Numerical simulations of multiple scattering of the f−f-mode by flux tubes

We use numerial simulations to study the absorption and phase shift of surface-gravity waves caused by groups of magnetic flux tubes. The dependence of the scattering coefficients with the distance between the tubes and their positions is analyzed for several cases with two or three flux tubes embedded in a quiet Sun atmosphere. The results are compared with those obtained neglecting completely or partially multiple scattering effects. We show that multiple scattering has a significant impact on the absorption measurements and tends to reduce the phase shift. We also consider more general cases of ensembles of randomly distributed flux tubes, and we have evaluated the effects on the scattering measurements of changing the number of tubes included in the bundle and the average distance between flux tubes. We find that for the longest wavelength incoming waves multiple scattering enhances the absorption, and its efficiency increases with the number of flux tubes and the reduction of the distance between them.Comment: Accepted for publication in The Astrophysical Journa

Evaluation of the capability of local helioseismology to discern between monolithic and spaghetti sunspot models

The helioseismic properties of the wave scattering generated by monolithic and spaghetti sunspots are analyzed by means of numerical simulations. In these computations, an incident f or p1 mode travels through the sunspot model, which produces absorption and phase shift of the waves. The scattering is studied by inspecting the wavefield, computing travel-time shifts, and performing Fourier-Hankel analysis. The comparison between the results obtained for both sunspot models reveals that the differences in the absorption coefficient can be detected above noise level. The spaghetti model produces an steep increase of the phase shift with the degree of the mode at short wavelengths, while mode-mixing is more efficient for the monolithic model. These results provide a clue for what to look for in solar observations to discern the constitution of sunspots between the proposed monolithic and spaghetti models.Comment: Accepted for publication in The Astrophysical Journa

Helioseismic holography of simulated sunspots: magnetic and thermal contributions to travel times

Wave propagation through sunspots involves conversion between waves of acoustic and magnetic character. In addition, the thermal structure of sunspots is very different than that of the quiet Sun. As a consequence, the interpretation of local helioseismic measurements of sunspots has long been a challenge. With the aim of understanding these measurements, we carry out numerical simulations of wave propagation through sunspots. Helioseismic holography measurements made from the resulting simulated wavefields show qualitative agreement with observations of real sunspots. We use additional numerical experiments to determine, separately, the influence of the thermal structure of the sunspot and the direct effect of the sunspot magnetic field. We use the ray approximation to show that the travel-time shifts in the thermal (non-magnetic) sunspot model are primarily produced by changes in the wave path due to the Wilson depression rather than variations in the wave speed. This shows that inversions for the subsurface structure of sunspots must account for local changes in the density. In some ranges of horizontal phase speed and frequency there is agreement (within the noise level in the simulations) between the travel times measured in the full magnetic sunspot model and the thermal model. If this conclusion proves to be robust for a wide range of models, it would suggest a path towards inversions for sunspot structure.Comment: Accepted for publication in The Astrophysical Journa

Validating Forward Modeling and Inversions of Helioseismic Holography Measurements

Here we use synthetic data to explore the performance of forward models and inverse methods for helioseismic holography. Specifically, this work presents the first comprehensive test of inverse modeling for flows using lateral-vantage (deep-focus) holography. We derive sensitivity functions in the Born approximation. We then use these sensitivity functions in a series of forward models and inversions of flows from a publicly available magnetohydrodynamic quiet-Sun simulation. The forward travel times computed using the kernels generally compare favorably with measurements obtained by applying holography, in a lateral-vantage configuration, on a 15-hour time series of artificial Dopplergrams extracted from the simulation. Inversions for the horizontal flow components are able to reproduce the flows in the upper 3Mm of the domain, but are compromised by noise at greater depths.Comment: accepted for publication by the Astrophysical

Testing Helioseismic-Holography Inversions for Supergranular Flows Using Synthetic Data

Supergranulation is one of the most visible length scales of solar convection and has been studied extensively by local helioseismology. We use synthetic data computed with the Seismic Propagation through Active Regions and Convection (SPARC) code to test regularized-least squares (RLS) inversions of helioseismic holography measurements for a supergranulation-like flow. The code simulates the acoustic wavefield by solving the linearized three-dimensional Euler equations in Cartesian geometry. We model a single supergranulation cell with a simple, axisymmetric, mass-conserving flow. The use of simulated data provides an opportunity for direct evaluation of the accuracy of measurement and inversion techniques. The RLS technique applied to helioseismic-holography measurements is generally successful in reproducing the structure of the horizontal flow field of the model supergranule cell. The errors are significant in horizontal-flow inversions near the top and bottom of the computational domain as well as in vertical-flow inversions throughout the domain. We show that the errors in the vertical velocity are due largely to cross talk from the horizontal velocity.Comment: 22 pages, 12 figues, accepted for publication in Solar Physic

Helioseismology of Pre-Emerging Active Regions II: Average Emergence Properties

We report on average subsurface properties of pre-emerging active regions as compared to areas where no active region emergence was detected. Helioseismic holography is applied to samples of the two populations (pre-emergence and without emergence), each sample having over 100 members, which were selected to minimize systematic bias, as described in Leka et al. We find that there are statistically significant signatures (i.e., difference in the means of more than a few standard errors) in the average subsurface flows and the apparent wave speed that precede the formation of an active region. The measurements here rule out spatially extended flows of more than about 15 m/s in the top 20 Mm below the photosphere over the course of the day preceding the start of visible emergence. These measurements place strong constraints on models of active region formation.Comment: 15 pages, 10 figures, ApJ (published

Reconstruction of Solar Subsurfaces by Local Helioseismology

Local helioseismology has opened new frontiers in our quest for understanding of the internal dynamics and dynamo on the Sun. Local helioseismology reconstructs subsurface structures and flows by extracting coherent signals of acoustic waves traveling through the interior and carrying information about subsurface perturbations and flows, from stochastic oscillations observed on the surface. The initial analysis of the subsurface flow maps reconstructed from the 5 years of SDO/HMI data by time-distance helioseismology reveals the great potential for studying and understanding of the dynamics of the quiet Sun and active regions, and the evolution with the solar cycle. In particular, our results show that the emergence and evolution of active regions are accompanied by multi-scale flow patterns, and that the meridional flows display the North-South asymmetry closely correlating with the magnetic activity. The latitudinal variations of the meridional circulation speed, which are probably related to the large-scale converging flows, are mostly confined in shallow subsurface layers. Therefore, these variations do not necessarily affect the magnetic flux transport. The North-South asymmetry is also pronounced in the variations of the differential rotation ("torsional oscillations"). The calculations of a proxy of the subsurface kinetic helicity density show that the helicity does not vary during the solar cycle, and that supergranulation is a likely source of the near-surface helicity.Comment: 17 pages, 10 figures, in "Cartography of the Sun and the Stars", Editors: Rozelot, Jean-Pierre, Neiner, Corali

Precise measurements of UV atomic lines: Hyperfine structure and isotope shifts in the 398.8 nm line of Yb

We demonstrate a technique for frequency measurements of UV transitions with sub-MHz precision. The frequency is measured using a ring-cavity resonator whose length is calibrated against a reference laser locked to the $D_2$ line of $^{87}$Rb. We have used this to measure the 398.8 nm ${^1S}_0 \leftrightarrow {^1P}_1$ line of atomic Yb. We report isotope shifts of all the seven stable isotopes, including the rarest isotope $^{168}$Yb. We have been able to resolve the overlapping $^{173}$Yb($F = 3/2$) and $^{172}$Yb transitions for the first time. We also obtain high-precision measurements of excited-state hyperfine structure in the odd isotopes, $^{171}$Yb and $^{173}$Yb. The measurements resolve several discrepancies among earlier measurements.Comment: 7 pages, 6 figure

SDO/HMI survey of emerging active regions for helioseismology

Observations from the Solar Dynamics Observatory (SDO) have the potential for allowing the helioseismic study of the formation of hundreds of active regions, which would enable us to perform statistical analyses. Our goal is to collate a uniform data set of emerging active regions observed by the SDO/HMI instrument suitable for helioseismic analysis up to seven days before emergence. We restricted the sample to active regions that were visible in the continuum and emerged into quiet Sun largely avoiding pre-existing magnetic regions. As a reference data set we paired a control region (CR), with the same latitude and distance from central meridian, with each emerging active region (EAR). We call this data set, which is currently comprised of 105 emerging active regions observed between May 2010 and November 2012, the SDO Helioseismic Emerging Active Region (SDO/HEAR) survey. To demonstrate the utility of a data set of a large number of emerging active regions, we measure the relative east-west velocity of the leading and trailing polarities from the line-of-sight magnetogram maps during the first day after emergence. The latitudinally averaged line-of-sight magnetic field of all the EARs shows that, on average, the leading (trailing) polarity moves in a prograde (retrograde) direction with a speed of 121 +/- 22 m/s (-70 +/- 13 m/s) relative to the Carrington rotation rate in the first day. However, relative to the differential rotation of the surface plasma, the east-west velocity is symmetric, with a mean of 95 +/- 13 m/s. The SDO/HEAR data set will not only be useful for helioseismic studies, but will also be useful to study other features such as the surface magnetic field evolution of a large sample of EARs.Comment: Accepted by Astronomy and Astrophysics, 11 figures, one longtable; update corrects units in Figure