TN 0043: Recalibration of measurements in the TASS database

Michael Richmond
June 19, 1998
Revision: #5 980927 Key Words: photometry

Table of contents:

• How good is the "raw" TASS data
  Not really sure. But the photometric calibration is probably adding significant noise to differential measurements.

I have started to work on the several different corrections needed to re-calibrate ALL of the data currently sitting in the TASS database. This Technical Note is a record of the process.

The plan is to go through several iterations of reduction.

• "raw" -- data as it sits in the database right now
• check for, and correction for, any remaining color terms (in any of the cameras)
  In progress, Aug 2, 1998
• check for, and correction for, any remaining trends versus Declination (in any of the cameras)
  none found, so no correction
• (?) test via calibration of "secondary" standards and comparison with additional photometric catalogs
  not done, no plans to do so
• application of corrections to the TASS database
  after removing color terms, no more

The entire process is now finished.

How good is the "raw" TASS data?

I am using the word "raw" to describe data which has been submitted to the TASS database for archiving. It isn't really "raw", having gone through:

• dark subtraction
• flatfielding
• conversion from image to star list
• photometric calibration within the "STAR" extraction program

Nonetheless, I'll use that term to describe the current (June 19, 1998) contents of the TASS database.

The goal is to modify the measurements (only slightly, we hope) so that they adhere more closely to the standard Johnson-Cousins magnitude scale. For our purposes, that means the magnitude scale defined by Landolt's lists of equatorial standard stars. See his papers

• "UBVRI photometric standard stars around the celestial equator", Astronomical Journal, vol 88, p 439-460, 1983
• "UBVRI photometric standard stars in the magnitude range 11.5-16.0 around the celestial equator", Astronomical Journal vol 104, p 340-371, 1992

It may turn out that we don't detect enough of the Landolt stars in some parts of the sky to use them for calibration; if so, we'll have to find some other sources of good photometric standards.

Let's look first at all the cases in which TASS cameras detect and measure a Landolt standard star. I will examine all TASS data, at all declinations, for matches to Landolt standards. I find

      12174 TASS detections which match Landolt standards
        268 different Landolt standards overall
          4 different sites contributing measurements
         71 different nights with observations

One way to describe the quality of the TASS calibration is to calculate the overall mean difference from Landolt magnitudes, and the standard deviation of the differences.

                                  V              R             I
  =======================================================================
  number of stars              4699           2085          5390
  mean difference (mag)           0.014          0.061         0.049
  standard dev of mean (mag)      0.195          0.178         0.188

Now, the question is: is this the best we can do? Or is there some way to improve the agreement between TASS and Landolt measurements of the same stars?

The differences are very small in the mean (which is good) but not so small in their deviation from the mean (which is bad). So, my initial answer to "Is this the best we can do?" is a tentative "No."

One way to look for places in which we can improve is simply to plot the residuals against a number of different variables, and look for some correlations. If a plot of residual versus magnitude shows a strong trend, perhaps there's a problem with non-linearity of TASS cameras. Or if we see several nights stand out with large residuals, we may remove them from the calibration steps.

Let me therefore provide plots of the residuals, in the sense TASS magnitude minus Landolt magnitude, for several different variables. Below are plots of

• For V, then R, then I
  • residuals vs. magnitude
  • residuals vs. patch (RA, or position on the sky)
  • residuals vs. night
  • residuals vs. stellar color
• for sites B (Gombert), D (JHU/APL), G (Gutzwiller), H (Droege)
  • residuals vs. dec for each camera

V-band values:

R-band values:

I-band values:

A quick summary of the data might be:

• no sign of significant error as a function of magnitude (phew!); the errors do increase with magnitude, as expected. The brightest magnitude bin (mag 6) is probably affected by saturation.
• some indication of individual patches which stand out from the mean calibration. This may be due to patches with very few stars, or patches observed only once, or on a bad night.
• some indication for a few "bad" nights
• (all cameras combined) most show no strong indication of trends with stellar color, over a narrow range of colors: about 1 mag in (V-I). However, the only R-band camera, at site H, shows a color-dependent error: red stars, (V-R) = 1, are about 0.2 mag too faint.
• (each camera individually) no strong indications of trends with declination. Site D (JHU/APL) a weak trend for stars at its southern edge to be fainter than Landolt, and stars at its northern edge to be slightly brighter than Landolt.

I tried looking at the residual versus patch during a single night, hoping to distinguish good nights from bad. But I discovered instead that almost every night has only a single patch of Landolt stars; a few nights cover two patches, but with few stars in the second one. Rats!

Corrections to the "raw" TASS data

As shown above, the only clear systematic error I found in the "raw" TASS data is a color term in the R-band magnitudes from site H (Tom Droege's triplet). An unweighted linear fit to the data yields an equation for the mean difference in the sense (TASS - Landolt) of

 (1a)   (TASS V) - (Landolt V) =  0.047   - 0.038*(Landolt V - Landolt I)   
                                        +/- 0.012

 (1b)   (TASS R) - (Landolt R) = -0.013   + 0.159*(Landolt V - Landolt R)   
                                        +/- 0.030

 (1c)   (TASS R) - (Landolt R) =  0.050   - 0.001*(Landolt V - Landolt I)   
                                        +/- 0.011

In order to remove this systematic error in the TASS R-band magnitudes, we really need to solve an equation that looks like this:

 (2)    (TASS R) - (Landolt R) =    a   +    b * (TASS V - TASS R)

However, I am -- admittedly -- too lazy to do the inversion. Well, I tried it, actually, but gave up after the algebra covered a page and didn't appear to be approaching the desired form. What I did succeed in doing was checking the size of the errors that we make if we use the coefficients from the first equation in the second one; that is, if we compute a correction to TASS R-band magnitudes via

 (3)    (TASS R) - (Landolt R) = -0.013 + 0.1593*(TASS V - TASS R)

1. make no correction: in this case, the error in catalog R-band magnitude shows a clear trend with color. The error reaches a size of about 0.30 magnitudes at (V-R) = 2.0.
2. make the improper correction: a color-dependent error still occurs, but its size decreases to about 0.05 mag at (V-R) = 2.0.
3. make the proper correction: should remove the color-dependent error entirely, but I can't figure out the coefficients.

I created a new table in my copy of the TASS database, called cor_cat, which contains only "good" stars (those detected on at least 10 occasions). I applied the correction in equation (3) above to the R-band magnitudes, and left the V-band and I-band magnitudes alone. It is this cor_cat table which is accessed by the TASS archive database routines.