arXiv subjects

T. L. Duvall Jr

Publications and source records attributed to T. L. Duvall Jr.

7 recordsLinked to original sources

arXiv2020

Acoustic wave propagation through solar granulation: Validity of effective-medium theories, coda waves

Context. The frequencies, lifetimes, and eigenfunctions of solar acoustic waves are affected by turbulent convection, which is random in space and in time. Since the correlation time of solar granulation and the periods of acoustic waves ($\sim$5 min) are similar, the medium in which the waves propagate cannot a priori be assumed to be time independent. Aims. We compare various effective-medium solutions with numerical solutions in order to identify the approximations that can be used in helioseismology. For the sake of simplicity, the medium is one dimensional. Methods. We consider the Keller approximation, the second-order Born approximation, and spatial homogenization to obtain theoretical values for the effective wave speed and attenuation (averaged over the realizations of the medium). Numerically, we computed the first and second statistical moments of the wave field over many thousands of realizations of the medium (finite-amplitude sound-speed perturbations are limited to a 30 Mm band and have a zero mean). Results. The effective wave speed is reduced for both the theories and the simulations. The attenuation of the coherent wave field and the wave speed are best described by the Keller theory. The numerical simulations reveal the presence of coda waves, trailing the coherent wave packet. These late arrival waves are due to multiple scattering and are easily seen in the second moment of the wave field. Conclusions. We find that the effective wave speed can be calculated, numerically and theoretically, using a single snapshot of the random medium (frozen medium); however, the attenuation is underestimated in the frozen medium compared to the time-dependent medium. Multiple scattering cannot be ignored when modeling acoustic wave propagation through solar granulation.

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arXiv2018

Acoustic tomography of solar convective flows and structures

We present a new method for helioseismic diagnostics of the three-dimensional structure of sound speed, magnetic fields and flow velocities in the convection zone by inversion of acoustic travel-time data. The data are measurements of the time for acoustic waves to travel between points on the solar surface and surrounding annuli obtained from continuous observations at the South Pole in 1991 and from high-resolution observations from the Solar and Heliospheric Observatory (SOHO) in 1996. The travel time of the waves depends primarily on the sound speed perturbations and the velocity of flow along the ray paths. The effects of the sound speed perturbations and flows can be separated by measuring the travel time of waves propagating in opposite directions along the same ray paths. Magnetic fields result in anisotropy of the wave speed. A 3D inversion method based on Fermat's Principle and a regularized least-squares technique have been applied to infer the properties of convection in the quiet Sun and in active regions.

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arXiv2012

Systematic Center-to-Limb Variation in Measured Helioseismic Travel Times and Its Effect on Inferences of Solar Interior Meridional Flows

We report on a systematic center-to-limb variation in measured helioseismic travel times, which must be taken into account for an accurate determination of solar interior meridional flows. The systematic variation, found in time-distance helioseismology analysis using SDO/HMI and SDO/AIA observations, is different in both travel-time magnitude and variation trend for different observables. It is not clear what causes this systematic effect. Subtracting the longitude-dependent east-west travel times, obtained along the equatorial area, from the latitude-dependent north-south travel times, obtained along the central meridian area, gives remarkably similar results for different observables. We suggest this as an effective procedure for removing the systematic center-to-limb variation. The subsurface meridional flows obtained from inversion of the corrected travel times are approximately 10 m/s slower than those obtained without removing the systematic effect. The detected center-to-limb variation may have important implications in the derivation of meridional flows in the deep interior, and needs a better understanding.

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arXiv2011

Investigation of a Sunspot Complex by Helioseismology

Sunspot regions often form complexes of activity that may live for several solar rotations, and represent a major component of the Sun's magnetic activity. It had been suggested that the close appearance of active regions in space and time might be related to common subsurface roots, or "nests" of activity. EUV images show that the active regions are magnetically connected in the corona, but subsurface connections have not been established. We investigate the subsurface structure and dynamics of a large complex of activity, NOAA 10987-10989, observed during the SOHO/MDI Dynamics run in March-April 2008, which was a part of the Whole Heliospheric Interval (WHI) campaign. The active regions in this complex appeared in a narrow latitudinal range, probably representing a subsurface toroidal flux tube. We use the MDI full-disk Dopplergrams to measure perturbations of travel times of acoustic waves traveling to various depths by using time-distance helioseismology, and obtain sound-speed and flow maps by inversion of the travel times. The subsurface flow maps show an interesting dynamics of decaying active regions with persistent shearing flows, which may be important for driving the flaring and CME activity, observed during the WHI campaign. Our analysis, including the seismic sound-speed inversion results and the distribution of deep-focus travel-time anomalies, gave indications of diverging roots of the magnetic structures, as could be expected from $Ω$-loop structures. However, no clear connection in the depth range of 0-48 Mm among the three active regions in this complex of activity was detected.

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arXiv2010

Local helioseismology of sunspot regions: comparison of ring-diagram and time-distance results

Local helioseismology provides unique information about the subsurface structure and dynamics of sunspots and active regions. However, because of complexity of sunspot regions local helioseismology diagnostics require careful analysis of systematic uncertainties and physical interpretation of the inversion results. We present new results of comparison of the ring-diagram analysis and time-distance helioseismology for active region NOAA 9787, for which a previous comparison showed significant differences in the subsurface sound-speed structure, and discuss systematic uncertainties of the measurements and inversions. Our results show that both the ring-diagram and time-distance techniques give qualitatively similar results, revealing a characteristic two-layer seismic sound-speed structure consistent with the results for other active regions. However, a quantitative comparison of the inversion results is not straightforward. It must take into account differences in the sensitivity, spatial resolution and the averaging kernels. In particular, because of the acoustic power suppression, the contribution of the sunspot seismic structure to the ring-diagram signal can be substantially reduced. We show that taking into account this effect reduces the difference in the depth of transition between the negative and positive sound-speed variations inferred by these methods. Further detailed analysis of the sensitivity, resolution and averaging properties of the local helioseismology methods is necessary for consolidation of the inversion results. It seems to be important that both methods indicate that the seismic structure of sunspots is rather deep and extends to at least 20 Mm below the surface, putting constraints on theoretical models of sunspots.

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arXiv2008

Helioseismology of Sunspots: Confronting Observations with Three-Dimensional MHD Simulations of Wave Propagation

The propagation of solar waves through the sunspot of AR 9787 is observed using temporal cross-correlations of SOHO/MDI Dopplergrams. We then use three-dimensional MHD numerical simulations to compute the propagation of wave packets through self-similar magneto-hydrostatic sunspot models. The simulations are set up in such a way as to allow a comparison with observed cross-covariances (except in the immediate vicinity of the sunspot). We find that the simulation and the f-mode observations are in good agreement when the model sunspot has a peak field strength of 3 kG at the photosphere, less so for lower field strengths. Constraining the sunspot model with helioseismology is only possible because the direct effect of the magnetic field on the waves has been fully taken into account. Our work shows that the full-waveform modeling of sunspots is feasible.

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arXiv2007

Time-distance helioseismology: Sensitivity of f-mode travel times to flows

Time-distance helioseismology has shown that f-mode travel times contain information about horizontal flows in the Sun. The purpose of this study is to provide a simple interpretation of these travel times. We study the interaction of surface-gravity waves with horizontal flows in an incompressible, plane-parallel solar atmosphere. We show that for uniform flows less than roughly 250 m s$^{-1}$, the travel-time shifts are linear in the flow amplitude. For stronger flows, perturbation theory up to third order is needed to model waveforms. The case of small-amplitude spatially-varying flows is treated using the first-order Born approximation. We derive two-dimensional Fréchet kernels that give the sensitivity of travel-time shifts to local flows. We show that the effect of flows on travel times depends on wave damping and on the direction from which the observations are made. The main physical effect is the advection of the waves by the flow rather than the advection of wave sources or the effect of flows on wave damping. We compare the two-dimensional sensitivity kernels with simplified three-dimensional kernels that only account for wave advection and assume a vertical line of sight. We find that the three-dimensional f-mode kernels approximately separate in the horizontal and vertical coordinates, with the horizontal variations given by the simplified two-dimensional kernels. This consistency between quite different models gives us confidence in the usefulness of these kernels for interpreting quiet-Sun observations.

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