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Changes in high-degree mode characteristics with magnetic activity

Richard S. Bogart, Sarbani Basu, & H. M. Antia

Abstract

We compare mode frequencies and other characteristics as determined from ring-diagram analysis of selected small regions of the Sun exhibiting strong variations in magnetic activity. These regions were observed with the Michelson Doppler Imager (MDI) on SOHO in its high-resolution mode during several years from solar minimum to maximum. To better understand the systematic uncertainties in fitting the ridges to the high-resolution data, we compare our results with those for the same regions concurrently observed in the MDI full-disc mode. We find that the the properties of high degree p-modes are different in active and quiet regions and that the magnitude of the changes depend on the activity level.

Introduction - Analysis

Ring-diagram analysis affords us the opportunity to determine the effect of surface magnetic activity on the propagation and generation and absorption of near-surface helioseismic modes by isolating the regions studied (Hindman et al., 2000). In order to improve the spatial isolation of active regions, and also to incorporate information on very high-degree modes near the surface, we have chosen to analyze data taken with the high-resolution (1.3 arc-sec) mode of MDI. In order to compare the results with those achieved in the normal mode, we have selected data from the few intervals during which concurrent full-disc and high-resolution Doppler data. The available data are limited to the periods 13--19 June and 30 June -- 14 July in 1997, 5 Mar. -- 10 Apr. 1998, and 14--28 May 2001. Spatial coverage is restricted by the high-resolution field of view and telemetry limitations to a 1024*600 pixel (11*6.5 arc-min) subraster of that field. The regions studied are shown in Table 1.

Regions of diameters 15° heliographic centered on the target locations have been mapped and tracked for 4096 minutes, which is about the maximum length of time a point on the Sun remains in the MDI high-resolution field of view, using the procedures described in Bogart et al. (2000). The spatial-temporal power spectra of the tracked data are then fit using the method described in Basu and Antia (1999).
Date CR Longitude Latitude1 MAI1 Latitude2 MAI2
1997.06.15 1923 40.0 +10.0 0.336 +20.0 1.912
1998.04.07 1933 100.0 +5.0 0.068 +15.0 0.960
1998.05.04 1934 100.0 +5.0 0.481 +15.0 0.415
2001.05.16 1976 230.0 +10.0 56.370 +17.5 46.350
2001.05.18 1976 205.0 +10.0 1.802 +17.5 1.945
2001.05.24 1976 130.0 +10.0 88.177 +17.5 24.297
For purposes of selection and comparison we have defined a local Magnetic Area Index, whose values for the individual tracked regions are given in the table. The Index is calculated by mapping similar regions to the tracked Doppler data (but using an azimuthal equal-area projection rather than Postel's projection) from the MDI full-disc magnetograms taken during the tracking interval, and averaging the absolute values of all field values greater than or equal to 50 gauss, which is several times the standard deviation of the normally-distributed core of quiet-sun values.

We attempted to analyze smaller regions 10° diameter) for better isolation of the active sites. When the regione sizes were reduced even from 15° to 10° diameter, however, we were unable to determine sufficiently complete mode sets (see Figure 1). Nevertheless, the high-resolution data do allow for the incorporation of higher-degree modes, but there are still uncertainties due to the unknown and varying scale ratio between the high-resolution and full-disc observing modes. We thus focus here on comparisons of parameters for the modes that can be fit in both high-resolution and full-disc data at the same scale.

Results

When we compare mode frequencies for the same regions in the full-disc and high-resolution observing modes, we see that there is a consistent and substantial offset at higher latitudes that is not present at lower latitudes (Figure 2). We attribute this to uncorrected position-dependent scale errors in the high-resolution field. Not surprisingly, we see similar effects in the fit parameters Ux and Uy representing the response to transverse flows (Figure 3). These location-dependent effects dominate any possible effects associated with the difference between the magnetically active regions in CR 1976:230 and the quiet regions.

In order to isolate the magnetic activity effects on oscillations, we have compared results for two quiet regions during Carrington Rotation 1976 (May 2001) with four very active areas at the same latitudes seen in the high resolution field a few days before and after the quiet longitude. When we do so, we see that there is a significant increase in frequency (of the order 0.1% or more), with a clear positive frequency dependence, and at least a suggestion that the the frequency increase associated with magnetic activity is proportional to the activity index defined here. (See Figures Figure 4.) Examining the frequency differences as a function of the mode turning points (Figure 5), we see evidence that the effect extends at least to a depth of 15 Mm, increasing somewhat with depth. This is consistent with the sound speed increases beneath sunspots seen in time-distance analysis (Kosovichev et al. 2000).

There is an increase in mode width in the active areas, peaking at around 3.5 mHz, but the dependence of its amplitude (or frequency location) on activity index is not so clear ( Figure 6). It is more pronounced at the lower latitude. Likewise, there is an increase in the absolute value of the mostly negative asymmetry parameters ( Figure 7) in the active regions at low latitude, but at higher latitude the amplitude of the effect is diminshed or even reversed. The magnetic activity is clearly influencing the excitation and damping of the oscillations; these effects deserve further investigation.

Conclusions

We cannot yet obtain sufficiently good mode-sets for analysis with a spatial resolution of less than about 15 ° heliographic (0.04 RO); progress in improving the spatial resolution may involve hybrid sets of modes from different scales of analysis. At the present resolution there is, as expected, generally good agreement between mode-sets determined from coincident high-resolution and full-disc resolution MDI Dopplergrams. We attribute the consistent frequency differences seen farther from disc center to uncorrected variations in the plate scale and optical distortion. There is evidence that these effects increase with wavenumber and may vary with time, but apparently not with the magnetic activity level.

The mode frequencies are higher in regions of magnetic activity compared with quiet regions at the same latitude; this effect increases dramtically with mode degree. The sound-speed effects associated with magnetic activity are most pronounced near the surface. A significant increase in mode width in active regions, peaking at around 3.5 mHz, suggests enhanced mode damping in these regions. There is also evidence of increased asymmetry of the modes on active regions. This is also consistent with a significant role of magnetic activity in the mode excitation and damping processes. Magnetic activity does not noticeably affect the inferred near-surface flow velocities; if anything, the sub-surface velocity determinations may be somewhat less noisy in the active than the quiet regions.

References

  1. Basu, S. and H.M. Antia: Large-scale Flows in the Solar Interior: Effect of Asymmetry in Peak Profiles. Ap. J. 525, 517; 1999.
  2. Bogart, R.S., J, Schou, S. Basu, D.A. Haber, F. Hill and H.M. Antia: Spatially-resolved Analysis of the Upper Convectiopn Zone. Symposium IAU 203, Recent Insights Into the Physics of the Sun and Heliosphere: Highlights from SOHO and Other Space Missions, ed. P. Brekke, B. Fleck & J. B . Gurman, 183; 2001.
  3. Hindman, B.W., D.A. Haber, J. Toomre and R.S. Bogart: Local Fractional Frequency Shifts Used as Tracers of Magnetic Activity. Solar Physics 192, 363; 2000.
  4. Kosovichev, A.G., T.L. Duvall Jr. and P.H. Scherrer: Time-Distance Inversion Methods and Results. Solar Physics 192, 159; 2000.

Figures

  1. Frequency differences for individual modes
    Comparison of mode fits for regions of diameter 10° (left) and 15° (right) for three regions (two active and one quiet) of CR1976 (May 2001). The differences between the frequencies of the fits from the data in the high-resolution field and the data in the same areas from the full-disc field are plotted as a function of frequency. The values are symbol coded by mode order as follows:

  2. Frequency differences between full-disc and high-resolution observations for selected locations Fractional frequency differences for the same modes, coded as in the previous figure, are shown as a function of degree.

  3. Horizontal velocity differences between full-disc and high-resolution observations for selected locations. The differences in the fit parameters Ux and Uy, representing the depth-integrated response to flows in the zonal and meridional directions, are shown for individual modes as a function of frequency, with the same order codes. Differences are shown for quiet regions and two active areas.
    1. Ux: positive values represent a westward (super-rotational) flow with respect to the local assumed differential rotation rate.
    2. Uy: positive values represent a northward meridional flow.


  4. Frequency differences between sample active and quiet regions in CR 1976. For the same latitudes, the individual mode frequency differences between the quiet site (longitude 205°) and the active areas (longitudes 230° and 130°) are shown, plotted as a function of mode frequency. Open circles are for data derived from the full-disc observations, solid circles from the high-resolution data. Apart from greater scatter in the full-disc data, there are no systematic differences between the two sets evident

  5. Weighted frequency differences between active and quiet regions. For the four sample comparison regions at the same latitudes and nearby longitudes, the individual mode frequency differences, scaleed by the inverse mode mass, are shown as a function of the classical mode turning point.

  6. Differences in mode width between the active and quiet sites in CR 1976.

  7. Differences in mode asymmetry between active and quiet sites. What is plotted is the difference between the absolute values of the asymmetry parameters; most of the asymmetries are of the same sign.

    Unpublished Figures

    1. Full-disc magnetograms at times analyzed:
      1. 1923:040 (1997.06.15_07:00)
      2. 1933:100 (1998.03.10_13:45)
      3. 1934:100 (1998.04.06_20:45)
      4. 1976:230 (2001.05.16_13:30)
      5. 1976:205 (2001.05.18_11:00)
      6. 1976:130 (2001.05.24_03:00)
      The superimposed grid of lines of Carrington latitude and longitude is spaced at 15°.

    2. Portion of magnetograms in available high-resolution field at times analyzed:
      1. 1923:040
      2. 1933:100
      3. 1934:100
      4. 1976:230
      5. 1976:205
      6. 1976:130
      The superimposed grid of lines of Carrington latitude and longitude in the magnified view below is spaced at 5°.

    3. Magnetic Activity Indices for 15° regions centred at various heliographic locations within the MDI high-resolution field of view over multiple transits.
      1. Longitude 40°, May - July 1997
      2. Longitude 105°, March - May 1998
      3. Longitude 210°, April - June 2001
      4. Longitude 225°, April - June 2001


    4. Comparisons of mode fits in regions of different diameters
      1. Frequency differences for individual modes Comparison of mode fits for regions of diameter 10° (left) and 15° (right) for three regions (two active and one quiet) of CR1976 (May 2001). The differences between the frequencies of the fits from the data in the high-resolution field and the data in the same areas from the full-disc field are plotted as a function of frequency. The values are color coded by mode order as follows:
        • n = 0: Black
        • n = 1: Red
        • n = 2: Green
        • n = 3: Blue
        • n = 4: Cyan
      2. Histograms of the frequency differences for comparison modes sets in four magnetically quiet regions of diameter 15° (left) and 10°. The heliographic longitude for the comparison sets from CR1976 is 205°.


    5. Trends in the frequency differences between full-disc and high-resolution observations
      1. Time dependence at low latitude
      2. Latitude dependence at different times
      3. Same, but plotted as a function of wavenumber rather than frequency


    6. Frequency differences between full-disc and high-resolution observations for all target regions in CR 1976. Note the consistent offset at higher latitude, attributable to plate-scale errors, and evident mode dependency at higher latitude, especially at longitude 230 °; in the frequency dependence; it is evidently not correlated with magnetic activity. That the apparent mode dependency is really a dependence on wavenumber is made clear in c.
      1. Frequency differences plotted as a function of frequency
      2. Same plotted as a function of wavenumber
      3. Frequency differences for Lon 230, Lat 17.5, plotted as functions of frequency (top) and wavenumber. The color coding is not by mode but by degree and frequency:
        • f < 3000 (l < 500): Red
        • 3000 < f < 4000 (500 < l < 800): Green
        • f > 4000 (l > 800): Blue


    7. Frequency differences between active and quiet regions in CR 1976 at the same latitudes for both full-disc and high-resolution obsevations (all modes combined). No significant resolution-dependent differences evident.

    8. Frequency differences between the active sites (Lon 230, 130) and the quiet sites in CR 1976 (Lon 205), from high-resolution data, for the same modes
      1. Frequency differences as a function of frequency
      2. Same as 8a, but with the frequency differences scaled by inverse mode mass
      3. Same as 8a, but plotted as a function of mode turning point
      4. Same as 8b, but plotted as a function of mode turning point


    9. Comparison of frequencies between two active sites in CR 1976
      1. frequency differences vs. frequency
      2. same, scaled by inverse mode mass
      3. same, plotted as function of mode turning point


    10. Differences in mode width between the active and quiet sites in CR 1976

    11. Differences in mode asymmetry between the active and quiet sites in CR 1976
      1. Asymmetry values for all modes in each of the three regions (two active, one quiet) at each of the two latitudes for CR 1976. Asymmetry values for the actives areas are shown in red, those for the quiet areas in black.
      2. Differences in the asymmetry between the quiet and active regions in CR 1976; what is plotted is the difference between the absolute values of the asymmetry parameters; most of the asymmetries are of the same sign anyway,


    12. Zonal and meridional velocity parameters for the full-disc and high-resoluton data in selected regions
      1. Zonal velocity mode parameters - the black points are for the full-disc data, red points for the high-resolution data
      2. Zonal velocity differences (high-resolution - full-disc) for modes of different orders
      3. Meridional velocity mode parameters as in 12a
      4. Meridional velocity differences as in 12b