AAS Meeting #194 -
Chicago, Illinois, May/June 1999
PAPER 93.03
Supergranules and Photospheric Motions Near the Solar Poles
R. S. Bogart, J. G. Beck, R. I. Bush,& J. Schou
Stanford University
Introduction
Since the SOHO launch in 1995, there have been seven opportunities for
the Michelson Doppler Imager (MDI) to provide continuous Dopplergrams of
the solar poles over extended intervals of time. Because of the nearly
constant and uniform focus of the MDI images over small regions it is
possible to resolve and track supergranules across the pole at these times.
Seismic analysis of global modes from the MDI data has previously hinted at
the possibility of a polar vortex in the upper convection zone. We report
here on the first analysis of polar surface motions inferred from MDI data
covering a total of about 2000 hours during five polar observing windows,
including two full months around the south polar apparition of 1998.
Because of the lack of seeing and scattered light and excellent pointing
stability, the Michelson Doppler Imager (MDI) on the Solar and Heliospheric
Observatory (SOHO) makes excellent Doppler observations near the solar limb,
despite its moderate spatial resolution (2"). Its ability to observe
continuously for times comparable to and longer than the typical lifetime
of supergranules makes it an ideal instrument for studying the behaviour
of these features of predomiminantly horizontal flow whose maximum signal
is at the limb. Although the SOHO orbit is inclined to the Sun's rotation
axis at about the same small angle as the Earth (7.25 deg), the stability
and continuity of MDI full-disc Dopplergrams make them a potential rich
source of data on supergranules and large-scale flows near the solar poles.
Available Data
During the 3.5 years since SOHO launch on 2 Dec. 1995, there have been seven
opportunities to observe the poles at their maximum tilt toward the observer.
For a period of about two months around each such solstice, the inclination
of SOHO to the solar equator |B| exceeds 6.25 deg, and the pole is more than
6" (three pixels) from the limb. (see Table I). The first of these occurred
during the spacecraft and instrument checkout and calibration period before
the commencement of nominal observations. Although there were two periods
of more than a day when continuous full-disc Dopplergrams were made with
MDI, the data were test data only, not taken in normal sequences, and they
have not been calibrated. There may be useful information in them,
paricularly when combined with the unique set of observations made on
5 Mar 1996, when the spacecraft was temporarily pointed to place the south
pole within MDI's restricted field of high spatial resolution (0".65).
These data are not considered here. The sixth opportunity for polar
observing occurred during the extended period (25 Jun - 4 Nov 1998)
when normal operations and communications were interrupted by a serious
spacecraft emergency. Although there have been long periods of continuous
"full-disc" coverage during the seventh polar observing opportunity (5 Feb -
7 Apr 1999), virtually all of these were made in a new observing mode that
crops pixels near the limb out of the telemetry stream and so the polar
region data were lost.
Table I. Optimum opportunities for MDI observations of the solar poles
|B| > 6.25 (3 pixels from pole to limb)
1. 1996.02.05 - 1996.04.05
1a 1996.02.17_20:00 - 1996.02.19_15:05 (hours 27428 - 27471) (43)
(level 0 only)
1b 1996.03.28_01:00 - 1996.03.31_07:30 (hours 28368 - 28447) (75)
(level 0 only)
2. 1996.08.07 - 1996.10.10
2a 1996.08.18_17:10 - 1996.08.23_03:00 (hours 31817 - 31922) (106)
2b 1996.09.17_17:40 - 1996.09.22_01:35 (hours 32537 - 32641) (105)
3. 1997.02.04 - 1997.04.06
3a 1997.02.13_10:30 - 1997.02.18_15:20 (hours 36106 - 36231) (126)
3b 1997.03.12_14:20 - 1997.03.17_00:45 (hours 36758 - 36864) (107)
4. 1997.08.08 - 1997.10.09
4 1997.08.10_14:30 - 1997.08.14_01:05 (hours 40382 - 40465) (84)
5. 1998.02.05 - 1998.04.06
5 1998.02.05_00:00 - 1998.03.03_09:00 (hours 44664 - 45296) (633)
part of Dynamics Campaign IIIa (beginning 1998.01.09_10:50)
1998.03.05_02:20 - 1998.04.06_23:59 (hours 45338 - 46127) (790)
part of Dynamics Campaign IIIb (ending 1998.04.10_08:00)
6. 1998.08 - 1998.10
no data - spacecraft emergency
7. 1999.02.05 - 1999.04.07
1999.02.11_03:30 - 1999.02.14_07:30 (63)
1999.02.19_00:40 - 1999.02.23_02:40 (74)
1999.03.13_01:20 - 1999.03.15_23:45 (71)
The Movie
MDI Dopplergrams taken at a cadence of one per minute have been mapped
and averaged together in one-hour frames for each of the five observing
intervals to make the movies being shown. (The two parts of Dynamics
Campaign III, separated by a 31-hour gap due to a spacecraft emergency
but otherwise identical, have been combined into a single interval as the
length of the gap is short compared to the overall duration.) The calibrated
velocity data are first corrected for the line-of-sight component of
spacecraft orbital motion and detrended with a uniform model of differential
rotation and convective limb-shift. They are then projected onto the
heliographic coordinate system using a stereographic projection centered
at the appropriate pole and with a fixed direction for Carrington longitudes.
The map angles are chosen so that the 0 longitude runs down from the center
of the maps centered at the north pole and up from the center of those centered
at the south pole. All mapped Dopplergrams within a clock hour, comprising
a SOI dataset, are then averaged together. Mapping to the Carrington system
before averaging has the effect of removing the spatial smearing that would
result from rotation of features past the observer, at least to first order.
Although the overall data filling factor is high, typically about 97%, there
are numerous missing or corrupted Dopplergrams, and occasional gaps of up to
several hours. Gaps of up to five hours' duration are simply filled in by
linear interpolation between the surrounding images - there are ten such
gaps during the two-month south-pole series of 1998. Interpolated frames
in the movie do not have date-time labels. Longer gaps are simply blanked
out. Apart from the gap already mentioned, the only other is a 6-hour gap
in the first north-pole sequence (1997 Feb).
Each of the four short (5-day) sequences 2a, 2b, 3a, 3b, and 4, is shown
four times in the movie, twice showing a heliographic 15 deg grid for
orientation and twice without the grid. The long 2-month sequence is then
also shown twice with the grid and twice without, the second of each pair
being sped up a factor of two. After that the two-month sequence at the
south pole withthe grid overlay loops repeatedly.
The animation below shows the polar view for only sequence 2a,
1998.08.18_17:00 - 1996.08.23_03:00.
Supergranulation and Surface Rotation
Supergranules are plainly visible without evident distortion at very high
latitudes in the movies. Naturally they exhibit substantial eastward proper
motion relative to the Carrington coordinate system. We have made initial
estimates of the differential rotation at high latitudes inferred from
supergranule tracking simply by reprojecting and averaging the detrended
Doppler data again, this time with a sinusoidal equal-area projection
centered on a fixed Carrington longitude, so that physical displacements
(in meters) along a parallel over a given time are proportional to image
displacement at all latitudes. In temporal stack plots of individual
latitudes the proper motion of a supergranule is proportional to the
slope of the feature. Figure 1 shows examples of such stack plots for
six selected latitudes from the 107-hour sequence around the south pole
in March 1997.
Figure 1
Line-of-sight velocity as function of distance from the central Carrington
longitude along the parallel (horizontal) vs. time (vertical, running from
bottom to top), for several latitude strips
Latitude 60 S 
Latitude 65 S 
Latitude 70 S 
Latitude 75 S 
Latitude 80 S 
Latitude 85 S 
This initial set of maps of supergranulation shows striking evidence for
a polar vortex, a spin-up in the Carrington frame near the pole (see
Table 2). While the mean proper motion at -60° is quite consistent with
standard measures of differential rotation at that latitude, and the
differential rotation curve persists to -65°, there apears to be a
turnover before -70°, with a velocity shear several times the magnitude
of that of the mid-latitude differential rotation. The extrapolated polar
rotation rate is about 2 microrad/sec, a period of 36 days.
Table II. Mean zonal proper motions of supergranules at high latitudes
1997.03.12-17
Latitude u ± RMS equivalent delta-rot (microrad/sec)
-60° -165 (42) 0.47
-65° -183 (48) 0.62
-70° -175 (44) 0.74
-75° -128 (31) 0.71
-80° -132 (65) 1.09
-85° - 65 (13) 1.07
Polar Flows
Any steady cross-polar flow should be seen in the line of sight as a
periodic signal with period equal to the rotation period at the pole,
longer than the Carrington period but perhaps not as much longer as
the standard models of differential rotation imply. In Figure 2 we
show the average residual Doppler signal in a small (1 square degree)
area centered on the south pole as a function of time during the two-month
observing window of Feb. - Apr. 1998. Substantial quasi-periodic
excursions of amplitude ~100 m/s are present, but the typical periods
are only 5-10 days (slight peak in the power spectrum at 1 microHertz).
Since this is much longer than the typical lifetimes of supergranules,
it appears from this very preliminary result that there may possibly be a
two- or three-sector structure of quasi-steady flows with a vertex
away from the pole.
Research supported by SOI-MDI NASA grant NAG5-3077 at Stanford University.