”ASYMPTOTIC PARABOLA” FITS FOR SMOOTHING GENERALLY ASYMMETRIC LIGHT CURVES

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.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.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

Second-generation protoplanetary discs around evolved binaries: a high-resolution polarimetric view with SPHERE/IRDIS

Binary post-asymptotic giant branch (post-AGB) stars are products of a poorly understood binary interaction process that occurs during the AGB phase. These systems comprise a post-AGB primary star, a main-sequence secondary companion and a stable circumbinary disc. Studying the structure and properties of these circumbinary discs is crucial for gaining insight into the binary interaction process that governs post-AGB binaries as well as comprehending the disc's creation, evolution, and its interaction with the post-AGB binary system. We aim to use near-infrared polarimetric imaging to investigate the morphology and potential substructures of circumbinary discs around eight representative post-AGB binary stars. To achieve this, we performed polarimetric differential imaging in H and Y bands using the high-angular resolution capabilities of the European Southern Observatory-Very Large Telescope/SPHERE-Infra-Red Dual-beam Imaging and Spectroscopy instrument. We resolved the extended circumbinary disc structure for a diverse sample of eight post-AGB binary systems. Our analysis provided the first estimates of the disc scale height for two of the systems: IW Car and IRAS 15469-5311. We also investigated the morphological differences between the full discs (with the inner rim at the dust sublimation radius) and transition discs (which are expected to have larger inner cavities), as well as similarities to protoplanetary discs around young stellar objects. We found that the transition discs displayed a more intricate and asymmetric configuration. Surprisingly, no correlation was found between the overresolved flux in near-infrared interferometric data and the polarimetric observations, suggesting that scattering of light on the disc surface may not be the primary cause of the observed overresolved flux component. © 2023 The Author(s) Published by Oxford University Press on behalf of Royal Astronomical Society.Immediate accessThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

Transition disc nature of post-AGB binary systems confirmed by mid-infrared interferometry

Context. Many properties of circumbinary discs around evolved post-asymptotic giant branch (post-AGB) binary systems are similar to those of protoplanetary discs around young stars. The deficits of near-infrared (near-IR) flux in the spectral energy distributions (SEDs) of these systems hints towards large dust-free cavities that are reminiscent of transition discs as are commonly observed around young stars. Aims. We aim to assess the size of the inner rim of six post-AGB binary systems with lack in the near-IR like this. We used resolved mid-infrared (mid-IR) high-angular resolution observations of VLTI/MATISSE and VLTI/MIDI. The inner rim of only one such system was previously resolved. We compared these inner rim sizes to five systems with available MATISSE data that were identified to host a disc starting at the dust sublimation radius. Methods. We used geometric ring models to estimate the inner rim sizes, the relative flux contributions of the star, the ring, and an over-resolved emission, the orientation of the ring, and the spectral dependences of the components. Results. We find that the inner dust rims of the targets with a lack of near-IR excess in their SEDs are ∼2.5 to 7.5 times larger than the theoretical dust sublimation radii, and inner rim sizes of the systems that do not show this deficit are similar to those of their theoretical dust sublimation radii. The physical radii of the inner rims of these transition discs around post-AGB binaries are 3–25 au, which are larger than the disc sizes inferred for transition discs around young stars with VLTI/MIDI. This is due to the higher stellar luminosities of post-AGB systems compared to young stars, implying larger dust sublimation radii and thus larger physical inner radii of the transition disc. Conclusions. With mid-IR interferometric data, we directly confirm the transition disc nature of six circumbinary discs around post-AGB binary systems. Future observational and modelling efforts are needed to progress in our understanding of the structure, origin, and evolution of these transition discs

Instabilities in interacting binary stars

The types of instability in the interacting binary stars are reviewed. The project "Inter-Longitude Astronomy" is a series of smaller projects on concrete stars or groups of stars. It has no special funds, and is supported from resources and grants of participating organizations, when informal working groups are created. Totally we studied 1900+ variable stars of different types. The characteristic timescale is from seconds to decades and (extrapolating) even more. The monitoring of the first star of our sample AM Her was initiated by Prof. V.P. Tsesevich (1907-1983). Since more than 358 ADS papers were published. Some highlights of our photometric and photo-polarimetric monitoring and mathematical modelling of interacting binary stars of different types are presented: classical, asynchronous, intermediate polars and magnetic dwarf novae (DO Dra) with 25 timescales corresponding to different physical mechanisms and their combinations (part "Polar"); negative and positive superhumpers in nova-like and many dwarf novae stars ("Superhumper"); eclipsing "non-magnetic" cataclysmic variables; symbiotic systems ("Symbiosis"); super-soft sources (SSS, QR And); spotted (and not spotted) eclipsing variables with (and without) evidence for a current mass transfer ("Eclipser") with a special emphasis on systems with a direct impact of the stream into the gainer star's atmosphere, or V361 Lyr-type stars. Other parts of the ILA project are "Stellar Bell" (interesting pulsating variables of different types and periods - M, SR, RV Tau, RR Lyr, Delta Sct) and "Novice"(="New Variable") discoveries and classification with a subsequent monitoring for searching and studying possible multiple components of variability. Special mathematical methods have been developed to create a set of complementary software for statistically optimal modelling of variable stars of different types.Comment: Non-Stable Universe: Energetic Resources, Activity Phenomena and Evolutionary Processes, 19-23 September 2016, ed. Areg Mickaelian, Haik Harutyunian and Elena Nikoghosyan, Astronomical Society of the Pacific (ASP) Conference Series, 2017, in pres