The Astrophysical Journal, 570:855–864, 2002 May 10 # 2002. The American Astronomical Society. All rights reserved. Printed in U.S.A.
EVOLVING SUBMERGED MERIDIONAL CIRCULATION CELLS WITHIN THE UPPER CONVECTION ZONE REVEALED BY RING-DIAGRAM ANALYSIS Deborah A. Haber, Bradley W. Hindman, and Juri Toomre JILA and Department of Astrophysical and Planetary Sciences, University of Colorado, Boulder, CO 80309-0440;
[email protected]
Richard S. Bogart and Rasmus M. Larsen CSSA-HEPL, Stanford University, Stanford, CA 94305-4085
and Frank Hill National Solar Observatory, 950 North Cherry Avenue, Tucson, AZ 85726 Received 2001 June 25; accepted 2002 January 15
ABSTRACT 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. Subject headings: Sun: activity — Sun: helioseismology — Sun: interior — Sun: rotation
cessfully mapping the Sun’s differential rotation throughout the convection zone and deeper radiative interior (e.g., Thompson et al. 1996; Schou et al. 1998). Such global methods, however, are insensitive to meridional circulations. Local-domain helioseismic techniques such as ring-diagram analysis (e.g., Haber et al. 1998, 2000; Gonza´lez-Herna´ndez et al. 1998; Basu, Antia, & Tripathy 1999), time-distance methods (e.g., Giles et al. 1997, 1998; Duvall & Gizon 2000; Korzennik 2001; Chou & Dai 2001), and poleward and equatorward wave decomposition (Braun & Fan 1998) have been exploited to seek and measure meridional flows beneath the photosphere. Through a combination of these local helioseismic techniques, a general picture of the meridional circulation within the near-surface layers has been deduced. The meridional flow is reported to be poleward in both the northern and southern hemispheres and increases in speed with latitude from zero near the equator to a maximum of about 20 m s1 . Furthermore, within the upper 2% of the Sun by radius there appears to be little variation with depth. Our recent measurements of the meridional flow using ring-diagram analysis of SOI-MDI data from successive years have revealed substantial variations in the meridional flow from year to year. These variations often produce meridional circulations that are at times quite different from the simple scenario described above. In particular, we have detected the existence of a submerged circulation cell within the northern hemisphere during the years 1998–2001, which broke the antisymmetric pattern of the flow seen in 1996 and 1997. The cell first appeared in 1998, and in subsequent years its boundary migrated back and forth in latitude. In 1999, the cell reached its nearest approach to the equator and at the same time its upper boundary was closest to the
1. INTRODUCTION
Large-scale circulations within the solar interior are crucial components of the global dynamo responsible for the Sun’s 22-year magnetic activity cycles. Within dynamo models, the preferred mechanism for amplifying the Sun’s magnetic field is the stretching of weak poloidal fields into strong toroidal fields by rotational shear within the tachocline region at the base of the convection zone. In turn, this shear and the overall differential rotation are established by a combination of Reynolds stresses from the rotationally influenced turbulent convection and by the associated meridional circulations, which jointly control the transport of angular momentum within the tachocline and throughout the convection zone (Miesch et al. 2000; Elliot, Miesch, & Toomre 2000; Gilman 2000; Miesch 2000; Brun & Toomre 2001). Since meridional circulations have a prominent role in determining the differential rotation of the solar convection zone, the detection and measurement of meridional flows within the Sun have been pressing research goals. Using direct Doppler velocity measurements, meridional flows at the solar surface have been detected (e.g., LaBonte & Howard 1982; Hathaway et al. 1996). With the advent of the GONG network (Harvey et al. 1996), the Solar Oscillations Investigation (SOI) with the Michelson Doppler Imager (MDI) on the Solar and Heliospheric Observatory (SOHO; Scherrer et al. 1995) and the TON network (Chou et al. 1995), it has also become possible to deduce the Sun’s meridional circulation below the surface using helioseismology. Helioseismology has traditionally used the global-scale pmode oscillations to probe the solar interior, thereby suc855
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surface. In 2000, the cell retreated northward and downward, and in 2001 the cell advanced southward and upward once more. We present in x 2 the dense-pack data analysis approach that makes these findings possible. In x 3, we show synoptic maps of the large-scale subsurface flows deduced from the dense-pack observations. In x 4, we display longitudinal and temporal averages of the meridional flow as a function of depth, latitude, and year. These averaged flows reveal the existence of the submerged cell with reversed circulation. In x 5, we present the averages of the zonal flow that coexists with the meridional circulations. In x 6, we discuss uncertainties in the measurement technique, and in x 7, we discuss the significance of our findings.
2. DENSE-PACK RING-DIAGRAM APPROACH
In the presence of flows, acoustic waves with the same horizontal wavenumber propagating in opposite directions have their frequencies split by the Doppler effect. Such frequency splittings are used in ring-diagram analysis to measure flow velocities averaged over the depths where the modes have significant amplitude. In mathematical terms, the size of the frequency splitting is D! ¼ k x U, where k is the horizontal wavenumber and U is the integral over depth of the horizontal flow velocity weighted by a kernel that is approximately the kinetic energy density of the acoustic wave. In the local helioseismic technique of ring-diagram analysis, a localized region of a Doppler image of the Sun is tracked in a sequence of images, remapped, and apodized before being Fourier transformed in three dimensions (two in space and one in time) to form a power spectrum (Bogart et al. 1995; Haber et al. 1998). Here, we have studied individual spatial regions or tiles that are about 15 across and are tracked for about 27 hr using the differential surface rotation rate of Snodgrass (1984; see Table 1). The remapping utilizes Postel’s projection, which preserves the distances along great circles (Haber et al. 1995; Bogart et al. 1995). The oscillation power within the spectrum is distributed along curved surfaces that, when cut at constant frequency, appear as a set of nested rings, each corresponding to a mode of different radial order n of the solar wave guide. These rings are nearly circular in shape, with centers dis-
Vol. 570 TABLE 1 Tracking Rate Latitude (deg)
=2 (nHz)
v (m s1 )
52.5 .......................... 45.0 .......................... 37.5 .......................... 30.0 .......................... 22.5 .......................... 15.0 .......................... 7.5............................ 0.0............................
385 404 420 433 442 447 450 451
1685 1767 1837 1892 1932 1957 1970 1974
Note.—Tracking rate in terms of the sidereal rotation rate and the linear rotational velocity v as a function of latitude. These rates correspond to the surface rotation rate of Snodgrass 1984: =2 ¼ 451 nHz 55 nHz sin2 80 nHz sin4 . For reference, the Carrington rotation rate equals 456 nHz or 1994 m s1 .
placed slightly from the origin because of the splitting of the mode frequencies. Figures 1a–1c show how the rings appear for three different frequencies. Each spectrum is filtered with a frequency independent function to minimize the anisotropy in ring power caused by imperfections in the MDI camera (see Haber et al. 2000 for details). During this filtering process, we simultaneously reduce the number of data points around each ring to increase processing speed. This angular subsampling is achieved by interpolating the power spectra from their original Cartesian wavenumber grids to polar grids, removing the high-order azimuthal components by Fourier filtering, and subsampling the data in azimuth (Schou & Bogart 1998). The resulting power spectra are then fitted with predefined functions to obtain the frequency splitting for each mode as a function of mode order n and horizontal wavenumber k (or equivalently harmonic degree l ¼ k R ). We fit the rings with the Lorentzian profile P¼
A 2
ð! !0 þ kx Ux þ ky Uy Þ þ 2
þ
b0 ; k3
Fig. 1.—(a)–(c) Cross sectional cuts of a three-dimensional ring-diagram power spectrum at three different cyclic frequencies !=2. The spectrum is computed from a temporal sequence of 16 Doppler velocity images. Each ring corresponds to a unique radial order n of the solar wave guide, with the outermost ring being the f-mode and the inner rings the p-modes. Flows generate Doppler shifts of the mode frequency, which manifest as slight displacements of the rings. (d ) Representative kernels for an RLS inversion of ring-diagram frequency splittings plotted as a function of depth below the photosphere. The centroids of the kernels are located at depths of 0.9, 2.0, 3.1, 4.4, 5.8, 7.1, and 10.2 Mm; as the centroid increases in depth, the kernels become less localized.
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Fig. 2.—(a)–(c) Dense-pack ring-diagram maps covering much of the solar disk showing horizontal velocities relative to fixed Carrington longitude for 3 sequential days of observation spanning 1999 April 7–10. The velocities were obtained from inversion using kernels with centroids at a depth of 7.1 Mm below the photosphere. The velocity field is represented with scaled arrows that denote flow speed and direction. Underlying the arrow field are magnetograms in which red and green denote surface magnetic fields of opposite polarity. The flows are richly evolving from day to day. There also exist large-scale persistent patterns that coexist with the more rapidly varying flows. In particular, active regions appear as zones of convergence and possible subduction. A reference scaling arrow of 30 m s1 is indicated. The measurement uncertainty in any component of the flow is typically 3 m s1 .
where P is the oscillation power for a wave with a temporal ^ þ ky ^y. frequency ! and a horizontal wavenumber k ¼ kx x ^ and ^ The vectors x y point in the prograde and northward directions, respectively. The profile is specified by six fitting parameters: two Doppler shifts (kx Ux and ky Uy ) for waves propagating in the orthogonal zonal and meridional directions, the background power b0 , and the mode’s central frequency !0 , width C, and amplitude A (Haber et al. 1998, 2000). Waves with different wavenumbers possess different vertical eigenfunctions, thereby sampling the flow field over distinct depth intervals. Therefore, each frequency splitting possesses information about the velocity field over a different range of depths. The frequency splittings are passed through a regularized least-squares (RLS) inversion procedure to obtain measurements of the mean zonal and meridional flows for the analysis region as a function of depth within the upper 15 Mm of the convection zone (Thompson et al. 1996; Haber et al. 2000). The depth dependences of a selection of mode kernels used in the RLS inversion are shown in Figure 1d. Near the surface, many wave modes are available for kernel construction, and the kernels with a centroid near the surface are sharply peaked. As the centroid of the kernel increases in depth, there are fewer available modes in our analysis that penetrate that deeply, and the inversion’s depth resolution in turn becomes poorer. An individual ring-diagram analysis provides an estimate of the horizontal flow as a function of depth at only a single site on the solar surface. To map the flows over much of the solar surface, we perform ring-diagram analyses at many sites on the solar disk. In practice, we conduct 189 separate ring-diagram analyses filling the solar disk out to 60 from disk center with overlapping analysis regions. Each region is 16 (apodized to 15 diameter disks) with centers separated by 7=5 in latitude and longitude. This arrangement of analysis regions, or tiles, is called a dense pack and allows the horizontal flow to be mapped over a substantial fraction of the solar disk. We can follow the evolution of the horizontal flow field by analyzing the dense-pack mosaic of regions on
a series of consecutive days. We perform this dense-pack analysis program on full-disk MDI Dynamics Program data, which typically consist of continuous observations lasting several months of every year starting in 1996. Displayed as a vector diagram, Figure 2 shows the flows obtained on 3 consecutive days for the dense-pack mosaic at a depth of 7.1 Mm below the photosphere. Such maps reveal large-scale streaming flows that may well be called solar subsurface weather (SSW). These weather-like flow patterns possess both a richly evolving component that changes from day to day and slowly evolving mean flows that coexist with the rapidly varying component. Active regions consistently appear as zones of convergence and order the flow over the 7 days that any particular region remains visible within the dense-pack mosaic. These slowly evolving flows are more clearly revealed in temporal and longitudinal averages of the flow data. Such averages will be presented in the following three sections. 3. SYNOPTIC MAPS OF GLOBAL FLOW PATTERNS
Synoptic maps of the horizontal flow field are generated by averaging the dense-pack flows at a given latitude and Carrington longitude over a period of 7 days. This corresponds to the time it takes for solar rotation to sweep a particular site on the solar surface across the dense-pack mosaic. Over 4500 separate ring-diagram analyses are needed to generate one synoptic map, with the relative contribution of each measurement weighted by its formal RLS inversion error. Figure 3 shows the mean flow at a depth of 7.1 Mm for two complete Carrington rotations: rotation 1923 from the relatively quiet year 1997 and rotation 1948 from the magnetically active year 1999. In both maps, the flows possess a prograde zonal component and a poleward meridional circulation. The zonal flow is measured relative to the surface rotation rate of Snodgrass (1984; see Table 1), and the observed net prograde flow is a consequence of the increase in the rotation rate that is observed within the near-surface shear layer. In the syn-
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Fig. 3.—Synoptic maps of subsurface flows of SSW studied during Carrington rotations (a) CR 1923 (from 1997) and (b) CR 1948 (from 1999), obtained by 7 day averaging at sites in the dense-pack mosaic at given latitudes and longitudes, based on inversions sampling a depth of 7.1 Mm. Time advances from right to left. Underlying the flow vectors are synoptic magnetograms with the polarities of the stronger fields marked in red and green. In 1997, when the Sun was relatively quiet, there appear distinctive meandering perturbations to a global-scale mean flow. In contrast, in 1999 the northern hemisphere exhibits major changes, with a submerged cell of reversed meridional circulation now evident. This cell appears as the zone of equatorward flow near the top of the map. The boundary between the midlatitude and low-latitude meridional circulation cells in the northern hemisphere is corrugated with longitude and is beaded by the presence of active regions. The measurement error in any particular component of the flow is about 1 m s1 .
optic map corresponding to a period of low magnetic activity (Fig. 3a, lower panel), we see coexisting with these global-scale flows a low-order undulation in longitude with azimuthal orders m ranging from 4 to 6. This flow is reminiscent of the jet stream flow present in the Earth’s atmosphere and may be an inertial wave response (e.g., Ulrich 2001). When consecutive Carrington rotations are examined, the pattern is not stable. The transitory nature of this undulatory pattern is typical of the convective structures that are seen in numerical simulations of turbulent solar convection (e.g., Miesch et al. 2000; Brun & Toomre 2001). The largescale convective cells in such simulations distort and propagate relative to a particular reference frame and are often unidentifiable from one rotation to the next. Figure 3b (upper panel) is a synoptic map of subsurface flows from a time of pronounced magnetic activity, revealing striking changes in behavior from the flows in 1997 (Fig. 3a). Many of the large-scale flow patterns are clearly correlated with the presence of magnetic activity. Active regions appear as zones of convergent flow and probably subduction just as they do in the daily flow maps. Further, within
the northern hemisphere there exists at midlatitudes a zone of reversed meridional circulation. The boundary between this midlatitude cell and the low-latitude zone possessing poleward flow is rumpled in longitude and coincides roughly with the location of active regions. However, this is not a universal property. In later years, the boundary shifts in location to latitudes higher than the active region band.
4. MEAN MERIDIONAL FLOWS
The zone of reversed meridional circulation in the northern hemisphere is not visible in synoptic maps for flows immediately below the solar surface, such as at a depth of 0.9 Mm. Therefore, the reversed circulation corresponds to a submerged cell. This property is more clearly revealed in longitudinal averages of the synoptic maps. Figure 4 presents a vector plot of the mean meridional flow as a function of depth and latitude in successive years for each of the six Dynamics Program intervals. Those regions with southerly flow are shaded gray, and contours of equal flow speed
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Fig. 4.—Meridional flow averaged in time and longitude, shown as a function of latitude and depth for Dynamics Program intervals in the past six years. Underlying the vector fields are contours of constant meridional flow, with contours labeled in m s1 . Regions of southerly flow are indicated by negative contours and are shaded gray. Starting in 1998, an additional circulation cell appears in the northern hemisphere (positive latitudes). This cell manifests as a submerged region of equatorward flow lying below poleward flow at the surface and appearing as the gray zone within the northern hemisphere. There is substantial evolution in the latitudinal extent of this cell as sampled during each annual interval. The breaking of symmetry between the southern hemisphere, which has fairly uniform flow, and the northern hemisphere, which has varying multiple cells, is quite striking.
have been superposed with the arrows. The submerged cell appears as the gray region within the northern hemisphere. When the submerged cell is absent, as in 1996 and 1997, the meridional flow is nearly independent of depth and antisymmetric about the equator, with poleward flow increasing from zero near the equator to a maximum of roughly 20–30 m s1 at higher latitudes. (This latitudinal variation is also illustrated in Fig. 6, showing cuts of the meridional flow at
two depths.) From 1998 onward, as a result of the submerged cell, this antisymmetry is broken. Within the northern hemisphere, the submerged meridional circulation cell disrupts the orderly poleward flow of earlier years. The simple and unvarying poleward flow of the southern hemisphere is largely unchanged. The additional cell first appeared in 1998 at high latitudes and greater depths. By 1999, the submerged cell had expanded equatorward and
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upward, reaching within 20 of the equator and 2 Mm of the surface. In 2000 the cell receded and in 2001 it advanced equatorward once again. For those years in which the submerged cell is present, the poleward flow at low latitudes is noticeably weakened except in the surface layers. Remarkably, the surface seems to be unaffected by the presence of the additional cell; the flow continues to stream poleward in the surface layers even though the equatorward flow of the submerged cell is lurking just below. The depth dependence of the meridional flow exhibits a great deal of richness. Figure 5 presents profiles of the flow with depth as extracted from Figure 4 at latitudes of 45 north and south. These profiles clearly indicate that within the southern hemisphere, the meridional flow within the upper 15 Mm of the convection zone is largely independent of depth. There is evidence for a slightly faster surface flow and an enhanced flow at a depth of 5 Mm at the highest southern latitudes. However, these features do not persist throughout the six years of observation. Within the northern hemisphere, the meridional flow has more striking depth dependence. In 1999 and 2001, when the submerged cell is present at 45 north, the poleward-streaming surface layers occupy the upper 3–5 Mm. Below this narrow surface zone exists the submerged cell in which the direction of the meridional flow is reversed and the flow rapidly increases with depth.
Vol. 570 5. MEAN ZONAL FLOWS
In addition to meridional circulations, our ring-diagram analyses of the dense-pack mosaic generate detailed measurements of the zonal flow. Figure 6 shows both the zonal and meridional flows as a function of latitude at two different depths (0.9 and 7.1 Mm) for the 6 consecutive years. As deduced by global-mode helioseismology, the Sun’s rotation rate increases rapidly with depth in a surface shear layer that spans the entire range of depths probed by our ring-diagram analyses. In order to show the zonal velocity at different depths on the same scale, a depth-dependent offset has been removed. This offset is –0.5 m s1 at a depth of 0.9 Mm and 18.8 m s1 at a depth of 7.1 Mm. The variation of the offset over the 15 Mm depth range probed by our ring-diagram analyses is comparable to the change in rotation rate that occurs over the same depth range measured using global helioseismology (Haber et al. 2000). The zonal flow is dominated by bands of somewhat faster rotation, which appear at latitudes of roughly 30 north and south in 1996. By 2001, these fast bands have migrated toward the equator to latitudes of 10 north and south. Such banding flows have been called ‘‘ torsional oscillations ’’ and have been observed previously by direct Doppler measurements of the surface (e.g., Howard & LaBonte 1980; Hathaway et al. 1996; Ulrich 1998), by f-mode studies (Kosovichev & Schou 1997), by global p-mode analyses (Howe et al. 2000a, 2000b), and by local helioseismic methods (Haber et al. 2000, 2001; Basu & Antia 2000; Duvall & Gizon 2000). These flows appear to be associated with the latitudes at which active regions emerge, although the zonal fast bands precede the magnetic activity by roughly 10 in latitude as both phenomena migrate equatorward with advancing solar cycle. In contrast with the global-mode analyses, ring-diagram analyses are sensitive to north-south asymmetries in the flows. In the years 1997–2000, the zonal flows at low latitudes are largely symmetric about the equator. At higher latitudes, however, there is a pronounced asymmetric component in the flows. In 1996 and 2001, the zonal flows possess strong asymmetries at all latitudes. For example, in 2001 the fast band in the northern hemisphere mostly disappears as a result of the emergence of a zone of slow rotation at a latitude of 30 north. Meanwhile, the southern fast band has continued its orderly march toward the equator. Features within the meridional and zonal flows appear to be weakly connected. As can be seen in the right-hand panels of Figure 6, the mean meridional flow rises from zero near the equator to a maximum located between 10 and 25 in latitude. In the absence of the submerged cell with reversed circulation, the flow becomes roughly constant at latitudes higher than these maxima. These maxima are coincident with the zonal fast bands, and as the fast bands migrate toward the equator as the solar cycle progresses, the maxima in the meridional flow move as well, causing a steepening of the gradient at the equator. Hints of this steepening have been observed in previous ring-diagram studies (Basu & Antia 2000; Haber et al. 2000, 2001).
6. UNCERTAINTIES IN MEASUREMENT Fig. 5.—Depth profiles of the mean meridional flow extracted from Fig. 4 at latitudes 45 north and south for 1997, 1999, and 2001. The existence of the additional cell in the northern hemisphere is revealed in 1999 and 2001 by the reversal of flow direction as the depth increases.
The ring-diagram analysis procedure yields error estimates for each fitted parameter based on the broadness of the fitting minima. These formal errors are propagated
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Fig. 6.—Longitudinal and temporal means of the zonal flows (left panels) and meridional flows (right panels) at depths of 0.9 Mm (dashed curve) and 7.1 Mm (solid curve) obtained from the dense-pack mosaics. Each panel corresponds to the average over yearly Dynamics Program intervals as indicated. The error bars shown are 10 times larger than our estimated formal errors in order to be visible. The zonal velocity plots for each year have been offset by subtracting a depth-dependent constant. Propagating zonal fast bands are seen to migrate toward the equator as the solar cycle progresses. The meridional flow is largely poleward, except from 1998 to 2001, when an additional circulation cell is present in the northern hemisphere. At the depth of 7.1 Mm, this additional cell appears as a weakening or reversal of the meridional circulation in the northern hemisphere.
through the inversion and are typically amplified depending on the trade-off chosen between the radial resolution of the inversion (or the localization of the inversion kernels) and the amplification of the errors. We have chosen the trade-off parameters such that the velocity profiles remain fairly smooth and the relative velocity error is no more than about 15% within the upper 15 Mm. Below this depth, the error estimates become quite large and the depth resolution poor. This is largely a result of the small number of measured modes that penetrate that deeply below the surface. Because of the increasing magnitude of the errors and the broadening of the kernels that occurs for the larger target depths, we do not present our inversion results at depths below 15 Mm, even though some of the modes used in the inversions can sample down to 35 Mm. The relative error of about 15% within any given ring-diagram inversion converts into a formal error in any velocity component of about 3 m s1 at a depth of 7.1 Mm. The longitudinal and temporal averaging that is performed on the measurements from many sites to compute the mean flows and the synoptic maps reduces these errors substantially. The typical error for each velocity component in the synop-
tic maps is about 1 m s1 , and about 0.5 m s1 in the longitudinally averaged flows shown in Figures 4, 5, and 6 at the 7.1 Mm depth. At a depth of 15 Mm, the formal errors in the mean flows are still only about 2 m s1 . The ring-diagram technique is also subject to systematic errors introduced by the MDI instrument and the analysis scheme itself. The optical properties of MDI are not understood sufficiently well that the errors generated by the instrument can be directly removed. We can, however, estimate the size of such systematic errors by averaging the velocity measurements at fixed locations within the densepack matrix (and hence at fixed locations in the camera’s image field) over all of the observing days within a given Dynamics Program interval. Figures 7a–7c show such average velocities at a depth of 7.1 Mm for three separate intervals in 1997, 1999, and 2001. In each velocity field, the longitudinal average of the meridional and zonal flow has been subtracted to remove as much of the solar signal as possible. A major focus change occurred between the Dynamics Program periods in 1997 and 1999. In 1996 and 1997, the camera was set intentionally out of best focus. The resulting velocity field as a function of disk location (Fig.
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Fig. 7.—(a)–(c) Estimates of systematic errors across the field of view in velocities determined through inversion at a depth of 7.1 Mm in 1997, 1999, and 2001. The largest gradients in the error estimates occur at the edges of the dense-pack matrix. The differences among these years sampled are related to changes in the instrument focus. From 1998 onward, the camera was placed in sharpest focus, which yields weak gradients in the systematic errors except at the edges. (d ) Temporal averages of the formal errors across the field of view in 1997 for velocities deduced at a depth of 7.1 Mm. The standard deviations associated with the errors in the zonal and meridional directions are displayed here as components of a vector. The formal errors appear to be largely independent of location and have a typical value of 3 m s1 in either direction. These average formal errors provide a reasonable estimate for the likely scatter in a given ring-diagram measurement.
7a) has variations across the field of view with a total change of 20–30 m s1 from one side of the dense-pack mosaic to the other. In later years, the camera was placed in sharpest focus, and the resulting variations across the field of view are substantially different. Most of the systematic field-ofview variation occurs at the edges of the dense-pack mosaic. The variation across most of the center of the field is relatively small, with a total change from site to site fivefold smaller than in 1997. The field-of-view variation is not related to a spatial dependence across the solar disk of the formal measurement errors. Figure 7d shows the average of the formal errors from 1997 at fixed locations on the disk at a depth of 7.1 Mm. The formal error is nearly uniform across the densepack mosaic and is an unlikely explanation for the observed field-of-view velocity variation. A more reasonable source for the field-of-view effect is the existence of image scale variations across the MDI camera due to optical imperfections, such as a tilt of the CCD array with respect to the optical axis. Such imperfections can cause incorrect tracking of the flows and corresponding spurious zonal velocities. The image scale variations across the disk cause misidentification of the wavelength of acoustic waves, which has a direct impact on the depth of velocity features ascribed by the helioseismic inversions. Another source of systematic error is an incorrect measurement of the Sun’s rotation axis on the image field. A misalignment of this axis produces a spurious meridional flow resulting from the mixing of the large rotation rate into the meridional direction. Such a misalignment has been measured once or twice (C. Toner 2001, private communication) to be about 0=2, resulting in a false meridional flow that is 6 m s1 at the equator. We have generated our synoptic maps (Fig. 3) and mean flows (Figs. 4, 5, and 6) with and without the inclusion of the edges of the dense-pack mosaic that appear to have the largest field-of-view variations. The flows in these two cases are slightly different. However, the existence of the submerged meridional cell with reversed circulation in the northern hemisphere is insensitive to whether or not the edges are part of the averaging process. Similarly, we have found that inclusion of the meridional flow produced by the misalignment of the solar rotation axis cannot generate the
flows attributed to the submerged cell, although they can modify the amplitude and spatial extent of the cell. Other features, such as the migration of the zonal bands toward the equator, the colocation of the zonal bands and maximal meridional flow, and the relative constancy of the meridional flow with depth, are all independent of these systematic errors. Therefore, the mean properties of the flow appear to be a robust result despite the existence of velocity changes across the field of view. 7. DISCUSSION
Earlier studies of the Sun’s meridional circulation made through Doppler measurements of the flow velocity at the solar surface have not reported the presence of multiple cells within a given hemisphere. The additional midlatitude cell that we have detected in the years 1998 to the present is a submerged cell in the northern hemisphere, which, over the course of the last four years, has spanned different depths below the surface. Positioned above the additional cell is a poleward surface streaming flow, which is largely unaltered by the presence of the submerged cell. Therefore, direct Doppler measurements that sample the flow at the surface are insensitive to the presence of the submerged cell. Indeed, many local helioseismic studies that exclusively utilize fmodes would also fail to detect the flow reversal that marks the cell’s presence. The f-modes in such studies do not penetrate deeply enough to sample the flow within the submerged cell. Helioseismic techniques that use p-mode oscillations, such as our local-domain ring-diagram method, are able to sample more deeply. Our inversion procedure generates reasonable kernels down to a depth of about 15 Mm below the photosphere. Below this depth there exists an insufficient number of modes with deep enough penetration to form well-localized kernels. The submerged cell with reversed meridional circulation that we observe in the northern hemisphere extends as far down as we can sample. Therefore, we cannot say how deeply the northern hemisphere’s submerged cell penetrates. There does exist evidence that the cell is more deeply rooted. Using time-distance methods, Giles (1999) reported the beginnings of an additional cell in the meridional circulation in 1998 at latitudes greater than
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50 north and for depths as great as 27 Mm. We believe that the cell Giles observed and the cell revealed by our ring-diagram analyses are the same structure. Other studies of the meridional flow within the deep convection zone are largely in disagreement. Using time-distance techniques, Chou & Dai (2001) find evidence for the existence of multiple cells and reversed meridional circulations within both hemispheres in 1998–2000. However, the actual depth at which these perturbations are present is difficult to determine because depth inversions of their measurements have not been performed. Our results and the findings of other ring-diagram studies (Gonza´lez-Herna´ndez et al. 1999; Basu & Antia 2000) agree that the meridional flow is poleward within the near-surface layers, although the flow speeds are somewhat different. In deeper layers, these other studies either were performed in years before the submerged cell appeared (Gonza´lezHerna´ndez et al. 1999) or do not report flows at sufficient depths to sample the submerged meridional cell (Basu & Antia 2000). The dynamical implications of the presence of multiple meridional circulation cells is difficult to ascertain without a better understanding of the vertical structure of such cells. There are many different possibilities, including a single cell in depth with a deep return flow, multiple cells stacked on top of one another, and meridional circulations significant only within restricted depth layers such as the near surface. Each of these possibilities has different dynamical consequences on the advection of angular momentum and the redistribution of magnetic fields. Presently, we have obtained only measurements of meridional circulations within the near-surface shear layer. Thus, we cannot distinguish between different cell structures at greater depths. Within the near-surface shear layer, however, we can make estimates of the transport achieved. Figure 8 shows the specific latitudinal angular momentum flux associated with the advection of angular momentum by the mean meridional circulation measured by our ring-diagram analyses at three depths. In 1997, when the meridional flow is largely antisymmetric about the equator and the submerged cell is absent, the resulting angular momentum flux, in the absence of compensating stresses, would cause a gradual slowing of the equator and an acceleration of the midlatitudes. In 1999 and 2001, the submerged cell with reversed circulation results in an equatorward (negative) transport of angular momentum within the midlatitudes of the northern
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hemisphere. This would tend to cause an even larger acceleration of the northern midlatitudes than when the submerged cell is absent, but all could be offset by changes in the radial angular momentum flux, which we cannot assess because our technique is insensitive to vertical flows. In contrast to the northern hemisphere, the angular momentum flux by the meridional circulation in the southern hemisphere is consistently poleward (negative) at all depths. At first glance, the lack of depth variation in this flow (as in Figs. 4 and 5) appears to be quite innocuous. It must be kept in mind, however, that the density contrast across the layer that we sample is immense. The mean fluid density changes by a factor of about 300 over the range in depths of 1–10 Mm. Therefore, the angular momentum carried by the relatively constant meridional circulation also changes by such a factor. This novel feature has not been anticipated by theoretical models. Over the six years that we have dense-pack measurements, we have not observed multiple cells within the southern hemisphere. We do not understand why the development of multiple cells appears in such an asymmetric fashion. One might think asymmetries in the distribution and strength of active regions and other magnetic features might control the development of multiple cells through Lorentz forces on the flows. Upon careful consideration, however, this explanation fails. Although the amount of magnetic activity (as measured by the average magnetic flux) is larger in the northern hemisphere during 1999 and 2000, this was not the case in 1998 when the submerged cell first appeared. The lack of a mechanism, magnetic or otherwise, to explain the breaking of equatorial symmetry through the development of additional meridional circulation cells is not as severe as one might think. There are no fundamental reasons why the meridional flow in the two hemispheres must be symmetric. Computational studies of turbulent solar convection in spherical shells (e.g., Miesch et al. 2000; Brun & Toomre 2001) show that large-scale convective structures that are not symmetric about the equator are frequently present. Since the turbulent dynamics itself does not require equatorial symmetry, there is little reason to expect that the meridional circulations, which arise from selforganization of the turbulence, should possess such symmetries either. Even though magnetism does not explain the existence of additional meridional circulation cells, one might think that
Fig. 8.—Specific latitudinal angular momentum fluxes achieved by the mean meridional circulation deduced from our ring-diagram analyses, showing variation with latitude at the three depths of 0.9, 7.1, and 10.2 Mm for 1997, 1999, and 2001. A positive flux is directed northward. In the southern hemisphere, the specific flux is nearly invariant with depth. The presence of the submerged reversed cell in the northern hemisphere in 1999 and 2001 changes the sense of the transport at the greater depths.
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it could play a role in the spatial propagation of such features. In 1999, the latitudinal boundary of the submerged cell is marked by active regions like posts on a meandering fence. This seems to indicate that the latitudinal boundary of the cell is controlled by the locations of activity. However, this well-defined correlation between the cell boundary and the presence of active regions is not present in other years. Furthermore, the poleward streaming of the meridional flow within the surface layers appears unaffected by the presence of magnetism. This is particularly incongruous, considering that the Lorentz forces associated with the magnetic field are strongest in those layers. The most likely explanation is that the submerged cell is responding to weak stresses imposed by underlying deep convection, which may in turn be connected to the latitudes of active region emergence. The recent findings of global helioseismology that the rotation rate possesses localized features that evolve with time, such as the propagation of zonal banding flows in the upper convection zone (Kosovichev & Schou 1997; Howe et al. 2000b) and oscillations of the rotation rate near the tachocline with a 1.3 yr period (Howe et al. 2000a), have revealed that the solar convection zone is much more inter-
esting than simple models for solar convection and the global dynamo might indicate. Our findings that the meridional circulation within the near-surface layers, and conceivably deeper layers, also exhibits rich variations on timescales comparable to the solar cycle indicate that the dynamics in general are more complicated than many have thought. To develop an understanding of why multiple cells develop and how such structures influence the transport of angular momentum and magnetic field throughout the convection zone, we must not only learn how to measure the meridional circulations deeper within the Sun, but we must make a continuing effort to probe and map solar flows over all phases of the Sun’s 22 year magnetic cycle. We thank Jørgen Christensen-Dalsgaard, Douglas Gough, Jesper Schou, and Mike Thompson for useful advice and discussions. This research was supported by NASA through grants NAG 5-7996 and NAG 5-8133, and by NSF through grant ATM-9731676. The SOI-MDI project is supported by NASA grant NAG 5-3077 to Stanford University. SOHO is a project of international cooperation between ESA and NASA.
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