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Sub-photospheric acoustic resonators allow for the formation of standing p-mode oscillations by reflecting acoustic waves with frequencies below the acoustic cut-off frequency. We employ the Klein–Gordon equation with a piecewise acoustic potential to study the characteristic frequencies of intermediate-degree p modes, modified by the cut-off effect. For a perfectly reflective photosphere, provided by the infinite value of the acoustic cut-off frequency, characteristic discrete frequencies of the trapped p modes are fully prescribed by the width of the acoustic potential barrier. Finite values of the acoustic cut-off frequency result in the reduction of p-mode frequencies, associated with the decrease in the sound speed by the cut-off effect. For example, for a spherical degree of |$\ell = 100$|⁠ , characteristic p-mode frequencies are found to decrease by up to 200 µHz and the effect is more pronounced for higher radial harmonics. The frequency separation between two consecutive radial harmonics is shown to behave non-asymptotically with non-uniform spacing in the radial harmonic number due to the cut-off effect. We also show how the 11-yr variability of the Sun's photospheric magnetic field can result in the p-mode frequency shifts through the link between the acoustic cut-off frequency and the plasma parameter |$\beta$|⁠. Using this model, we readily reproduce the observed typical amplitudes of the p-mode frequency shift and its phase behaviour relative to other 11-yr solar cycle proxies. The use of the developed model for comparison with observations requires its generalization for 2D effects, more realistic profiles of the acoustic potential, and broad-band stochastic drivers. [ABSTRACT FROM AUTHOR]

Context. Helioseismic inversions largely rely on sensitivity kernels, in which 3D spatial functions describe how the changes in the solar interior translate into the change in helioseismic observables. These sensitivity kernels in most cases come from the forward modelling that is used in the most advanced solar models. Aims. We aim to test the sensitivity kernels by comparing their volume integrals with measured values from helioseismic travel times. Methods. By manipulating the tracking rate, we mimicked the additional zonal velocity in the Dopplergram datacubes. These datacubes were then processed by a standard travel-time measurements pipeline. We investigated the dependence of the east-west travel time averaged over a box around the disc centre on the implanted tracking velocity. The slope of this dependence is directly proportional to the total volume integral of the sensitivity kernel that corresponds to the travel-time geometry that is used. Results. The agreement between measurements and models for travel times that are computed with a ridge filtering is very good to acceptable. The dependence we sought to determine indeed resembles a linear function, and its slope agrees with the expected volume integral from the forward-modelled sensitivity kernel. The agreement is poorer for the phase-speed filtered datacubes. The disagreement is particularly strong for the slowest phase speeds (filters td1–td4). For the higher phase speeds, our result indicates that the measured kernel integrals are systematically larger than expected from the forward modelling. We admit our testing procedure may not be appropriate for high phase speeds and higher radial modes. [ABSTRACT FROM AUTHOR]

Context. Stellar oscillations are key to unravelling stellar properties, such as their mass, radius, and age. This in turn enables us to date and characterize their exoplanetary systems. The amplitudes of acoustic (p-) modes in solar-like stars are intrinsically linked to their convective turbulent excitation source, which in turn is influenced by magnetism. In the observations of the Sun and stars, the mode amplitudes are modulated following their magnetic activity cycles: the higher the magnetic field, the lower the mode amplitudes. When the magnetic field is strong, it can even inhibit acoustic modes, which are not detected in most of the solar-like stars that are strongly magnetically active. Magnetic fields are known to freeze convection when they stronger than a critical value: the so-called on-off approach is used in the literature. Aims. We investigate the impact of magnetic fields on the stochastic excitation of acoustic modes. Methods. First, we generalise the forced-wave equation formalism, including the effects of magnetic fields. Second, we assess how convection is affected by magnetic fields using results from the magnetic mixing-length theory. Results. We provide the source terms of the stochastic excitation, including a new magnetic source term and the Reynolds stresses. We derive scaling laws for the mode amplitudes that take both the driving and the damping into account. These scalings are based on the inverse Alfvén dimensionless parameter: The damping increases with the magnetic field and reaches a saturation threshold when the magnetic field is strong. The driving of the modes diminishes when the magnetic field becomes stronger and the turbulent convection is weaker. Conculsions. As expected from the observations, we find that a stronger magnetic field diminishes the resulting mode amplitudes. The evaluation of the inverse Alfvén number in stellar models provides a means for estimating the expected amplitudes of acoustic modes in magnetically active solar-type stars. [ABSTRACT FROM AUTHOR]

Context. Acoustic waves in the Sun are affected by the atmospheric layers, but this region is often ignored in forward models because it increases the computational cost. Aims. The purpose of this work is to take the solar atmosphere into account without significantly increasing the computational cost. Methods. We solved a scalar-wave equation that describes the propagation of acoustic modes inside the Sun using a finite-element method. The boundary conditions used to truncate the computational domain were learned from the Dirichlet-to-Neumann operator, that is, the relation between the solution and its normal derivative at the computational boundary. These boundary conditions may be applied at any height above which the background medium is assumed to be radially symmetric. Results. We show that learned infinite elements lead to a numerical accuracy similar to the accuracy that is obtained for a traditional radiation boundary condition in a simple atmospheric model. The main advantage of learned infinite elements is that they reproduce the solution for any radially symmetric atmosphere to a very good accuracy at low computational cost. In particular, when the boundary condition is applied directly at the surface instead of at the end of the photosphere, the computational cost is reduced by 20% in 2D and by 60% in 3D. This reduction reaches 70% in 2D and 200% in 3D when the computational domain includes the atmosphere. Conclusions. We emphasize the importance of including atmospheric layers in helioseismology and propose a computationally efficient method to do this. [ABSTRACT FROM AUTHOR]

ABSTRACT: In many rotating fluids, the lowest order force balance is between gravity, pressure, and rotational acceleration (‘GPR’ balance). Terrestrial GPR balance takes the form of geostrophy and hydrostasy, which together yield the terrestrial thermal wind equation. By contrast, stellar GPR balance is an oblateness equation, which determines the departures of the thermal variables from spherical symmetry; its curl yields the ‘stellar thermal wind equation’. In this sense, the stellar thermal wind should be viewed not as a consequence of geostrophy, but of baroclinicity in the oblateness. Here, we treat the full stellar oblateness, including the thermal wind, using pressure coordinates. We derive the generalized stellar thermal wind equation and identify the parameter regime for which it holds. In the case of the Sun, not considering the full oblateness has resulted in conflicting calculations of the theoretical aspherical temperature anomaly. We provide new calculation here and find that the baroclinic anomaly is ∼3–60 times smaller than the barotropic anomaly. Thus, the anomaly from the thermal wind may not be measurable helioseismically, but if measurement were possible, this would potentially yield a new way to bracket the depth of the solar tachocline.

Various types of inertial modes have been observed and identified on the Sun, including the equatorial Rossby modes, critical-latitude modes, and high-latitude modes. Recent observations have further reported the detection of equatorially antisymmetric radial vorticity modes that propagate in a retrograde direction about three times faster than those of the equatorial Rossby modes, when seen in the corotating frame with the Sun. Here, we study the properties of these equatorially antisymmetric vorticity modes using a realistic linear model of the Sun's convection zone. We find that they are essentially non-toroidal, involving a substantial radial flow at the equator. Thus, the background density stratification plays a critical role in determining their dispersion relation. The solar differential rotation is also found to have a significant impact by introducing the viscous critical layers and confining the modes near the base of the convection zone. Furthermore, we find that their propagation frequencies are strikingly sensitive to the background superadiabaticity, δ, because the buoyancy force acts as an additional restoring force for these non-toroidal modes. The observed frequencies are compatible with the linear model only when the bulk of the convection zone is weakly subadiabatic (−5 × 10−7 ≲ δ ≲ −2.5 × 10−7). Our result is consistent with but tighter than the constraint independently derived in a previous study (δ < 2 × 10−7), employing the high-latitude inertial mode. It is implied that, below the strongly superadiabatic near-surface layer, the bulk of the Sun's convection zone might be much closer to adiabatic than typically assumed or it may even be weakly subadiabatic. [ABSTRACT FROM AUTHOR]

Context. The 11 yr solar cycle is known to affect the global modes of solar acoustic oscillations. In particular, p mode frequencies increase with solar activity. Aims. We propose a new method to detect the solar cycle from the p-mode autocorrelation function, and we validate this method using VIRGO/SPM photometric time series from solar cycles 23 and 24. Methods. The p-mode autocorrelation function shows multiple wavepackets separated by time lags of ∼123 min. Using a one-parameter fitting method (from local helioseismology), we measure the seismic travel times from each wavepacket up to skip number 40. Results. We find that the travel-time variations due to the solar cycle strongly depend on the skip number, with the strongest signature in odd skips from 17 to 31. Taking the noise covariance into account, the travel-time perturbations can be averaged over all skip numbers to enhance the signal-to-noise ratio. Conclusions. This method is robust to noise, simpler to implement than peak bagging in the frequency domain, and is promising for asteroseismology. We estimate that the activity cycle of a Sun-like star should be detectable with this new method in Kepler-like observations down to a visual magnitude of mK ∼ 11. However, for fainter stars, activity cycles are easier to detect in the photometric variability on rotational timescales. [ABSTRACT FROM AUTHOR]

Analysis of f-mode frequencies has provided a measure of the radius of the Sun which is lower, by a few hundredths per cent, than the photospheric radius determined by direct optical measurement. Part of this difference can be understood by recognizing that it is primarily the variation of density well beneath the photosphere of the star that determines the structure of these essentially adiabatic oscillation modes, not some aspect of radiative intensity. In this paper we attempt to shed further light on the matter, by considering a differently defined, and dynamically more robust, seismic radius, namely one determined from p-mode frequencies. This radius is calibrated by the distance from the centre of the Sun to the position in the subphotospheric layers where the first derivative of the density scale height changes essentially discontinuously. We find that radius is more-or-less consistent with what is suggested by the f modes. In addition, the interpretation of the radius inferred from p modes leads us to understand more deeply the role of the total mass constraint in the structure inversions. This enables us to reinterpret the sound-speed inversion, suggesting that the positions of the photosphere and the adiabatically stratified layers in the convective envelope differ non-homologously from those of the standard solar model. [ABSTRACT FROM AUTHOR]

We present solar low-degree rotational splitting values based on a new analysis of Sun-as-a-star observations from the Birmingham Solar Oscillations Network, covering a 16 425-d period from 1976 December 31 to 2021 December 20 with a duty cycle of 57 per cent. The splitting values are estimated from the power spectrum using a Markov chain Monte Carlo sampling method, and we also present for comparison the results from an analysis of 100 realizations of synthetic data with the same resolution and gap structure. Comparison of the scatter in the results from the synthetic realizations with their estimated uncertainties suggests that for this data set the formal uncertainty estimates are about 30 per cent too small. An upward bias in the splittings at frequencies above 2200  μ Hz, where the components are not fully resolved, is seen in both the observed and synthetic data. When this bias is taken into account, our results are consistent with a frequency-independent synodic rotational splitting value of 400 nHz. [ABSTRACT FROM AUTHOR]

In this work we theoretically investigate the effect of curvature on the slow-mode oscillations in coronal loop arcade. A simple model of an arc circle magnetic slab is used to simulate curved coronal magnetic structures. Solving the set of magnetohydrodynamic (MHD) equations for a compressible plasma, we obtain the dispersion relation that governs the compressible MHD modes in the model. A band of slow body modes with phase speeds close to the internal tube speed and a single hybrid slow mode with phase speed close to the external tube speed are found to exist under typical coronal circumstances. The principal slow body and hybrid modes both produce radial kink-like displacements of the slab axis and distort its cross-section. These motions are accompanied with the dominating longitudinal oscillations. Such mode properties may result in Doppler shift and intensity oscillations as well as oscillating spatial displacements, observed in coronal loops. A number of observations of long-period oscillations in arcade loops are interpreted on the basis of the developed theory. [ABSTRACT FROM AUTHOR]

Nuclear reaction rates are a fundamental yet uncertain ingredient in stellar evolution models. The astrophysical S -factor pertaining to the initial reaction in the proton–proton (pp) chain is uncertain at the 1 per cent level, which contributes a systematic but generally unpropagated error of similar order in the theoretical ages of stars. In this work, we study the prospect of improving the measurement of this and other reaction rates in the pp chain and CNO cycle using helioseismology and solar neutrinos. We show that when other aspects of the solar model are improved, then it shall be possible using current solar data to improve the precision of this measurement by nearly an order of magnitude and hence the corresponding uncertainty on the ages of low-mass stars by a similar amount. [ABSTRACT FROM AUTHOR]

Context. Activity on the far side of the Sun is routinely studied through the analysis of the seismic oscillations detected on the near side using helioseismic techniques such as phase-shift sensitive holography. Detections made through those methods are limited to strong active regions due to the need for a high signal-to-noise ratio. Recently, the neural network FarNet was developed to improve these detections. This network extracts more information from helioseismic far-side maps, enabling the detection of smaller and weaker active regions. Aims. We aim to create a new machine learning tool, FarNet-II, which further increases FarNet's scope, and to evaluate its performance in comparison to FarNet and the standard helioseismic method for detecting far-side activity. Methods. We developed FarNet-II, a neural network that retains some of the general characteristics of FarNet but improves the detections in general, as well as the temporal coherence among successive predictions. The main novelties of the new neural network are the implementation of attention and convolutional long short-term memory (ConvLSTM) modules. A cross-validation approach, training the network 37 times with a different validation set for each run, was employed to leverage the limited amount of data available. We evaluate the performance of FarNet-II using three years of extreme ultraviolet observations of the far side of the Sun acquired with the Solar Terrestrial Relations Observatory (STEREO) as a proxy of activity. The results from FarNet-II were compared with those obtained from FarNet and the standard helioseismic method using the Dice coefficient as a metric. Given that the application of the ConvLSTM modules can affect the accuracy as a function of the position on the sequence, we take this potential dependency into account in the evaluation. Results. FarNet-II achieves a Dice coefficient that improves that of FarNet by over 0.2 points for every output position on the sequences from the evaluation dates. Its improvement over FarNet is higher than that of FarNet over the standard method. Conclusions. The new network is a very promising tool for improving the detection of activity on the far side of the Sun given by pure helioseismic techniques. Space weather forecasts can potentially benefit from the higher sensitivity provided by this novel method. [ABSTRACT FROM AUTHOR]

We investigated the solar cycle dependence on the presence and periodicity of the Quasi-Biennial Oscillation (QBO). Using helioseismic techniques, we used solar oscillation frequencies from the Global Oscillations Network Group (GONG), Michelson Doppler Imager (MDI), and Helioseismic and Magnetic Imager (HMI) in the intermediate-degree range to investigate the frequency shifts over Cycles 23 and 24. We also examined two solar activity proxies, the F 10.7 index and the Mg  ii index, for the last four solar cycles to study the associated QBO. The analyses were performed using Empirical Mode Decomposition (EMD) and the Fast Fourier Transform (FFT). We found that the EMD analysis method is susceptible to detecting statistically significant Intrinsic Mode Functions (IMFs) with periodicities that are overtones of the length of the data set under examination. Statistically significant periodicities, which were not due to overtones, were detected in the QBO range. We see a reduced presence of the QBO in Cycle 24 compared to Cycle 23. The presence of the QBO was not sensitive to the depth to which the p-mode travelled, nor the average frequency of the p-mode. The analysis further suggested that the magnetic field responsible for producing the QBO in frequency shifts of p-modes is anchored above approximately 0.95 R⊙. [ABSTRACT FROM AUTHOR]

We examine the solar-cycle variation of the power in the low-degree helioseismic modes by looking at binned power spectra from 45 yr of observations with the Birmingham Solar Oscillations Network, which provides a more robust estimate of the mode power than that obtained by peak fitting. The solar-cycle variation of acoustic mode power in the 5-min band is clearly seen. Unusually, even though Cycle 24 was substantially weaker in terms of surface magnetic activity than Cycle 23, the reduction in mode power at solar maximum is very similar for the two cycles, suggesting that the relationship between mode power and magnetic activity is more complex than has previously been thought. This is in contrast to the mode frequencies, which show a strong correlation with activity with only subtle differences in the response across different solar cycles. [ABSTRACT FROM AUTHOR]

Kink oscillations of a curved coronal slab with finite plasma-β, simulating a loop arcade, are examined. Perpendicular propagation, i.e. propagation along the arcade axis (ky > 0) is taken into account. Two surface modes, labelled as faster and slower mode, are found to exist in the model. In the zero-β limit, the faster mode is a vertically polarized kink mode and the slower mode produces bending motions polarized along the arcade axis, provided |$k_y^{-1}$| is of the order of or larger than the slab thickness a. Otherwise, if |$k_y^{-1}$| is much less than a , the faster mode results in periodic displacement of a loop arcade along its axis and the slower mode has mixed properties. The phase speeds of both modes are very similar when |$k_y^{-1}\sim a$|⁠ , and they tend to the external and internal Alfvén speeds when ky → 0. As the internal plasma-β becomes finite and grows, the phase speed of the faster mode increases and that of the slower mode decreases. When β i > 0, these modes are a superposition of vertical kink motions and those that are oriented along the arcade axis, both supplemented with the significant cross-averaged density perturbations. It seems promising to use the obtained results for interpreting quasi-periodic pulsations, in terms of kink oscillations of flaring high-β loops, provided the developed theory is applicable to the torroidal single loop model when choosing an appropriate ky. [ABSTRACT FROM AUTHOR]

Convective-core overshoot mixing is a significant uncertainty in stellar evolution. Because numerical simulations and turbulent convection models predict exponentially decreasing radial rms turbulent velocity, a popular treatment for overshoot mixing is to apply a diffusion process with an exponentially decreasing diffusion coefficient. It is important to investigate the parameters of the diffusion coefficient because they determine the efficiency of the mixing in the overshoot region. In this paper, we have investigated the effects of the core overshoot mixing on the properties of the core in solar models. We have constrained the parameters of the overshoot model by using helioseismic inferences and the observation of the solar 8B neutrino flux. For solar-mass stars, the core overshoot mixing helps to prolong the lifetime of the convective core developed at the zero-age main sequence. If the strength of the mixing is sufficiently high, then the convective core in a solar model could survive until the present solar age, leading to large deviations of the sound speed and density profiles compared with the helioseismic inferences. The 8B neutrino flux also favours a radiative solar core. These observations provide a constraint on the parameters of the exponential diffusion model of the convective overshoot mixing. A limited asteroseismic investigation of 13 Kepler low-mass stars with 1.0 < M /M⊙ < 1.5 shows a mass-dependent range of the overshoot parameter. The overshoot mixing processes for different elements are analysed in detail. It is found that the exponential diffusion overshoot model leads to different effective overshoot mixing lengths for elements with different nuclear equilibrium time-scales. [ABSTRACT FROM AUTHOR]

Below the acoustic cut-off frequency, oscillations are trapped within the solar interior and become resonant. However, signatures of oscillations persist above the acoustic cut-off frequency, and these travelling waves are known as pseudo-modes. Acoustic oscillation frequencies are known to be correlated with the solar cycle, but the pseudo-mode frequencies are predicted to vary in antiphase. We have studied the variation in pseudo-mode frequencies with time systematically through the solar cycle. We analysed Sun-as-a-star data from Variability of Solar Irradiance and Gravity Oscillations (VIRGO), and Global Oscillations at Low Frequencies (GOLF), as well as the decomposed data from Global Oscillation Network (GONG) for harmonic degrees 0 ≤ l ≤ 200. The data cover over two solar cycles (1996–2021, depending on instrument). We split them into overlapping 100-d long segments and focused on two frequency ranges, namely 5600– |$6800\, \rm \mu Hz$| and 5600– |$7800\, \rm \mu Hz$|⁠. The frequency shifts between segments were then obtained by fitting the cross-correlation function between the segments' periodograms. For VIRGO and GOLF, we found no significant variation of pseudo-mode frequencies with solar activity. However, in agreement with previous studies, we found that the pseudo-mode frequency variations are in antiphase with the solar cycle for GONG data. Furthermore, the pseudo-mode frequency shifts showed a double-peak feature at their maximum, which corresponds to solar activity minimum, and is not seen in solar activity proxies. An, as yet unexplained, pseudo-periodicity in the amplitude of the variation with harmonic degree l is also observed in the GONG data. [ABSTRACT FROM AUTHOR]

Context. Over the past 40 years, helioseismology has been enormously successful in the study of the solar interior. A shortcoming has been the lack of a convincing detection of the solar g modes, which are oscillations driven by gravity and are hidden in the deepest part of the solar body – its hydrogen-burning core. The detection of g modes is expected to dramatically improve our ability to model this core, the rotational characteristics of which have, until now, remained unknown. Aims. We present the identification of very low frequency g modes in the asymptotic regime and two important parameters that have long been waited for: the core rotation rate, and the asymptotic equidistant period spacing of these g modes. Methods. The GOLF instrument on board the SOHO space observatory has provided two decades of full-disk helioseismic data. The search for g modes in GOLF measurements has been extremely difficult because of solar and instrumental noise. In the present study, the p modes of the GOLF signal are analyzed differently: we search for possible collective frequency modulations that are produced by periodic changes in the deep solar structure. Such modulations provide access to only very low frequency g modes, thus allowing statistical methods to take advantage of their asymptotic properties. Results. For oscillatory periods in the range between 9 and nearly 48 h, almost 100 g modes of spherical harmonic degree 1 and more than 100 g modes of degree 2 are predicted. They are not observed individually, but when combined, they unambiguously provide their asymptotic period equidistance and rotational splittings, in excellent agreement with the requirements of the asymptotic approximations. When the period equidistance has been measured, all of the individual frequencies of each mode can be determined. Previously, p-mode helioseismology allowed the g-mode period equidistance parameter P0 to be bracketed inside a narrow range, between approximately 34 and 35 min. Here, P0 is measured to be 34 min 01 s, with a 1 s uncertainty. The previously unknown g-mode splittings have now been measured from a non-synodic reference with very high accuracy, and they imply a mean weighted rotation of 1277 ± 10 nHz (9-day period) of their kernels, resulting in a rapid rotation frequency of 1644 ± 23 nHz (period of one week) of the solar core itself, which is a factor 3.8 ± 0.1 faster than the rotation of the radiative envelope. Conclusions. The g modes are known to be the keys to a better understanding of the structure and dynamics of the solar core. Their detection with these precise parameters will certainly stimulate a new era of research in this field.

A new time–distance far-side imaging technique was recently developed by utilizing multiple multi-skip acoustic waves. The measurement procedure is applied to 11 years of Doppler observations from the Solar Dynamics Observatory/Helioseismic and Magnetic Imager, and over 8000 far-side images of the Sun have been obtained with a 12-hour temporal cadence. The mean travel-time shifts in these images unsurprisingly vary with the solar cycle. However, the temporal variation does not show good correlations with the magnetic activity in their respective northern or southern hemisphere, but show very good anti-correlation with the global-scale magnetic activity. We investigate four possible causes of this travel-time variation. Our analysis demonstrates that the acoustic waves that are used for mapping the Sun's far side experience surface reflections around the globe, where they may interact with surface or near-surface magnetic field and carry travel-time deficits with them. The mean far-side travel-time shifts from these acoustic waves therefore vary in phase with the Sun's magnetic activity. [ABSTRACT FROM AUTHOR]

The Sun has a near-surface shear layer (NSSL), within which the angular velocity decreases rapidly with radius. We provide an explanation of this layer based on the thermal wind balance equation. Since convective motions are not affected by solar rotation in the top layer of the convection zone, we argue that the temperature falls at the same rate at all latitudes in this layer. This makes the thermal wind term very large in this layer and the centrifugal term has also to become very large to balance it, giving rise to the NSSL. From the values of differential rotation Ω(r < r c, θ) at radii less than a radius r c, we can calculate the temperature difference Δ T (r , θ) with respect to the standard solar model at different points of the convection zone by making use of the thermal wind balance equation. Then, we again use this equation in the top layer to calculate Ω(r > r c, θ) there from Δ T (r , θ). We carry on this exercise using both an analytical expression of the differential rotation and the actual data provided by helioseismology. We find that our theoretical results of the NSSL match the observational data reasonably well for r c ≈ 0.96R⊙, giving an estimate of the radius till which the convective motions are affected by the solar rotation. [ABSTRACT FROM AUTHOR]

The solar gravitational moments J 2 n are important astronomical quantities whose precise determination is relevant for solar physics, gravitational theory and high precision astrometry, and celestial mechanics. Accordingly, we propose in the present work to calculate new values of J 2 n (for n  = 1, 2, 3, 4, and 5) using recent two-dimensional rotation rates inferred from the high-resolution Solar Dynamics Observatory / Helioseismic and Magnetic Imager helioseismic data spanning the whole solar activity cycle 24. To this aim, a general integral equation relating J 2 n to the solar internal density and rotation is derived from the structure equations governing the equilibrium of slowly rotating stars. For comparison purpose, the calculations are also performed using rotation rates obtained from a recently improved analysis of Solar and Heliospheric Observatory / Michelson Doppler Imager heliseismic data for solar cycle 23. In agreement with earlier findings, the results confirmed the sensitivity of high-order moments (n > 1) to the radial and latitudinal distribution of rotation in the convective zone. The computed value of the quadrupole moment J 2 (n  = 1) is in accordance with recent measurements of the precession of Mercury's perihelion deduced from high precision ranging data of the MESSENGER spacecraft. The theoretical estimate of the related solar oblateness Δ⊙ is consistent with the most accurate space-based determinations, particularly the one from Reuven Ramathy High-Energy Solar Spectroscopic Imager /Solar Aspect Sensor. [ABSTRACT FROM AUTHOR]

We consider the possibility of a varying speed of light based on a unit of length defined with a rigid rod or atomic standard. The reference for comparison is the international standard for the meter based on the transit of light, defined so that c is constant. If these two units do not correspond over time, then the gravitational constant G as measured with each will not be in agreement. We relate changes in the speed of light in atomic units of length to changes in G measured in the two systems. Reported experimental data that constrain yearly changes in G are sufficient to bound changes in c. Experimental constraints on |$|\dot{G}/G|$| based on spacecraft microwave ranging and on helioseismology indicate that presently |$|{\dot{c}/c}|\le.55 \times 10^{-12}\, \textrm {yr}^{-1}$|⁠. If this result is extended in epoch by relating c to a power of the scale factor, a n , then variation in c is constrained by | n | <.0080. The approach is distinct from other efforts to constrain |$\dot{c}$| in being based on data from within the Solar system instead of cosmological observations. A relationship between c and the fine-structure constant is identified that potentially provides tighter constraints. [ABSTRACT FROM AUTHOR]

The properties of axisymmetric magnetohydrodynamic wave modes are studied for the model of coronal magnetic tube, consisting of a central cord with homogeneous axial magnetic field, surrounded by an annulus with twisted magnetic field. This model mimics the coronal loops with radially localized magnetic twist. The derived dispersion relation is solved numerically. A number of limiting cases are examined analytically. The two families of axisymmetric modes are found to exist in the model. The first one includes an infinite number of fast-sausage modes (FSMs), modified by the twist and the second one is a set of modes with frequencies, lying in a narrow band, closed to Alfvén frequency of a twisted layer ωA0. The fundamental FSM (the mode of the lowest radial order) exists as a trapped mode for the entire range of axial wavenumbers. Its phase speed is always below the Alfvén speed of a magnetically twisted layer. This mode has a weak dispersion in the range of long and intermediate wavelengths. The higher radial order FSMs were found to be less sensitive to the presence of the magnetic twist. Both the fundamental FSM in the case of a weak magnetic twist and a set of symmetric modes for arbitrary twist have very similar frequencies, which are nearly equal to ωA0. This property implies that aforementioned wave modes behave like Alfvén torsional modes in the twisted annulus and like the radial modes in the untwisted core and environment, moreover they are strongly coupled. The main results of the study are discussed in the framework of their applications to coronal seismology. [ABSTRACT FROM AUTHOR]

Several attempts have been made to observe whether solar flares excite acoustic modes since Charles Wolff suggested this possibility almost 50 yr ago. We look for the impact of flares on the amplitude of solar acoustic modes and other effects that are also affecting the mode amplitude. Solar acoustic mode amplitudes are known to be sensitive to magnetic fields. As flares usually occur in the presence of strong magnetic fields and most likely are the by-product of magnetic reconnection, we show how the magnetic field in and around the flaring region affects the mode amplitude. The mode amplitudes were obtained using ring-diagram analysis, which was first applied to a single event, the largest flare in the space age (the 'Halloween Flare', SOL2003-10-28T11:00), using MDI (Michelson Doppler Imager) data. Then, using HMI (Helioseismic and Magnetic Imager) data, the analysis was applied to the regions corresponding to the flares observed during the high-activity phase of cycle 24 and that fall into two groups. These two groups consist of small (10–60 erg cm−2 s−1) and large (>1200 erg cm−2 s−1) peak-flux flares, based on the Heliophysics Event Knowledgebase (HEK). The first set is used as a comparison to the results of the strong flares in the second set. After applying several corrections in order to take into account several sources of bias, we did not find any amplification in the inferred mode amplitude due to flaring activity larger than a 10  per cent uncertainty. [ABSTRACT FROM AUTHOR]

Solar magnetic fields are believed to originate from the base of convection zone. However, it has been difficult to obtain convincing observational evidence of the magnetic fields in the deep convection zone. The goal of this study is to investigate whether solar meridional flows can be used to detect the magnetic-field effects. Meridional flows are axisymmetric flows on the meridional plane. Our result shows that the flow pattern in the entire convection zone changes significantly from solar minimum to maximum. The changes all centered around active latitudes, suggesting that the magnetic fields are responsible for the changes. The results indicate that the meridional flow can be used to detect the effects of magnetic field in the deep convection zone. The results have been published in the Astrophysical Journal (lc2018). [ABSTRACT FROM AUTHOR]

It has been shown over and over again that the parameters of solar p modes vary through the solar activity cycle: frequencies, amplitudes, lifetimes, energies. However, so far, the rates at which energy is supplied to the p modes have not been detected to be sensitive to the level of magnetic activity. We set out to re-inspect their temporal behaviour over the course of the last two Schwabe cycles. For this, we use Global Oscillation Network Group (GONG) p-mode parameter tables. We analyse the energy supply rates for modes of harmonic degrees l = 0–150 and average over the azimuthal orders and, subsequently, over modes in different parameter ranges. This averaging greatly helps in reducing the noise in the data. We find that energy supply rates are anticorrelated with the level of solar activity, for which we use the F 10.7 index as a proxy. Modes of different mode frequency and harmonic degrees show varying strengths of anticorrelation with the F 10.7 index, reaching as low as r = −0.82 for low frequency modes with l = 101–150. In this first dedicated study of solar p-mode energy supply rates in GONG data, we find that they do indeed vary through the solar cycle. Earlier investigations with data from other instruments were hindered by being limited to low harmonic degrees or by the data sets being too short. We provide tables of time-averaged energy supply rates for individual modes as well as for averages over disjunct frequency bins. [ABSTRACT FROM AUTHOR]

The meridional circulation of the Sun, which is observed to be poleward at the surface, should have a return flow at some depth. Since large-scale flows like the differential rotation and the meridional circulation are driven by turbulent stresses in the convection zone, these flows are expected to remain confined within this zone. Current observational (based on helioseismology) and theoretical (based on dynamo theory) evidences point towards an equatorward return flow of the meridional circulation at the bottom of the convection zone. Assuming the mean values of various quantities averaged over turbulence to be axisymmetric, we study the large-scale flows in solar-like stars on the basis of a 2D mean field theory. Turbulent stresses in a rotating star can transport angular momentum, setting up a differential rotation. The meridional circulation arises from a slight imbalance between two terms which try to drive it in opposite directions: a thermal wind term (arising out of the higher efficiency of convective heat transport in the polar regions) and a centrifugal term (arising out of the differential rotation). To make these terms comparable, the poles of the Sun should be slightly hotter than the equator. We discuss the important role played by the meridional circulation in the flux transport dynamo model. The poloidal field generated by the Babcock-Leighton process at the surface is advected poleward, whereas the toroidal field produced at the bottom of the convection zone is advected equatorward. The fluctuations in the meridional circulation (with coherence time of about 30–40 yr) help in explaining many aspects of the irregularities in the solar cycle. Finally, we discuss how the Lorentz force of the dynamo-generated magnetic field can cause periodic variations in the large-scale flows with the solar cycle. [ABSTRACT FROM AUTHOR]

The development of space-borne missions has significantly improved the quality of the measured spectra of solar-like oscillators. Their p-mode line profiles can now be resolved, and the asymmetries inferred for a variety of stars other than the Sun. However, it has been known for a long time that the asymmetries of solar p-modes are reversed between the velocity and the intensity spectra. Understanding the origin of this reversal is necessary in order to use asymmetries as a tool for seismic diagnosis. For stars other than the Sun, only the intensity power spectrum is sufficiently resolved to allow for an estimation of mode asymmetries. We recently developed an approach designed to model and predict these asymmetries in the velocity power spectrum of the Sun and to successfully compare them to their observationally derived counterpart. In this paper we expand our model and predict the asymmetries featured in the intensity power spectrum. We find that the shape of the mode line profiles in intensity is largely dependent on how the oscillation-induced variations of the radiative flux are treated, and that modelling it realistically is crucial to understanding asymmetry reversal. Perturbing a solar-calibrated grey atmosphere model, and adopting the quasi-adiabatic framework as a first step, we reproduce the asymmetries observed in the solar intensity spectrum for low-frequency modes. We conclude that, unlike previously thought, it is not necessary to invoke an additional mechanism (e.g. non-adiabatic effects, coherent non-resonant background signal) to explain asymmetry reversal. This additional mechanism is necessary, however, to explain asymmetry reversal for higher-order modes. [ABSTRACT FROM AUTHOR]

Context. The frequencies, lifetimes, and eigenfunctions of solar acoustic waves are affected by turbulent convection, which is random in space and in time. Since the correlation time of solar granulation and the periods of acoustic waves (∼5 min) are similar, the medium in which the waves propagate cannot a priori be assumed to be time independent. Aims. We compare various effective-medium solutions with numerical solutions in order to identify the approximations that can be used in helioseismology. For the sake of simplicity, the medium is one dimensional. Methods. We consider the Keller approximation, the second-order Born approximation, and spatial homogenization to obtain theoretical values for the effective wave speed and attenuation (averaged over the realizations of the medium). Numerically, we computed the first and second statistical moments of the wave field over many thousands of realizations of the medium (finite-amplitude sound-speed perturbations are limited to a 30 Mm band and have a zero mean). Results. The effective wave speed is reduced for both the theories and the simulations. The attenuation of the coherent wave field and the wave speed are best described by the Keller theory. The numerical simulations reveal the presence of coda waves, trailing the ballistic wave packet. These late arrival waves are due to multiple scattering and are easily seen in the second moment of the wave field. Conclusions. We find that the effective wave speed can be calculated, numerically and theoretically, using a single snapshot of the random medium (frozen medium); however, the attenuation is underestimated in the frozen medium compared to the time-dependent medium. Multiple scattering cannot be ignored when modeling acoustic wave propagation through solar granulation. [ABSTRACT FROM AUTHOR]

The Sun is the most studied and well-known star, and as such, solar fundamental parameters are often used to bridge gaps in the knowledge of other stars, when these are required for modelling. However, the two most powerful and precise independent methodologies currently available to infer the internal solar structure are in disagreement. We aim to show the potential impact of composition choices in the overall evolution of a star, using the Sun as example. To this effect, we create two Standard Solar Models and a comparison model using different combinations of metallicity and relative element abundances and compare evolutionary, helioseismic, and neutrino-related properties for each. We report differences in age for models calibrated to the same point on the HR diagram, in red giant branch, of more than 1 Gyr, and found that the current precision level of asteroseismic measurements is enough to differentiate these models, which would exhibit differences in period spacing of 1.30–2.58 per cent. Additionally, we show that the measurement of neutrino fluxes from the carbon–nitrogen–oxygen cycle with a precision of around 17 per cent, which could be achieved by the next generation of solar neutrino experiments, could help resolve the stellar abundance problem. [ABSTRACT FROM AUTHOR]

Context. The Sun constitutes an excellent laboratory of fundamental physics. With the advent of helioseismology, we were able to probe its internal layers with unprecendented precision and thoroughness. However, the current state of solar modelling is still stained by tedious issues. One of these central problems is related to the disagreement between models computed with recent photospheric abundances and helioseismic constraints. The observed discrepancies raise questions on some fundamental ingredients entering the computation of solar and stellar evolution models. Aims. We used solar evolutionary models as initial conditions for reintegrating their structure using Ledoux discriminant inversions. The resulting models are defined as seismic solar models, satisfying the equations of hydrostatic equilibrium. These seismic models will allow us to better constrain the internal structure of the Sun and provide complementary information to that of calibrated standard and non-standard models. Methods. We used inversions of the Ledoux discriminant to reintegrate seismic solar models satisfying the equations of hydrostatic equilibrium. These seismic models were computed using various reference models with different equations of state, abundances, and opacity tables. We checked the robustness of our approach by confirming the good agreement of our seismic models in terms of sound speed, density, and entropy proxy inversions, as well as frequency-separation ratios of low-degree pressure modes. Results. Our method allows us to determine the Ledoux discriminant profile of the Sun with an excellent accuracy and compute full profiles of this quantity. Our seismic models show an agreement with seismic data of ≈0.1% in sound speed, density, and entropy proxy after seven iterations in addition to an excellent agreement with the observed frequency-separation ratios. They surpass all standard and non-standard evolutionary models including ad hoc modifications of their physical ingredients that aim to reproduce helioseismic constraints. Conclusions. The obtained seismic Ledoux discriminant profile, as well as the full consistent structure obtained from our reconstruction procedure paves the way for renewed attempts at constraining the solar modelling problem and the missing physical processes acting in the solar interior by breaking free from the hypotheses of evolutionary models. [ABSTRACT FROM AUTHOR]

Aims. This paper describes the Polarimetric and Helioseismic Imager on the Solar Orbiter mission (SO/PHI), the first magnetograph and helioseismology instrument to observe the Sun from outside the Sun-Earth line. It is the key instrument meant to address the top-level science question: How does the solar dynamo work and drive connections between the Sun and the heliosphere? SO/PHI will also play an important role in answering the other top-level science questions of Solar Orbiter, while hosting the potential of a rich return in further science. Methods. SO/PHI measures the Zeeman effect and the Doppler shift in the Fe I 617.3 nm spectral line. To this end, the instrument carries out narrow-band imaging spectro-polarimetry using a tunable LiNbO3 Fabry-Perot etalon, while the polarisation modulation is done with liquid crystal variable retarders. The line and the nearby continuum are sampled at six wavelength points and the data are recorded by a 2k × 2k CMOS detector. To save valuable telemetry, the raw data are reduced on board, including being inverted under the assumption of a Milne-Eddington atmosphere, although simpler reduction methods are also available on board. SO/PHI is composed of two telescopes; one, the Full Disc Telescope, covers the full solar disc at all phases of the orbit, while the other, the High Resolution Telescope, can resolve structures as small as 200 km on the Sun at closest perihelion. The high heat load generated through proximity to the Sun is greatly reduced by the multilayer-coated entrance windows to the two telescopes that allow less than 4% of the total sunlight to enter the instrument, most of it in a narrow wavelength band around the chosen spectral line. Results. SO/PHI was designed and built by a consortium having partners in Germany, Spain, and France. The flight model was delivered to Airbus Defence and Space, Stevenage, and successfully integrated into the Solar Orbiter spacecraft. A number of innovations were introduced compared with earlier space-based spectropolarimeters, thus allowing SO/PHI to fit into the tight mass, volume, power and telemetry budgets provided by the Solar Orbiter spacecraft and to meet the (e.g. thermal) challenges posed by the mission's highly elliptical orbit. [ABSTRACT FROM AUTHOR]

The dispersive properties of fast oscillations in a coronal plasma slab are studied. These oscillations are assumed to be generated by an external source, located at a finite distance from the slab. It is shown that the problem reduces to examination of the normal modes of a system, consisting of a slab cavity and a finitely distant rigid boundary. The relation that governs the eigenfrequencies of the system is derived. Both the kink and the sausage modes are excited. The main finding indicates that the principal kink mode is trapped not for all axial wavenumbers. It has a non-zero cut-off wavenumber and can exist either as a trapped mode or as a leaky mode. This cut-off tends to zero for infinitely distant sources, in accordance with the well-known result from the normal mode analysis. The expressions for the frequency and damping rate of the leaky principal kink mode are derived. The effect of a finitely distant rigid boundary on the higher transverse-order kink modes and all the sausage modes is found to be only minor, when the distance between the source and the slab is much more than the transverse size of the slab. The applications of the obtained results in coronal seismology are discussed. [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 have only recently been unambiguously identified in Helioseimsic and Magnetic Imager (HMI) and Michelson Doppler Imager maps of flows near the solar surface. So far this has not been done with the Global Oscillation Network Group (GONG) ground-based observations, which have different noise properties. Aims. We use 17 years of GONG++ data to identify and characterize solar Rossby waves using ring-diagram helioseismology. We compare directly with HMI ring-diagram analysis. Methods. Maps of the radial vorticity were obtained for flows within the top 2Mm of the surface for 17 years of GONG++ data. The data were corrected for systematic effects including the annual periodicity related to the B0 angle. We then computed the Fourier components of the radial vorticity of the flows in the co-rotating frame. We performed the same analysis on the HMI data that overlap in time. Results. We find that the solar Rossby waves have measurable amplitudes in the GONG++ sectoral power spectra for azimuthal orders between m = 3 and m = 15. The measured mode characteristics (frequencies, lifetimes, and amplitudes) from GONG++ are consistent with the HMI measurements in the overlap period from 2010 to 2018 for m ≤ 9. For higher-m modes the amplitudes and frequencies agree within two sigmas. The signal-to-noise ratio of modes in GONG++ power spectra is comparable to those of HMI for 8 ≤ m ≤ 11, but is lower by a factor of two for other modes. Conclusions. The GONG++ data provide a long and uniform data set that can be used to study solar global-scale Rossby waves from 2001. [ABSTRACT FROM AUTHOR]

Context. The advent of space-borne missions has substantially increased the number and quality of the measured power spectrum of solar-like oscillators. It now allows for the p-mode line profiles to be resolved and facilitates an estimation of their asymmetry. The fact that this asymmetry can be measured for a variety of stars other than the Sun calls for a revisiting of acoustic mode asymmetry modelling. This asymmetry has been shown to be related to a highly localised source of stochastic driving in layers just beneath the surface. However, existing models assume a very simplified, point-like source of excitation. Furthermore, mode asymmetry could also be impacted by a correlation between the acoustic noise and the oscillating mode. Prior studies have modelled this impact, but only in a parametrised fashion, which deprives them of their predictive power. Aims. In this paper, we aim to develop a predictive model for solar radial p-mode line profiles in the velocity spectrum. Unlike the approach favoured by prior studies, this model is not described by free parameters and we do not use fitting procedures to match the observations. Instead, we use an analytical turbulence model coupled with constraints extracted from a 3D hydrodynamic simulation of the solar atmosphere. We then compare the resulting asymmetries with their observationally derived counterpart. Methods. We model the velocity power spectral density by convolving a realistic stochastic source term with the Green's function associated with the radial homogeneous wave equation. We compute the Green's function by numerically integrating the wave equation and we use theoretical considerations to model the source term. We reconstruct the velocity power spectral density and extract the line profile of radial p-modes as well as their asymmetry. Results. We find that stochastic excitation localised beneath the mode upper turning point generates negative asymmetry for v < vmax and positive asymmetry for v > vmax. On the other hand, stochastic excitation localised above this limit generates negative asymmetry throughout the p-mode spectrum. As a result of the spatial extent of the source of excitation, both cases play a role in the total observed asymmetries. By taking this spatial extent into account and using a realistic description of the spectrum of turbulent kinetic energy, both a qualitative and quantitative agreement can be found with solar observations performed by the GONG network. We also find that the impact of the correlation between acoustic noise and oscillation is negligible for mode asymmetry in the velocity spectrum. [ABSTRACT FROM AUTHOR]

The frequency, νmax, at which the envelope of pulsation power peaks for solar-like oscillators is an important quantity in asteroseismology. We measure νmax for the Sun using 25 yr of Sun-as-a-star Doppler velocity observations with the Birmingham Solar-Oscillations Network (BiSON), by fitting a simple model to binned power spectra of the data. We also apply the fit to Sun-as-a-star Doppler velocity data from Global Oscillation Network Group and Global Oscillations at Low Frequency, and photometry data from VIRGO/SPM on the ESA/NASA SOHO spacecraft. We discover a weak but nevertheless significant positive correlation of the solar νmax with solar activity. The uncovered shift between low and high activity, of |$\simeq 25\, \rm \mu Hz$|⁠ , translates to an uncertainty of 0.8 per cent in radius and 2.4 per cent in mass, based on direct use of asteroseismic scaling relations calibrated to the Sun. The mean νmax in the different data sets is also clearly offset in frequency. Our results flag the need for caution when using νmax in asteroseismology. [ABSTRACT FROM AUTHOR]

Magnetohydrodynamic dynamo modelling shows that the large-scale solar meridional plasma flow plays an important role in governing the dynamics of the sunspot cycle. Observations indicate that meridional flow velocities at each solar latitude and depth vary over time and are asymmetric across the equator. Here, using helioseismic observations we explore the temporal variation in the hemispherical asymmetry of near-surface residual (time-varying) component of the Sun's meridional flow velocity. The meridional flow velocities obtained from Global Oscillation Network Group (GONG) and Helioseismic and Magnetic Imager (HMI) onboard Solar Dynamics Observatory (SDO) ring-diagram pipelines are used in this work. Our data set covers the declining phase of cycle 23 and cycle 24 (from July 2001 till December 2018) and the flow velocities are poleward for the observed depth range. We observe a time delayed anticorrelation between the hemispherical asymmetry in near-surface meridional flow velocities and the sunspot cycle quantified in terms of magnetic flux and sunspot number. Interestingly, asymmetry in meridional flow velocity precedes the asymmetry in sunspot cycle by 3.1–3.5 yr. We propose that meridional flow asymmetry is a precursor of asymmetry in hemispherical cycle strength. The symmetric component of meridional flow is observed to be positively correlated with the corresponding symmetric components of the magnetic cycle, also with a time delay. Our analysis sets important constraints on theories for the origin of meridional plasma flow asymmetries and its temporal variations and is relevant for understanding the role of plasma flux transport processes in determining hemispheric asymmetry in the sunspot cycle. [ABSTRACT FROM AUTHOR]

Context. The Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO) satellite has been observing the Sun since 2010. The uninterrupted series of Dopplergrams are ideal for studying the dynamics of the upper solar convection zone. Within the Joint Science Operations Center (JSOC) the time–distance inversions for flows and sound-speed perturbations were introduced. The automatic pipeline has produced flow and sound-speed maps every 8 h. We verify the results of JSOC inversions by comparing the data products to equivalent results from inverse modelling obtained by an independent inversion pipeline. Aims. We compared the results from the JSOC pipeline for horizontal flow components and the perturbations of the speed of sound at set of depths with equivalent results from an independently implemented pipeline using a different time–distance inversion scheme. Our inversion pipeline allows inversion for all quantities at once while allowing minimisation of the crosstalk between them. This gives us an opportunity to discuss the possible biases present in the JSOC data products. Methods. For the tests we used the subtractive optimally localised averaging (SOLA) method with a minimisation of the cross-talk. We compared three test inversions for each quantity at each target depth. At first, we used the JSOC setup to reproduce the JSOC results. Subsequently, we used the extended pipeline to improve these results by incorporating more independent travel-time measurements but keeping the JSOC-indicated localisation in the Sun. Finally, we inverted for flow components and sound-speed perturbations using a localisation kernel with properties advertised in the JSOC metadata. Results. We successfully reproduced the horizontal flow components. The sound-speed perturbations are strongly affected by the high level of the cross-talk in JSOC products. This leads to larger amplitudes in the inversions for the sound-speed perturbations. Different results were obtained when a target function localised around the target depth was used. This is a consequence of non-localised JSOC averaging kernels. We add that our methodology also allows inversion for the vertical flow. [ABSTRACT FROM AUTHOR]

Context. Solar gravity modes (g modes) are buoyancy waves that are trapped in the solar radiative zone and have been very difficult to detect at the surface. Solar g modes would complement solar pressure modes (p modes) in probing the central regions of the Sun, for example the rotation rate of the core. Aims. A detection of g modes using changes in the large frequency separation of p modes has recently been reported. However, it is unclear how p and g modes interact. The aim of this study is to evaluate to what extent g modes can perturb the frequencies of p modes. Methods. We computed the first-order perturbation to global p-mode frequencies due to a flow field and perturbations to solar structure (e.g. density and sound speed) caused by a g mode. We focused on long-period g modes and assumed that the g-mode perturbations are constant in time. The surface amplitude of g modes is assumed to be 1 mm s−1, which is close to the observational limit set by Doppler observations. Results. Gravity modes do perturb p-mode frequencies to first order if the harmonic degree of the g mode is even and if its azimuthal order is zero. The effect is extremely small. For dipole and quadrupole p modes, all frequency shifts are smaller than 0.1 nHz, or 2 × 10−8 in relative numbers. This is because the relative perturbation to solar structure quantities caused by a g mode of realistic amplitude is of the order of 10−6–10−5. Additionally, we find that structural changes dominate over advection. Surprisingly, the interaction of g and p modes takes place to a large part near the surface, where p modes spend most of their propagation times and g modes generate the largest relative changes to solar structure. This is due to the steep density stratification, which compensates the evanescent behaviour of g modes in the convection zone. Conclusions. It appears to be impossible to detect g modes solely through their signature in p-mode frequency shifts. Whether g modes leave a detectable signature in p-mode travel times under a given observational setup remains an open question. [ABSTRACT FROM AUTHOR]

We study dispersion properties of fast-sausage waves in a radially structured coronal magnetic tube with continuous radial density distribution. The models, containing either a non-uniform core or inhomogeneous external medium are considered. The dispersion relations are obtained for a power law density distribution in the corresponding non-uniform region, where the power-law index controls the steepness of the tube boundary. The governing wave equations with varying coefficients were solved with the Wentzel–Kramers–Brillouin (WKB) approximation. The model with the non-uniform core supports the existence of trapped and leaky sausage modes. The density non-uniformity in the core modifies the values of cut-off wave numbers k c. The smaller values of cut-offs, normalized to the effective tube radius r 0, correspond to the smaller power index p. The wave dispersion (i.e. d V ph/d k) decreases for smaller p. This occurs in the range of not too small longitudinal wave numbers k > k c. For the model, containing inhomogeneous environment the basic dispersion properties are generally identical to that for the monolithic tube model, studied in Lopin & Nagorny (2015b). The waves are trapped for all wave numbers, if the power-law index 0 < n < 2. There are both trapped and leaky regimes for n ≥ 2. The wave dispersion decreases for smaller n , in the range of the intermediate values of the longitudinal wave numbers k > k c. The seismological application of the obtained results is discussed. [ABSTRACT FROM AUTHOR]