arXiv subjects

Shravan M. Hanasoge

Publications and source records attributed to Shravan M. Hanasoge.

32 records · Page 2Linked to original sources

arXiv2017

Sensitivity of Helioseismic Measurements of Normal-mode Coupling to Flows and Sound-speed Perturbations

In this article, we derive and compute the sensitivity of measurements of coupling between normal modes of oscillation in the Sun to underlying flows. The theory is based on first-Born perturbation theory, and the analysis is carried out using the formalism described by \citet{lavely92}. Albeit tedious, we detail the derivation and compute the sensitivity of specific pairs of coupled normal modes to anomalies in the interior. Indeed, these kernels are critical for the accurate inference of convective flow amplitudes and large-scale circulations in the solar interior. We resolve some inconsistencies in the derivation of \citet{lavely92} and reformulate the fluid-continuity condition. We also derive and compute sound-speed kernels, paving the way for inverting for thermal anomalies alongside flows.

astro-ph.SR↗

arXiv2017

Numerical analysis of the lattice Boltzmann method for simulation of linear acoustic waves

We analyse a linear lattice Boltzmann (LB) formulation for simulation of linear acoustic wave propagation in heterogeneous media. We employ the single-relaxation-time Bhatnagar-Gross-Krook (BGK) as well as the general multi-relaxation-time (MRT) collision operators. By calculating the dispersion relation for various 2D lattices, we show that the D2Q5 lattice is the most suitable model for the linear acoustic problem. We also implement a grid-refinement algorithm for the LB scheme to simulate waves propagating in a heterogeneous medium with velocity contrasts. Our results show that the LB scheme performance is comparable to the classical second-order finite-difference schemes. Given its efficiency for parallel computation, the LB method can be a cost effective tool for the simulation of linear acoustic waves in complex geometries and multiphase media.

physics.comp-ph↗

arXiv2016

Strategies in seismic inference of supergranular flows on the Sun

Observations of the solar surface reveal the presence of flows with length scales of around $35$ Mm, commonly referred to as supergranules. Inferring the sub-surface flow profile of supergranules from measurements of the surface and photospheric wavefield is an important challenge faced by helioseismology. Traditionally, the inverse problem has been approached by studying the linear response of seismic waves in a horizontally translationally invariant background to the presence of the supergranule; following an iterative approach that does not depend on horizontal translational invariance might perform better, since the misfit can be analyzed post iterations. In this work, we construct synthetic observations using a reference supergranule, and invert for the flow profile using surface measurements of travel-times of waves belonging to modal ridges $f$ (surface-gravity) and $p_{1}$ through $p_{7}$ (acoustic). We study the extent to which individual modes and their combinations contribute to infer the flow. We show that this method of non-linear iterative inversion tends to underestimate the flow velocities as well as inferring a shallower flow profile, with significant deviations from the reference supergranule near the surface. We carry out a similar analysis for a sound-speed perturbation and find that analogous near-surface deviations persist, although the iterations converge faster and more accurately. We conclude that a better approach to inversion would be to expand the supergranule profile in an appropriate basis, thereby reducing the number of parameters being inverted for and appropriately regularizing them.

astro-ph.SR↗

arXiv2015

Simulating acoustic waves in spotted stars

Acoustic modes of oscillation are affected by stellar activity, however it is unclear how starspots contribute to these changes. Here we investigate the nonmagnetic effects of starspots on global modes with angular degree $\ell \leq 2$ in highly active stars, and characterize the spot seismic signature on synthetic light curves. We perform 3D time-domain simulations of linear acoustic waves to study their interaction with a model starspot. We model the spot as a 3D change in the sound speed stratification with respect to a convectively stable stellar background, built from solar Model S. We perform a parametric study by considering different depths and perturbation amplitudes. Exact numerical simulations allow the investigation of the wavefield-spot interaction beyond first order perturbation theory. The interaction of the axisymmetric modes with the starspot is strongly nonlinear. As mode frequency increases, the frequency shifts for radial modes exceed the value predicted by linear theory, while the shifts for the $\ell=2, m=0$ modes are smaller than predicted by linear theory, with avoided-crossing-like patterns forming between the $m=0$ and $m=1$ mode frequencies. The nonlinear behavior increases with increasing spot amplitude and/or decreasing depth. Linear theory still reproduces the correct shifts for nonaxisymmetric modes. In the nonlinear regime the mode eigenfunctions are not pure spherical harmonics, but rather a mixture of different spherical harmonics. This mode mixing, together with the frequency changes, may lead to misidentification of the modes in the observed acoustic power spectra.

astro-ph.SR↗

arXiv2013

The Quest to Understand Supergranulation and Large-Scale Convection in the Sun

Surface granulation of the Sun is primarily a consequence of thermal transport in the outer 1 % of the radius. Its typical scale of about 1 - 2 Mm is set by the balance between convection, free-streaming radiation, and the strong density stratification in the surface layers. The physics of granulation is well understood, as demonstrated by the close agreement between numerical simulation, theory, and observation. Superimposed on the energetic granular structure comprising high-speed flows, are larger scale long-lived flow systems (~ 300 m/s) called supergranules. Supergranulation has a typical scale of 24 - 36 Mm. It is not clear if supergranulation results from the interaction of granules or is causally linked to deep convection or a consequence of magneto-convection. Other outstanding questions remain: how deep are supergranules? How do they participate in global dynamics of the Sun? Further challenges are posed by our lack of insight into the dynamics of larger scales in the deep convection region. Recent helioseismic constraints have suggested that convective velocity amplitudes on large scales may be overestimated by an order of magnitude or more, implying that Reynolds stresses associated with large-scale convection, thought to play a significant role in the sustenance of differential rotation and meridional circulation, might be two orders of magnitude weaker than theory and computation predict. While basic understanding on the nature of convection on global scales and the maintenance of global circulations is incomplete, progress is imminent, given substantial improvements in computation, theory and helioseismic inferences.

astro-ph.SR↗

arXiv2013

Measurements and Kernels for Source-Structure Inversions in Noise Tomography

Seismic noise cross correlations are used to image crustal structure and heterogeneity. Typically, seismic networks are only anisotropically illuminated by seismic noise, a consequence of the non-uniform distribution of sources. Here, we study the sensitivity of such a seismic network to structural heterogeneity in a 2-D setting. We compute finite-frequency cross-correlation sensitivity kernels for travel-time, waveform-energy and waveform-difference measurements. In line with expectation, wavespeed anomalies are best imaged using travel times and the source distribution using cross-correlation energies. Perturbations in attenuation and impedance are very difficult to image and reliable inferences require a high degree of certainty in the knowledge of the source distribution and wavespeed model (at least in the case of transmission tomography studied here). We perform single-step Gauss-Newton inversions for the source distribution and the wavespeed, in that order, and quantify the associated Cramér-Rao lower bound. The inversion and uncertainty estimate are robust to errors in the source model but are sensitive to the theory used to interpret of measurements. We find that when classical source-receiver kernels are used instead of cross-correlation kernels, errors appear in the both the inversion and uncertainty estimate, systematically biasing the results. We outline a computationally tractable algorithm to account for distant sources when performing inversions.

astro-ph.EP↗

arXiv2012

The influence of noise sources on cross-correlation amplitudes

We use analytical examples and asymptotic forms to examine the mathematical structure and physical meaning of the seismic cross correlation measurement. We show that in general, cross correlations are not Green's functions of medium, and may be very different depending on the source distribution. The modeling of noise sources using spatial distributions as opposed to discrete collections of sources is emphasized. When stations are illuminated by spatially complex source distributions, cross correlations show arrivals at a variety of time lags, from zero to the maximum surface-wave arrival time. Here, we demonstrate the possibility of inverting for the source distribution using the energy of the full cross-correlation waveform. The interplay between the source distribution and wave attenuation in determining the functional dependence of cross correlation energies on station-pair distance is quantified. Without question, energies contain information about wave attenuation. However, the accurate interpretation of such measurements is tightly connected to the knowledge of the source distribution.

astro-ph.EP↗

arXiv2012

Subsurface Supergranular Vertical Flows as Measured Using Large Distance Separations in Time-Distance Helioseismology

As large--distance rays (say, 10\,-\,$24 ^\circ$) approach the solar surface approximately vertically, travel times measured from surface pairs for these large separations are mostly sensitive to vertical flows, at least for shallow flows within a few Mm of the solar surface. All previous analyses of supergranulation have used smaller separations and have been hampered by the difficulty of separating the horizontal and vertical flow components. We find that the large separation travel times associated with supergranulation cannot be studied using the standard phase-speed filters of time-distance helioseismology. These filters, whose use is based upon a refractive model of the perturbations, reduce the resultant travel time signal by at least an order of magnitude at some distances. More effective filters are derived. Modeling suggests that the center--annulus travel time difference $[δt_{\rm{oi}}]$ in the separation range $Δ=10$\,-\,$24 ^\circ$ is insensitive to the horizontally diverging flow from the centers of the supergranules and should lead to a constant signal from the vertical flow. Our measurement of this quantity, $5.1 \pm 0.1\secs$, is constant over the distance range. This magnitude of signal cannot be caused by the level of upflow at cell centers seen at the photosphere of $10\ms$ extended in depth. It requires the vertical flow to increase with depth. A simple Gaussian model of the increase with depth implies a peak upward flow of $240\ms$ at a depth of $2.3\Mm$ and a peak horizontal flow of $700\ms$ at a depth of $1.6\Mm$.

astro-ph.SR↗

arXiv2011

Lattice Boltzmann Method for Electromagnetic Wave Propagation

We present a new Lattice Boltzmann (LB) formulation to solve the Maxwell equations for electromagnetic (EM) waves propagating in a heterogeneous medium. By using a pseudo-vector discrete Boltzmann distribution, the scheme is shown to reproduce the continuum Maxwell equations. The technique compares well with a pseudo-spectral method at solving for two-dimensional wave propagation in a heterogeneous medium, which by design contains substantial contrasts in the refractive index. The extension to three dimensions follows naturally and, owing to the recognized efficiency of LB schemes for parallel computation in irregular geometries, it gives a powerful method to numerically simulate a wide range of problems involving EM wave propagation in complex media.

astro-ph.IM↗

arXiv2009

A Wave Scattering Theory of Solar Seismic Power Haloes

Spatial maps of the high-pass frequency filtered time-averaged root-mean-squared (RMS) Doppler velocities tend to show substantial decrements within regions of strong field and curiously, randomly distributed patches of enhancement in the vicinity. We propose that these haloes or enhancements are a consequence of magnetic-field-induced mode mixing (scattering), resulting in the preferential powering of waves that possess strong surface velocity signatures (i.e. scattering from low to high wavenumbers). Evidently, this process can occur in the reverse, and therefore in order to determine if the haloes are indeed caused by mode mixing, we must answer the question: {\it how are acoustic waves scattered by magnetic fields?} Through simulations of the interactions between waves and sunspots and models of plage, we demonstrate that the high to low modal order scattering channels are favoured. With increasing frequency and consequently, decreasing wavelength, a growing number of modes are scattered by the sunspot, thereby rendering the enhancements most visible around the high-frequency parts of the spectrum. The haloes obtained from the simulations are on the same order of magnitude but weaker than those observed. We also present observational evidence to support this theory: observations of active region AR9787 are firstly frequency filtered to isolate the 5-6 mHz signals and secondly, decomposed into three wavenumber bandpasses, $l - [0,400], [400,800], [800,2222]$. With increasing wavenumber, the extent of the halo effect is seen increase dramatically, in line with theoretical expectation.

astro-ph.SR↗

arXiv2009

Measuring Meridional Circulation in the Sun

Measuring the depth variation of the meridional flows is important for understanding the solar cycle, at least according to a number of dynamo models. While attempting to extend the early observations of \citet{giles_thesis} of time-distance measurements of flow, we have stumbled upon some systematic errors that can affect these measurements: 1) the additional distance traveled by radiation coming from points away from disk center causes an apparent `shrinking' Sun, that is an apparent flow towards the disk center and 2) in measurements away from the central longitude, the rotation signal can leak into meridional flow signals. Attempts to understand and overcome these systematic problems will be presented. Forward models based on ray theory have been applied in order to test the sensitivity of travel times to various models.

astro-ph.SR↗

arXiv2008

Multiple scattering of waves by a pair of gravitationally stratified flux tubes

We study the near-field coupling of a pair of flux tubes embedded in a gravitationally stratified environment. The mutual induction of the near-field {\it jackets} of the two flux tubes can considerably alter the scattering properties of the system, resulting in sizable changes in the magnitudes of scattering coefficients and bizarre trends in the phases. The dominant length scale governing the induction zone turns out to be approximately half the horizontal wave length of the incident mode, a result that fits in quite pleasantly with extant theories of scattering. Higher-$β$ flux tubes are more strongly coupled than weaker ones, a consequence of the greater role that the near-field jacket modes play in the such tubes. We also comment on the importance of incorporating the effects of multiple scattering when studying the effects of mode absorption in plage and interpreting related scattering measurements. That the near-field plays such an important role in the scattering process lends encouragement to the eventual goal of observationally resolving sub-wavelength features of flux tubes using techniques of helioseismology.

astro-ph↗

arXiv2008

Sub-Wavelength Resolution Imaging of the Solar Deep Interior

We derive expectations for signatures in the measured travel times of waves that interact with thermal anomalies and jets. A series of numerical experiments that involve the dynamic linear evolution of an acoustic wave field in a solar-like stratified spherical shell in the presence of fully 3D time-stationary perturbations are performed. The imprints of these interactions are observed as shifts in wave travel times, which are extracted from these data through methods of time-distance helioseismology \citep{duvall}. In situations where at least one of the spatial dimensions of the scatterer was smaller than a wavelength, oscillatory time shift signals were recovered from the analyses, pointing directly to a means of resolving sub-wavelength features. As evidence for this claim, we present analyses of simulations with spatially localized jets and sound-speed perturbations. We analyze 1 years' worth solar observations to estimate the noise level associated with the time differences. Based on theoretical estimates, Fresnel zone time shifts associated with the (possible) sharp rotation gradient at the base of the convection zone are of the order 0.01 - 0.1 s, well below the noise level that could be reached with the currently available amount of data ($\sim 0.15-0.2$ s with 10 yrs of data).

astro-ph↗

arXiv2008

Seismic Halos Around Active Regions: An MHD Theory

Comprehending the manner in which magnetic fields affect propagating waves is a first step toward constructing accurate helioseismic models of active region sub-surface structure and dynamics. Here, we present a numerical method to compute the linear interaction of waves with magnetic fields embedded in a solar-like stratified background. The ideal Magneto-Hydrodynamic (MHD) equations are solved in a 3-dimensional box that straddles the solar photosphere, extending from 35 Mm within to 1.2 Mm into the atmosphere. One of the challenges in performing these simulations involves generating a Magneto-Hydro-Static (MHS) state wherein the stratification assumes horizontal inhomogeneity in addition to the strong vertical stratification associated with the near-surface layers. Keeping in mind that the aim of this effort is to understand and characterize linear MHD interactions, we discuss a means of computing statically consistent background states. Power maps computed from simulations of waves interacting with thick flux tubes of peak photospheric field strengths 600 G and 3000 G are presented. Strong modal power reduction in the `umbral' regions of the flux tube enveloped by a halo of increased wave power are seen in the simulations with the thick flux tubes. These enhancements are also seen in Doppler velocity power maps of active regions observed in the Sun, leading us to propose that the halo has MHD underpinnings.

astro-ph↗