Search

Magnetic flux generated within the solar interior emerges to the surface, forming active regions (ARs) and sunspots. Flux emergence may trigger explosive events—such as flares and coronal mass ejections, and therefore understanding emergence is useful for space-weather forecasting. Evidence of any pre-emergence signatures will also shed light on subsurface processes responsible for emergence. In this paper, we present a first analysis of EARs from the Solar Dynamics Observatory/Helioseismic Emerging Active Regions dataset using deep convolutional neural networks (CNN) to characterize pre-emergence surface magnetic field properties. The trained CNN classifies between pre-emergence line-of-sight magnetograms and a control set of nonemergence magnetograms with a true skill statistic (TSS) score of approximately 85% about 3 hr prior to emergence and approximately 40% about 24 hr prior to emergence. Our results are better than a baseline classification TSS obtained using discriminant analysis (DA) of only the unsigned magnetic flux, although a multivariable DA produces TSS values consistent with the CNN. We develop a network-pruning algorithm to interpret the trained CNN and show that the CNN incorporates filters that respond positively as well as negatively to the unsigned magnetic flux of the magnetograms. Using synthetic magnetograms, we demonstrate that the CNN output is sensitive to the length scale of the magnetic regions, with small-scale and intense fields producing maximum CNN output and possibly a characteristic pre-emergence pattern. Given increasing popularity of deep learning, the techniques developed here to interpret the trained CNN—using network pruning and synthetic data—are relevant for future applications in solar and astrophysical data analysis. [ABSTRACT FROM AUTHOR]

Context. The spatial power spectrum of supergranulation does not fully characterize the underlying physics of turbulent convection. For example, it does not describe the non-Gaussianity in the horizontal flow divergence. Aims. Our aim is to statistically characterize the spatial pattern of solar supergranulation beyond the power spectrum. The next-order statistic is the bispectrum. It measures correlations of three Fourier components and is related to the nonlinearities in the underlying physics. It also characterizes how a skewness in the dataset is generated by the coupling of three Fourier components. Methods. We estimated the bispectrum of supergranular horizontal surface divergence maps that were obtained using local correlation tracking (LCT) and time-distance helioseismology (TD) from one year of data from the helioseismic and magnetic imager on-board the solar dynamics observatory starting in May 2010. Results. We find significantly nonzero and consistent estimates for the bispectrum using LCT and TD. The strongest nonlinearity is present when the three coupling wave vectors are at the supergranular scale. These are the same wave vectors that are present in regular hexagons, which have been used in analytical studies of solar convection. At these Fourier components, the bispectrum is positive, consistent with the positive skewness in the data and consistent with supergranules preferentially consisting of outflows surrounded by a network of inflows. We use the bispectral estimates to generate synthetic divergence maps that are very similar to the data. This is done by a model that consists of a Gaussian term and a weaker quadratic nonlinear component. Using this method, we estimate the fraction of the variance in the divergence maps from the nonlinear component to be of the order of 4-6%. Conclusions. We propose that bispectral analysis is useful for understanding the dynamics of solar turbulent convection, for example for comparing observations and numerical models of supergranular flows. This analysis may also be useful to generate synthetic flow fields. [ABSTRACT FROM AUTHOR]

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 sensitive to subsurface north-south flows. To reduce noise, the travel times were averaged over travel distances from 6° to 30°; the mean distance corresponds to a p-mode lower turning point of 0.91 R⊙. The 21-year time series of travel-time measurements was split into three seven-year subsets and transformed to obtain power spectra in a corotating frame. Results. The power spectra all show peaks near the frequencies of the classical sectoral Rossby waves for azimuthal wavenumbers in the range 3 ≤ m ≤ 15. The mode frequencies and linewidths of the modes with m ≤ 9 are consistent with a previous study whereas modes with m ≥ 10 are shifted toward less negative frequencies by 10–20 nHz. While most of these modes have e-folding lifetimes on the order of a few months, the longest lived mode, m = 3, has an e-folding lifetime of more than one year. For each mode, the rms velocity at the equator is in the range of 1–3 m s−1, with the largest values for m ∼ 10. No evidence for the m = 2 sectoral mode is found in the power spectrum, implying that the rms velocity of this mode is below ∼0.5 m s−1. Conclusions. This work confirms the existence of equatorial global Rossby waves in the solar interior over the past two solar cycles and shows that time-distance helioseismology is a promising technique to study them deep in the convection zone. [ABSTRACT FROM AUTHOR]

Context. 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. Aims. 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. Methods. 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. We illustrate the method by considering the 3D acoustic wave equation in an axisymmetric reference solar model, ignoring the effects of gravity on the waves. The symmetry of the background model around the rotation axis implies that the Green's function can be written as a sum of longitudinal Fourier modes, leading to a set of independent 2D problems. We use a high-order finite-element method to solve the 2D wave equation in frequency space. The computation is embarrassingly parallel, with each frequency and each azimuthal order solved independently on a computer cluster. Results. We compute travel-time sensitivity kernels in spherical geometry for flows, sound speed, and density perturbations under the first Born approximation. Convergence tests show that travel times can be computed with a numerical precision better than one millisecond, as required by the most precise travel-time measurements. Conclusions. The method presented here is computationally efficient and will be used to interpret travel-time measurements in order to infer, e.g., the large-scale meridional flow in the solar convection zone. It allows the implementation of (full-waveform) iterative inversions, whereby the axisymmetric background model is updated at each iteration. [ABSTRACT FROM AUTHOR]

Acoustic modes of oscillation are affected by stellar activity, however it is unclear how starspots contribute to these changes. Here we investigate the nonmagnetic effects of starspots on global modes with angular degree l ⩽ 2 in highly active stars, and characterize the spot seismic signature on synthetic light curves. We perform 3D time-domain simulations of linear acoustic waves to study their interaction with a model starspot. We model the spot as a 3D change in the sound speed stratification with respect to a convectively stable stellar background, built from solar Model S. We perform a parametric study by considering different depths and perturbation amplitudes. Exact numerical simulations allow the investigation of the wavefield-spot interaction beyond first order perturbation theory. The interaction of the axisymmetric modes with the starspot is strongly nonlinear. As mode frequency increases, the frequency shifts for radial modes exceed the value predicted by linear theory, while the shifts for the l = 2;m = 0 modes are smaller than predicted by linear theory, with avoided-crossing-like patterns forming between the m = 0 and m = 1 mode frequencies. The nonlinear behavior increases with increasing spot amplitude and/or decreasing depth. Linear theory still reproduces the correct shifts for nonaxisymmetric modes. In the nonlinear regime the mode eigenfunctions are not pure spherical harmonics, but rather a mixture of different spherical harmonics. This mode mixing, together with the frequency changes, may lead to misidentification of the modes in the observed acoustic power spectra. [ABSTRACT FROM AUTHOR]

The Solar Dynamics Observatory/Helioseismic and Magnetic Imager (SDO/HMI) filtergrams, taken at six wavelengths around the Fe i 6173.3 Å line, contain information about the line-of-sight velocity over a range of heights in the solar atmosphere. Multi-height velocity inferences from these observations can be exploited to study wave motions and energy transport in the atmosphere. Using realistic convection-simulation datasets provided by the STAGGER and MURaM codes, we generate synthetic filtergrams and explore several methods for estimating Dopplergrams. We investigate at which height each synthetic Dopplergram correlates most strongly with the vertical velocity in the model atmospheres. On the basis of the investigation, we propose two Dopplergrams other than the standard HMI-algorithm Dopplergram produced from HMI filtergrams: a line-center Dopplergram and an average-wing Dopplergram. These two Dopplergrams correlate most strongly with vertical velocities at the heights of 30 - 40 km above (line center) and 30 - 40 km below (average wing) the effective height of the HMI-algorithm Dopplergram. Therefore, we can obtain velocity information from two layers separated by about a half of a scale height in the atmosphere, at best. The phase shifts between these multi-height Dopplergrams from observational data as well as those from the simulated data are also consistent with the height-difference estimates in the frequency range above the photospheric acoustic-cutoff frequency. [ABSTRACT FROM AUTHOR]

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 (Fréchet 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. [ABSTRACT FROM AUTHOR]

The Sun supports a rich spectrum of internal waves that are continuously excited by turbulent convection. The Global Oscillation Network Group (GONG) network and the SOHO/MDI ( Solar and Heliospheric Observatory/Michelson Doppler Imager) space instrument provide an exceptional database of spatially resolved observations of solar oscillations, covering more than an entire sunspot cycle (11 years). Local helioseismology is a set of tools for probing the solar interior in three dimensions using measurements of wave travel times and local mode frequencies. Local helioseismology has discovered ( a) near-surface vector flows associated with convection, ( b) 250 m s−1 subsurface horizontal outflows around sunspots, ( c) ∼50 m s−1 extended horizontal flows around active regions (converging near the surface and diverging below), ( d) the effect of the Coriolis force on convective flows and active region flows, ( e) the subsurface signature of the 15 m s−1 poleward meridional flow, ( f) a ±5 m s−1 time-varying depth-dependent component of the meridional circulation around the mean latitude of activity, and ( g) magnetic activity on the farside of the Sun. [ABSTRACT FROM AUTHOR]

We study the sensitivity of wave travel times to steady and spatially homogeneous horizontal flows added to a realistic simulation of the solar convection performed by Robert F. Stein, Ake Nordlund, Dali Georgobiani, and David Benson. Three commonly used definitions of travel times are compared. We show that the relationship between travel-time difference and flow amplitude exhibits a non-linearity depending on the travel distance, the travel-time definition considered, and the details of the time – distance analysis (in particular, the impact of the phase-speed filter width). For times measured using a Gabor wavelet fit, the travel-time differences become nonlinear in the flow strength for flows of about 300 m s−1, and this non-linearity reaches almost 60% at 1200 m s−1 (relative difference between actual travel time and expected time for a linear behavior). We show that for travel distances greater than about 17 Mm, the ray approximation predicts the sensitivity of travel-time shifts to uniform flows. For smaller distances, the ray approximation can be inaccurate by more than a factor of three. [ABSTRACT FROM AUTHOR]

The Sun’s magnetic field is generated by subsurface motions of the convecting plasma. The latitude at which the magnetic field emerges through the solar surface (as sunspots) drifts toward the equator over the course of the 11-year solar cycle. We use helioseismology to infer the meridional flow (in the latitudinal and radial directions) over two solar cycles covering 1996–2019. Two data sources are used, which agree during their overlap period of 2001–2011. The time-averaged meridional flow is shown to be a single cell in each hemisphere, carrying plasma toward the equator at the base of the convection zone with a speed of ~4 meters per second at 45° latitude. Our results support the flux-transport dynamo model, which explains the drift of sunspot-emergence latitudes through the meridional flow. [ABSTRACT FROM AUTHOR]