Shravan M. Hanasoge

Anomalously weak solar convection

Convection in the solar interior is thought to comprise structures on a spectrum of scales. This conclusion emerges from phenomenological studies and numerical simulations, though neither covers the proper range of dynamical parameters of solar convection. Here, we analyze observations of the wavefield in the solar photosphere using techniques of time-distance helioseismology to image flows in the solar interior. We downsample and synthesize 900 billion wavefield observations to produce 3 billion cross-correlations, which we average and fit, measuring 5 million wave travel times. Using these travel times, we deduce the underlying flow systems and study their statistics to bound convective velocity magnitudes in the solar interior, as a function of depth and spherical-harmonic degree ℓ. Within the wavenumber band ℓ < 60, convective velocities are 20–100 times weaker than current theoretical estimates. This constraint suggests the prevalence of a different paradigm of turbulence from that predicted by existing models, prompting the question: what mechanism transports the heat flux of a solar luminosity outwards? Advection is dominated by Coriolis forces for wavenumbers ℓ < 60, with Rossby numbers smaller than approximately 10-2 at r/R⊙ = 0.96, suggesting that the Sun may be a much faster rotator than previously thought, and that large-scale convection may be quasi-geostrophic. The fact that isorotation contours in the Sun are not coaligned with the axis of rotation suggests the presence of a latitudinal entropy gradient.

Seismic constraints on rotation of Sun-like star and mass of exoplanet

Rotation is thought to drive cyclic magnetic activity in the Sun and Sun-like stars. Stellar dynamos, however, are poorly understood owing to the scarcity of observations of rotation and magnetic fields in stars. Here, inferences are drawn on the internal rotation of a distant Sun-like star by studying its global modes of oscillation. We report asteroseismic constraints imposed on the rotation rate and the inclination of the spin axis of the Sun-like star HD 52265, a principal target observed by the CoRoT satellite that is known to host a planetary companion. These seismic inferences are remarkably consistent with an independent spectroscopic observation (rotational line broadening) and with the observed rotation period of star spots. Furthermore, asteroseismology constrains the mass of exoplanet HD 52265b. Under the standard assumption that the stellar spin axis and the axis of the planetary orbit coincide, the minimum spectroscopic mass of the planet can be converted into a true mass of , which implies that it is a planet, not a brown dwarf.

Computational acoustics in spherical geometry : Steps toward validating helioseismology

Throughout the past decade, detailed helioseismic analyses of observations of solar surface oscillations have led to advances in our knowledge of the structure and dynamics of the solar interior. Such analyses involve the decomposition of time series of the observed surface oscillation pattern into its constituent wave modes, followed by inversion procedures that yield inferences of properties of the solar interior. While this inverse problem has been a major focus in recent years, the corresponding forward problem has received much less attention. We aim to rectify this situation by taking the first steps toward validating and determining the efficacy of the helioseismic measurement procedure. The goal of this effort is to design a means to perform differential studies of various effects such as flows and thermal perturbations on helioseismic observables such as resonant frequencies, travel-time shifts, etc. Here we describe our first efforts to simulate wave propagation within a spherical shell, which extends from 0.2 to about 1.0004 R☉ (where R☉ is the radius of the Sun) and which possesses a solar-like stratification. We consider a model containing no flows that will serve as a reference model for later studies. We discuss the computational procedure, some difficulties encountered in a simulation of this kind, and the means to overcome them. We also present techniques used to validate the simulation.

Validation of Helioseismology through Forward Modeling: Realization Noise Subtraction and Kernels

Through a series of numerical simulations of the near-surface acoustic wavefield of the Sun, we show the utility of the forward approach in local helioseismology. We demonstrate and apply a method to subtract a large fraction of the realization noise from the simulated data. The ability to attain high signal-to-noise ratios from brief forward calculations implies that computational resources are less of a bottleneck, making this alternate method for investigations of the solar interior very feasible. We put this method to use by deriving sensitivity kernels for sound-speed perturbations and source suppression for the background state in our computations using techniques of time-distance helioseismology, all from merely 48 hr of artificial data.

Validated helioseismic inversions for 3D vector flows

Context. According to time‐distance helioseismology, information about internal fluid motions is encoded in the travel times of solar waves. The inverse problem consists of inferring three-dimensional vector flows from a set of travel-time measurements. While only few tests of the inversions have been done, it is known that the retrieval of the small-amplitude vertical flow velocities is problematic. A thorough study of biases and noise has not been carried out in realistic conditions. Aims. Here we investigate the potential of time‐distance helioseismology to infer three-dimensional convective velocities in the near-surface layers of the Sun. We developed a new Subtractive Optimally Localised Averaging (SOLA) code suitable for pipeline pseudo-automatic processing. Compared to its predecessor, the code was improved by accounting for additional constraints in order to get the right answer within a given noise level. The main aim of this study is to validate results obtained by our inversion code. Methods. We simulate travel-time maps using a snapshot from a numerical simulation of solar convective flows, realistic Born traveltime sensitivity kernels, and a realistic model of travel-time noise. These synthetic travel times are inverted for flows and the results compared with the known input flow field. Additional constraints are implemented in the inversion: cross-talk minimization between flow components and spatial localization of inversion coe cients. Results. Using modes f , p1 through p4, we show that horizontal convective flow velocities can be inferred without bias, at a signal-tonoise ratio greater than one in the top 3.5 Mm, provided that observations span at least four days. The vertical component of velocity (vz), if it were to be weak, is more di cult to infer and is seriously a ected by cross-talk from horizontal velocity components. We emphasise that this cross-talk must be explicitly minimised in order to retrieve vz in the top 1 Mm. We also show that statistical averaging over many di erent areas of the Sun allows for reliably measuring of average properties of all three flow components in the top 5.5 Mm of the convection zone.

THE ADJOINT METHOD APPLIED TO TIME-DISTANCE HELIOSEISMOLOGY

For a given misfit function, a specified optimality measure of a model, its gradient describes the manner in which one may alter properties of the system to march toward a stationary point. The adjoint method, arising from partial-differential-equation-constrained optimization, describes a means of extracting derivatives of a misfit function with respect to model parameters through finite computation. It relies on the accurate calculation of wavefields that are driven by two types of sources, namely, the average wave-excitation spectrum, resulting in the forward wavefield, and differences between predictions and observations, resulting in an adjoint wavefield. All sensitivity kernels relevant to a given measurement emerge directly from the evaluation of an interaction integral involving these wavefields. The technique facilitates computation of sensitivity kernels (Frechet derivatives) relative to three-dimensional heterogeneous background models, thereby paving the way for nonlinear iterative inversions. An algorithm to perform such inversions using as many observations as desired is discussed.

SEISMIC CONSTRAINTS ON INTERIOR SOLAR CONVECTION

We constrain the velocity spectral distribution of global-scale solar convective cells at depth using techniques of local helioseismology. We calibrate the sensitivity of helioseismic waves to large-scale convective cells in the interior by analyzing simulations of waves propagating through a velocity snapshot of global solar convection via methods of time-distance helioseismology. Applying identical analysis techniques to observations of the Sun, we are able to bound from above the magnitudes of solar convective cells as a function of spatial convective scale. We find that convection at a depth of r/R ☉ = 0.95 with spatial extent l < 20, where l is the spherical harmonic degree, comprises weak flow systems, on the order of 15 m s–1 or less. Convective features deeper than r/R ☉ = 0.95 are more difficult to image due to the rapidly decreasing sensitivity of helioseismic waves.

SCATTERING OF ACOUSTIC WAVES BY A MAGNETIC CYLINDER: ACCURACY OF THE BORN APPROXIMATION

With the aim of studying magnetic effects in time-distance helioseismology, we use the first-order Born approximation to compute the scattering of acoustic plane waves by a magnetic cylinder embedded in a uniform medium. We show, by comparison with the exact solution, that the travel-time shifts computed in the Born approximation are everywhere valid to first order in the ratio of the magnetic to the gas pressures. We also show that for arbitrary magnetic field strength, the Born approximation is not valid in the limit where the radius of the magnetic cylinder tends to zero.

NUMERICAL MODELS OF TRAVEL-TIME INHOMOGENEITIES IN SUNSPOTS

We investigate the direct contribution of strong, sunspot-like magnetic fields to helioseismic wave travel-time shifts via two numerical forward models, a three-dimensional ideal MHD solver and MHD ray theory. The simulated data cubes are analyzed using the traditional time-distance center-to-annulus measurement technique. We also isolate and analyze the direct contribution from purely thermal perturbations to the observed travel-time shifts, confirming some existing ideas and bringing forth new ones: (i) that the observed travel-time shifts in the vicinity of sunspots are largely governed by MHD physics, (ii) the travel-time shifts are sensitively dependent on frequency and phase-speed filter parameters and the background power below the p 1 ridge, and finally, (iii) despite its seeming limitations, ray theory succeeds in capturing the essence of the travel-time variations as derived from the MHD simulations.

Multichannel Three-Dimensional SOLA Inversion for Local Helioseismology

Inversions for local helioseismology are an important and necessary step for obtaining three-dimensional maps of various physical quantities in the solar interior. Frequently, the full inverse problems that one would like to solve prove intractable because of computational constraints. Due to the enormous seismic data sets that already exist and those forthcoming, this is a problem that needs to be addressed. To this end, we present a very efficient linear inversion algorithm for local helioseismology. It is based on a subtractive optimally localized averaging (SOLA) scheme in the Fourier domain, utilizing the horizontal-translation invariance of the sensitivity kernels. In Fourier space the problem decouples into many small problems, one for each horizontal wave vector. This multichannel SOLA method is demonstrated for an example problem in time–distance helioseismology that is small enough to be solved both in real and Fourier space. We find that both approaches are successful in solving the inverse problem. However, the multichannel SOLA algorithm is much faster and can easily be parallelized.