A&A 462, 753-762 (2007)
DOI: 10.1051/0004-6361:20065910
J.-M. Malherbe1 - J. Moity1 - J. Arnaud2 - Th. Roudier3
1 - LESIA, Observatoire de Paris, Section de Meudon, 92195 Meudon Cedex, France
2 - Laboratoire d'Astrophysique, Observatoire Midi Pyrénées, 14 avenue Edouard Belin,
31400 Toulouse, France
3 - Laboratoire d'Astrophysique, Observatoire Midi Pyrénées, 57 avenue d'Azereix, PB
826, 65008 Tarbes Cedex, France
Received 26 June 2006 / Accepted 28 September 2006
Abstract
Context. A new polarimeter has been installed at the focus of the 50 cm refractor of the Lunette Jean Rösch (LJR), previously known as Turret Dome, Pic du Midi, France, for spectroscopic observations of weak solar magnetic fields. Fields can be derived through the Hanle effect from the depolarization of the second solar spectrum (i.e. the linearly polarized spectrum at the limb).
Aims. We present the first observations with spatial resolution based on the new device performed with the large 8 m Echelle spectrograph, or recorded in imagery mode through narrow band filters. The observations started in April 2004, especially in the blue part of the spectrum where our instrumentation has a particularly good efficiency. The capabilities and the characteristics of the new instrument are briefly described. We observed several lines of the second solar spectrum with the slit of the spectrograph orthogonal to the limb to study the polarization as a function of limb distance (which is related to altitude in the atmosphere), and several spectral windows in imagery to determine the average continuum polarization.
Methods. The polarimeter uses Nematic Liquid Crystal (NLC) technology at the primary focus of the refractor, in spectroscopic or imagery mode.
Results. A continuous polarization profile through the limb is presented for the photospheric SrI 460.7 nm line, the low chromospheric BaII 455.4 nm line, and the CaI 422.7 nm line within a distance of 120
,
together with measurements of the mean continuum polarization obtained in imagery mode. Preliminary results of the polarization of the SrI 460.7 nm line are also shown at 40
from the limb, as a function of the brightness of structures visible in the continuum (granulation). They reveal a tendency for the polarization to be weaker in dark features (intergranules) than in bright ones (granules), suggesting a stronger magnetic field in intergranular lanes. As example the enigmatic and weak polarization signal in the core of the NaD1 589.6 nm line is presented.
Conclusions. Some aspects of the spatial variation of the polarization with respect to the granulation pattern require further investigation at higher spatial resolution.
Key words: polarization - instrumentation: polarimeters - instrumentation: spectrographs - Sun: photosphere - Sun: chromosphere - Sun: magnetic fields
The second solar spectrum is the linearly polarized spectrum observed on the limb of the sun. It is as rich as the ordinary intensity spectrum, but the two spectra are very different. The second solar spectrum is generated by coherent scattering due to the anisotropy of the radiation field, both with and without magnetic fields. The polarization rate is generally small (typical 1% or less) and decreases in the presence of magnetic fields. This well known effect is called Hanle depolarization and is generally observed in Stokes Q/I, which characterizes the linear polarization parallel to the limb. But another aspect of the Hanle effect (rotation of the plane of polarization) may also induce signals in Stokes U/I. The first spectral survey of the second solar spectrum was performed at the Kitt Peak Observatory in Stokes Q/I by Stenflo et al. (1983a,b) from the Ultra Violet to the near Infra Red. It was then followed by a much more sensitive survey by Gandorfer (2000, 2002) using the ZIMPOL polarimeter. The second solar spectrum requires polarization free telescopes to be best recorded; for optical designs that introduce instrumental polarization (such as coelostats or Coudé telescopes), specific calibrations or epochs of observation (such as the equinoxes) may be necessary. Telescopes or refractors with axial symmetry such as THEMIS or the Pic du Midi LJR are well suited for this.
Observations of the second solar spectrum opened a new field of investigation and have led to many applications: in atomic physics, new polarization phenomena have been discovered, involving rare atomic elements, molecules and unexplored processes of quantum mechanics, such as interference, optical pumping or hyperfine structure; in solar physics, new diagnostics of spatially unresolved turbulent and weak magnetic fields have been proposed, in a complementary way to the Zeeman effect for stronger and resolved fields. For a comprehensive overview, see Stenflo (2003a,b, 2004, 2006).
The second solar spectrum has many polarized lines, as shown by atlases, but many transitions depolarize the continuum. Line depressions below the continuum polarization level look like absorption lines of the intensity spectrum, while lines more polarized than the continuum look like emission lines. Stenflo (2004) noticed from observations made at two different periods (1995, close to the minimum activity, and 2000, near maximum) that the proportion of absorption-like and emission-like transitions varies, which suggests the influence of hidden (weak and unresolved) magnetic fields, through the Hanle depolarization mechanism (less polarization at the solar maximum in the presence of stronger magnetics fields). Hence, the analysis of long term variations of the second solar spectrum could be a powerful tool to follow the magnetism along the solar cycle.
We describe the new Nematic Liquid Crystal (NLC) polarimeter operating at the Pic du Midi LJR since April 2004, following a previous version (installed in 2003) described by Malherbe et al. (2004), which used another technology (Ferroelectric Liquid Crystal, FLC). We present the first observations obtained with this new instrument in various lines, with spatial resolution, in spectroscopic mode, or in imagery mode through narrow band filters, and compare our results to ones in the literature.
The experiment setup is described in detail in the appendices or on line at the Web page http://www.lesia.obspm.fr/~malherbe/papers/index.html. We give here a short summary.
The Pic du Midi LJR is a 50 cm aperture refractor (f = 6.5 m)
supported by an equatorial mount. The beam has axial
symmetry along the optical axis. Polarization
analysis is achieved before transmission to the spectrograph
by a flat mirror at 45
(Fig. 1), therefore
instrumental polarization is minimized. The spatial resolving power
is 0.3
.
The primary image is
magnified 10 times at the secondary focus F2 (f = 65 m) where the slit
of the spectrograph is located. We used a new prototype of a liquid crystal polarimeter between focus F1 and F2. It was used for the first time in April 2004. The polarimeter
has the following elements (Fig. 1):
We used for this work a simplified version of the
polarimeter, running only with one retarder ( = 0) so that
the output signal becomes
.
Stokes parameters
are obtained
sequentially
with
.
This property was used by
Roudier et al. (2006) for high resolution Zeeman magnetometry on the disk. In the present paper, we are interested only in
which were derived from
this formula with
.
Since measurements of
(where P is any Stokes parameter) are not simultaneous, our polarimeter can operate with a good efficiency in two particular domains:
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Figure 1: The optical setup between the primary focus F1 and the secondary focus F2 in spectroscopic mode (the 50 cm refractor is located on the optical axis at left). |
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We used the 8 m Littrow Echelle spectrograph
(Mouradian et al. 1980). The interference order is isolated by
10 nm bandpass filters (order 10 at 590 nm for NaD1, 13 at 455 nm for SrI and BaII,
14 at 420 nm for CaI). For the previous orders, the
dispersion lies respectively around 55 mm, 72 mm and 77 mm per nanometer.
The spectrum obtained at the focus of the spectrograph (60 mm
90 mm) is
reduced about 10 times on the CCD camera, so that the
spatial pixel size on the detector is 0.2
along the slit direction and the
spectral pixel size is 1.1 pm
(in the blue part of the spectrum). The exposure time was typically 50 ms during our runs around 450 nm at
(limb distance of 10
)
with the 0.6
140
slit.
Since a pair of images
has a photometric precision of
about 10-2, one hour of observation at the limb at 450 nm allows to reach
a precision of roughly 10-4. It is even possible to measure
weaker polarization signals by integrating in the solar direction
along the slit. In the case of total integration, a single pair of
images
will deliver a precision better than 10-3,
and after one hour of observations, a ratio better than 10-5 can be achieved.
Flat field observations are made around disk center in the quiet sun where
linear polarization signals should vanish. It is essential to precisely determine
the transmission of the instrument for the two states of
polarization. The zero level is a function of wavelength in the spectral range
(typical Q/I slope of
about 5
10-4 per nm which is corrected in data processing).
In the following, full sets of data consisting of thousands of
images of the same region at the limb, plus a series of flat field images
taken at disk center in both polarizations and terminated by dark current images, are analysed.
The stability of polarization measurements may be affected by
several effects, such as solar, but also seeing and instrumental
variations. It was noticed in the past that the image quality
deteriorates when the main objective holder is heated by the sun.
For that reason, P. Mehltretter suggested to protect the holder by
a reflective ring with a clear aperture corresponding to the
diameter of the lens. We discovered recently that instrumental
depolarization (up to -25%) occurs without the ring two hours
before and after the meridian. In order to check the stabilizing
effect of the ring, we observed continuously, on May 10, 2005, the
linear polarization of SrI 460.7 nm at the South pole with the
slit of the spectrograph (0.6
140
)
parallel to
the solar limb, at about 10
.
Results averaged
along the slit are displayed in Fig. 2. While the
intensity curve shows the variation of solar irradiance during
observations, the polarization rate Q/I measured in the line core
lies around 0.8% to 0.9% with only small fluctuations (
), which are mainly due to variations of the limb distance
which can change within a few arcsec between each test, as we do
not have a precise guiding system. Thus, if some instrumental
depolarization remains, it is not easily detectable.
During the numerous test runs, we checked the effects of cirrus,
which are thin clouds of ice at high altitude in the troposphere
(6000-10 000 m), and other cirrus type clouds such as
cirrocumulus, which are denser. The depolarizing effect of cirrus
is well known and has been studied by atmospheric researchers (see
for instance Chen et al. 2002) in the following way: they measure
with a telescope the depolarization of the back- scattered light
coming from a linearly polarized laser beam (Lidar
depolarization). While the backscatter signal of linearly
polarized laser light by spherical particles (cloud droplets)
remains totally polarized, it is not the case when particles are
non- spherical (such as ice crystals, snow or dust particles,
aerosols). The classification of particle shapes is an application
of Lidar depolarization in ice clouds (Noel et al. 2002, 2004).
Here we checked related phenomena by measuring the depolarization
of the solar SrI 460.7 nm and BaII 455.4 nm (Fig. 3)
lines through cirrus or cirrocumulus of various optical thickness
(density) along the line of sight. This quantity was easily
determined using observations made a few minutes before or after
their passage (it is defined by the relation
,
where I0 and I are respectively the
intensity in the absence or presence of clouds). The two figures
show a strong depolarizing effect on the linear polarization of
solar lines (up to a factor of 2 for dense cirrus). The
depolarization mechanism is unclear: it may be due to the physical
nature of the clouds, but an easier explanation can be proposed.
Our experiment differs from Lidar measurements because the sun is
an extended source, mostly unpolarized. When observing through
clouds, an amount of scattered light which is not polarized could
be included, because large amounts of such light come from the
solar disk. Thus observing close to the limb, partially polarized
light (generated by scattering effects in the solar atmosphere at
the limb) could be mixed with unpolarized light (generated by
scattering effects in the clouds of unpolarized light of the
disk). In that case, the net result should be a decrease of the
polarization signal measured with a clear sky. We conclude that
clouds should be absolutely avoided during solar polarimetry
experiments.
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Figure 2:
Stability of the SrI 460.7 nm linear polarization.
Dotted line: polarization rate Q/I as a function of time measured at ![]() ![]() |
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Figure 3:
Depolarization of the SrI 460.7 nm line (crosses) and the BaII 455.4 nm line (stars)
by atmospheric cirrus as
a function of cloud optical density for ![]() |
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On May 15, 2004, we observed the linear polarization of the SrI 460.7 nm line at the South pole with the slit of the spectrograph
(0.6
140
)
parallel to the limb, at various
distances. For each distance (10
,
20
,
40
,
80
and 160
corresponding to
= 0.15, 0.2, 0.3,
0.4, 0.55), we obtained in a few minutes short series of 400 pairs
of spectra
,
which were integrated along the solar
direction to achieve a sensitivity smaller than 10-4 in the
line core. The corresponding polarization rates were found
respectively to be 1.0%, 0.8%, 0.6%, 0.4%, and 0.2%, as shown
in Fig. 4. We estimate the precision of the limb
distance at
1
,
due to seeing fluctuations and some
mechanical instability of the refractor. The zero polarization level
is fixed by the flat field at disk center.
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Figure 4:
Q/I for the SrI 460.7 nm line at various distances of the limb (10
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On May 14, 2004, we also observed at the West limb with the slit
of the spectrograph perpendicular to the limb. With this
orientation of the slit, it is not possible to observe at the
poles, because we cannot rotate the image of the sun at the focus
of the refractor. We checked for the absence of active regions.
A long sequence of 6400 pairs of images
was obtained
over one hour, to reach a precision of 2
10-4 in the line
core for each pixel along the slit, and better in the continuum.
Fluctuations of the limb positions were tracked and corrected by
the software. Figure 5 shows the map
(where
is the wavelength and x the spatial coordinate)
obtained after the processing of the 12 800 spectra. The limb is at
the top of the figure. Polarization fringes are not visible
because the polarization signal is high and increases towards the
limb, both in the continuum and in the line core.
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Figure 5:
I ( left) and Q/I ( right) images of SrI 460.7 nm.
Abscissa: the wavelength (bandwidth of 0.35 nm, pixel size of 1.1 pm); ordinates: the solar direction x along the slit (field of view 140
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Figure 6:
Q/I variations in the SrI 460.7 nm line centre (solid line) and in the continuum
at 460.84 nm (dotted line) as a function
of limb distance in arcsec (values of ![]() |
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Figure 7:
Q/I for the SrI 460.7 nm line at various distances of the limb (5
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From Fig. 5, we derived the polarization profile in
the line core and in the continuum as a function of limb distance,
as presented in Fig. 6, where the spatial pixel was
brought from 0.2
to 1.0
in order to improve the
signal to noise ratio roughly to 104. The polarization rate
at the limb was found in the line core to be 1.8% (respectively
0.5% in the continuum). The error bar due to image motion, such
as intensity fluctuations
which correspond to
seeing induced cross talk, increases dramatically from a few 0.01% to 0.2% at the limb where intensity vanishes. We suspect
from Fig. 6 an offset of the zero polarization level
of about 0.05% (visible on the continuum), which means that the
zero established by the flat field has slightly shifted in time
during the observing run. Up to now, determinations of Q/I have
been obtained mainly for some discrete distances of the limb
(Stenflo et al. 1997; Faurobert et al. 2001; Bommier et al. 2005). Faurobert et al. (2001) obtained results that are
consistent with the presence of a weak turbulent magnetic field
between 20 and 30 G, while Bommier et al. (2005) deduced 46 G from
their observations. Sanchez Almeida (2005) showed that SrI 460.7 nm depolarization measurements indicate that 40% only of the quiet sun could be filled by magnetic fields weaker than 60 G, the
remaining part being above the quiet sun. The spatial variations
of the polarization signal shown in Fig. 6 over 120
were interpreted by Derouich et al. (2006), who determined vertical variations of the turbulent magnetic field in the sun's photosphere.
From Fig. 5, we also derived profiles of
(see Fig. 7) for various distances
(5
,
10
,
20
and 80
corresponding to
= 0.1, 0.15, 0.2 and 0.4), which corroborate the results of
Fig. 4 (except for the continuum). Our results at 5
from the limb (Q/I = 1.2%) are in good agreement with
previous measurements. Gandorfer (2002) found a polarization peak
of 1.2% at line center from observations made in 2001. Bommier
& Molodij (2002) obtained 1.15%, and Faurobert et al. (2001)
0.95% from observations both made with THEMIS in 2000. Stenflo et al. (1997) reported 1.5%. Other observations have been compiled
by Trujillo Bueno et al. (2004). But all authors observed near the
poles, so that the comparison with us is not straightforward (West
limb), with different instruments and methods. We could expect the
polarization rate to vary with the solar cycle; it could be lower
near the maximum of the cycle, because the magnetic fields are
stronger. But we think that the heterogeneity of measurements does
not allow anyone to conclude firmly about variations along the 11 years cycle. Observing with the slit orthogonal to the limb has
the advantage of allowing a precise determination (1
)
of
the distance to the limb. We therefore suggest systematic
observations along the solar cycle with the same setup, to study
the temporal variation of the polarization of SrI 460.7 nm in quiet regions.
We investigated also the spatial variation of the polarization of
the SrI 460.7 nm line at constant limb distance. According to
Trujillo Bueno et al. (2004), the turbulent magnetic field in the
granular regions could be much weaker than what is required to
explain the depolarization in the SrI line. Hence, the
intergranular regions could exhibit relatively strong fields
capable of producing most of the SrI depolarization. For that
reason, it is important to observe at constant limb distance with
good spatial resolution in order to distinguish bright and dark
features, such as granules or intergranules. Such observations
require rare seeing conditions, with a thin slit (0.3
).
But, as the contrast decreases towards the limb, and as the
perspective effect increases, it is not possible to observe as
close to the limb as is usually done. We started this program on
September 17, 2004, at medium resolution with a slit of
0.6
at 40
from the limb (
= 0.3), with a short
exposure time (50 ms). We decided to class the large amount (300 000) of observed spectra
as a function of the continuum intensity as seen in the vicinity of the SrI line core,
the darkest regions corresponding to intergranular lanes and the
brightest to the granules. As contrasts remain low, even at this
limb distance, the data processing has to treat very carefully
intensity fluctuations that may arise from the sky and atmospheric
transmission variations. For this purpose, a light curve was drawn
and used to correct each spectrum of the sequence in order to keep
the same photometry. Individual spectra were classified into 20 intervals in increasing order of continuum intensity, then summed
to improve the signal to noise ratio. Mean Stokes
and
were computed, and the linear polarization rate
was derived for each interval of continuum
intensity. The full range of available intensities varies from 0.94 to 1.06 times the average intensity, so that the amplitude of
each interval corresponds to 0.006 times the mean continuum
intensity. Inside each interval, the number of I+Q and I-Q profiles was kept identical in order to combine consecutive pairs
of polarizations, but it changes from one interval to the next (as
shown by Fig. 8, histogram of intensities). The
polarization ratio Q/I in the line core increases with the
continuum intensity (Fig. 8), suggesting that the
depolarization due to the Hanle effect could be higher in dark
regions (intergranules) than in bright regions (granules), which
could be the signature of higher magnetic fields in dark regions
(intergranules). At our knowledge, this observation is the first one, so that this preliminary result needs to be confirmed by new
observations at higher spatial resolution, with a thinner slit,
and at various distances from the limb.
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Figure 8: Polarization in the SrI 460.7 nm line as a function of the continuum intensity (arbitrary units). The dashed line is the histogram of intensities and represents the number of spectra of each interval (the peak corresponds to 30 000 spectra). The solid line is the Q/I ratio in the line core, while the dotted line is the Q/I ratio in the continuum. Values on the abscissa lie in the range 0.955 to 1.045 times the mean continuum value. |
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Observations of the BaII 455.4 nm line were performed with the
slit orthogonal to the limb on May 15, 2004. This line is of great
interest because the core is formed in the low chromosphere.
Observational diagnostics of the center to limb variation of the
polarization may be used to investigate the weak and turbulent
magnetic fields in the low chromosphere. Observations were made at
the West limb, and during one hour, 8000 pairs of images were recorded, in order to reach a precision of 2
10-4 in
the line core for each pixel along the slit, and better in the
continuum. Figure 9 shows the map
obtained after the processing of the 16 000 spectra which were
coaligned both in the spatial and the spectral directions. The
limb is at the top of the figure. A strong polarization in the low
chromosphere can be noticed in the line core, above the solar limb
defined by the continuum.
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Figure 9:
I ( left) and Q/I ( right) images of BaII 455.4 nm.
Abscissa: the wavelength (bandwidth of 0.35 nm, pixel size of 1.1 pm); ordinates: the solar direction x along the slit (field of view 140
![]() ![]() |
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From Fig. 9, we derived the polarization profile in
the line core and in the continuum as a function of limb distance,
as presented in Fig. 10, where the pixel size is
magnified to 1.0
in order to improve the signal to noise
ratio roughly to 104. The polarization rate in the line core
at the limb was found to be 1.1% (respectively 0.5% in the
continuum). The error bar due to image motion, such as intensity
fluctuations
,
increases drastically from a few 0.01% to 0.2% near the limb (where intensity vanishes). The polarization peaks of the line core and continuum are shifted by 2
to 3
(chromospheric line). The spatial
variations of the polarization will be used later to model the
vertical structure of the turbulent magnetic field in the low
chromosphere. From Fig. 9, we also derived profiles
of Q/I (see Fig. 11) for various limb distances (0
,
5
,
10
,
20
and 60
corresponding to
= 0.0, 0.1, 0.15, 0.2 and 0.35). The
polarization profile shows the same structure in the wings as
previously observed by Stenflo & Keller (1997): they attributed
the hyperfine structure to odd isotopes, whereas the central peak
is due to even isotopes. They measured polarization degrees of 1.2% at
= 0.1, which can be compared to ours (0.6%) and
other values of Bommier & Molodij (2000) and Gandorfer (2002),
who found respectively 0.55% and 0.8% in the line core.
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Figure 10:
Q/I variations in the BaII 455.4 nm line centre (solid line) and in the continuum
at 455.29 nm (dotted line) as a function
of limb distance in arcsec (values of ![]() ![]() ![]() |
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Figure 11:
Q/I for the BaII 455.4 nm line at various distances of the limb (0
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Observations of the CaI 422.7 nm line were performed with the slit
orthogonal to the limb on May 15, 2004. The core of this line is
formed in the chromosphere. Observations were made at the West
limb, and during 40 mn, 2400 pairs of images
were
recorded, in order to reach a precision of 2
10-4 in the
line core for each pixel along the slit. Figure 12 shows
the map
obtained after the processing of the 4800 spectra which were coaligned both in the spatial and the spectral
directions. The limb is at the top of the figure. The line core
and both wings show strong polarizations near the limb.
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Figure 12:
I ( left) and Q/I ( right) images of CaI 422.7 nm.
Abscissa: the wavelength (bandwidth of 0.35 nm, pixel size of 1.0 pm); ordinates: the solar
direction x along the slit (field of view 140
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From Fig. 12, we deduced the spatial variations of the
polarization in the line core and in the continuum as a function
of limb distance as shown in Fig. 13 where the pixel
size was brought from 0.2
to 1.0
to improve the
signal to noise ratio. The polarization rate near the limb was
found to be 1.8% in the line core, 3.3% and 2.6% respectively
in the blue and red wings, and 0.8% in the pseudo continuum at
422.92 nm. The error bar due to image motion increases strongly
from a few 0.01% to 0.2% at the limb. From Fig. 12,
we also derived profiles of
(see
Fig. 14) for various distances (0
,
5
,
10
,
20
and 80
corresponding to
= 0.0,
0.1, 0.15, 0.2, and 0.4). At
= 0.1, Gandorfer (2002) found
near the South pole 2.2% in the red wing and a comparable value (2.1%) in the core; in our data, the polarization in the core at
= 0.1 (1.2%) is less than in the red wing (1.8%). Center
to limb variation of the polarization of CaI 422.7 nm has been
studied by Bianda et al. (1998, 2003); they obtained similar
polarization behaviors with highly fluctuating polarization
degrees in the Doppler core (in the range 1.8%-3.6% at
=
0.1 in quiet polar regions, down to 0.6% in an active region; in
contrast the wings remained stable), and interpreted the spatial
variation of this feature as the result of Hanle depolarization
due to the presence of magnetic fields of 5-15 G in the low to
mid chromosphere. Bianda et al. (1999) measured Stokes Q and U and
showed that the Hanle effect appears to be confined to the line
core. But Bianda et al. (2003) discovered in some cases that
depolarization and rotation of the plane of polarization may also
occur in the wings. Holzreuter et al. (2005) and Fluri et al.
(2006) suggested that the triplet peak structure of CaI 422.7 nm
is mainly due to radiative transfer effects with partial frequency
redistribution (PRD) effects.
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Figure 13:
Q/I variations in the CaI 422.7 nm line centre (solid line), in the
blue wing at 422.62 nm (dotted line), in the red wing at
422.72 nm (dashed line) and in the continuum at 422.92 nm (dashed dotted line) as a function
of limb distance in arcsec (values of ![]() ![]() ![]() ![]() |
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Figure 14:
Q/I for the CaI 422.7 nm line at various distances of the limb (0
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The polarization of the continuum can be studied in spectroscopic
mode, as a function of wavelength, but it can also be studied in
imagery mode, through narrow (0.3 nm) interference filters, as
done for instance by Wiehr & Bianda (2003), or by Stenflo et al.
(2002), with a very selective (0.02 nm) Universal Birefringent
Filter. This has the advantage, compared to spectroscopy, of
allowing high spatial resolution polarimetry
in a 2D field of view; the disadvantage is that the polarization is integrated in wavelength
over the transmission function of the filter. Nevertheless, with
narrow filters of 1 nm or less, precise measurements of the
continuum polarization can be achieved, especially towards the red
part of the spectrum. In our case, the filters are wide and
comparable to those used by Leroy (1972) with 10 nm of full width
at half maximum; we observed the blue part of the spectrum, so
that many spectral lines are integrated and affect the results.
However, these measurements can be related to the values obtained
from spectroscopy and show the capability of our instrument to
measure the continuum polarization. The instrumental setup of the
polarimeter is identical to the one used in spectroscopy. The
field of view is 100
120
with a pixel size of 0.1
,
which was reduced to 0.2
by binning. The
exposure time through 10 nm interference filters is of the order
of 5 ms with a neutral density between 1 and 2, according to the
spectral range. This means that exposure times would continue to
be very short (10 ms) even with narrow filters (less than 1 nm).
For each observation, 2400 pairs of images
were recorded
on October 26, 2005, near the West limb, in a quiet area, for
about 15 mn, together with a flat field sequence of 800 pairs of
images
at disk center. For each individual image, the
flat field was successfully used to correct pixel response over
the 2D field of view, and also to correct transmission differences
between the two states of polarization. It also provided the zero polarization level. The limb position was tracked in the x direction and the curvature of the limb was corrected. Image
summation over the whole sequence and integration along the y axis
were performed in order to increase the signal to noise ratio. Figure 15 shows the final image got in the
continuum at 460 nm around the SrI 460.7 nm line. This Q/I image
clearly shows the variation of the continuum polarization in the
vicinity of the limb.
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Figure 15:
Intensity I(x,y) ( left) and polarization Q/I(x,y) images ( right) of the limb through an interference filter of 10 nm bandwidth centered at 460 nm, the field of view is about 100
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On October 26, 2005, we observed about 20 different spectral
ranges from 390 to 670 nm, but we present only here the results
obtained in the continuum of spectral lines which are discussed in
this paper. Figure 16 shows the polarization
ratio Q/I integrated in the y direction (parallel to the limb)
together with the intensity curve that gives the limb position
(inflexion point). The error bar represents intensity fluctuations (
)
due to image motion corresponding to seeing-induced cross talk. Of course, values obtained closer than 1
from the limb have to be regarded with caution. The
polarization degree Q/I reaches 0.35% at the limb and 0.16% at
.
The measure of the continuum polarization is very
difficult at the limb, for at least two reasons: the polarization
is much less than in the core of polarized spectral lines, and the
intensity drops at the limb and is affected by atmospheric
turbulence. Thus, the error bar increases towards 0.1% at the
limb (located at x = 16
), so that below the inflexion
point, the result is meaningless. However, it remains in agreement
with the values obtained in the neighborhood of SrI 460.7 nm in
spectroscopic mode (Q/I = 0.5% at the limb and Q/I = 0.2% at
,
over a narrow bandwidth of 0.02 nm, see Fig. 6).
![]() |
Figure 16:
Polarization rate Q/I of the continuum through an interference
filter of 10 nm bandwidth centered at 460 nm, as a function of limb
distance in arcsec (values of ![]() |
Open with DEXTER |
Figure 17 shows results around 455 nm. The
polarization degree Q/I reaches 0.35% at the limb and 0.18% at
,
which is in fairly good agreement with the
determination using the previous filter at 460 nm. At the limb,
located at x = 18
,
the error barr is 0.1%. As this
spectral range contains the BaII 455.4 nm line, we can compare to
the results of Fig. 10 which give Q/I = 0.5% at the
limb and Q/I = 0.2% at
over a bandwidth of 0.02 nm.
We found through the wide 10 nm bandwidth filters polarization
degrees smaller than those obtained by spectroscopic means (0.45%
if the offset suspected previously is subtracted), or through
narrow filters, as reported by Wiehr & Bianda (2003): they got
0.45% close to the limb (0.3
or
= 0.02) with narrow
(0.3 nm) filters at 450 nm, in agreement with the theoretical
polarization continuum model of Fluri & Stenflo (1999). We
suggest that our underestimation could be explained by the
presence, in the blue part of the spectrum, of numerous spectral
lines that depolarize the continuum, as discussed by Fluri &
Stenflo (2003). The polarization of the continuum was also
modelled by Stenflo (2005) using data from the second solar
spectrum atlas (Ganddorfer 2002). At
,
the model gives
at 450 nm values around 0.1%, somewhat smaller than the ones
obtained by us and by Wiehr & Bianda (2003).
![]() |
Figure 17:
Polarization rate Q/I of the continuum through an interference
filter of 10 nm bandwidth centered at 455 nm, as a function of limb
distance in arcsec (values of ![]() |
Open with DEXTER |
Figure 18 shows results around 420 nm. The
polarization degree Q/I reaches 0.53% near the limb and 0.40% at
.
At the limb, located at x = 13
,
the error bar
is again 0.1%. As this spectral interval contains the CaI 422.7 nm line, we can compare the imagery data to the spectroscopic
results of Fig. 13 which give Q/I = 1% at the limb
and Q/I = 0.4% at
for the pseudo continuum at 422.92 nm. The atlas of Gandorfer gives in comparison 0.55% at
for the same wavelength. This is higher than values predicted
by Fluri & Stenflo (1999) or by Stenflo (2005) for the continuum
with respectively 0.25% and 0.20%. This discrepancy is easily
explainable: first, the polarization observed through the filter
is affected by the presence of depolarizing lines and the strong
polarized region around the CaI line; secondly, the spectroscopic
measure at 422.92 nm is overestimated because, at this wavelength,
we are still in the very broad wings of the CaI 422.7 nm line.
![]() |
Figure 18:
Polarization rate Q/I of the continuum through an interference
filter of 10 nm bandwidth centered at 420 nm, as a function of limb
distance in arcsec (values of ![]() |
Open with DEXTER |
Observations of the NaI D1 589.6 nm spectral line have been
reported by Stenflo & Keller (1997) and Stenflo et al. (2000a,b) as anomalous polarization, with a polarization peak in the Doppler core. They found with ZIMPOL a polarization rate around 0.1% at 5
from the limb. NaI D1 is theoretically
unpolarizable, unlike NaI D2 589.0 nm; quantum interference
between both transitions was investigated successfully to explain
the overall polarization pattern. Although it has been
demonstrated that fine and hyperfine structure (splitting due to
nuclear spin) in combination with optical pumping must play a role
in the scattering polarization in the sodium lines (Landi 1998; Casini & Manso Sainz 2005), the nature of the Na D1 line polarization still remains an enigma. Other anomalous
polarizations corresponding to D1 transitions of the same class
(
)
were also discovered by Stenflo et al. (2000a), as BaII 493.4 nm,
SiII 637.1 nm, AlI 669.8 nm, VI 6111.1 nm or LiI 670.8 nm.
We performed new observations of the weak polarization of NaI D1 589.6 nm on July 9, 2004 at 10
(
)
of the South
pole, with the slit (0.6
140
)
parallel to the
limb direction, and an exposure time of 20 ms. Several series of
1600 pairs of images
were obtained and we selected the
best one. The precision obtained in the line core, after
integration along the slit, was about 2.5
10-5. The result
is displayed in Fig. 19. A polarization peak in the
line core appears clearly (maximum 0.25%) and corroborates
previous results. Stenflo et al. (2000b) reported observations
showing that the polarization of the NaI D1 core may vary in the
range 0.1% to 0.25% in time and also according to the location
on the sun. Martinez Pillet et al. (2001) noticed also spatial
variations. In agreement with Stenflo et al. (2000a,b), the
polarization peak of Fig. 19 does not have the
characteristic antisymmetric shape of scattering polarization,
which suggests, according to Trujillo Bueno et al. (2002) the
presence of weak magnetic fields. On the contrary, Bommier &
Molodij (2002) found at THEMIS a pure antisymmetric polarization
shape with respect to the line center with Q/I smaller than 0.1%.
![]() |
Figure 19: Q/I profile of the NaI D1 589.6 nm line as a function of wavelength (in nm), together with the intensity profile (arbitrary units). Polarization fringes are partly corrected. |
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Figure 19 shows that observations are slightly affected
by polarization fringes. They are very hard to remove because the
pattern appearing on flat field images at disk center is not the
same, so that fringes do not match. It was only possible to
attenuate them. We averaged the ratio
along the
solar direction for observations and flat field, in order to
detect the shift of the fringe network by cross correlation. Then
the fringe pattern of the flat field was subtracted from the limb
data. We succeeded in attenuating fringes by a factor of two.
We have presented the new polarimetric instrumentation operating
since 2004 at the Lunette Jean Rösch, Pic du Midi, in
spectroscopic or imagery mode, allowing one to sequentially
measure the whole set of Stokes parameters using Nematic Liquid
Crystal cells. The present version of this polarimeter has still
some limitations which will be removed in the future. In
particular, polarization signals
(
P = Q, U, V) are
analyzed sequentially with a linear polarizer. A new analyser is
under development, consisting of a birefringent linear polarizing
beam splitter which will allow one to simultaneously observe both
signals, so that
will be focused at the same time on the
CCD detector. As a consequence, the field of view will be reduced
by a factor of two, from 140
to 70
along the sun.
This improvement is of special importance for the polarimetry of
specific solar structures observed on the disk (active regions,
flux tubes) or at the limb (spicules, prominences) which require
perfect coalignment of both signals, in order to eliminate seeing
induced polarimetric cross talk. But observations of the second
solar spectrum do not suffer from this default, because of
statistical effects due to the large number (thousands) of spectra
required to achieve a high enough signal to noise ratio. Beam
exchange will be available with the new device especially for the
measurement of weak polarization signals.
Observations of the second solar spectrum have been undertaken
with the new polarimeter. We present observations of the linear
polarization Q/I with a spatial resolution of SrI 460.7 nm, BaII 455.4 nm and CaI 422.7 nm lines and show spatial variations of the
polarization through the limb. The polarization rate at the limb
reaches 1.8% and 1.2% in the core of SrI and BaII, and more than 2% in the core (up to 3% in the wings) of CaI. Such results
concerning the variation of the linear polarization as a function
of limb distance are of interest in probing the variation of weak
turbulent magnetic fields as a function of depth in the solar
atmosphere. Spatial variations of SrI 460.7 nm were investigated
at 40
from the limb, and preliminary results show that
dark regions (intergranules) could be less polarized than bright
regions (granules), suggesting stronger magnetic fields in
intergranular lanes. Continuum polarization was measured in the
vicinity of lines, and also in imagery mode, through wide (10 nm)
interference filters. Finally, results of observations of weak
polarizations are illustrated by the NaI D1 line with the
confirmation of a symmetric polarization peak. These results have
been obtained in general in poor seeing conditions; some aspects
of the spatial variations of the second solar spectrum, in
particular the distribution of the polarization in the
photospheric and chromospheric network, require new observations
at higher spatial resolution, together with the determination of
the Stokes U parameter. This will be the topic of further work.
Acknowledgements
This paper is the result of two years of tests and observing campaigns. We thank the anonymous referee who provided helpful and detailed comments and suggestions. We are indebted to Ch. Coutard, engineer in optics, for his help in the optical setup of the experiment and his support in observations. The spectrograph and the MSDP device were designed by Z. Mouradian and by P. Mein under the auspices of Observatoire de Paris and CNRS. This work was supported by Observatoire de Paris, Observatoire Midi Pyrénées, CNRS (UMR 8109 and UMR 5572) and the Programme National Soleil Terre (PNST). Special thanks are due to the Pic du Midi Observatory staff for their technical assistance during our numerous stays.
The Pic du Midi LJR is a 50 cm aperture refractor (focal length of
6.45 m for = 550 nm at the primary focus F1) on an equatorial mount. The beam has an axial symmetry along the optical axis. Polarization analysis is achieved before transmission to the
spectrograph by a flat mirror at 45
(Fig. A.1), therefore instrumental
polarization is minimized. The spatial resolving power (including
the refractor and the spectrograph) is 0.3
in the yellow
part of the spectrum. The primary image is magnified 10 times at
the secondary focus F2 where the slit of the spectrograph is
located, according to the magnification lens, providing an equivalent focal length of 65 m so that the spectrograph operates
at f/130. We used a new prototype of a liquid crystal polarimeter
between focus F1 and F2. It was used for the first time in April 2004 in a simplified version and upgraded to the full Stokes version in September 2004.
![]() |
Figure A.1: The optical setup between the primary focus F1 and the secondary focus F2 in spectroscopic mode (the 50 cm refractor is located on the optical axis at left). |
The polarimeter receives white light and has the following elements (Fig. A.1):
![]() |
Figure A.2: The two variable retarders (at left) and the magnifying lens (at right) in the beam near focus F1 with wires for temperature control and modulation. |
The signal S provided by the polarimeter with two NLC is given by:
We use for observations which do not require the full Stokes
configuration a simplified version of the polarimeter, running only
with one retarder (no possible U determination). In such a configuration (
is permanently set to zero), the
polarimeter allows in practice modulation from zero to three quarter
waves, providing analysis either of the circular or linear
polarization of light. Hence, Stokes parameters
are
obtained sequentially from the output signal:
Since measurements of
(where P is any Stokes parameter) are not simultaneous,
our polarimeter can operate with a good efficiency in two particular domains:
We used the 8 m Littrow Echelle spectrograph
(Fig. A.4) built by Paris Observatory at the LJR twenty years ago and modified later for 2D spectro imagery (MSDP). The dispersive element is a grating (316 rules/mm, blaze angle 63$^$26)
that provides a typical dispersion of 50 mm per nm at
the focus of the spectrograph. The interference order is isolated
by filters of typically 10 nm bandwidth. The spectrum obtained at
the focus of the spectrograph is reduced to form on a CCD camera
from LaVision (Germany) with temperature control (Peltier cooling
at -10
C). This is a shutterless interline scan camera using
a detector with microlenses manufactured by Sony (1376
1040,
square pixels). The spatial pixel size on the CCD is
0.2
along the slit direction and the spectral pixel size
around 1.1 pm (in the blue part of the spectrum) in our setup.
Each pixel can accumulate up to 20 000 electrons corresponding to
a dynamic of 12 bits (readout noise of 4-5 electrons, gain of 4 electrons per analog digital unit). In general, we work in the
continuum at 0.8 times the saturation level giving approximately a signal to noise ratio of 120, corresponding to a photometric
accuracy of 0.8
10-2. In the core of the lines (smaller
number of photons), this precision can drop to about 1.6
10-2. The exposure time is typically 50 ms during our runs around 450 nm at
(limb distance of 10
)
with
the 0.6
slit.
Our polarimetric observations consist of shooting sequentially as
fast as possible pairs of images
(typically 700 pixels
in the solar direction x 300 pixels in the spectral direction).
The polarimeter is able to run at 40 Hz, but in practice we are
limited by exposure times and by the readout speed of our CCD camera and data acquisition system, so that the maximum speed is
at best 10 Hz around 450 nm, including polarimetric modulation.
Since a pair of images
has a photometric precision of
about 10-2, one hour of observation at the limb at 450 nm
allows us to reach roughly 10-4 with the average throughput
of 5 images/s. It is even possible to attain weaker polarization
signals by integrating partially or totally in the solar direction
along the slit (700 pixels). In the case of total integration, a single pair of images
will deliver a precision better than 10-3, and after one hour of observations, a ratio better
than 10-5 can be achieved.
Flat field observations are made around disk center in the quiet
sun where linear polarization signals should vanish. But good flat
fielding is a difficult challenge at the LJR because the
spectrograph is attached to the refractor (in equatorial mount)
and moves with time, producing very small but permanent mechanical
shifts. For that reason, the spectral line has to be precisely
tracked by the software at sub pixel precision in the direction of
dispersion. For observations on the disk, the transversalium is
followed in the direction of the slit, while for observations with
the slit perpendicular to the limb, the position of the limb
itself is detected by the software with about 1
accuracy,
depending on seeing. The flat field is consequently never done
exactly in the same conditions than the observing run. In
particular, polarization fringes cannot be properly corrected by
the flat field procedure. They are not important for polarizations
in the range 10-3 to 10-2 but have to be considered
carefully for polarizations of 10-4 or smaller. We have two kinds of fringes: filter fringes (mainly due to the interference
filter) which have a level of about 1% to 2% of the continuum
and vanish in the difference between two consecutive states of polarization, and polarization
fringes (due to the variable retarders), which are more than 100 times fainter (0.01% of the
continuum) and which appear only after a long time of integration in the
difference between alternate polarizations. Such fringes are hard to treat, because the
residual pattern generally shifts slowly during the observing run and is comparable to
weak solar polarizations signals (10-4). Flat fielding is very useful to precisely determine
the transmission of the instrument for the two states of polarization
(a difference of about 0.2% is typical, depending on the line, because the transmission
of the NLC varies slightly with retardance). We make the assumption that the polarization
rate is null at disk center in the quiet sun, and determine the zero level of the
polarization signal from the flat field as a function of wavelength
(the retardance in the observed spectral range varies faintly with wavelength and
consequently induces a Q/I slope of about 5
10-4 per nm which is easily corrected
by a linear adjustment).
The stability of polarization measurements may be affected by several effects, such as solar, but also seeing and instrumental variations. It was noticed in the past that the image quality deteriorates when the main objective holder is heated by the sun. For that reason, P. Mehltretter suggested to protect the holder with a reflective ring with clear aperture corresponding exactly to the diameter of the lens (Fig. A.5). We discovered that instrumental depolarization (up to -25%) occurs without the ring two hours before and after the meridian. With the ring, we measured only small fluctuations which are mainly due to variations of the limb distance which can move within a few arcsec between each test, as we do not have a precise guiding system. In conclusion, if some instrumental depolarization remains, it is not easily detectable.
The instrumental setup is presented in Fig. B.1. The
polarimetry system is identical to the one used in spectroscopy,
but the magnification is smaller (2), so that we work at f/30
instead of f/130 in spectro polarimetry. The field of view is
100
120
with a pixel size of 0.1
.
The
detector is installed on the optical rail, at the location of the
injection mirror to the spectrograph which is removed for the
circumstance.
![]() |
Figure B.1: The optical setup between the primary focus F1 and the secondary focus F2 in imagery mode (the 50 cm refractor is located on the optical axis at left). |
From a technical point of view, we know that the present version
of our polarimeter has still some limitations which will be
removed in the future. In particular, polarization signals
(P = Q, U, V) are observed sequentially because the analyser is
a simple (high quality) dichroic linear polarizer. A new device is
under development to replace it (Fig. C.1),
consisting of a birefringent linear polarizing beam splitter
shifter which will allow one to observe simultaneously both
signals, so that
will be focused at the same time on the
CCD detector. As a consequence, the field of view will be reduced
by a factor of two, from 140
to 70
along the sun.
The beam splitter shifter will be tested by the end of 2006 and
will be located at focus F2 (Fig. C.2) just
after the entrance slit of the spectrograph. This improvement is
of special importance for the polarimetry of specific solar
structures observed on the disk (active regions, flux tubes) or at
the limb (spicules, prominences) which require perfect coalignment
of both signals, in order to eliminate seeing induced polarimetric
cross talk. But observations of the second solar spectrum do not
suffer from this default, because of statistical effects due to
the large number (thousands) of spectra required to achieve a
convenient signal to noise ratio. Beam exchange will be available
with the new beam splitter, especially for the measurement of weak
polarization signals.
![]() |
Figure C.2: The experiment setup in spectroscopic mode with the polarizing beam splitter shifter (end 2006). |