arXiv subjects

Harsh Mathur

Publications and source records attributed to Harsh Mathur.

At least 19 recordsLinked to original sources

arXiv2025

The H$\alpha$ line as a probe of chromospheric magnetic fields

We explore the diagnostic potential of the H$\alpha$ line for probing the chromospheric magnetic field using a realistic 3D radiative magnetohydrodynamic (rMHD) model. The Stokes profiles of the H$\alpha$ line are synthesized through full 3D radiative transfer under the field-free approximation, alongside the Ca II 8542 {\AA} and Fe I 6173 {\AA} lines for comparison. The line-of-sight (LOS) magnetic fields are inferred using the weak field approximation (WFA) for theH$\alpha$ and Ca II 8542 {\AA} lines, while the Fe I 6173 {\AA} line is analyzed through Milne-Eddington inversion techniques. The comparison between the inferred LOS magnetic field maps and the magnetic fields in the rMHD model revealed that the H$\alpha$ line core primarily probes the chromospheric magnetic field at log tau_500 = -5.7, which corresponds to higher layers than the Ca II 8542 {\AA} line core, which is most sensitive to conditions at log tau_500 = -5.1. On average, the Stokes V profiles of the H$\alpha$ line core form 500 km higher than those of the Ca II 8542 {\AA} line core. The H$\alpha$ polarization signals persist after adding noise, and with noise at the level of 10^-3 Ic, most simulated magnetic structures remain visible. These findings suggest that spectropolarimetric observations of the H$\alpha$ line can provide complementary insights into the stratification of the magnetic field at higher altitudes, especially when recorded simultaneously with widely used chromospheric diagnostics such as the Ca II 8542 {\AA} line.

astro-ph.SR↗

arXiv2025

Clustering analysis of Ca {\sc i} 4227 line polarization using magnetohydrodynamic simulations of the solar atmosphere

Ca {\sc i} 4227 \AA\, line is a strong resonance line formed in the Solar chromosphere. At the limb, it produces the largest scattering polarization signal. So far, modeling the linear polarization in this line has been limited to the use of one-dimensional semi-empirical models of the solar atmosphere. In this paper, we use three-dimensional magnetohydrodynamical models of the solar atmosphere as well as 1.5D radiative transfer to understand the formation of linear polarization profiles due to resonance scattering in this line at a near limb position. Using three-dimensional magnetohydrodynamical models of the solar atmosphere, in this paper, we perform 1.5D radiative transfer calculations to understand the formation of linear polarization profiles due to resonance scattering in this line at a near limb position. We focus on studying the sensitivity of the resonance scattering polarization to the temperature and the density structures in the atmosphere. We do not include the effects of magnetic and velocity fields in this study. We use clustering analysis to identify linear polarization profiles with similar shape and group them accordingly for our study. We analyze the structure of the linear polarization profiles across 14 clusters, each representing different realizations of the solar atmosphere. Using source function ratio plots at various wing and core wavelength positions, we provide a qualitative explanation of linear polarization profiles in these clusters.

astro-ph.SR↗

arXiv2024

Simultaneous spectropolarimetric observations in the H$\alpha$ and Ca II 8662 {\AA} lines of an active region

We present spectropolarimetric observations of an active region recorded simultaneously in the H$\alpha$ Ca II 8662 {\AA} lines. The sunspot exhibits multiple structures, including a lightbridge and a region where Ca II 8662 {\AA} line core is in emission. Correspondingly, the H$\alpha$ line core image displays brightening in the emission region, with the spectral profiles showing elevated line cores. The stratification of the line-of-sight magnetic field is inferred through non-LTE multiline inversions of the Ca II 8662 {\AA} line and the weak field approximation over the H$\alpha$ line. The field strength inferred from the H$\alpha$ line core is consistently smaller than that inferred from inversions at $\log \tau_{500}$ = $-$4.5. However, the study finds no correlation between the WFA over the core of the H$\alpha$ line and that inferred from inversions at $\log \tau_{500}$ = $-$4.5. In regions exhibiting emission features, the morphology of the magnetic field at $\log \tau_{500}$ = $-$4.5 resembles that at $\log \tau_{500}$ = $-$1, with slightly higher or comparable field strengths. The magnetic field morphology inferred from the core of the H$\alpha$ line is also similar to that inferred from the full spectral range of the H$\alpha$ line in the emission region. The field strength inferred in the lightbridge at $\log \tau_{500}$ = $-$1 is smaller than the surrounding umbral regions and comparable at $\log \tau_{500}$ = $-$4.5. Similarly, the field strength inferred in the lightbridge from the WFA over the H$\alpha$ line appears lower compared to the surrounding umbral regions.

astro-ph.SR↗

arXiv2023

Modified Newtonian Dynamics as an Alternative to the Planet Nine Hypothesis

A new class of Kuiper belt objects that lie beyond Neptune with semimajor axes greater than 250 astronomical units show orbital anomalies that have been interpreted as evidence for an undiscovered ninth planet. We show that a modified gravity theory known as MOND (Modified Newtonian Dynamics) provides an alternative explanation for the anomalies using the well-established secular approximation. We predict that the major axes of the orbits will be aligned with the direction towards the galactic center and that the orbits cluster in phase space, in agreement with observations of Kuiper belt objects from the new class. Thus MOND, which can explain galactic rotation without invoking dark matter, might also be observable in the outer solar system.

gr-qc↗

arXiv2023

Does H$\alpha$ Stokes~$V$ profiles probe the chromospheric magnetic field? An observational perspective

We investigated the diagnostic potential of the Stokes $V$ profile of the H$\alpha$ line to probe the chromospheric line-of-sight (LOS) magnetic field ($B_{\mathrm{LOS}}$) by comparing the $B_{\mathrm{LOS}}$ inferred from the weak field approximation (WFA) with that of inferred from the multi-line inversions of the Ca II 8542 {\AA}, Si I 8536 {\AA} and Fe I 8538 {\AA} lines using the STiC inversion code. Simultaneous spectropolarimetric observations of a pore in the Ca II 8542 {\AA} and H$\alpha$ spectral lines obtained from the SPINOR at the Dunn Solar Telescope on the 4th of December, 2008 are used in this study. The WFA was applied on the Stokes $I$ and $V$ profiles of H$\alpha$ line over three wavelength ranges viz.: around line core ($\Delta\lambda=\pm0.35$ {\AA}), line wings ($\Delta\lambda=[-1.5, -0.6]$ and $[+0.6, +1.5]$ {\AA}) and full spectral range of the line ($\Delta\lambda=\pm1.5$ {\AA}) to derive the $B_{\mathrm{LOS}}$. We found the maximum $B_{\mathrm{LOS}}$ strengths of $\sim+800$ and $\sim+600$ G at $\log\tau_{\mathrm{500}}$ = $-$1 and $-$4.5, respectively in the pore. The morphological map of the $B_{\mathrm{LOS}}$ inferred from the H$\alpha$ line core is similar to the $B_{\mathrm{LOS}}$ map at $\log\tau_{\mathrm{500}}$ = $-$4.5 inferred from multi-line inversions. The $B_{\mathrm{LOS}}$ map inferred from the H$\alpha$ line wings and full spectral range have a similar morphological structure to the $B_{\mathrm{LOS}}$ map inferred at $\log\tau_{\mathrm{500}}$ = $-$1. The $B_{\mathrm{LOS}}$ estimated from H$\alpha$ using WFA is weaker by a factor of $\approx 0.53$ than that of inferred from the multi-line inversions.

astro-ph.SR↗

arXiv2023

Solar Mean Magnetic Field of the Chromosphere

The Solar Mean Magnetic Field (SMMF) is the mean value of the line of sight (LOS) component of the solar vector magnetic field averaged over the visible hemisphere of the Sun. So far, the studies on SMMF have mostly been confined to the magnetic field measurements at the photosphere. In this study, we calculate and analyse the SMMF using magnetic field measurements at the chromosphere, in conjunction with that of photospheric measurements. For this purpose, we have used full disk LOS magnetograms derived from spectropolarimetric observations carried out in Fe I 630.15 nm and Ca II 854.2 nm by the Synoptic Optical Long term Investigations of the Sun (SOLIS)/Vector Spectromagnetograph (VSM) instrument during 2010 to 2017. It is found from this study that the SMMF at the chromosphere is weaker by a factor of 0.60 compared to the SMMF at the upper photosphere. The correlation analysis between them gives a Pearson correlation coefficient of 0.80. The similarity and reduced intensity of the chromospheric SMMF with respect to the photospheric SMMF corroborate the idea that it is the source of the Interplanetary Magnetic Field (IMF).

astro-ph.SR↗

arXiv2022

Properties of shock waves in the quiet Sun chromosphere

Short-lived (100s or less), sub-arcsec to a couple of arcsec size features of enhanced brightenings in the narrowband images at the $\mathrm{H_{2V}}$ and $\mathrm{K_{2V}}$ positions of the Ca II H and K lines in the quiet Sun are known as bright grains. With simultaneous observations of a quiet Sun internetwork region in the Fe I 6173 {\AA}, Ca II 8542 {AA}, and Ca II K lines acquired by the CRisp Imaging Spectro-Polarimeter and the CHROMospheric Imaging Spectrometer instruments on the Swedish 1-m Solar Telescope, we performed multi-line non-local thermodynamic equilibrium inversions using the STockholm inversion Code to infer the time-varying stratified atmosphere's physical properties such as the temperature, line-of-sight (LOS) velocity, and microturbulence. The Ca II K profiles of bright grains show enhancement in the $\mathrm{K_{2V}}$ peak intensities with absence of the $\mathrm{K_{2R}}$ features. At the time of maximum enhancement in the $\mathrm{K_{2V}}$ peak intensities, we found average enhancements in temperature at lower chromospheric layers (at $\log\tau_{500}$ $\simeq$ $-$4.2) of about 1.1 kK with maximum enhancement of about 4.5 kK. These temperature enhancements are colocated with upflows, as strong as $-$6 $\mathrm{km\;s^{-1}}$, in the direction of the LOS. The LOS velocities at upper chromospheric layers at $\log\tau_{500}$ < $-$4.2 show consistent downflows greater than $+$8 $\mathrm{km\;s^{-1}}$. The retrieved value of microturbulence in the atmosphere of bright grains is negligible at chromospheric layers. The study provides observational evidence to support the interpretation that the bright grains observed in narrowband images at the $\mathrm{H_{2V}}$ and $\mathrm{K_{2V}}$ positions of the Ca II H and K lines are manifestations of upward propagating acoustic shocks against a background of downflowing atmospheres.

astro-ph.SR↗

arXiv2020

Evading Anderson localization in a one-dimensional conductor with correlated disorder

We show that a one dimensional disordered conductor with correlated disorder has an extended state and a Landauer resistance that is non-zero in the limit of infinite system size in contrast to the predictions of the scaling theory of Anderson localization. The delocalization transition is not related to any underlying symmetry of the model such as particle-hole symmetry. For a wire of finite length the effect manifests as a sharp transmission resonance that narrows as the length of the wire is increased. Experimental realizations and applications are discussed including the possibility of constructing a narrow band light filter.

cond-mat.mes-hall↗

arXiv2020

Vibrational Spectrum of Granular Packings With Random Matrices

The vibrational spectrum of granular packings can be used as a signature of the jamming transition, with the density of states at zero frequency becoming non-zero at the transition. It has been proposed previously that the vibrational spectrum of granular packings can be approximately obtained from random matrix theory. Here we show that although the density of states predicted by random matrix theory does not agree with certain aspects of dynamical numerical simulations, the correlations of the density of states, which---in contrast to the density of states---are expected to be universal, do show good agreement between dynamical numerical simulations of bead packs near the jamming point and the analytic predictions of the Laguerre orthogonal ensemble of random matrices. At the same time, there is clear disagreement with the Gaussian orthogonal ensemble. These findings establish that the Laguerre ensemble correctly reproduces the universal statistical properties of jammed granular matter and exclude the Gaussian orthogonal ensemble. We also present a random lattice model which is a physically motivated variant of the random matrix ensemble. Numerical calculations reveal that this model reproduces the known features of the vibrational density of states of granular matter, while also retaining the correlation structure seen in the Laguerre random matrix theory. We propose that the random lattice model can therefore be applied the understand not only the spectrum but more general properties of the vibration of bead packs including the spatial structure of modes both at the jamming point and far from it.

cond-mat.dis-nn↗

arXiv2020

Single Shot Spectroscopic Design Aspects

High time cadence Spectro Polarimetry allows the feasibility of studying magnetic field evolution coupled with the plasma flows. Such a high cadence solar spectropolarimetry if developed will allow one to study magnetic field evolution in eruptive processes like solar flares, prominence eruptions, etc. A single shot solar spectroscopy was recently demonstrated at Multi Application Solar Telescope (MAST) at Udaipur Solar Observatory. The snapshot spectroscopy is performed by sampling the pupil plane using the lenslet array to get multiple images of the field of view (FOV), which are then collimated and the collimated beam is made to pass through an FP Etalon in collimated mode. As the distance from the FP axis increases, the peak transmitted wavelength shift towards the bluer side. Using a prefilter with a full width half maximum (FWHM) less than the free spectral range (FSR) of FP, combined with an imaging lens, we can get multiple images of FOV on image plane with a blue shift in spectra as we move radially outwards from the optical axis.

astro-ph.IM↗

arXiv2019

Symmetry breaking, strain solitons and mechanical edge modes in monolayer antimony

Two-dimensional materials exhibit a variety of mechanical instabilities accompanied by spontaneous symmetry breaking. Here we develop a continuum description of the buckling instability of antimonene sheets. Regions of oppositely directed buckling constitute domains separated by domain walls that are solitons in our model. Perturbations about equilibrium propagate as waves with a gapped dispersion in the bulk but there is a gapless mode with linear dispersion that propagates along the domain walls in a manner reminiscent of the electronic modes of topological insulators. We establish that monolayer antimonene is a mechanical topological insulator by demonstrating a mapping between our continuum model and an underlying Dirac equation of the symmetry class BDI which is known to be a topological insulator in one dimension and a weak topological insulator in two dimensions. Monolayer antimony can be produced by exfoliation as well as epitaxy and the effects predicted in this paper should be accessible to standard experimental tools such as scanning probe microscopy and Raman spectroscopy. We surmise that the effects studied here (namely low scale symmetry breaking, strain solitons and gapless edge modes) are not limited to antimonene but are common features of two dimensional materials.

cond-mat.mes-hall↗

arXiv2018

Contact interactions and Kronig-Penney Models in Hermitian and PT-symmetric Quantum Mechanics

The delta function potential is a simple model of zero-range contact interaction in one dimension. The Kronig-Penney model is a one-dimensional periodic array of delta functions that models the energy bands in a crystal. Here we investigate contact interactions that generalize the delta function potential and corresponding generalizations of the Kronig-Penney model within conventional and parity-time symmetric quantum mechanics (PTQM). In conventional quantum mechanics we determine the most general contact interaction compatible with self-adjointness; in PTQM we consider interactions that are symmetric under the combined transformation PT. In both cases we find that the most general interaction has four independent real parameters; depending on the parameter values the interaction can support more bound states than the conventional delta function. In the PT case the two bound state energies can be both real or a complex conjugate pair, with the transition corresponding to the breaking of PT-symmetry. The scattering states for the PT case are also found to exhibit spontaneous breaking of PT-symmetry. We investigate the energy bands when the generalized contact interactions are repeated periodically in space in one dimension. In the Hermitian case we find that the two bound states result in two narrow bands generically separated by a gap. These bands intersect at a single point in the Brillouin zone as the interaction parameters are varied. Near the intersection the bands form a massless Dirac cone. In the PT-symmetric case, as the parameters of the contact interaction are varied the two bound state bands undergo a PT-symmetry breaking transition wherein the two band energies go from being real to being a complex conjugate pair. The PT-symmetric Kronig-Penney model provides a simple soluble example of the transition which has the same form as in other models of PT-symmetric crystals.

quant-ph↗

arXiv2018

The Effect of Forcing on Vacuum Radiation

Vacuum radiation has been the subject of theoretical study in both cosmology and condensed matter physics for many decades. Recently there has been impressive progress in experimental realizations as well. Here we study vacuum radiation when a field mode is driven both parametrically and by a classical source. We find that in the Heisenberg picture the field operators of the mode undergo a Bogolyubov transformation combined with a displacement, in the Schr\"odinger picture the oscillator evolves from the vacuum to a squeezed coherent state. Whereas the Bogolyubov transformation is the same as would be obtained if only the parametric drive were applied the displacement is determined by both the parametric drive and the force. If the force is applied well after the parametric drive then the displacement is the same as would be obtained by the action of the force alone and it is essentially independent of $t_f$, the time lag between the application of the force and the parametric drive. If the force is applied well before the parametric drive the displacement is found to oscillate as a function of $t_f$. This behavior can be understood in terms of quantum interference. A rich variety of behavior is observed for intermediate values of $t_f$. The oscillations can turn off smoothly or grow dramatically and decrease depending on strength of the parametric drive and force and the durations for which they are applied. The displacement depends only on the Fourier component of the force at a single resonant frequency when the forcing and the parametric drive are well separated in time. However for a weak parametric drive that is applied at the same time as the force we show that the displacement responds to a broad range of frequencies of the force spectrum. Implications of our findings for experiments are briefly discussed.

quant-ph↗

arXiv2018

The Radial Acceleration Relation and a Magnetostatic Analogy in Quasilinear MOND

Recently a remarkable relation has been demonstrated between the observed radial acceleration in disk galaxies and the acceleration predicted on the basis of baryonic matter alone. Here we study this relation within the framework of the modified gravity model MOND. The field equations of MOND automatically imply the radial acceleration relation for spherically symmetric galaxies, but for disk galaxies deviations from the relation are expected. Here we investigate whether these deviations are of sufficient magnitude to bring MOND into conflict with the observed relation. In the quasilinear formulation of MOND, to calculate the gravitational field of a given distribution of matter, an intermediate step is to calculate the "pristine field", which is a simple nonlinear function of the Newtonian field corresponding to the same distribution of matter. Hence, to the extent that the quasilinear gravitational field is approximately equal to the pristine field, the radial acceleration relation will be satisfied. We show that the difference between the quasilinear and pristine fields obeys the equations of magnetostatics, the curl of the pristine field serves as the source for the difference in the two fields, much as currents serve as sources for the magnetic field. Using the magnetostatic analogy we numerically study the difference between the pristine and quasilinear fields for simple model galaxies with a Gaussian profile. Our principal finding is that the difference between the fields is small compared to the observational uncertainties and that quasilinear MOND is therefore compatible with the observed radial acceleration relation.

astro-ph.GA↗

arXiv2017

The particle in a box in PT quantum mechanics and an electromagnetic analog

In PT quantum mechanics a fundamental principle of quantum mechanics, that the Hamiltonian must be hermitian, is replaced by another set of requirements, including notably symmetry under PT, where P denotes parity and T denotes time reversal. Here we study the role of boundary conditions in PT quantum mechanics by constructing a simple model that is the PT symmetric analog of a particle in a box. The model has the usual particle in a box Hamiltonian but boundary conditions that respect PT symmetry rather than hermiticity. We find that for a broad class of PT-symmetric boundary conditions the model respects the condition of unbroken PT-symmetry, namely that the Hamiltonian and the symmetry operator PT have simultaneous eigenfunctions, implying that the energy eigenvalues are real. We also find that the Hamiltonian is self-adjoint under the PT inner product. Thus we obtain a simple soluble model that fulfils all the requirements of PT quantum mechanics. In the second part of this paper we formulate a variational principle for PT quantum mechanics that is the analog of the textbook Rayleigh-Ritz principle. Finally we consider electromagnetic analogs of the PT-symmetric particle in a box. We show that the isolated particle in a box may be realized as a Fabry-Perot cavity between an absorbing medium and its conjugate gain medium. Coupling the cavity to an external continuum of incoming and outgoing states turns the energy levels of the box into sharp resonances. Remarkably we find that the resonances have a Breit-Wigner lineshape in transmission and a Fano lineshape in reflection; by contrast in the corresponding hermitian case the lineshapes always have a Breit-Wigner form in both transmission and reflection.

quant-ph↗

arXiv2017

An Electrostatic Analogy for Symmetron Gravity

The symmetron model is a scalar-tensor theory of gravity with a screening mechanism that suppresses the effect of the symmetron field at high densities characteristic of the solar system and laboratory scales but allows it to act with gravitational strength at low density on the cosmological scale. We elucidate the screening mechanism by showing that in the quasi-static Newtonian limit there are precise analogies between symmetron gravity and electrostatics for both strong and weak screening. For strong screening we find that large dense bodies behave in a manner analogous to perfect conductors in electrostatics. Based on this analogy we find that the symmetron field exhibits a lightning rod effect wherein the field gradients are enhanced near the ends of pointed or elongated objects. An ellipsoid placed in a uniform symmetron gradient is shown to experience a torque. By symmetry there is no gravitational torque in this case. Hence this effect unmasks the symmetron and might serve as the basis for future laboratory experiments. The symmetron force between a point mass and a large dense body includes a component corresponding to the interaction of the point mass with its image in the larger body. None of these effects have counterparts in the Newtonian limit of Einstein gravity. We discuss the similarities between symmetron gravity and the chameleon model as well as the differences between the two.

gr-qc↗

arXiv2016

An analysis of the LIGO discovery based on Introductory Physics

Binary black hole mergers are analyzed using concepts from introductory physics. Drawing upon Newtonian mechanics, dimensional considerations, and analogies between gravitational and electromagnetic waves, we are able to explain the principal features of LIGO's data and make order of magnitude estimates of key parameters of the event by inspection of the data. Our estimates of the black hole masses, the distance to the event, the initial separation of the pair, and the stupendous total amount of energy radiated are all in good agreement with the best fit values of these parameters obtained by the LIGO-VIRGO collaboration.

gr-qc↗

arXiv2016

Exploring extra dimensions with scalar waves

This paper provides a pedagogical introduction to the physics of extra dimensions focussing on the ADD, Randall-Sundrum and DGP models. In each of these models, the familiar particles and fields of the standard model are assumed to be confined to a four dimensional space-time called the brane; the brane is a slice through a higher dimensional space-time called the bulk. The geometry of the ADD, Randall-Sundrum and DGP space-times is described and the relation between Randall-Sundrum and Anti-de-Sitter space-time is explained. The necessary differential geometry background is introduced in an appendix that presumes no greater mathematical preparation than multivariable calculus. The ordinary wave equation and the Klein-Gordon equation are briefly reviewed followed by an analysis of the propagation of scalar waves in the bulk in all three extra-dimensional models. We also calculate the scalar field produced by a static point source located on the brane for all three models. For the ADD and Randall-Sundrum models at large distances the field looks like that of a point source in four space-time dimensions but at short distances it crosses over to a form appropriate to the higher dimensional space-time. For the DGP model the field has the higher dimensional form at long distances rather than short. The scalar field results provide qualitative insights into the corresponding behavior of gravitational fields. In particular the explanation within the ADD and Randall-Sundrum model of the weakness of gravity compared to other forces is discussed as are the implications of the two models for colliders and other experiments.

gr-qc↗