Fraile Detection of Solar $$-Modes by Fossat et al.

The internal gravity modes of the Sun are notoriously difficult to detect, and the claimed detection of gravity modes presented by Fossat et al. (Astron. Astrophys.604, A40, 2017) is thus very exciting. Given the importance of these modes for understanding solar structure and dynamics, the results must be robust. While Fossat et al. described their method and parameter choices in detail, the sensitivity of their results to several parameters was not presented. Therefore, we test the sensitivity of the results to a selection of the parameters. The most concerning result is that the detection vanishes when we adjust the start time of the 16.5-year velocity time-series by a few hours. We conclude that this reported detection of gravity modes is extremely fragile and should be treated with utmost caution.     

Propagating Linear Waves in Convectively Unstable Stellar Models: A Perturbative Approach

Linear time-domain simulations of acoustic oscillations are unstable in the stellar convection zone. To overcome this problem it is customary to compute the oscillations of a stabilized background stellar model. The stabilization affects the result, however. Here we propose to use a perturbative approach (running the simulation twice) to approximately recover the acoustic wave field while preserving seismic reciprocity. To test the method we considered a 1D standard solar model. We found that the mode frequencies of the (unstable) standard solar model are well approximated by the perturbative approach within 1 μHz for low-degree modes with frequencies near 3 mHz. We also show that the perturbative approach is appropriate for correcting rotational-frequency kernels. Finally, we comment that the method can be generalized to wave propagation in 3D magnetized stellar interiors because the magnetic fields have stabilizing effects on convection.     

High-Resolution Mapping of Flows in the Solar Interior: Fully Consistent OLA Inversion of Helioseismic Travel Times

To recover the flow information encoded in travel-time data of time?–?distance helioseismology, accurate forward modeling and a robust inversion of the travel times are required. We accomplish this using three-dimensional finite-frequency travel-time sensitivity kernels for flows along with a (2+1)-dimensional (2+1D) optimally localized averaging (OLA) inversion scheme. Travel times are measured by ridge filtering MDI full-disk Doppler data and the corresponding Born sensitivity kernels are computed for these particular travel times. We also utilize the full noise-covariance properties of the travel times, which allow us to accurately estimate the errors for all inversions. The whole procedure is thus fully consistent. Because of ridge filtering, the kernel functions separate in the horizontal and vertical directions, motivating our choice of a 2+1D inversion implementation. The inversion procedure also minimizes cross-talk effects among the three flow components, and the averaging kernels resulting from the inversion show very small amounts of cross-talk. We obtain three-dimensional maps of vector solar flows in the quiet Sun at horizontal spatial resolutions of 7?10 Mm using generally 24 hours of data. For all of the flow maps we provide averaging kernels and the noise estimates. We present examples to test the inferred flows, such as a comparison with Doppler data, in which we find a correlation of 0.9. We also present results for quiet-Sun supergranular flows at different depths in the upper convection zone. Our estimation of the vertical velocity shows good qualitative agreement with the horizontal vector flows. We also show vertical flows measured solely from f-mode travel times. In addition, we demonstrate how to directly invert for the horizontal divergence and flow vorticity. Finally we study inferred flow-map correlations at different depths and find a rapid decrease in this correlation with depth, consistent with other recent local helioseismic analyses.     

Seismic tomography of the near solar surface

Surface gravity waves have been used to probe flows in the two megameters beneath the photosphere using the techniques of timedistance helioseismology. The results suggest that supergranule velocities are smaller than at the surface. The outward flow outside a sunspot penumbra (the moat) is observed, as is an inward flow in the region beyond the moat.     

POLAR investigation of the Sun—POLARIS

The POLAR Investigation of the Sun (POLARIS) mission uses a combination of a gravity assist and solar sail propulsion to place a spacecraft in a 0.48 AU circular orbit around the Sun with an inclination of 75° with respect to solar equator. This challenging orbit is made possible by the challenging development of solar sail propulsion. This first extended view of the high-latitude regions of the Sun will enable crucial observations not possible from the ecliptic viewpoint or from Solar Orbiter. While Solar Orbiter would give the first glimpse of the high latitude magnetic field and flows to probe the solar dynamo, it does not have sufficient viewing of the polar regions to achieve POLARIS’s primary objective: determining the relation between the magnetism and dynamics of the Sun’s polar regions and the solar cycle.

Helioseismology of Time-Varying Flows Through The Solar Cycle

Flows in the upper convection zone are measured by helioseismology on a wide variety of scales. These include differential rotation and meridional circulation, local flows around complexes of magnetic activity and sunspots, and convective flows. The temporal evolution of flows through cycle 23 reveals connections between mass motions in the solar interior and the large-scale characteristics of the magnetic cycle. Here I summarize the latest observations and their implications. Observations from local helioseismology suggest that subsurface flows around active regions introduce a solar-cycle variation in the meridional circulation.     

3D Numerical Simulations of <Emphasis Type="Italic">f</Emphasis>-Mode Propagation Through Magnetic Flux Tubes

Three-dimensional numerical simulations have been used to study the scattering of a surface-gravity wave packet by vertical magnetic-flux tubes, with radii from 200 km to 3 Mm, embedded in stratified polytropic atmosphere. The scattered wave has been found to consist primarily of m=0 (axisymmetric) and m=1 modes. The ratio of the amplitude of these two modes was found to be strongly dependent on the radius of the flux tube. The kink mode is the dominant mode excited in tubes with a small radius, while the sausage mode is dominant for large tubes. Simulations of this type provide a simple, efficient, and robust way to start to understand the seismic signature of flux tubes, which have recently begun to be observed.     

Constructing Semi-Empirical Sunspot Models for Helioseismology

One goal of helioseismology is to determine the subsurface structure of sunspots. In order to do so, it is important to understand first the near-surface effects of sunspots on solar waves, which are dominant. Here we construct simplified, cylindrically-symmetric sunspot models that are designed to capture the magnetic and thermodynamics effects coming from about 500 km below the quiet-Sun τ ₅₀₀₀=1 level to the lower chromosphere. We use a combination of existing semi-empirical models of sunspot thermodynamic structure (density, temperature, pressure): the umbral model of Maltby et al. (1986, Astrophys. J. 306, 284) and the penumbral model of Ding and Fang (1989, Astron. Astrophys. 225, 204). The OPAL equation-of-state tables are used to derive the sound-speed profile. We smoothly merge the near-surface properties to the quiet-Sun values about 1 Mm below the surface. The umbral and penumbral radii are free parameters. The magnetic field is added to the thermodynamic structure, without requiring magnetostatic equilibrium. The vertical component of the magnetic field is assumed to have a Gaussian horizontal profile, with a maximum surface field strength fixed by surface observations. The full magnetic-field vector is solenoidal and determined by the on-axis vertical field, which, at the surface, is chosen such that the field inclination is 45° at the umbral – penumbral boundary. We construct a particular sunspot model based on SOHO/MDI observations of the sunspot in active region NOAA 9787. The helioseismic signature of the model sunspot is studied using numerical simulations of the propagation of f, p ₁, and p ₂ wave packets. These simulations are compared against cross-covariances of the observed wave field. We find that the sunspot model gives a helioseismic signature that is similar to the observations.     

Constructing and Characterising Solar Structure Models for Computational Helioseismology

In local helioseismology, numerical simulations of wave propagation are useful to model the interaction of solar waves with perturbations to a background solar model. However, the solution to the linearised equations of motion include convective modes that can swamp the helioseismic waves that we are interested in. In this article, we construct background solar models that are stable against convection, by modifying the vertical pressure gradient of Model S (Christensen-Dalsgaard et al., 1996, Science 272, 1286) relinquishing hydrostatic equilibrium. However, the stabilisation affects the eigenmodes that we wish to remain as close to Model S as possible. In a bid to recover the Model S eigenmodes, we choose to make additional corrections to the sound speed of Model S before stabilisation. No stabilised model can be perfectly solar-like, so we present three stabilised models with slightly different eigenmodes. The models are appropriate to study the f and p ₁ to p ₄ modes with spherical harmonic degrees in the range from 400 to 900. Background model CSM has a modified pressure gradient for stabilisation and has eigenfrequencies within 2% of Model S. Model CSM_A has an additional 10% increase in sound speed in the top 1 Mm resulting in eigenfrequencies within 2% of Model S and eigenfunctions that are, in comparison with CSM, closest to those of Model S. Model CSM_B has a 3% decrease in sound speed in the top 5 Mm resulting in eigenfrequencies within 1% of Model S and eigenfunctions that are only marginally adversely affected. These models are useful to study the interaction of solar waves with embedded three-dimensional heterogeneities, such as convective flows and model sunspots. We have also calculated the response of the stabilised models to excitation by random near-surface sources, using simulations of the propagation of linear waves. We find that the simulated power spectra of wave motion are in good agreement with an observed SOHO/MDI power spectrum. Overall, our convectively stabilised background models provide a good basis for quantitative numerical local helioseismology. The models are available for download from http://www.mps.mpg.de/projects/seismo/NA4/ .     

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.