This note was written as I prepared material for a poster presented at the meeting of the American Astronomical Society in San Diego, in June 1998. You can find a copy of materials on the poster elsewhere; look there for more light curves of known and new variables.
Table of contents:
I have started to work on the night-to-night corrections for small subsets of the data. This can provide improved differential photometry.
Since a picture is worth a thousand words, let me just present picture after picture, with a few words for each.
Tycho V mag Nstar std error of mean stdev of mean
---------------------------------------------------------------------------
7 < V < 9 2075 0.97 arcsec 0.85 arcsec
9 < V < 11 9301 1.45 1.67
11 < V < 15 1425 1.97 2.10
There appear to be no systematic offsets in either direction, also good.
In fact, there were only 6 good matches between the Dayton and Landolt lists. Bleah. The differences in V and I were small:
star Landolt V deltaV Landolt I deltaI
----------------------------------------------------------
BD-2_524 10.31 0.03 -0.06
HD 84971 8.64 0.03 -0.04
G14_55 11.34 -0.64 0.38 ??
HD210894 9.17 0.01 0.05
F108 12.96 0.04 -0.23 blue star
HD12021 8.87 0.06 0.01
HD121968 10.26 -0.03 0.05
Arne Henden has supplied UBVRI photometry for stars near the celestial equator. The most recent version of this catalog contains 730 stars. Most lie outside the Dayton triplet's Declination range, but there are about 20 or so matches. Most of these are fainter than 11'th magnitude, so the TASS data is of low precision. Still, the agreement is not good. Below, I list the mean difference delta between the magnitudes of stars in Glenn's photom3.out catalog and Arne's UBVRI catalog.
magnitude range
10 - 12 12-15
N delta sigma N delta sigma
----------------------------------------------------------------
V-band 7 -0.15 0.33 11 0.49 0.68
I-band 15 0.57 1.03 3 0.25 0.46
On the other hand, there were a LOT of matches between the Hipparcos/Tycho data and the Dayton dataset. As I understand it, these were the stars used to calibrate the Dayton master photometry file. We should expect the mean offset to be very close to zero. And, indeed, it is so.
It is necessary to convert the Tycho photometry to something closer to the Johnson-Cousins scale via the equation (supplied by Arne Henden)
V = TychoV - 0.090*(TychoB - TychoV)
There are only a relatively few Tycho stars with meaningful
(V-I) colors, all determined from the ground (the satellite didn't
have any I-band detector). I used only the sensible ones, and
ignored all other values.
After making this conversion, I get the following mean differences between a single star's Tycho "V" and TASS V values:
V-band I-band
N mean stdev N mean stdev
------------------------------------------------------------------
all stars 12711 0.02 0.15 1099 0.03 0.14
7 < V < 9 2072 0.023 0.11 729 0.025 0.11
9 < V < 11 9235 0.024 0.15 370 0.048 0.17
11 < V < 15 1404 0.018 0.23 2 0.29 0.01
It appears that the scatter does decrease for brighter stars, but not as much as we might hope. There are several reasons for the large scatter:
Some pictures to illustrate the photometry:
No trend vs. Dec appears in the I-band photometry, but there is a clear systematic error in the V-band photometry as a function of Declination:
The sense of the error is that stars near the northern edge of
Glenn's images appear to be brighter than they ought to be,
relative to stars at the southern edge.
This feels like a flatfielding error.
The blue line in the figure above is a fit to the median of the
distribution every half-degree:
Corrected TychoV - TASS V = 0.154 + (0.039*Dec) mag
where "Dec" is measured in degrees. The formal uncertainty in
the slope is +/- 0.006 mag/degree.
If I subtract this trend from the Dayton V-band data, I can produce a nice, flat graph of residuals vs. Declination:
Now the mean offset is very close to zero, but the scatter is not reduced; it's about the same as it was in the original version:
V-band
N mean stdev
---------------------------------------
all stars 12711 -0.014 0.15
7 < V < 9 2177 0.005 0.11
9 < V < 11 8934 0.001 0.13
11 < V < 15 1660 -0.124 0.22
Conclusion: the scatter is (I hope) caused by night-to-night variations. If the variations are simply a zero-point offset, there's hope of finding and correcting for them on each night. That might possibly reduce the scatter somewhat.
Let me preface this section by stating that I should have looked carefully at the work of Glenn Gombert and Arne Henden. Glenn's photom3.dat compilation, produced from the Dayton triplet and reduced by Arne Henden's collate and difcal programs, already has very small night-to-night scatter: for bright stars (7 < V < 10), the scatter is only 0.02-0.03 magnitudes for most stars; a minority of stars have significantly larger scatter:
I had hoped that it might be possible to reduce the night-to-night differential photometry of a single star from the value in Glenn's photom3.dat datafile. One might
In brief, I divided Glenn's data into sections 10 degrees wide, with no overlap. I then analyzed each section independently, looking at data in that area from all nights. I choose to use only bright stars, (7 < V < 11) and (6 < I < 9), to determine the night-to-night variations. I weighted each star by the inverse of its uncertainty in the difcal output. Typically, there were 40-150 stars in each section.
The results showed clearly that some nights were better than others. The procedure yields an estimate of the uncertainty in the adjustment for each night; a good night will have a small uncertainty (because all its stars will match up neatly with their overall mean values), while a bad night will have large uncertainty. Below is a plot of the uncertainties for each night: note that since there were several sections covered during each night, there are several points in the plot below for each night.
Clearly, a few nights are much worse than the others: 50723, 50725, 50910 are especially bad. It turns out that most of 50723 is decent -- it's only two of its sections (the ones covering 0 < RA < 10 and 0 < RA < 20 degrees) that are really poor. I discarded bad sections from further analysis.
My first attempt at this differential differential photometry (as Arne put it, accurately) is a little shaky. I lost the zero-point of the V-band magnitude scale, and re-set it by comparing bright stars to Tycho stars in each section; in essence, I re-did the job of the original image-processing software. Stupid. I must re-do it more properly. But the results are rewarding: for the bright stars used in the ensemble solution, the night-to-night scatter is indeed smaller than it was at the start:
The ridge line of the distribution here is about 0.02-0.03 magnitudes, all the way from V = 7 to V = 10. That's about the same as before -- no improvement. But do note that there are fewer stars with much larger scatter. I think this is due almost entirely to my elimination of the "bad" nights.
Here's the scatter vs. magnitude plot for the bright stars in I-band, processed with my ensemble photometry code. The ridge line again runs about 0.02-0.03 mag.
Whether we use the photom3.dat data, or the version I calculated, we should be able to make very nice plots of the differential magnitude for selected stars -- such as variables. We can also use this data to find variables -- you can see in the plot above that there are a number of stars which are far above the typical scatter. My analysis gets rid of many of the stars with spuriously (I think) large scatter, so it will be easier to start with it.
Keep in mind that there probably is a small systematic error in the zero-point of my magnitudes; I wouldn't be surprised if it's as large as 0.10 mag. But, as long as we use this modified dataset for differential purposes only, that's okay.
Should TASS expect to find any new variable stars in the area covered by the Dayton triplet? The answer is "yes". Look at the distributio on the sky of the previously-known variable stars:
It's clear that most of these variables were found on just a few photographic plates. And it's also clear that there must be many, many more variables in this area of the sky.
I used the Welch-Stetson algorithm (see AJ 105, 1813 [1993], or the Winter 1995 issue of CCD Astronomy) to search for variables in the output of the ensemble photometry. In brief, the method looks for stars with deviations from the mean magnitude which are correlated in two passbands (V and I). In order to make it work properly, I had to come up with reasonable values for the uncertainty in each individual magnitude measurement. I looked at the difcal output to come up with the following uncertainties in a single differential magnitude:
mag 6-7 7-8 8-9 9-10 10-11 11-12 12-13 13-14 >14 --------------------------------------------------------------------- V-band 0.02 0.02 0.02 0.02 0.03 0.04 0.05 0.09 0.14 I-band 0.02 0.02 0.02 0.02 0.03 0.05 0.09 0.15 --
The output values of the variability index were typically less than 5. I looked only at stars with index values above 10 or 20. There were a lot of "fake variables" -- stars with large index values because of a single faint magnitude measurement, almost always in the I-band. Most of these bad I-band measurements came from one or two nights that slipped through my attempts to remove them from the solution.
But about half the stars with large values of the index turned out to be real variables. Unfortunately, the Dayton dataset covers a period a bit too short (only about 100 days) to get periods for most of the obvious variable stars, which have long periods.
Let me show off just two nice plots -- there are lots more, but I don't have time or space to include them all here. First, a long period variable:
Second, what looks like a short-period variable of some kind (or, possibly, just a star in a bad spot of the sky, maybe next to another star). We really need more data to confirm objects like this.
In fact, we really need more data for all the candidates. The best cases have only 20 epochs of observation. To get a good period, one typically needs 40 or so (so I am told).
Below is a list of the variable-star candidates I judged to be reasonably good, based on visual inspection of the light curves. Some may be listed in the Hipparcos variabilty catalogue.
# new variable star candidates from the Dayton TASS dataset # # coordinates are equinox J2000. Listed magnitudes are those of # the first detection of the star (not the mean value). # # RA Dec V I comments 0.4112 -3.7564 12.71 9.67 LPV, period ~120 days 0.5812 -1.5154 14.52 13.64 2.3474 -1.5749 14.29 13.88 2.9506 -1.4379 11.23 10.28 7.0912 -2.3230 14.59 14.08 11.2894 -2.2661 14.35 14.18 14.6167 -1.6636 7.71 6.73 14.8471 -4.2818 12.64 11.78 short period 15.4730 -2.5412 13.88 13.50 40.0094 -2.9301 10.29 9.80 40.6497 -3.0734 12.79 9.15 42.2359 -4.0906 10.14 9.32 44.0787 -2.3482 9.61 8.99 45.5023 -2.9403 8.95 8.42 45.5464 -3.9596 10.11 9.37 292.7657 -2.6774 11.27 7.58 294.8458 -4.4109 11.06 7.54 295.7640 -4.1515 13.15 9.01 295.8184 -3.3978 13.71 10.06 LPV, amp > 1 mag in V 299.6186 -2.4580 12.91 9.27 LPV, amp > 1 mag in V 299.9719 -3.9990 13.32 7.22 305.3077 -4.2125 10.04 6.86 305.5477 -2.3577 14.27 13.86 305.7769 -3.6896 11.84 8.28 308.7154 -2.7153 12.31 8.12 period ~80? days 310.7576 -1.7471 9.60 7.13 312.0801 -2.2664 12.75 9.32 313.8522 -2.3609 11.79 9.38 314.7909 -4.1855 8.65 7.89 315.1558 -1.8752 13.93 12.91 315.3574 -3.8867 11.43 8.32 315.7433 -1.6308 10.24 7.79 315.8776 -3.6964 10.81 9.48 315.9872 -2.1676 10.14 9.43 LPV, small amplitude? 317.2910 -2.5739 10.87 8.68 317.4305 -2.3398 11.33 10.35 317.9650 -1.7527 10.78 8.49 322.3323 -2.2350 12.44 9.52 323.5841 -2.4658 10.98 8.58 326.9826 -2.6153 11.07 8.21 327.7030 -3.0308 13.80 12.81 328.1159 -1.9146 14.47 13.57 328.4519 -3.1744 9.76 8.23 328.8980 -3.0120 10.43 9.62 329.3700 -4.1722 10.68 6.71 LPV 330.3240 -3.5130 14.56 13.24 334.1850 -2.5185 11.03 9.44 334.2107 -3.7786 12.75 9.62 338.8844 -2.9418 7.99 6.88 339.5198 -2.0895 10.66 9.68 340.5238 -3.4441 11.27 10.74 relatively sharp peak? 341.3167 -2.2268 12.83 12.00 348.3155 -2.7363 11.34 7.63 348.8592 -2.8784 13.86 12.88 350.6029 -2.2283 11.51 10.25 small amplitude? 357.6848 -3.1220 14.18 14.18 357.8123 -2.7639 12.94 10.62
No, we didn't. I understand the reason I didn't notice many of the known variables, but there are a few which I feel I _ought_ to have noticed.
First, compare the distribution on the sky of the previously-known variables (blue), the candidates I chose from the Dayton data (red), and those in both sets (black):
It turns out that Glenn's data has a few gaps in RA: one of them
falls around RA = 80 degrees, where one big clump of known variables
lies. Rats.
Now, some numbers:
At first glance, this doesn't look good: why did I fail to pick out so many of the variable stars which the TASS cameras actually did detect? There are several reasons, each of which plays a part:
period (days) < 10 10100 100-150 150-200 > 200
-----------------------------------------------------------------
noticed 2 0 2 2 2
didn't notice 20 4 2 4 4
amplitude (mag) < 0.5 0.5-1.5 1.5-2.5 2.5-3.5 > 3.5
-----------------------------------------------------------------
noticed 2 8 1 1 4
didn't notice 50 24 9 3 7
And then there were a few stars that just fell through the cracks. For example, W Aql, a long-term, large-amplitude variable star, shows obvious monotonic variation in V and I in the TASS data. Why didn't I see it? Because there was one discrepant I-band measurement (from a bad night) which threw the Welch-Stetson statistic way off --- to a large negative value. Since I only examined stars with large positive indices, I didn't look at the TASS data for W Aql -- so I didn't notice it. I did look at the TASS light curves for VW Aql, another long-term variable, but it had only 3 data points in V and 3 in I; so I said, "Forget it -- it might just be coincidence that the light curves vary together."
Overall, I am not unhappy with the results of my search for variability. I didn't find all the known variables, but I think a combination of factors explains why.
In addition, there are some bona fide variable stars which I noticed, and which were not previously known. With additional observations, we will be able to confirm some of the other suspects, and discard some which turn out to be constant.