[vsnet-campaign-be 110] Of comp stars, extinction, and colors...

[Thom Gandet <tgandet@mindspring.com>]

...but not of cabbages or kings!

   I've been asked what stars I would choose as comparison stars for
Theta CrB, and also about possible zero-point errors when comparison
stars of widely different colors are used.  These issues are closely
bound to achieving more precise visual estimates.

   Iot Ser and Eps Her are the two primary comparison stars I plan to
use, and Eta CrB and Chi Boo will be the check stars.  Here are my 
reasons for choosing those stars.  The logic of my reasons have
applicability to choosing comparison stars in general, especially
for blue variables.

   Only Eps Her and Bet CrB are brighter than Theta CrB at maximum.
Of course, at least one comp star brighter and one comp star fainter
than the variable must be used always.  But because of the large
zenith distance between Eps Her and Theta CrB, the magnitudes must
be corrected for differential extinction (see below).  As for Bet
CrB, I don't trust its future behavior despite its recent
quiescence, and my own practice is to eliminate known variables
where the known range in V is >~ 0.03 mags; an Alpha CVn 
variable is more or less predictable, but sorting that out seems to
me additional work that is made unnecessary choosing more constant
comparison stars whenever possible.

   Of the remaining stars, Iot Ser has the advantage over the rest:
it is closest to Theta CrB in ZD and in color.  However, to keep the
extinction correction <0.05 mag., zenith distances must be kept
<~40for Iot Ser.

   Because I always aim to have two comparison stars and two check
stars, I chose Eta CrB to compare with Chi CrB and Iot Ser - Eta
CrB is bracketed in magnitude by Chi Boo and Iot Ser.  I chose
Eta CrB for its (relatively) close color; this compromise in
the color difference requirement is acceptable here only for
check stars and only if the color difference is <~0.5 mag.

   Applying extinction corrections, for visual observers, doesn't
have to be time consuming or complex.  Extinction corrections are
applied to all observations made here.  For ZD differences under
~1 extinction corrections should always applied for ZDs > 60
For example, at ZD=~75 the two stars must be <~2apart in ZD
to result in differential extinction <=0.05 mag.

   As an example of the large combined error that results from
large color differences and differential extinction, I assumed
that Theta CrB is at V=4.23 (v=4.20).  The following cases use Eps
Crb and Eps Her as comparison stars in and assume the step values
are what an "average" observer can reasonably be expected to make:

     1) If V magnitudes uncorrected for extinction are used and the
observations are made at the minimum ZD of Theta Crb (~11at
Tucson), the V magnitude of Theta Crb will be estimated as 
approximately 0.07 magnitudes too bright; this is due entirely to
the color difference between Eps CrB and Theta CrB.  If extinction
is taken into account Theta CrB will be estimated as only 0.03 mag.
too bright.

    2) If uncorrected v magnitudes are used (again, at ZD of ~11,
then Theta CrB will be estimated as approximately 0.03 mags. too
bright (in the v system); converting the v magnitude* to the V
system, the V magnitude is correct (in the V system).

    3) Still using uncorrected v magnitudes but a ZD of 45 then
Theta CrB will be estimated as 0.6 magnitudes too faint (in the v
system); converting the v magnitude to the V system, the V magnitude
will be 0.63 magnitudes too faint.  The contribution to the error
is almost entirely due to not correcting for extinction.

   [*  The v magnitudes have been calculated using the formula:
v = V+0.21*(B-V), which comes from an AAVSO study of the response
of the "average" observer; other studies (thanks John for the info
on that from the UK!) have determined color coefficients as low as
0.15.  These values are approximate and empirical, and the AAVSO
study showed that the color coefficient was significantly different
for different observers.  In fact, on theoretical grounds alone, v
(and V, speaking somewhat loosely) are dependent on (U-B) color as
well, so that the formula would look something like:
                v = V + a*(B-v) + b*(U-B).]

   In fact, because of the strong color dependency, the AAVSO uses
only comparison stars with (B-V)<~1.0 for blue variables (if my
memory is right) whenever possible.  (For the sake of completeness,
I believe, but am not certain, that a later AAVSO study showed
that the color coefficient was closer to 0.20.)

   The above calculations are based on an extinction coefficient,
k, of about 0.25, which is ok for a middling average site.  They
assume the extinction coefficient is constant throughout the year
and has no wavelength dependence.  In fact, k changes seasonally
and, at low levels, throughout the night; it is also wavelength
dependent.  The variation in k may prove to be another source of
error in visual observations that could be beaten down.

   I have a paper in preparation for the Journal of the AAVSO on
making more precise visual observations, but the main points of 
that paper are presented here.

Cordially,
Thom Gandet

-- 
************************************************************************
                      Lizard Hollow Observatory
                      Thomas L. Gandet, Director
                            PO Box 77021                   
                      Tucson, AZ 85703-7021  USA
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