Author: Michael Richmond, Arne Henden, Michael Gutzwiller, Herb Johnson Date: 970529 Revision: #5 970615 Key Words: photometry, observation
This is the final version of this Note, finished after the AAS meeting on June 10, 1997.
Since this Note draws upon the work of so many people, it really should have many authors. I've listed several at the top, but others should feel free to let me know if they would like to be added.
Table of Contents:
This Note describes estimates of statistical uncertainty in stellar photometric measurements, and the results when applied to real data. Sample Mark III images in V and I bands were analyzed as described below to produce the mean and standard deviation from the mean for measurements across several nights. Plots of standard deviation vs. mean magnitude show the effects of magnitude on standard deviation, as well as instrumental effects at bright magnitudes. Searches for "interesting" objects in two different ways both reveal candidates for further study.
There were three fields selected for special study by the TASS group in Spring 1997. The three fields A, B, C are:
Field A: RA = 12:30 - 12:45 Dec = +0 (gal lat ~ 65 degrees, ecliptic)
Field B: RA = 08:45 - 09:00 Dec = +0 (gal lat ~ 28 degrees)
Field C: RA = 16:30 - 16:45 Dec = +0
This Technical Note describes the data collected for Field A,
during the period January 8, 1997, to May 12, 1997,
(Julian Date 2,450,457 to 2,450,581),
and Field B, during the period December 15, 1996, to April 9, 1997
(Julian Date 2,450,432 to 2,450,548).
In the course of this document, dates will sometimes
be quoted as "Truncated Julian Date", defined herein
as
Truncated Julian Date = TJD = Julian Date - 2,450,000
The duration of the study is therefore about 134 days in Field A,
and about 116 days in Field B.
Data was supplied from 4 TASS sites:
number of good nights
site observer code Field A Field B
Batavia, IL Tom Droege H 14 12
Cincinnati, OH Mike Gutzwiller D 15 10
East Braintree, VT Michael Richmond C 1 1
Miama Valley, OH Glenn Gombert B 4 0
------------------
35 23
At each site, triplets consisting of two I-band and one V-band
cameras scanned the sky near the equator simulataneously, usually separated
by 15 degrees in Right Ascension.
Arne Henden used his suite of programs to collate, match, and apply color transformations to the raw magnitude measurements. I am using his compilations fielda.dif and fieldb.dif as the source of all data presented in this Note. Although each site (sometimes) recorded two I-band and one V-band measurement per night, the software averaged the two I-band measurements together. It lists the time of the V-band exposure as the Julian Date of the (V, average I) pair. This should make very little difference for the vast majority of stars; only variables with very short periods (less than one day) might be compromised by this procedure.
Below are some histograms showing the gross properties of the stellar photometry in each Field.
Properties of Field A.
Properties of Field B.
Note that the number of stars which passed all the requirements of the COLLATE program is about the same in each field, roughly 1500 stars observed at least 3 times, and roughly 650 stars observed at least 10 times. It is a little surprising that more stars are not catalogued in Field B, since it lies closer to the Milky Way. In the classic paper, Mean Distribution of Stars according to Apparent Magnitude and Galactic Latitude, by Frederick H. Seares, P. J. Van Rhijn, Mary C. Joyner, and Myrtle L. Richmond (no known relation), ApJ 62, 320 (1925), the authors derive mean numbers of stars per square degree as a function of galactic latitude. They find roughly twice as many stars at galactic latitude b=25 degrees than at b=60 degrees, for stars with photographic magnitude between 11 and 13. Going back to the raw star lists from the Vermont triplet, I see that the lists for Field B do contain about twice as many sources as those for Field A. There are several reasons why the COLLATE'd lists might discard the "extra" stars in the more crowded Field B -- the "extra" stars might be near the plate limit, have poor astrometry, suffer from crowding, disappear on some nights, etc. -- but I'm not sure which one is correct.
There are three ways to estimate the uncertainty in the measurement of a stellar magnitude. The program which extracts the magnitude from an image can try to calculate the uncertainty, based upon a combination of photon noise and errors in sky subtraction. All programs used to measure TASS frames already do this, producing a quantity we may call the internal uncertainty. However, this does not -- and cannot -- take into account a number of factors, such as errors in the transformation from the instrumental to the standard magnitude scale, errors due to crowding, edge effects, and other systematic effects.
Another method to estimate uncertainty takes many of these factors into account automatically, by comparing magnitude estimates for the same star taken at different times and on different nights. If the star is truly constant, then any variation from night to night is a combination of the internal uncertainty described above, plus errors or differences in the data analysis and reduction from one night to the next (or from one site to the next). Given a set of measurements of the same star on different nights, one can calculate the mean magnitude and the standard deviation of values from the mean. This standard deviation, or external uncertainty, is (almost) always larger than the internal uncertainty.
A third way is to use an ensemble of stars in the neighborhood of a particular star. One can make the assumption that all the stars in the ensemble are truly constant; then, given a number of observations of the ensemble, one can determine how much one must shift the all the magnitudes from one particular night fainter or brighter to make them agree optimally with the average of the magnitudes from all the other other nights. If this sounds a little confusing, try reading the paper CCD Ensemble Photometry on an Inhomogeneous Set of Exposures, by R. K. Honeycutt (PASP 104, 435, 1992). Arne Henden's DIFCAL program uses the comparison stars in the ensemble to define an estimate of the uncertainty of the particular star of interest, which is not included in the calculations itself.
If one is looking at a series of observations of a star over some period of time to check for variability, the external uncertainty is the quantity one naturally computes.
I took the collated and diff'd files produced by Arne Henden (with names like fielda.dif) and ran through them to compute the mean and standard deviation from the mean for all measurements of the same star. The product was a file similar in format to the .dif files, but with some additional information:
You can download two big data files (2+ MBytes each)
if you wish, but they are probably not the best files to grab.A more useful data file is produced by taking just the first entry for each star in the big file; it contains the star's ID number, position, a single measurement in V and I (ignore these), but in addition the mean magnitude in V and I (aha!) and the standard deviation in V and I (double aha!); plus, it has the number of times that the star was measured. These datafiles, which I call fielda.single (189 KBytes) and fieldb.single (194 KBytes), are just what we need to examine in detail the accuracy of TASS measurements.
For example, one can simply plot the standard deviation of measurements for one star against that star's mean magnitude. We expect that the scatter should rise as one looks at fainter and fainter stars ... and, indeed, it does.
Below are a number of GIF figures, showing exactly this plot for Fields A and B. For Field A, there are three plots in V, and three in I: one for all stars detected at least 3 times, one for stars detected at least 5 times, and one for stars detected at least 10 times, in each passband. For Field B, two plots each in V and I, for stars detected at least 3 times and at least 10 times during the study period.
First, let's look at the V-band plots for Field A.
Next, we can look at the I-band plots:
Now, let's switch to Field B, and examine the V-band plots.
Finally, here are the Field B, I-band plots.
Some points which are immediately clear:
This kind of plot is the same that Arne used to create the fieldx.var lists, where he included only those stars more than 2 sigma from the mean curve. The .var lists are highly contaminated by stars with only a few measures, but they should contain most of the easily discovered variables. The other big contamination is from close companions. We remove them in FASTT by looking at the fwhmx/fwhmy ratios and also the pure astrometric errors, but this is more difficult with the TASS systems unless they are properly set up with good focus and drift scan rates.
Each graph shows a characteristic shape, a sort of parabolic curve upwards as one moves to fainter magnitudes. One can define the typical uncertainty in a TASS measurement by the ridge line of this curve; it's not the only way to define an uncertainty, but it's a common one. I divided the stars into bins one magnitude wide, centered on integer values of magnitude (i.e. 7.0 < V < 8.0, etc.) and calculated the median value of all standard deviations within that bin. Here's the result:
mean magnitude
7 8 9 10 11 12 13 14
-------------------------------------------------------------------
Field A
num of stars(V) 2 8 22 56 114 210 301 43
median dev(V) 0.078 0.046 0.047 0.052 0.071 0.117 0.195 0.215
num of stars(I) 9 17 50 98 201 267 109 1
median dev(I) 0.031 0.027 0.033 0.051 0.091 0.155 0.211 ---
Field B
num of stars(V) 2 10 38 83 187 325 126 2
median dev(V) 0.014 0.038 0.040 0.053 0.085 0.141 0.154 0.121
num of stars(I) 11 32 83 160 301 171 11 0
median dev(I) 0.039 0.037 0.039 0.064 0.098 0.146 0.200 ---
The table includes all stars with at least 3 observations in the appropriate passband. I calculated the median values for those stars with more observations, but it was basically the same.
Note that there is little difference between the deviation from the mean in the two Fields. One might expect the scatter to be larger in Field B, since it is more crowded, but the process by which stars are selected by the COLLATE program may remove some such "contaminated" stars.
Once we have both internal (individually for every detection of a star) and external (for all detections of a star combined) estimates of the uncertainty in the magnitude of a star, it's logical to compare them. Recall that, for this comparison, we are using the data from Henden's "fielda.dif" file which are labelled sigV and sigI as the internal error estimates; there are produced from the ensemble of comparison stars. We would expect that the internal estimate should be somewhat smaller than the external estimate, since there really must be variations in sky conditions, calibration, etc., from night to night and camera to camera.
Below are plotted the ratio internal/external for each detection of each star in Field A. We expect that the values should be smaller than 1.0. First we plot the V-band ratios:
And now the I-band ratios:
It's clear that reality meets our expectations for the faint stars -- say, less than V=10 or I=9.5. For the bright stars, the average is about 1.0, with a considerable tail of values above unity. For the very faintest stars, the ratio is often much smaller than 1.0: the internal estimates are too small by a factor of several. This makes sense, since in an ensemble of stars used for comparison, many stars are averaged together, and the overall uncertainty should be much less than the uncertainty in the measurement of a single star. Thus, for faint stars, we expect the ratio internal/external to be very roughly (1/sqrt(N)), where N is the number of stars in the ensemble.
In order to find variable stars in the datafiles fielda.single and fieldb.single, one can try several different methods. Here are the ones I applied to the data:
I wrote a program to plot external scatter in V versus mean V magnitude, as shown in the figures above. The program allows the user to point the cursor at any point in the diagram to select a star of interest; it then plots the light curve of the star in both V and I.
So, I spent an hour or so clicking on the stars which appeared far above the ridge line in the diagrams. One would expect true variable stars to lie in this area, but one must also beware of boring, constant stars which have one or two bad magnitudes; they also appear in above the main group. I looked at the light curves by eye, and judged each candidate to be good, fair or poor in a rather subjective way. I rated a star highly if it showed a pattern to its residuals, or if it varied in the same direction in both V and I simultaneously.
Here is a list of the stars I chose as either good or fair: you can click on a star's ID to see a plot of its light curve.
Star ID RA Dec quality notes
Field A
271 186.7608 -0.6216 fair GSC 4941:395
518 187.7910 -2.0670 fair SAO 132882
699 188.5854 -1.1772 good BP Vir; GSC 4948:401; IRAS 12317-0054
726 188.6651 -0.6326 fair GSC 4948:57
1100 190.2649 -0.6204 good MG found; SAA 138910; K5; IRAS 12385-0020
1127 190.3701 -1.7066 fair GSC 4949:843
1328 191.2854 -0.4616 fair GSC 4949:1092
1333 191.3202 -0.2781 good galaxy NGC 4666?
Field B
203 130.5291 -1.1421 fair
617 131.9681 0.1073 fair
778 132.5180 -0.4331 fair
1134 133.7624 0.1577 fair
1177 133.9859 0.8861 fair eclipsing binary?
1046 133.4522 -0.5503 fair
Now, there are also stars which others have suspected of being variable, which I did not notice in my procedure:
Star ID RA Dec quality notes
148 186.1863 -0.2530 hidden FASTT, HS 535
413 187.3903 -1.0578 MG found it
509 187.7557 -0.3604 hidden FASTT, HS 537
Now, of these stars, the two marked hidden are part of the big clump of stars along the ridge line in the sigma-vs-mag graphs; however, the Field A star with ID 509, which Mike Gutzwiller noticed as a good candidate, is indeed above the ridge line; it has about twice the standard deviation from the mean that one would expect for a star of its V magnitude. I didn't find it because I just didn't search deeply enough into the main group of stars.
I modified my program to plot external scatter in I versus mean I magnitude, as shown in the figures above. The program allows the user to point the cursor at any point in the diagram to select a star of interest; it then plots the light curve of the star in both V and I.
Once again spending about an hour picking the points which lay farthest above the ridge line in the graph, I ended up with the following "good" and "fair" candidates; note that I also picked some of them based on sigma(V) vs. V mag.
Star ID RA Dec quality in V? notes
Field A
245 186.6954 -2.1538 fair no
307 186.9425 -2.3856 fair no
409 187.3645 -1.2003 fair no
413 187.3903 -1.0578 good no MG found it
496 187.7193 -2.4153 fair no
621 188.2617 -2.2910 good no
699 188.5854 -1.1772 good yes BP Vir
728 188.6729 -0.2367 poor no very red: V-I=5
1100 190.2649 -0.6204 good yes MG found; SAA 138910; K5; IRAS 12385-0020
1146 190.4748 -2.0905 fair no
1156 190.4954 -1.4141 fair yes
1476 192.0287 -0.3222 fair no
Field B
99 130.1277 -1.2768 good no very red, see below
126 130.2473 -0.6962 fair no very red, see below
342 131.0110 -2.2414 fair no
1134 133.7624 0.1577 fair yes
1152 133.8488 -0.8818 fair no
1177 133.9859 0.8861 fair yes
There are several reasons that very red stars are often variable; most of them boil down to the reason that red giants with extended envelopes are prey to atmospheric instabilities. Red giant and supergiant stars tend to have very long timescales of variation, so it's likely that over the period of this study (134 days at most), many would show only a trend to fainter or brighter magnitudes. The amplitude of variation can be several magnitudes (for Miras), or below the threshold of detection for TASS images (about 0.1 mag).
I plotted the stars on a graph with I magnitude on the X-axis and color (V-I) on the Y-axis, then picked the reddest stars and plotted their light curves. I looked for candidates which showed a gentle but consistent trend in their brightness. Here are the candidates that appeared reasonable; those marked with a "yes" in the in I? column were also chosen as candidates based on the sigI vs. I plot.
Star ID RA Dec V-I quality in I? notes
Field A
555 187.9408 -1.5389 1.79 fair no
699 188.5854 -1.1772 3.38 good yes BP Vir
859 189.2287 -0.4948 1.87 fair no
1100 190.2649 -0.6204 1.64 good yes MG found; see VR
Field B
99 130.1277 -1.2768 3.96 good yes see VR
126 130.2473 -0.6962 5.23 fair yes see VR
212 130.5658 -2.0923 2.24 fair no
918 133.0211 -2.1467 1.92 fair no
604 131.9330 -2.0559 2.55 fair no
1484 135.4312 -0.5221 2.12 fair no
See the section below, Selected Red Stars, for more information on objects which have "see VR" in the Notes column above.
I suspect that the duration of the experiment was too short to reveal significant variation in some of the reddest stars; time will tell.
Arne Henden adds some notes of caution about searching for variables in the current dataset, which contains at most 20 or so observations of any particular star in each passband. Stars which have periods much shorter than the length of a survey can be hard to find, since one needs many points on their light curves to show a clear pattern of rise and fall. With only a few data points, their light curves can resemble random scatter with only slightly higher amplitude than that of pure noise. Arne says:
My rule of thumb is 30-40 data points are necessary to find short-period stars, especially with 0.05mag quality photometry.
So, the results shown above are probably only the tip of an iceberg of short-period and/or low-amplitude variables in the field. We just need more observations per star ... and it would help to decrease the error in each measurement, too.
There are several very red stars in each field, which fall far to the right of the main body of objects in the (V-I) histograms for Field A and Field B. I did a little extra check on these stars, to see if there is information about them in the astronomical literature. I was able to find quite a bit of extra information on stars TASS A728 and B126, plus IRAS measurements for TASS B99 and B1429.
One very red star which stands out in Field A has ID 728, at position
J2000: 12:34:41.5 -00:14:12 or 188.6729, -0.2367
1950: 12:32:07.8 +00:02:20
The star is much, much brighter in I than in V: V=13.61, I=8.40, thus (V-I)=5.20. For example, here are V-band (on the left) and I-band (on the right) pictures of the field taken by the Vermont triplet on UT March 8, 1997:
The fan-like shape of the star in the I-band image is due to the optics of the I-band camera; the star doesn't actually appear extended in the optical.
Looking up this position in SIMBAD, I found two catalogued sources:
StM 172 from Stephenson, C. B. ApJ 301, 927 (1986)
IRAS 12321+0002 from the IRAS Point Source Catalog
Stephenson, ApJ 301, 927 (1992): Stephenson made an objective-prism survey of the northern sky (Dec > -25) more than 10 degrees from the galactic plane. He looked for cool giant stars, and used them to do galactic dynamics. In his paper, this star appears in a table without a number, but SIMBAD and the literature call it number 172. Stephenson listed an approximate magnitude V > 13.5 (the TASS value is V = 13.6) and classified its spectrum as M7:, indicating some uncertainty.
Sharples et al., MNRAS 272, 139 (1995): These authors use a subset of Stephenson's stars in their study of galactic dynamics. They list infrared magnitudes and some spectroscopic data for StM 172:
J = 5.05
H = 4.01
K = 3.59
L = 3.26
E(B-V) = 0.00
radial velocity = -4 km/sec
TiO line index = 0.59
CaII triplet equivalent width = 0.9 Angstrom
Here, J, H, K, L are magnitudes in 4 different infrared passbands,
and E(B-V) is the estimated reddening
(the amount by which the B-band is extinguished more
then the V-band) along the line
of sight; the value 0.0 means that the authors think there's
little interstellar material between us and the star.
The TiO line index is a measure of the strength of the
titanium oxide absorption bands, and
the CaII triplet equivalent width
is a measure of the strength of the absorption due
to singly-ionized calcium ion at wavelengths
near 8478, 8542 and 8662 Angstroms.
IRAS Point Source Catalog: The star appears in a catalog made by the IRAS satellite. Its flux was measured to be
12 microns: flux = 5.10 Jansky
25 microns: flux = 2.45 Jansky
60 microns: flux = 0.56: Jansky
100 microns: flux < 1.0 Jansky
Put it all together, and it appears that star A728
is a very cool, giant star.
It is unusually far from the galactic plane.
J2000: 08:40:59.4 -00:41:46 or 130.2493 -0.6962
1950: 08:38:26.2 -00:31:03
It has the following synonyms and references (as found in SIMBAD):
12 micron 25 60 100
16.81 7.38 1.30 < 1.0
Star B99 has TASS magnitudes V=11.93, I=7.97, and color (V-I) = 3.96. It is at position
J2000: 08:40:30.7 -01:16:37 or 130.1277 -1.2768
1950: 08:37:58.0 -01:05:55
It appears in the IRAS Point Source Catalog as
IRAS 08379-0105, and has fluxes
12 micron 25 60 100
0.77 < 0.33 < 0.40 < 1.0
Star B1429 has TASS magnitudes V=12.12, I=8.24, and color (V-I) = 3.88. It is at position
J2000: 09:00:48.2 -01:33:38 or 135.2010 -1.5606
1950: 08:58:15.7 -01:21:51
It appears in the IRAS Point Source Catalog as
IRAS 08582-0121, and has fluxes
12 micron 25 60 100
0.95 0.51 < 0.40 < 1.0
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