Astronomy & Astrophysics manuscript no. delmoro07˙LR c© ESO 2021
November 10, 2021
3D photospheric velocity field of a Supergranular cell
Del Moro, D., Giordano, S. and Berrilli, F.
Dipartimento di Fisica, Università di Roma “Tor Vergata”, I-00133 Roma, Italy
Received date will be inserted by the editor; accepted date will be inserted by the editor
ABSTRACT
Aims. We investigate the plasma flow properties inside a Supergranular (SG) cell, in particular its interaction with small
scale magnetic field structures.
Methods. The SG cell has been identified using the magnetic network (CaII wing brightness) as proxy, applying the
Two-Level Structure Tracking (TST) to high spatial, spectral and temporal resolution observations obtained by IBIS.
The full 3D velocity vector field for the SG has been reconstructed at two different photospheric heights. In order to
strengthen our findings, we also computed the mean radial flow of the SG by means of cork tracing. We also studied the
behaviour of the horizontal and Line of Sight plasma flow cospatial with cluster of bright CaII structures of magnetic
origin to better understand the interaction between photospheric convection and small scale magnetic features.
Results. The SG cell we investigated seems to be organized with an almost radial flow from its centre to the border. The
large scale divergence structure is probably created by a compact region of constant up-flow close to the cell centre. On
the edge of the SG, isolated regions of strong convergent flow are nearby or cospatial with extended clusters of bright
CaII wing features forming the knots of the magnetic network.
Key words. Sun:photosphere – Sun:magnetic fields – Methods:data analysis
1. Introduction
Solar research is currently working on understanding how
turbulent convection on the Sun transports mass and en-
ergy through the convective zone, how it couples with the
magnetic field and how it manages to deposit in the higher
parts of the solar atmosphere the energy released from the
corona. Among the different approaches to these questions,
observations of the solar photosphere are essential, as they
provide the only direct look at what is happening just below
the solar surface. The hierarchy of surface features found
on the photosphere are the visible representation of the
plasma flows beneath the photosphere and are customar-
ily classified by size and lifetime as patterns of granula-
tion (1 Mm, 0.2 hr), mesogranulation (5-10 Mm, 5 hr)
and supergranulation (15-35 Mm, 24 hr). These features
have been initially regarded as direct manifestation of var-
ious sized convection cells existing in the convection zone
(Schrijver et al., 1997; Raju et al., 1999); lately, the idea
is consolidating that meso and supergranulation are sig-
natures of a collective interaction of granular cells (Rast,
2003; Roudier et al., 2003; Berrilli et al., 2005). Despite
years of intensive studies, the character of their motions
remains not completely understood (Beck & Duvall, 2000;
Krishan et al., 2002; Berrilli et al., 2004; Del Moro et al.,
2004; DeRosa & Toomre, 2004). The aim of the study we
present is to investigate the origin of the supergranular (SG)
flow field: directly convective or a collective interaction of
smaller convective features.
The study performed by Simon & Leighton (1964) initi-
ated the campaign to characterize supergranular flows.
Outflows on SG scales have been observed to sweep
embedded granules and magnetic flux elements toward
Send offprint requests to: delmoro@roma2.infn.it
convergence lanes between cells (Leighton, 1964; Zwaan,
1978; Rimmele, 1989; Shine et al., 2000). Such behaviour
causes the chromospheric transition CaII k line to be
a good proxy for the network of intercellular lanes due
to the higher magnetic elements density in the SG
perimeters. The advent of full-disk Doppler imaging, pro-
vided by the MDI onboard SOHO spacecraft, has con-
siderably improved our capability to study such fea-
tures (Hathaway et al., 2002; DeRosa & Toomre, 2004;
Paniveni et al., 2004; Meunier et al., 2007); but direct ob-
servations of supergranular flows are still hindered by the
fact that there is no contrast on supergranular scales in visi-
ble light, observations in CaII only provide the cell network
boundaries and Doppler images show SG only away from
disk centre.
At present, the only methods to reconstruct the full 3D
vector velocity field are direct Doppler measurement in
combination with a tracking type measure for the velocity
horizontal component (above the τ = 1 surface) or Local
Helioseismology (below the τ = 1 surface). To gain com-
plete insight of the dynamics of the plasma flows inside a
SG structure, we need a spatial and temporal resolution still
not reached by local helioseismology, while to obtain the
3D velocity field through the other method, observations
with very high spatial, spectral and temporal resolution are
necessary. With the assumption that granule motions are
mainly driven by plasma flows (Rieutord et al., 2001), it is
possible to employ the TST to infer the horizontal velocity
field.
In this work we reconstruct the 3D velocity field of a sin-
gle SG structure and investigate in detail its plasma flow
using data acquired with the IBIS spectrometer, trying to
discern whether the SG pattern has a convective nature or
is originated by small scale structure interaction.
http://arxiv.org/abs/0704.0578v2
2 Del Moro et al.: 3D photospheric velocity field of a SG cell
Fig. 1. A representative synoptic panel from the 16th October 2003 dataset. Upper left panel: Ca II wing intensity
image. Upper middle panel: Doppler velocity field computed from FeI 709.0 nm line scan. Upper right panel: FeI 709.0
nm line core intensity Lower left panel: Doppler velocity field computed from FeII 722.4 nm line scan. Lower middle
panel: FeII 722.4 nm line core intensity. Lower right panel: Continuum (near 709.0 nm) intensity image.
Line Wavelength zTcore FWHMRFI
zVline FWHMRFI
[nm] [km] [km] [km] [km]
FeI 709.0 ≃100 ∼300 ≃140 ∼300
FeII 722.4 ≃50 ∼200 ≃70 ∼200
Table 1. Line RF peak depths. Depths are in km above the level τ500nm = 1.
2. Observations
The data utilized in this analysis have been acquired with
the IBIS (Interferometric BIdimensional Spectrometer) 2D
spectrometer (Cavallini et al., 2001; Cavallini, 2006) on
October 16, 2003 (from 14:24 UT to 17:32 UT).
We imaged a roundish network cell near the solar disk cen-
tre (SLAT=7.8N, SLONG=3.6E). When observed in MDI
high-resolution magnetograms, all the features outlining
the cell exhibit negative polarity and seem to survive for
at least 10 hours, with little or no evolution.
The full dataset consists of 600 sequences, containing a 16
image scan of the FeI 709.0 nm line, a 14 image scan of
the FeII 722.4 nm line and 5 spectral images in the wing
(line centre + 12 nm) of the CaII 854.2 nm line, imag-
ing a round Field of View (FoV) of about 80” diameter.
Each monochromatic image was acquired with a 25 ms ex-
posure time by a 12bit CCD detector, whose pixel scale
was 0.17′′·pixel−1. The time required for the acquisition of
a single sequence was 19 s, thus setting the temporal res-
olution. Each image was reduced with the standard IBIS
pipeline (Janssen & Cauzzi, 2006; Giordano et al., 2007),
correcting for CCD non linearity effects, dark current, gain
table and blue shift. The Line of Sight (LoS) velocity fields
were computed for the Fe I and Fe II lines by means of
Doppler shifts, evaluated, pixel by pixel, fitting a Gaussian
on the line profile. In order to remove the orbital contribu-
tion, we set to zero the average value of each LoS velocity
image. The 5-minutes oscillations were removed applying a
3D Fourier filter in the kh −ω domain with a cut-off veloc-
ity of 7 km·s−1 both on intensity and velocity image series.
After the whole reduction process and selecting only the
period of good seeing we are left with a 30 minutes dataset
imaging a square FoV of ∼ 50”. An example of the im-
ages of this reduced dataset is shown in Fig. 1. The mean
resolution due to the seeing of the CaII images is 0.35”;
the mean resolution of the LoS velocity images, the inten-
sity continuum images and the line core images is instead
0.45”, somewhat degraded by both the reduction pipeline
and the kh − ω filtering.
In order to obtain information about the depth dependence
of a photospheric quantity by associating a suitable ‘for-
mation zone’ with a line, it is possible to consider its ef-
Del Moro et al.: 3D photospheric velocity field of a SG cell 3
fect on the line characteristic as linear perturbations and
to study the Response Function RF of the emergent line
characteristic at the observed wavelengths within the line.
In particular, the RF Ip is, at each depth, the function we
must use to weigh the perturbation p in order to get the
variation of the emergent intensity I (Caccin et al., 1977).
This approach has been employed to derive the RF IT and
Fig. 2. Core intensity fields of FeII 722.4 nm (z≃50 km)
and FeI 709.0 nm (z≃100 km ) in comparison with con-
tinuum image (z≃0 km) and CaII 854.2 nm wing intensity
field (z≃150 km) (Qu & Xu , 2002). The z axis is greatly
exaggerated with respect to the x-y axes in order to allow
a better visualization.
V for the spectral lines FeI 709.0 nm and FeII 722.4 nm
(Del Moro, 2005).
In Table 1 we report the photospheric depths of the line
core RF IT maximum (zTcore), and of the mean RF
V maxi-
mum (zVline) for the two spectral lines. We also report the
RF full width at half maximum for the two spectral lines:
these rather large values imply broad formation zones for
both the FeI 709.0 nm and FeII 722.4 nm Doppler velocity
and core intensity signals.
3. 3D Velocity Field
The TST procedure (Del Moro, 2004) has been applied on
the continuum image series and on both the FeII 722.4 nm
and FeI 709.0 nm Doppler field series, in order to retrieve
the horizontal velocity field at different depths of the solar
atmosphere.
To minimize the effect of the proper motion of the
granules, which are used as trackers of the mean plasma
flow, we computed the horizontal velocity field using all
the structures that were tracked, so that statistically at
least one tracker is present in each interpolated horizontal
velocity field pixel, as suggested by Behan (2000). This
means we used a grid step of ∼ 1.5 Mm and a temporal
window of ∼ 30 min. Possibly, this would not completely
remove the noise associated with granule proper motions
or residuals from the 5-min oscillation filtering, but should
minimize it.
Combining the horizontal velocity fields retrieved from
Fig. 3. 3D representation of velocity vectors extracted from
continnum (z≃0 km), FeII 722.4 nm (z≃70 km) and FeI
709.0 nm (z≃140 km). Cone size is proportional to the ve-
locity vector module: the yellowish cone corresponds to 1
km·s−1. The z axis is greatly exaggerated with respect to
the x-y axes in order to allow a better visualization.
the Dopplergrams by the TST and the Doppler LoS
velocity, the 3D vector field has been reconstructed for
the FeII 722.4 nm and FeI 709.0 nm lines. We are aware
that associating the vector fields to precise heights in the
photosphere is an oversemplification, as can be readily
understood from the large FWHM reported in Table 1,
nevertheless, we did it for the sake of a good visualization:
in Fig. 3 we show the mean 3D velocity field associated to
the the dataset.
In both the 3D fields we retrieved, the vector velocity
appears to be structured quite coherently with the SG
feature visible in the CaII wing images.
In order to further investigate the structuring of the
velocity field, we computed the average continuum (upper
panel of Fig. 4) and CaII wing (bottom panel of Fig. 4)
intensity images, the average Dopplergram from FeII 722.4
nm (middle panel of Fig. 4) and the average Dopplergram
from FeI 709.0 nm (upper panel of Fig. 4) and correlated
them. While the average continuum image does not show
any evident signal, there is a significant correlation between
strong downflows and bright CaII features, in particular
for the complex cluster of features in the lower part of the
FoV. This issue can be at least partially explained by the
coherence of the 3D velocity field with the SG structure.
We expanded this study by comparing the averaged images
with the horizontal velocity field extracted by the TST
from granules as seen in the continuum and up-flows from
the FeI 709.0 nm Doppler images.
We excluded from this analysis the FeII 722.4 nm Doppler
images because we found its horizontal velocity field to be
not as reliable as the others. This is due to the TST finding
less than optimal number of features to track because
of the shallowness of the FeII 722.4 nm line. A shallow
line Doppler shift is much harder to measure by the LoS
velocity reconstruction procedure, resulting in a more
noisy dopplergram. This noise is interpreted by the TST
as a fast variation of the structures, therefore causing a lot
of them to be rejected for the tracking. As a consequence,
the TST finds too few trackers in the 722.4 Doppler for
the divergence field to be reliably reconstructed.
4 Del Moro et al.: 3D photospheric velocity field of a SG cell
The horizontal velocity fields extracted by the TST are
Fig. 4. Upper panel: average continuum image with the
horizontal velocity field (obtained by tracking granules)
represented as red arrows. The granules were tracked by ap-
plying the TST to the continuum image time series. Lower
panel: divergence field computed from the interpolated hor-
izontal velocity field.
shown superimposed on the average images in the left
panels of Fig. 4 and Fig. 5, above the associated 2D
divergence images. The values of the divergence fields
range from +0.25 km s−1 Mm−1 in the brightest part of
the image to −0.25 km s−1 Mm−1 in the darkest parts.
The continuum granules and FeI 709.0 nm up-flow fields
show a divergent flow from the centre of the SG structure
and convergent flows in the border of the SG structure. In
detail, these two fields agree very well, showing a single,
large divergent feature in the centre of the SG, whose mean
value is about +0.1 km s−1 Mm−1, almost completely
surrounded by convergent flows of the same magnitude.
The peak divergence signals we retrieved both in the
centre and in the periphery of the SG cell are an order
of magnitude larger than the averaged values reported by
Meunier et al. (2007). This discrepancy probably stems
mainly from the different temporal and spatial averaging
processes in the divergence reconstruction and marginally
from the different resolution of the two datasets.
The structuring of the divergence field is very compatible
with a net flow from the centre of the SG to its border.
Fig. 5. Upper panel: average FeI 709.0 nm Doppler velocity
image with the horizontal velocity field (obtained by track-
ing up-flows) represented as red arrows. The up-flows were
tracked by applying the TST to the FeI 709.0 nm Doppler
velocity field time series. Lower panel: divergence field com-
puted from the interpolated horizontal velocity field.
Moreover, examining the LoS velocity fields, we found a
strong and stable up-flow region nearby the divergence
maximum, with a mean FeII 722.4 nm Doppler veloc-
ity value of Vc ∼200 m·s
−1 for almost the whole time
span. This last region is liable to be the origin of the
divergence signal we measured, possibly as suggested by
Rieutord et al. (2000); Roudier et al. (2003).
Observing the divergence images (bottom panels of Fig. 4
and Fig. 5) extracted from the horizontal velocity fields,
the supergranule is outlined by convergences on ∼ 66%
of its circumference, while the bright cluster area clearly
visible in the CaII wing image does not seem to be a region
of strong convergence, despite the fact that it is mostly
formed of down-flows.
This region has a mean FeII 722.4 nm Doppler velocity
value Vc ∼-100 m·s
−1 for the whole dataset time span (T
≃ 0.5 hour), and it seems to mantain similar values also for
the part of the observations discarded for the loss of spatial
resolution due to worsening seeing condition. A similar
cluster of bright CaII structures is present in the upper-left
part of the FoV, but its associated downflow shows a
much smaller coherence: it has a mean FeII 722.4 nm
Doppler velocity value Vc ∼-50 m·s
−1 for more than half
Del Moro et al.: 3D photospheric velocity field of a SG cell 5
of the time span, then it drops to ∼-20 m·s−1. Whether
or not downflow regions like these may be organizing the
SG pattern, as predicted by Rast (2003), is a question
we cannot address due to the short duration of our dataset.
4. Horizontal Flow Analysis via Cork Tracking
To further extract information about the plasma motion
inside the SG structure, we tracked the evolution of tracers
(corks) passively advected by instantaneous velocity and
intensity fields. The corks, initially randomly spread over
the FoV, are moved following the local gradient towards
sites of minimum intensity or of minimum velocity in the
case of intensity or velocity fields, respectively. We will com-
pare the final and initial positions of the corks, which will
give us information about the motion of downflows in the
field of view. Corks are tracked for ∼ 16 minutes (a time
sufficiently longer than the characteristic time scale of pho-
tospheric fields (Müller et al., 2001; Berrilli et al., 2002) to
let the cork settle in a downflow feature and track it for
a while) and their initial and final position are stored. As
corks tend to accumulate in long lasting downflow struc-
tures, new corks are added each ∼ 5 minutes in order to
also track structures forming during the observations. In
Fig. 6 we report the result of the cork tracing for a contin-
uum image series and for both the FeII 722.4 nm and the
FeI 709.0 nm Doppler fields. In particular, we plotted the
difference between the final and initial distances from the
image centre of the corks versus their initial distances from
the image centre. The alignment effect of the scatter plot is
due to an inverse linear relationship between the ρstart and
the δρ of corks with different initial postions which end in
the same ‘attractor’ and therefore share their final position.
As the image is centred on the SG structure, this will give us
information about a possible difference of mean flows inside
and outside the SG. In order to investigate the properties
of the distribution, we fit on the scatter plots a sigmoidal
function:
A1 −A2
1 + e(x−x0)/dx
+A2 (1)
so that x0 will tell where the transition between the two
values A1 and A2 of the distribution takes place and dx
will tell how fast this transition is. The parameters of the
fit are retrieved by a recursive Levenberg-Marquardt min-
imization algorithm. The fits agree in retrieving positive
values of A1 and near zero values for A2 (Table 2). This
means that the corks inside a circle of radius x0 from the
image centre tend to increase their radial distance, while
the corks outside have no preferred direction in their mo-
tion. Several simulations on randomly generated velocity
fields showed that we can neglect the contribute from
corks whose initial position is so near to the image centre
that they are biased towards positive radial displacement.
Finally, we tested the robustness of these results against
the initial guesses and against the SG centre position in
the FoV. The retrieved parameters do not depend on these
factors, as long as the initial guesses are of the same order
of magnitude of the convergence values or the FoV shift is
less than 2.5 Mm.
In Fig. 4 we show the mean intensity fields associated to
the plots in Fig. 6, with superimposed the location of the
change of the A value represented as an annulus of mean
Fig. 6. Cork displacements versus initial positions. Top
Panel: results of the cork tracking for the intensity field
from continuum images. Central Panel: results of the cork
tracking for the vertical velocity field extracted from FeII
722.4 nm. Bottom Panel: results of the cork tracking for
the vertical velocity field extracted from FeI 709.0 nm. Each
scatter plot has been fitted with a sigmoidal function (equa-
tion 1). The retrieved fits are overplotted on the relative
scatter plots.
radius x0 and thickness 2dx. The three annular shapes
essentially agree in retrieving the same SG diameter of
∼ 25 Mm.
The width of the annuli, instead, seems to depend on
the atmospheric altitude. In the upper panel of Fig. 8
we report the value of dx computed by the sigmoidal fits
versus the photospheric height. Error bars represent the
standard deviation from the fit.
Recently, Berrilli et al. (2002) found a similar height
dependence of the statistical properties of granular
flows. In particular, they reported an intense braking
in the first ∼ 120 km of the photosphere, confirmed by
Puschmann et al. (2005) and a damping effect that filtered
6 Del Moro et al.: 3D photospheric velocity field of a SG cell
A1 A2 x0 dx
[Mm] [Mm] [Mm] [Mm]
Continuum Intensity 0.49 ± 0.02 0.08 ± 0.01 11.3± 0.2 0.3± 0.2
FeII 722.4 LoS Velocity 0.61 ± 0.03 −0.09± 0.02 12.0± 0.2 1.1± 0.2
FeI 709.0 LoS Velocity 0.67 ± 0.08 −0.09± 0.03 10.9± 0.7 2.9± 0.6
Table 2. Parameters of the sigmoidal fits to the scatter plots reported in Fig. 6.
out small features in higher atmospheric layers, letting only
large flow features penetrate into the upper photosphere.
The same process can explain the broadening of the SG
border we found: in higher layers the corks are collected in
larger and fewer downflow structures. As more corks are
collected by the same structures, the number of indepen-
dent tracers is decreased and similarly the precision of the
retrieval of the boundary is decreased.
Instead, we can exclude that such a smoothing effect is
due to data reduction or seeing, because in that case the
SG border retrieved from the FeI 709.0 nm LoS field would
have been thinner than the one retrieved from the FeII
722.4 nm LoS field, as the latter shows lower contrast
features, more prone to be degraded by the loss of spatial
resolution.
Due to the form of equation 1, the difference A1 − A2,
divided for the time allotted to the corks to move, will
give the mean radial velocity experienced by the corks.
We plot in the bottom panel of Fig. 8 the radial velocity
retrieved from the three scatter plots as a function of the
photospheric altitude. Error bars represent the standard
deviation from the fit.
To account for these results, we assume that the large and
more coherent features present in the LoS dopplergrams
are reliable to retrieve the radial velocity measure, while
the measure from the continuum images is somewhat
reduced by the presence of tiny structures which are more
turbulent in their motion. Such structures are not present
in the higher layers dopplergrams because of the damping
effect already discussed.
We therefore discard the value obtained from the WL
dataset because it is probably smeared by the turbulent
motions of very small scale features and take into account
only the two values retrieved from the higher layers,
retrieving a mean velocity of 0.75± 0.05 km s−1.
Such a value for the flows from the SG structure centre
is consistent with the literature (Simon & Leighton,
1964; Hathaway et al., 2002; Paniveni et al., 2004;
Meunier et al., 2007).
5. Conclusions
The study of the full 3D velocity field of a SG shows that
strong downflows are located on the border of the super-
granular structure, but also that the mean granular flow
regresses from the centre to the periphery of the SG.
The divergence images show that the SG structure is out-
lined by convergence sites on ∼ 66% of its border. The
retrieved divergence values show a nearly radial flow of
∼ 0.1 km s−1 Mm−1 from the centre of the SG and con-
vergent flows of the same magnitude in its border.
The analysis of the evolution of passive tracers on inten-
sity and velocity fields shows that inside the SG structure
there is a preferential radial flow towards the SG border of
0.75± 0.05 km s−1.
The height behaviour of the thickness of the SG border,
again retrieved via cork tracing, shows an increase of the
border width with height. This is probably due to a filter-
ing effect with height, which preferentially allows large flow
features to penetrate into the upper photospheric layers.
The large and CaII bright cluster of structures in the lower
part of the FoV, is not a site of strong convergence, but
is a site of long-lasting downflows. We also found a strong
and stable upflow nearby the centre of the cell, liable to
organize the CaII bright structures by sweeping them out
of the SG cell.
The result presented in this paper are extracted from a sub-
set of a longer timeseries of excellent spectral and temporal
resolution, but varying spatial quality due to seeing. The
used 30 min subset is characterized by a constant and good
spatial resolution. This allowed us to detect precisely the
flow associated with the SG. Anyhow, our analysis would
have greatly benefited from a longer time sequence and
other SG structures to analyze. In the future, we plan to
apply this analysis to a collection of SG structures, so as
to derive some statistical describer and possibly generalize
the results.
Acknowledgements. We thank the referee, T. Roudier, for suggestions
and comments that have signicantly improved this paper. Part of
this work was supported by Rome “Tor Vergata” University Physics
Department grants. The data were acquired by instruments operated
by the National Solar Observatory. The National Solar Observatory
is a Division of the National Optical Astronomy Observatories,
which is operated by the Association of Universities for Research
in Astronomy, Inc., under cooperative agreement with the National
Science Foundation. DDM thanks the High Altitude Observatory for
support and C. Sormani for helpful comments. The authors aknowl-
edge k. Janssen for the development of the IBIS data reduction
pipeline, V. Penza for the calculation of the line RFs and M. Rast
for very useful discussions and comments.
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Fig. 7. Mean images with superimposed the SG dimen-
sion extracted from the cork tracking. Top Panel: mean FeI
709.0 nm Doppler image with SG extracted from from FeI
709.0 nm Dopplergrams (∼ 140 km). Central Panel: mean
FeII 722.4 nm Doppler image with SG extracted from from
FeII 722.4 nm Dopplergrams (∼ 70 km). Bottom Panel:
mean CaII 854.2 nm wing image with SG extracted from
the intensity continuum images (∼ 0 km).
8 Del Moro et al.: 3D photospheric velocity field of a SG cell
-20 0 20 40 60 80 100 120 140 160 180 200
Photospheric Altitude (km)
-20 0 20 40 60 80 100 120 140 160 180 200
Photospheric Altitude [km]
Fig. 8. Top panel: dx (annulus width) versus photospheric
height. Bottom panel: radial velocity versus photospheric
height.
	Introduction
	Observations
	3D Velocity Field
	Horizontal Flow Analysis via Cork Tracking
	Conclusions

  We investigate the plasma flow properties inside a Supergranular (SG) cell,
in particular its interaction with small scale magnetic field structures. The
SG cell has been identified using the magnetic network (CaII wing brightness)
as proxy, applying the Two-Level Structure Tracking (TST) to high spatial,
spectral and temporal resolution observations obtained by IBIS. The full 3D
velocity vector field for the SG has been reconstructed at two different
photospheric heights. In order to strengthen our findings, we also computed the
mean radial flow of the SG by means of cork tracing. We also studied the
behaviour of the horizontal and Line of Sight plasma flow cospatial with
cluster of bright CaII structures of magnetic origin to better understand the
interaction between photospheric convection and small scale magnetic features.
The SG cell we investigated seems to be organized with an almost radial flow
from its centre to the border. The large scale divergence structure is probably
created by a compact region of constant up-flow close to the cell centre. On
the edge of the SG, isolated regions of strong convergent flow are nearby or
cospatial with extended clusters of bright CaII wing features forming the knots
of the magnetic network.

Introduction
Solar research is currently working on understanding how
turbulent convection on the Sun transports mass and en-
ergy through the convective zone, how it couples with the
magnetic field and how it manages to deposit in the higher
parts of the solar atmosphere the energy released from the
corona. Among the different approaches to these questions,
observations of the solar photosphere are essential, as they
provide the only direct look at what is happening just below
the solar surface. The hierarchy of surface features found
on the photosphere are the visible representation of the
plasma flows beneath the photosphere and are customar-
ily classified by size and lifetime as patterns of granula-
tion (1 Mm, 0.2 hr), mesogranulation (5-10 Mm, 5 hr)
and supergranulation (15-35 Mm, 24 hr). These features
have been initially regarded as direct manifestation of var-
ious sized convection cells existing in the convection zone
(Schrijver et al., 1997; Raju et al., 1999); lately, the idea
is consolidating that meso and supergranulation are sig-
natures of a collective interaction of granular cells (Rast,
2003; Roudier et al., 2003; Berrilli et al., 2005). Despite
years of intensive studies, the character of their motions
remains not completely understood (Beck & Duvall, 2000;
Krishan et al., 2002; Berrilli et al., 2004; Del Moro et al.,
2004; DeRosa & Toomre, 2004). The aim of the study we
present is to investigate the origin of the supergranular (SG)
flow field: directly convective or a collective interaction of
smaller convective features.
The study performed by Simon & Leighton (1964) initi-
ated the campaign to characterize supergranular flows.
Outflows on SG scales have been observed to sweep
embedded granules and magnetic flux elements toward
Send offprint requests to: delmoro@roma2.infn.it
convergence lanes between cells (Leighton, 1964; Zwaan,
1978; Rimmele, 1989; Shine et al., 2000). Such behaviour
causes the chromospheric transition CaII k line to be
a good proxy for the network of intercellular lanes due
to the higher magnetic elements density in the SG
perimeters. The advent of full-disk Doppler imaging, pro-
vided by the MDI onboard SOHO spacecraft, has con-
siderably improved our capability to study such fea-
tures (Hathaway et al., 2002; DeRosa & Toomre, 2004;
Paniveni et al., 2004; Meunier et al., 2007); but direct ob-
servations of supergranular flows are still hindered by the
fact that there is no contrast on supergranular scales in visi-
ble light, observations in CaII only provide the cell network
boundaries and Doppler images show SG only away from
disk centre.
At present, the only methods to reconstruct the full 3D
vector velocity field are direct Doppler measurement in
combination with a tracking type measure for the velocity
horizontal component (above the τ = 1 surface) or Local
Helioseismology (below the τ = 1 surface). To gain com-
plete insight of the dynamics of the plasma flows inside a
SG structure, we need a spatial and temporal resolution still
not reached by local helioseismology, while to obtain the
3D velocity field through the other method, observations
with very high spatial, spectral and temporal resolution are
necessary. With the assumption that granule motions are
mainly driven by plasma flows (Rieutord et al., 2001), it is
possible to employ the TST to infer the horizontal velocity
field.
In this work we reconstruct the 3D velocity field of a sin-
gle SG structure and investigate in detail its plasma flow
using data acquired with the IBIS spectrometer, trying to
discern whether the SG pattern has a convective nature or
is originated by small scale structure interaction.
http://arxiv.org/abs/0704.0578v2
2 Del Moro et al.: 3D photospheric velocity field of a SG cell
Fig. 1. A representative synoptic panel from the 16th October 2003 dataset. Upper left panel: Ca II wing intensity
image. Upper middle panel: Doppler velocity field computed from FeI 709.0 nm line scan. Upper right panel: FeI 709.0
nm line core intensity Lower left panel: Doppler velocity field computed from FeII 722.4 nm line scan. Lower middle
panel: FeII 722.4 nm line core intensity. Lower right panel: Continuum (near 709.0 nm) intensity image.
Line Wavelength zTcore FWHMRFI
zVline FWHMRFI
[nm] [km] [km] [km] [km]
FeI 709.0 ≃100 ∼300 ≃140 ∼300
FeII 722.4 ≃50 ∼200 ≃70 ∼200
Table 1. Line RF peak depths. Depths are in km above the level τ500nm = 1.
2. Observations
The data utilized in this analysis have been acquired with
the IBIS (Interferometric BIdimensional Spectrometer) 2D
spectrometer (Cavallini et al., 2001; Cavallini, 2006) on
October 16, 2003 (from 14:24 UT to 17:32 UT).
We imaged a roundish network cell near the solar disk cen-
tre (SLAT=7.8N, SLONG=3.6E). When observed in MDI
high-resolution magnetograms, all the features outlining
the cell exhibit negative polarity and seem to survive for
at least 10 hours, with little or no evolution.
The full dataset consists of 600 sequences, containing a 16
image scan of the FeI 709.0 nm line, a 14 image scan of
the FeII 722.4 nm line and 5 spectral images in the wing
(line centre + 12 nm) of the CaII 854.2 nm line, imag-
ing a round Field of View (FoV) of about 80” diameter.
Each monochromatic image was acquired with a 25 ms ex-
posure time by a 12bit CCD detector, whose pixel scale
was 0.17′′·pixel−1. The time required for the acquisition of
a single sequence was 19 s, thus setting the temporal res-
olution. Each image was reduced with the standard IBIS
pipeline (Janssen & Cauzzi, 2006; Giordano et al., 2007),
correcting for CCD non linearity effects, dark current, gain
table and blue shift. The Line of Sight (LoS) velocity fields
were computed for the Fe I and Fe II lines by means of
Doppler shifts, evaluated, pixel by pixel, fitting a Gaussian
on the line profile. In order to remove the orbital contribu-
tion, we set to zero the average value of each LoS velocity
image. The 5-minutes oscillations were removed applying a
3D Fourier filter in the kh −ω domain with a cut-off veloc-
ity of 7 km·s−1 both on intensity and velocity image series.
After the whole reduction process and selecting only the
period of good seeing we are left with a 30 minutes dataset
imaging a square FoV of ∼ 50”. An example of the im-
ages of this reduced dataset is shown in Fig. 1. The mean
resolution due to the seeing of the CaII images is 0.35”;
the mean resolution of the LoS velocity images, the inten-
sity continuum images and the line core images is instead
0.45”, somewhat degraded by both the reduction pipeline
and the kh − ω filtering.
In order to obtain information about the depth dependence
of a photospheric quantity by associating a suitable ‘for-
mation zone’ with a line, it is possible to consider its ef-
Del Moro et al.: 3D photospheric velocity field of a SG cell 3
fect on the line characteristic as linear perturbations and
to study the Response Function RF of the emergent line
characteristic at the observed wavelengths within the line.
In particular, the RF Ip is, at each depth, the function we
must use to weigh the perturbation p in order to get the
variation of the emergent intensity I (Caccin et al., 1977).
This approach has been employed to derive the RF IT and
Fig. 2. Core intensity fields of FeII 722.4 nm (z≃50 km)
and FeI 709.0 nm (z≃100 km ) in comparison with con-
tinuum image (z≃0 km) and CaII 854.2 nm wing intensity
field (z≃150 km) (Qu & Xu , 2002). The z axis is greatly
exaggerated with respect to the x-y axes in order to allow
a better visualization.
V for the spectral lines FeI 709.0 nm and FeII 722.4 nm
(Del Moro, 2005).
In Table 1 we report the photospheric depths of the line
core RF IT maximum (zTcore), and of the mean RF
V maxi-
mum (zVline) for the two spectral lines. We also report the
RF full width at half maximum for the two spectral lines:
these rather large values imply broad formation zones for
both the FeI 709.0 nm and FeII 722.4 nm Doppler velocity
and core intensity signals.
3. 3D Velocity Field
The TST procedure (Del Moro, 2004) has been applied on
the continuum image series and on both the FeII 722.4 nm
and FeI 709.0 nm Doppler field series, in order to retrieve
the horizontal velocity field at different depths of the solar
atmosphere.
To minimize the effect of the proper motion of the
granules, which are used as trackers of the mean plasma
flow, we computed the horizontal velocity field using all
the structures that were tracked, so that statistically at
least one tracker is present in each interpolated horizontal
velocity field pixel, as suggested by Behan (2000). This
means we used a grid step of ∼ 1.5 Mm and a temporal
window of ∼ 30 min. Possibly, this would not completely
remove the noise associated with granule proper motions
or residuals from the 5-min oscillation filtering, but should
minimize it.
Combining the horizontal velocity fields retrieved from
Fig. 3. 3D representation of velocity vectors extracted from
continnum (z≃0 km), FeII 722.4 nm (z≃70 km) and FeI
709.0 nm (z≃140 km). Cone size is proportional to the ve-
locity vector module: the yellowish cone corresponds to 1
km·s−1. The z axis is greatly exaggerated with respect to
the x-y axes in order to allow a better visualization.
the Dopplergrams by the TST and the Doppler LoS
velocity, the 3D vector field has been reconstructed for
the FeII 722.4 nm and FeI 709.0 nm lines. We are aware
that associating the vector fields to precise heights in the
photosphere is an oversemplification, as can be readily
understood from the large FWHM reported in Table 1,
nevertheless, we did it for the sake of a good visualization:
in Fig. 3 we show the mean 3D velocity field associated to
the the dataset.
In both the 3D fields we retrieved, the vector velocity
appears to be structured quite coherently with the SG
feature visible in the CaII wing images.
In order to further investigate the structuring of the
velocity field, we computed the average continuum (upper
panel of Fig. 4) and CaII wing (bottom panel of Fig. 4)
intensity images, the average Dopplergram from FeII 722.4
nm (middle panel of Fig. 4) and the average Dopplergram
from FeI 709.0 nm (upper panel of Fig. 4) and correlated
them. While the average continuum image does not show
any evident signal, there is a significant correlation between
strong downflows and bright CaII features, in particular
for the complex cluster of features in the lower part of the
FoV. This issue can be at least partially explained by the
coherence of the 3D velocity field with the SG structure.
We expanded this study by comparing the averaged images
with the horizontal velocity field extracted by the TST
from granules as seen in the continuum and up-flows from
the FeI 709.0 nm Doppler images.
We excluded from this analysis the FeII 722.4 nm Doppler
images because we found its horizontal velocity field to be
not as reliable as the others. This is due to the TST finding
less than optimal number of features to track because
of the shallowness of the FeII 722.4 nm line. A shallow
line Doppler shift is much harder to measure by the LoS
velocity reconstruction procedure, resulting in a more
noisy dopplergram. This noise is interpreted by the TST
as a fast variation of the structures, therefore causing a lot
of them to be rejected for the tracking. As a consequence,
the TST finds too few trackers in the 722.4 Doppler for
the divergence field to be reliably reconstructed.
4 Del Moro et al.: 3D photospheric velocity field of a SG cell
The horizontal velocity fields extracted by the TST are
Fig. 4. Upper panel: average continuum image with the
horizontal velocity field (obtained by tracking granules)
represented as red arrows. The granules were tracked by ap-
plying the TST to the continuum image time series. Lower
panel: divergence field computed from the interpolated hor-
izontal velocity field.
shown superimposed on the average images in the left
panels of Fig. 4 and Fig. 5, above the associated 2D
divergence images. The values of the divergence fields
range from +0.25 km s−1 Mm−1 in the brightest part of
the image to −0.25 km s−1 Mm−1 in the darkest parts.
The continuum granules and FeI 709.0 nm up-flow fields
show a divergent flow from the centre of the SG structure
and convergent flows in the border of the SG structure. In
detail, these two fields agree very well, showing a single,
large divergent feature in the centre of the SG, whose mean
value is about +0.1 km s−1 Mm−1, almost completely
surrounded by convergent flows of the same magnitude.
The peak divergence signals we retrieved both in the
centre and in the periphery of the SG cell are an order
of magnitude larger than the averaged values reported by
Meunier et al. (2007). This discrepancy probably stems
mainly from the different temporal and spatial averaging
processes in the divergence reconstruction and marginally
from the different resolution of the two datasets.
The structuring of the divergence field is very compatible
with a net flow from the centre of the SG to its border.
Fig. 5. Upper panel: average FeI 709.0 nm Doppler velocity
image with the horizontal velocity field (obtained by track-
ing up-flows) represented as red arrows. The up-flows were
tracked by applying the TST to the FeI 709.0 nm Doppler
velocity field time series. Lower panel: divergence field com-
puted from the interpolated horizontal velocity field.
Moreover, examining the LoS velocity fields, we found a
strong and stable up-flow region nearby the divergence
maximum, with a mean FeII 722.4 nm Doppler veloc-
ity value of Vc ∼200 m·s
−1 for almost the whole time
span. This last region is liable to be the origin of the
divergence signal we measured, possibly as suggested by
Rieutord et al. (2000); Roudier et al. (2003).
Observing the divergence images (bottom panels of Fig. 4
and Fig. 5) extracted from the horizontal velocity fields,
the supergranule is outlined by convergences on ∼ 66%
of its circumference, while the bright cluster area clearly
visible in the CaII wing image does not seem to be a region
of strong convergence, despite the fact that it is mostly
formed of down-flows.
This region has a mean FeII 722.4 nm Doppler velocity
value Vc ∼-100 m·s
−1 for the whole dataset time span (T
≃ 0.5 hour), and it seems to mantain similar values also for
the part of the observations discarded for the loss of spatial
resolution due to worsening seeing condition. A similar
cluster of bright CaII structures is present in the upper-left
part of the FoV, but its associated downflow shows a
much smaller coherence: it has a mean FeII 722.4 nm
Doppler velocity value Vc ∼-50 m·s
−1 for more than half
Del Moro et al.: 3D photospheric velocity field of a SG cell 5
of the time span, then it drops to ∼-20 m·s−1. Whether
or not downflow regions like these may be organizing the
SG pattern, as predicted by Rast (2003), is a question
we cannot address due to the short duration of our dataset.
4. Horizontal Flow Analysis via Cork Tracking
To further extract information about the plasma motion
inside the SG structure, we tracked the evolution of tracers
(corks) passively advected by instantaneous velocity and
intensity fields. The corks, initially randomly spread over
the FoV, are moved following the local gradient towards
sites of minimum intensity or of minimum velocity in the
case of intensity or velocity fields, respectively. We will com-
pare the final and initial positions of the corks, which will
give us information about the motion of downflows in the
field of view. Corks are tracked for ∼ 16 minutes (a time
sufficiently longer than the characteristic time scale of pho-
tospheric fields (Müller et al., 2001; Berrilli et al., 2002) to
let the cork settle in a downflow feature and track it for
a while) and their initial and final position are stored. As
corks tend to accumulate in long lasting downflow struc-
tures, new corks are added each ∼ 5 minutes in order to
also track structures forming during the observations. In
Fig. 6 we report the result of the cork tracing for a contin-
uum image series and for both the FeII 722.4 nm and the
FeI 709.0 nm Doppler fields. In particular, we plotted the
difference between the final and initial distances from the
image centre of the corks versus their initial distances from
the image centre. The alignment effect of the scatter plot is
due to an inverse linear relationship between the ρstart and
the δρ of corks with different initial postions which end in
the same ‘attractor’ and therefore share their final position.
As the image is centred on the SG structure, this will give us
information about a possible difference of mean flows inside
and outside the SG. In order to investigate the properties
of the distribution, we fit on the scatter plots a sigmoidal
function:
A1 −A2
1 + e(x−x0)/dx
+A2 (1)
so that x0 will tell where the transition between the two
values A1 and A2 of the distribution takes place and dx
will tell how fast this transition is. The parameters of the
fit are retrieved by a recursive Levenberg-Marquardt min-
imization algorithm. The fits agree in retrieving positive
values of A1 and near zero values for A2 (Table 2). This
means that the corks inside a circle of radius x0 from the
image centre tend to increase their radial distance, while
the corks outside have no preferred direction in their mo-
tion. Several simulations on randomly generated velocity
fields showed that we can neglect the contribute from
corks whose initial position is so near to the image centre
that they are biased towards positive radial displacement.
Finally, we tested the robustness of these results against
the initial guesses and against the SG centre position in
the FoV. The retrieved parameters do not depend on these
factors, as long as the initial guesses are of the same order
of magnitude of the convergence values or the FoV shift is
less than 2.5 Mm.
In Fig. 4 we show the mean intensity fields associated to
the plots in Fig. 6, with superimposed the location of the
change of the A value represented as an annulus of mean
Fig. 6. Cork displacements versus initial positions. Top
Panel: results of the cork tracking for the intensity field
from continuum images. Central Panel: results of the cork
tracking for the vertical velocity field extracted from FeII
722.4 nm. Bottom Panel: results of the cork tracking for
the vertical velocity field extracted from FeI 709.0 nm. Each
scatter plot has been fitted with a sigmoidal function (equa-
tion 1). The retrieved fits are overplotted on the relative
scatter plots.
radius x0 and thickness 2dx. The three annular shapes
essentially agree in retrieving the same SG diameter of
∼ 25 Mm.
The width of the annuli, instead, seems to depend on
the atmospheric altitude. In the upper panel of Fig. 8
we report the value of dx computed by the sigmoidal fits
versus the photospheric height. Error bars represent the
standard deviation from the fit.
Recently, Berrilli et al. (2002) found a similar height
dependence of the statistical properties of granular
flows. In particular, they reported an intense braking
in the first ∼ 120 km of the photosphere, confirmed by
Puschmann et al. (2005) and a damping effect that filtered
6 Del Moro et al.: 3D photospheric velocity field of a SG cell
A1 A2 x0 dx
[Mm] [Mm] [Mm] [Mm]
Continuum Intensity 0.49 ± 0.02 0.08 ± 0.01 11.3± 0.2 0.3± 0.2
FeII 722.4 LoS Velocity 0.61 ± 0.03 −0.09± 0.02 12.0± 0.2 1.1± 0.2
FeI 709.0 LoS Velocity 0.67 ± 0.08 −0.09± 0.03 10.9± 0.7 2.9± 0.6
Table 2. Parameters of the sigmoidal fits to the scatter plots reported in Fig. 6.
out small features in higher atmospheric layers, letting only
large flow features penetrate into the upper photosphere.
The same process can explain the broadening of the SG
border we found: in higher layers the corks are collected in
larger and fewer downflow structures. As more corks are
collected by the same structures, the number of indepen-
dent tracers is decreased and similarly the precision of the
retrieval of the boundary is decreased.
Instead, we can exclude that such a smoothing effect is
due to data reduction or seeing, because in that case the
SG border retrieved from the FeI 709.0 nm LoS field would
have been thinner than the one retrieved from the FeII
722.4 nm LoS field, as the latter shows lower contrast
features, more prone to be degraded by the loss of spatial
resolution.
Due to the form of equation 1, the difference A1 − A2,
divided for the time allotted to the corks to move, will
give the mean radial velocity experienced by the corks.
We plot in the bottom panel of Fig. 8 the radial velocity
retrieved from the three scatter plots as a function of the
photospheric altitude. Error bars represent the standard
deviation from the fit.
To account for these results, we assume that the large and
more coherent features present in the LoS dopplergrams
are reliable to retrieve the radial velocity measure, while
the measure from the continuum images is somewhat
reduced by the presence of tiny structures which are more
turbulent in their motion. Such structures are not present
in the higher layers dopplergrams because of the damping
effect already discussed.
We therefore discard the value obtained from the WL
dataset because it is probably smeared by the turbulent
motions of very small scale features and take into account
only the two values retrieved from the higher layers,
retrieving a mean velocity of 0.75± 0.05 km s−1.
Such a value for the flows from the SG structure centre
is consistent with the literature (Simon & Leighton,
1964; Hathaway et al., 2002; Paniveni et al., 2004;
Meunier et al., 2007).
5. Conclusions
The study of the full 3D velocity field of a SG shows that
strong downflows are located on the border of the super-
granular structure, but also that the mean granular flow
regresses from the centre to the periphery of the SG.
The divergence images show that the SG structure is out-
lined by convergence sites on ∼ 66% of its border. The
retrieved divergence values show a nearly radial flow of
∼ 0.1 km s−1 Mm−1 from the centre of the SG and con-
vergent flows of the same magnitude in its border.
The analysis of the evolution of passive tracers on inten-
sity and velocity fields shows that inside the SG structure
there is a preferential radial flow towards the SG border of
0.75± 0.05 km s−1.
The height behaviour of the thickness of the SG border,
again retrieved via cork tracing, shows an increase of the
border width with height. This is probably due to a filter-
ing effect with height, which preferentially allows large flow
features to penetrate into the upper photospheric layers.
The large and CaII bright cluster of structures in the lower
part of the FoV, is not a site of strong convergence, but
is a site of long-lasting downflows. We also found a strong
and stable upflow nearby the centre of the cell, liable to
organize the CaII bright structures by sweeping them out
of the SG cell.
The result presented in this paper are extracted from a sub-
set of a longer timeseries of excellent spectral and temporal
resolution, but varying spatial quality due to seeing. The
used 30 min subset is characterized by a constant and good
spatial resolution. This allowed us to detect precisely the
flow associated with the SG. Anyhow, our analysis would
have greatly benefited from a longer time sequence and
other SG structures to analyze. In the future, we plan to
apply this analysis to a collection of SG structures, so as
to derive some statistical describer and possibly generalize
the results.
Acknowledgements. We thank the referee, T. Roudier, for suggestions
and comments that have signicantly improved this paper. Part of
this work was supported by Rome “Tor Vergata” University Physics
Department grants. The data were acquired by instruments operated
by the National Solar Observatory. The National Solar Observatory
is a Division of the National Optical Astronomy Observatories,
which is operated by the Association of Universities for Research
in Astronomy, Inc., under cooperative agreement with the National
Science Foundation. DDM thanks the High Altitude Observatory for
support and C. Sormani for helpful comments. The authors aknowl-
edge k. Janssen for the development of the IBIS data reduction
pipeline, V. Penza for the calculation of the line RFs and M. Rast
for very useful discussions and comments.
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Fig. 7. Mean images with superimposed the SG dimen-
sion extracted from the cork tracking. Top Panel: mean FeI
709.0 nm Doppler image with SG extracted from from FeI
709.0 nm Dopplergrams (∼ 140 km). Central Panel: mean
FeII 722.4 nm Doppler image with SG extracted from from
FeII 722.4 nm Dopplergrams (∼ 70 km). Bottom Panel:
mean CaII 854.2 nm wing image with SG extracted from
the intensity continuum images (∼ 0 km).
8 Del Moro et al.: 3D photospheric velocity field of a SG cell
-20 0 20 40 60 80 100 120 140 160 180 200
Photospheric Altitude (km)
-20 0 20 40 60 80 100 120 140 160 180 200
Photospheric Altitude [km]
Fig. 8. Top panel: dx (annulus width) versus photospheric
height. Bottom panel: radial velocity versus photospheric
height.
	Introduction
	Observations
	3D Velocity Field
	Horizontal Flow Analysis via Cork Tracking
	Conclusions
