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The pattern of migrating zonal flow bands associated with the solar cycle, known as the torsional oscillation, has been monitored with continuous global helioseismic observations by the Global Oscillations Network Group, together with those made by the Michelson Doppler Imager onboard the Solar and Heliosepheric Observatory and its successor the Helioseismic and Magnetic Imager onboard the Solar Dynamics Observatory, since 1995, giving us nearly two full solar cycles of observations. We report that the flows now show traces of the mid-latitude acceleration that is expected to become the main equatorward-moving branch of the zonal flow pattern for Cycle 25. Based on the current position of this branch, we speculate that the onset of widespread activity for Cycle 25 is unlikely to be earlier than the middle of 2019., Comment: 8 pages, 5 figures, accepted by ApJL 5 July 2018

Using continuous observations for 22 years from ground-based network GONG and space-borne instruments MDI onboard {\it SoHO} and HMI onboard {\it SDO}, we report both global and local properties of the convection zone and their variations with time., Comment: To appear in the Proceedings of IAU Symposium 340 held at Jaipur (February 2018)

Magnetic fields extend from the solar interior through the atmosphere. The formation and evolution of active regions can be studied by measuring subsurface flows with local helioseismology. The emergence of magnetic flux from the solar convection zone is associated with acoustic perturbation signatures. In near-surface layers, the average dynamics can be determined for emerging regions. MHD simulations of the emergence of a twisted flux tube show how magnetic twist and free energy are transported from the interior into the corona and the dynamic signatures associated with such transport in the photospheric and sub-photospheric layers. The subsurface twisted flux tube does not emerge into the corona as a whole in emerging active regions. Shear flows at the polarity inversion line and coherent vortical motions in the subsurface flux tubes are the major means by which twist is transported into the corona, leading to the formation of sigmoid-shaped coronal magnetic fields capable of driving solar eruptions. The transport of twist can be followed from the interior by using the kinetic helicity of subsurface flows as a proxy of magnetic helicity; this quantity holds great promise for improving the understanding of eruptive phenomena. Waves are not only vital for studying the link between the solar interior and the surface but for linking the photosphere with the corona as well. Acoustic waves that propagate from the surface into the magnetically structured, dynamic atmosphere undergo mode conversion and refraction. These effects enable atmospheric seismology to determine the topography of magnetic canopies in the solar atmosphere. Inclined magnetic fields lower the cut-off frequency so that low frequency waves can leak into the outer atmosphere. Recent high resolution, high cadence observations of waves and oscillations in the solar atmosphere, have lead to a renewed interest in the potential role of waves as a heating mechanism. In light of their potential contribution to the heating of the solar atmosphere, some of the recent observations of waves and oscillations and ongoing modelling efforts are reviewed.

The Whole Heliosphere Interval (WHI) was an international observing and modeling effort to characterize the 3-D interconnected “heliophysical” system during this solar minimum, centered on Carrington Rotation 2068, March 20 – April 16, 2008. During the latter half of the WHI period, the Sun presented a sunspot-free, deep solar minimum type face. But during the first half of CR 2068 three solar active regions flanked by two opposite-polarity, low-latitude coronal holes were present. These departures from the quiet Sun led to both eruptive activity and solar wind structure. Most of the eruptive activity, i.e., flares, filament eruptions and coronal mass ejections (CMEs), occurred during this first, active half of the interval. We determined the source locations of the CMEs and the type of associated region, such as active region, or quiet sun or active region prominence. To analyze the evolution of the events in the context of the global solar magnetic field and its evolution during the three rotations centered on CR 2068, we plotted the CME source locations onto synoptic maps of the photospheric magnetic field, of the magnetic and chromospheric structure, of the white light corona, and of helioseismological subsurface flows. Most of the CME sources were associated with the three dominant active regions on CR 2068, particularly AR 10989. Most of the other sources on all three CRs appear to have been associated with either isolated filaments or filaments in the north polar crown filament channel. Although calculations of the flux balance and helicity of the surface magnetic features did not clearly identify a dominance of one region over the others, helioseismological subsurface flows beneath these active regions did reveal a pronounced difference among them. These preliminary results suggest that the “twistedness” (i.e., vorticity and helicity) of subsurface flows and its temporal variation might be related to the CME productivity of active regions, similar to the relationship between flares and subsurface flows. Fil: Webb, D. F.. Boston College; Estados Unidos Fil: Cremades Fernandez, Maria Hebe. Universidad Tecnologica Nacional; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina Fil: Sterling, A. C.. National Aeronautics And Space Administration; Estados Unidos Fil: Mandrini, Cristina Hemilse. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; Argentina Fil: Dasso, Sergio Ricardo. Consejo Nacional de Investigaciónes Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Astronomía y Física del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomía y Física del Espacio; Argentina Fil: Gibson, S. E.. High Altitude Observatory; Estados Unidos Fil: Haber, D. A.. State University Of Colorado Boulder; Estados Unidos Fil: Komm, R. W.. National Solar Observatory; Estados Unidos Fil: Petrie, G. J. D.. National Solar Observatory; Estados Unidos Fil: McIntosh, P. S.. Heliosynoptics; Estados Unidos Fil: Welsch, B. T.. University of California; Estados Unidos Fil: Plunkett, S. P.. Spece Sciences División. Naval Research Laboratory; Estados Unidos

We study the temporal variation of subsurface flows associated with active regions within 16 Mm of the solar surface. We have analyzed the subsurface flows of nearly 1000 active and quiet regions applying ring-diagram analysis to Global Oscillation Network Group (GONG) Dopplergram data. We find that newly emerging active regions are characterized by enhanced upflows and fast zonal flows in the near-surface layers, as expected for a flux tube rising from deeper layers of the convection zone. The subsurface flows associated with strong active regions are highly twisted, as indicated by their large vorticity and helicity values. The dipolar pattern exhibited by the zonal and meridional vorticity component leads to the interpretation that these subsurface flows resemble vortex rings, when measured on the spatial scales of the standard ring-diagram analysis.

We apply discriminant analysis to 1023 active regions and their subsurface-flow parameters, such as vorticity and kinetic helicity density, with the goal of distinguishing between flaring and non-flaring active regions. We derive synoptic subsurface flows by analyzing GONG high-resolution Doppler data with ring-diagram analysis. We include magnetic-flux values in the discriminant analysis derived from NSO Kitt Peak and SOLIS synoptic maps binned to the same spatial scale as the helioseismic analysis. For each active region, we determine the flare information from GOES and include all flares within 60° central meridian distance to match the coverage of the ring-diagram analysis. The subsurface-flow characteristics improve the ability to distinguish between flaring and non-flaring active regions. For the C- and M-class flare category, the most important subsurface parameter is the so-called structure vorticity, which estimates the horizontal gradient of the horizontal-vorticity components. The no-event skill score, which measures the improvement over predicting that no events occur, reaches 0.48 for C-class flares and 0.32 for M-class flares, when the structure vorticity at three depths combined with total magnetic flux are used. The contributions come mainly from shallow layers within about 2 Mm of the surface and layers deeper than about 7 Mm.

We show here a component of the meridional circulation developing at medium-high latitudes (40-50 degrees) before the new solar cycle starts. Like the torsional oscillation of the zonal flows, this extra circulation seems to precede the onset of magnetic activity at the solar surface and move slowly towards lower latitudes. However, the behavior of this component differs from that of the torsional oscillation regarding location and convergence towards the equator at the end of the cycle. The observation of this component before the magnetic regions appear at the solar surface has only been possible due to the prolonged solar minimum. The results could settle the discussion as to whether the extra component of the meridional circulation around the activity belts, which has been known for some time, is or is not an effect of material motions around the active regions., ApJ Letters (accepted)

We report on the analysis of subsurface vorticity/helicity measurements for flare producing and quiet active regions. We have developed a parameter to investigate whether large, decreasing kinetic helicity density commonly occurs prior to active region flaring. This new parameter is effective at separating flaring and non-flaring active regions and even separates among C-, M-, and X-class flare producing regions. In addition, this parameter provides advance notice of flare occurrence, as it increases 2-3 days before the flare occurs. These results are striking on an average basis, though on an individual basis there is still considerable overlap between flare associated and non-flare associated values. We propose the following qualitative scenario for flare production: subsurface rotational kinetic energy twists the magnetic field lines into an unstable configuration, resulting in explosive reconnection and a flare.

We study the zonal flow in solar subsurface layers, analyzing about six years of GONG++ high-resolution Doppler data with ring-diagram analysis. We focus on the variation of zonal flow with magnetic activity over a range of depths from the surface to about 16 Mm. There is a positive correlation between unsigned magnetic flux and zonal flow at most depths. We calculate the average zonal flow for a quiet- and an active-region subset defined as dense-pack locations with an unsigned magnetic flux less than 3.4 G and locations with greater than 65.0 G, respectively. The average zonal flow of active regions is about 4 m s−1 larger than the average flow of quiet regions. This difference increases slightly with increasing depth, which might be explained by a nonradial inclination of the flux tubes or a different extent in depth of different magnetic features. The difference shows no apparent pattern in time and latitude, which makes it unlikely that it is simply a manifestation of the torsional-oscillation pattern. As a byproduct, we find that the size of the North – South asymmetry of the rotation rate decreases during the same epoch.

We measure the relation between divergence and vorticity of subsurface horizontal flows as a function of unsigned surface magnetic flux. Observations from the Michelson Doppler Imager (MDI) Dynamics Program and Global Oscillation Network Group (GONG) have been analyzed with a standard ring-diagram technique to measure subsurface horizontal flows from the surface to a depth of about 16 Mm. We study residual horizontal flows after subtracting large-scale trends (low-order polynomial fits in latitude) from the measured velocities. On average, quiet regions are characterized by weakly divergent horizontal flows and small anticyclonic vorticity (clockwise in the northern hemisphere), while locations of high activity show convergent horizontal flows combined with cyclonic vorticity (counterclockwise in the northern hemisphere). Divergence and vorticity of horizontal flows are anticorrelated (correlated) in the northern (southern) hemisphere. This is especially noticeable at greater depth, where the relation between divergence and vorticity of horizontal flows is nearly linear. These trends show a slight reversal at the highest levels of magnetic flux; the vorticity amplitude decreases at the highest flux levels, while the divergence changes sign at depths greater than about 10 Mm. The product of divergence and vorticity of the horizontal flows, a proxy of the vertical contribution to the kinetic helicity density, is on average negative (positive) in the northern (southern) hemisphere. The helicity proxy values are greater at locations of high magnetic activity than at quiet locations.

Near-surface flows measured by the ring-diagram technique of local helioseismology show structures that persist over multiple rotations. We examine these phenomena using data from the Global Oscillation Network Group (GONG) and the Helioseismic and Magnetic Imager (HMI) and show that a correlation analysis of the structures can be used to estimate the rotation rate as a function of latitude, giving a result consistent with the near-surface rate from global helioseismology and slightly slower than that obtained from a similar analysis of the surface magnetic field strength. At latitudes of $60^{\circ}$ and above, the HMI flow data reveal a strong signature of a two-sided zonal flow structure. This signature may be related to recent reports of “giant cells” in solar convection.

We search for a relation between flows below active regions and flare events occurring in those active regions. For this purpose, we determine the subsurface flows from high-resolution Global Oscillation Network Group (GONG) and Michelson Doppler Imager (MDI) Dynamics Program data using the ring-diagram technique. We then calculate the vorticity of the flows associated with active regions and compare it with a proxy of the total X-ray flare intensity of these regions using data from the Geostationary Operation Environmental Satellite (GOES). We have analyzed 408 active regions with X-ray flare activity from GONG and 159 active regions from MDI data. Both data sets lead to similar results. The maximum unsigned zonal and meridional vorticity components of active regions are correlated with the total flare intensity; this behavior is most apparent at values greater than 3.2 × 10-5 W m-2. These vorticity components show a linear relation with the logarithm of the flare intensity that is dependent on the maximum unsigned magnetic flux; vorticity values are proportional to the product of total flare intensity and maximum unsigned magnetic flux for flux values greater than about 36 G. Active regions with strong flare intensity show a dipolar pattern in the zonal and meridional vorticity component that reverses at depths between ~2 and 5 Mm. A measure of this pattern shows the same kind of relation with total flare intensity as the vorticity components. The vertical vorticity component shows no clear relation to flare activity.

We study the North–South asymmetry of zonal and meridional components of horizontal, solar subsurface flows during the years 2001–2004, which cover the declining phase of solar cycle 23. We measure the horizontal flows from the near-surface layers to 16 Mm depth by analyzing 44 consecutive Carrington rotations of Global Oscillation Network Group (GONG) Doppler images with a ring-diagram analysis technique. The meridional flow and the errors of both flow components show an annual variation related to the B 0-angle variation, while the zonal flow is less affected by the B 0-angle variation. After correcting for this effect, the meridional flow is mainly poleward but it shows a counter cell close to the surface at high latitudes in both hemispheres. During the declining phase of the solar cycle, the meridional flow mainly increases with time at latitudes poleward of about 20˚, while it mainly decreases at more equatorward latitudes. The temporal variation of the zonal flow in both hemispheres is significantly correlated at latitudes less than about 20˚. The zonal flow is larger in the southern hemisphere than the northern one, and this North–South asymmetry increases with depth. Details of the North–South asymmetry of zonal and meridional flow reflect the North–South asymmetry of the magnetic flux. The North–South asymmetries of the flows show hints of a variation with the solar cycle.

We compare changes in the frequencies of solar acoustic modes with degree between 0 and 2, as derived from Global Oscillation Network Group (GONG), Birmingham Solar Oscillations Network (BiSON) and Michelson Doppler Imager (MDI) spectra obtained between 1995 and 2003. We find that, after the solar-activity dependence has been removed from the frequencies, there remain variations that appear to be significant, and are often well correlated between the different data sets. We consider possible explanations for these fluctuations, and conclude that they are likely to be related to the stochastic excitation of the modes. The existence of such fluctuations has possible relevance to the analysis of other low-degree acoustic mode spectra such as those from solar-type stars.

Migrating bands of weak, zonal flow, associated with the activity bands in the solar cycle, have been observed at the solar surface for some time. More recently, these flows have been probed deep within the convection zone using global helioseismology and examined in more detail close to the surface with the techniques of local helioseismology. We compare the near-surface results from global and local helioseismology using data from the Michelson Doppler Imager and the Global Oscillation Network Group with surface Doppler velocity measurements from the Mount Wilson 150-foot tower and find that the results are in reasonable agreement, with some explicable differences in detail. All of the data sets show zones of faster rotation approaching the equator from mid-latitudes during the solar cycle, with a variation at any given location that can be approximately, but not completely, described by a single sinusoid and an amplitude that does not drop off steeply below the surface.

The nine-year span of medium-degree helioseismic data from the Global Oscillation Network Group (GONG) and the Michelson Doppler Imager (MDI) allows us to study the evolving zonal flows in the solar convection zone over the rising phase, maximum, and early declining phase of solar cycle 23. Using two independent two-dimensional rotation inversion techniques, we investigate the depth profile of the flow pattern known as the torsional oscillation. The observations suggest that the flows penetrate deep within the convection zone—perhaps to its base—even at low latitudes, and that the phase of the pattern is approximately constant along lines of constant rotation rather than lines of constant latitude.

We search for a relation between subsurface flows below active regions and flare events occurring in those regions. For this purpose, we use a ring-diagram analysis to determine the subsurface flows from high-resolution Global Oscillation Network Group (GONG) and Michelson Doppler Imager (MDI) data and derive the kinetic helicity as a measure of the topology of the subsurface flows. We compare it with X-ray flare data from the Geostationary Operational Environmental Satellite (GOES). We study active regions in three Carrington rotations (CR 1982, 1988, and 2009), which represent different levels of flare activity. The maximum value of the unsigned kinetic helicity density associated with each active region correlates remarkably well with the total flare X-ray intensity of the active regions; active regions with strong flare activity show large values of kinetic helicity density in subsurface flows.

We use the ring-diagram technique of local helioseismology to study the amplitude and line width of high-degree solar acoustic modes from 474 days of data from the Michelson Doppler Imager Dynamics program, covering the period 1996-2002. The 2002 data are compared with contemporaneous data from the Global Oscillations Network Group network. The results, once instrumental effects have been removed, show a strong dependence of the amplitude and lifetime of the modes on the local magnetic flux, with the amplitude and lifetime decreasing in the 5 minute band and a reversed trend at high frequencies. We relate these findings to results from global modes and from other approaches for analyzing high-degree local oscillations.

Helioseismic analysis of solar global oscillations allows investigation of the internal structure of the Sun. One important test of the reliability of the inferences from helioseismology is that the results from independent sets of contemporaneous data are consistent with one another. Here we compare mode frequencies from the Global Oscillation Network Group and Michelson Doppler Imager on board SOHO and resulting inversion results on the Sun's internal structure. The average relative differences between the data sets are typically less than 1 x 10(exp -5) substantially smaller than the formal errors in the differences; however, in some cases the frequency differences show a systematic behavior that might nonetheless influence the inversion results. We find that the differences in frequencies are not a result of instrumental effects but are almost entirely related to the data pipeline software. Inversion of the frequencies shows that their differences do not result in any significant effects on the resulting inferences on solar structure. We have also experimented with fitting asymmetric profiles to the oscillation power spectra and find that, compared with the symmetric fits, this causes no significant change in the inversion results.

Approximately 5 years of the l = 0 time series from the GONG project have been analyzed using the algorithm developed for the BiSON zero-dimensional data. The data cover the period 1995-2000. The results are compared with those from a parallel analysis of contemporaneous BiSON data and also with the results of the traditional GONG analysis of the low-degree time series. The spectra analyzed were prepared using the multitaper spectral analysis technique used in the recent reanalysis of the GONG data. We consider both solar cycle trends and temporally averaged values for mode frequencies, line widths, amplitudes, and asymmetry parameters.

We derive the angular momentum as a function of radius and time with the help of the rotation rates resulting from inversions of helioseismic data obtained from the Global Oscillation Network Group (GONG) and the Michelson Doppler Imager (MDI) and the density distribution from a model of the Sun. The base of the convection zone can be identified as a local maximum in the relative angular momentum after subtracting the contribution of the solid-body rotation. The angular momentum as a function of radius shows the strongest temporal variation near the tachocline. This variation extends into the lower convection zone and into the radiative interior and is related to the 1.3 yr periodicity found in the equatorial rotation rate of the tachocline. In the upper convection zone, we find a small systematic variation of the angular momentum that is related to torsional oscillations. The angular momentum integrated from the surface to a lower limit in the upper convection zone provides a hint that the torsional oscillation pattern extends deep into the convection zone. This is supported by other quantities such as the coefficients of a fit of Legendre polynomials to the rotation rates as a function of latitude. The temporal variation of the coefficient of P4, indicative of torsional oscillations, suggests that the signature of these flows in the inversion results extend to about r ≈ 0.83 R☉. With the lower limit of integration placed in the middle or lower convection zone, the angular momentum fluctuates about the mean without apparent trend, i.e., the angular momentum is conserved within the measurement errors. However, when integrated over the layers slightly below the convection zone (0.60-0.71 R☉), the angular momentum shows the 1.3 yr period and hints at a long-term trend that might be related to the solar activity cycle.

Convective motions affect the solar p-modes by shifting their frequencies. In comparison to the frequency splitting caused by the differential rotation, this is only a small additional effect. As the spatial resolution of the inversions for the differ- ential rotation becomes better, it is important to know how these additional frequency shifts modify the splitting coefficients and how these two effects might be disentangled. Therefore we carry out a numerical experiment. We use quasi-degenerate pertur- bation theory to create frequencies of p-modes that are affected by differential rotation and by large-scale flows. The simulated frequency sets are analyzed and inverted for differential rotation. We use changes in the (l ,ν ) coverage, the multiplets, and the inversion results as diagnostics to draw conclusions about the detectability of large-scale flows in global helioseismic data. The result is a detectability limit of the order of 10ms −1 for large-scale flows in the convection zone. A sectoral poloidal flow with greater amplitude will lead to a noticeable distortion of the rotation rate, while a zonal poloidal flow with greater amplitude will lead to distorted even-a coefficients and disrupted multiplets. In this study, we search for large-scale, long-lived struc- tures in the convection zone by using global helioseismol- ogy results combined with quasi-degenerate perturbation the- ory and numerical simulations. We concentrate on changes in the (l ,ν ) coverage, the multiplets, and the inversion results and derive detectability limits for the velocity of large-scale structures. The motivation for this study is two-fold. On the one hand, the internal structure of the Sun has been determined with in- creasing accuracy within the last few years. Especially with the availability of high-quality helioseismic data the properties of the differential rotation and its depth dependence have been studied in great detail by inverting oscillation data. Because of the improving resolution of the solar interior, it is necessary to know about smaller effects of physical processes in the sun on the solar oscillations and their influences on the inversion results.

Using contemporaneous helioseismic data from the Global Oscillation Network Group (GONG) and Michelson Doppler Imager (MDI) onboard SOHO, we compare frequency-splitting data and resulting inversions about the Sun's internal rotation. Helioseismology has been very successful in making detailed and subtle inferences about the solar interior. But there are some significant differences between inversion results obtained from the MDI and GONG projects. It is important for making robust inferences about the solar interior that these differences are located and their causes eliminated. By applying the different analysis pipelines developed by the projects not only to their own data but also to the data from the other project, we conclude that the most significant differences arise not from the observations themselves but from the different frequency estimation analyses used by the projects. We find that the GONG pipeline results in substantially fewer fitted modes in certain regions. The most serious systematic differences in the results, with regard to rotation, appear to be an anomaly in the MDI odd-order splitting coefficients around a frequency of 3.5 mHz and an underestimation of the low-degree rotational splittings in the GONG algorithm.

Preface.- Buoyant Magnetic Loops Generated by Global Convective Dynamo Action.- Helioseismic Holography of an Artificial Submerged Sound Speed Perturbation and Implications for the Detection of Pre-emergence Signatures of Active Regions.- Active Regions with Superpenumbral Whirls and Their Subsurface Kinetic Helicity.- A Study of Connections Between Solar Flares and Subsurface Flow Fields of Active Regions.- A Full-Sun Magnetic Index from Helioseismology Inferences.- Far- and Extreme-UV Solar Spectral Irradiance and Radiance from Simplified Atmospheric Physical Models.- Survey and Merging of Sunspot Catalogs.- Sunspot Group Development in High Temporal Resolution.- Migration and Extension of Solar Active Longitudinal Zones.- Cyclic and Long-Term Variation of Sunspot Magnetic Fields.- Apparent Solar Tornado-Like Prominences.- Forecasting the Maxima of Solar Cycle 24 with Coronal Fe XIV Emission.- Coronal Magnetic Field Evolution from 1996 to 2012: Continuous Non-Potential Simulations.- Different Periodicities in the Sunspot Area and the Occurrence of Solar Flares and Coronal Mass Ejections in Solar Cycle 23-24.- Do Solar Coronal Holes Affect the Properties of Solar Energetic Particle Events?- From Predicting Solar Activity to Forecasting Space Weather: Practical Examples of Research-to-Operations and Operations-to-Research.

NASA's Solar Dynamics Observatory (SDO) mission has provided a large amount of new data on solar dynamics and magnetic activities during the rising phase of the current and highly unusual solar cycle. These data are complemented by the continuing SOHO mission, and by ground-based observatories that include the GONG helioseismology network and the New Solar Telescope. Also, the observations are supported by realistic numerical simulations on supercomputers. This unprecedented amount of data provides a unique opportunity for multi-instrument investigations that address fundamental problems of the origin of solar magnetic activity at various spatial and temporal scales. This book demonstrates that the synergy of high-resolution multi-wavelength observations and simulations is a key to uncovering the long-standing puzzles of solar magnetism and dynamics. This volume is aimed at researchers and graduate students active in solar physics and space science. Previously published in Solar Physics journal, Vol. 287/1-2, 2013.

We apply empirical mode decomposition (EMD) and Hilbert analysis to time series of rotation residuals at all latitudes and at all depths in the convection zone derived from 49 Global Oscillation Network Group data sets covering the period 1995 May 7 to 2000 May 15. Hilbert analysis combined with EMD is a tool to analyze nonlinear and nonstationary signals and is used to localize events in time-frequency space. We calculate Hilbert power spectra, power as a function of time and frequency, for each time series in order to determine whether the rotation rate in the convection zone shows any other systematic temporal variation besides the so-called torsional oscillation pattern in the upper convection zone and the periodicity of 1.3 yr near the base of the convection zone. In other regions of the convection zone, the temporal variations of the rotation residuals are compatible with a noise signal except near about 0.86 R☉ in radius, where we find indications of a long-term period of about 6 yr. However, it is uncertain whether this signal is of solar origin, since the available data set is too short to rule out the possibility of an artifact. In addition, we calculate the amount of power contained in the torsional oscillation signal as a function of time, latitude, and radius to study the variation of the torsional oscillation pattern. The depth to which the pattern extends apparently changes with time. For example, at midlatitudes the pattern extends to deeper layers with increasing time. The degree of stationarity doubles from the surface to about 0.92 R☉ in radius, which indicates that the torsional oscillation pattern disappears with increasing depth in agreement with previous results.

We present measurements of mode width, Γ, and mean square velocity power, , derived from all currently processed 108 day Global Oscillation Network Group (GONG) time series and discuss their implications for p-mode excitation and damping. Assuming stochastic excitation, we estimate the energy per mode, E, and the energy supply rate, dE/dt. For modes with l = 9-150, the mean square velocity power and the mode energy peak at about 3.15 mHz reaching values of ≈ 1.4 × 103 cm2 s-2 and E ≈ 2.2 × 1028 ergs. The energy supply rate reaches a maximum value of dE/dt ≈ 2.5 × 1023 ergs s-1 near 3.6 mHz. The mode width shows the familiar "plateau" between 2.5 and 3.1 mHz with a "dip" near 2.9 mHz, which is strongest for l ≈ 40. This dip is most prominent during solar cycle minimum and disappears with increasing magnetic activity. The energy supply rate decreases on average by about 2.7% from the previous activity minimum to the currently highest level of activity. The solar cycle variation of dE/dt shows no frequency dependence, which is in marked contrast to the other mode parameters. The mode parameters are adequately represented by power laws in several frequency ranges, for example, dE/dt ~ ν6.89±0.07 for 2.4 mHz ≤ ν < 3.0 mHz and dE/dt ~ ν-5.62±0.27 for 3.75 mHz ≤ ν < 4.5 mHz. The solar cycle variation of these parameters can then be expressed as changes of a few percent in the power-law exponents and multipliers. Our results agree reasonably well with previous studies of Birmingham Solar-Oscillations Network and Big Bear Solar Observatory data.

We have detected changes in the rotation of the sun near the base of its convective envelope, including a prominent variation with a period of 1.3 years at low latitudes. Such helioseismic probing of the deep solar interior has been enabled by nearly continuous observation of its oscillation modes with two complementary experiments. Inversion of the global-mode frequency splittings reveals that the largest temporal changes in the angular velocity Ω are of the order of 6 nanohertz and occur above and below the tachocline that separates the sun's differentially rotating convection zone (outer 30% by radius) from the nearly uniformly rotating deeper radiative interior beneath. Such changes are most pronounced near the equator and at high latitudes and are a substantial fraction of the average 30-nanohertz difference in Ω with radius across the tachocline at the equator. The results indicate variations of rotation close to the presumed site of the solar dynamo, which may generate the 22-year cycles of magnetic activity.

We search for a solar cycle variation in mode widths and amplitudes derived from 3-month GONG time series. The variation of mode width and amplitude observed in GONG data are the combined effects of fill factor, temporal variation, and measurement uncertainties. The largest variation is caused by the fill factor resulting in modes with increased width and reduced amplitude when fill is lower. We assume that the solar cycle variation is the only other systematic variation beside the temporal window function effect. We correct all currently available data sets for the fill factor and simultaneously derive the solar cycle variation. We find an increase of about 3% on average in mode width from the previous minimum to Oct. 1998 and a decrease of about 7% and 6% in mode amplitude and mode area (width x amplitude). We find no l dependence of the solar-cycle changes. As a function of frequency, these changes show a maximum between 2.7 and 3.3 mHz with about 47% higher than average values for mode width and about 29% and 36% higher ones for mode amplitude and area. We estimate the significance of these rather small changes by a pre-whitening method and find that the results are significant at or above the 99.9% level with mode area showing the highest level of significance and mode width the lowest. The variation in background amplitude is most likely not significant and is consistent with a zero change.

We have analyzed 27 3 month sets of Global Oscillaiton Network Group (GONG) data from the end of cycle 22 and the beginning of cycle 23 and here present evidence of significant shifts in the central frequencies and the even a-coefficients of the frequency splittings of the modes. The temporal behavior of the even a-coefficients is better reproduced by the corresponding coefficients of a Legendre polynomial decomposition of the surface magnetic field than by the total flux; i.e., the temporal variation is strongly correlated with the latitudinal distribution of the surface magnetic activity. These changes are consistent with available data from previous solar cycles. The even a-coefficients, which sense the asphericity of the solar structure, appear to show similar temporal evolution at all depths. The odd a-coefficients, which sense the internal differential rotation, show no significant variation with time or depth. In particular they show no significant correlation with either the magnetic flux or with the corresponding odd Legendre components of the flux. This suggests that the solar cycle related variation of the oscillation frequencies is not due to contamination of observed Doppler shifts by the surface magnetic fields.

Estimates of solar normal mode frequencies from helioseismic observations can be improved by using Multitaper Spectral Analysis (MTSA) to estimate spectra from the time series, then using wavelet denoising of the log spectra. MTSA leads to a power spectrum estimate with reduced variance and better leakage properties than the conventional periodogram. Under the assumption of stationarity and mild regularity conditions, the log multitaper spectrum has a statistical distribution that is approximately Gaussian, so wavelet denoising is asymptotically an optimal method to reduce the noise in the estimated spectra. We find that a single m-upsilon spectrum benefits greatly from MTSA followed by wavelet denoising, and that wavelet denoising by itself can be used to improve m-averaged spectra. We compare estimates using two different 5-taper estimates (Stepian and sine tapers) and the periodogram estimate, for GONG time series at selected angular degrees l. We compare those three spectra with and without wavelet-denoising, both visually, and in terms of the mode parameters estimated from the pre-processed spectra using the GONG peak-fitting algorithm. The two multitaper estimates give equivalent results. The number of modes fitted well by the GONG algorithm is 20% to 60% larger (depending on l and the temporal frequency) when applied to the multitaper estimates than when applied to the periodogram. The estimated mode parameters (frequency, amplitude and width) are comparable for the three power spectrum estimates, except for modes with very small mode widths (a few frequency bins), where the multitaper spectra broadened the modest compared with the periodogram. We tested the influence of the number of tapers used and found that narrow modes at low n values are broadened to the extent that they can no longer be fit if the number of tapers is too large. For helioseismic time series of this length and temporal resolution, the optimal number of tapers is less than 10.

International audience; We study synoptic maps of solar subsurface flows covering six Carrington rotations (2050 to 2055). The subsurface flows are determined with a ring-diagram analysis of GONG high-resolution Doppler data. We identify the locations of coronal holes in synoptic maps of EUV images at 195Å from the EIT instrument and determine the characteristics of associated subsurface flows. We study two long-lived coronal holes that are present during this epoch. We find that large-scale patterns are present in the subsurface flows but appear to be unrelated to these coronal holes. The horizontal subsurface flows associated with the two long-lived coronal holes are weakly divergent (upflows) with small cyclonic vorticity. These flows are thus similar to subsurface flows of quiet regions with regard to the vertical flows and similar to flows of active regions with regard to vorticity.

The temporal variation of the horizontal velocity in subsurface layers beneath three different types of active regions is studied using the technique of ring diagrams. In this study, we select active regions (ARs) 10923, 10930, 10935 from three consecutive Carrington rotations: AR 10930 contains a fast-rotating sunspot in a strong emerging active region while other two have non-rotating sunspots with emerging flux in AR 10923 and decaying flux in AR 10935. The depth range covered is from the surface to about 12 Mm. In order to minimize the influence of systematic effects, the selection of active and quiet regions is made so that these were observed at the same heliographic locations on the solar disk. We find a significant variation in both components of the horizontal velocity in active regions as compared to quiet regions. The magnitude is higher in emerging-flux regions than in the decaying-flux region, in agreement with earlier findings. Further, we clearly see a significant temporal variation in depth profiles of both zonal and meridional flow components in AR 10930, with the variation in the zonal component being more pronounced. We also notice a significant influence of the plasma motion in areas closest to the rotating sunspot in AR 10930 while areas surrounding the non-rotating sunspots in all three cases are least affected by the presence of the active region in their neighborhood., Solar Physics (in press), includes 11 figures

In this paper, we compare components of the horizontal flow below the solar surface in and around regions consisting of rotating and non-rotating sunspots. Our analysis suggests that there is a significant variation in both components of the horizontal flow at the beginning of sunspot rotation as compared to the non-rotating sunspot. In most cases, the flows in surrounding areas are relatively small. However, there is a significant influence of the motion on flows in an area closest to the sunspot rotation., 4 pages including 3 figures; Proceedings of IAU Symposium 273 "Physics of Sun and Star Spots" Eds. D.P. Choudhary and K.G. Strassmeier

While sunspots are easily observed at the solar surface, determining their subsurface structure is not trivial. There are two main hypotheses for the subsurface structure of sunspots: the monolithic model and the cluster model. Local helioseismology is the only means by which we can investigate subphotospheric structure. However, as current linear inversion techniques do not yet allow helioseismology to probe the internal structure with sufficient confidence to distinguish between the monolith and cluster models, the development of physically realistic sunspot models are a priority for helioseismologists. This is because they are not only important indicators of the variety of physical effects that may influence helioseismic inferences in active regions, but they also enable detailed assessments of the validity of helioseismic interpretations through numerical forward modeling. In this paper, we provide a critical review of the existing sunspot models and an overview of numerical methods employed to model wave propagation through model sunspots. We then carry out an helioseismic analysis of the sunspot in Active Region 9787 and address the serious inconsistencies uncovered by \citeauthor{gizonetal2009}~(\citeyear{gizonetal2009,gizonetal2009a}). We find that this sunspot is most probably associated with a shallow, positive wave-speed perturbation (unlike the traditional two-layer model) and that travel-time measurements are consistent with a horizontal outflow in the surrounding moat., Comment: 73 pages, 19 figures, accepted by Solar Physics

We examine the evolution of the zonal flow pattern in the upper solar convection zone during the current extended solar minimum, and compare it with that during the previous minimum. The results suggest that a configuration matching that at the previous minimum was reached during 2008, but that the flow band corresponding to the new cycle has been moving more slowly towards the equator than was observed in the previous cycle, resulting in a gradual increase in the apparent length of the cycle during the 2007 -- 2008 period. The current position of the lower-latitude fast-rotating belt corresponds to that seen around the onset of activity in the previous cycle., 10 pages, 4 figures, submitted to ApJ Letters

We present the most recent results on the short-period variations in the solar rotation rate near the base of the convection zone. The 1.3-year period which was reported in the early years of solar cycle 23 appears not to persist after 2001, but there are hints of fluctuations at a different period during the declining phase of the cycle.

Ring-diagram analysis, a local helioseismology technique, has proven to be very useful for studying solar subsurface velocity flows down to a depth of about 0.97 R☉. The depth range is determined by the modes used in this type of analysis, and thus depends on the size of the area analyzed. Extending the area allows us to detect lower spherical harmonic degree (l) modes which, at a constant frequency, penetrate deeper in the Sun. However, there is a compromise between the size of the area and the validity of the plane-wave approximation used by the technique. We present the results of applying the ring diagrams to 30° diameter areas over the solar surface in an attempt to reach deeper into the solar interior. Meridional flows for 25 consecutive Carrington rotations (1985-2009) are derived by applying this technique to Global Oscillation Network Group (GONG) and Michelson Doppler Imager (MDI) data. This covers a time span of almost 2 yr, starting at the beginning of 2002. The amplitude of the meridional flow shows a variation of the order of 5 m s-1 during this period. Our results indicate that the flows increase toward the interior of the Sun for the depth range studied. We find a 1 yr periodicity in the appearance of an equatorward meridional cell at high latitudes that coincides with maximum values of the solar inclination toward the Earth (B0 angle).

We study long-lived activity complexes and their current helicity at the solar surface and their kinetic helicity below the surface. The current helicity has been determined from synoptic vector magnetograms from the NSO/SOLIS facility, and the kinetic helicity of subsurface flows has been determined with ring-diagram analysis applied to full-disk Dopplergrams from NSO/GONG and SDO/HMI. Current and kinetic helicity of activity complexes follow the hemispheric helicity rule with mainly positive values (78%; 78%, respectively, with a 95% confidence level of 31%) in the southern hemisphere and negative ones (80%; 93%, respectively, with a 95% confidence level of 22% and 14%, respectively) in the northern hemisphere. The locations with the dominant sign of kinetic helicity derived from Global Oscillation Network Group (GONG) and SDO/HMI data are more organized than those of the secondary sign even if they are not part of an activity complex, while locations with the secondary sign are more fragmented. This is the case for both hemispheres even for the northern one where it is not as obvious visually due to the large amount of magnetic activity present as compared to the southern hemisphere. The current helicity shows a similar behavior. The dominant sign of current helicity is the same as that of kinetic helicity for the majority of the activity complexes (83% with a 95% confidence level of 15%). During the 24 Carrington rotations analyzed here, there is at least one longitude in each hemisphere where activity complexes occur repeatedly throughout the epoch. These active longitudes are identifiable as locations of strong current and kinetic helicity of the same sign.

We measure the horizontal flows in the outer 2% of the Sun by analyzing 14 consecutive Carrington rotations of Global Oscillation Network Group (GONG) Doppler images and two of Michelson Doppler Imager (MDI) Dynamics Program data with the ring-diagram technique. The zonal and meridional flows show no variation with activity at low to medium activity levels (below 71 G). At active region locations, the zonal flow increases with increasing activity; active regions rotate faster than their quieter surroundings. The meridional flow at active region locations is more equatorward than on average at depths less than about 10 Mm; the flow converges toward the mean latitude of activity. At depths greater than about 10 Mm, some active region locations show poleward and others equatorward motions indicating strong outflows from active regions. The estimated vertical flow decreases with increasing activity levels except at active region locations at depths greater than about 10 Mm; active regions show downflows near the surface and upflows at depths greater than about 10 Mm. The velocity errors increase somewhat with increasing activity at flux levels below 71 G, but they increase rapidly up to about 2 times the median error at higher flux values. This increase occurs at all depths. The flows averaged over all longitudes show the patterns expected from solar cycle variations. The quiet and the intermediate activity subsets show the same flow pattern, while the active region subset shows a mixture of solar cycle flow pattern and local flow behavior.

We analyze Global Oscillation Network Group (GONG) and Michelson Doppler Imager (MDI) observations obtained during Carrington rotation 1988 (2002 March 30-April 26) with a ring-diagram technique in order to measure the zonal and meridional flow components in the upper solar convection zone. We derive daily flow maps over a range of depths up to 16 Mm on a spatial grid of 75 in latitude and longitude covering ±60° in latitude and central meridian distance and combine them to make synoptic flow maps. We begin exploring the dynamics of the near-surface layers and the interaction between flows and magnetic flux by deriving fluid dynamics descriptors such as divergence and vorticity from these flow maps. Using these descriptors, we derive the vertical velocity component and the kinetic helicity density. For this particular Carrington rotation, we find that the vertical velocity component is anticorrelated with the unsigned magnetic flux. Strong downflows are more likely associated with locations of strong magnetic activity. The vertical vorticity is positive in the northern hemisphere and negative in the southern hemisphere. At locations of magnetic activity, we find an excess vorticity of the same sign as that introduced by differential rotation. The vertical gradient of the zonal flow is mainly negative except within 2 Mm of the surface at latitudes poleward of about 20°. The zonal-flow gradient appears to be related to the unsigned magnetic flux in the sense that locations of strong activity are also locations of large negative gradients. The vertical gradient of the meridional flow changes sign near about 7 Mm, marking a clear distinction between near-surface and deeper layers. GONG and MDI data show very similar results. Differences occur mainly at high latitudes, especially in the northern hemisphere, where MDI data show a counter cell in the meridional flow that is not present in the corresponding GONG data.

Helioseismic observations have detected small temporal variations of the rotation rate below the solar surface corresponding to the so-called `torsional oscillations' known from Doppler measurements of the surface. These appear as bands of slower and faster than average rotation moving equatorward. Here we establish, using complementary helioseismic observations over four years from the GONG network and from the MDI instrument on board SOHO, that the banded flows are not merely a near-surface phenomenon: rather they extend downward at least 60 Mm (some 8% of the total solar radius) and thus are evident over a significant fraction of the nearly 200 Mm depth of the solar convection zone., Comment: 4 pages, 4 figures To be published in ApJ Letters (accepted 3/3/2000)

We derive the kinetic helicity density of subsurface flows applying ring-diagram analysis to Global Oscillation Network Group (GONG) data. Here, we focus on flows derived from times series of 8 hours and compare them to daily values for a high- and a low-activity sample. Compared with daily values, the horizontal flows derived from 8-hour time series are reasonable near disk center and less reliable near the limb. Also, the errors are larger for shorter time series. A dipolar helicity pattern is present in the flows derived from 8-hour and 24-hour time series of flare-productive active region 10808. For the quiet-Sun sample, the subsurface kinetic helicity is considerably smaller without any pattern.

Meridional circulation has become a key element in the solar dynamo flux transport models. Available helioseismic observations from several instruments, Taiwan Oscillation Network (TON), Global Oscillation Network Group (GONG) and Michelson Doppler Imager (MDI), have made possible a continuous monitoring of the solar meridional flow in the subphotospheric layers for the last solar cycle, including the recent extended minimum. Here we review some of the meridional circulation observations using local helioseismology techniques and relate them to magnetic flux transport models.