J. Hirzberger1 - E. Wiehr2
1 - Institut für Physik, IGAM, Universitätsplatz 5,
8010 Graz, Austria
2 -
Universitäts-Sternwarte,
Geismarlandstraße 11, 37083 Göttingen, Germany
Received 31 January 2005 / Accepted 22 March 2005
Abstract
We observe solar limb faculae at an unprecedented spatial
resolution with the new 1 m Swedish Solar Telescope SST on La Palma.
Speckle-reconstructed images are used to study 4475 limb facular grains
simultaneously in the 430 nm G-band and the
continuum
up to only 1'' from the limb (
). No
systematic contrast decrease is found even a few arcsec from the solar
limb. The facular grains appear to be "projected'' on the limb-side
neighboring granules; approaching the disc center, the corresponding
features occur as inter-granular G-band bright points. Independently,
we took spectra with the French-Italian THEMIS telescope on Tenerife
and find that the known "line-gap effect'' from disc center disappears
near the limb. Here, the facular continuum is enhanced whereas
the normalized profiles are unchanged with respect to the undisturbed
neighborhood.
Key words: Sun: photosphere - Sun: faculae, plages
The solar surface is widely covered by small magnetic flux concentrations,
even outside active regions and during the minimum of the solar cycle.
They are identifiable by an intensity excess in the cores of absorption
lines. These line-core brightenings are organized in "plages''
particularly visible in H
or Ca II K filtergrams. In the continuum they occur only at very high spatial
resolution as tiny brightenings of the "solar filigree'' located in the
inter-granular lanes (Dunn & Zirker 1973). At larger helio-centric
angles, however, continuum structures become visible which consist of
bright facular grains (e.g. Muller 1975). The spatial relation
between these continuum (i.e. white light) facular regions and the H
or Ca II K plages (Beckers 1976; Spruit 1976) gives strong indication
that the bright facular grains represent the limb occurrence of small-scale
magnetic flux concentrations which, near solar disk center, are visible as
bright points in the "G-band'' CH absorption bands (e.g., Muller & Roudier
1984).
The transition from the disc-center appearance of small-scale magnetic
flux concentrations as G-band bright points (BP) to their limb appearance
as facular grains will be of central importance for the understanding of
their geometry. The facular contrast has been found to increase from
disk center to heliocentric angles
(Auffret
& Muller 1991; Sánchez Cuberes et al. 2002); for
these authors found the facular grains' intensity excess to decrease
toward the limb. Okunev & Kneer (2004) found a monotonic
decrease of the intensity contrast of polar faculae from
towards the limb. Ortiz et al. (2002) found from MDI observations
a contrast maximum near
which, however, becomes less
significant with increasing magnetic flux density. At the much
higher spatial resolution of speckle reconstructed images, de Boer et al. (1997) as well as Sütterlin et al. (1999) found no indication for a contrast maximum up to
(
)
which could fit Oritz et al.
(2002) if the pronounced limb facular grains exhibit stronger magnetic
fields. On the other side, Auffret & Muller (1991) found the contrast
maximum near
to be less pronounced for small
features, this disagrees to some extent with Ortiz et al. (2002).
Spatially highly resolved images of plage regions (e.g. Fig. 1)
readily give the qualitative impression that the number density of magnetic
flux concentrations (e.g., BP per active region) markedly decreases from
disk center to the limb. Indeed, Auffret & Muller (1991) found the number
density to decrease by almost a factor of 10 from disk center to
.
Sánchez Cuberes et al. (2002) found a decrease
of the number density of large facular grains with decreasing
.
This seems to point to a selection effect of the visibility of small-scale
magnetic flux concentrations near the limb, which may be due to the
particular geometry.
Auffret & Muller (1991) found for the quiet network mean sizes which
increase from
(300 km) at disk center to
at
.
However, Wiehr et al. (2004) found
for the disk center most frequent BP diameters near 160 km with a clear
decrease toward both, smaller and larger sizes. The upper diameter
limit near 280 km as well as the absence of a marked drop of the
brightness between 200 and 280 km does not indicate a transition to
"invisible'' magnetic features of sizes between BP and pores.
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Figure 1:
Speckle reconstructed image of limb facular regions
taken with the 1 m SST on July 15, 2003, in the 487.5 nm
continuum; field of view: approximately
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The finding that BP are smaller and more frequent than typical facular
grains suggests that one should investigate their spectral signature.
Plage regions near disk center show absorption lines with reduced
central depression (i.e., enhanced line-core intensity; e.g.,
Stellmacher & Wiehr 1971) which, at sufficient spatial resolution,
occur as "line gaps'' (Chapman & Sheeley 1977). This effect traces
small-scale magnetic flux concentrations not only in strong
chromospheric lines (as e.g. H
or Ca II K), but in
any line-core. The reduced central line depression even occurs in
ionized lines such as from Fe II (Stellmacher & Wiehr 1971), which
might have been expected to become stronger (due to the enhanced
ionization in the hot facular atmosphere). This apparent discrepancy
has been explained (Stellmacher & Wiehr 1979) by a spatial smearing
of a hot flux concentration with surrounding granules and
intergranules in the spectra. The disappearance of that "residual
intensity effect'' near the limb (Stellmacher & Wiehr 1973) is a hint
for the dominant role of the geometry and the lateral radiation
through the flux concentration for the visibility of facular grains near
the limb. We thus also present spectra of magnetically insensitive lines
in limb faculae.
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Figure 2:
Faculae near a spot group (NOAA 0409)
at
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We used the new 1 m Swedish Solar Telescope on La Palma (SST; Scharmer
et al. 2003) in July 2003 to observe facular regions near the solar limb.
Images in the continuum at nm were taken simultaneously with
"G-band'' images at
nm. The pixel size is
and the exposure time was varied between 4 ms and 10 ms to obtain
optimal count numbers at all heliocentric angles. The tip-tilt mirror
of the SST assured an effective correction for image motion. Bursts of
some dozens of images were reconstructed using the speckle-masking
method (Weigelt 1977; Pehlemann & von der Lühe 1989; de Boer
1996). An example is shown in Fig. 1.
The center-to-limb variation (CLV) of the continuum and the G-band
intensities of the quiet Sun,
and
,
have been determined from locations in-between the facular grains,
and agree with the CLV of the photospheric LTE model by Holweger
(1967). We finally remove that CLV from our images, thus obtaining a
"flat'' intensity distribution up to the limb, allowing an
easy determination of the intensity excess of facular grains:
![]() |
(1) |
For an automatic recognition of the grains, a band-pass filter was
applied and structures were selected which exceed a certain intensity
threshold (Roudier & Muller 1987). Fourier filtering was carried out
in order to remove residual noise (at high spatial wave-numbers k)
and intensity fluctuations at scales much larger than the size of
facular grains (low k). These large-scale intensity fluctuations can
be clearly recognized in the original images (e.g. in that shown in
Fig. 1) and might be caused by five minute oscillations.
The Fourier filter F has the following analytical form:
![]() |
(2) |
Independently, we took spectra at the French-Italian solar telescope
THEMIS on Tenerife on May 23 through 25, 2001, of limb faculae and,
for comparison, of disc center plage regions. In order to avoid
magnetic line broadening, we observed the un-split lines Ti I 522.27,
Fe II 722.45, Fe I 557.6, Fe I 543.45, and the
small-split lines Fe II 526.48 (
)
and
Ni I 543.58 (
). These lines cover a large range of
excitation potential and formation height and extend the observations by
Stellmacher & Wiehr (1979) since taken simultaneously and at higher
spatial resolution. The raw spectra were corrected for the dark and the gain
matrices.
At the unprecedented high spatial resolution achieved in our speckle
reconstructed images, limb facular grains appear to be "projected'' on
the limb-side neighboring granules, whereas center-wards, a pronounced
dark lane is visible (Fig. 2). This confirms the finding
by Lites et al. (2004) and has been successfully modeled by Carlsson
et al. (2004), Keller et al. (2004) and Steiner (2005). The
brightening arises from the deep view into the atmosphere due to
the depressed iso-
surfaces in the quasi-evacuated flux concentration.
The "dark lanes'' are explained by cool regions inside the flux concentration
and above the center-ward granule (Keller et al. 2004; Steiner 2005) where
the temperature gradient is smaller than at corresponding optical depths
in the surroundings.
![]() |
Figure 3:
Mean spatial scans through facular grains at
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For quantitative comparison with model calculations (e.g., Steiner 2005),
we determine spatial scans through bright "projected'' facular grains and
their adjacent dark lanes along the direction perpendicular to the solar limb.
For this purpose, the respective structures (see Fig. 2) were
spatially aligned such that the intensity minima of the "dark lanes'' occur
at the same x-position (left panels of Fig. 3). In the right
panels of Fig. 3, averages of these scans are plotted in units
of the average intensity
of the surrounding quiet photosphere.
The spatial scans in Fig. 3 show intensity distributions with a
maximum and rather flat limb-ward decrease indicating a smooth transition
from the granular hot walls to the quiet photosphere, in agreement
with Steiner (2005). The various intensity maxima yield average values over
all scans in the subfield of
and
for the 587.5 nm continuum
and the G-band, respectively. In order to exclude intergranular
surroundings, we additionally distinguish features of brightness excess
for which
and
,
respectively,
establish the above values. The spatial extension of the whole
brightening is larger than
.
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Figure 4:
Facular regions at
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The "dark lanes'' appear as significant minima with average intensities of
and
.
Center-wards of the "dark lanes'' (i.e., leftwards in
Fig. 3) the intensity increases rather steeply up to
from the intensity minimum, then flattens markedly,
eventually reaching
and IG0. The
observed width of the intensity depression is not larger than twice
the width of the strong intensity gradient, i.e.
.
The inflection points, however, occur about
limb-wards and
center-wards from the minimum, suggesting an average width of
the dark lane near
.
According to Steiner (2005) the dark
lane "samples the deep cool layers''; Keller et al. (2004) present a sketch
showing that the maximum contribution stems from colder material "above
the centerward granule and inside the flux concentration''.
![]() |
Figure 5:
Same as Fig. 3, but for different
structures at
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At smaller angles, however, "projected'' and non-"projected''
structures occur in close spatial proximity. Box-a in Fig. 4
gives an example of a chain of several BP without pronounced
"brightness projection'' onto the limbside neighboring granule. The
corresponding spatial scans in Fig. 5 show "dark lanes''
with
and
in the G-band and the continuum,
respectively. The intensity excess in the G-band amounts to
.
In the continuum, however, the
intensity does not exceed that of the neighboring granules.
The middle panels in Fig. 5 (box-b in Fig. 4) show spatial scans across bright structures which, unlike BP, are not completely separated from the limb-sided granule. However, they also do not show a clear "projection'' onto the limbside granule. The lower panels of Fig. 5 give spatial scans across structures with a clear "projection effect'' (box c in Fig. 4).
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Figure 6: Maximum (solid and dotted lines) of faculae and minimum (dashed and dot-dot-dot-dashed lines) intensities of facular "dark lanes'' from averaged profiles vs. the heliocentric angle. |
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Figure 6 shows the variation of the spatial scans with the
heliocentric angle .
The data points have been derived from
selected facular areas (as e.g. in Fig. 2) and do not
denote a statistical mean. The intensity maxima increase up to
and remain constant or slightly decrease
towards larger
.
The minimum intensities of the facular lanes
exhibit an opposite behavior so that the contrast of the maximum
relative to the adjacent lanes achieves a maximum at
.
This trend is quite clear for the
587.5 nm continuum but is not that pronounced in the G-band.
The distances between the intensity minima of the "dark lanes'' and
the maxima of the hot wall effect are approximately
at
(see Fig. 3). We find no systematic
variation of these distances with
.
Figure 7 shows scatter plots of the 4475 facular grains
detected by means of the algorithm described in Sect. 2.1. The
maximum sizes (Fig. 7a) reach A=199 pixel which
corresponds to a projected area of 0.185 Mm2 (each pixel being
equivalent to 0.00176 arcsec2). The maximum continuum intensity
excess occurs at
(Fig. 7b). Most of the facular grains are located in
an interval
which is in agreement
with findings by Sütterlin et al. (1999).
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Figure 7:
Scatter plots of all 4475 facular grains detected in
the
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In Fig. 8 we display the CLV of various quantities
averaged in bins of width
.
The over-plotted error bars denote standard deviations in each bin.
The maximum and the mean intensity excesses of the entire sample of 4475 facular grains (Fig. 8, middle) show no
significant variation with the heliocentric angle. This is in
contrast to earlier measurements (e.g. Lawrence 1988; Auffret &
Muller 1991; Sánchez Cuberes et al. 2002; Okunev & Kneer 2004),
but confirms the findings by de Boer et al. (1997) and
by Sütterlin et al. (1999) extending them from
to
.
We do not find indication
for a substantial change in the smooth CLV for
as reported by Topka et al. (1997) who, however, refer to
conglomerates of magnetic structures considerably larger than those
revealed in the present observations.
The areas (measured in pixel squares) remain remarkably constant with
(upper left panel). This closely agrees with Steiner
(2005; solid dots in the right hand in his Figs. 2 and 4), but it
disagrees with Auffret & Muller (1991). Simple correction for
geometric foreshortening (dividing by
)
would yield an
increase of the "true'' areas toward the very limb (upper right panel
of our Fig. 8) and thus contradict to some extent
the results of Sánchez Cuberes et al. (2002) who found a decrease
of the number of large de-projected areas towards the limb. However,
it seems doubtful whether a division by
yields reasonable
information, since the facular brightening occurs at the "hot wall''
rather than on the solar surface.
The sizes of the limb facular grains show a clear dependence on their
brightness (Fig. 8; lower right panel) in the sense that
larger limb facular grains are brighter. This may yield a selection
effect which favors the detection of larger grains near the limb, and
may partly explain the abovementioned discrepancies.
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Figure 8:
CLV of the facular grain areas, de-projected areas
( upper), maximum and mean continuum intensity excesses,
averaged in bins of
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Figure 9:
Profiles of absorption lines with zero or negligible Zeeman
effect in a limb facular grain at
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The spectral signature of the facular grains is of importance for a
realistic theoretical modelling. In Fig. 9 we give
typical profiles of the non-magnetic lines taken simultaneously in an
isolated limb facular grain at
.
It shows the
pronounced continuum excess, but almost no change of the line depression
when normalized to the adjacent continuum. This finding supports the
results by Stellmacher & Wiehr (1979) at higher spatial resolution and
with more confidence since observed simultaneously.
For comparison, we show in Fig. 10 the same line profiles
as in Fig. 9, but for a disk center plage region showing
a pronounced "line gap'' in the spectrum. The significant residual
intensity enhancement is positive for all lines independent of
their excitation or equivalent width; however, its amount increases
with the line strength, in good agreement with Stellmacher & Wiehr
(1979). The corresponding continua do not show any excess, as to be
expected for the finite spatial resolution achieved in the spectra
(about
)
as compared to the extremely small size of
the tiny magnetic structures (see, e.g., Wiehr et al. 2004).
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Figure 10: The "residual intensity effect'' of a "line gap'' at disc center in absorption lines with zero or negligible Zeeman effect; line profiles from the "gap'' location (full) compared with a neighboring non-magnetic region (dotted lines). |
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The disappearance of the "residual intensity effect'' in the continuum-normalized line profiles of limb facular grains can be explained by the spatial displacement of the line-cores with respect to their corresponding continuum (Stellmacher & Wiehr 1991, 2001) originating from the formation height of the line-core above that of the continuum seen at an oblique line-of-sight. This "geometric elevation'' of the line-cores in regions very close to the limb has the result that a wavelength scan starting at the spatial location of the bright facular continuum misses the "corresponding'' line-core location since the latter is spatially displaced toward the limb. In turn, a spectral scan that crosses the facular location of the line-core gives a continuum limb-wards of the maximum facular intensity. This spatial offset has so far not been considered in modelling line profiles of facular grains near the limb.
Our two-dimensional images at unprecedented spatial resolution show
that limb facular grains are clearly visible up to
,
i.e., cos
.
This extends former results by de Boer et al. (1997) and by Sütterlin et al.
(1999) which excluded a contrast decrease at cos
,
to
cos
.
The spatial scans through the two-dimensional images yield profiles and
maximum values which agree with model calculations by Steiner (2005),
which, however, do not make predictions for large helio-centric
angles up to
.
In particular, the question of whether
the models yield a constant intensity excess down to cos
is uncertain; this equally holds for the model calculations by Keller
et al. (2004) and by Carlsson et al. (2004). Steiner & Stenflo (1990)
find for a "hot cloud'' in upper layers, fed by the lateral radiation of
the hot walls, a "secondary'' contrast maximum in close proximity to
the limb. Our data, however, indicate a smooth variation of the CLV.
On the other hand, such a "hot cloud'' (Rogerson 1961) was used to explain
measurements of an enhanced solar oblateness in presence of pronounced
facular plages (e.g., Chapman & Ziegler 1996; Bruls & Solanki 2002).
Also the "hillock model'' by Schatten et al. (1986), predicting
elevated iso-
surfaces in the flux concentration, might offer
a possible explanation of the substantial contrast at the extreme limb.
Still more critical than the intensity excess at the extreme limb is the occurrence of "dark lanes'' even at very large helio-centric angles, where the cold "bottom'' of a small-scale flux concentration is barely visible. Steiner (2005) calculates that these lanes do not arise exclusively from the "bottom'' of the flux concentration but to a large extent from the immediate vicinity where photon escape towards the flux sheet occurs. Compared to the models, the smaller lanes observed might point to remaining problems with the accurate treatment of (lateral) radiative transfer.
The co-existence of "projected'' (i.e., facular grain type) and
roundish (i.e., BP type) structures at
may
be explained by a large variety of magnetic field inclinations
which could either counterbalance the "projection on the hot wall''
or enhance it. The required field inclinations up to
agree with Beck et al. (2005) who found a large variety of field
inclinations. Much earlier, Wiehr (1978) found spatial displacements
at disc center between maxima of field strengths and corresponding
Ca II K brightness excesses of up to 2'', indicating
for Ca II K formation at h=1250 km an inclination of as much
as
.
Stangl & Hirzberger (2005) found spatial displacements
up to
for a formation height distance of 200 km; this
corresponds to inclinations of
.
A comprehensive treatment
of the inclination of plage fields was given by Martinez Pillet et al. (1997).
The nature of facular grains at the extreme limb should be studied in more detail by both very high resolution observations and model calculations at largest helio-centric angles.
Acknowledgements
We are grateful to Drs. W. Schüssler, O. Steiner and G. Stellmacher as well as to an anonymous referee for valuable comments. We thank the staff members from the SST and the THEMIS for their support. The SST telescope on La Palma island is operated by the "Swedish Academy of Sciences'' at the Spanish "Observatorio del Roque de los Muchachos'' (IAC). The THEMIS telescope on Tenerife is operated by the French "Centre National de la Recherche Scientifique'' and the Italian "Consiglio Nazionale delle Ricerche'' at the Spanish "Observatorio del Teide'' of the Instituto de Astrofísica de Canarias.