efficiency of finding variables in the Dayton data

[Stupendous Man <richmond@a188-l009.rit.edu>]

  I have added more material to TN 41, most of it in a new section
at the end.  I'll append the new material to this e-mail message,
but you'll have to read the TN itself to see the new pictures.

  Executive summary: I only noticed about 15 percent of the
    previously-known variable stars which do appear in the
    Dayton dataset.  But there are good reasons for me to have
    missed most of them.

                                          Michael

-------------------- new portion of TN 41 follows ------------------------


<P>
<h4>
<a name="variables">Variable stars in the Dayton dataset</a>
</h4>
<P>
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:
<p>
<a href="./tn0041.images/knownvar.gif">
<img src="./tn0041.images/knownvar.gif" height=433 width=602>
</a>
<P>
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.


<P>
I used the Welch-Stetson algorithm 
(see AJ 105, 1813 [1993], or the Winter 1995 issue of 
<i>CCD Astronomy</i>) 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 <b>difcal</b> output to come up with the following
uncertainties in a single differential magnitude:
<pre>
   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    --
</pre>

<P>
The output values of the <b>variability index</b> were typically
less than 5.  I looked only at stars with <b>index</b> values
above 10 or 20. 
There were a lot of "fake variables" -- stars with large 
<b>index</b> 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.

<P>
But about half the stars with large values of the <b>index</b>
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.

<P>
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:
<p>
<a href="./tn0041.images/cand.32_68631.gif">
<img src="./tn0041.images/cand.32_68631.gif" height=615 width=757>
</a>

<P>
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.
<p>
<a href="./tn0041.images/cand.2_10082.gif">
<img src="./tn0041.images/cand.2_10082.gif" height=613 width=753>
</a>

<P>
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).

<P>
<h4>
<a name="efficiency">Did we find all the variables?</a>
</h4>
<P>
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.

<P>
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):
<p>
<a href="./tn0041.images/knownvar_cand.gif">
<img src="./tn0041.images/knownvar_cand.gif" height=436 width=605>
</a>
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.

<P>
Now, some numbers:
<UL>
<LI> previously-known variables in the area which match to stars
      detected in the Dayton data: 135
 <UL>
 <LI> which I <b>did</b> notice in my quick scan for variables: 16
 <LI> which I <b>did not</b> notice in my scan for variables:  119
 </UL>

<LI> previously-unknown variables in the area which I noticed as
      good candidates: 86
</UL>

<P>
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:
<UL>
<LI> few observations: 55% of the 119 I missed had only 3 observations,
       and 76% had <= 5 observations.  With few epochs, variability
       doesn't stand out 
<LI> short period: the easiest stars to pick out as variables are
       those with long periods, since their light curve show
       monotonic inclines or declines.  Of the 119 stars I missed,
       many had short periods.  Here's the distribution of periods
       for stars I did notice, and those I didn't:
<pre>
            period (days)      < 10     10­100    100-150   150-200  > 200
          -----------------------------------------------------------------
            noticed              2         0         2         2       2
            didn't notice       20         4         2         4       4
</pre>
<LI> small amplitude: with only a few measurements, only large amplitude
       variations stand out.  For stars with listed "min" and "max"
       magnitudes, here are the distributions:
<pre>
            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
</pre>
<LI> faintness: some of the known variables are fainter than V = 14
       at peak.  Such stars will have very low signal-to-noise ratio
       in the TASS data.
</UL>

<P>
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 <i>negative</i> value.
Since I only examined stars with large <i>positive</i> 
indices, I didn't look at the TASS data for W Aql -- so I didn't notice it.
I <i>did</i> 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."

<P>
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.

<P>
In addition, there are some <b>undisputedly bona fide</b> 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.



</body>
</html>