residuals are slightly larger than those in I-band, probably due to the systematic change in V-band sensitivity as a function of position on the focal plane which I described in Technical Note 97. In other words, the corrections I applied aren't perfect.
I applied this solution to all the instrumental magnitudes taken on the six good nights. The result is a LOT of calibrated magnitudes: 1,507,073 pairs of V and I measurements, in fact.
But how can one evaluate the results?
When we tried to combine Mark III measurements of the same star on different nights, we ran into a problem: "spurious doubles", caused by different detections falling just outside the chosen matching radius. This problem is exacerbated if one uses the detections themselves to define the (RA, Dec) position of each star: if one keeps a running average of the positions, the center can wander within a circle of several arcseconds.
Arne Henden made the suggestion a long time ago that one should create a "seed" catalog, based on some other astronomical survey which goes far deeper than the TASS measurements. If one always matches new detections against this static "seed" catalog, one will avoid the problem of wandering positions. Good idea.
So, I used a combination of the UCAC2 and Tycho-2 catalogs to create a "seed" table. I restricted the selection to stars between Dec = -10 and Dec = +20 (the region covered by the TOM1 camera) and magnitudes less than 17. I started with the UCAC2, but then added (bright) stars from Tycho-2 which didn't appear in the UCAC2. The result is a "seed" reference catalog containing 10,964,649 stars.
Now, once there was a reference, I then walked through the large set of calibrated Mark IV measurements. For each star, I checked to see if there was a "match" within the existing reference catalog. What radius should denote a "match?" The difference in position between reference and TASS position depends on magnitude: the RMS of this difference is about 0.5 arcsec for bright stars (V < 10), rises to 1.3 arcsec for V = 12, and almost 3 arcsec for V > 13. I decided to be conservative and use a matching radius of 10 arcseconds.
There were still some stars which had no match in the "seed" catalog. Some few of these are probably real detections of transient objects -- asteroids -- but most are due to blends of stars. I added a new entry to the reference catalog for these un-matched stars, and marked them for future reference. As a check, I looked at the distribution of magnitudes for these inserted stars: out of a sample of 4022 such stars (lying between RA = 0 and RA = 10 degrees)
5 have V mag = 9
24 10
149 11
1461 12
2431 13
433 >= 14
As expected, most of them are the faint stars, which have the largest errors in position.
As a second check, I examined the number of these "inserted" stars as function of RA.
There's a spike of these "inserted" stars between RA = 75 and RA = 150 -- which is exactly where the Milky Way crosses the celestial equator. This makes sense: it's due to crowding, which causes the Mark IV to blend together nearby stars and derive improper positions.
We should mark with a flag any Mark IV measurements which happen to fall within roughly 45 arcseconds of another star which is roughly as bright, or perhaps up to 2 mag fainter.
Once all the measurements are put into the database, we can then gather all the measurements of a single real star in this way: pick all detections which match to the same reference catalog entry. I wrote a short script to do this. It applies a set of conditions to the detections:
For all surviving entries, the script calculates the unweighted mean magnitude and standard deviation from the mean, in each passband.
The result is a set of mean calibrated magnitudes for 243,491 stars. How good are they?
Look at an internal property: the standard deviation from the mean. First in V:
Now, in I:
Now, a pair of external comparisons, against other calibrated magnitudes of stars in the same region. We can compare them to Landolt equatorial standards. There SHOULD be good agreement, since we calibrated the TASS measurements against these stars...
N mean diff stdev
-------------------------------------------------------------------
V: 54 -0.009 0.037 after removing outliers
I: 55 -0.001 0.047 after removing outliers
There are a few outliers, but always in the sense that the TASS measurements are brighter than the Landolt values. I have checked them, and find that in each case, the outliers are stars with companions of comparable brightness within 40 arcseconds.
Another external check is to compare the average TASS measurements to those of stars in Arne Henden's collection of photometry in fields of interest (usually surrounding variable stars of some sort). Note the change in vertical scale -- these differences are larger than those against the Landolt stars, in large part because they include fainter stars.
N mean diff stdev
-------------------------------------------------------------------
V: 41 -0.022 0.115 V < 12
27 -0.187 0.297 V > 12
I: 41 0.022 0.169 V < 12
27 -0.109 0.207 V > 12
There is a clear systematic trend in the residuals in the V-band especially: the TASS measurements of faint stars are fainter than they ought to be. I find this to be a common problem of aperture photometry of faint stars if one uses apertures of fixed size -- as the Mark IV pipeline does.
One may reduce a fraction of the TASS Mark IV data in the traditional manner, as long as one restricts the analysis to really good nights. One must estimate the extinction coefficient, since the observational procedure doesn't give enough leverage to deduce it from the data itself. The results are fair: the scatter in V-band has a floor around 0.05 mag, and in I-band around 0.04 mag. The quality of the photometry decreases in crowded fields, and there is a systematic error for stars fainter than V=12.5 or so. I think that we can correct for this error, but that remains to be seen.