Wavelet analysis of a magnetogram

I analyze a quiet-Sun magnetogram with an orthogonal wavelet transform, which allows me to define an entropy measure. The entropy measure of the magnetogram as a function of spatial scale obeys a scaling law, which leads to a fractal dimension ofD _f = 1.7. Furthermore, the entropy scaling law is directly related to the intermittency of magnetic features, which increases for decreasing spatial scales, as expected for a turbulent signal. In this context, the scaling law parameter can be interpreted as a fractional reduction in volume from one step of the turbulent cascade to the next.Operated by the Association of Universities for Research in Astronomy, Inc., under cooperative agreement with the National Science Foundation.     

Variations in solar sub-surface rotation from GONG data 1995–1998

We have completed an analysis of the first 35 GONG Months (1 GM = 36 days) covering the last solar minimum and the rising phase of cycle 23. The mode parameters have been estimated from 33 time series, each of 3-GM duration, with centers spaced by 1 GM. We report on the temporal evolution of the rotational splitting coefficients up to 15th order. The coefficients do not correlate well with any surface magnetic flux measure yet considered, but we find small but significant trends in their temporal evolution. Inverting the coefficients for two-dimensional rotation information and looking at deviations from the mean produces a picture of a systematic zonal flow migrating towards lower latitudes during the rising phase of the cycle. This flow is probably associated with the torsional oscillation. Similar trends are seen in the 1986–1990 BBSO data.     

Solar-Cycle Variation of Subsurface-Flow Divergence: A Proxy of Magnetic Activity?

We study the solar-cycle variation of subsurface flows from the surface to a depth of 16 Mm. We have analyzed Global Oscillation Network Group (GONG) Dopplergrams with a ring-diagram analysis covering about 15 years and Helioseismic and Magnetic Imager (HMI) Dopplergrams covering more than 6 years. After subtracting the average rotation rate and meridional flow, we have calculated the divergence of the horizontal residual flows from the maximum of Solar Cycle 23 through the declining phase of Cycle 24. The subsurface flows are mainly divergent at quiet regions and convergent at locations of high magnetic activity. The relationship is essentially linear between divergence and magnetic activity at all activity levels at depths shallower than about 10 Mm. At greater depths, the relationship changes sign at locations of high activity; the flows are increasingly divergent at locations with a magnetic activity index (MAI) greater than about 24 G. The flows are more convergent by about a factor of two during the rising phase of Cycle 24 than during the declining phase of Cycle 23 at locations of medium and high activity (about 10 to 40 G MAI) from the surface to at least 10 Mm. The subsurface divergence pattern of Solar Cycle 24 first appears during the declining phase of Cycle 23 and is present during the extended minimum. It appears several years before the magnetic pattern of the new cycle is noticeable in synoptic maps. Using linear regression, we estimate the amount of magnetic activity that would be required to generate the precursor pattern and find that it should be almost twice the amount of activity that is observed.     

Solar-Cycle Variation of Subsurface Zonal Flow

We study the solar-cycle variation of the zonal flow in the near-surface layers of the solar convection zone from the surface to a depth of 16 Mm covering the period from mid-2001 to mid-2013 or from the maximum of Cycle 23 through the rising phase of Cycle 24. We have analyzed Global Oscillation Network Group (GONG) and Helioseismic and Magnetic Imager (HMI) Dopplergrams with a ring-diagram analysis. The zonal flow varies with the solar cycle showing bands of faster-than-average flows equatorward of the mean latitude of activity and slower-than-average flows on the poleward side. The fast band of the zonal flow and the magnetic activity appear first in the northern hemisphere during the beginning of Cycle 24. The bands of fast zonal flow appear at mid-latitudes about three years in the southern and four years in the northern hemisphere before magnetic activity of Cycle 24 is present. This implies that the flow pattern is a direct precursor of magnetic activity. The solar-cycle variation of the zonal flow also has a poleward branch, which is visible as bands of faster-than-average zonal flow near 50° latitude. This band appears first in the southern hemisphere during the rising phase of the Cycle 24 and migrates slowly poleward. These results are in good agreement with corresponding results from global helioseismology.     

The Global Context of Solar Activity During the Whole Heliosphere Interval Campaign

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??C?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.     

Characteristic size and diffusion of quiet sun magnetic patterns

We have previously studied large-scale motions using high-resolution magnetograms taken from 1978 to 1990 with the NSO Vacuum Telescope on Kitt Peak. Latitudinal and longitudinal motions were determined by a two-dimensional crosscorrelation analysis of pairs of consecutive daily observations using small magnetic features as tracers. Here we examine the shape and amplitude of the crosscorrelation functions. We find a characteristic length scale as indicated by the FWHM of the crosscorrelation functions of 16.6 ± 0.2 Mm. The length scale is constant within ±45° latitude and decreases by about 5% at 52.5° latitude; i.e., the characteristic size is almost latitude independent. The characteristic scale is within 3% of the average value during most times of the solar cycle, but it increases during cycle maximum at latitudes where active regions are present. For the time period 1978–1981 (solar cycle maximum), the length scale increases up to 1.7 Mm or 10% at 30° latitude. In addition, we derive the average amplitude of the crosscorrelation functions, which reflects the diffusion of magnetic elements and their evolutionary changes (including formation and decay). We find an average value of 0.091 ± 0.003 for the crosscorrelation amplitude at a time lag of one day, which we interpret as being caused by the combined effect of the lifetime of magnetic features and a diffusion process. Assuming a lifetime of one day, we find a value of 120 km² s^–1 for the diffusion constant, while a lifetime of two days leads to 230 km² s^–1.Operated by the Association of Universities for Research in Astronomy, Inc. under cooperative agreement with the National Science Foundation.     

Subsurface Zonal and Meridional Flow During Cycles 23 and 24

We study the solar-cycle variation of subsurface flows from the surface to a depth of 16 Mm. We have used ring-diagram analysis to analyze Dopplergrams obtained with the Michelson Doppler Imager (MDI) Dynamics Program, the Global Oscillation Network Group (GONG), and the Helioseismic and Magnetic Imager (HMI) instrument. We combined the zonal and meridional flows from the three data sources and scaled the flows derived from MDI and GONG to match those from HMI observations. In this way, we derived their temporal variation in a consistent manner for Solar Cycles 23 and 24. We have corrected the measured flows for systematic effects that vary with disk positions. Using time-depth slices of the corrected subsurface flows, we derived the amplitudes and times of the extrema of the fast and slow zonal and meridional flows during Cycles 23 and 24 at every depth and latitude. We find an average difference between maximum and minimum amplitudes of \(8.6 \pm0.4~\mbox{m}\,\mbox{s}^{-1}\) for the zonal flows and \(7.9 \pm0.3~\mbox{m}\,\mbox{s}^{-1}\) for the meridional flows associated with Cycle 24 averaged over a depth range from 2 to 12 Mm. The corresponding values derived from GONG data alone are \(10.5 \pm0.3~\mbox{m}\,\mbox{s}^{-1}\) for the zonal and \(10.8 \pm0.3~\mbox{m}\,\mbox{s}^{-1}\) for the meridional flow. For Cycle 24, the flow patterns are precursors of the magnetic activity. The timing difference between the occurrence of the flow pattern and the magnetic one increases almost linearly with increasing latitude. For example, the fast zonal and meridional flow appear \(2.1 \pm 0.6\) years and \(2.5\pm 0.6\) years, respectively, before the magnetic pattern at \(30^{\circ}\) latitude in the northern hemisphere, while in the southern hemisphere, the differences are \(3.2 \pm 1.2\) years and \(2.6 \pm 0.6\) years. The flow patterns of Cycle 25 are present and have reached \(30^{\circ}\) latitude. The amplitude differences of Cycle 25 are about 22% smaller than those of Cycle 24, but are comparable to those of Cycle 23. Moreover, polynomial fits of meridional flows suggest that equatorward meridional flows (counter-cells) might exist at about \(80^{\circ}\) latitude except during the declining phase of the solar cycle.     

Emerging and Decaying Magnetic Flux and Subsurface Flows

We study the temporal variation of subsurface flows of 788 active regions and 978 quiet regions. The vertical-velocity component used in this study is derived from the divergence of the measured horizontal flows using mass conservation. The horizontal flows cover a range of depths from the surface to about 16 Mm and are determined by analyzing about five years of GONG high-resolution Doppler data with ring-diagram analysis. We determine the change in unsigned magnetic flux during the disk passage of each active region using MDI magnetograms binned to the ring-diagram grid. We then sort the data by their flux change from decaying to emerging flux and divide the data into five subsets of equal size. The average vertical flows of the emerging-flux subset are systematically shifted toward upflows compared to the grand average values of the complete data set, whereas the average flows of the decaying-flux subset show comparably more pronounced downflows especially near 8 Mm. For flux emergence, upflows become stronger with time with increasing flux at depths greater than about 10 Mm. At layers shallower than about 4 Mm, the flows might start to change from downflows to upflows, when flux emerges, and then back to downflows after the active regions are established. The flows in the layers between these two depth ranges show no response to the emerging flux. In the case of decaying flux, the flows change from strong upflows to downflows at depths greater than about 10 Mm, whereas the flows do not change systematically at other depths. A cross-correlation analysis shows that the flows in the near-surface and the deeper layers might change about one day before flux emerges. The flows associated with the quiet regions fluctuate with time but do not show any systematic variation.