arXiv subjects

S. Shelyag

Publications and source records attributed to S. Shelyag.

At least 19 recordsLinked to original sources

arXiv2025

Periodic patterns in simple biological differential delay models

Periodic patterns in dynamical behaviours of biological models described by simple form differential delay equations are studied. Mathematical models are given by a class of scalar delay differential equations with a multiplicative time periodic mixed coefficient and a nonlinear delayed negative feedback. The dynamics is studied analytically with supportive numerical simulation and justification of the theoretical outcomes. The principal nonlinearity involving the state variable is of the negative feedback type, the periodic multiplicative coefficient can change its sign, leading to equations with mixed positive-negative feedback. The existence of slowly oscillating periodic solutions of two different types is established. The theoretical analysis and derivation are based on the reduction of dynamics in the delay equations to that of interval maps. The theoretical outcomes are verified and supported by comprehensive numerical computations. The differential delay equations considered are generalisations of some well-known autonomous models from biological applications.

math.DS↗

arXiv2021

Constraining the magnetic vector in the quiet solar photosphere and the impact of instrumental degradation

With the advent of next generation high resolution telescopes, our understanding of how the magnetic field is organized in the internetwork (IN) photosphere is likely to advance.We aim to evaluate the extent to which we can retrieve information about the magnetic vector in the IN photosphere using inversions. We use snapshots produced from high resolution 3D magnetohydrodynamic (MHD) simulations and employ the Stokes Inversions based on Response functions (SIR) code to produce synthetic observables in the near infrared spectral window observed by the GREGOR Infrared Spectrograph (GRIS), which contains the highly magnetically sensitive photospheric Fe I line pair at 15648.52 A and 15652.87 A. We perform nearly 14 million inversions to test how well the true MHD atmospheric parameters can be constrained. Finally, we degrade the synthetic Stokes vectors spectrally and spatially to GREGOR resolutions and examine how this influences observations, considering the impact of stray light, spatial resolution and signal-to-noise (S-to-N). We find the depth-averaged parameters can be recovered by the inversions of the undegraded profiles, and by adding gradients to magnetic field strength, inclination and line of sight velocity we show an improvement in the chi squared value is achieved. We evaluate the extent to which we can constrain these parameters at various optical depths, with the kinematic and thermodynamic parameters sensitive deeper in the atmosphere than the magnetic parameters. We find the S-to-N and spatial resolution play a significant role in determining how the atmosphere appears and the magnetic and kinematic parameters are invariant upon inclusion of unpolarized stray light. We studied a linear polarization feature which resembles those recently observed by GRIS, appearing as loop-like structures with similar magnetic flux density.

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arXiv2020

Global Stability and Periodicity in a Glucose-Insulin Regulation Model with a Single Delay

A two-dimensional system of differential equations with delay modelling the glucose-insulin interaction processes in the human body is considered. Sufficient conditions are derived for the unique positive equilibrium in the system to be globally asymptotically stable. They are given in terms of the global attractivity of the fixed point in a limiting interval map. The existence of slowly oscillating periodic solutions is shown in the case when the equilibrium is unstable. The mathematical results are supported by extensive numerical simulations. It is shown that typical behaviour in the system is the convergence to either a stable periodic solution or to the unique stable equilibrium. The coexistence of several periodic solutions together with the stable equilibrium is demonstrated as a possibility.

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arXiv2019

Using the Stokes V widths of Fe I lines for diagnostics of the intrinsic solar photospheric magnetic field

The goal of this study is to explore a novel method for the solar photospheric magnetic field diagnostics using Stokes V widths of different magnetosensitive Fe~I spectral lines. We calculate Stokes I and V profiles of several Fe I lines based on a one-dimensional photospheric model VAL C using the NICOLE radiative transfer code. These profiles are used to produce calibration curves linking the intrinsic magnetic field values with the widths of blue peaks of Stokes V profiles. The obtained calibration curves are then tested using the Stokes profiles calculated for more realistic photospheric models based on MHD models of magneto-convection. It is shown that the developed Stokes V widths (SVW) method can be used with various optical and near-infrared lines. Out of six lines considered in this study, FeI 6301 line appears to be the most effective: it is sensitive to fields over ~200G and does not show any saturation up to ~2kG. Other lines considered can also be used for the photospheric field diagnostics with this method, however, only in narrower field value ranges, typically from about 100G to 700-1000G. The developed method can be a useful alternative to the classical magnetic line ratio method, particularly when the choice of lines is limited.

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arXiv2019

Stellar Surface Magneto-Convection as a Source of Astrophysical Noise III. Sun-as-a-star Simulations and Optimal Noise Diagnostics

Stellar surface magnetoconvection (granulation) creates asymmetries in the observed stellar absorption lines that can subsequently manifest themselves as spurious radial velocities shifts. In turn, this can then mask the Doppler-reflex motion induced by orbiting planets on their host stars, and represents a particular challenge for determining the masses of low-mass, long-period planets. Herein, we study this impact by creating Sun-as-a-star observations that encapsulate the granulation variability expected from 3D magnetohydrodynamic simulations. These Sun-as-a-star model observations are in good agreement with empirical observations of the Sun, but may underestimate the total variability relative to the quiet Sun due to the increased magnetic field strength in our models. We find numerous line profile characteristics linearly correlate with the disc-integrated convection-induced velocities. Removing the various correlations with the line bisector, equivalent width, and the V_asy indicator may reduce ~50-60% of the granulation noise in the measured velocities. We also find that simultaneous photometry may be a key diagnostic, as our proxy for photometric brightness also allowed us to remove ~50% of the granulation-induced radial velocity noise. These correlations and granulation-noise mitigations breakdown in the presence of low instrumental resolution and/or increased stellar rotation, as both act to smooth the observed line profile asymmetries.

astro-ph.EP↗

arXiv2018

Signatures of quiet Sun reconnection events in Ca~{\sc ii}, H$α$ and Fe~{\sc i}

We use observations of quiet Sun (QS) regions in the H$α$ 6563 Å, Ca~{\sc ii} 8542 Å\, and Fe~{\sc i} 6302 Å lines. We observe brightenings in the wings of the H$α$ and Ca~{\sc ii} combined with observations of the interacting magnetic concentrations observed in the Stokes signals of Fe~{\sc i}. These brightenings are similar to Ellerman bombs (EBs), i.e. impulsive bursts in the wings of the Balmer lines which leave the line cores unaffected. Such enhancements suggest that these events have similar formation mechanisms to the classical EBs found in active regions, with the reduced intensity enhancements found in the QS regions due to a weaker feeding magnetic flux. The observations also show that the quiet Sun Ellerman bombs (QSEBs) are formed at a higher height in the upper photosphere than the photospheric continuum level. Using simulations, we investigate the formation mechanism associated with the events and suggest that these events are driven by the interaction of magnetic field-lines in the upper photospheric regions. The results of the simulation are in agreement with observations when comparing the light-curves, and in most cases we found that the peak in the Ca~{\sc ii} 8542 Å wing occurred before the peak in H$α$ wing. Moreover, in some cases, the line profiles observed in Ca~{\sc ii} are asymmetrical with a raised core profile. The source of heating in these events is shown by the MURaM simulations and is suggested to occur 430 km above the photosphere.

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arXiv2018

Analysis of 3D plasma motions in a chromospheric jet formed due to magnetic reconnection

Within the framework of resistive MHD, implementing the C7 equilibrium atmosphere model and a 3D potential magnetic field realistic configuration, we simulate the formation of a plasm jet with the morphology, upward velocity up to 130 km/s and timescale formation between 60 and 90 s after beginning of simulation, similar to those expected for Type II spicules. Initial results of this simulation were published in Paper (e.g., González-Avilés et al. 2018) and present paper is devoted to the analysis of transverse displacements and rotational type motion of the jet. Our results suggest that 3D magnetic reconnection may be responsible for the formation of the jet in Paper (González-Avilés et al. 2018). In this paper, by calculating times series of the velocity components $v_x$ and $v_y$ in different points near to the jet for various heights we find transverse oscillations in agreement with spicule observations. We also obtain a time-distance plot of the temperature in a cross-cut at the plane $x=$0.1 Mm and find significant transverse displacements of the jet. By analyzing temperature isosurfaces of $10^{4}$ K with the distribution of $v_x$, we find that if the line-of-sight (LOS) is approximately perpendicular to the jet axis then there is both motion towards and away from the observer across the width of the jet. This red-blue shift pattern of the jet is caused by rotational motion, initially clockwise and anti-clockwise afterwards, which could be interpreted as torsional motion. From a nearly vertical perspective of the jet the LOS velocity component shows a central blue-shift region surrounded by red-shifted plasma.

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arXiv2018

Stellar Surface Magneto-Convection as a Source of Astrophysical Noise II. Center-to-Limb Parameterisation of Absorption Line Profiles and Comparison to Observations

Manifestations of stellar activity (such as star-spots, plage/faculae, and convective flows) are well known to induce spectroscopic signals often referred to as astrophysical noise by exoplanet hunters. For example, setting an ultimate goal of detecting true Earth-analogs demands reaching radial velocity (RV) precisions of ~9 cm/s. While this is becoming technically feasible with the latest generation of highly stabilised spectrographs, it is astrophysical noise that sets the true fundamental barrier on attainable RV precisions. In this paper we parameterise the impact of solar surface magneto-convection on absorption line profiles, and extend the analysis from the solar disc centre (Paper I) to the solar limb. Off disc-centre, the plasma flows orthogonal to the granule tops begin to lie along the line-of-sight and those parallel to the granule tops are no longer completely aligned with the observer. Moreover, the granulation is corrugated and the granules can block other granules, as well as the intergranular lane components. Overall, the visible plasma flows and geometry of the corrugated surface significantly impact the resultant line profiles and induce centre-to-limb variations in shape and net position. We detail these herein, and compare to various solar observations. We find our granulation parameterisation can recreate realistic line profiles and induced radial velocity shifts, across the stellar disc, indicative of both those found in computationally heavy radiative 3D magnetohydrodynamical simulations and empirical solar observations.

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arXiv2018

Flows and magnetic field structures in reconnection regions of simulations of the solar atmosphere: do flux pile-up models work?

We study the process of magnetic field annihilation and reconnection in simulations of magnetised solar photosphere and chromosphere with magnetic fields of opposite polarities and constant numerical resistivity. Exact analytical solutions for reconnective annihilations are used to interpret the features of magnetic reconnection in simulations of flux cancellation in the solar atmosphere. We use MURaM high-resolution photospheric radiative magneto-convection simulations to demonstrate the presence of magnetic field reconnection consistent with the magnetic flux pile-up models. Also, a simulated data-driven chromospheric magneto-hydrodynamic simulation is used to demonstrate magnetic field and flow structures, which are similar to the ones theoretically predicted. Both simulations demonstrate flow and magnetic field structures roughly consistent with accelerated reconnection with magnetic flux pile-up. The presence of standard Sweet-Parker type reconnection is also demonstrated in stronger photospheric magnetic fields.

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arXiv2018

Analysis of unresolved photospheric magnetic field structure using Fe I 6301 and 6302 lines

Early magnetographic observations indicated that magnetic field in the solar photosphere has unresolved small-scale structure. Near-infrared and optical data with extremely high spatial resolution show that these structures have scales of few tens of kilometres, which are not resolved in the majority of solar observations. The goal of this study is to establish the effect of unresolved photospheric magnetic field structure on Stokes profiles observed with relatively low spatial resolution. Ultimately, we aim to develop methods for fast estimation of the photospheric magnetic filling factor and line-of-sight gradient of the photospheric magnetic field, which can be applied to large observational data sets. We exploit 3D MHD models of magneto-convection developed using MURAM code. Corresponding profiles of Fe I 6301.5 and 6302.5 $\mathrmÅ$ spectral lines are calculated using NICOLE radiative transfer code. The resulting I and V Stokes [x,y,$λ$] cubes with reduced spatial resolution of 150 km are used to calculate magnetic field values as they would be obtained in observations with Hinode/SOT or SDO/HMI. Three different methods of the magnetic filling factor estimation are considered: the magnetic line ratio method, Stokes V width method and a simple statistical method. We find that the statistical method and the Stokes V width method are sufficiently reliable for fast filling factor estimations. Furthermore, we find that Stokes $I\pm V$ bisector splitting gradient can be used for fast estimation of line-of-sight gradient of the photospheric magnetic field.

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arXiv2018

I. Jet Formation and Evolution due to 3D Magnetic Reconnection

Using simulated data-driven three-dimensional resistive MHD simulations of the solar atmosphere, we show that magnetic reconnection can be responsible of the formation of jets with characteristic of Type II spicules. For this, we numerically model the photosphere-corona region using the C7 equilibrium atmosphere model. The initial magnetic configuration is a 3D potential magnetic field, extrapolated up to the solar corona region from a dynamic realistic simulation of solar photospheric magnetoconvection model which is mimicking quiet-Sun. In this case we consider a uniform and constant value of the magnetic resistivity of $12.56 ~Ω~{\rm m}$. We have found that formation of the jets depends on the Lorentz force, which helps to accelerate the plasma upwards. Analyzing various properties of the jet dynamics, we found that the jet structure shows Doppler shift near to regions with high vorticity. The morphology, upward velocity, covering a range up to 100 $\rm km$ $\rm s^{-1}$, and life-time of the estructure, bigger than 100 ${\rm s}$, are similar to those expected for Type II spicules.

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arXiv2016

Heating of the partially ionized solar chromosphere by waves in magnetic structures

In this paper, we show a "proof of concept" of the heating mechanism of the solar chromosphere due to wave dissipation caused by the effects of partial ionization. Numerical modeling of non-linear wave propagation in a magnetic flux tube, embedded in the solar atmosphere, is performed by solving a system of single-fluid quasi-MHD equations, which take into account the ambipolar term from the generalized Ohm's law. It is shown that perturbations caused by magnetic waves can be effectively dissipated due to ambipolar diffusion. The energy input by this mechanism is continuous and shown to be more efficient than dissipation of static currents, ultimately leading to chromospheric temperature increase in magnetic structures.

astro-ph.SR↗

arXiv2016

Modelling the Rossiter-McLaughlin Effect: Impact of the Convective Centre-to-Limb Variations in the Stellar Photosphere

Observations of the Rossiter-McLaughlin (RM) effect provide information on star-planet alignments, which can inform planetary migration and evolution theories. Here, we go beyond the classical RM modelling and explore the impact of a convective blueshift that varies across the stellar disc and non-Gaussian stellar photospheric profiles. We simulated an aligned hot Jupiter with a 4 d orbit about a Sun-like star and injected centre-to-limb velocity (and profile shape) variations based on radiative 3D magnetohydrodynamic simulations of solar surface convection. The residuals between our modelling and classical RM modelling were dependent on the intrinsic profile width and v sin i; the amplitude of the residuals increased with increasing v sin i, and with decreasing intrinsic profile width. For slowly rotating stars the centre-to-limb convective variation dominated the residuals (with amplitudes of 10s of cm/s to ~1 m/s); however, for faster rotating stars the dominant residual signature was due a non-Gaussian intrinsic profile (with amplitudes from 0.5-9 m/s). When the impact factor was 0, neglecting to account for the convective centre-to-limb variation led to an uncertainty in the obliquity of ~10-20 degrees, even though the true v sin i was known. Additionally, neglecting to properly model an asymmetric intrinsic profile had a greater impact for more rapidly rotating stars (e.g. v sin i = 6 km/s), and caused systematic errors on the order of ~20 degrees in the measured obliquities. Hence, neglecting the impact of stellar surface convection may bias star-planet alignment measurements and consequently also theories on planetary migration and evolution.

astro-ph.EP↗

arXiv2015

Alfvén Wave Heating of the Solar Chromosphere: 1.5D models

Physical processes which may lead to solar chromospheric heating are analyzed using high-resolution 1.5D non-ideal MHD modelling. We demonstrate that it is possible to heat the chromospheric plasma by direct resistive dissipation of high-frequency Alfvén waves through Pedersen resistivity. However this is unlikely to be sufficient to balance radiative and conductive losses unless unrealistic field strengths or photospheric velocities are used. The precise heating profile is determined by the input driving spectrum since in 1.5D there is no possibility of Alfvén wave turbulence. The inclusion of the Hall term does not affect the heating rates. If plasma compressibility is taken into account, shocks are produced through the ponderomotive coupling of Alfvén waves to slow modes and shock heating dominates the resistive dissipation. In 1.5D shock coalescence amplifies the effects of shocks and for compressible simulations with realistic driver spectra the heating rate exceeds that required to match radiative and conductive losses. Thus while the heating rates for these 1.5D simulations are an overestimate they do show that ponderomotive coupling of Alfvén waves to sound waves is more important in chromospheric heating than Pedersen dissipation through ion-neutral collisions.

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arXiv2015

Spectropolarimetrically accurate magnetohydrostatic sunspot model for forward modelling in helioseismology

We present a technique to construct a spectropolarimetrically accurate magneto-hydrostatic model of a large-scale solar magnetic field concentration, mimicking a sunspot. Using the constructed model we perform a simulation of acoustic wave propagation, conversion and absorption in the solar interior and photosphere with the sunspot embedded into it. With the $6173\mathrmÅ$ magnetically sensitive photospheric absorption line of neutral iron, we calculate observable quantities such as continuum intensities, Doppler velocities, as well as full Stokes vector for the simulation at various positions at the solar disk, and analyse the influence of non-locality of radiative transport in the solar photosphere on helioseismic measurements. Bisector shapes were used to perform multi-height observations. The differences in acoustic power at different heights within the line formation region at different positions at the solar disk were simulated and characterised. An increase in acoustic power in the simulated observations of the sunspot umbra away from the solar disk centre was confirmed as the slow magneto-acoustic wave.

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arXiv2015

Ellerman Bombs with Jets: Cause and Effect

Ellerman Bombs (EBs) are thought to arise as a result of photospheric magnetic reconnection. We use data from the Swedish 1-m Solar Telescope (SST), to study EB events on the solar disk and at the limb. Both datasets show that EBs are connected to the foot-points of forming chromospheric jets. The limb observations show that a bright structure in the H$α$ blue wing connects to the EB initially fuelling it, leading to the ejection of material upwards. The material moves along a loop structure where a newly formed jet is subsequently observed in the red wing of H$α$. In the disk dataset, an EB initiates a jet which propagates away from the apparent reconnection site within the EB flame. The EB then splits into two, with associated brightenings in the inter-granular lanes (IGLs). Micro-jets are then observed, extending to 500 km with a lifetime of a few minutes. Observed velocities of the micro-jets are approximately 5-10 km s$^{-1}$, while their chromospheric counterparts range from 50-80 km s$^{-1}$. MURaM simulations of quiet Sun reconnection show that micro-jets with similar properties to that of the observations follow the line of reconnection in the photosphere, with associated H$α$ brightening at the location of increased temperature.

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arXiv2015

Directional Time-Distance Probing of Model Sunspot Atmospheres

A crucial feature not widely accounted for in local helioseismology is that surface magnetic regions actually open a window from the interior into the solar atmosphere, and that the seismic waves leak through this window, reflect high in the atmosphere, and then re-enter the interior to rejoin the seismic wave field normally confined there. In a series of recent numerical studies using translation invariant atmospheres, we utilised a "directional time-distance helioseismology" measurement scheme to study the implications of the returning fast and Alfvén waves higher up in the solar atmosphere on the seismology at the photosphere (Cally & Moradi 2013; Moradi & Cally 2014). In this study, we extend our directional time-distance analysis to more realistic sunspot-like atmospheres to better understand the direct effects of the magnetic field on helioseismic travel-time measurements in sunspots. In line with our previous findings, we uncover a distinct frequency-dependant directional behaviour in the travel-time measurements, consistent with the signatures of MHD mode conversion. We found this to be the case regardless of the sunspot field strength or depth of its Wilson depression. We also isolated and analysed the direct contribution from purely thermal perturbations to the measured travel times, finding that waves propagating in the umbra are much more sensitive to the underlying thermal effects of the sunspot.

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arXiv2015

The Dynamics of Rapid Redshifted and Blueshifted Excursions in the Solar Halpha line

We analyse high temporal and spatial resolution time-series of spectral scans of the Halpha line obtained with the CRisp Imaging SpectroPolarimeter (CRISP) instrument mounted on the Swedish Solar Telescope. The data reveal highly dynamic, dark, short-lived structures known as Rapid Redshifted and Blueshifted Excursions (RREs, RBEs) that are on-disk absorption features observed in the red and blue wings of spectral lines formed in the chromosphere. We study the dynamics of RREs and RBEs by tracking their evolution in space and time, measuring the speed of the apparent motion, line-of-sight Doppler velocity, and transverse velocity of individual structures. A statistical study of their measured properties shows that RREs and RBEs have similar occurrence rates, lifetimes, lengths, and widths. They also display non-periodic, non-linear transverse motions perpendicular to their axes at speeds of 4 - 31 km/s. Furthermore, both types of structures either appear as high speed jets and blobs that are directed outwardly from a magnetic bright point with speeds of 50 - 150 km/s, or emerge within a few seconds. A study of the different velocity components suggests that the transverse motions along the line-of-sight of the chromospheric flux tubes are responsible for the formation and appearance of these redshifted/blueshifted structures. The short lifetime and fast disappearance of the RREs/RBEs suggests that, similar to type II spicules, they are rapidly heated to transition region or even coronal temperatures. We speculate that the Kelvin-Helmholtz instability triggered by observed transverse motions of these structures may be a viable mechanism for their heating.

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