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An experiment carried out at the Brookhaven National Laboratory over a period of almost 8 years acquired 364 measurements of the beta-decay rates of a sample of ${}^{32}\mbox{Si}$ and, for comparison, of a sample of ${}^{36}\mbox{Cl}$ . The experimenters reported finding ' small periodic annual deviations of the data points from an exponential decay ... of uncertain origin'. We find that power-spectrum and spectrogram analyses of these datasets show evidence not only of the annual oscillations, but also of transient oscillations with frequencies near 11 year and 12.5 year. Similar analyses of 358 measurements of the solar neutrino flux acquired by the Super-Kamiokande neutrino observatory over a period of about 5 years yield evidence of an oscillation near 12.5 year and another near 9.5 year. An oscillation near 12.5 year is compatible with the influence of rotation of the radiative zone. We suggest that an oscillation near 9.5 year may be indicative of rotation of the solar core, and that an oscillation near 11 year may have its origin in a tachocline between the core and the radiative zone. Modulation of the solar neutrino flux may be attributed to an influence of the Sun's internal magnetic field by the Resonant Spin Flavor Precession (RSFP) mechanism, suggesting that neutrinos and neutrino-induced beta decays can provide information about the deep solar interior. [ABSTRACT FROM AUTHOR]

The base of the convection zone and the tachocline play a major role in the study of the dynamics of the Sun, especially in the solar dynamo. Here, we present a phase-sensitive helioseismic holography method to infer changes in the sound-speed profile of the solar interior. We test the technique using numerically simulated data by Zhao et al. ( Astrophys. J. 702, 1150, ) with sound-speed perturbations at $0.7 R_{\odot }$. The technique adequately recovers the perturbed sound-speed profile and is seen to be capable of detecting changes in the sound speed as low as 0.05 %. We apply the method to two GONG solar time series of approximately one year, each comprising 13 Bartels rotations, BR2295-BR2307 and BR2387-BR2399, near the maximum and at a minimum of solar activity, respectively. We successfully recover a sound-speed variation with respect to a standard solar model, consistent with previous results. However, we fail to recover a realistic sound-speed variation between maximum and minimum. [ABSTRACT FROM AUTHOR]

The structure of the Sun's corona varies with the solar-cycle phase, from a near spherical symmetry at solar maximum to an axial dipole at solar minimum. It is widely accepted that the large-scale coronal structure is governed by magnetic fields that are most likely generated by dynamo action in the solar interior. In order to understand the variation in coronal structure, we couple a potential-field source-surface model with a cyclic dynamo model. In this coupled model, the magnetic field inside the convection zone is governed by the dynamo equation; these dynamo-generated fields are extended from the photosphere to the corona using a potential-field source-surface model. Assuming axisymmetry, we take linear combinations of associated Legendre polynomials that match the more complex coronal structures. Choosing images of the global corona from the Mauna Loa Solar Observatory at each Carrington rotation over half a cycle (1986 - 1991), we compute the coefficients of the associated Legendre polynomials up to degree eight and compare with observations. We show that at minimum the dipole term dominates, but it fades as the cycle progresses; higher-order multipolar terms begin to dominate. The amplitudes of these terms are not exactly the same for the two limbs, indicating that there is a longitude dependence. While both the 1986 and the 1996 minimum coronas were dipolar, the minimum in 2008 was unusual, since there was a substantial departure from a dipole. We investigate the physical cause of this departure by including a North-South asymmetry in the surface source of the magnetic fields in our flux-transport dynamo model, and find that this asymmetry could be one of the reasons for departure from the dipole in the 2008 minimum. [ABSTRACT FROM AUTHOR]

Our previous semi-analytic treatment of $f$- and $p$-mode multiple scattering from ensembles of thin flux tubes (Hanson and Cally, Astrophys. J. 781, 125, ; 791, 129, ) is extended by allowing both sausage and kink waves to freely escape at the top of the model using a radiative boundary condition there. As expected, this additional avenue of escape, supplementing downward loss into the deep solar interior, results in substantially greater absorption of incident $f$- and $p$-modes. However, less intuitively, it also yields mildly to substantially smaller phase shifts in waves emerging from the ensemble. This may have implications for the interpretation of seismic data for solar plage regions, and in particular their small measured phase shifts. [ABSTRACT FROM AUTHOR]

We study the combined effects of convection and radiative diffusion on the evolution of thin magnetic flux tubes in the solar interior. Radiative diffusion is the primary supplier of heat to convective motions in the lower convection zone, and it results in a heat input per unit volume of magnetic flux tubes that has been ignored by many previous thin flux tube studies. We use a thin flux tube model subject to convection taken from a rotating spherical shell of turbulent, solar-like convection as described by Weber, Fan, and Miesch ( Astrophys. J. 741, 11, ; Solar Phys. 287, 239, ), now taking into account the influence of radiative heating on 10 Mx flux tubes, corresponding to flux tubes of large active regions. Our simulations show that flux tubes of ≤ 60 kG that are subject to solar-like convective flows do not anchor in the overshoot region, but rather drift upward because of the increased buoyancy of the flux tube earlier in its evolution, which results from including radiative diffusion. Flux tubes of magnetic field strengths ranging from 15 kG to 100 kG have rise times of ≤ 0.2 years and exhibit a Joy's Law tilt-angle trend. Our results suggest that radiative heating is an effective mechanism by which flux tubes can escape from the stably stratified overshoot region. Moreover, flux tubes do not necessarily need to be anchored in the overshoot region to produce emergence properties similar to those of active regions on the Sun. [ABSTRACT FROM AUTHOR]

The increased amount of information provided by ongoing missions such as the Solar Dynamics Observatory (SDO) represents a great challenge for the understanding of basic questions such as the internal structure of sunspots and how they evolve with time. Here, we contribute with the exploitation of new data, to provide a better understanding of the separate growth and decay of sunspots, umbra, and penumbra. Using fuzzy sets to compute separately the areas of sunspot umbra and penumbra, the growth and decay rates for active regions NOAA 11117, NOAA 11428, NOAA 11429, and NOAA 11430 are computed from the analysis of intensitygrams obtained by the Helioseismic and Magnetic Imager onboard SDO. A simplified numerical model is proposed for the decay phase, whereby an empirical irrotational and uniformly convergent horizontal velocity field interacting with an axially symmetric and height-invariant magnetic field reproduces the large-scale features of the much more complex convection observed inside sunspots. [ABSTRACT FROM AUTHOR]

The accuracy of helioseismic measurement is limited by the stochastic nature of solar oscillations. In this article I use a Gaussian statistical model of the global seismic wave field of the Sun to investigate the noise limitations of direct-modeling analysis of convection-zone-scale flows. The theoretical analysis of noise is based on hypothetical data that cover the entire photosphere, including the portions invisible from the Earth. Noise estimates are derived for measurements of the flow-dependent couplings of global-oscillation modes and for combinations of coupling measurements that isolate vector-spherical-harmonic components of the flow velocity. For current helioseismic observations, which sample only a fraction of the photosphere, the inferred detection limits are best regarded as optimistic limits. The flow-velocity fields considered in this work are assumed to be decomposable into vector-spherical-harmonic functions of degree less than five. The problem of measuring the general velocity field is shown to be similar enough to the well-studied problem of measuring differential rotation to permit rough estimates of flow-detection thresholds to be gleaned from past helioseismic analysis. I estimate that, with existing and anticipated helioseismic datasets, large-scale flow-velocity amplitudes of a few tens of ${\rm m\,s^{-1}}$ should be detectable near the base of the convection zone. [ABSTRACT FROM AUTHOR]

We search for a signature of helicity flow from the solar interior to the photosphere and chromosphere. For this purpose, we study two active regions, NOAA 11084 and 11092, that show a regular pattern of superpenumbral whirls in chromospheric and coronal images. These two regions are good candidates for comparing magnetic/current helicity with subsurface kinetic helicity because the patterns persist throughout the disk passage of both regions. We use photospheric vector magnetograms from SOLIS/VSM and SDO/HMI to determine a magnetic helicity proxy, the spatially averaged signed shear angle (SASSA). The SASSA parameter produces consistent results leading to positive values for NOAA 11084 and negative ones for NOAA 11092 consistent with the clockwise and counter-clockwise orientation of the whirls. We then derive the properties of the subsurface flows associated with these active regions. We measure subsurface flows using a ring-diagram analysis of GONG high-resolution Doppler data and derive their kinetic helicity, hz. Since the patterns persist throughout the disk passage, we analyze synoptic maps of the subsurface kinetic helicity density. The sign of the subsurface kinetic helicity is negative for NOAA 11084 and positive for NOAA 11092; the sign of the kinetic helicity is thus anticorrelated with that of the SASSA parameter. As a control experiment, we study the subsurface flows of six active regions without a persistent whirl pattern. Four of the six regions show a mixture of positive and negative kinetic helicity resulting in small average values, while two regions are clearly dominated by kinetic helicity of one sign or the other, as in the case of regions with whirls. The regions without whirls follow overall the same hemispheric rule in their kinetic helicity as in their current helicity with positive values in the southern and negative values in the northern hemisphere. [ABSTRACT FROM AUTHOR]

We study heliospheric propagation and some space weather aspects of three Earth-directed interplanetary coronal mass ejections (ICMEs), successively launched from the active region AR 11158 in the period 13 – 15 February 2011. From the analysis of the ICME kinematics, morphological evolution, and in situ observations, we infer that the three ICMEs interacted on their way to Earth, arriving together at 1 AU as a single interplanetary disturbance. Detailed analysis of the in situ data reveals complex internal structure of the disturbance, where signatures of the three initially independent ICMEs could be recognized. The analysis also reveals compression and heating of the middle ICME, as well as ongoing magnetic reconnection between the leading and the middle ICME. We present evidence showing that the propagation of these two, initially slower ICMEs, was boosted by the fastest, third ICME. Finally, we employ the ground-based cosmic ray observations, to show that this complex disturbance produced a single cosmic ray event, i.e., a simple Forbush decrease (FD). The results presented provide a better understanding of the ICME interactions and reveal effects that should be taken into account in forecasting of the arrival of such compound structures. [ABSTRACT FROM AUTHOR]

We describe and apply a new helioseismic method for measuring solar subsurface axisymmetric meridional and zonal flow. The method is based on a theoretical model of the response of global-oscillation eigenfunctions to the flow velocity and uses cross spectra of the time-varying coefficients in the spherical-harmonic expansion of the photospheric Doppler-velocity field. Eigenfunction changes modify the leakage matrix, which describes the sensitivity of the spherical-harmonic coefficients to the global-oscillation modes. The form of the leakage matrix in turn affects the theoretically expected spherical-harmonic cross spectra. Estimates of internal meridional and zonal flow were obtained by fitting the theoretical flow-dependent cross spectra to spherical-harmonic cross spectra computed from approximately 500 days of full-disk Dopplergrams from the Helioseismic and Magnetic Imager (HMI) on the SDO spacecraft. The zonal-flow measurements, parameterized in the form of “ a” coefficients, substantially agree with measurements obtained from conventional global-mode-frequency analysis. The meridional-flow estimates, in the form of depth-weighted averages of the flow velocity, are similar to estimates obtained from earlier analyses, for oscillation modes that penetrate the outermost one-third of the convection zone. For more deeply penetrating modes, the inferred flow velocity increases significantly with penetration depth, indicating the need for either a modification of the simple conveyor-belt picture of meridional flow or improvement in the cross-spectral model. [ABSTRACT FROM AUTHOR]

Helioseismology has been widely acclaimed as having been a great success: it appears to have answered nearly all the questions that we originally asked, some with unexpectedly high precision. We have learned how the sound speed and matter density vary throughout almost all of the solar interior – something which not so very long ago was generally considered to be impossible – we have learned how the Sun rotates, and we have a beautiful picture, on a coffee cup, of the thermal stratification of a sunspot, and also an indication of the material flow around it. We have tried, with some success at times, to apply our findings to issues of broader relevance: the test of the General Theory of Relativity via planetary orbit precession (now almost forgotten because the issue has convincingly been closed, albeit no doubt temporarily) the solar neutrino problem, the manner of the transport of energy from the centre to the surface of the Sun, the mechanisms of angular-momentum redistribution, and the workings of the solar dynamo. The first two were of general interest to the broad scientific community beyond astronomy, and were, quite rightly, principally responsible for our acclaimed success; the others are still in a state of flux. [ABSTRACT FROM AUTHOR]

We consider the dissipative evolution of a spherical magnetic vortex with a force-free internal structure, located in a resistive medium and held in equilibrium by the potential external field. The magnetic field inside the sphere is force-free (the model of Chandrasekhar in Proc. Natl. Acad. Sci. 42, 1, ). Topologically, it is a set of magnetic toroids enclosed in spherical layers. A new exact MHD solution has been derived, describing a slow, uniform, radial compression of a magnetic spheroid under the pressure of an ambient field, when the plasma density and pressure are growing inside it. There is no dissipation in the potential field outside the sphere, but inside the sphere, where the current density can be high enough, the magnetic energy is continuously converted into heat. Joule dissipation lowers the magnetic pressure inside the sphere, which balances the pressure of the ambient field. This results in radial contraction of the magnetic sphere with a speed defined by the conductivity of the plasma and the characteristic spatial scale of the magnetic field inside the sphere. Formally, the sphere shrinks to zero within a finite time interval (magnetic collapse). The time of compression can be relatively small, within a day, even for a sphere with a radius of about 1 Mm, if the magnetic helicity trapped initially in the sphere (which is proportional to the number of magnetic toroids in the sphere) is quite large. The magnetic system is open along its axis of symmetry. On this axis, the magnetic and electric fields are strictly radial and sign-variable along the radius, so the plasma will be ejected along the axis of magnetic sphere outwards in both directions (as jets) at a rate much higher than the diffusive one, and the charged particles will be accelerated unevenly, in spurts, creating quasi-regular X-ray spikes. The applications of the solution to solar flares are discussed. [ABSTRACT FROM AUTHOR]

This paper reviews some of the many 3D numerical experiments of the emergence of magnetic fields from the solar interior and the subsequent interaction with the pre-existing coronal magnetic field. The models described here are idealised, in the sense that the internal energy equation only involves the adiabatic, Ohmic and viscous shock heating terms. However, provided the main aim is to investigate the dynamical evolution, this is adequate. Many interesting observational phenomena are explained by these models in a self-consistent manner. [ABSTRACT FROM AUTHOR]

We compute the change in the Lorentz force integrated over the outer solar atmosphere implied by observed changes in vector magnetograms that occur during large, eruptive solar flares. This force perturbation should be balanced by an equal and opposite force perturbation acting on the solar photosphere and solar interior. The resulting expression for the estimated force change in the solar interior generalizes the earlier expression presented by Hudson, Fisher, and Welsch ( Astron. Soc. Pac. CS-383, 221, ), providing horizontal as well as vertical force components, and provides a more accurate result for the vertical component of the perturbed force. We show that magnetic eruptions should result in the magnetic field at the photosphere becoming more horizontal, and hence should result in a downward (toward the solar interior) force change acting on the photosphere and solar interior, as recently argued from an analysis of magnetogram data by Wang and Liu ( Astrophys. J. Lett. 716, L195, ). We suggest the existence of an observational relationship between the force change computed from changes in the vector magnetograms, the outward momentum carried by the ejecta from the flare, and the properties of the helioseismic disturbance driven by the downward force change. We use the impulse driven by the Lorentz-force change in the outer solar atmosphere to derive an upper limit to the mass of erupting plasma that can escape from the Sun. Finally, we compare the expected Lorentz-force change at the photosphere with simple estimates from flare-driven gasdynamic disturbances and from an estimate of the perturbed pressure from radiative backwarming of the photosphere in flaring conditions. [ABSTRACT FROM AUTHOR]

Inversions for local helioseismology are an important and necessary step for obtaining three-dimensional maps of various physical quantities in the solar interior. Frequently, the full inverse problems that one would like to solve prove intractable because of computational constraints. Due to the enormous seismic data sets that already exist and those forthcoming, this is a problem that needs to be addressed. To this end, we present a very efficient linear inversion algorithm for local helioseismology. It is based on a subtractive optimally localized averaging (SOLA) scheme in the Fourier domain, utilizing the horizontal-translation invariance of the sensitivity kernels. In Fourier space the problem decouples into many small problems, one for each horizontal wave vector. This multichannel SOLA method is demonstrated for an example problem in time-distance helioseismology that is small enough to be solved both in real and Fourier space. We find that both approaches are successful in solving the inverse problem. However, the multichannel SOLA algorithm is much faster and can easily be parallelized. [ABSTRACT FROM AUTHOR]

The Helioseismic and Magnetic Imager onboard the Solar Dynamics Observatory (SDO/HMI) provides continuous full-disk observations of solar oscillations. We develop a data-analysis pipeline based on the time-distance helioseismology method to measure acoustic travel times using HMI Doppler-shift observations, and infer solar interior properties by inverting these measurements. The pipeline is used for routine production of near-real-time full-disk maps of subsurface wave-speed perturbations and horizontal flow velocities for depths ranging from 0 to 20 Mm, every eight hours. In addition, Carrington synoptic maps for the subsurface properties are made from these full-disk maps. The pipeline can also be used for selected target areas and time periods. We explain details of the pipeline organization and procedures, including processing of the HMI Doppler observations, measurements of the travel times, inversions, and constructions of the full-disk and synoptic maps. Some initial results from the pipeline, including full-disk flow maps, sunspot subsurface flow fields, and the interior rotation and meridional flow speeds, are presented. [ABSTRACT FROM AUTHOR]

Internal gravity waves excited by overshoot at the bottom of the convection zone can be influenced by rotation and by the strong toroidal magnetic field that is likely to be present in the solar tachocline. Using a simple Cartesian model, we show how waves with a vertical component of propagation can be reflected when traveling through a layer containing a horizontal magnetic field with a strength that varies with depth. This interaction can prevent a portion of the downward traveling wave energy flux from reaching the deep solar interior. If a highly reflecting magnetized layer is located some distance below the convection zone base, a duct or wave guide can be set up, wherein vertical propagation is restricted by successive reflections at the upper and lower boundaries. The presence of both upward and downward traveling disturbances inside the duct leads to the existence of a set of horizontally propagating modes that have significantly enhanced amplitudes. We point out that the helical structure of these waves makes them capable of generating an α-effect, and briefly consider the possibility that propagation in a shear of sufficient strength could lead to instability, the result of wave growth due to over-reflection. [ABSTRACT FROM AUTHOR]

Evidence for an anomalous annual periodicity in certain nuclear-decay data has led to speculation on a possible solar influence on nuclear processes. We have recently analyzed data concerning the decay rates of Cl and Si, acquired at the Brookhaven National Laboratory (BNL), to search for evidence that might be indicative of a process involving solar rotation. Smoothing of the power spectrum by weighted-running-mean analysis leads to a significant peak at frequency 11.18 year, which is lower than the equatorial synodic rotation rates of the convection and radiative zones. This article concerns measurements of the decay rates of Ra acquired at the Physikalisch-Technische Bundesanstalt (PTB) in Germany. We find that a similar (but not identical) analysis yields a significant peak in the PTB dataset at frequency 11.21 year, and a peak in the BNL dataset at 11.25 year. The change in the BNL result is not significant, since the uncertainties in the BNL and PTB analyses are estimated to be 0.13 year and 0.07 year, respectively. Combining the two running means by forming the joint power statistic leads to a highly significant peak at frequency 11.23 year. We will briefly comment on the possible implications of these results for solar physics and for particle physics. [ABSTRACT FROM AUTHOR]

Wolff ( Astrophys. J. 193, 721, ) introduced the concept of g-mode coupling within the solar interior. Subsequently, Wolff developed a more quantitative model invoking a reciprocal interaction between coupled g modes and burning in the solar core. Coupling is proposed to occur for constant values of the spherical harmonic degree [ ℓ] creating rigidly rotating structures denoted as sets( ℓ). Power would be concentrated near the core and the top of radiative zone [RZ] in narrow intervals of longitude on opposite sides of the Sun. Sets( ℓ) would migrate retrograde in the RZ as function of ℓ and their intersections would deposit extra energy at the top of the RZ. It is proposed that this enhances sunspot eruptions at particular longitudes and at regular time intervals. Juckett and Wolff ( Solar Phys. 252, 247, ) detected this enhancement by viewing selected spherical harmonics of sunspot patterns within stackplots twisted into the relative rotational frames of various sets( ℓ). In subsequent work, the timings of the set( ℓ) intersections were compared to the sub-decadal variability of the sunspot cycle. Seventeen sub-decadal intersection frequencies (0.63 – 7.0 year) were synchronous with 17 frequencies in the sunspot time-series with a mean correlation of 0.96. Six additional non-11-year frequencies (periods of 8.0 to 28.7 year) are now shown to be nearly synchronous between sunspot variability and the model. Two additional intersections have the same frequency as the solar cycle itself and peak during the rising phase of the solar cycle. This may be partly responsible for cycle asymmetry. These results are evidence that some of the solar-cycle variability may be attributable to deterministic components that are intermixed with a broad-spectrum stochastic and long-term chaotic background. [ABSTRACT FROM AUTHOR]

Helioseismic techniques such as ring-diagram analysis have often been used to determine the subsurface structural differences between solar active and quiet regions. Results obtained by inverting the frequency differences between the regions are usually interpreted as the sound-speed differences between them. These in turn are used as a measure of temperature and magnetic-field strength differences between the two regions. In this paper we first show that the “sound-speed” difference obtained from inversions is actually a combination of sound-speed difference and a magnetic component. Hence, the inversion result is not directly related to the thermal structure. Next, using solar models that include magnetic fields, we develop a formulation to use the inversion results to infer the differences in the magnetic and thermal structures between active and quiet regions. We then apply our technique to existing structure inversion results for different pairs of active and quiet regions. We find that the effect of magnetic fields is strongest in a shallow region above 0.985 R⊙ and that the strengths of magnetic-field effects at the surface and in the deeper ( r<0.98 R⊙) layers are inversely related ( i.e., the stronger the surface magnetic field the smaller the magnetic effects in the deeper layers, and vice versa). We also find that the magnetic effects in the deeper layers are the strongest in the quiet regions, consistent with the fact that these are basically regions with weakest magnetic fields at the surface. Because the quiet regions were selected to precede or follow their companion active regions, the results could have implications about the evolution of magnetic fields under active regions. [ABSTRACT FROM AUTHOR]

Recently, Juckett and Wolff ( Solar Phys. 252, 247, ) showed that the timing and longitude of sunspot patterns has some correspondence with a model based on coupled g modes. The model maximizes the nonlinear coupling of those g modes sharing harmonic degree ℓ to generate a “set( ℓ)” that assists its own excitation by locally enhancing nuclear burning. Each set( ℓ) has oscillatory power concentrated at two longitudes, on opposite sides of the Sun and drifts slowly retrograde within the radiative zone (RZ) at a rate that depends on ℓ. When the strong longitudes of two or more sets overlap, wave dissipation adds extra energy to that locality at the base of the convective envelope increasing convection and then sunspot activity. We compare the main subdecadal sunspot frequencies with the intersections of sets derived from ℓ=2 – 11 and G, where G represents unresolvable high- ℓ modes that rotate similarly to the RZ. After determining the set( ℓ) spatial phases, we show that 17 subdecadal oscillations with periods in the range 0.6 to 7.0 years (4.5 to 50 nHz), generated by 23 unique intersections of the 11 sets, are synchronous with 17 corresponding frequencies in the sunspot time series. After optimizing parameters, we find a mean correlation of 0.96 for synchrony among the 17 waveform pairs. These 17 frequencies constitute the bulk of the non-noise subdecadal frequency domain of the sunspot variation. We conclude that the sunspot series contains oscillatory components with the same temporal phases and frequencies as various set( ℓ) intersections spanning the past ≈ 100 years. This additional evidence for the role of coupled g modes in sunspot dynamics suggests that more of sunspot variability can be understood with nonmagnetic fluid mechanics than popularly thought. [ABSTRACT FROM AUTHOR]

Temporal variations of the subsurface meridional flow with the solar cycle have been reported by several authors. The measurements are typically averaged over periods of time during which surface magnetic activity existed in the regions where the velocities are calculated. The present work examines the possible contamination of these measurements due to the extra velocity fields associated with active regions plus the uncertainties in the data obtained where strong magnetic fields are present. We perform a systematic analysis of more than five years of GONG data and compare meridional flows obtained by ring-diagram analysis before and after removing the areas of strong magnetic field. The overall trend of increased amplitude of the meridional flow towards solar minimum remains after removal of large areas associated with surface activity. We also find residual circulation toward the active belts that persists even after the removal of the surface magnetic activity, suggesting the existence of a global pattern or longitudinally-located organized flows. [ABSTRACT FROM AUTHOR]

Solar g-modes are global oscillations that would exist primarily in the radiative zone (RZ) and would be excited by either convective overshoot or nuclear burning in the core. Wolff and O’Donovan ( Astrophys. J. 661, 568, ) proposed a non-linear coupling of g-modes into groups that share the same harmonic degree ℓ. Each group (denoted set( ℓ)) exhibits a unique retrograde rotation rate with respect to the RZ that depends mainly on ℓ. The coupling yields a standing wave (nearly stationary in longitude) that has two angularly defined hot spots offset from the equator on opposite sides of the Sun that would deposit energy asymmetrically in the lower convective envelope (CE). It is anticipated that when two or more groups overlap in longitude, an increase in local heating would influence the distribution of sunspots. In this paper, we scanned a multitude of rotational reference frames for sunspot clustering to test for frames that are concordant with the rotation of these g-modes sets. To achieve this, spherical harmonic filtering of sunspot synoptic maps was used to extract patterns consistent with coalesced g-modes. The latitude band, with minimal differential rotation, was sampled from each filtered synoptic map and layered into a stackplot. This was progressively shifted, line-by-line, into different rotational reference frames. We have detected long-lived longitudinal alignments, spanning 90 years of solar cycles, which are consistent with the rotation rate of the deep solar interior as well as other rotational frames predicted by the coupled g-mode model. Their sidereal rotation rates of 370.0, 398.8, 412.7, 418.3, 421.0, 424.2 and 430.0 nHz correspond, respectively, to coupled g-modes for ℓ = 2 through 7 and G, where G is a set with high ℓ values or a group of such sets (unresolved) that rotate almost as fast as the RZ. While the clustering in these reference frames offers new approaches for studying the longitudinal behavior of solar activity, it tentatively leads to the more profound conclusion that a portion of the driving force for sunspot occurrence is linked to energy extracted from the solar core and deposited at the top of the RZ by solar g-modes. [ABSTRACT FROM AUTHOR]

We present results of nonlinear, two-dimensional, numerical simulations of magneto-acoustic wave propagation in the photosphere and chromosphere of small-scale flux tubes with internal structure. Waves with realistic periods of three to five minutes are studied, after horizontal and vertical oscillatory perturbations are applied to the equilibrium model. Spurious reflections of shock waves from the upper boundary are minimized by a special boundary condition. This has allowed us to increase the duration of the simulations and to make it long enough to perform a statistical analysis of oscillations. The simulations show that deep horizontal motions of the flux tube generate a slow (magnetic) mode and a surface mode. These modes are efficiently transformed into a slow (acoustic) mode in the v A< c S atmosphere. The slow (acoustic) mode propagates vertically along the field lines, forms shocks, and remains always within the flux tube. It might effectively deposit the energy of the driver into the chromosphere. When the driver oscillates with a high frequency, above the cutoff, nonlinear wave propagation occurs with the same dominant driver period at all heights. At low frequencies, below the cutoff, the dominant period of oscillations changes with height from that of the driver in the photosphere to its first harmonic (half period) in the chromosphere. Depending on the period and on the type of the driver, different shock patterns are observed. [ABSTRACT FROM AUTHOR]

Helioseismic global modes change in time, in particular on time scales of the solar cycle. These changes show, in fact, strong correlation with the magnetic activity cycle of the Sun, indicating that a most likely cause of the variation of the mode characteristics, such as frequency, is the magnetic field. In the present paper I attempt to find out in what ways and to what degree the magnetic atmosphere of the Sun can influence the f and p modes of helioseismology. Frequency shifts of the order of a microhertz, line widths of the order of a nanohertz, and penetration depths of the order of a megameter are obtained. [ABSTRACT FROM AUTHOR]

The solar rotation profile is well constrained down to about 0.25 R ⊙ thanks to the study of acoustic modes. Since the radius of the inner turning point of a resonant acoustic mode is inversely proportional to the ratio of its frequency to its degree, only the low-degree p modes reach the core. The higher the order of these modes, the deeper they penetrate into the Sun and thus they carry more diagnostic information on the inner regions. Unfortunately, the estimates of frequency splittings at high frequency from Sun-as-a-star measurements have higher observational errors because of mode blending, resulting in weaker constraints on the rotation profile in the inner core. Therefore inversions for the solar internal rotation use only modes below 2.4 mHz for ℓ≤3. In the work presented here, we used an 11.5-year-long time series to compute the rotational frequency splittings for modes ℓ≤3 using velocities measured with the GOLF instrument. We carried out a theoretical study of the influence of the low-degree modes in the region from 2 to 3.5 mHz on the inferred rotation profile as a function of their error bars. [ABSTRACT FROM AUTHOR]

We review the impact of global helioseismology on key questions concerning the internal structure and dynamics of the Sun and consider the exciting challenges the field faces as it enters a fourth decade of science exploitation. We do so with an eye on the past, looking at the perspectives global helioseismology offered in its earlier phases, in particular the mid-to-late 1970s and the 1980s. We look at how modern, higher quality, longer datasets coupled with new developments in analysis have altered, refined, and changed some of those perspectives and opened others that were not previously available for study. We finish by discussing outstanding challenges and questions for the field. [ABSTRACT FROM AUTHOR]

To recover the flow information encoded in travel-time data of time – distance helioseismology, accurate forward modeling and a robust inversion of the travel times are required. We accomplish this using three-dimensional finite-frequency travel-time sensitivity kernels for flows along with a (2+1)-dimensional (2+1D) optimally localized averaging (OLA) inversion scheme. Travel times are measured by ridge filtering MDI full-disk Doppler data and the corresponding Born sensitivity kernels are computed for these particular travel times. We also utilize the full noise-covariance properties of the travel times, which allow us to accurately estimate the errors for all inversions. The whole procedure is thus fully consistent. Because of ridge filtering, the kernel functions separate in the horizontal and vertical directions, motivating our choice of a 2+1D inversion implementation. The inversion procedure also minimizes cross-talk effects among the three flow components, and the averaging kernels resulting from the inversion show very small amounts of cross-talk. We obtain three-dimensional maps of vector solar flows in the quiet Sun at horizontal spatial resolutions of 7−10 Mm using generally 24 hours of data. For all of the flow maps we provide averaging kernels and the noise estimates. We present examples to test the inferred flows, such as a comparison with Doppler data, in which we find a correlation of 0.9. We also present results for quiet-Sun supergranular flows at different depths in the upper convection zone. Our estimation of the vertical velocity shows good qualitative agreement with the horizontal vector flows. We also show vertical flows measured solely from f-mode travel times. In addition, we demonstrate how to directly invert for the horizontal divergence and flow vorticity. Finally we study inferred flow-map correlations at different depths and find a rapid decrease in this correlation with depth, consistent with other recent local helioseismic analyses. [ABSTRACT FROM AUTHOR]

Gravity modes are the best probes to infer the properties of the solar radiative zone, which represents 98% of the Sun’s total mass. It is usually assumed that high-frequency g modes give information about the structure of the solar interior whereas low-frequency g modes are more sensitive to the solar dynamics (the internal rotation). In this work, we develop a new methodology, based on the analysis of the almost constant separation of the dipole gravity modes, to introduce new constraints on the solar models. To validate this analysis procedure, several solar models – including different physical processes and either old or new chemical abundances (from, respectively, Grevesse and Noels ( Origin and Evolution of the Elements 199, Cambridge University Press, Cambridge, 15, ) and Asplund, Grevesse, and Sauval ( Cosmic Abundances as Records of Stellar Evolution and Nucleosynthesis CS-336, Astron. Soc. Pac., San Francisco, 25 – 38, )) – have been compared to another model used as a reference. The analysis clearly shows that this methodology has enough sensitivity to distinguish among some of the models, in particular, among those with different compositions. The comparison of the models with the g-mode asymptotic signature detected in GOLF data favors the ones with old abundances. Therefore, the physics of the core – obtained through the analysis of the g-mode properties – is in agreement with the results obtained in the previous studies based on the acoustic modes, which are mostly sensitive to more external layers of the Sun. [ABSTRACT FROM AUTHOR]

The temporal changes in the two-dimensional patterns of sunspot groups, spanning 125 years (1650 Carrington Rotations), were previously analyzed using surface spherical harmonics (SSHs) (Juckett, 2003) in an attempt to quantify properties of the active longitudes among sunspot distributions. Common trends in the oscillations of both the amplitudes and spatial phases of sectoral combinations of SSHs were examined. The amplitude analysis revealed strong evidence for the second and third harmonics of the 11-year cycle across all SSHs, plus evidence for other structured variations spanning both longer and shorter time scales. In this report, temporal oscillations above the second harmonic reveal a dispersion relationship with respect to order, m, in the m = l and m = l–1 SSH modes. Furthermore, the relationship between amplitude and abrupt spatial phase transitions for these oscillations is consistent with the behavior of standing waves. Under this assumption, each standing-wave half-cycle is identified by spatial phase transitions between $$\frac{3}{4}\pi$$ and π. This was used to convert the SSH amplitude series for each mode from a rectified version of the standing wave to an estimate of the full cycle. Spectral analysis yielded a dispersion relation over the SSH order range m = 1 to m = 18 spanning the cycle periods from the 11-year solar cycle down to that of the well-documented, but ill-understood 1.3 and 1.8 year quasi-periodic cycles of the quasi-biennial oscillation. Examination of the spatial phase patterns of the SSH modes suggests that the longitudinal variations in sunspot clustering are a complex phenomena with patterns occurring in several time scales. The standing wave trait of the SSH modes may offer evidence uniting the dynamo waves in the convective zone to interfacial oscillations in the tachocline. [ABSTRACT FROM AUTHOR]

The Solar and Heliospheric Observatory (SOHO) is a space mission that forms part of the Solar-Terrestrial Science Program (STSP), developed in a collaborative effort by the European Space Agency (ESA) and the National Aeronautics and Space Administration (NASA). The STSP constitutes the first 'cornerstone' of ESA's long-term programme known as 'Space Science - Horizon 2000'. The principal scientific objectives of the SOHO mission are a) to reach a better understanding of the structure and dynamics of the solar interior using techniques of helioseismology, and b) to gain better insight into the physical processes that form and heat the Sun's corona, maintain it and give rise to its acceleration into the solar wind. To achieve these goals, SOHO carries a payload consisting of 12 sets of complementary instruments. SOHO is a three-axis stabilized spacecraft with a total mass of 1850 kg; 1150 W of power will be provided by the solar panels. The payload weighs about 640 kg and will consume 450 W in orbit. SOHO will be launched by an ATLAS II-AS and will be placed in a halo orbit around the Sun-Earth L1 Lagrangian point where it will be continuously pointing to Sun centre with an accuracy of 10 arcsec. Pointing stability will be better than 1 arcsec over 15 min intervals. The SOHO payload produces a continuous science data stream of 40 kbits/s which will be increased by 160 kbits/s whenever the solar oscillations imaging instrument is operated in its highrate mode. Telemetry will be received by NASA's Deep Space Network (DSN). Planning, coordination and operation of the spacecraft and the scientific payload will be conducted from the Experiment Operations Facility (EOF) at NASA's Goddard Space Flight Center (GSFC). [ABSTRACT FROM AUTHOR]