”Asymptotic parabola” fits for smoothing generally asymmetric light curves
Дата
2015
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Одеський національний університет імені І. І. Мечникова
Анотація
A computer program is introduced,
which allows to determine statistically optimal approximation
using the "Asymptotic Parabola" fit, or, in other
words, the spline consisting of polynomials of order 1,2,1,
or two lines ("asymptotes") connected with a parabola.
The function itself and its derivative is continuous. There
are 5 parameters: two points, where a line switches to a
parabola and vice versa, the slopes of the line and the curvature
of the parabola. Extreme cases are either the parabola
without lines (i.e.the parabola of width of the whole
interval), or lines without a parabola (zero width of the
parabola), or "line+parabola" without a second line. Such
an approximation is especially effective for pulsating variables,
for which the slopes of the ascending and descending
branches are generally different, so the maxima and
minima have asymmetric shapes. The method was initially
introduced by Marsakova and Andronov
(1996OAP.....9...127M) and realized as a computer program
written in QBasic under DOS. It was used for dozens
of variable stars, particularly, for the catalogs of the
individual characteristics of pulsations of the Mira
(1998OAP....11...79M) and semi-regular (200OAP....13..116C)
pulsating variables. For the eclipsing variables with nearly
symmetric shapes of the minima, we use a "symmetric"
version of the "Asymptotic parabola". Here we introduce a
Windows-based program, which does not have DOS limitation
for the memory (number of observations) and
screen resolution. The program has an user-friendly interface
and is illustrated by an application to the test signal
and to the pulsating variable AC Her.
Опис
Ключові слова
Stars: variable – stars, binary – stars, cataclysmic – stars: pulsating
Бібліографічний опис
Odessa Astronomical publications = Одесские астрономические публикации = Одеські астрономічні публікації