Author: Michael Richmond Date: 960903 Revision: #1 960903 Key Words: photometry, filters, catalogs
This technical note contains an analysis of a very small portion of the data collected by triplet #3, located in East Braintree, Vermont (longitude 72:40, latitude +44:03, altitude 1520 feet), on August 21, 1996. It is concerned primarily with the photometric properties of the TASS cameras, and their relationship to the standard Johnson-Cousins magnitude scale.
During the night, the cameras scanned over a number of fields in which Arlo Landolt has measured photometry in the Johnson-Cousins UBVRI system. See his papers
I concentrated on the following Selected Areas:
name RA (2000.0) Dec (2000.0) number of Landolt stars SA 113 21:41 +00:30 46 SA 114 22:41 +01:00 13 SA 115 23:42 +01:00 9
I was able to get I-V-I coverage of SA113 and SA115, but only V-I for SA114 (some house lights that came on briefly in the middle of the night obscured stars in the East I-band frame of SA114). I used the XVista programs to process the frames, which I broke up into 1100-row segments (thus, each segment was about 15 minutes long, or about 4 degrees, and 3 degrees wide).
When I tried to compare the detected star lists with Landolt's catalogs, I discovered that many of the Landolt stars were not detected; a few were too bright, many were too close to other stars to be measured separately, and many others were fainter than could be seen on the TASS images. In order to get the largest possible sample for comparing Landolt and TASS magnitudes, I displayed each image and compared it by eye with finding charts for the Landolt fields; I measured manually aperture magnitudes for each unblended, unsaturated star.
My image reduction and measurement routines need some work; improvements to the methods, and tuning the parameters to match the TASS images, should (I hope) allow me to use the automatically generated stars lists in the future.
After comparing the TASS images with Landolt fields, I was able to identify a number of Landolt's standards in each image. The Table below describes the properties of each image and the number of stars I was able to measure:
Table 1. Properties of TASS images of Landolt fields
sky skysig FWHM aperture radius
field file dir filter (ADU) (ADU) pix (arcsec) pix (arcsec) Nstar
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SA113 n_4c E I 1363 28 3.5-4.4 (49-61) 4.0 (55.5) 14
n_5b S V 228 16 1.5-2.1 (21-29) 2.0 (27.8) 23
n_6a W I 1888 32 2.8 (39) 2.8 (38.9) 19
SA114 n_6b S V 198 16 1.5-2.0 (21-28) 2.0 (27.8) 12
n_7a W I 1820 41* 2.8 (39) 2.8 (38.9) 7
SA115 n_6c E I 1198 28 3.7-4.3 (51-57) 4.5 (62.5) 9
n_7b S V 193 17 1.4-1.9 (19-26) 2.0 (27.8) 8
n_8a W I 1618 29 2.8 (39) 2.8 (38.9) 3
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Notes: assumes pixel scale=13.88 arcsec/pixel
sky varies in frame n_7a: brighter to East
focus is worse on N side of frame n_6c
focus is better on S side of frame n_8a
most of the SA115 stars fell outside of frame n_8a
Some stars were barely visible in the TASS images, so faint that it was impossible to make any accurate measurement of their brightness. Nevertheless, these stars were clearly present. It is possible that objects falling into this No-Man's-Land could be useful under special circumstances: if a nova is discovered inside the area covered by TASS, one could go back to pre-discovery images and search the known position of the nova for evidence of its presence. There is a definite difference in the limiting magnitude of an image, depending on the manner in which one defines the phrase:
When I tried to measure the brightness of Landolt's standard stars, I found the following limiting magnitudes:
Now, the West I-band image:
Here's a table of the stellar magnitudes in this area, taken from the Landolt papers:
star RA Dec V I SA113_366 21:41:54 +00:29:21 13.537 12.326 SA113_372 21:42:02 +00:28:36 13.681 12.915 SA113_260 21:41:48 +00:23:52 12.406 11.800 SA113_267 21:41:56 +00:20:44 7.653 7.071 SA113_475 21:41:51 +00:39:19 10.306 9.208
As for the brightest stars that can be measured accurately, I discovered that a few of the brightest stars in the fields didn't match the Landolt magnitudes very well. Most of these stars showed evidence for saturation in their radial profiles -- that is, a plot of intensity vs. radius revealed that the innermost part of the profile was flat. The stars which appeared to be saturated had magnitudes
Summing up, I conclude that the range over which these images showed stars which could be calibrated photometrically is
Once I had identified standard stars in the Landolt fields, I could calculate the sky brightness. First, I used a large aperture (radius = 10 pixels = 139 arcsec) to integrate the light around a bright, relatively isolated star; that yielded the count/magnitude relationship for the image. Next, I measured the sky value in the image, fitting a Gaussian to a histogram of binned pixel values. The fitted sky values are shown in Table 1. I then converted the sky value from counts per pixel to counts per square arcsecond, using a pixel size of 13.88 arcseconds per pixel, close to that found in TASS Technical Note 9 and TASS Technical Note 10. Finally, given the ratio of brightness between the integrated light from the star and the light in a single square arcsecond, I could calculate the magnitude of that square arcsecond. The results are shown below.
Table 2. Measurements of Sky Brightness
field file dir filter sky (mag/sq. arcsec) approx EDT zenith angle
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SA113 n_4c E I 18.1 23:30 44
SA115 n_6c E I 18.2 01:30 44
SA113 n_5b S V 20.8 00:30 46
SA114 n_6b S V 20.9 01:30 46
SA115 n_7b S V 20.9 02:30 46
SA113 n_6a W I 18.5 01:30 44
SA114 n_7a W I 18.5 02:30 44
SA115 n_8a W I 18.6 03:30 44
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Notes: sunset occurred at 19:46, sunrise at 06:00
moonset 23:46, moonrise at 13:18
For comparison, Garstang (Publications of the Astronomical Society of the Pacific, vol 101, p. 306 [1989]) lists the following values of sky brightness at several observatory sites (his list includes many more sites, too).
sky brightness in V (mag/sq.arcsec)
site year zenith angle=0 zenith angle=45
Lick 1966 20.8 20.4
Palomar 1972 21.5 21.7
Kitt Peak 1987 21.9
Sac Peak 1978 21.9 21.7
Lowell 1982 21.1 20.8
CTIO 1988 21.6
I'm very happy with the measured value of V=20.9 (at zenith angle 45 degrees) for the TASS site in Vermont. It's not world-class, by any means, but it's better than the brightness at a few professional observatories, and certainly much better than that in New Jersey.
My main goal in this analysis was to find the color terms for the TASS cameras; that is, the corrections one must apply to convert raw, instrumental magnitudes measured with the TASS equipment to the standard Johnson-Cousins UBVRI magnitude system. In the simplest form, these equations would be
V = v + k1*(v - i) (1a)
I = i + k2*(v - i) (1b)
where
V,I are the magnitudes in the Johnson-Cousins system
v,i are the instrumental magntitudes
Note that one can also write the color terms in a slightly different form, using the known magnitudes as the independent variables:
v = V + k1'*(V - I) (2a)
i = I + k2'*(V - I) (2b)
Given a set of standard stars of known brightness in the standard
system, it is easist to solve equations 2a and 2b to find
the primed coefficients k1' and k2'.
In order to convert the raw, instrumental magnitudes onto the
standard system, however, one must solve for coefficients
k1 and k2.
In general, it is true that the magnitude of the primed and unprimed coefficients are approximately equal. I wanted to find out if the TASS natural system -- that is, the response of the camera lenses, filters, optical window and CCD chip -- came close to matching the Johnson-Cousins system (which is defined formally by two reflections off aluminum, a filter, and a photodiode). The closer the match, the easier it will be to transform the TASS magnitudes to the standard scale, and the more accurate will be the transformations.
I will compare the measured and standard magnitudes for stars detected in several the Landolt fields, and solve equations 2a and 2b for the primed color terms. The closer the coefficients are to zero, the better.
For each field, I measured aperture magnitudes in the images, and compared them with tabulated magnitudes from the Landolt papers. The simplest comparison states that the two sets of magnitudes are have no color-dependent terms (i.e. k1' = k2 = 0.0), and seeks a single offset that will convert the measured to the standard magnitudes.
V = v + zp
I = i + zp
I split the stars into bright and faint subsamples for this task,
and calculated the required offset for the entire sample, plus
each subsample:
Here are the results:
Table 3. Photometric solutions in Landolt fields -- no color terms
all stars "bright" stars "faint" stars
field images zp sig N zp sig N zp sig N
--------------------------------------------------------------------------
SA 113 V 4.51 0.07 16 4.50 0.03 6 4.51 0.09 10
East I 4.99 0.15 10 5.03 0.06 6 4.93 0.24 4
West I 4.38 0.08 14 4.33 0.02 5 4.40 0.10 9
SA 114 V 4.60 0.04 11 4.60 0.05 8 4.61 0.02 3
West I 4.34 0.05 7 4.32 0.02 3 4.36 0.06 4
SA 115 V 4.57 0.03 8 4.56 0.03 6 4.59 0.01 2
East I 5.03 0.12 9 4.96 0.03 5 5.11 0.14 4
West I 4.37 0.02 3 4.37 0.02 3
--------------------------------------------------------------------------
Notes: "bright" stars are V <= 12.0, I <= 10.0
The next level of approximation allows the existence of a color terms -- that is, the value of the coefficients k1' and k2' in equations 2a and 2b are allowed to be non-zero. For this calculation, I used all stars, given them equal weight (which is not the proper thing to do).
Table 4. Photometric solutions in Landolt fields -- with color terms
all stars
field images zp coeff sig N 95% conf of coeff
--------------------------------------------------------------------------
SA 113 V 4.41 0.11 0.07 16 +/- 0.17
East I 4.85 0.17 0.16 10 +/- 0.45
West I 4.49 -0.14 0.08 14 +/- 0.19
SA 114 V 4.57 0.03 0.08 11 +/- 0.08
West I 4.31 0.02 0.05 7 +/- 0.10
SA 115 V 4.56 0.01 0.03 8 +/- 0.11
East I 5.26 -0.27 0.11 9 +/- 0.37
West I 4.37 -0.16 0.02 3 +/- 3.20
--------------------------------------------------------------------------
Note that in no case is a color coefficient significantly
different from zero.
This is good news -- it means that the TASS and Johnson-Cousins
photometric systems are not very different, and that
it should be possible to convert between the two with
reasonable accuracy.
However, I do not believe that I have enough information to
make a true photometric solution; that would require
two or three times as many stars as I measured for this night.
Shown below are plots of the differences between instrumental
and standard magnitude, as a function of standard (V-I) color,
for each of the fields listed above.
My triplet has I-band filters in the cameras pointed to the East and West of the meridian. Stars pass first through the East I-band camera, and two hours later, through the West I-band camera. The East camera points over my parents' house, and is therefore likely to be contaminated by scattered light; as Table 2 shows, the "sky" brightness is considerably higher in the Eastern camera. Moreover, the East camera was less well focussed than the West camera during this run.
Nevertheless, one can compare the raw, instrumental magnitudes of stars detected by both cameras. This should give some indication of the internal accuracy of measurements, and provide an estimate of the smallest variations in light which might be detected over many nights.
Since the Eastern I-band image of SA 114 was contaminated by house lights, there are only two fields for this comparison. I show below the differences between measured aperture magnitudes of Landolt standard stars; there are, of course, many more stars in the field which could be used in such a comparison.
Table 5. Comparison of raw East and West I-band photometry
all stars "bright" stars "faint" stars
field difference zp sig N zp sig N zp sig N
--------------------------------------------------------------------------
SA 113 East - West 0.69 0.05 8 0.69 0.05 8
SA 115 East - West 0.57 0.01 3 0.57 0.01 3
--------------------------------------------------------------------------
Notes: "bright" stars are I <= 10.0
There are certainly too few stars from which to draw any firm
conclusion, but it seems reasonable that one might be able to
detect variations of less than 0.1 magnitude over the course
of several hours by comparing photometry from the East and
West cameras of a triplet.