Ring-diagram Analysis Research Articles

The Linear Sensitivity of Helioseismic Ring Diagrams to Local Flows

Ring-diagram analysis is a technique of local helioseismology used to infer plasma flows in the solar convection zone which generates intermediate data products known as ring-fitting parameters. Knowing the sensitivity of ring-fitting parameters to actual flows in the Sun is important for interpreting these measurements. Working in plane-parallel geometry, we compute the linear sensitivity of ring-fitting parameters to small changes in the local power spectrum and then compute the sensitivity of the power spectrum to time-independent weak local flows. We combine these two results to obtain the three-dimensional Frechet kernels that give the linear sensitivity of ring-fitting parameters to both vertical and horizontal local mass flows. We find that ring measurements are essentially only sensitive to flows that are within the spatial region for which the ring diagram is computed. In addition, we find that the depth dependence of the sensitivity is essentially given by the mode kinetic energy density, as has traditionally been assumed. We show that the exact form of the sensitivity of ring measurements depends on the details of the fitting procedure.

Frequencies of solar oscillations for global and local helioseismology

AbstractBasically, there are two approaches for the analysis of helioseismic data. First, local helioseismology measurements and inversions and, second, global helioseismology which consists in measurements and inversions of p‐mode frequencies and frequency splittings. Both the advantages and disadvantages of global helioseismology and the local technique of ringdiagram analysis are discussed. Also discussed are two fitting methodologies for use in global helioseismology. Finally, a modification of the traditional global helioseismology approach is suggested which allows the extension of spherical harmonic decompositions for local helioseismic studies. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

North – South Asymmetry of Zonal and Meridional Flows Determined From Ring Diagram Analysis of Gong ++ Data

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 B0-angle variation, while the zonal flow is less affected by the B0-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.

Photospheric, chromospheric and helioseismic signatures of a large flare in super-active region NOAA 10486

NOAA 10486 produced several powerful flares, including the 4B/X17.2 superflare of October 28, 2003/11:10 UT. This flare was extensively covered by theHα and GONG instruments operated at the Udaipur Solar Observatory (USO). The central location of the active region on October 28,2003 was well-suited for the ring diagram analysis to obtain the 3-D power spectra and search for helioseismic response of this large flare on the amplitude, frequency and width of the p-modes. Further, using USO observations, we have identified the sites of new flux emergences, large proper motions and line-of-sight velocity flows in the active region and their relationship with the flare.

Meridional Circulation Variability from Large‐Aperture Ring‐Diagram Analysis of Global Oscillation Network Group and Michelson Doppler Imager Data

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).

Kinetic Helicity Density in Solar Subsurface Layers and Flare Activity of Active Regions

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.

Local Helioseismology

We review the current status of local helioseismology, covering both theoretical and observational results. After a brief introduction to solar oscillations and wave propagation through in-homogeneous media, we describe the main techniques of local helioseismology: Fourier-Hankel decomposition, ring-diagram analysis, time-distance helioseismology, helioseismic holography, and direct modeling. We discuss local helioseismology of large-scale flows, the solar-cycle dependence of these flows, perturbations associated with regions of magnetic activity, and solar supergranulation.

Local Modulation of Solar Oscillations by Magnetic Fields

The amplitudes of solar oscillations measured in Doppler velocity are modulated by the presence of a strong photospheric magnetic field. Here we show that the amount of modulation cannot be predicted solely on the local photospheric magnetic field strength. Qualitatively, magnetic fields of similar strength have similar effects on the oscillations. Quantitatively, however, we find a ‘neighborhood effect’, so that the presence of a nearby sunspot affects oscillations in the area in its vicinity that has normal quiet-Sun magnetic field strength. Thus, different types of magnetic regions alter the oscillatory power to a varying degree, and the p-mode power within regions of similar magnetic field strength is more reduced if there is a sunspot present. The neighborhood effect falls off with distance from the sunspot. We also show that our measurements of the power modulation, in which we look at the effects on oscillations pixel by pixel, can be made consistent with results of amplitude modulation of modes as obtained from ring-diagram analysis of active regions, but only if the neighborhood effect on quiet-Sun regions is taken into account.

Flare-Induced Excitation of Solar p modes

Solar flares release large amounts of energy at different layers of the solar atmosphere, including at the photosphere in the case of exceptionally major events. Therefore, it is expected that large flares would be able to excite acoustic waves on the solar surface, thereby affecting the p-mode oscillation characteristics. We have applied the ring-diagram analysis technique to 3-D power spectra obtained for different flare regions in order to study how flares affect the amplitude, frequency and width of the acoustic modes. Data from the Michelson Doppler Imager (MDI) on board the Solar and Heliospheric Observatory (SOHO) has been used. We have used data obtained for several active regions of the current solar cycle that have produced flares. In most cases, during the period of high flare activity, power in p modes appears to be larger when compared to that in non-flaring regions of similar magnetic field strength.

Evolving Submerged Meridional Circulation Cells within the Upper Convection Zone Revealed by Ring‐Diagram Analysis

Using the local helioseismic technique of ring-diagram analysis applied to Michelson Doppler Imager (MDI) Dynamics Program data from the Solar and Heliospheric Observatory, we have discovered that the meridional flow within the upper convection zone can develop additional circulation cells whose boundaries wander in latitude and depth as the solar cycle progresses. We report on the large-scale meridional and zonal flows that we observe from 1996 to 2001. In particular, we discuss the appearance and evolution of a submerged meridional cell during the years 1998-2001, which arose in the northern hemisphere and disrupted the orderly poleward flow and symmetry about the equator that is typically observed. The meridional flows in the southern and northern hemispheres exhibit striking asymmetry during the past four years of the advancing solar cycle. Such asymmetry and additional circulation cells should have profound impact on the transport of angular momentum and magnetic field within the surface layers. These flows may have a significant role in the establishment and maintenance of the near-surface rotational shear layer.

Ring Diagram Analysis of the Characteristics of Solar Oscillation Modes in Active Regions

The presence of intense magnetic fields in and around sunspots is expected to modify solar structure and oscillation frequencies. Applying the ring diagram technique to data from the Michelson Doppler Imager on board the Solar and Heliospheric Observatory, we analyze the characteristics of high-degree f- and p-modes near active regions and compare them with the characteristics of the modes in quiet regions. As expected from earlier results, the f- and p-mode frequencies of high-degree modes are found to be significantly larger in magnetically active regions. In addition, we find that the power in both f- and p-modes is lower in active regions while the widths of the peaks are larger, indicating smaller lifetimes. We also find that the oscillation modes are more asymmetric in active regions than those in quiet regions, indicating that modes in active regions are excited closer to the surface. While the increase in mode frequency is monotonic in frequency, all other characteristics show more complex frequency dependences.

New Developments in Local Area Helioseismology

Several techniques are used to study local areas in helioseismology, including time-distance helioseismology, acoustic imaging/holography, and ring diagram analysis. These techniques can be used to study flows, magnetic fields, and temperature inhomogeneities. The “local” area studied can be as small as a supergranule, or as large as the entire convection zone in the case of meridional circulation as studied by Giles and colleagues. Active regions have been studied with some interesting results, with complicated flow patterns below sunspots and detectable sound speed inhomogeneities in the 10 Mm below the spots. Another interesting result is the detection of sunspots on the back side of the Sun by Lindsey and Braun using the holography technique. A confirmation of their result using the time-distance technique is presented.

Spatially-resolved Analysis of the Upper Convection Zone

Ring-diagram analysis of MDI data has revealed systematic patterns in global flow patterns in the early phase of the cycle. We report on variations and trends seen in the flows in subsequent years.

A Synoptic View of the Subphotospheric Horizontal Velocity Flows in the Sun

Ring diagram analysis, a technique of local helioseismology, has been applied to 120 regions of 15° × 15° over the solar surface in order to study the mass motions in the upper layers of the convection zone. The horizontal flows from ~0.95 R☉ up to the surface have been investigated in a region spanning 360° in longitude and about 75° in latitude. The regions were tracked in groups of five centered at 0, ±15°, and ±30° in latitude over a timespan of ±768 minutes from central meridian crossing. More than 30,000 full-disk Dopplergrams taken by the Solar Oscillation Investigation/Michelson Doppler Imager (SOI/MDI) on the Solar and Heliospheric Observatory (SOHO) spacecraft have been analyzed to create a synoptic map. The images were taken during the first SOI Dynamics Program in 1996 May and June and have a pixel size of ~2'' allowing coverage in l up to 1200. The p-modes analyzed cover a range of 0 ≤ n ≤ 7 and 183 ≤ l ≤ 999. The estimated velocity vectors provide information on the size and structure of large-scale flows. The flows exhibit markedly meridional behavior between 0.975 and 0.997 R☉. The zonal component is mainly ruled by the differential rotation.

Solar rotation in the subphotospheric layers

The solar rotation rate at latitudes 0°, 15° and 30° has been inferred by averaging the results of 120 regions of 15°×15°, which have been studied over a total area of about 75° in latitude and 360° in longitude. A local helioseismology technique, the ring diagram analysis method, has been used to analyse the horizontal velocity vectors from about 0.95 R⊙ up to the surface. Our results are in very good agreement with those of other authors over most of the depth range. However, near the surface we find sharp local features which are not reported in other studies. The independent measurements of the rotation rate in the north and south hemispheres show asymmetries below 0.975 R⊙. The data used are full-disc dopplergrams taken by Solar Oscillation Investigation/Michelson Doppler Imager (SOI/MDI) on board of the SOlar and Heliospheric Observatory (SOHO) during its first Dynamic Program, between 1996 May and June.

Large‐Scale Flows in the Solar Interior: Effect of Asymmetry in Peak Profiles

Ring diagram analysis can be used to study large scale velocity fields in the outer part of the solar convection zone. All previous works assume that the peak profiles in the solar oscillation power spectrum are symmetric. However, it has now been demonstrated that the peaks are not symmetric. In this work we study how the explicit use of asymmetric peak profiles in ring-diagram analysis influences the estimated velocity fields. We find that the use of asymmetric profiles leads to significant improvement in the fits, but the estimated velocity fields are not substantially different from those obtained using a symmetric profile to fit the peaks. The resulting velocity fields are compared with those obtained by other investigators.

Ring Diagram Analysis of Near‐Surface Flows in the Sun

Ring diagram analysis of solar oscillation power spectra obtained from Michelson Doppler Imager data is carried out to study the velocity fields in the outer part of the solar convection zone. The three-dimensional power spectra are fitted to a model that has a Lorentzian profile in frequency and includes the advection of the wave front by horizontal flows in order to obtain the two components of the subsurface flows as a function of the horizontal wave number and radial order of the oscillation modes. This information is then inverted using the optimally localized averages method and regularized least squares method to infer the variation in horizontal flow velocity with depth. The average rotation velocity at different latitudes obtained by this technique agrees reasonably with helioseismic estimates made using frequency-splitting data. The shear layer just below the solar surface appears to consist of two parts, with the outer part measuring up to a depth of 4 Mm where the velocity gradient does not show any reversal up to a latitude of 60°. In the deeper part the velocity gradient shows reversal in sign around a latitude of 55°. The zonal flow velocities inferred in the outermost layers appear to be similar to those obtained by other measurements. A meridional flow from equator poleward is found. It has a maximum amplitude of about 30 m s-1 near the surface, and the amplitude is nearly constant in the outer shear layer.

Meridional Flows from Ring Diagram Analysis

In order to search for meridional circulation in the solar envelope, we have applied ring diagram analysis to a set of small regions over the surface. The helioseismic data consist of Solar Oscillation Investigation/Michelson Doppler Imager Dopplergrams taken over a time span of about 50 hr (~3000 images) on 1998 June 20-22. The regions studied cover 115° in latitude centered on the equator and 30° in longitude. We find poleward flows between r/ R=0.97 and the surface. There is no evidence in this depth range for the return path of these meridional flows. The temporal stability of these flows will be discussed after the analysis of a synoptic map obtained using the same technique.

Time Evolution of Horizontal Subsurface Flows in the Sun

A ring-diagram analysis technique has been applied to a region of the Sun of about 15 deg2 area close to the disk center at dates chosen for several solar rotations in 1996: April 5, May 1, May 28, June 27, July 23, August 20, August 21, and September 18. The horizontal velocity flows inferred directly beneath the solar surface have thus been obtained for the same region of the Sun at the given dates. The data have been obtained at the Observatorio del Teide and the Tashkent stations with the Taiwan Oscillation Network (TON), consisting of 1080 × 1080 pixel Ca II K-line intensity images. The stability of the results, the stability of the method, and the possible temporal evolution of the subsurface flows have been studied from the results. A rotation curve for the differential radial solar rotation down to the first 27 Mm of depth at the equator is also suggested and qualitatively compared to results obtained by other authors.

On the Reliability of Ring Diagram Analysis

A comparison between the results of applying a ring diagram analysis to two data sets is described in order to check the quality of the two sets and the reliability of the method. The series used have been obtained with two different helioseismological instruments with the same spatial resolution. A section of 30 × 30 deg2 about the disk center has been tracked during 512 minutes over a series of images taken simultaneously by the Taiwan Oscillation Network instrument station at the Observatorio del Teide and the Michelson Doppler Imager on board the Solar and Heliospheric Observatory. Three-dimensional power spectra have been constructed from both series and fitted to get horizontal velocity flows as a function of frequency. Finally, an inversion process has been applied to obtain the depth dependence of the average velocity vector in a depth range of 0-25 Mm below the solar surface. The results show an acceptable correlation between the velocities obtained from the fitting of the spectra of both data sets in spite of the different kinds of noise affecting the two instruments. However, the correlation drops when comparing the velocities obtained after the inversion process based on these results.