STATISTICALLY OPTIMAL MODELING OF FLAT ECLIPSES AND EXOPLANET TRANSITIONS. THE “WALL-SUPPORTED POLYNOMIAL” (WSP) ALGORITMS - Andrych, K. D.; Andronov, I. L.; Chinarova, L. L. (Одеські астрономічні публікації, 2017)
The  methods  for  determination  of  the  characteristics of the extrema are discussed with an application to irregularly spaced data, which are characteristic  for photometrical observations of variable stars. We introduce  new  special  functions,  which  were  named  as  the  “Wall-Supported Polynomial” (WSP) of different orders. It is a parabola (WSP), constant line (WSL) or an “asymptotic”  parabola  (WSAP)  with  “walls”  corresponding  to more  inclined descending and ascending branches of the  light curve. As the interval is split generally into 3 parts, the  approximations  may  be  classified  as  a  “nonpolynomial splines”. These  approximations  extend  a  parabolic/linear  fit  by adding  the  “walls”  with  a  shape,  which  asymptotically corresponds to the brightness variations near phases of the  inner contact. The fits are compared to that proposed by Andronov (2010, 2012) and Mikulasek (2015) and modified for the case of data near the bottom of eclipses instead of wider intervals of the light curve. The WSL method is preferred for total eclipses showing a brightness standstill. The WSP and WSAP may be generally recommended in a case  of  transit  eclipses,  especially  by  exoplanets.  Other two  methods, as  well as the symmetrical polynomials of statistically optimal order, may be recommended in a general case of non-total eclipses.   The method was illustrated by application to observations of a  newly discovered  eclipsing binary GSC 3692-00624  =  2MASS  J01560160+5744488,  for  which  the WSL method provides 12 times better accuracy