arXiv subjects

Paul H. Bryant

Publications and source records attributed to Paul H. Bryant.

5 recordsLinked to original sources

arXiv2016

On the Interactive-Beating-Modes Model: Generation of Asymmetric Multiplet Structures and Explanation of the Blazhko Effect

This paper considers a nonlinear coupling between a radial and a nonradial mode of nearly the same frequency. The results may be of general interest, but in particular have application to the "beating-modes model" of the Blazhko effect which was recently shown to accurately reproduce the light curve of RR Lyr. For weak coupling, the two modes do not phase-lock and they retain separate frequencies, but the coupling nevertheless has important consequences. Upon increasing the coupling strength from zero, an additional side-peak emerges in the spectrum forming an asymmetric triplet centered on the fundamental. As the coupling is further increased, the amplitude of this side-peak increases and the three peaks are also pulled towards each other, decreasing the Blazhko frequency. Beyond a critical coupling strength, phase-locking occurs between the modes. With appropriate choice of coupling strength, this "interactive beating-modes model" can match the side-peak amplitude ratio of any star. The effects of nonlinear damping are also explored and found to generate additional side-peaks of odd order. Consistent with this, the odd side-peaks are found to be favored in V808 Cyg. It is also shown that the Blazhko effect generates a fluctuating "environment" that can have a modulatory effect on other excited modes of the star. An example is found in V808 Cyg where the modulation is at double the Blazhko frequency. An explanation is found for this mysterious doubling, providing additional evidence in favor of the model.

astro-ph.SR↗

arXiv2015

Is the apparent period-doubling in Blazhko stars actually an illusion?

The light curves of many Blazhko stars exhibit intervals in which successive pulsation maxima alternate between two levels in a way that is characteristic of period-doubling. In addition, hydrocode models of these stars have clearly demonstrated period-doubling bifurcations. As a result, it is now generally accepted that these stars do indeed exhibit period-doubling. Here we present strong evidence that this assumption is incorrect. The alternating maxima likely result from the presence of one or more near-resonant modes which appear in the stellar spectra and are slightly but significantly offset from 3/2 times the fundamental frequency. We show that a previously proposed explanation for the presence of these peaks is inadequate. The phase-slip of the dominant near-resonant peak in RR Lyr is shown to be fully correlated with the parity of the observed alternations, providing further strong evidence that the process is nonresonant and cannot be characterized as period-doubling. The dominant near-resonant peak in V808 Cyg has side-peaks spaced at twice the Blazhko frequency. This apparent modulation indicates that the peak corresponds to a vibrational mode and also adds strong support to the beating-modes model of the Blazhko effect which can account for the doubled frequency. The modulation also demonstrates the "environment" altering effect of large amplitude modes which is shown to be consistent with the amplitude equation formalism.

astro-ph.SR↗

arXiv2015

Is the Blazhko effect the beating of a near-resonant double-mode pulsation?

In this paper it is shown that the Blazhko effect may result from a near-resonant type of multi-mode pulsation, where two (or sometimes more) periodic oscillations with slightly different frequencies gradually slip in phase, producing a beat frequency type of modulation. Typically one of these oscillations is strongly non-sinusoidal. Two oscillations are sufficient for the standard Blazhko effect; additional oscillations are needed to explain multi-frequency modulation. Previous work on this hypothesis by Arthur N. Cox and others is extended in this paper by developing a simple (non-hydro) model that can accurately reproduce several important features found in Kepler data for RR Lyr, including the pulsation waveform, the upper and lower Blazhko envelope functions and the motion, disappearance and reappearance of the bump feature. The non-sinusoidal oscillation is probably generated by the fundamental mode and the other oscillations are probably generated by nonradial modes. This model provides an explanation for the strong asymmetry observed in the side peak spectra of most RR Lyrae stars. The motion and disappearance of the bump feature are shown to be an illusion, just an artifact of combining the oscillations. V445 Lyr is presented as an example with dual modulation. The mysterious double-maxima waveform observed for this star is explained, providing additional strong evidence that this beating-modes hypothesis is correct. Problems with other recent explanations of the Blazhko effect are discussed in some detail.

astro-ph.SR↗

arXiv2014

A Hybrid Mode Model of the Blazhko Effect, Shown to Accurately Fit Kepler Data for RR Lyr

The waveform for Blazhko stars can be substantially different during the ascending and descending parts of the Blazhko cycle. A hybrid model, consisting of two component oscillators of the same frequency, is proposed as a means to fit the data over the entire cycle. One component exhibits a sawtooth-like velocity waveform while the other is nearly sinusoidal. One method of generating such a hybrid is presented: a nonlinear model is developed for the first overtone mode, which, if excited to large amplitude, is found to drop strongly in frequency and become highly non-sinusoidal. If the frequency drops sufficiently to become equal to the fundamental frequency, the two can become phase locked and form the desired hybrid. A relationship is assumed between the hybrid mode velocity and the observed light curve, which is approximated as a power series. An accurate fit of the hybrid model is made to actual Kepler data for RR Lyr. The sinusoidal component may tend to stabilize the period of the hybrid which is found in real Blazhko data to be extremely stable. It is proposed that the variations in amplitude and phase might result from a nonlinear interaction with a third mode, possibly a nonradial mode at 3/2 the fundamental frequency. The hybrid model also applies to non-Blazhko RRab stars and provides an explanation for the light curve bump. A method to estimate the surface gravity is also proposed.

astro-ph.SR↗

arXiv2009

Parameter and State Estimation of Experimental Chaotic Systems Using Synchronization

We examine the use of synchronization as a mechanism for extracting parameter and state information from experimental systems. We focus on important aspects of this problem that have received little attention previously, and we explore them using experiments and simulations with the chaotic Colpitts oscillator as an example system. We explore the impact of model imperfection on the ability to extract valid information from an experimental system. We compare two optimization methods: an initial value method and a constrained method. Each of these involve coupling the model equations to the experimental data in order to regularize the chaotic motions on the synchronization manifold. We explore both time dependent and time independent coupling. We also examine both optimized and fixed (or manually adjusted) coupling. For the case of an optimized time dependent coupling function u(t) we find a robust structure which includes sharp peaks and intervals where it is zero. This structure shows a strong correlation with the location in phase space and appears to depend on noise, imperfections of the model, and the Lyapunov direction vectors. Comparison of this result with that obtained using simulated data may provide one measure of model imperfection. The constrained method with time dependent coupling appears to have benefits in synchronizing long datasets with minimal impact, while the initial value method with time independent coupling tends to be substantially faster, more flexible and easier to use. We also describe a new method of coupling which is useful for sparse experimental data sets. Our use of the Colpitts oscillator allows us to explore in detail the case of a system with one positive Lyapunov exponent. The methods we explored are easily extended to driven systems such as neurons with time dependent injected current.

nlin.CD↗