Supergranules are divergent 30-Mm sized cellular flows observed everywhere at the solar photosphere. Their place in the hierarchy of convective structures and their origin remain poorly understood (Rincon et al., 2018). Estimating supergranular depth is of particular interest since this may help point to the underlying physics. However, their subsurface velocity profiles have proven difficult to ascertain. Birch et al. (2006) had suggested that helioseismic inferences would benefit from an ensemble average over multiple realizations of supergranules due to the reduction in realization noise. Bhattacharya et al. (2017) used synthetic forward-modelled seismic wave travel times and demonstrated the potential of helioseismic inversions at recovering the flow profile of an average supergranule that is separable in the horizontal and vertical directions, although the premise of this calculation has since been challenged by Ferret (2019). In this work we avoid this assumption and carry out a validation test of helioseismic travel-time inversions starting from plausible synthetic non-separable profiles of an average supergranule. We compute seismic wave travel times and sensitivity kernels by simulating wave propagation through this background. We find that, while the ability to recover the exact profile degrades based on the number of parameters involved, we are nevertheless able to recover the peak depth of our models in a few iterations where the measurements are presumably above the noise cutoff. This represents an important step towards unraveling the physics behind supergranules, as we start appreciating the parameters that we may reliably infer from a time-distance helioseismic inversion.
We analyze spectral properties of solar convection in the range of depths from 0 to 19~Mm using subsurface flow maps obtained by the time-distance heiioseismology analysis of solar-oscillation data from the Helioseismic and Magnetic Imager (HMI) onboard Solar Dynamics Observatory (SDO) from May 2010 to September 2020. The results reveal a rapid increase of the horizontal flow scales with the depth, from supergranulation to giant-cell scales, and support the evidence of large-scale convection, previously detected by tracking the motion of supergranular cells on the surface. The total power of c…
Solar supergranulation presents us with many mysteries. For example, previous studies in spectral space found that supergranulation has wave-like properties. Here we study, in real space, the wave-like evolution of the average supergranule over a range of spatial scales (from 10 to 80 Mm). We complement this by characterizing the evolution of the associated network magnetic field. We use one year of data from the Helioseismic and Magnetic Imager (HMI) to measure horizontal near-surface flows near the solar equator by applying time-distance helioseismology on Dopplergrams and granulation tracki…
Time--Distance Helioseismology Data Analysis Pipeline for Helioseismic and Magnetic Imager onboard Solar Dynamics Observatory (SDO/HMI) and Its Initial Results
The pattern of migrating zonal flow bands associated with the solar cycle, known as the torsional oscillation, has been monitored with continuous global helioseismic observations by the Global Oscillations Network Group, together with those made by the Michelson Doppler Imager onboard the Solar and Heliosepheric Observatory and its successor the Helioseismic and Magnetic Imager onboard the Solar Dynamics Observatory, since 1995, giving us nearly two full solar cycles of observations. We report that the flows now show traces of the mid-latitude acceleration that is expected to become the main e…
We develop a helioseismic inversion algorithm that can be used to recover sub-surface vertical profiles of 2-dimensional supergranular flows from surface measurements of synthetic wave travel times. We carry out seismic wave-propagation simulations through a 2-dimensional section of a flow profile that resembles an averaged supergranule, and a starting model that has flows only at the surface. We assume that the wave measurements are entirely without realization noise for the purpose of our test. We expand the vertical profile of the supergranule stream function on a basis of B-splines. We ite…
Improving methods for determining the subsurface structure of sunspots from their seismic signature requires a better understanding of the interaction of waves with magnetic field concentrations. We aim to quantify the impact of changes in the internal structure of sunspots on local helioseismic signals. We have numerically simulated the propagation of a stochastic wave field through sunspot models with different properties, accounting for changes in the Wilson depression between 250 and 550 km and in the photospheric umbral magnetic field between 1500 and 3500 G. The results show that travel-…
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 numeri…
Spectral analysis of the spatial structure of solar subphotospheric convection is carried out for subsurface flow maps constructed using the time--distance helioseismological technique. The source data are obtained from the Helioseismic and Magnetic Imager (HMI) onboard Solar Dynamics Observatory (SDO) from 2010 May to 2020 September. A spherical-harmonic transform is applied to the horizontal-velocity-divergence field at depths from 0 to 19~Mm. The range of flow scales is fairly broad in shallow layers and narrows as the depth increases. The horizontal flow scales rapidly increase with depth,…
A time-distance helioseismic technique, similar to the one used by Ilonidis et al (2011), is applied to two independent numerical models of subsurface sound-speed perturbations to determine the spatial resolution and accuracy of phase travel time shift measurements. The technique is also used to examine pre-emergence signatures of several active regions observed by the Michelson Doppler Imager (MDI) and the Helioseismic Magnetic Imager (HMI). In the context of similar measurements of quiet sun regions, three of the five studied active regions show strong phase travel time shifts several hours …
A time-distance measurement technique is derived to isolate phase travel time anisotropy caused by subsurface horizontal magnetic fields, and a method which uses the measured anisotropy to estimate the field's orientation is also derived. A simulation of acoustic waves propagating in a uniform, inclined magnetic field with solar background structure is used to verify the derived technique. Then, the procedure is applied to a numerical simulation of a sunspot, for which the subsurface state is known, to provide context for the results obtained from the study of several sunspots observed by the …
Today's picture of the internal solar rotation rate profile results essentially from helioseismic analyses of frequency splittings of resonant acoustic waves. Here we present another, complementary estimation of the internal solar rotation rate using the perturbation of the shape of the acoustic waves. For this purpose, we extend a global helioseismic approach developed previously for the investigation of the meridional flow \cite{schad11, schad12, schad13} to work on the components of the differential rotation. We discuss the effect of rotation on mode eigenfunctions and thereon based observa…
A helioseismic statistical waveform analysis of subsurface flow was performed on two 720-day time series of SOHO/MDI Medium-l spherical-harmonic coefficients. The time series coincide with epochs of high and low solar activity. Time-dependent coupling-strength coefficients b(s,t;n,l) of modes of the same radial order n and degree l, but different azimuthal order m, were inferred from the waveform analysis. These coefficients are sensitive to flows and general aspherical structure. For odd values of s << l, the coefficient b(s,t;n,l) measures an average over depth of the amplitude of one spheri…
New York University Abu Dhabi（纽约大学阿布扎比校区）；Max-Planck-Institut für Sonnensystemforschung（马克斯·普朗克太阳系研究所）；Georg-August-Universität Göttingen（格奥尔格-奥古斯特-哥廷根大学）；Tata Institute of Fundamental Research（塔塔基础研究所）
The inversion of ring fit parameters to obtain subsurface flow maps in ring-diagram analysis for 8 years of SDO observations is computationally expensive, requiring ~3200 CPU hours. In this paper we apply machine learning techniques to the inversion in order to speed up calculations. Specifically, we train a predictor for subsurface flows using the mode fit parameters and the previous inversion results, to replace future inversion requirements. We utilize Artificial Neural Networks as a supervised learning method for predicting the flows in 15 degree ring tiles. To demonstrate that the machine…
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)
Context. Solar Rossby waves (r modes) have recently been discovered in the near-surface horizontal flow field using the techniques of granulation-tracking and ring-diagram analysis applied to six years of SDO/HMI data. Aims. Here we apply time-distance helioseismology to the combined SOHO/MDI and SDO/HMI data sets, which cover 21 years of observations from May 1996 to April 2017. The goal of this study is to provide an independent confirmation over two solar cycles and in deeper layers of the Sun. Methods. We have measured south-north helioseismic travel times along the equator, which are sens…
