Time-distance helioseismology and related techniques show great promise for probing the structure and dynamics of the subphotospheric layers of the Sun. Indeed time-distance helioseismology has already been applied to make inferences about structures and flows under sunspots and active regions, to map long-lived convective flow patterns, and so on. Yet certainly there are still many inadequacies in the current approaches and, as the data get better and the questions we seek to address get more subtle, methods that were previously regarded as adequate are no longer acceptable. Here we give a short and partial description of outstanding problems in local helioseismology, using time-distance helioseismology as a guiding example.
Near-surface flows measured by the ring-diagram technique of local helioseismology show structures that persist over multiple rotations. We examine these phenomena using data from the {\em Global Oscillation Network Group} (GONG) and the {\em Helioseismic and Magnetic Imager} (HMI) and show that a correlation analysis of the structures can be used to estimate the rotation rate as a function of latitude, giving a result consistent with the near-surface rate from global helioseismology and slightly slower than that obtained from a similar analysis of the surface magnetic field strength. At latit…
Context. Several upcoming helioseismology space missions are very limited in telemetry and will have to perform extensive data compression. This requires the development of new methods of data compression. Aims. We give an overview of the influence of lossy data compression on local helioseismology. We investigate the effects of several lossy compression methods (quantization, JPEG compression, and smoothing and subsampling) on power spectra and time-distance measurements of supergranulation flows at disk center. Methods. We applied different compression methods to tracked and remapped Doppler…
We discuss current advances in forward and inverse modeling for local helioseismology. We report theoretical uniqueness results, in particular the Novikov-Agaltsov reconstruction algorithm, which is relevant to solving the non-linear inverse problem of time-distance helioseismology (finite amplitude pertubations to the medium). Numerical experiments were conducted to determine the number of frequencies required to reconstruct density and sound speed in the solar interior.
Time-distance helioseismology is a set of powerful tools to study features below the Sun's surface. Inverse methods are needed to interpret time-distance measurements, with many examples in the literature. However, techniques that utilize a more statistical approach to inferences, and broadly used in the astronomical community, are less-commonly found in helioseismology. This article aims to introduce a potentially powerful inversion scheme based on Bayesian probability theory and Monte Carlo sampling that is suitable for local helioseismology. We describe the probabilistic method and how it i…
The study of solar oscillations (helioseismology) has been a very successful method of researching the Sun. Helioseismology teaches us about the structure and mean properties of the Sun. Together with mid-resolution data, the local properties were uncovered in quiet-Sun regions. However, magnetic fields affect the oscillations and prevent us from studying the properties of magnetically active regions with helioseismology. We aim to create a new methodology to suppress the negative effects of magnetic fields on solar oscillations and measure plasma properties close to active regions. The method…
The purpose of deep-focusing time--distance helioseismology is to construct seismic measurements that have a high sensitivity to the physical conditions at a desired target point in the solar interior. With this technique, pairs of points on the solar surface are chosen such that acoustic ray paths intersect at this target (focus) point. Considering acoustic waves in a homogeneous medium, we compare travel-time and amplitude measurements extracted from the deep-focusing cross-covariance functions. Using a single-scattering approximation, we find that the spatial sensitivity of deep-focusing tr…
Flow vorticity is a fundamental property of turbulent convection in rotating systems. Solar supergranules exhibit a preferred sense of rotation, which depends on the hemisphere. This is due to the Coriolis force acting on the diverging horizontal flows. We aim to spatially resolve the vertical flow vorticity of the average supergranule at different latitudes, both for outflow and inflow regions. To measure the vertical vorticity, we use two independent techniques: time-distance helioseismology (TD) and local correlation tracking of granules in intensity images (LCT) using data from the Heliose…
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…
A set of 464-min high-resolution high-cadence observations were acquired for a region near the Sun's disk center using the Interferometric BI-dimensional Spectrometer (IBIS) installed at the Dunn Solar Telescope. Ten sets of Dopplergrams are derived from the bisector of the spectral line corresponding approximately to different atmospheric heights, and two sets of Dopplergrams are derived using MDI-like algorithm and center-of-gravity method. These data are then filtered to keep only acoustic modes, and phase shifts are calculated between Doppler velocities of different atmospheric heights as …
Local helioseismology provides a unique opportunity to investigate the subsurface structure and dynamics of active regions and their effect on the large-scale flows and global circulation of the Sun. We use measurements of plasma flows in the upper convection zone, provided by the Time-Distance Helioseismology Pipeline developed for analysis of solar oscillation data obtained by Helioseismic and Magnetic Imager (HMI) on Solar Dynamics Observatory (SDO), to investigate the subsurface dynamics of emerging active region NOAA 11726. The active region emergence was detected in deep layers of the co…
Local helioseismology has so far relied on semi-analytical methods to compute the spatial sensitivity of wave travel times to perturbations in the solar interior. These methods are cumbersome and lack flexibility. Here we propose a convenient framework for numerically solving the forward problem of time-distance helioseismology in the frequency domain. The fundamental quantity to be computed is the cross-covariance of the seismic wavefield. We choose sources of wave excitation that enable us to relate the cross-covariance of the oscillations to the Green's function in a straightforward manner.…
The interpretation of helioseismic measurements, such as wave travel-time, is based on the computation of kernels that give the sensitivity of the measurements to localized changes in the solar interior. These are computed using the ray or the Born approximation. The Born approximation is preferable as it takes finite-wavelength effects into account, but can be computationally expensive. We propose a fast algorithm to compute travel-time sensitivity kernels under the assumption that the background solar medium is spherically symmetric. Kernels are typically expressed as products of Green's fun…
Understanding the Travel-time Asymmetry of Acoustic Waves in Sunspots With Time-distance Helioseismology
Peking University（北京大学）；National Space Science Center, Chinese Academy of Sciences（中国科学院国家空间科学中心）；Instituto de Astrofísica de Canarias（加那利天体物理研究所）；Universidad de La Laguna（拉古纳大学）；Indian Institute of Astrophysics（印度天体物理研究所）；KU Leuven（荷语鲁汶大学）
Context. Local helioseismology has detected spatially extended converging surface flows into solar active regions. These play an important role in flux-transport models of the solar dynamo. Aims. We aim to validate the existence of the inflows by deriving horizontal flow velocities around active regions with local correlation tracking of granulation. Methods. We generate a six-year long-time series of full-disk maps of the horizontal velocity at the solar surface by tracking granules in continuum intensity images provided by the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics…
We extend an existing Born approximation method for calculating the linear sensitivity of helioseismic travel times to flows from Cartesian to spherical geometry. This development is necessary for using the Born approximation for inferring large-scale flows in the deep solar interior. In a first sanity check, we compare two $f-$mode kernels from our spherical method and from an existing Cartesian method. The horizontal and total integrals agree to within 0.3 %. As a second consistency test, we consider a uniformly rotating Sun and a travel distance of 42 degrees. The analytical travel-time dif…
Continuous high-cadence and high-spatial resolution Dopplergrams allow us to study sub-surface dynamics that may be further extended to explore precursors of visible solar activity on the surface. Since the p-mode power is absorbed in the regions of high magnetic field, the inferences in these regions are often presumed to have large uncertainties. In this paper, using the Dopplergrams from space-borne Helioseismic Magnetic Imager (HMI), we compare horizontal flows in a shear layer below the surface and the photospheric layer in and around active regions. The photospheric flows are calculated …
In this dissertation, several components of large-scale solar flows are studied observationally: solar equatorial Rossby waves (waves of radial vorticity), large-scale convection, and surface flows around active regions. Maps of horizontal flows are derived from photospheric observations by the Helioseismic and Magnetic Imager (HMI) aboard the Solar Dynamics Observatory (SDO) using two different techniques: granulation tracking and local helioseismology. First, the eigenfunctions of solar Rossby waves are measured from helioseismic ring-diagram flow maps with a correlation method and a spectra…
Context. In local helioseismology, the travel times of acoustic waves propagating in opposite directions along the same meridian inform us about horizontal flows in the north-south direction. The longitudinal averages of the north-south helioseismic travel-time shifts vary with the sunspot cycle. Aims. We aim to study the contribution of inflows into solar active regions to this solar-cycle variation. Methods. To do so, we identify the local flows around active regions in the horizontal flow maps obtained from correlation tracking of granulation in SDO/HMI continuum images. We compute the forw…
A crucial feature not widely accounted for in local helioseismology is that surface magnetic regions actually open a window from the interior into the solar atmosphere, and that the seismic waves leak through this window, reflect high in the atmosphere, and then re-enter the interior to rejoin the seismic wave field normally confined there. In a series of recent numerical studies using translation invariant atmospheres, we utilised a "directional time-distance helioseismology" measurement scheme to study the implications of the returning fast and Alfvén waves higher up in the solar atmosphere …
Recent hydrodynamical simulations of convection in a solar-like model suggest that penetrative convective flows at the boundary of the convective envelope modify the thermal background in the overshooting layer. Based on these results, we implement in one-dimensional stellar evolution codes a simple prescription to modify the temperature gradient below the convective boundary of a solar model. This simple prescription qualitatively reproduces the behaviour found in the hydrodynamical simulations, namely a local heating and smoothing of the temperature gradient below the convective boundary. We…
Improving the Understanding of Subsurface Structure and Dynamics of Solar Active Regions (A white paper submitted to the decadal survey for solar and space Physics (Heliophysics) -- SSPH 2024-2033)
The inference of flows of material in the interior of the Sun is a subject of major interest in helioseismology. Here we apply techniques of Full Waveform Inversion (FWI) to synthetic data to test flow inversions. In this idealized setup, we do not model seismic realization noise, training the focus entirely on the problem of whether a chosen supergranulation flow model can be seismically recovered. We define the misfit functional as a sum of L_2 norm deviations in travel times between prediction and observation, as measured using short-distance f and p_1 filtered and large-distance unfiltered…
