arXiv subjects

Bradley W. Hindman

Publications and source records attributed to Bradley W. Hindman.

At least 37 records · Page 2Linked to original sources

arXiv2018

Exploring the Influence of Density Contrast on Solar Near-Surface Shear

The advent of helioseismology has determined in detail the average rotation rate of the Sun as a function of radius and latitude. These data immediately reveal two striking boundary layers of shear in the solar convection zone (CZ): a tachocline at the base, where the differential rotation of the CZ transitions to solid-body rotation in the radiative zone, and a 35-Mm-thick near-surface shear layer (NSSL) at the top, where the rotation rate slows by about 5% with increasing radius. Though asteroseismology cannot probe the differential rotation of distant stars to the same level of detail that helioseismology can achieve for the Sun, it is possible that many cool stars with outer convective envelopes possess similar differential rotation characteristics, including both a tachocline and a NSSL. Here we present the results of 3D global hydrodynamic simulations of spherical-shell convection for a Sun-like star at different levels of density contrast across the shell. The simulations with high stratification possess characteristics of near-surface shear, especially at low latitudes. We discuss in detail the dynamical balance of torques giving rise to the NSSL in our models and interpret what these balances imply for the real Sun. We further discuss the dynamical causes that may serve to wipe out near-surface shear at high latitudes, and conclude by offering some theories as to how this problem might be tackled in future work.

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arXiv2018

The Role of Downflows in Establishing Solar Near-Surface Shear

The dynamical origins of the Sun's tachocline and near-surface shear layer (NSSL) are still not well understood. We have attempted to self-consistently reproduce a NSSL in numerical simulations of a solar-like convection zone by increasing the density contrast across rotating, 3D spherical shells. We explore the hypothesis that high density contrast leads to near-surface shear by creating a rotationally unconstrained layer of fast flows near the outer surface. Although our high-contrast models do have near-surface shear, it is confined primarily to low latitudes (between $\pm15^\circ$). Two distinct types of flow structures maintain the shear dynamically: rotationally $\textit{constrained}$ Busse columns aligned with the rotation axis and fast, rotationally $\textit{unconstrained}$ downflow plumes that deplete angular momentum from the outer fluid layers. The plumes form at all latitudes, and in fact are more efficient at transporting angular momentum inward at high latitudes. The presence of Busse columns at low latitudes thus appears essential to creating near-surface shear in our models. We conclude that a solar-like NSSL is unobtainable from a rotationally unconstrained outer fluid layer alone. In numerical models, the shear is eliminated through the advection of angular momentum by the meridional circulation. Therefore, a detailed understanding how the solar meridional circulation is dynamically achieved will be necessary to elucidate the origin of the Sun's NSSL.

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arXiv2018

A Novel Approach to Resonant Absorption of the Fast MHD Eigenmodes of a Coronal Arcade

The arched field lines forming coronal arcades are often observed to undulate as magnetohydrodynamic (MHD) waves propagate both across and along the magnetic field. These waves are most likely a combination of resonantly coupled fast magnetoacoustic waves and Alfvén waves. The coupling results in resonant absorption of the fast waves, converting fast wave energy into Alfvén waves. The fast eigenmodes of the arcade have proven difficult to compute or derive analytically, largely because of the mathematical complexity that the coupling introduces. When a traditional spectral decomposition is employed, the discrete spectrum associated with the fast eigenmodes is often subsumed into the continuous Alfvén spectrum. Thus fast eigenmodes, become collective modes or quasi-modes. Here we present a spectral decomposition that treats the eigenmodes as having real frequencies but complex wavenumbers. Using this procedure we derive dispersion relations, spatial damping rates, and eigenfunctions for the resonant, fast eigenmodes of the arcade. We demonstrate that resonant absorption introduces a fast mode that would not exist otherwise. This new mode is heavily damped by resonant absorption, only travelling a few wavelengths before losing most of its energy.

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arXiv2018

Prandtl-Number Effects in High-Rayleigh-Number Spherical Convection

Convection is the predominant mechanism by which energy and angular momentum are transported in the outer portion of the Sun. The resulting overturning motions are also the primary energy source for the solar magnetic field. An accurate solar dynamo model therefore requires a complete description of the convective motions, but these motions remain poorly understood. Studying stellar convection numerically remains challenging; it occurs within a parameter regime that is extreme by computational standards. The fluid properties of the convection zone are characterized in part by the Prandtl number $\mathrm{Pr}=ν/κ$, where $ν$ is the kinematic viscosity and $κ$ is the thermal diffusion; in stars, $\mathrm{Pr}$ is extremely low, $\mathrm{Pr}\approx 10^{-7}$. The influence of $\mathrm{Pr}$ on the convective motions at the heart of the dynamo is not well understood since most numerical studies are limited to using $\mathrm{Pr}\approx1$. We systematically vary $\mathrm{Pr}$ and the degree of thermal forcing, characterized through a Rayleigh number, to explore its influence on the convective dynamics. For sufficiently large thermal driving, the simulations reach a so-called convective free-fall state where diffusion no longer plays an important role in the interior dynamics. Simulations with a lower $\mathrm{Pr}$ generate faster convective flows and broader ranges of scales for equivalent levels of thermal forcing. Characteristics of the spectral distribution of the velocity remain largely insensitive to changes in $\mathrm{Pr}$. Importantly, we find that $\mathrm{Pr}$ plays a key role in determining when the free-fall regime is reached by controlling the thickness of the thermal boundary layer.

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arXiv2016

The Emergence of Solar Supergranulation as a Natural Consequence of Rotationally-Constrained Interior Convection

We investigate how rotationally-constrained, deep convection might give rise to supergranulation, the largest distinct spatial scale of convection observed in the solar photosphere. While supergranulation is only weakly influenced by rotation, larger spatial scales of convection sample the deep convection zone and are presumably rotationally influenced. We present numerical results from a series of nonlinear, 3-D simulations of rotating convection and examine the velocity power distribution realized under a range of Rossby numbers. When rotation is present, the convective power distribution possesses a pronounced peak, at characteristic wavenumber $\ell_\mathrm{peak}$, whose value increases as the Rossby number is decreased. This distribution of power contrasts with that realized in non-rotating convection, where power increases monotonically from high to low wavenumbers. We find that spatial scales smaller than $\ell_\mathrm{peak}$ behave in analogy to non-rotating convection. Spatial scales larger than $\ell_\mathrm{peak}$ are rotationally-constrained and possess substantially reduced power relative to the non-rotating system. We argue that the supergranular scale emerges due to a suppression of power on spatial scales larger than $\ell\approx100$ owing to the presence of deep, rotationally-constrained convection. Supergranulation thus represents the largest non-rotationally-constrained mode of solar convection. We conclude that the characteristic spatial scale of supergranulation bounds that of the deep convective motions from above, making supergranulation an indirect measure of the deep-seated dynamics at work in the solar dynamo. Using the spatial scale of supergranulation in conjunction with our numerical results, we estimate an upper bound of 10 m s$^{-1}$ for the Sun's bulk rms convective velocity.

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arXiv2015

Eigenmodes of three-dimensional magnetic arcades in the Sun's corona

We develop a model of coronal-loop oscillations that treats the observed bright loops as an integral part of a larger 3-D magnetic structure comprised of the entire magnetic arcade. We demonstrate that magnetic arcades within the solar corona can trap MHD fast waves in a 3-D waveguide. This is accomplished through the construction of a cylindrically symmetric model of a magnetic arcade with a potential magnetic field. For a magnetically dominated plasma, we derive a governing equation for MHD fast waves and from this equation we show that the magnetic arcade forms a 3-D waveguide if the Alfvén speed increases monotonically beyond a fiducial radius. Both magnetic pressure and tension act as restoring forces, instead of just tension as is generally assumed in 1-D models. Since magnetic pressure plays an important role, the eigenmodes involve propagation both parallel and transverse to the magnetic field. Using an analytic solution, we derive the specific eigenfrequencies and eigenfunctions for an arcade possessing a discontinuous density profile. The discontinuity separates a diffuse cylindrical cavity and an overlying shell of denser plasma that corresponds to the bright loops. We emphasize that all of the eigenfunctions have a discontinuous axial velocity at the density interface; hence, the interface can give rise to the Kelvin-Helmholtz instability. Further, we find that all modes have elliptical polarization with the degree of polarization changing with height. However, depending on the line of sight, only one polarization may be clearly visible.

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arXiv2015

The Spectral Amplitude of Stellar Convection and its Scaling in the High-Rayleigh-Number Regime

Convection plays a central role in the dynamics of any stellar interior, and yet its operation remains largely-hidden from direct observation. As a result, much of our understanding concerning stellar convection necessarily derives from theoretical and computational models. The Sun is, however, exceptional in that regard. The wealth of observational data afforded by its proximity provides a unique testbed for comparing convection models against observations. When such comparisons are carried out, surprising inconsistencies between those models and observations become apparent. Both photospheric and helioseismic measurements suggest that convection simulations may overestimate convective flow speeds on large spatial scales. Moreover, many solar convection simulations have difficulty reproducing the observed solar differential rotation due to this apparent overestimation. We present a series of 3-dimensional (3-D) stellar convection simulations designed to examine how the amplitude and spectral distribution of convective flows are established within a star's interior. While these simulations are non-magnetic and non-rotating in nature, they demonstrate two robust phenomena. When run with sufficiently high Rayleigh number, the integrated kinetic energy of the convection becomes effectively independent of thermal diffusion, but the spectral distribution of that kinetic energy remains sensitive to both of these quantities. A simulation that has converged to a diffusion-independent value of kinetic energy will divide that energy between spatial scales such that low-wavenumber power is overestimated, and high-wavenumber power is underestimated relative to a comparable system possessing higher Rayleigh number. We discuss the implications of these results in light of the current inconsistencies between models and observations.

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arXiv2015

Helioseismic Imaging of Fast Convective Flows Throughout the Near-Surface Shear Layer

Using a new implementation of ring-diagram helioseismology, we ascertain the strength and spatial scale of convective flows throughout the near-surface shear layer. Our ring-diagram technique employs highly overlapped analysis regions and an efficient method of 3D inversion to measure convective motions with a resolution that ranges from $3 \ \mathrm{Mm}$ at the surface to $80 \ \mathrm{Mm}$ at the base of the layer. We find the rms horizontal flow speed to peak at $427 \ \mathrm{m \ s^{-1}}$ at the photosphere and fall to a minimum of $124 \ \mathrm{m \ s^{-1}}$ between $20 \ \mathrm{Mm}$ and $30 \ \mathrm{Mm}$. From the velocity amplitude and the dominant horizontal scales seen at each depth, we infer the level of rotational influence on convection to be low near the surface, but transition to a significant level at the base of the near-surface shear layer with a Rossby number varying between 2.2 to as low as 0.1.

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arXiv2014

Five-minute oscillation power within magnetic elements in the solar atmosphere

It has long been known that magnetic plage and sunspots are regions in which the power of acoustic waves is reduced within the photospheric layers. Recent observations now suggest that this suppression of power extends into the low chromosphere and is also present in small magnetic elements far from active regions. In this paper we investigate the observed power supression in plage and magnetic elements, by modelling each as a collection of vertically aligned magnetic fibrils and presuming that the velocity within each fibril is the response to buffeting by incident $p$ modes in the surrounding field-free atmosphere. We restrict our attention to modeling observations made near solar disk center, where the line-of-sight velocity is nearly vertical and hence, only the longitudinal component of the motion within the fibril contributes. Therefore, we only consider the excitation of axisymmetric sausage waves and ignore kink oscillations as their motions are primarily horizontal. We compare the vertical motion within the fibril with the vertical motion of the incident $p$ mode by constructing the ratio of their powers. In agreement with observational measurements we find that the total power is suppressed within strong magnetic elements for frequencies below the acoustic cut-off frequency. We also find that the magnitude of the power deficit increases with the height above the photosphere at which the measurement is made. Further, we argue that the area of the solar disk over which the power suppression extends increases as a function of height.

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arXiv2014

Multi-Ridge Fitting for Ring-Diagram Helioseismology

Inferences of sub-surface flow velocities using local domain ring-diagram helioseismology depend on measuring the frequency splittings of oscillation modes seen in acoustic power spectra. Current methods for making these measurements utilize maximum-likelihood fitting techniques to match a model of modal power to the spectra. The model typically describes a single oscillation mode, and each mode in a given power spectrum is fit independently. We present a new method that produces measurements with greater reliability and accuracy by fitting multiple modes simultaneously. We demonstrate how this method permits measurements of sub-surface flows deeper into the Sun while providing higher uniformity in data coverage and velocity response closer to the limb of the solar disk. While the previous fitting method performs better for some measurements of low-phase-speed modes, we find this new method to be particularly useful for high phase-speed modes and small spatial areas.

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arXiv2013

An Interpretation of Flare-Induced and Decayless Coronal-Loop Oscillations as Interference Patterns

We present an alternative model of coronal-loop oscillations which considers that the waves are trapped in a 2D waveguide formed by the entire arcade of field lines. This differs from the standard 1D model which treats the waves as the resonant oscillations of just the visible bundle of field lines. Within the framework of our 2D model, the two types of oscillations that have been observationally identified, flare-induced waves and "decayless" oscillations, can both be attributed to MHD fast waves. The two components of the signal differ only because of the duration and spatial extent of the source that creates them. The flare-induced waves are generated by strong localized sources of short duration, while the decayless background can be excited by a continuous, stochastic source. Further, the oscillatory signal arising from a localized, short-duration source can be interpreted as a pattern of interference fringes produced by waves that have traveled diverse routes of various pathlengths through the waveguide. The resulting amplitude of the fringes slowly decays in time with an inverse square root dependence. The details of the interference pattern depend on the shape of the arcade and the spatial variation of the Alfvén speed. The rapid decay of this wave component, which has previously been attributed to physical damping mechanisms that remove energy from resonant oscillations, occurs as a natural consequence of the interference process without the need for local dissipation.

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arXiv2013

Equilibrium models of coronal loops that involve curvature and buoyancy

We construct magnetostatic models of coronal loops in which the thermodynamics of the loop is fully consistent with the shape and geometry of the loop. This is achieved by treating the loop as a thin, compact, magnetic fibril that is a small departure from a force-free state. The density along the loop is related to the loop's curvature by requiring that the Lorentz force arising from this deviation is balanced by buoyancy. This equilibrium, coupled with hydrostatic balance and the ideal gas law, then connects the temperature of the loop with the curvature of the loop without resorting to a detailed treatment of heating and cooling. We present two example solutions: one with a spatially invariant magnetic Bond number (the dimensionless ratio of buoyancy to Lorentz forces) and the other with a constant radius of curvature of the loop's axis. We find that the density and temperature profiles are quite sensitive to curvature variations along the loop, even for loops with similar aspect ratios.

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arXiv2012

Kink Oscillations of a Curved, Gravitationally Stratified Coronal Loop

Loops of magnetic field in the corona are observed to oscillate and these oscillations have been posited to be the superposition of resonant kink waves. To date, most analyses of these oscillations have concentrated on calculating the frequency shifts that result from spatial variation in the kink wave speed. Further, most have ignored gravity and treated the loop as a straight tube. Here we ignore spatial variation in the wave speed, but self-consistently include the effects of gravity and loop curvature in both the equilibrium loop model and in the wave equation. We model a coronal loop as an isolated, thin, magnetic fibril that is anchored at two points in the photosphere. The equilibrium shape of the loop is determined by a balance between magnetic buoyancy and magnetic tension, which is characterized by a Magnetic Bond Number ε, that is typically small |ε| << 1. This balance produces a loop that has a variable radius of curvature. The resonant kink waves of such a loop come in two polarizations that are decoupled from each other: waves with motion completely within the plane of the loop (normal oscillations) and waves with motions that are completely horizontal, perpendicular to the plane of the loop (binormal oscillations). We solve for the eigensolutions of both polarizations using perturbation theory for small Magnetic Bond Number. For modes of the same order, normal oscillations have smaller eigenfrequencies than binormal oscillations. The additional forces of buoyancy and magnetic tension from the curvature of the loop increase and decrease the mode frequencies, respectively. The ratio of the frequencies of the first overtone to the fundamental mode is modified by the inclusion of buoyancy and curvature. We find that the normal polarization possesses a frequency ratio that exceeds the canonical value of 2, whereas the binormal polarization has a ratio less than 2.

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arXiv2011

An Improved Method for Fitting p-Mode Profile Asymmetries

In a power spectrum of the Sun's acoustic waves, the p modes have distinctly skewed frequency profiles. Furthermore, the asymmetry is observed to have the opposite sign in power spectra made from line-of-sight velocity and continuum intensity. The asymmetry and its reversal in sign has previously been explained using a combination of mechanisms that involve the acoustic source. A localized acoustic source within an acoustic cavity naturally generates asymmetric profiles through wave interference; however, the sign of the asymmetry due to this mechanism is identical for all observables. The reversal of the asymmetry between velocity and intensity observations has been attributed to the visibility of the source itself (i.e., "correlated noise"). In this paper, I will show that asymmetry generated by a localized source can be interpreted as either a wave interference effect in physical space, or a mode interference effect in spectral space. I advocate a new mode-fitting procedure based on this new interpretation, whereby the complex phases of all the modes determine the mode asymmetries. Further, I suggest that information about the acoustic source function is encapsulated in the amplitude of each mode, and present a scheme by which the source function can be obtained from measured mode amplitudes by standard helioseismic inversion techniques.

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arXiv2011

Axisymmetric Scattering of p Modes by Thin Magnetic Tubes

We examine the scattering of acoustic p-mode waves from a thin magnetic fibril embedded in a gravitationally stratified atmosphere. The scattering is mediated through the excitation of slow sausage waves on the magnetic tube, and only the scattering of the monopole component of the wavefield is considered. Since such tube waves are not confined by the acoustic cavity and may freely propagate along the field lines removing energy from the acoustic wavefield, the excitation of fibril oscillations is a source of acoustic wave absorption as well as scattering. We compute the mode mixing that is achieved and the absorption coefficients and phase shifts. We find that for thin tubes the mode mixing is weak and the absorption coefficient is small and is a smooth function of frequency over the physically relevant band of observed frequencies. The prominent absorption resonances seen in previous studies of unstratified tubes are absent. Despite the relatively small absorption, the phase shift induced can be surprisingly large, reaching values as high as 15 degree for f modes. Further, the phase shift can be positive or negative depending on the incident mode order and the frequency.

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arXiv2011

Gyroscopic Pumping in the Solar Near-Surface Shear Layer

We use global and local helioseismic inversions to explore the prevailing dynamical balances in the solar Near-Surface Shear Layer (NSSL). The differential rotation and meridional circulation are intimately linked, with a common origin in the turbulent stresses of the upper solar convection zone. The existence and structure of the NSSL cannot be attributed to the conservation of angular momentum by solar surface convection, as is often supposed. Rather, the turbulent angular momentum transport accounts for the poleward meridional flow while the often overlooked meridional force balance maintains the mid-latitude rotational shear. We suggest that the base of the NSSL is marked by a transition from baroclinic to turbulent stresses in the meridional plane which suppress Coriolis-induced circulations that would otherwise establish a cylindrical rotation profile. The turbulent angular momentum transport must be non-diffusive and directed radially inward. Inferred mean flows are consistent with the idea that turbulent convection tends to mix angular momentum but only if the mixing efficiency is inhomogeneous and/or anisotropic. The latitudinal and longitudinal components of the estimated turbulent transport are comparable in amplitude and about an order of magnitude larger than the vertical component. We estimate that it requires 2--4% of the solar luminosity to maintain the solar NSSL against the inertia of the mean flow. Most of this energy is associated with the turbulent transport of angular momentum out of the layer, with a spin-down time scale of $\sim$ 600 days. We also address implications of these results for numerical modeling of the NSSL.

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arXiv2009

Helioseismic detection of deep meridional flow

Steady meridional flow makes no first-order perturbation to the frequencies of helioseismic normal modes. It does, however, Doppler shift the local wavenumber, thereby distorting the eigenfunctions. For high-degree modes, whose peaks in a power spectrum are blended into continuous ridges, the effect of the distortion is to shift the locations of those ridges. From this blended superposition of modes, one can isolate oppositely directed wave components with the same local horizontal wavenumber and measure a frequency difference which can be safely used to infer the subsurface background flow. But such a procedure fails for the components of the more-deeply-penetrating low-degree modes that are not blended into ridges. Instead, one must analyze the spatial distortions explicitly. With a simple toy model, we illustrate one method by which that might be accomplished by measuring the spatial variation of the oscillation phase. We estimate that by this procedure it might be possible to infer meridional flow deep in the solar convection zone.

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arXiv2009

Subsurface Circulations within Active Regions

Using high-resolution ring analysis (HRRA) we deduce subsurface flows within magnetic active regions and within quiet sun. With this procedure we are capable of measuring flows with a horizontal spatial resolution of 2 degrees in heliographic angle (or roughly 20 Mm). From the resulting flow fields we deduce mean inflow rates into active regions, mean circulation speeds around active regions, and probability density functions (PDFs) of properties of the flow field. These analyses indicate that active regions have a zonal velocity that exceeds that of quiet sun at the same latitude by 20 m/s, yet active regions advect poleward at the same rate as quiet sun. We also find that almost all active regions possess a mean inflow (20-30 m/s) and a cyclonic circulation (~5 m/s) at their peripheries, whereas their cores, where the sunspots are located, are zones of strong anticyclonic outflow (~50 m/s). From the PDFs, we find that active regions modify the structure of convection with a scale greater than that of supergranulation. Instead of possessing an asymmetry between inflows and outflows (with a larger percentage of the surface occupied by outflows), as is seen in quiet sun, active regions possess symmetric distributions.

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