A&A 420, 1141-1152 (2004)
DOI: 10.1051/0004-6361:20035660
J. Rybák 1 - H. Wöhl 2 - A. Kucera 1 - A. Hanslmeier 3 - O. Steiner 2
1 - Astronomical Institute of the Slovak Academy of
Sciences,
05960 Tatranská Lomnica, Slovakia
2 -
Kiepenheuer-Institut für Sonnenphysik,
Schöneckstr. 6,
79104 Freiburg, Germany
3 -
Institut für Geophysik, Astrophysik und
Meteorologie,
Universitätsplatz 5, 8010 Graz, Austria
Received 11 November 2003 / Accepted 15 March 2004
Abstract
High resolution observations of solar granulation
near the solar limb are used in a search for hydrodynamic
shocks caused by an abrupt braking of the fast (probably supersonic)
horizontal flow of the granular plasma towards the intergranular lane.
Shock signatures in the spectral line of Fe II 6456.38 Å of one
particular observed shock event are investigated in detail.
Evolution, amplitude, and spatial relation of the spectral line
characteristics of the shock event are in agreement with predictions from
numerical simulations for such shock phenomena in the solar photosphere.
The dimensions and amplitudes of the observed shock signatures
are comparable to predicted values when seeing and
instrumental effects as well as a possible obliqueness of the shock
front with respect to the observer's line-of-sight are taken into account.
The temporal evolution of such an event is observed for the first time.
The stable and declining phase of the event were studied
for a time period of almost 2 min.
A particular relationship was found between the shock event and
a nearby G-band bright point located 2'' from the shock event.
It is suggestive that the observed shock is a
causal consequence of the magnetic flux concentration, traced
by the G-band bright point.
Such a type of shock can appear outside the flux concentrations
as a consequence of a rapid flux-tube motion.
Key words: Sun: photosphere - Sun: granulation - line: profiles - shock waves
In the past two decades it has become feasible to study the non-stationary nature of the photospheric layers with the help of numerical simulations. First comprehensive simulations treated non-magnetic solar granulation (e.g., Nordlund 1984; Stein & Nordlund 1989; Steffen et al. 1989). While these simulations included a sophisticated treatment of radiative transfer and sub-grid turbulence models, other numerical work included less physics but concentrated on a detailed treatment of turbulence, both in 2D and 3D (e.g., Cattaneo et al. 1989, 1990; Malagoli et al. 1990). Simulations of convective motion including magnetic field have been carried out in 3D by Nordlund (1986) and Weiss et al. (1996) and more recently by Cattaneo (1999), Emonet & Cattaneo (2001), Stein & Nordlund (2002) or Vögler & Schüssler (2003) and in 2D in a series of papers by Deinzer et al. (1984a,b), Knölker et al. (1988), Grossman-Doerth et al. (1988, 1994), and by Hurlburt & Toomre (1988), Fox et al. (1999), and Ploner et al. (1999). Steiner et al. (1998) simulated the dynamical interaction of a preexisting magnetic flux sheet with a fully developed granular convection while Grossman-Doerth et al. (1988) studied the formation of flux sheets in a non-stationary convective environment. The latter two works include the computation of synthetic spectra from simulation snapshots thus enabling the prediction of spectral features, which can be looked for in observed high spatial and spectral resolution spectra of solar granulation.
Table 1:
Atomic parameters and height of formation of the Fe II lines
selected for observations of shock signatures.
and
stand for the excitation
potential of the lower level and the equivalent width of the
line, respectively. The Landé factors are given for the cases of
LS coupling and the empirical values.
The height of formation was calculated according to the MACKKL
model of the solar photosphere
(Maltby et al. (1986)
by Gadun (2000).
References: 1 - Allende Prieto & Garciá López (1998);
2 - Moore (1972); 3 - Kurucz (1990);
4 - Solanki & Stenflo (1985); 5 - Moore et al. (1966).
Simulations have predicted supersonic horizontal flows of granular plasma as a consequence of the non-adiabatic cooling at the solar surface. The collision of the horizontal flow of neighbouring granules leads to the formation of a pair of shocks which travel from the intergranular lane upstream toward the granule centres (Cattaneo et al. 1989, 1990; Malagoli et al. 1990; Steffen & Freytag 1991; Steiner et al. 1994; Solanki et al. 1996; Gadun 2000). The first attempt to confirm the existence of these horizontally moving shocks was made by Nesis et al. (1992). The observational evidence for such flows in the intergranular lanes was based on the negative correlation between the line width and the continuum intensity. They argued that the excess in line width was caused by turbulence introduced by the shock that brakes the supersonic flow back to a subsonic one in the intergranular lane. Later, Nesis et al. (1993) found the region of the enhanced turbulence to be concentrated at the borders of granules, especially when there exists a steep velocity gradient. High resolution observations made by Solanki et al. (1996) qualitatively confirmed the trend of the relation found by Nesis et al. (1992). On the other hand Solanki et al. (1996) showed, based on numerical simulations, that spectral lines that originate in the intergranular lanes are broader even in the absence of any horizontal supersonic flow and associated shock front. The latter however seem to be prerequisite for the line broadening when observed near the solar limb. The direct spatial identification of enhanced line broadening at the boundaries of some granules, supports the interpretation of the line broadening in terms of shocks that are formed near granular boundaries as a consequence of the colliding horizontal granular flow.
Steiner et al. (1998) detected three types of shocks in 2D MHD simulations of a magnetic flux sheet in interaction with granulation depending on the place of origin and direction of propagation. Type I shocks belong to the deceleration zone of the horizontal granular flow on the edge of the intergranular lane. This type is in agreement with the previously predicted shock from non-magnetic simulations made by Cattaneo et al. (1989, 1990) and other authors and is not related to the presence of the flux sheet. Type II shocks are caused by the swaying motion of the flux sheet when a fast motion of the sheet pushes the plasma in front of it creating a vertically oriented bow shock moving horizontally. Type III shocks are found to be horizontally oriented and propagating upward within the flux sheet itself. This type is generated by the deformation of the flux sheet and tube-mode coupling due to the dynamics of convection.
Each of the three types of shocks can be expected
to produce signatures in spectral lines.
In order to distinguish them their temporal evolution, direction of propagation,
and their location with respect to the granular/intergranular
intensity and the magnetic pattern must be determined.
As we concentrate on horizontal flows in the following, type III shocks
are not considered.
The aim of this paper is to give direct
evidence for shocks in the solar photosphere
including their temporal development using
high spatial and spectral resolution observations of the photospheric
lines, given in Table 1.
A preliminary report was given by Kucera et al.
(2003).
Predictions of the shock signatures from the numerical
simulations are summarized in Sect. 2 and our observations
are described in Sects. 3 and 4.
Results on the observed spectral signatures of
the suspected shock events are given in Sect. 5.
Discussion of the results and a comparison of the observed shock signatures to
the G-band intensity pattern and to synthetic spectral line profiles
are presented in Sect. 6.
Final conclusions are provided in Sect. 7.
Radiative transfer analysis of numerical simulations predict distinctive signatures of spectral profiles when a shock travels through the formation region of the spectral line in the photosphere. These shock signatures can be summarized as follows:
Similar results were found by Gadun & Hanslmeier (2000) who also showed that the relative position of shock signatures in the line width and in the residual line intensity changes depending on the inclination of the line-of-sight with respect to the shock orientation.
A careful selection of Fe II lines in the visible wavelength range of the spectrum was performed. The amplitude of the expected shock signatures in the Fe II spectral line profile (Gadun 2000; Gadun & Hanslmeier 2000), the formation heights, and other suitable lines near the chosen Fe II lines as well as the presence of any line blends were considered. Finally, only two Fe II lines (4993.35 Å and 6456.38 Å) were selected from eight suitable lines when we also considered the limitations of the spectrograph and our aim to measure at least two different spectral regions simultaneously in order to increase the number of measured lines (Table 1). These lines probe intermediate layers of the photosphere.
Observations were carried out with the Vacuum Tower Telescope (VTT) (Schröter et al. 1985) at the Observatorio del Teide, Tenerife, Spain. The Adaptive Optics (AO) of the National Solar Observatory at Sacramento Peak (Sunspot, USA) was allocated on loan for a test deployment at the VTT (Rimmele et al. 1999). The experimental setup of the AO was used successfully to compensate for pointing errors due to guiding inaccuracies and/or seeing for most of the observing time. The actual position of the spectrograph slit on the projected solar surface was recorded using the slit-jaw (SJ) imaging system (Kentischer 1995). In particular a G-band filter of 9 Å bandpass centred at 4306 Å was used for the slit-jaw image acquisition. A large Echelle spectrograph with the predisperser was used to produce high resolution spectra in two different spectral regions at the same time.
This paper is based on measurements taken on April 27,
2000 when two spectral regions (both about 3 Å wide)
around the selected Fe II lines were recorded.
The spectrograph slit was oriented perpendicularly to
the horizon to allow post-facto compensation for
differential refraction.
The width of the slit was equivalent to 0.5''.
The spectral data were acquired with two
12 bit XEDAR CCD cameras of
frame.
The spatial sampling was 0.125''/pixel and the
spectral sampling was 2.14 mÅ/pixel and 3.09 mÅ/pixel
for the first and second spectral region, respectively.
The spectra were acquired simultaneously
with an exposure time of 1 s and a dwell time of 3 s.
The SJ system was equipped with a
16 bit DALSA digital camera operated with an exposure time
of 5 ms and with a cadence of 2 frames per second.
The spatial sampling was 0.107''/pixel.
The data were taken near the solar limb (
)
and a spot in the active region NOAA 8967 was used
as a target for the AO tracking.
The seeing conditions were of medium quality allowing for an estimated
spatial resolution of about 0.5''.
Despite the fact the AO was used to track a relatively high intensity
gradient (small spot) few intervals of lower contrast and also random
motion of the solar image for a few tens of an arcsecond occurred during
the measurements as can be seen from Fig. 1.
Part of the slit crossed the penumbra of the spot and the rest
of the slit covered the quiet atmosphere toward the limb.
The slit was oriented perpendicular to the horizon, 50
off the north-south direction.
The whole observing run started at 10:20:54 UT and
lasted for 15 min.
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Figure 1:
Temporal and spatial behaviour (
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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The spectra were photometrically reduced over the
100'' spatial distance along the slit.
The precise reduction procedure (Wöhl et al. 2002)
was applied. This procedure takes the temporal changes of the flat field
conditions into account by splitting the flat-field matrix into two
components - one stable in time connected to camera artefacts, the
other one variable in time reflecting the long-term drift of the
spectrograph.
High frequency noise was removed from the individual
spectra by optimal filtering (Gray 1976).
The effects of filtering were carefully checked so as
not to deform the profiles of the lines.
The polynomial approximation of the dispersion was
determined from the averaged disk centre spectra using the
wavelength data of Moore et al. (1966).
The zero point of the wavelength scale was adjusted
according to the average positions of lines derived from all the
spectra of the run.
The intensity scale was normalized using the
quasi-continua in the spectra taking into account their
relation to the true continuum level (Neckel 1999).
The centre-to-limb darkening of the continuum intensity
was corrected for.
The reference continuum intensity was calculated
as the average value of the continua of all the spectra of
the run.
Each spectrum was normalized according to this
reference continuum intensity.
The following spectral characteristics were calculated for each
spectral line in all the spectra of the run:
- the continuum intensity,
- the residual line intensity,
- the Doppler velocity of the line,
- the full width at half depth, and
- the equivalent width of the line.
The zero value of the Doppler velocity,
,
was derived
from the mean spatial and temporal position of the line in the whole run
when the convective blue shift and its centre-to-limb variation has
been taken into account.
Velocities toward the observer are negative.
The equivalent widths have been calculated excluding
the far wings to prevent contamination by blends.
The SJ images have also been photometrically reduced
correcting for the mean dark current and the mean flat-field frames
using the procedures provided by Langhans
(2000).
The narrow field of the SJ image along the slit was
extracted (
)
and
co-aligned with the spectra and the empirically determined
differential refraction was corrected for.
The SJ images acquired during the best seeing
conditions were selected for comparison with the acquired
spectra.
According to the predictions of the numerical
simulations a search for possible shock signatures
was performed in that part of the data set pertaining
to a quiet region atmosphere
(
min).
The only signature used in this search was the line
width,
,
of the Fe II 6456.38 Å line.
The line width was selected as it shows the
most remarkable line signature of the shock as was demonstrated by the
simulation of spectral profiles by Solanki et al. (1996),
Steiner et al. (1998), and
Gadun & Hanslmeier (2000).
The line-width enhancement is produced by the large velocity gradient across the shock.
In this paper only the results of the event with the most significant
signature in line width are presented.
This
-event appeared at
at a distance
of 70'' from the mentioned spot toward the limb.
The temporal and spatial behaviour of the spectral
characteristics of the selected
-event is shown in Fig. 1.
This event is located at 3.3'' on the spatial scale of
Fig. 1 and following figures.
Only the stationary and declining phase of the selected
-event
can be followed as the onset phase of the event had taken place
before the start of the observations.
The average value of
was derived taking the limb-darkening
into account.
Representative spatial scans of the spectral
characteristics for three temporal instances and for a reference moment
are displayed in Fig. 2.
From Figs. 1 and 2
the following properties and relations between the spectral characteristics of
the
-event can be derived:
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Figure 2:
Representative spatial scans of the Fe II
6456.38 Å spectral characteristics for three time instances
(0.05, 0.4 and 1.16 min) during
the event (solid lines of different thickness)
and for a reference time (dashed line).
The scans were extracted
from Fig. 1.
The temporal evolution of the line width,
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Figure 3:
Profiles of the Co I 6455.0 Å, Ca I 6455.6 Å,
and Fe II 6456.38 Å spectral lines of the ![]() ![]() |
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Besides the discussed -event a smaller event is
located at position 5.8'' (toward disk centre) that shows
an increase of
by 16%.
Its position on the slit relative to
other spectral characteristics is similar to the former event with
the exception that no excess is found with regard to
.
Also, smaller amplitudes for
are measured for
this event.
Moreover the velocity amplitude does not decrease
as drastically as in the former case towards the end of the event
(different to the
-amplitude difference of
1000 m s-1 in the former case).
In the opposite direction (towards the limb) no enhancement
of
is found along the slit over a distance of more than
10''.
Besides the spectral characteristics,
typical spectral profiles of the -event were examined together with
a reference profile at the same centre-to-limb distance.
These profiles of the Fe II 6456.38 Å line and of
two neighbouring lines of Ca I 6455.6 Å and
Co I 6455.0 Å are shown in
Fig. 3.
The Fe II line profile of the
-event shows,
in addition to the already
reported enhancement of
,
an increase of
,
and
a significant blue shift.
There is a clear line asymmetry in that the red wing of the
profile is less steep.
Moreover, the profiles of the Ca I
and Co I lines display in all aspects a similar qualitative behaviour as
was found for the Fe II line.
Examples of the G-band slit-jaw images acquired
during the -event are shown in
Fig. 4.
These SJ-images were prepared in a way that the
-event is located in the middle of each panel, underneath the vertical dark
slit at the position of 3.3''.
The SJ-images show that besides a very weak regular
granular pattern, there was a G-band bright point located
very near the
-event in the direction of the limb
at 3.8'' in the direction perpendicular to and 2.4'' along the slit.
The intensity evolution of the G-band bright point is shown in Fig. 5. The bright point lasted for more than half a minute with roughly the same maximum intensity. During this period the intensity of the G-band bright point varied due to the variable seeing conditions from 1.10 to 1.18 relative to the mean G-band intensity. Then the intensity declines for 1.5 min. An image of exceptionally high contrast, taken at t=1.02 min during the declining phase of the bright point, shows a bright point intensity of 1.19, indicating that the high-intensity phase may have lasted for more than 1 min or that the previous maximum bright point intensities (e.g., t=0.07 and t=0.41 min) could be even higher than 1.2. After two minutes, the bright point had diminished to the typical granular maximum intensity of the surrounding field.
The distance between the -event and the G-band
bright point is
in the plane of sky corresponding
to 2.08
0.43'' on the solar surface.
The mean value of this distance and its standard deviation
were calculated
from the distances of the bright point to the averaged
-event
position in all SJ-frames within the first minute of the measurement.
The errors obtained here come from motions of the
SJ-image caused by seeing.
No systematic motion of the
-event and the G-band
bright point was detected under the particular seeing
conditions.
Comparing the evolution of the G-band bright
point intensity and the changes of the line width,
,
during the
-event,
a constant phase is seen over the first minute of
the measurement.
In the second minute, a more rapid dimming of the G-band bright point
intensity than the slower decline of
was observed.
The selected -event fulfills the basic properties
of a shock signature according to the predictions of
numerical simulations obtained for shocks outside
magnetic field concentrations (Sect. 1).
The event is located at the border of a granule as
marked by the largest gradient of the continuum intensity,
.
Its position can be clearly distinguished, both, from
the granulum area and also from the middle of the
intergranular lane (Figs. 1
and 2).
The event is co-spatial with a significant increase
of the residual line intensity,
,
indicating that the
plasma inside the event is heated up above the border of the
granulum.
The largest gradient of the Doppler velocity,
,
is
detected at the position of the event, with a maximum velocity
difference of 1200 m s-1.
The plasma moves toward the observer on the limb side of
the
-event with a velocity component along the
line-of-sight of more than 1000 m s-1.
At the position of the
-event this motion stops
completely.
On the opposite side, the intergranular plasma is at rest
during the
-event.
These properties of the
-event are in agreement
with the predictions of numerical simulations made by
Steffen & Freytag (1991),
Steffen et al. (1994),
Solanki et al. (1996),
Steiner et al. (1998), and by
Gadun & Hanslmeier (2000).
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Figure 4:
Evolution of the G-band SJ image in the surroundings
of the ![]() ![]() ![]() |
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From Figs. 1 and 2 we see that the intergranular lanes
located at positions 1'' and 4'' that
harbour downward motion in the bottom photospheric layers
are not co-spatial with the enhancement of the line width, ,
so that the latter is not an immediate consequence of the
intergranular downflow.
This confirms the conclusion made by Solanki et al.
(1996) that observations on the limb do not
show an increase of the line width
from the
downward motion in the intergranular lane.
Both, the spatial extension and the amplitude of the
shock signatures are affected by the finite width of the spectral line
formation-region, seeing and instrumental effects, and the orientation
of the shock front relative to the spectrograph slit.
Hence, the measured spatial extent of
the -signature appears to be larger than the actual width of the shock front,
and the enhancement of the line width in the
-event and the gradient in
Doppler velocity across the
-event is actually larger than detected.
Therefore, the actually observed values of these parameters
can be much different from the ones predicted from numerical simulations with
grid constants much smaller than 0.1''.
In order to estimate these effects we have computed synthetic profiles
of Fe II 6456.38 Å from a plane-parallel standard solar atmosphere
(Vernazza et al. 1981)
in which we assume to exist a horizontal, height-independent, constant velocity
field vx(x) that abruptly stops at x = 0, mimicking a shock front,
so that
vx(x) = v0 for x < 0 and
vx(x) = 0 for
.
The spectral lines are computed along slanted lines-of-sight with
so that the line is blue-shifted for x < 0.
Figure 6 shows the line-core Doppler velocity,
,
and
the line width,
,
as a function of
space for the full spatial resolution of 10 km (solid line curve) and for a
simulated spatial resolution of 0.25'' achieved by a Gaussian blur over
individual ray profiles (dashed curve).
The dotted curve shows the corresponding value,
when we additionally assume that the shock front is not perpendicular to
the slit but inclined to it by
,
which amounts to an
additional box-car averaging of 0.5'' width.
The value of v0 is chosen to be 3 km s-1 in which case the
"shock front'' would
move with a velocity
to the left
(where c1,2 is the speed of sound up- and downstream the shock front)
consistent with results of numerical simulations, which show shock front
speeds of typically a few km s-1.
First we notice that even in the case of full spatial
resolution, the infinitely thin "shock front'' results in a finite width
of the spectral signature (FWHM of
)
of 0.26''
.
Correspondingly, a finite horizontal spatial
resolution of only 0.25'' does not dramatically change these values.
The maximum value of
decreases
from 126 to 125 mÅ and the width of the
-signal increases from 0.26''to 0.3''.
A substantial decrease of max(
)
to 119 mÅ and an substantial
increase of the signal width to 0.57'' ensues when inclining the shock front
by
with respect to the direction of the slit.
Note, that this is an idealized model and that the shape and values of
and
strongly depend on the actual velocity field and the thermal structure of
the atmosphere.
However, it gives a good indication for changes due to degradation effects.
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Figure 5: Temporal evolution of the maximum intensity of the G-band bright point. The figure shows the maximum intensity of the bright point (solid line), the maximum intensity of the granular pattern found on the opposite side of the slit (dotted line), and the average intensity of the G-band image (dashed line). The triangles mark the first three G-band images shown in Fig. 4. |
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Figure 6:
Spectral signature of a discontinuous
flow field with
vx(x) = v0 for x<0 and
vx(x) = 0 for ![]() ![]() ![]() ![]() |
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Figure 7:
Histogram of the normalized line widths,
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Both Fe II lines and also the other medium (Ca I 6455.6 Å), weak (Co I 6455.0 Å) and strong (Fe I 4994.11 Å) lines display qualitatively very similar temporal and spatial variations of the spectral characteristics. The formation heights of these lines are 110 and 205 km for the Fe II lines and 170, 40, and 470 km for Ca I, Co I, and Fe I lines, respectively (see Table 1 for details). This hints at the whole middle and upper photosphere being influenced by the fast motion of the plasma which abruptly stops at the interface from the granulum to the intergranular lane.
The -events seem to coincide with
enhanced non-thermal motion as was put forward by Nesis et al.
(1993).
These authors found large velocity gradient within a small spatial
range just at the borders of granules: not at arbitrary position
within the intergranular lane.
Different from Nesis et al. (1993),
our observations show large velocity gradients in combination
with a line width excess near disk limb, which hints at a sharp gradient in
the velocity of the (horizontal) flow.
Similar observations at almost the same
heliocentric angle were presented by Solanki et al.
(1996).
Their most significant events show values
of the line width excess (25-35%), the equivalent
width excess (8%), and the residual line intesity changes (20%)
similar to our results.
The Doppler velocity differences across the
events are smaller (typically up to 600 m s-1) than in our case.
The most extreme profiles of all the lines we have observed
show a blue line asymmetry with a bisector shift of up to - 2 km s-1.
It is in agreement with the asymmetry of the Ni I line found by
Solanki et al. (1996).
No double profiles were found in the case of our -event,
unlike to some of the synthesized results presented by Solanki et al.
(1996).
Nevertheless, the explanation of this phenomenon, originally proposed
by Solanki et al. (1996) for a moderate jump in velocity,
remains valid for our observations, too: the line absorption is
produced by two separated plasma volumes of two different Doppler
velocities, for example, by the preshock and postshock medium with one
volume of plasma at high (or supersonic) speed with significant blue-shift
of a few km s-1 and the other volume at rest on which this motion is braking.
More than 50 granules of different size and lifetime that were
present within the slit length of 123'' (with respect to the real
solar surface) were followed for 15 min.
For a statistical investigation, normalized line widths,
fw, N were calculated dividing every line width, ,
by the
mean value of the line width at the corresponding limb distance, which varies
between 145 and 150 mÅ.
The resulting histogram, shown in Fig. 7, contains
all the measurement points of the observed space-time domain of
s.
The distribution of the normalized line widths,
,
consists of two components.
The central, main component is nearly Gaussian, positioned at
0.993 and its Gaussian width is 0.122.
The second component, located within a range from
1.1 up to 1.3,
is very weak and contains just 0.45% of all the values that enter the
distribution.
This component is supposed to be caused by shocks waves because
the intergranular lanes do not show any
significant line broadening at large viewing angles as
was shown by Solanki et al. (1996).
The range of values of the second component
is in line with the result of the
signature derived from
the idealized shock model of Fig. 6.
Therefore, the fraction of the time-space domain that shows
spectral lines affected by a shock wave can be estimated to
maximum 0.45% in the case of our observation.
The threshold for the occurence of shocks is found to be
110% of the mean value at the given
.
The area of the central component surpassing this
threshold is 4.24% of the whole distribution so that the ratio of the
second component area to the central one in this range
is
0.11.
In total only 12 events of enhanced
above the specified
threshold of 110% were detected.
The duration of these events is from 1 to 3 min.
Only 2 of these events exceed the threshold of 120% above which limit
the central component does not interfere.
Although there is no tool to unambiguously disentangle the
events of enhanced
within the intermediate range from 110 to 120%,
using the statistical
approach we can thus estimate an upper limit for the relative occurence of
-events caused by shocks of 0.45% of the observed
time-space domain.
Supersonic flow (mainly horizontally directed) was predicted to cover an area of
3-4% of the solar surface at any one time by numerical hydrodynamic
simulations performed by Stein & Nordlund (1998).
This coverage is qualitatively also in agreement with predictions
of other numerical simulations (e.g., Cattaneo et al.
1990; Malagoli et al. 1990).
However, not all of this area is expected to produce a line broadening but only
a fraction pertaining to the shock front, so that the above quoted number can be
considered at best an upper limit for the area fraction of
-events produced
by shock waves.
In addition, Solanki et al. (1996) show that in order
to see a significant shock
signature in line profiles the shock front must be viewed close to head-on,
which is a rare case in three spatial dimensions.
Comparing the occurence of shock signatures (0.45%) to the area
coverage of supersonic flow predicted by numerical simulations (3-4%)
we can conclude that only at about 10% of this area shows signs
of shock waves.
Several other examples of extremely distorted spectral line profiles have been presented from spatially highly resolved measurements by, e.g., Steffen & Freytag (1991), Holweger & Kneer (1989), Wiehr & Kneer (1988), and Amer & Kneer (1993). Generally, all these examples represent only single snapshots of spectra and not the temporal evolution of the events.
However we can compare our results with numerical
simulations of the temporal evolution of the solar atmosphere
presented by Steiner et al. (1998) that explicitly allow
for the formation of shock waves.
Their video sequences
show several shock events from where we can estimate the duration
and spatial dimension of the temperature peak in the post-shock medium.
In agreement with these predictions our event(s)
are of durations of a few minutes, all lasting less than 15 min.
The typical horizontal extension of the simulated
post-shock temperature enhancements is a few tenth
of an arcsecond.
This value is in agreement with the spatial extent along the slit
of our -event of 0.5'' when both, the actual
slit width of 0.5'' and the theoretical spatial
resolution of the instrument of 0.25'' are taken into account.
Two types of G-band bright points have been found in the solar photosphere (Berger & Title 2001). The first type appears on the edges of bright, rapidly expanding granules and are non-magnetic in nature. The second one is co-spatial with a magnetic element and is located in intergranular lanes (Muller et al. 2000; Berger & Title 2001; Langhans et al. 2002). The G-band bright point found in our measurements can be interpreted as intergranular as it is not connected to any large, rapidly expanding granule (Fig. 4). Its peak contrast of 1.2 is comparable to the average contrast of G-band bright points. The duration of the observed bright point is also in agreement with the average lifetimes of bright points (Berger & Title 1996).
In an attempt to answer the question on the causal
relation between the observed G-band bright point found
2.08'' away from the -event and the
-event we can
summarize the following findings:
Using the 12 identified events of enhanced line width
the average lifetime of the events was found to be 2 min.
We can estimate that one event can be expected in
a time-space domain of roughly
when the total duration of the observation, the slit length with respect to the real
surface, and the number of identified events are taken into account.
Additional events may have escaped detection because they were below
the threshold of 110% of the mean value of the line width at the
given
.
Moreover, this estimation of the spatiotemporal frequency of
enhanced
phenomena cannot be translated directly into a probability
for detecting a shock signature as some of these phenomena may have a
physical origin, different from the only event discussed here.
It should be emphasized that performing this particular type of studies is only possible with an extremely high spatial resolution. On-line corrections of image distortions (Schmidt & Kentischer 1995; von der Lühe et al. 2003) are necessary to perform successful measurements of the temporal evolution of shock signatures in the solar photosphere. In particular, large image field corrections are needed considering the sparse occurence of significant shock signatures. In our case the observed event was quite far from the subfield corrected by the AO setup, which caused some periods of reduced image quality (Fig. 1). Dual-conjugated AO (Berkefeld et al. 2003) may help to overcome these problems in future.
We have observed variations of spectral line characteristics and changes of the line profiles that are, when compared with numerical simulations of convection in the solar granulation, further indications for the existence of hydrodynamic shocks in the solar photosphere. Agreement was also found with respect to the amplitudes of the spectral characteristics during the event when seeing and instrumental effects are taken into account. These results are in line with the findings of Solanki et al. (1996).
Both, the stable and the declining phases of the shock event were followed for the first time. A possible relation of the shock event with a nearby G-band bright point was investigated, indicating a causal relationship. A final conclusion whether the fast flow and associated discontinuity (shock) are caused by either the swaying motion of the flux concentration or by the granular flow not related to the magnetic field cannot definitely be made. The temporal and spatial coincidence of both features suggests that the flow and shock is a consequence of the swaying or random motion of the magnetic flux concentration, while the spatial coincidence of the line-broadening event with the edge of a granule favours interpretation in terms of a shock that was solely generated by the granular flow.
Acknowledgements
The VTT is operated by the Kiepenheuer-Institut für Sonnenphysik, Freiburg, at the Observatorio del Teide of the Instituto de Astrofísica de Canarias. We would like to thank M. Sigwarth and T. Berkefeld for the operation of the AO during our campaign and K. Langhans for his help with the SJ DALSA camera. We thank the referee whose comments greatly helped us to improve the paper. This work was supported by the Slovak grant agency VEGA (2/3015/23) and by the Deutsche Forschungsgemeinschaft grant (DFG 436 SLK 113/7). This research is part of the European Solar Magnetism Network (EC/RTN contract HPRN-CT-2002-00313). A.H., A.K. and J.R. thank the Austrian and Slovak Academies of Sciences for financing the exchange of scientists. A.H. acknowledges the support of the Austrian Fonds zur Förderung der Wissenschaftlichen Forschung. Finally we would like to acknowledge our late colleague A.S. Gadun who originally initiated this project attracting our interest to this topic.