[vsnet-chat 76] Re: Times of minima

[Fraser Farrell <fraserf@dove.net.au>]

G'day Rudolf (and other readers),

On 1997-02-13 rudolfn@physics.muni.cz said to all:
   >Today I thought a bit about determining times of eclipsing binaries
   >minimum. I found some program on VSNET HP but there were no
   >documentation so I didn't use it. There are certainly many ways how

You are referring to "AVE" ?  I also had a look for documentation at
astro.gea.cesca.es without success.  Maybe one of our Spanish-speaking
readers could post a "how to use AVE" document in English language?

   >to determine time of minimum but what shall I do if minimum is not
   >symetric? And of course is there some alghoritm to determine time

You could try Pogson's Method.  Quick explanation - first draw the
eclipse lightcurve, then draw horizontal lines connecting the points of
equal magnitude on each side of the eclipse. Then find the mid points of
each of these horizontal lines.  Then draw a "line of best fit" through
these midpoints.  Where _this_ line intersects the lightcurve is the
time of minimum.

   >of RR Lyr, delta Sct or delta Cep time of maxima? I know that this
   >question is not very suitable for many of readers but there are not
   >just CVs :-) Of course this could be useful for some eclisping CVs

Most of my observing is of periodic variables - but don't tell anyone I
said that... :)

Your question is part of a more general question: "where is the maximum
(or minimum) of this lightcurve?".  There are lots of ways to determine
this mathematically, but all methods (that I know of) need to know the
mathematical equation which best fits the lightcurve.

One way to get that equation is to do a Discrete Fourier Transform of
the lightcurve; then attempt to combine the Transform's "periods" in a
way that reproduces the original lightcurve.  Unfortunately the
Transforms of typical DCEP, EA, UG stars contain many "periods" - some
false - which can be combined in endless ways.

For a specific maximum (or minimum), you could try fitting a Cubic
Spline or Bezier Curve to the portion of lightcurve you are interested
in.  Then find the max/min of the Spline or Bezier equation.

These mathematical problems are discussed in books of analytical
geometry or algebra. I will not attempt to explain further.  My math
talent is limited because I often fell asleep during math lectures,
after too much observing at night!

However, I am working to include  "ability to find maxima/minima" into
VSSPlot 2.00; because I would like the program to show O-C diagrams,
ephemerides, and other interesting things.  Progress on the new VSSPlot
has been a bit slow due to the large number of school and public
astronomy sessions I have been doing.  I have also been rather busy
developing our new Web site.

Hopefully VSSPlot 2.00 will be finished in the next few weeks, including
lots of documentation. Please be patient and your problem should be
solved soon.


cheers,

Fraser Farrell
Variable Stars Group
Astronomical Society of South Australia

WWW: http://vsnet.gist.net.au/assa/   email: fraserf@dove.net.au
traditional:  GPO Box 199, Adelaide, SA 5001, Australia

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