This note compares the properties of data from the Dayton triplet, reduced in two ways: the "old" way used Mike Gutzwiller's Star program; the "new" way also used Star, but afterwards applies corrections via Flatcomp. Glenn described his re-reduction in an E-mail message; read it for details.
For the impatient, the bottom line is that the new reduction procedure does produce better photometry (as expected), and slightly better astrometry, too (not expected). Most important, to my mind, is that the new procedure removes a systematic photometric error in Declination seen in the earlier results. Since the new dataset contains fewer stars than the earlier one, an exact, star-by-star comparison isn't possible, and it is possible that the observed improvements are due to the particular mix of stars chosen by Glenn for re-reduction.
Glenn sent me a copy of a "master" photometry file on Aug 18, 1998. All data in it was gathered by the Dayton TASS triplet. There are 14 nights of data in the file gathered some time in 1997 (I don't know which nights, or the interval from first to last). I believe that the settings on the Flatcomp program were
The file contains entries for a grand total of 54,767 stars, distributed on the sky as shown below.
All stars were observed on at least 3 nights, with a maximum of 10 nights in the V-band and 15 nights in the I-band.
We can tabulate the internal scatter as a function of apparent magnitude:
Stdev from mean mag, data from Dayton triplet
<= 9 9-10 10-11 11-12 12-13 13-14 14-15
-----------------------------------------------------------------------
V-band
new N 635 1498 3473 7907 14907 21154 5194
new sigma(V) 0.023 0.020 0.024 0.035 0.066 0.139 0.210
old sigma(V) 0.053 0.053 0.059 0.078 0.112 0.159 0.181
I-band
new N 2108 3456 7525 13608 18817 9245 8
new sigma(I) 0.027 0.031 0.040 0.068 0.122 0.187 0.174
old sigma(I) 0.041 0.055 0.081 0.120 0.168 0.192 0.242
The values in rows labelled "old sigma(V)" and "old sigma(I)" come from an earlier compilation of Dayton data, called photom3.out (you can read more about Dayton compilations). Remember that the "old" dataset contains about twice as many stars as the "new" one; the rows labelled "new N" above apply only to the new data.
It seems clear that the new compilation has an internal scatter which is smaller than the old one, by almost a factor of two in some magnitude ranges. In fact, the photometric scatter of the new compilation is not far above the theoretical scatter due to photon noise (see a section of Technical Note 32 for details of the theoretical calculations).
corrected Tycho V = (Tycho V) - 0.090 (Tycho B - Tycho V)
We may then form a difference
delta V = (corrected Tycho V) - (TASS V)
As in
an earlier analysis,
we ignore outliers by discarding any stars with
abs(delta V) > 0.80 mag.
Breaking the stars into groups based on their apparent brightness, we find
Difference (Tycho - TASS) magnitudes
V-band I-band
N mean stdev N mean stdev
-----------------------------------------------------------------------------
7 < V < 9
new 987 0.04 0.07 341 0.01 0.08
old 2072 0.02 0.11 729 0.03 0.11
9 < V < 11
new 4320 0.04 0.11 162 0.01 0.15
old 9235 0.02 0.15 370 0.05 0.17
11 < V < 15
new 835 -0.08 0.20
old 1404 0.02 0.23
all
new 6105 0.03 0.13 500 0.01 0.11
old 12711 0.02 0.15 1099 0.03 0.14
In the table above, "new" rows contain data from the new compilation of Dayton data processed with Flatcomp, while "old" rows contain data taken from an earlier analysis of data.
We conclude
In the earlier analysis, I found that the Dayton data had a small systematic error in V-band magnitude as a function of Declination. As I understand it, the Flatcomp program is designed specifically to remove such systematic effects, by splitting the 3-degree-wide TASS image into a number of narrow strips in Declination, and adding zero-point corrections to each strip.
So, we expect that there should be no systematic trends in (Tycho - TASS) photometry as a function of position on the sky. And -- that is exactly what we find (thank goodness):
There are also no systematic effects as a function of Right Ascension.
First, let's match up stars in the new Dayton dataset against the Tycho catalog, and look at the difference between the two sets of positions. The Tycho catalog is of much higher accuracy and precision than TASS, so we can take its values as "the truth." If we require a coincidence of 5 arcsec or less between the TASS and Tycho positions, we find 6123 matches between the two catalogs. The differences show no obvious trend or offset:
The differences are distributed as follows:
Difference in position (Tycho - TASS), in arcsec
0 - 1 1 - 2 2 - 3 3 - 4 4 - 5
----------------------------------------------------------------------------
number 4043 1525 339 143 73
percentage 66% 25% 6% 2% 1%
The median difference is about 0.75 arcsec.
This looks very good -- but remember that we're only considering a special sample of all TASS detections:
The output of the difcal program includes an internal estimate of uncertainty in each position coordinate, both RA and Dec. How good are those estimates? Well, we can compare the actual error in position (Tycho - TASS) to the estimated error in position. For each star, let's calculate a ratio
abs(actual error in RA)
e(RA) = ---------------------------
estimated uncertainty in RA
and similarly for e(Dec).
We can plot a histogram of these ratios:
In the majority of cases, the actual error is smaller than the estimated one. Now, if the estimated error had a perfect "1-sigma" distribution, then 2/3 of the actual errors would be smaller than the estimated one. And, mirabile dictu, when we add up all the stars, we find that
Having used the Tycho catalog to find the accuracy of the new Dayton dataset, we can compare its performance against that of the old dataset. Here's a table with the overall errors in position as a function of magnitude, for both datasets:
Error in position (arcsec) as a function of V-band magnitude
num stars mean error stdev of mean
------------------------------------------------------------------------
7 < V < 9 new 992 0.87 0.68
old 2075 0.97 0.85
9 < V < 11 new 4325 0.94 0.78
old 9301 1.45 1.67
11 < V < 15 new 843 1.18 0.91
old 1425 1.97 2.10
The new dataset has significantly more accurate positions than the old one. This confuses me -- I can't figure out how the Flatcomp procedure could improve positions. Perhaps the difference is due simply to the different set of stars included in the two datasets?
Astronomers rarely use apparent magnitudes in diagrams like this, because they depend not only on the intrinsic properties of a star, but also on the star's distance from us. Nevertheless, one can pick out two features in this plot: a pair of vertical fingers reaching up out of the blob of stars down near the bottom. It turns out that the fingers contain stars from two different populations in our galaxy: stars in the left-hand finger, which are relatively blue, live in the disk of the Milky Way. They are typically young (only a few billion years old). Stars in the right-hand finger, which are relatively red, are part of the Milky Way's halo. They are older, born perhaps 10 billion years ago, when the galaxy itself was still forming.
In an ordinary color-magnitude diagram, the brightness of each star is precisely proportional to its intrinsic luminosity. We can make such a diagram two ways:
(abs mag M) = (apparent mag m) - [5*log(D) - 5]
Obviously, the TASS cameras can detect only stars in our own galaxy, scattered throughout our solar neighborhood. We are forced to use method 2, which requires knowing the distances to thousands of stars. Fortunately, the Hipparcos satellite measured distances for many stars, all over the sky.
I matched stars from the new Dayton compilation to the Hipparcos catalog, accepting only those within 5 arcseconds. There were 6123 matches. I then discarded any star with
parallax <= 5*(uncertainty in parallax)
according to the Hipparcos values.
This pared the list down to a mere 183 matches!
For each of these stars, I used the Hipparcos parallax to
calculate a distance, then used that distance to convert the
observed TASS V-band magnitude into an absolute V-band magnitude.
Finally, I could plot a proper V,(V-I) color-magnitude diagram:
On this diagram, the Main Sequence runs from upper left to lower right. Stars on the Main Sequence are burning hydrogren into helium in their cores. There are two other features weakly visible: a giant branch in the upper right (stars which are burning hydrogen in shells around an inert core) and (possibly) a horizontal branch at upper left (stars which are burning helium in their core).
Compare this V,(V-I) diagram to similar ones collected from several different stellar populations:
