Draft version June 8, 2021
Preprint typeset using LATEX style emulateapj v. 08/22/09
SPECTROPOLARIMETRIC OBSERVATIONS OF THE CA II 8498 Å AND 8542 Å LINES IN THE QUIET SUN
A. Pietarila
, H. Socas-Navarro
High Altitude Observatory, National Center for Atmospheric Research2, 3080 Center Green, Boulder, CO 80301, USA
T. Bogdan
Space Environment Center, National Oceanic and Atmospheric Administration, 325 Broadway, Boulder, CO 80305, USA
Draft version June 8, 2021
ABSTRACT
The Ca II infrared triplet is one of the few magnetically sensitive chromospheric lines available for
ground-based observations. We present spectropolarimetric observations of the 8498 Å and 8542 Å
lines in a quiet Sun region near a decaying active region and compare the results with a simulation
of the lines in a high plasma-β regime. Cluster analysis of Stokes V profile pairs shows that the two
lines, despite arguably being formed fairly close, often do not have similar shapes. In the network, the
local magnetic topology is more important in determining the shapes of the Stokes V profiles than the
phase of the wave, contrary to what our simulations show. We also find that Stokes V asymmetries
are very common in the network, and the histograms of the observed amplitude and area asymmetries
differ significantly from the simulation. Both the network and internetwork show oscillatory behavior
in the Ca II lines. It is stronger in the network, where shocking waves, similar to those in the high-β
simulation, are seen and large self-reversals in the intensity profiles are common.
Subject headings: polarization, Sun: chromosphere, waves
1. INTRODUCTION
Our understanding of solar magnetic fields
outside active regions has increased signifi-
cantly during the last years. This is due to
new and better instrumentation (e.g., THEMIS,
Paletou & Molodij 2001; VSM on SOLIS,
Keller & The Solis Team 2001; Swedish Solar Telescope,
Scharmer, Bjelksjo, Korhonen, Lindberg, & Petterson
2003; Solar Optical Telescope on Hinode, Shimizu
2004; and SPINOR, Socas-Navarro et al. 2006), better
diagnostic techniques (see for example Bellot Rubio
2006 for a review on inversion techniques) and advanced
numerical simulations (Stein & Nordlund 2006 and
references therein). A large portion of the work has
focused on photospheric magnetic fields. Only now we
are starting to have adequate tools for investigating
chromospheric magnetism in more detail. (For a review
of chromospheric magnetic fields see Lagg (2005)). This
is not surprising considering the numerous difficulties in
observing chromospheric magnetic fields, interpreting
the data, and performing realistic MHD simulations.
There are two different sets of lines that are often used
for chromospheric spectropolarimetry, the He I infrared
(IR) triplet at 10830 Å, and the Ca II IR triplet at
8500 Å. Both line sets have their advantages and dis-
advantages. The He I lines are formed over a relatively
thin layer, and therefore observations can be inverted us-
ing a simple Milne-Eddington model. The drawback is
that while the formation range is fairly narrow, the pre-
cise formation height remains uncertain, and the Milne-
Eddington inversions do not give any information on
1 Institute of Theoretical Astrophysics, University of Oslo,
P.O.Box 1029 Blindern, N-0315 Oslo, Norway
2 The National Center for Atmospheric Research (NCAR) is
sponsored by the National Science Foundation.
the atmospheric gradients. The lines are also sensitive
to the Paschen-Back effect, which must be included in
the inversion code (Socas-Navarro et al. 2004). Further-
more, simulating the He I lines is difficult since coronal
irradiation has a non-negligible effect on their formation
(Andretta & Jones 1997). In contrast, the formation of
the Ca II IR lines is fairly well understood (Lites et al.
1982). The broad Ca II lines sample a large region of the
atmosphere, from the photosphere to the lower chromo-
sphere. However, the Ca II lines are formed in nonLTE,
making inversions considerably more cumbersome.
Several investigations using the Ca II IR lines have
studied intensity and velocity oscillations in the quiet
Sun (e.g. Lites et al. 1982; Deubner & Fleck 1990)
or, alternatively, magnetic fields in active regions (e.g.
Socas-Navarro et al. 2000a). In both cases the lines have
proven useful as diagnostics of the solar chromosphere.
In this paper we present results of spectropolarimetric
observations of two of the lines in an enhanced network
region. We have both spatial maps and time series data.
The observations show that the Ca II lines are formed in
a very interesting region, namely the region where the
atmosphere is transforming from a plasma dominated
(β >> 1) to a magnetic field dominated (β << 1) regime
in terms of dynamic force balance. Wave propagation
is clearly seen in the highly dynamic magnetic regions,
whereas the weakly magnetic internetwork is found to
be less variable. Interestingly, the two Ca II lines ex-
hibit significant differences even though in calculations
they are formed fairly close together. The importance of
gradients in the chromospheric network is clearly demon-
strated by the prevalence of asymmetric Stokes V profiles
in the data.
The paper is arranged as follows: in § 2 the data and
their reduction are addressed. Results of analyzing the
data using different approaches are presented in § 3. We
http://arxiv.org/abs/0704.0617v1
performed cluster analyses on the Stokes V profiles to
classify them and to describe spatial patterns seen in the
data. Statistics, such as profile amplitudes and asym-
metries, are presented. The time dependent behavior of
the lines in different network and internetwork regions
is also discussed. In § 4 the observations are compared
to simulations of the lines in a high plasma-β regime
(Pietarila et al. 2006, hereafter P06). Finally, in § 5 the
main results are summarized and discussed.
2. OBSERVATIONS AND DATA REDUCTION
The Spectro-Polarimeter for INfrared and Optical Re-
gions (SPINOR, Socas-Navarro et al. 2006) at the Dunn
Solar telescope, Sacramento Peak Observatory, was used
to observe two of the Ca II infrared triplet lines at 8498
Å and 8542 Å, as well as two photospheric Fe I lines at
8497 Å and 8538 Å. The setup included several other
lines but because of computer problems only data from
the two Ca lines which used the ASP TI TC245 cameras
were recorded fully. The data have 256 points in both
the wavelength and spatial position with a typical noise
level of 6 × 10−4 Ic (1 σ deviation from the mean) and
a spectral sampling of 25 mÅ. The pixel height corre-
sponds to ≈ 0.38 arcseconds on the solar surface along
the slit. We observed a quiet Sun region near disk center
at S17.3 W32.1 on May 19, 2005 at 14:14 UT. An MDI-
magnetogram of the region is shown in Figure 1. The
slit was positioned in the vicinity of a decaying active re-
gion, AR10763, but avoided flux concentrations from the
active region (i.e., plages). A time series consisting of 99
time steps of short scans (3 slit positions), with a spacing
of 0.375 arcseconds each, was acquired during variable
seeing conditions. The cadence is ≈ 10 seconds (i.e., a
given slit position was repeated every 30 s). The time
series was followed by a 63 step raster centered around
the position where the slit was during the time series.
The raster step size was 0.375 arcseconds. Adaptive op-
tics (AO, Rimmele 2000) were used during the observ-
ing sequence but the compromised seeing conditions did
not allow for continuous locking onto granulation. This
caused the slit to jump occasionally, making the longest
period with a stationary slit in the time series 17 time
steps (8.5 min). The spatial resolution varied during the
sequences being at best less than an arc second, but on
average a factor of two worse.
Standard procedures for flat field and bias were used
for the data reduction. Instrumental polarization was re-
moved using the available calibration data, as explained
in Socas-Navarro et al. (2006). No absolute wavelength
calibration was attempted because no suitable telluric
lines are present. Instead a wavelength calibration using
spatial pixels devoid of magnetic field was done by fitting
the average spectrum to the Kitt Peak FTS-spectral at-
las (Neckel & Labs 1984). The FTS atlas was also used
to find the normalization factor for the intensities to the
quiet Sun continuum intensities. Because of detector flat-
field residuals and prefilter shape, the continua in the raw
data from both detectors are tilted. The tilts were re-
moved a posteriori by subtracting a linear fit (y = a+bλ)
obtained by matching the continuum intensity levels to
those of the FTS atlas.
The data were analyzed using both the raster and time
series for statistical purposes. The period when the slit
was stationary on the solar disk was used to study the
time-dependent behavior of the lines. Because of the
short length of this period, we do not present any Fourier
analysis of the data. To make a classification of Stokes
V profile morphologies, we did cluster analyses based
on a Principal Component Analysis (PCA) in a similar
manner as the work of Sánchez Almeida & Lites (2000)
and Khomenko et al. (2003) for photospheric lines. We
computed amplitudes for Stokes I and V profiles. Be-
cause the Ca line intensity profiles often exhibit strong
self-reversals, no proxies for atmospheric velocities, such
as lines’ centers of gravity or bisectors, are adequate.
For those Stokes V profiles with amplitudes greater than
7 × 10−3 Ic, (i.e. ≥ 10σ), amplitude and area asymme-
tries were also calculated.
The amplitude asymmetry of a Stokes V profile is de-
fined by (Mart́ınez Pillet 1997):
ab − ar
ab + ar
, (1)
where ab and ar are the unsigned extrema of the blue
and red lobes of the Stokes V profile.
The area asymmetry of a Stokes V profile is defined by
(Mart́ınez Pillet 1997):
σA = s
V (λ)dλ
|V (λ)|dλ
, (2)
where s is the sign of the blue lobe. Because of the broad,
deep lines and large velocities (compared with the pho-
tosphere) present in the chromosphere, the choice of the
integration range for the area asymmetries is non-trivial
for the Ca lines. We followed the same procedure as
in P06. In the weak field regime the Stokes V profile
is proportional to dI/dλ (strictly true only in the ab-
sence of atmospheric velocity and magnetic gradients).
Inspection of the data showed that most of the observed
Stokes V profiles have roughly the same structures as
the dI/dλ profiles. The intensity in the blue wing (λ0)
of the line profile was matched with a point in the red
wing (λ1) with the same intensity. The signal-to-noise in
the intensity profiles is much higher than in the Stokes V
profiles and also the slope is much steeper. This makes
matching points with the same value more accurate in
the intensity than in the Stokes V profiles. The selec-
tion of a wavelength to start the integration range was
made by choosing a wavelength point that is far enough
from the line core so that self-reversals are not an issue.
In our data this point, λ1, is at 600 mÅ from reference
wavelength of line center. The same value was used in
Magnetograms made from the 63 step scan are shown
in Figure 2. The panels are in order of increasing for-
mation height: Fe I 8497 Å, Fe I 8538 Å, Ca II 8498 Å
and Ca II 8542 Å. The lower part of the slit was located
above a flux concentration along the enhanced network
and the upper part over an internetwork region with very
little magnetic activity. The network becomes wider and
more diffuse with increasing line formation height as de-
scribed by Giovanelli (1980). Not all magnetic flux seen
in the photosphere can be identified in the chromosphere
Fig. 1.— MDI magnetogram showing the position of the slit for the time series and the map (rectangular region). The observed region
was close to the decaying active region, AR10763.
and vice versa. However, interpreting the chromospheric
magnetograms is difficult due to the self-reversed features
in the cores of the Ca line Stokes V profiles.
3. RESULTS
In Figure 3, Stokes I and V spectra of the solar sur-
face under the slit are shown for both Ca II lines as well
as the two photospheric Fe I lines in the Ca lines’ wings
(marked by arrows). Since the Fe I 8497 Å line is blended
in the Ca line’s wing and the Fe I 8538 Å line is very close
to the edge of the detector, no quantitative analysis is
done for them. No signal above the noise was recorded
in Stokes Q and U so they will not be addressed in what
follows. Residual vertical fringing caused by the polar-
ization modulator is visible in the Stokes V images. We
chose not to try to remove the fringing since its’ ampli-
tude is of the same order of magnitude as the noise.
The network, present in the lower part of the slit, is
associated with less absorption in the intensity profiles.
Both Ca lines often show self reversals, which are usually
stronger on the blue side of the line than in the red. The
Stokes V profiles of both Ca lines have large, extended
wings. At times, the profiles may have both polarities
present on the blue side of the core but in almost all
cases the far blue wing of the profile has the same po-
larity (i.e., opposite sign) as the red wing. The Stokes
I and V profiles of the chromospheric lines look distinc-
tively different from the photospheric lines: the Ca lines
have more structure, they are wider and exhibit more
spatial variation than the photospheric Fe lines. Some
differences are seen between the two Ca lines: the 8542
Å line is slightly broader, has more structure in the spec-
Fig. 2.— Magnetograms of the map deduced by using the weak field method (Landi Degl’Innocenti 1992). The Stokes V signal is
measured in units of Gauss. Vertical lines show the position of slit during the time series. First panel: Fe I 8497 Å, second panel: Fe I8538
Å, third panel: Ca II 8498 Å, third panel: Ca II 8542 Å. Location on the solar disk: S32.1, W17.3. The orientation of the magnetograms
is 180 degrees from the MDI magnetogram in Figure 1. The plotted symbols (∗, ✸ and △) on the images show where the pixels discussed
later in the text are located.
tra and also stronger absorption than the 8498 Å line.
The internetwork region, present in the upper part of
the slit, is mostly devoid of Stokes V signal, and Stokes I
is more homogeneous than in the network. Self reversals
are usually not seen in the profiles. A small portion of
the internetwork region has structures in Stokes I that
are similar to those seen in the magnetic region: Stokes I
is brighter than in the surrounding areas and the profiles
show some self reversals. Closer inspection of the images
reveals a visible, albeit a very small amplitude, Stokes V
signal.
The spatial patterns of Stokes I and V amplitudes and
asymmetries in the two Ca lines (Figure 4) are fairly
similar to one another. The network is clearly visible in
the Stokes I and V amplitudes, though it is more diffuse
in the 8542 Å line. There is a structure in the upper
part of the map that is seen best in the 8498 Å intensity
image. Parts of this structure appear also in both lines’
Stokes V amplitude and asymmetry images. The edges
of the network have more asymmetric Stokes V profiles.
This is seen clearly in the 8542 Å amplitude asymmetry.
Photospheric velocities can be estimated from the lo-
cations of the iron lines’ intensity minima. Except for
a nearly constant offset caused by the convective down
flows in the network, the internetwork and network re-
gions have very similar spatial and temporal patterns.
3.1. Classification of the Stokes V profiles
To classify the shapes of the 8498 Å and 8542 Å Stokes
V profile pairs we used PCA, (Rees et al. 2000) and clus-
ter analysis. The cluster analyses were performed sepa-
rately for the map and the time series. Here we present
a summary of the PCA procedure and cluster analysis
for completeness.
With the PCA we are able to reduce the number of
parameters needed to describe a given profile. Each pro-
file, S(λj), j = 1, ..., Nλ (Nλ is the number of wavelength
points in the profile) is composed of a linear combination
of eigenvectors ei(λj), i = 1, ..., n:
S(λj) = Σ
i=1ciei(λj), (3)
where the ci are appropriate constants. The eigenvectors
and constants for a given set of profiles are obtained from
a singular value decomposition (SVD, Rees et al. 2000,
Socas-Navarro et al. 2001) and form an orthonormal ba-
sis with Nλ eigenvectors:
j=1ei(λj)ek(λj) = δik. (4)
Not all eigenvectors contain the critical information
needed to reproduce the profiles, some of the eigenvec-
tors carry information about the noise pattern. We can
therefore truncate the series expansion and use only a
small number of eigenvectors and corresponding coeffi-
cients to reproduce a given profile. The PCA guarantees
that when expansion of Eq. 3 is truncated at a given
order m, the amount of information in the lower orders
is maximized.
We performed the SVD for the two 8498 Å and 8542
Å Stokes V profiles separately. The resulting orthonor-
mal bases, and also the cluster analysis, depend on the
subset of profiles used to construct it. Because of this
we included all Stokes V profiles from pixels where the
8498 Å Stokes V amplitude is above 7 × 10−3Ic, alto-
gether 13671 profiles. Visual inspection of the eigenvec-
tors shows that the first 11 eigenvectors (approximately)
Fig. 3.— Dispersed images of the slit. The arrows mark the locations of the two photospheric iron lines and the horizontal lines in the
intensity images are the hairlines used to spatially coalign the two detectors. Wavelengths are measured from 8498 Å (left) and 8542 Å
(right).
contain relevant information about the actual shape of
the profiles whereas the remainder are associated with
the noise patterns.
The Stokes V profile pairs, now described with 11 × 2
coefficients corresponding to the 11 × 2 eigenvectors in-
stead of 102 (51 for each profile) wavelength points, were
organized into a predefined number of clusters. Before
doing this the vectors consisting of the 22 coefficients
were standardized, i.e., no information of the absolute
Stokes V amplitudes is left, only the relative amplitudes
of the 8498 Å and 8542 Å profiles. Based on the values
of the coefficients, 6 cluster centers were identified using
the k-means method (MacQueen 1967). It starts with k
random clusters, which through iterations are changed to
minimize the variability within a cluster and maximize
it between clusters. Each profile pair is then assigned
to the nearest cluster center in the 22-dimensional Eu-
clidean space. The choice of number of clusters used for
the cluster analysis is non-trivial. Since each data point
is described by 22 numbers we cannot visually distinguish
patterns in the spatial distribution of the points. Instead
the number of clusters was defined by trial and error, i.e.
so that each profile type in the time series or map is rep-
resented and each cluster is still clearly distinct from one
another. For each cluster a profile was constructed using
the eigenvectors and the averaged 2 × 11 coefficients of
all profiles belonging to that cluster.
Cluster analysis of the map shows the shapes of Stokes
V profiles in network regions with different magnetic
topologies, whereas the time series analysis describes how
a set of profiles from a certain magnetic topology changes
with time.
The results for the map are shown in Figure 5. Above
each profile is the percentage of all profiles belonging to
the cluster, the mean distance in the Euclidean space
Fig. 4.— Maps of the 8498 Å and 8542 Å lines’ Stokes I amplitudes, Stokes V amplitudes, area asymmetries and amplitude asymmetries
in the raster scan. The horizontal line seen in the amplitude images is a hairline used to spatially coalign the detectors. The vertical line
shows the position of the slit during the time series. Note that x-axis is stretched compared with y-axis.
of the profiles to the cluster center, and the standard
deviation of the mean. The smaller the distance to the
cluster center, the more compact the cluster is and the
better the cluster describes the profiles. The standard
deviation is proportional to the spread of the distances
in each cluster. In general, clusters with the least number
of profiles belonging to them have larger mean distances.
Three points can be deduced from the figure. First,
asymmetric profiles should be common. In fact, they ap-
pear to be more common than symmetric ones. Second,
even though the two Ca lines are formed fairly close to
one another (the 8498 Å line core optical depth is unity at
about 1 Mm and the 8542 Å 0.2 Mm higher up in the ra-
diation hydrodynamic simulations by Carlsson and Stein
1997), the 8498 Å and 8542 Å profiles in a given cluster
are often clearly different from one another. Third, in
all cluster profiles the far-red wings have the same polar-
ity as the far-blue wings, indicating that the lower parts
along the line-of-sight of the atmosphere, where the wings
are formed, are dominated by a single magnetic polarity.
The clusters differ from one another in several differ-
ent ways: the degree of asymmetry, and distinct relation-
ships between the 8498 Å and 8542 Å line profiles, rel-
ative amplitudes, etc. However, quantitative measures,
such as profile asymmetries, of the clusters do not nec-
essarily represent the members of a given cluster very
well. For example, the variation of Stokes V amplitude
asymmetries within a cluster is large and the mean is
not necessarily the same as that of the cluster profile.
The cluster analysis retrieves qualitative similarities and
gives a basis for morphological classification, rather than
representing quantitative similarities within the data. To
illustrate this point, Figure 6 displays histograms of the
clusters showing the Stokes V amplitudes and asymme-
tries for all profiles belonging to a given cluster. Shown
in Figure 7 is the spatial distribution of the clusters. The
smallest network patches often consist of only cluster 1
and cluster 2 profiles. The middle of the largest network
patch is a mixture of different clusters.
In most cases, the profiles at the edges of the network
patches belong to cluster 1. This is the most common
cluster consisting of 35.6 % of all the profile pairs in
the map. The cluster 1 profiles are asymmetric, 8542
Å more so than 8498 Å, and they also have opposite
signs of amplitude and area asymmetries. The amplitude
histograms of profiles belonging to this cluster show that
they have in general low amplitudes, as one might expect
from profiles located at the edges of the network. The
large amplitude asymmetry in the 8542 Å cluster profile
is not seen in the observed profiles. In fact, only very few
profiles exhibit such large asymmetries and there is only a
slight tendency of the profiles having more often negative
than positive amplitude asymmetries. The cluster area
asymmetries are in better agreement with the observed
profiles belonging to this cluster.
Regions of cluster 2 profiles are often located adjacent
to patches of cluster 1 profiles. The cluster 2 profiles
account for 20.0 % of all profile pairs in the map. The
cluster profiles are fairly antisymmetric. This is seen in
the observed profiles as well: the asymmetry histograms
tend to be narrow and only slightly offset from zero. The
relative amplitudes of the two cluster profiles are very
different: the 8498 Å amplitude is a factor 3 larger. The
disproportionality is not as large in the observed profiles
though the amplitude histograms show that in general
8498 Å has a larger amplitude than 8542 Å. The range of
observed amplitudes is considerably larger than in cluster
Of the profile pairs in the map 14.1 % belong to cluster
3. Also, these profiles are often found in regions close to
the network edges by the patches of cluster 1 profiles.
Both cluster profiles have multiple lobes and are asym-
metric, 8498 Å more in amplitude and 8542 Å in area.
This is also seen in the histograms of the observed asym-
Fig. 5.— Results of cluster analysis of the Stokes V profile pairs in the map. Line on left is 8498 Å and on right 8542 Å. Shown are the
percentages of profile pairs belonging to each cluster, and the mean distance and its standard deviation of the profiles to the cluster center.
metries. There is a strong emission feature on the blue
side of the line in the 8498 Å cluster profile. It is weaker
in the 8542 Å profile. The histograms for cluster 3 are
nearly identical to those of cluster 1. This illustrates how
cluster analysis based on PCA is captures the qualitative
differences in the line profiles.
Cluster 4 consists of 13.5 % of the profile pairs. Most
of the observed profiles belonging to this cluster are near
to the middle of the largest network patches. The 8498 Å
cluster profile is dominated by a strong emission feature
in the blue lobe. This feature is not visible in the 8542 Å
cluster profile. The overlap between the two lines’ ampli-
tude histograms is fairly small. Also the cluster profiles
show this difference in the relative amplitudes: 8542 Å
has a significantly lower amplitude than 8498 Å. Except
for the 8542 Å area asymmetry histogram, all histograms
are centered around zero. The range of area asymmetries
in the 8542 Å line is large and the distribution is skewed
towards negative values. This trend in the 8542 Å area
asymmetries is seen in several of the clusters.
The patches of profiles belonging to the fifth cluster
(9.6 %) are also found in the less homogeneous middle
regions of the network elements. The 8498 Å cluster
Fig. 6.— Stokes V statistics of the map clusters. The histograms are for all profiles belonging to the given cluster and the dotted vertical
lines show the area and amplitude asymmetries for the cluster profiles.
profile has a factor 2 lower amplitude than 8542 Å. This
is not seen in the amplitude histograms but there is a
large overlap between the two histograms. The cluster
profiles are fairly antisymmetric and also the histograms
of observed profile asymmetries are centered around zero.
The 8542 Å area asymmetry is again the exception: it is
centered around a negative value.
Cluster 6 is the smallest cluster with 7.2 % of the pro-
files. Patches of cluster 6 profiles are located in regions
with cluster 4 and 5 profiles. The 8498 Å cluster profile is
very similar to that of cluster 5. Like cluster 5, the 8542
Å cluster 6 profile has a factor 2 larger amplitude and
the amplitude histograms overlap nearly entirely. All the
cluster 6 histograms are very similar to cluster 5. The
major difference between the two is that there is very
little structure in the 8542 Å line profile.
3.2. Time-dependent behavior
The cluster analysis results of the time series are shown
in Figure 8, and the spatio-temporal distribution is cap-
tured in Figure 9. The clusters consist of profiles at
rest with varying degrees of structure, and profiles where
the blue side is in emission. While there are temporal
changes in the clusters, there are no clear periodic pat-
terns visible. Most slit positions have a preferred cluster
or in some cases the slit position is dominated by two
clusters. Positions where more than 2 clusters are domi-
nant are rare.
Because the slit moved occasionally during the time
series, no meaningful power spectra can be made from
this data set. The time series data do however allow
for a qualitative analysis of the time-dependent behav-
ior. Comparing network and internetwork pixels reveals
some interesting features: the network, especially in the
intermediate flux regions, is very dynamic with propagat-
ing shock-like features and large self-reversals appearing
frequently in both Stokes I and V . In comparison, the
internetwork is less dynamic, intensity oscillations are
present but they are much weaker than in the network.
No structures indicating the presence of shocks, are seen
in the internetwork profiles. In agreement with prior ob-
servations of chromospheric lines (e.g., Noyes 1967), any
oscillation periods in the network appear to have a longer
period than in the internetwork.
We now examine three different regions, namely an
internetwork pixel, an intermediate flux network pixel,
and a strong network pixel.
3.2.1. Internetwork
In Figure 10 the time evolution of a typical internet-
work pixel is shown. The location of the pixel is marked
by an asterisk in Figure 2. The data were taken when
the slit was stationary. No Stokes V signal above the
noise level is seen in the pixel. The Stokes I profiles of
both Ca lines change periodically in width and position
of the line center, but no self-reversals are seen. Also,
the line-wing intensity shows some oscillations.
3.2.2. Intermediate flux network
The difference between the internetwork and network
regions with intermediate flux (Fig. 11) is dramatic: the
Fig. 7.— Spatial distribution of the clusters in the map. The black areas (0 cluster) correspond to regions where the Stokes V amplitudes
are below 7× 10−3Ic and where no cluster analysis was performed.
network region is much more dynamic, and highly asym-
metric profiles, in both lines Stokes I and V , are seen.
The time dependent behavior of the photospheric iron
line is quite similar to what is seen in the internetwork.
The Stokes I in both lines has a clearly oscillating be-
havior with bright, very asymmetric episodes followed
by a darker, more symmetric episodes. The period for
the oscillation is about 4 minutes, i.e. below that as-
sociated with the acoustic cutoff frequency (about 5.3
mHz). This may be caused by the presence of inclined
magnetic fields can lower effectively the acoustic cutoff
frequency (Bel & Leroy 1977). The time evolution of the
8542 Å Stokes I has a diagonal structure moving from
blue to red. This indicates the presence of propagating
compressible waves (Carlsson & Stein 1997). The bright
part, which corresponds to a large self-reversal, is clearly
shifted towards the blue. This is seen in the 8498 Å line
profiles as well, although these profiles tend to be more
flat-bottomed. In general, the self-reversals and over all
variation is larger in the blue wing than in the red. This
is true for all slit positions which exhibit strong time-
dependent behavior.
The Stokes V image of the 8498 Å line also shows
strong diagonal structures that coincide in time with the
dark phases of Stokes I. Inspection of individual pro-
files (Fig. 12) reveals a pattern of multiple lobes in the
Stokes V profiles. These lobes are on the blue side of the
line core and their amplitudes and positions vary period-
ically in time resulting in the diagonal structure seen in
the image. The lobes can be identified with the emission
features seen in the Stokes I profiles. The 8542 Å line
Stokes V image shows a pattern of a multi-lobed pro-
files whose amplitudes vary strongly in time. The large
Stokes V amplitude phase coincides with the bright, very
asymmetric phase seen in the intensity profiles. The red
wings always exhibit less structure and variation than
the blue wings.
3.2.3. Strong network
Stokes I and V profiles seen in the strong network re-
gions (Figs. 13 and 14) would appear at first glance to
be a mixture of the less dynamic internetwork and the
highly dynamic intermediate flux region. The Stokes I
profiles exhibit the same pattern of bright (more asym-
metric) and dark (less asymmetric) phases as seen in the
intermediate flux region. The difference between the two
phases is however not as large: the amplitude of the self-
reversals, especially in the 8542 Å intensity profiles, is
much smaller than in the intermediate flux case.
The Stokes V images resemble those of the intermedi-
ate flux region: some diagonal structures are seen, but
they are weaker. The 8542 Å line Stokes V profiles have a
time varying amplitude but the profiles are not as asym-
metric and they are not necessarily multi-lobed. The dif-
Fig. 8.— As Fig. 5 but for the time series.
ference between the time-dependent behavior of the red
and blue lobes of the profile, i.e. the red lobe varies less
in time, is even more clear here than in the intermediate
flux region.
3.3. Statistics
Histograms of the Stokes I amplitude integrated over
250 mÅ around the line core for the two Ca lines are
shown in the top-left panel of Figure 15. These his-
tograms include both the map and time-series profiles.
Because there are almost five times as many profiles in
the time-series as there are in the map, the histograms
are dominated by the time-series profiles. Both lines ex-
hibit a wide range of values. Except for the peaks at
low intensities, the histograms are fairly flat. The dark-
est (i.e. lowest core intensity or most absorption) am-
plitudes, are associated with the internetwork, and the
brightest with the network.
Histograms of the Stokes V amplitudes (top right panel
of Fig. 15) peak at the same value in both lines, 0.003 Ic,
but the 8498 Å histogram tail decays more slowly. Since
the 8498 Å line is formed slightly lower of the two and
the lines are roughly equally sensitive to magnetic fields
(effective Landé g factors are 1.07 and 1.10 for the 8498
Å and the 8542 Å lines, respectively), it is not surprising
that the 8498 Å histogram has the longer tail.
Fig. 9.— The spatio-temporal distributions of the clusters for the first slit position in the time series. The black areas correspond to
regions where the Stokes V amplitudes is ≤ 7×10−3Ic. The vertical lines show the period with the best seeing when the slit was stationary.
Both lines’ Stokes V amplitude asymmetry histograms
(bottom left panel of Fig. 15) have very similar shapes
and similar widths. There are more positive asymme-
tries in both lines: 56% in 8498 Å and 64 % in 8542
Å (Table 1). The mean amplitude asymmetries are also
positive, and the 8542 Å mean asymmetry is two times
larger. There are more negative amplitude asymmetries
in the 8542 Å map than in the time series. Non-zero am-
plitude asymmetries indicate at least one of two things:
the spatial pixels consist in most cases of at least two
atmospheric components that are shifted relative to one
another or that there are velocity and/or magnetic field
gradients present in the atmosphere.
The area asymmetry histograms (bottom right panel
of Fig. 15) of the two calcium lines repeat the pattern al-
ready seen in the cluster profiles: the 8542 Å histograms
is centered around a negative value and the 8498 Å is
centered at roughly zero, though the mean is slightly pos-
itive. The 8542 Å histogram is significantly wider than
the 8498 Å histogram. A multi-component atmosphere
alone cannot produce area asymmetries, so the existence
of non-zero area asymmetries indicates the presence of
velocity and possibly magnetic gradients in the atmo-
sphere.
In the 8542 Å line 66 % of the profiles have negative
area asymmetries whereas in the 8498 Å line the majority
of the profiles, 64 %, have positive area asymmetries (Ta-
ble 1). To better understand why the area asymmetry
histograms of the lines are so different, we need to look
at the components of the area asymmetry separately i.e.
the sign of the blue lobe and the total area of the Stokes
V profile. One possible cause for the difference in the
histograms might be that the distribution of signs of the
blue lobe is different in the two lines. Closer inspection
reveals that this is not the explanation. The vast major-
ity of both lines, over 80 %, have a negative sign. (Here
the sign is defined to be the sign of the local maximum
or minimum amplitude of the blue lobe). A second pos-
sible explanation is that the
V (λ)dλ is different in
the two lines. This is found to be the case. The 8542 Å
line has more profiles with a positive area and the 8498
Å has slightly more profiles with a negative area. (Note
that the sign of the area asymmetry is the product of
the sign of the blue lobe and the area; eq. 2.) The area
of the Stokes V profile is strongly affected by the emis-
sion features. These features, and their amplitudes, are
related to the self-reversals seen in the Stokes I profiles.
The self-reversals are stronger on the blue side of the line
core than on the red. In general, the blue lobes of the
Stokes V profiles have negative amplitudes and the effect
of the emission features is then to reduce the amplitude,
and in some cases, make it positive and this way reduce
the overall negative area.
The effect of the emission features on the amplitude
asymmetries is not as large because the amplitude will
be affected only if the emission feature is located at the
Fig. 10.— Time dependent behavior of Stokes I in an internetwork pixel. Location of the pixel is marked with an asterisk in Figure 2.
same wavelength as the maximum absolute amplitude.
Also if the profile has a wide blue lobe, i.e., the wings
contribute significantly, a local reduction in peak ampli-
tude is counterbalanced by a comparable signal in the
other parts of the blue lobe. The resulting profile will
have nearly the same amplitude in the blue lobe as be-
fore, but the area will be reduced leading to a smaller, or
even negative, area asymmetry. Since the self-reversals
are larger in the 8542 Å line, this scenario is more likely
to apply to it than the 8498 Å line.
Both lines’ area and amplitude asymmetries are found
to be inversely proportional to the Stokes V amplitudes.
The scatter, especially in the 8542 Å line, is fairly large.
PCA also allows us to ensure that the determination of
Stokes V asymmetries is not dominated by noise. Recon-
structing the profiles using only the 11 first eigenvectors
(i.e., essentially noise-free profiles) and then computing
the asymmetries reproduces the Stokes V amplitude and
asymmetry histograms. To test if the negative histogram
peak in the 8542 Å line is an artifact caused by data re-
duction, we computed area asymmetries for the datasets,
but after first removing the fringe pattern caused by the
optics. This did not alter the area asymmetry histogram.
Another artifact that could cause the offset is an incor-
rect subtraction of the tilt caused by the detector in the
continuum intensity. To remove the offset in the his-
tograms by means of changing the tilt causes a clearly
visible lopsidedness in the Stokes I profiles. Lastly, to
make sure that the choice of the integration range is not
the cause of the offset, we used a constant bandwidth
for area asymmetries and it also reproduces the 8542 Å
area histogram offset. (Besides these issues, there are no
other obvious artifacts that would cause the offset.) We
therefore conclude that the offset is not caused by the
fringing or incorrect subtraction of the tilt in the contin-
uum intensity.
4. COMPARISON OF OBSERVATIONS WITH A HIGH-β
SIMULATION
In P06 we synthesized Stokes profiles for the Ca IR
triplet lines in the high-β regime. This was done by
combining a radiation hydrodynamic code (see for exam-
ple Carlsson & Stein 1997) with a weak magnetic field
and using a nLTE Stokes inversion and synthesis code
(Socas-Navarro et al. 2000b) to produce, based on snap-
shots of the simulation, a time series of the lines’ Stokes
vectors. The simulation is driven by a photospheric ve-
locity piston and its dynamics are dominated by upward
propagating acoustic waves in a simple magnetic field
topology. The simulation shows that the radiative trans-
fer is very similar in all the Ca IR triplet lines. The
differences between the line behaviors in the simulation
are mainly due to the lines having slightly different for-
mation heights and thus experiencing a difference in the
amplitudes of the shocking waves: the higher the line is
formed, the larger the amplitude of the passing wave is.
In the simulation there is no feedback from the mag-
netic fields on the dynamics and the waves are purely
acoustic. The observations have limited spatial and tem-
poral resolutions whereas the simulation is much better
resolved.
4.1. Comparison of time dependent behavior
As the acoustic waves in the simulation propagate up-
wards and eventually form shocks, a time-varying pat-
Fig. 11.— Time dependent behavior of Stokes I and V in an intermediate flux pixel. Location of the pixel is marked with a diamond in
Figure 2.
Fig. 12.— Time evolution of individual Stokes I and V profiles in an intermediate flux pixel. Location of the pixel is marked with a
diamond in Figure 2.
Fig. 13.— Time evolution of Stokes I and V in a network pixel. Location of the pixel is marked with a triangle in Figure 2.
Fig. 14.— Time evolution of individual Stokes I and V profiles in a network pixel. Location of the pixel is marked with a triangle in
Figure 2.
Fig. 15.— Histograms of Stokes I and V amplitudes, and Stokes V amplitude and area asymmetries of the map and time-series.
tern of disappearing and reappearing Stokes V lobes is
seen (Fig. 16). The pattern is strongest in the highest
forming line, i.e. 8542 Å. Wave propagation is also seen
in the Stokes I profiles. There are no large self reversals
or brightenings, instead the position of the line minimum
changes periodically and forms a saw-tooth like pattern
where the red shift takes more time than the blue shift
phase.
If we first compare the simulated profiles to the in-
ternetwork observations (Fig. 10), we see that the
strong signatures of shocks seen in the simulation are not
present in the observations. In the simulation the Ca IR
triplet is formed in a region where the waves are just be-
ginning to shock. If the formation height of the lines or
the shocks in the simulation is off, compared to the real
Sun, by a small amount, even 50 km, the lines’ temporal
evolution may look very different. Another possible ex-
planation to why we see no strong indications of shocks
is the temporal and/or spatial resolution: there may be
several components oscillating out of phase relative to
one another in a given resolution element. However, the
photospheric velocities are very similar in the internet-
work and network, but the network profiles show strong
self-reversals. This suggests that spatial and temporal
resolution alone cannot explain the lack of strong signa-
tures of shocks in the internetwork.
Observations of the quiet Sun show varying degrees
of oscillatory power (compare for example Lites et al.
(1993) [Ca II H and K] or UV data of Judge et al. 2003,
McIntosh & Judge 2001 and Wikstøl et al. 2000). This
variation may be related to the local magnetic topology,
especially to the possible existence of a magnetic canopy
(McIntosh et al. 2003; Vecchio et al. 2006). The region
observed here was less oscillatory than average but still
not exceptionally quiet.
Both the simulated profiles and observed network pro-
files (Fig. 13) show time varying patterns where the
Stokes I and V amplitudes change periodically. In the
simulation the wave propagation manifests itself in the
Stokes I profiles most clearly as a shift of the line core
and the saw-tooth shape of the time series. In the ob-
servations, waves cause the lines’ periodically varying
self-reversals that result in alternating bright and dark
phases. There are indications of diagonal structures in
the observed Stokes I images, but they are not nearly
as clear as in the simulation. In the simulation the up-
ward propagating waves cause the blue and red lobes of
the Stokes V profiles to disappear alternately. In con-
trast, the observed time varying pattern in Stokes V
looks more complicated: there is much more structure
in the observed profiles, especially in the line cores, than
in the simulation. This is related to the simulated pro-
files not exhibiting strong self-reversals as seen in the
observations.
In the simulation, because of radiative cooling and ex-
pansion of the falling material, the down flows are in
general cooler than the up flows. In the synthesized pro-
files this manifests itself by the red wings of the Stokes
I profiles showing less variations, though the difference
with the blue wing is quite small. Similar behavior is also
seen in the observations: the self-reversals are in general
larger in the blue wing of the Stokes I profiles and the red
lobes of the Stokes V profiles show clearly less variation.
4.2. Comparison of statistics and Stokes V
morphologies
In the simulation the magnetic field decays exponen-
tially with height and therefore the Ca II Stokes V am-
plitudes are significantly lower than the Fe I 8497 Å am-
plitude. In the observations the Ca and Fe line Stokes V
profiles have roughly the same amplitudes. This may be
explained by the field decaying much slower with height
in the observations, or by the filling factor in the ob-
servations being smaller in the photosphere than in the
chromosphere.
Both Ca II lines’ observed Stokes V profiles have a sig-
nificant amount of signal in the wings. In the simulations
only the 8498 Å line Stokes V has extended wings with
large amplitudes (Fig. 4 in P06). The amount of signal
in the wings depends on the atmospheric magnetic field
Fig. 16.— Time evolution of Stokes I and V profiles in the high-β simulation (P06). The Stokes V signal in wavelength range -1.2 to -0.6
Å in the 8498 Å image is scaled down with factor 7.5 in order to display both the Ca II 8498 Å and Fe I 8497 Å lines in the same panel.
gradient. If there is no gradient the wings of all three
Ca lines have very little signal. Whereas a model atmo-
sphere with a constant field gradient produces profiles
where all lines, 8498 Å the most, have some signal in
the line wings and an exponential field produces profiles
with the largest wings. Depending on where the gradi-
ent is located and how strong the field is, the Ca lines
may or may not have similar Stokes V profiles. Based
on the profile shapes and relative amplitudes, it is ob-
vious that the magnetic topology in the observations is
different from the simulation.
Formation of area and amplitude asymmetries in the
simulation is coupled. The correlation is especially
strong in the 8542 Å line (upper row of Fig. 17). In
the 8498 Å Stokes V profiles the strong wings affect
the asymmetries, and the correlation is weaker. The
observed area and amplitude asymmetries of both lines
show less correlation. This is at least partly because the
observed profiles have more complex shapes than in the
simulation.
The lower panels in Figure 17 show the Stokes V asym-
metry histograms for the simulation. The observed his-
tograms are re-plotted to enable direct comparison. In
the simulation both lines’ amplitude and asymmetry his-
tograms are centered roughly around zero (percentage-
wise there are a couple of percent more negative than
positive asymmetries). This was not the case in the ob-
servations where all the asymmetries, except the 8542 Å
area asymmetry, have clearly more positive than nega-
tive values, i.e. the blue lobe is larger in area/amplitude
than the red lobe.
The observed 8498 Å profiles are more dynamic than
the simulated ones. Consequently the observed 8498 Å
asymmetry histograms are clearly wider than the simu-
lated. Because there is very little signal in the simulated
8542 Å Stokes V profile wings, when an upward propa-
gating wave causes a Stokes V lobe to disappear, there is
no signal in the line wing to contribute to the amplitude.
This leads to the extreme amplitude asymmetries in the
simulations and in the additional lobes at large values
in the simulated 8542 Å line area asymmetry histogram.
Since the observed profiles have a significant amount of
signal in the wings, the extreme amplitude asymmetries
are moderated, and no lobes at large values are seen in
the histogram.
5. CONCLUSIONS AND DISCUSSION
So far most spectropolarimetric studies using the
Ca II IR triplet lines have focused on active regions
(e.g., Socas-Navarro, Trujillo Bueno, & Ruiz Cobo
2000a; López Ariste, Socas-Navarro, & Molodij
2001; Socas-Navarro 2005;
Uitenbroek, Balasubramaniam, & Tritschler 2006).
The observations presented here show that these lines
are also promising candidates for studying the magnetic
chromosphere outside of active regions. Interpreting the
observations, however, is not straight forward.
The main results of the analysis presented here are:
• Classification of Stokes V profile shapes.
Asymmetric line profiles are very common and that
the two lines, despite being formed fairly close in a
geometrical sense, often do not have similar shapes.
Furthermore, the edges of the network patches ex-
hibit profile shapes different from those seen in the
center of the patches. The cluster analysis results,
as expected, in a qualitative, not quantitative, de-
scription of the profile shapes.
• Statistics of the line profiles.
The 8542 Å area asymmetry is predominantly neg-
ative; while the 8498 Å area asymmetry and the
amplitude asymmetries are usually positive.
• Time dependent behavior.
The enhanced network has very different dynamic
behavior compared with the internetwork. It is
more dynamic and the oscillation period, as seen
in both Stokes I and V , is greater than in the in-
ternetwork.
• Comparison with high-β simulation.
Oscillations are present in both the observations
and the simulation. The simulated profiles are
more dynamic than the observed internetwork pro-
files. The opposite is true for network profiles.
In the simulation, the formation of asymmetries is
more tightly coupled than what is seen in the ob-
servations. Except for the 8542 Å amplitude asym-
metry the observed profiles show a wider range of
asymmetries. And lastly, the peculiar negative area
asymmetries seen in the observed 8542 Å line and
the tendency of the other asymmetries to be posi-
tive are not reproduced by the simulation.
The tendency of large Stokes V asymmetries to de-
crease with an increasing signal amplitude has also been
observed in photospheric lines (Grossmann-Doerth et al.
1996). In the photosphere a magnetic canopy is one pos-
sible explanation: the canopy gives rise to asymmetries
in the lines, and as a flux tube diameter increases, the
relative contribution from the canopy to the Stokes V
signal decreases. In the photosphere the scatter in an
amplitude vs. asymmetry plot is significantly larger in
the area than in the amplitude. No large difference is
seen in the area and amplitude asymmetry scatters of
the Ca II lines.
In the quiet Sun photosphere, more positive
than negative Stokes V asymmetries are found
(Grossmann-Doerth et al. 1996). In contrast with 8498
Å line (where there is no large difference in the mean area
and amplitude asymmetries) the photospheric mean area
asymmetries are significantly smaller (4 % in the Fe I
6302 Å line) than the mean amplitude asymmetries (15
% in the Fe I 6302 Å line). The photospheric asymme-
tries are often attributed to multiple atmospheric compo-
nents within a resolution element. In the chromosphere,
however, gradients have to play a dominant role since
the formation of area asymmetries require them. An-
other piece of evidence of the importance of gradients
in the chromosphere is that Milne-Eddington inversions,
which include the Paschen-Back effect of the He I 10830
Å triplet, are not able to reproduce the observed area
asymmetries (Sasso & Solanki 2006).
Fig. 17.— Stokes V asymmetries of the simulated and observed profiles. Upper 4 panels show the correlation of amplitude and area
asymmetries in the simulated and observed Ca lines. The Pearson correlation coefficient for each case is given. The asterisk symbols show
the mean for each 0.1 wide bin and the error bars show the standard deviation. The lower panels are histograms of observed and simulated
amplitude and area asymmetries.
Khomenko et al. (2005) used a 3-dimensional magne-
toconvection model to synthesize photospheric magneti-
cally sensitive lines in the visible and IR. There are more
positive than negative Stokes V asymmetries in their syn-
thetic profiles. They found that reducing the spatial res-
olution increases the number of irregular stokes V pro-
files (though the number of strongly asymmetric profiles
decreases). They conclude that the asymmetries reflect
more inhomogeneities in the horizontal direction than in
the vertical. In the chromosphere large velocity gradients
are more common and variation in the vertical direction
are likely to be more important than variation in the hor-
izontal direction. When these two factors are combined
with the observed area asymmetries, one concludes that
the chromospheric asymmetries mainly reflect the line-of-
sight inhomogeneities, and not variations in the horizon-
tal direction. Despite the apparent similarities between
the photospheric and chromospheric Stokes V profiles,
the underlying mechanism causing the asymmetries does
not appear to be the same. Drawing parallels between
the chromosphere and photosphere is problematic since
the two regions exist in very different physical regimes.
The discrepancy between the Stokes V asymmetry his-
tograms of the observations and the simulation may be
related to the self-reversals. The simulated profiles ex-
hibit only small self-reversals. The observations show
large self-reversals in the Stokes I profiles and accompa-
nying emission features in the Stokes V profiles. These
features are stronger on the blue side of the line cores.
Another effect that contributes to the imbalance is that
that the down flow phase lasts longer. Our observations,
especially with a 5 second exposure time, sample more
profiles with red-shifts and positive asymmetries (since
there will be more emission on the blue side). However,
inspection of Fig. 16 shows the same to be true of the
simulations. If this is the case, why are there not more
positive than negative asymmetries in the simulation as
well?
The sample of these observations is limited because the
majority of the profiles are drawn from the same three
slit positions which sample the same local magnetic field
configuration. It would not be surprising if histograms
made of profiles from a variety of quiet-Sun magnetic
field topologies would have somewhat different shapes.
The complexity of the observed profiles makes the inter-
pretation of the area and amplitude asymmetries diffi-
cult. Because of multiple lobes and the strong signal in
the line wings, the asymmetries are not necessarily good
proxies for the overall complexity of the Stokes V pro-
files. This is especially true if the two asymmetries are
viewed separately.
It is a well known result that the network intensity
oscillations have a longer period than the internetwork
(e.g. Orrall 1966, Lites et al. 1993, Banerjee et al. 2001).
This has also been observed before in the Ca II IR
lines (Deubner & Fleck 1990). Why do the intermedi-
ate flux regions in our observations appear to be more
dynamic than the stronger flux regions? It may be re-
lated to a more complex magnetic topology at the edges
of the network patches. The observations show no sig-
nal above the noise in Stokes Q and U , so we can-
not draw any conclusions of possible horizontal fields.
Any signal would be affected by atomic polarization
(Manso Sainz & Trujillo Bueno 2003) making the inter-
pretation exceedingly complex. The filling factor in the
network is not likely to be very large, and is likely smaller
at the edges than in the center of the network patch. In-
versions by Bellot Rubio et al. (2000) of average Stokes
profiles in a plage region gave a filling factor of 0.5 a
z = 0 km. The filling factor in the photospheric net-
work can safely be assumed to be lower than this. In
fact, in recent inversions by Domı́nguez Cerdeña et al.
(2006), which included a small patch of network, the pho-
tospheric filling factor in the patch center was as small
as 0.1. The network magnetic fields must expand with
height and consequently the chromospheric filling fac-
tor must exceed photospheric values. Results of com-
paring photospheric and chromospheric magnetograms,
however, Zhang & Zhang (2000) suggest that the sizes
of the network magnetic elements are not very different
at the two heights . The chromospheric magnetograms in
the comparison are based on the Hβ line. Its interpreta-
tion is complicated by the magnetically sensitive blends
close to the line core, and the line may suffer from same
problems as the Hα line when used as a proxy for chro-
mospheric magnetic fields, namely that the photospheric
contribution to the polarization signal is not insignificant
(Socas-Navarro & Uitenbroek 2004). Lastly, the size of
network patches is not directly linked with the filling fac-
tor. We see some expansion of the network with height in
the magnetograms of the map (Fig. 2), especially when
comparing the Ca II 8498 Å and 8542 Å magnetograms.
But since the magnetograms were constructed by using
the weak field formula, and the network fields have gra-
dients and are not necessarily weak, the magnetograms
are not accurate. Also the choice of color scaling of the
images affects the comparison. However, the apparent
expansion is not necessarily an artifact, since expansion
of network seen in magnetograms has also been reported
by Giovanelli (1980).
Obviously we need to understand better the topology
of the network magnetic fields. To do this we plan to
perform nLTE inversions of these data in the near fu-
ture. The inversions will help further in understanding
the formation dynamics of the Ca II IR lines in the quiet
Sun, and hopefully reveal how the underlying atmosphere
differs from that used in the simulation. An important
question to answer is why the two Ca lines behave as
differently as they do. Having a time series taken during
good seeing would be helpful. Also in order to expand the
analysis to internetwork regions, better spatial resolution
is required. Another interesting question is how much
variation there is in dynamics in different internetwork
regions, and how well the differences can be explained in
terms of the surrounding magnetic fields as has been sug-
gested by Vecchio et al. (2006) based on imaging data of
Ca II 8542 Å Stokes I. To fully investigate this in detail
high quality data of the full Stokes vector are needed.
TABLE 1
Observed Stokes V asymmetries
8498 Å 8498 Å 8498 Å 8542 Å 8542 Å 8542 Å
< 0 (%) > 0 (%) mean (%) < 0 (%) > 0 (%) mean (%)
σa 43.2 55.7 3.1 36.6 61.4 6.3
σA 35.5 64.5 3.3 69.7 30.3 -6.8
Note. — Percentages of observed Ca II 8498 Å and 8542 Å Stokes V
amplitude and area asymmetries with negative (i.e. red lobe larger) and
positive (i.e. blue lobe larger) signs.
Thanks to Doug Gilliam, Joe Elrod and Mike Bradford for all their invaluable help during the observing run.
REFERENCES
Andretta, V. & Jones, H. P. 1997, ApJ, 489, 375
Banerjee, D., O’Shea, E., Doyle, J. G., & Goossens, M. 2001,
A&A, 371, 1137
Bel,N. & Leroy, B. 1977, A&A, 55, 239
Bellot Rubio, L. R. 2006, ArXiv Astrophysics e-prints
Bellot Rubio, L. R., Ruiz Cobo, B., & Collados, M. 2000, ApJ,
535, 489
Carlsson, M. & Stein, R. F. 1997, ApJ, 481, 500
Deubner, F.-L. & Fleck, B. 1990, A&A, 228, 506
Domı́nguez Cerdeña, I., Almeida, J. S., & Kneer, F. 2006, ApJ,
646, 1421
Giovanelli, R. G. 1980, Solar Phys., 68, 49
Grossmann-Doerth, U., Keller, C. U., & Schuessler, M. 1996,
A&A, 315, 610
Judge, P. G., Carlsson, M., & Stein, R. F. 2003, ApJ, 597, 1158
Keller, C. U. & The Solis Team. 2001, in ASP Conf. Ser. 236:
Advanced Solar Polarimetry – Theory, Observation, and
Instrumentation, ed. M. Sigwarth, 16–+
Khomenko, E. V., Collados, M., Solanki, S. K., Lagg, A., &
Trujillo Bueno, J. 2003, A&A, 408, 1115
Khomenko, E. V., Shelyag, S., Solanki, S. K. & Vögler, A. 2005,
A&A, 442, 1059
Lagg, A. 2005, in ESA SP-596: Chromospheric and Coronal
Magnetic Fields, ed. D. E. Innes, A. Lagg, & S. A. Solanki
Landi Degl’Innocenti,E. 1992, in Solar Observations: Techniques
and Interpretation, First Canary Islands Winter School of
Astrophysics, ed. F. Sanchez, M. Collados & M. Vazquez
Lites, B. W., Chipman, E. G., & White, O. R. 1982, ApJ, 253, 367
Lites, B. W., Rutten, R. J., & Kalkofen, W. 1993, ApJ, 414, 345
López Ariste, A., Socas-Navarro, H., & Molodij, G. 2001, ApJ,
552, 871
MacQueen, J. 1967, in Proceedings Fifth Berkeley Symposium on
Math. Stat. and Prob., ed. L. M. LeCam & J. Neyman, 281–+
Manso Sainz, R. & Trujillo Bueno, J. 2003, Physical Review
Letters, 91, 111102
Mart́ınez Pillet, V., L. B. W. . S. A. 1997, ApJ, 474, 810
McIntosh, S. W., Fleck, B., & Judge, P. G. 2003, A&A, 405, 769
McIntosh, S. W. & Judge, P. G. 2001, ApJ, 561, 420
Neckel, H. & Labs, D. 1984, Solar Phys., 90, 205
Noyes, R. W. 1967, in IAU Symp. 28: Aerodynamic Phenomena
in Stellar Atmospheres, ed. R. N. Thomas, 293–+
Orrall, F. Q. 1966, ApJ, 143, 917
Paletou, F. & Molodij, G. 2001, in ASP Conf. Ser. 236: Advanced
Solar Polarimetry – Theory, Observation, and Instrumentation,
ed. M. Sigwarth, 9–+
Pietarila, A., Socas-Navarro, H., Bogdan, T., Carlsson, M., &
Stein, R. F. 2006, ApJ, 640, 1142
Rees, D. E., López Ariste, A., Thatcher, J., & Semel, M. 2000,
A&A, 355, 759
Rimmele, T. R. 2000, in Proc. SPIE Vol. 4007, p. 218-231,
Adaptive Optical Systems Technology, Peter L. Wizinowich;
Ed., ed. P. L. Wizinowich, 218–231
Sánchez Almeida, J. & Lites, B. W. 2000, ApJ, 532, 1215
Sasso, C., Lagg, A. & Solanki, S. 2006, A&A, 456, 367
Scharmer, G. B., Bjelksjo, K., Korhonen, T. K., Lindberg, B., &
Petterson, B. 2003, in Innovative Telescopes and
Instrumentation for Solar Astrophysics. Edited by Stephen L.
Keil, Sergey V. Avakyan . Proceedings of the SPIE, Volume
4853, pp. 341-350 (2003)., ed. S. L. Keil & S. V. Avakyan,
341–350
Shimizu, T. 2004, in ASP Conf. Ser. 325: The Solar-B Mission and
the Forefront of Solar Physics, ed. T. Sakurai & T. Sekii, 3–+
Socas-Navarro, H. 2005, ApJ, 631, L167
Socas-Navarro, H., López Ariste, A., & Lites, B. W. 2001, ApJ,
553, 949
Socas-Navarro, H., Trujillo Bueno, J., & Landi Degl’Innocenti, E.
2004, ApJ, 612, 1175
Socas-Navarro, H., Trujillo Bueno, J., & Ruiz Cobo, B. 2000a,
Science, 288, 1398
—. 2000b, ApJ, 530, 977
Socas-Navarro, H. & Uitenbroek, H. 2004, ApJ, 603, L129
Socas-Navarro, H. et al. 2006, Solar Physics, 235, 55
Stein, R. F. & Nordlund, Å. 2006, ApJ, 642, 1246
Uitenbroek, H., Balasubramaniam, K. S., & Tritschler, A. 2006,
ApJ, 645, 776
Vecchio, A., Cauzzi, G., Reardon, K. P., Janssen, K. & Rimmele,
T. 2006, astro-ph/0611206
Wikstøl, Ø., Hansteen, V., Carlsson, M., & Judge, P. G. 2000,
Astrophys. J., 531, 1150
Zhang, H. & Zhang, M. 2000, Solar Phys., 196, 269
http://arxiv.org/abs/astro-ph/0611206

  The Ca II infrared triplet is one of the few magnetically sensitive
chromospheric lines available for ground-based observations. We present
spectropolarimetric observations of the 8498 A and 8542 A lines in a quiet Sun
region near a decaying active region and compare the results with a simulation
of the lines in a high plasma-beta regime. Cluster analysis of Stokes V profile
pairs shows that the two lines, despite arguably being formed fairly close,
often do not have similar shapes. In the network, the local magnetic topology
is more important in determining the shapes of the Stokes V profiles than the
phase of the wave, contrary to what our simulations show. We also find that
Stokes V asymmetries are very common in the network, and the histograms of the
observed amplitude and area asymmetries differ significantly from the
simulation. Both the network and internetwork show oscillatory behavior in the
Ca II lines. It is stronger in the network, where shocking waves, similar to
those in the high-beta simulation, are seen and large self-reversals in the
intensity profiles are common.

Draft version June 8, 2021
Preprint typeset using LATEX style emulateapj v. 08/22/09
SPECTROPOLARIMETRIC OBSERVATIONS OF THE CA II 8498 Å AND 8542 Å LINES IN THE QUIET SUN
A. Pietarila
, H. Socas-Navarro
High Altitude Observatory, National Center for Atmospheric Research2, 3080 Center Green, Boulder, CO 80301, USA
T. Bogdan
Space Environment Center, National Oceanic and Atmospheric Administration, 325 Broadway, Boulder, CO 80305, USA
Draft version June 8, 2021
ABSTRACT
The Ca II infrared triplet is one of the few magnetically sensitive chromospheric lines available for
ground-based observations. We present spectropolarimetric observations of the 8498 Å and 8542 Å
lines in a quiet Sun region near a decaying active region and compare the results with a simulation
of the lines in a high plasma-β regime. Cluster analysis of Stokes V profile pairs shows that the two
lines, despite arguably being formed fairly close, often do not have similar shapes. In the network, the
local magnetic topology is more important in determining the shapes of the Stokes V profiles than the
phase of the wave, contrary to what our simulations show. We also find that Stokes V asymmetries
are very common in the network, and the histograms of the observed amplitude and area asymmetries
differ significantly from the simulation. Both the network and internetwork show oscillatory behavior
in the Ca II lines. It is stronger in the network, where shocking waves, similar to those in the high-β
simulation, are seen and large self-reversals in the intensity profiles are common.
Subject headings: polarization, Sun: chromosphere, waves
1. INTRODUCTION
Our understanding of solar magnetic fields
outside active regions has increased signifi-
cantly during the last years. This is due to
new and better instrumentation (e.g., THEMIS,
Paletou & Molodij 2001; VSM on SOLIS,
Keller & The Solis Team 2001; Swedish Solar Telescope,
Scharmer, Bjelksjo, Korhonen, Lindberg, & Petterson
2003; Solar Optical Telescope on Hinode, Shimizu
2004; and SPINOR, Socas-Navarro et al. 2006), better
diagnostic techniques (see for example Bellot Rubio
2006 for a review on inversion techniques) and advanced
numerical simulations (Stein & Nordlund 2006 and
references therein). A large portion of the work has
focused on photospheric magnetic fields. Only now we
are starting to have adequate tools for investigating
chromospheric magnetism in more detail. (For a review
of chromospheric magnetic fields see Lagg (2005)). This
is not surprising considering the numerous difficulties in
observing chromospheric magnetic fields, interpreting
the data, and performing realistic MHD simulations.
There are two different sets of lines that are often used
for chromospheric spectropolarimetry, the He I infrared
(IR) triplet at 10830 Å, and the Ca II IR triplet at
8500 Å. Both line sets have their advantages and dis-
advantages. The He I lines are formed over a relatively
thin layer, and therefore observations can be inverted us-
ing a simple Milne-Eddington model. The drawback is
that while the formation range is fairly narrow, the pre-
cise formation height remains uncertain, and the Milne-
Eddington inversions do not give any information on
1 Institute of Theoretical Astrophysics, University of Oslo,
P.O.Box 1029 Blindern, N-0315 Oslo, Norway
2 The National Center for Atmospheric Research (NCAR) is
sponsored by the National Science Foundation.
the atmospheric gradients. The lines are also sensitive
to the Paschen-Back effect, which must be included in
the inversion code (Socas-Navarro et al. 2004). Further-
more, simulating the He I lines is difficult since coronal
irradiation has a non-negligible effect on their formation
(Andretta & Jones 1997). In contrast, the formation of
the Ca II IR lines is fairly well understood (Lites et al.
1982). The broad Ca II lines sample a large region of the
atmosphere, from the photosphere to the lower chromo-
sphere. However, the Ca II lines are formed in nonLTE,
making inversions considerably more cumbersome.
Several investigations using the Ca II IR lines have
studied intensity and velocity oscillations in the quiet
Sun (e.g. Lites et al. 1982; Deubner & Fleck 1990)
or, alternatively, magnetic fields in active regions (e.g.
Socas-Navarro et al. 2000a). In both cases the lines have
proven useful as diagnostics of the solar chromosphere.
In this paper we present results of spectropolarimetric
observations of two of the lines in an enhanced network
region. We have both spatial maps and time series data.
The observations show that the Ca II lines are formed in
a very interesting region, namely the region where the
atmosphere is transforming from a plasma dominated
(β >> 1) to a magnetic field dominated (β << 1) regime
in terms of dynamic force balance. Wave propagation
is clearly seen in the highly dynamic magnetic regions,
whereas the weakly magnetic internetwork is found to
be less variable. Interestingly, the two Ca II lines ex-
hibit significant differences even though in calculations
they are formed fairly close together. The importance of
gradients in the chromospheric network is clearly demon-
strated by the prevalence of asymmetric Stokes V profiles
in the data.
The paper is arranged as follows: in § 2 the data and
their reduction are addressed. Results of analyzing the
data using different approaches are presented in § 3. We
http://arxiv.org/abs/0704.0617v1
performed cluster analyses on the Stokes V profiles to
classify them and to describe spatial patterns seen in the
data. Statistics, such as profile amplitudes and asym-
metries, are presented. The time dependent behavior of
the lines in different network and internetwork regions
is also discussed. In § 4 the observations are compared
to simulations of the lines in a high plasma-β regime
(Pietarila et al. 2006, hereafter P06). Finally, in § 5 the
main results are summarized and discussed.
2. OBSERVATIONS AND DATA REDUCTION
The Spectro-Polarimeter for INfrared and Optical Re-
gions (SPINOR, Socas-Navarro et al. 2006) at the Dunn
Solar telescope, Sacramento Peak Observatory, was used
to observe two of the Ca II infrared triplet lines at 8498
Å and 8542 Å, as well as two photospheric Fe I lines at
8497 Å and 8538 Å. The setup included several other
lines but because of computer problems only data from
the two Ca lines which used the ASP TI TC245 cameras
were recorded fully. The data have 256 points in both
the wavelength and spatial position with a typical noise
level of 6 × 10−4 Ic (1 σ deviation from the mean) and
a spectral sampling of 25 mÅ. The pixel height corre-
sponds to ≈ 0.38 arcseconds on the solar surface along
the slit. We observed a quiet Sun region near disk center
at S17.3 W32.1 on May 19, 2005 at 14:14 UT. An MDI-
magnetogram of the region is shown in Figure 1. The
slit was positioned in the vicinity of a decaying active re-
gion, AR10763, but avoided flux concentrations from the
active region (i.e., plages). A time series consisting of 99
time steps of short scans (3 slit positions), with a spacing
of 0.375 arcseconds each, was acquired during variable
seeing conditions. The cadence is ≈ 10 seconds (i.e., a
given slit position was repeated every 30 s). The time
series was followed by a 63 step raster centered around
the position where the slit was during the time series.
The raster step size was 0.375 arcseconds. Adaptive op-
tics (AO, Rimmele 2000) were used during the observ-
ing sequence but the compromised seeing conditions did
not allow for continuous locking onto granulation. This
caused the slit to jump occasionally, making the longest
period with a stationary slit in the time series 17 time
steps (8.5 min). The spatial resolution varied during the
sequences being at best less than an arc second, but on
average a factor of two worse.
Standard procedures for flat field and bias were used
for the data reduction. Instrumental polarization was re-
moved using the available calibration data, as explained
in Socas-Navarro et al. (2006). No absolute wavelength
calibration was attempted because no suitable telluric
lines are present. Instead a wavelength calibration using
spatial pixels devoid of magnetic field was done by fitting
the average spectrum to the Kitt Peak FTS-spectral at-
las (Neckel & Labs 1984). The FTS atlas was also used
to find the normalization factor for the intensities to the
quiet Sun continuum intensities. Because of detector flat-
field residuals and prefilter shape, the continua in the raw
data from both detectors are tilted. The tilts were re-
moved a posteriori by subtracting a linear fit (y = a+bλ)
obtained by matching the continuum intensity levels to
those of the FTS atlas.
The data were analyzed using both the raster and time
series for statistical purposes. The period when the slit
was stationary on the solar disk was used to study the
time-dependent behavior of the lines. Because of the
short length of this period, we do not present any Fourier
analysis of the data. To make a classification of Stokes
V profile morphologies, we did cluster analyses based
on a Principal Component Analysis (PCA) in a similar
manner as the work of Sánchez Almeida & Lites (2000)
and Khomenko et al. (2003) for photospheric lines. We
computed amplitudes for Stokes I and V profiles. Be-
cause the Ca line intensity profiles often exhibit strong
self-reversals, no proxies for atmospheric velocities, such
as lines’ centers of gravity or bisectors, are adequate.
For those Stokes V profiles with amplitudes greater than
7 × 10−3 Ic, (i.e. ≥ 10σ), amplitude and area asymme-
tries were also calculated.
The amplitude asymmetry of a Stokes V profile is de-
fined by (Mart́ınez Pillet 1997):
ab − ar
ab + ar
, (1)
where ab and ar are the unsigned extrema of the blue
and red lobes of the Stokes V profile.
The area asymmetry of a Stokes V profile is defined by
(Mart́ınez Pillet 1997):
σA = s
V (λ)dλ
|V (λ)|dλ
, (2)
where s is the sign of the blue lobe. Because of the broad,
deep lines and large velocities (compared with the pho-
tosphere) present in the chromosphere, the choice of the
integration range for the area asymmetries is non-trivial
for the Ca lines. We followed the same procedure as
in P06. In the weak field regime the Stokes V profile
is proportional to dI/dλ (strictly true only in the ab-
sence of atmospheric velocity and magnetic gradients).
Inspection of the data showed that most of the observed
Stokes V profiles have roughly the same structures as
the dI/dλ profiles. The intensity in the blue wing (λ0)
of the line profile was matched with a point in the red
wing (λ1) with the same intensity. The signal-to-noise in
the intensity profiles is much higher than in the Stokes V
profiles and also the slope is much steeper. This makes
matching points with the same value more accurate in
the intensity than in the Stokes V profiles. The selec-
tion of a wavelength to start the integration range was
made by choosing a wavelength point that is far enough
from the line core so that self-reversals are not an issue.
In our data this point, λ1, is at 600 mÅ from reference
wavelength of line center. The same value was used in
Magnetograms made from the 63 step scan are shown
in Figure 2. The panels are in order of increasing for-
mation height: Fe I 8497 Å, Fe I 8538 Å, Ca II 8498 Å
and Ca II 8542 Å. The lower part of the slit was located
above a flux concentration along the enhanced network
and the upper part over an internetwork region with very
little magnetic activity. The network becomes wider and
more diffuse with increasing line formation height as de-
scribed by Giovanelli (1980). Not all magnetic flux seen
in the photosphere can be identified in the chromosphere
Fig. 1.— MDI magnetogram showing the position of the slit for the time series and the map (rectangular region). The observed region
was close to the decaying active region, AR10763.
and vice versa. However, interpreting the chromospheric
magnetograms is difficult due to the self-reversed features
in the cores of the Ca line Stokes V profiles.
3. RESULTS
In Figure 3, Stokes I and V spectra of the solar sur-
face under the slit are shown for both Ca II lines as well
as the two photospheric Fe I lines in the Ca lines’ wings
(marked by arrows). Since the Fe I 8497 Å line is blended
in the Ca line’s wing and the Fe I 8538 Å line is very close
to the edge of the detector, no quantitative analysis is
done for them. No signal above the noise was recorded
in Stokes Q and U so they will not be addressed in what
follows. Residual vertical fringing caused by the polar-
ization modulator is visible in the Stokes V images. We
chose not to try to remove the fringing since its’ ampli-
tude is of the same order of magnitude as the noise.
The network, present in the lower part of the slit, is
associated with less absorption in the intensity profiles.
Both Ca lines often show self reversals, which are usually
stronger on the blue side of the line than in the red. The
Stokes V profiles of both Ca lines have large, extended
wings. At times, the profiles may have both polarities
present on the blue side of the core but in almost all
cases the far blue wing of the profile has the same po-
larity (i.e., opposite sign) as the red wing. The Stokes
I and V profiles of the chromospheric lines look distinc-
tively different from the photospheric lines: the Ca lines
have more structure, they are wider and exhibit more
spatial variation than the photospheric Fe lines. Some
differences are seen between the two Ca lines: the 8542
Å line is slightly broader, has more structure in the spec-
Fig. 2.— Magnetograms of the map deduced by using the weak field method (Landi Degl’Innocenti 1992). The Stokes V signal is
measured in units of Gauss. Vertical lines show the position of slit during the time series. First panel: Fe I 8497 Å, second panel: Fe I8538
Å, third panel: Ca II 8498 Å, third panel: Ca II 8542 Å. Location on the solar disk: S32.1, W17.3. The orientation of the magnetograms
is 180 degrees from the MDI magnetogram in Figure 1. The plotted symbols (∗, ✸ and △) on the images show where the pixels discussed
later in the text are located.
tra and also stronger absorption than the 8498 Å line.
The internetwork region, present in the upper part of
the slit, is mostly devoid of Stokes V signal, and Stokes I
is more homogeneous than in the network. Self reversals
are usually not seen in the profiles. A small portion of
the internetwork region has structures in Stokes I that
are similar to those seen in the magnetic region: Stokes I
is brighter than in the surrounding areas and the profiles
show some self reversals. Closer inspection of the images
reveals a visible, albeit a very small amplitude, Stokes V
signal.
The spatial patterns of Stokes I and V amplitudes and
asymmetries in the two Ca lines (Figure 4) are fairly
similar to one another. The network is clearly visible in
the Stokes I and V amplitudes, though it is more diffuse
in the 8542 Å line. There is a structure in the upper
part of the map that is seen best in the 8498 Å intensity
image. Parts of this structure appear also in both lines’
Stokes V amplitude and asymmetry images. The edges
of the network have more asymmetric Stokes V profiles.
This is seen clearly in the 8542 Å amplitude asymmetry.
Photospheric velocities can be estimated from the lo-
cations of the iron lines’ intensity minima. Except for
a nearly constant offset caused by the convective down
flows in the network, the internetwork and network re-
gions have very similar spatial and temporal patterns.
3.1. Classification of the Stokes V profiles
To classify the shapes of the 8498 Å and 8542 Å Stokes
V profile pairs we used PCA, (Rees et al. 2000) and clus-
ter analysis. The cluster analyses were performed sepa-
rately for the map and the time series. Here we present
a summary of the PCA procedure and cluster analysis
for completeness.
With the PCA we are able to reduce the number of
parameters needed to describe a given profile. Each pro-
file, S(λj), j = 1, ..., Nλ (Nλ is the number of wavelength
points in the profile) is composed of a linear combination
of eigenvectors ei(λj), i = 1, ..., n:
S(λj) = Σ
i=1ciei(λj), (3)
where the ci are appropriate constants. The eigenvectors
and constants for a given set of profiles are obtained from
a singular value decomposition (SVD, Rees et al. 2000,
Socas-Navarro et al. 2001) and form an orthonormal ba-
sis with Nλ eigenvectors:
j=1ei(λj)ek(λj) = δik. (4)
Not all eigenvectors contain the critical information
needed to reproduce the profiles, some of the eigenvec-
tors carry information about the noise pattern. We can
therefore truncate the series expansion and use only a
small number of eigenvectors and corresponding coeffi-
cients to reproduce a given profile. The PCA guarantees
that when expansion of Eq. 3 is truncated at a given
order m, the amount of information in the lower orders
is maximized.
We performed the SVD for the two 8498 Å and 8542
Å Stokes V profiles separately. The resulting orthonor-
mal bases, and also the cluster analysis, depend on the
subset of profiles used to construct it. Because of this
we included all Stokes V profiles from pixels where the
8498 Å Stokes V amplitude is above 7 × 10−3Ic, alto-
gether 13671 profiles. Visual inspection of the eigenvec-
tors shows that the first 11 eigenvectors (approximately)
Fig. 3.— Dispersed images of the slit. The arrows mark the locations of the two photospheric iron lines and the horizontal lines in the
intensity images are the hairlines used to spatially coalign the two detectors. Wavelengths are measured from 8498 Å (left) and 8542 Å
(right).
contain relevant information about the actual shape of
the profiles whereas the remainder are associated with
the noise patterns.
The Stokes V profile pairs, now described with 11 × 2
coefficients corresponding to the 11 × 2 eigenvectors in-
stead of 102 (51 for each profile) wavelength points, were
organized into a predefined number of clusters. Before
doing this the vectors consisting of the 22 coefficients
were standardized, i.e., no information of the absolute
Stokes V amplitudes is left, only the relative amplitudes
of the 8498 Å and 8542 Å profiles. Based on the values
of the coefficients, 6 cluster centers were identified using
the k-means method (MacQueen 1967). It starts with k
random clusters, which through iterations are changed to
minimize the variability within a cluster and maximize
it between clusters. Each profile pair is then assigned
to the nearest cluster center in the 22-dimensional Eu-
clidean space. The choice of number of clusters used for
the cluster analysis is non-trivial. Since each data point
is described by 22 numbers we cannot visually distinguish
patterns in the spatial distribution of the points. Instead
the number of clusters was defined by trial and error, i.e.
so that each profile type in the time series or map is rep-
resented and each cluster is still clearly distinct from one
another. For each cluster a profile was constructed using
the eigenvectors and the averaged 2 × 11 coefficients of
all profiles belonging to that cluster.
Cluster analysis of the map shows the shapes of Stokes
V profiles in network regions with different magnetic
topologies, whereas the time series analysis describes how
a set of profiles from a certain magnetic topology changes
with time.
The results for the map are shown in Figure 5. Above
each profile is the percentage of all profiles belonging to
the cluster, the mean distance in the Euclidean space
Fig. 4.— Maps of the 8498 Å and 8542 Å lines’ Stokes I amplitudes, Stokes V amplitudes, area asymmetries and amplitude asymmetries
in the raster scan. The horizontal line seen in the amplitude images is a hairline used to spatially coalign the detectors. The vertical line
shows the position of the slit during the time series. Note that x-axis is stretched compared with y-axis.
of the profiles to the cluster center, and the standard
deviation of the mean. The smaller the distance to the
cluster center, the more compact the cluster is and the
better the cluster describes the profiles. The standard
deviation is proportional to the spread of the distances
in each cluster. In general, clusters with the least number
of profiles belonging to them have larger mean distances.
Three points can be deduced from the figure. First,
asymmetric profiles should be common. In fact, they ap-
pear to be more common than symmetric ones. Second,
even though the two Ca lines are formed fairly close to
one another (the 8498 Å line core optical depth is unity at
about 1 Mm and the 8542 Å 0.2 Mm higher up in the ra-
diation hydrodynamic simulations by Carlsson and Stein
1997), the 8498 Å and 8542 Å profiles in a given cluster
are often clearly different from one another. Third, in
all cluster profiles the far-red wings have the same polar-
ity as the far-blue wings, indicating that the lower parts
along the line-of-sight of the atmosphere, where the wings
are formed, are dominated by a single magnetic polarity.
The clusters differ from one another in several differ-
ent ways: the degree of asymmetry, and distinct relation-
ships between the 8498 Å and 8542 Å line profiles, rel-
ative amplitudes, etc. However, quantitative measures,
such as profile asymmetries, of the clusters do not nec-
essarily represent the members of a given cluster very
well. For example, the variation of Stokes V amplitude
asymmetries within a cluster is large and the mean is
not necessarily the same as that of the cluster profile.
The cluster analysis retrieves qualitative similarities and
gives a basis for morphological classification, rather than
representing quantitative similarities within the data. To
illustrate this point, Figure 6 displays histograms of the
clusters showing the Stokes V amplitudes and asymme-
tries for all profiles belonging to a given cluster. Shown
in Figure 7 is the spatial distribution of the clusters. The
smallest network patches often consist of only cluster 1
and cluster 2 profiles. The middle of the largest network
patch is a mixture of different clusters.
In most cases, the profiles at the edges of the network
patches belong to cluster 1. This is the most common
cluster consisting of 35.6 % of all the profile pairs in
the map. The cluster 1 profiles are asymmetric, 8542
Å more so than 8498 Å, and they also have opposite
signs of amplitude and area asymmetries. The amplitude
histograms of profiles belonging to this cluster show that
they have in general low amplitudes, as one might expect
from profiles located at the edges of the network. The
large amplitude asymmetry in the 8542 Å cluster profile
is not seen in the observed profiles. In fact, only very few
profiles exhibit such large asymmetries and there is only a
slight tendency of the profiles having more often negative
than positive amplitude asymmetries. The cluster area
asymmetries are in better agreement with the observed
profiles belonging to this cluster.
Regions of cluster 2 profiles are often located adjacent
to patches of cluster 1 profiles. The cluster 2 profiles
account for 20.0 % of all profile pairs in the map. The
cluster profiles are fairly antisymmetric. This is seen in
the observed profiles as well: the asymmetry histograms
tend to be narrow and only slightly offset from zero. The
relative amplitudes of the two cluster profiles are very
different: the 8498 Å amplitude is a factor 3 larger. The
disproportionality is not as large in the observed profiles
though the amplitude histograms show that in general
8498 Å has a larger amplitude than 8542 Å. The range of
observed amplitudes is considerably larger than in cluster
Of the profile pairs in the map 14.1 % belong to cluster
3. Also, these profiles are often found in regions close to
the network edges by the patches of cluster 1 profiles.
Both cluster profiles have multiple lobes and are asym-
metric, 8498 Å more in amplitude and 8542 Å in area.
This is also seen in the histograms of the observed asym-
Fig. 5.— Results of cluster analysis of the Stokes V profile pairs in the map. Line on left is 8498 Å and on right 8542 Å. Shown are the
percentages of profile pairs belonging to each cluster, and the mean distance and its standard deviation of the profiles to the cluster center.
metries. There is a strong emission feature on the blue
side of the line in the 8498 Å cluster profile. It is weaker
in the 8542 Å profile. The histograms for cluster 3 are
nearly identical to those of cluster 1. This illustrates how
cluster analysis based on PCA is captures the qualitative
differences in the line profiles.
Cluster 4 consists of 13.5 % of the profile pairs. Most
of the observed profiles belonging to this cluster are near
to the middle of the largest network patches. The 8498 Å
cluster profile is dominated by a strong emission feature
in the blue lobe. This feature is not visible in the 8542 Å
cluster profile. The overlap between the two lines’ ampli-
tude histograms is fairly small. Also the cluster profiles
show this difference in the relative amplitudes: 8542 Å
has a significantly lower amplitude than 8498 Å. Except
for the 8542 Å area asymmetry histogram, all histograms
are centered around zero. The range of area asymmetries
in the 8542 Å line is large and the distribution is skewed
towards negative values. This trend in the 8542 Å area
asymmetries is seen in several of the clusters.
The patches of profiles belonging to the fifth cluster
(9.6 %) are also found in the less homogeneous middle
regions of the network elements. The 8498 Å cluster
Fig. 6.— Stokes V statistics of the map clusters. The histograms are for all profiles belonging to the given cluster and the dotted vertical
lines show the area and amplitude asymmetries for the cluster profiles.
profile has a factor 2 lower amplitude than 8542 Å. This
is not seen in the amplitude histograms but there is a
large overlap between the two histograms. The cluster
profiles are fairly antisymmetric and also the histograms
of observed profile asymmetries are centered around zero.
The 8542 Å area asymmetry is again the exception: it is
centered around a negative value.
Cluster 6 is the smallest cluster with 7.2 % of the pro-
files. Patches of cluster 6 profiles are located in regions
with cluster 4 and 5 profiles. The 8498 Å cluster profile is
very similar to that of cluster 5. Like cluster 5, the 8542
Å cluster 6 profile has a factor 2 larger amplitude and
the amplitude histograms overlap nearly entirely. All the
cluster 6 histograms are very similar to cluster 5. The
major difference between the two is that there is very
little structure in the 8542 Å line profile.
3.2. Time-dependent behavior
The cluster analysis results of the time series are shown
in Figure 8, and the spatio-temporal distribution is cap-
tured in Figure 9. The clusters consist of profiles at
rest with varying degrees of structure, and profiles where
the blue side is in emission. While there are temporal
changes in the clusters, there are no clear periodic pat-
terns visible. Most slit positions have a preferred cluster
or in some cases the slit position is dominated by two
clusters. Positions where more than 2 clusters are domi-
nant are rare.
Because the slit moved occasionally during the time
series, no meaningful power spectra can be made from
this data set. The time series data do however allow
for a qualitative analysis of the time-dependent behav-
ior. Comparing network and internetwork pixels reveals
some interesting features: the network, especially in the
intermediate flux regions, is very dynamic with propagat-
ing shock-like features and large self-reversals appearing
frequently in both Stokes I and V . In comparison, the
internetwork is less dynamic, intensity oscillations are
present but they are much weaker than in the network.
No structures indicating the presence of shocks, are seen
in the internetwork profiles. In agreement with prior ob-
servations of chromospheric lines (e.g., Noyes 1967), any
oscillation periods in the network appear to have a longer
period than in the internetwork.
We now examine three different regions, namely an
internetwork pixel, an intermediate flux network pixel,
and a strong network pixel.
3.2.1. Internetwork
In Figure 10 the time evolution of a typical internet-
work pixel is shown. The location of the pixel is marked
by an asterisk in Figure 2. The data were taken when
the slit was stationary. No Stokes V signal above the
noise level is seen in the pixel. The Stokes I profiles of
both Ca lines change periodically in width and position
of the line center, but no self-reversals are seen. Also,
the line-wing intensity shows some oscillations.
3.2.2. Intermediate flux network
The difference between the internetwork and network
regions with intermediate flux (Fig. 11) is dramatic: the
Fig. 7.— Spatial distribution of the clusters in the map. The black areas (0 cluster) correspond to regions where the Stokes V amplitudes
are below 7× 10−3Ic and where no cluster analysis was performed.
network region is much more dynamic, and highly asym-
metric profiles, in both lines Stokes I and V , are seen.
The time dependent behavior of the photospheric iron
line is quite similar to what is seen in the internetwork.
The Stokes I in both lines has a clearly oscillating be-
havior with bright, very asymmetric episodes followed
by a darker, more symmetric episodes. The period for
the oscillation is about 4 minutes, i.e. below that as-
sociated with the acoustic cutoff frequency (about 5.3
mHz). This may be caused by the presence of inclined
magnetic fields can lower effectively the acoustic cutoff
frequency (Bel & Leroy 1977). The time evolution of the
8542 Å Stokes I has a diagonal structure moving from
blue to red. This indicates the presence of propagating
compressible waves (Carlsson & Stein 1997). The bright
part, which corresponds to a large self-reversal, is clearly
shifted towards the blue. This is seen in the 8498 Å line
profiles as well, although these profiles tend to be more
flat-bottomed. In general, the self-reversals and over all
variation is larger in the blue wing than in the red. This
is true for all slit positions which exhibit strong time-
dependent behavior.
The Stokes V image of the 8498 Å line also shows
strong diagonal structures that coincide in time with the
dark phases of Stokes I. Inspection of individual pro-
files (Fig. 12) reveals a pattern of multiple lobes in the
Stokes V profiles. These lobes are on the blue side of the
line core and their amplitudes and positions vary period-
ically in time resulting in the diagonal structure seen in
the image. The lobes can be identified with the emission
features seen in the Stokes I profiles. The 8542 Å line
Stokes V image shows a pattern of a multi-lobed pro-
files whose amplitudes vary strongly in time. The large
Stokes V amplitude phase coincides with the bright, very
asymmetric phase seen in the intensity profiles. The red
wings always exhibit less structure and variation than
the blue wings.
3.2.3. Strong network
Stokes I and V profiles seen in the strong network re-
gions (Figs. 13 and 14) would appear at first glance to
be a mixture of the less dynamic internetwork and the
highly dynamic intermediate flux region. The Stokes I
profiles exhibit the same pattern of bright (more asym-
metric) and dark (less asymmetric) phases as seen in the
intermediate flux region. The difference between the two
phases is however not as large: the amplitude of the self-
reversals, especially in the 8542 Å intensity profiles, is
much smaller than in the intermediate flux case.
The Stokes V images resemble those of the intermedi-
ate flux region: some diagonal structures are seen, but
they are weaker. The 8542 Å line Stokes V profiles have a
time varying amplitude but the profiles are not as asym-
metric and they are not necessarily multi-lobed. The dif-
Fig. 8.— As Fig. 5 but for the time series.
ference between the time-dependent behavior of the red
and blue lobes of the profile, i.e. the red lobe varies less
in time, is even more clear here than in the intermediate
flux region.
3.3. Statistics
Histograms of the Stokes I amplitude integrated over
250 mÅ around the line core for the two Ca lines are
shown in the top-left panel of Figure 15. These his-
tograms include both the map and time-series profiles.
Because there are almost five times as many profiles in
the time-series as there are in the map, the histograms
are dominated by the time-series profiles. Both lines ex-
hibit a wide range of values. Except for the peaks at
low intensities, the histograms are fairly flat. The dark-
est (i.e. lowest core intensity or most absorption) am-
plitudes, are associated with the internetwork, and the
brightest with the network.
Histograms of the Stokes V amplitudes (top right panel
of Fig. 15) peak at the same value in both lines, 0.003 Ic,
but the 8498 Å histogram tail decays more slowly. Since
the 8498 Å line is formed slightly lower of the two and
the lines are roughly equally sensitive to magnetic fields
(effective Landé g factors are 1.07 and 1.10 for the 8498
Å and the 8542 Å lines, respectively), it is not surprising
that the 8498 Å histogram has the longer tail.
Fig. 9.— The spatio-temporal distributions of the clusters for the first slit position in the time series. The black areas correspond to
regions where the Stokes V amplitudes is ≤ 7×10−3Ic. The vertical lines show the period with the best seeing when the slit was stationary.
Both lines’ Stokes V amplitude asymmetry histograms
(bottom left panel of Fig. 15) have very similar shapes
and similar widths. There are more positive asymme-
tries in both lines: 56% in 8498 Å and 64 % in 8542
Å (Table 1). The mean amplitude asymmetries are also
positive, and the 8542 Å mean asymmetry is two times
larger. There are more negative amplitude asymmetries
in the 8542 Å map than in the time series. Non-zero am-
plitude asymmetries indicate at least one of two things:
the spatial pixels consist in most cases of at least two
atmospheric components that are shifted relative to one
another or that there are velocity and/or magnetic field
gradients present in the atmosphere.
The area asymmetry histograms (bottom right panel
of Fig. 15) of the two calcium lines repeat the pattern al-
ready seen in the cluster profiles: the 8542 Å histograms
is centered around a negative value and the 8498 Å is
centered at roughly zero, though the mean is slightly pos-
itive. The 8542 Å histogram is significantly wider than
the 8498 Å histogram. A multi-component atmosphere
alone cannot produce area asymmetries, so the existence
of non-zero area asymmetries indicates the presence of
velocity and possibly magnetic gradients in the atmo-
sphere.
In the 8542 Å line 66 % of the profiles have negative
area asymmetries whereas in the 8498 Å line the majority
of the profiles, 64 %, have positive area asymmetries (Ta-
ble 1). To better understand why the area asymmetry
histograms of the lines are so different, we need to look
at the components of the area asymmetry separately i.e.
the sign of the blue lobe and the total area of the Stokes
V profile. One possible cause for the difference in the
histograms might be that the distribution of signs of the
blue lobe is different in the two lines. Closer inspection
reveals that this is not the explanation. The vast major-
ity of both lines, over 80 %, have a negative sign. (Here
the sign is defined to be the sign of the local maximum
or minimum amplitude of the blue lobe). A second pos-
sible explanation is that the
V (λ)dλ is different in
the two lines. This is found to be the case. The 8542 Å
line has more profiles with a positive area and the 8498
Å has slightly more profiles with a negative area. (Note
that the sign of the area asymmetry is the product of
the sign of the blue lobe and the area; eq. 2.) The area
of the Stokes V profile is strongly affected by the emis-
sion features. These features, and their amplitudes, are
related to the self-reversals seen in the Stokes I profiles.
The self-reversals are stronger on the blue side of the line
core than on the red. In general, the blue lobes of the
Stokes V profiles have negative amplitudes and the effect
of the emission features is then to reduce the amplitude,
and in some cases, make it positive and this way reduce
the overall negative area.
The effect of the emission features on the amplitude
asymmetries is not as large because the amplitude will
be affected only if the emission feature is located at the
Fig. 10.— Time dependent behavior of Stokes I in an internetwork pixel. Location of the pixel is marked with an asterisk in Figure 2.
same wavelength as the maximum absolute amplitude.
Also if the profile has a wide blue lobe, i.e., the wings
contribute significantly, a local reduction in peak ampli-
tude is counterbalanced by a comparable signal in the
other parts of the blue lobe. The resulting profile will
have nearly the same amplitude in the blue lobe as be-
fore, but the area will be reduced leading to a smaller, or
even negative, area asymmetry. Since the self-reversals
are larger in the 8542 Å line, this scenario is more likely
to apply to it than the 8498 Å line.
Both lines’ area and amplitude asymmetries are found
to be inversely proportional to the Stokes V amplitudes.
The scatter, especially in the 8542 Å line, is fairly large.
PCA also allows us to ensure that the determination of
Stokes V asymmetries is not dominated by noise. Recon-
structing the profiles using only the 11 first eigenvectors
(i.e., essentially noise-free profiles) and then computing
the asymmetries reproduces the Stokes V amplitude and
asymmetry histograms. To test if the negative histogram
peak in the 8542 Å line is an artifact caused by data re-
duction, we computed area asymmetries for the datasets,
but after first removing the fringe pattern caused by the
optics. This did not alter the area asymmetry histogram.
Another artifact that could cause the offset is an incor-
rect subtraction of the tilt caused by the detector in the
continuum intensity. To remove the offset in the his-
tograms by means of changing the tilt causes a clearly
visible lopsidedness in the Stokes I profiles. Lastly, to
make sure that the choice of the integration range is not
the cause of the offset, we used a constant bandwidth
for area asymmetries and it also reproduces the 8542 Å
area histogram offset. (Besides these issues, there are no
other obvious artifacts that would cause the offset.) We
therefore conclude that the offset is not caused by the
fringing or incorrect subtraction of the tilt in the contin-
uum intensity.
4. COMPARISON OF OBSERVATIONS WITH A HIGH-β
SIMULATION
In P06 we synthesized Stokes profiles for the Ca IR
triplet lines in the high-β regime. This was done by
combining a radiation hydrodynamic code (see for exam-
ple Carlsson & Stein 1997) with a weak magnetic field
and using a nLTE Stokes inversion and synthesis code
(Socas-Navarro et al. 2000b) to produce, based on snap-
shots of the simulation, a time series of the lines’ Stokes
vectors. The simulation is driven by a photospheric ve-
locity piston and its dynamics are dominated by upward
propagating acoustic waves in a simple magnetic field
topology. The simulation shows that the radiative trans-
fer is very similar in all the Ca IR triplet lines. The
differences between the line behaviors in the simulation
are mainly due to the lines having slightly different for-
mation heights and thus experiencing a difference in the
amplitudes of the shocking waves: the higher the line is
formed, the larger the amplitude of the passing wave is.
In the simulation there is no feedback from the mag-
netic fields on the dynamics and the waves are purely
acoustic. The observations have limited spatial and tem-
poral resolutions whereas the simulation is much better
resolved.
4.1. Comparison of time dependent behavior
As the acoustic waves in the simulation propagate up-
wards and eventually form shocks, a time-varying pat-
Fig. 11.— Time dependent behavior of Stokes I and V in an intermediate flux pixel. Location of the pixel is marked with a diamond in
Figure 2.
Fig. 12.— Time evolution of individual Stokes I and V profiles in an intermediate flux pixel. Location of the pixel is marked with a
diamond in Figure 2.
Fig. 13.— Time evolution of Stokes I and V in a network pixel. Location of the pixel is marked with a triangle in Figure 2.
Fig. 14.— Time evolution of individual Stokes I and V profiles in a network pixel. Location of the pixel is marked with a triangle in
Figure 2.
Fig. 15.— Histograms of Stokes I and V amplitudes, and Stokes V amplitude and area asymmetries of the map and time-series.
tern of disappearing and reappearing Stokes V lobes is
seen (Fig. 16). The pattern is strongest in the highest
forming line, i.e. 8542 Å. Wave propagation is also seen
in the Stokes I profiles. There are no large self reversals
or brightenings, instead the position of the line minimum
changes periodically and forms a saw-tooth like pattern
where the red shift takes more time than the blue shift
phase.
If we first compare the simulated profiles to the in-
ternetwork observations (Fig. 10), we see that the
strong signatures of shocks seen in the simulation are not
present in the observations. In the simulation the Ca IR
triplet is formed in a region where the waves are just be-
ginning to shock. If the formation height of the lines or
the shocks in the simulation is off, compared to the real
Sun, by a small amount, even 50 km, the lines’ temporal
evolution may look very different. Another possible ex-
planation to why we see no strong indications of shocks
is the temporal and/or spatial resolution: there may be
several components oscillating out of phase relative to
one another in a given resolution element. However, the
photospheric velocities are very similar in the internet-
work and network, but the network profiles show strong
self-reversals. This suggests that spatial and temporal
resolution alone cannot explain the lack of strong signa-
tures of shocks in the internetwork.
Observations of the quiet Sun show varying degrees
of oscillatory power (compare for example Lites et al.
(1993) [Ca II H and K] or UV data of Judge et al. 2003,
McIntosh & Judge 2001 and Wikstøl et al. 2000). This
variation may be related to the local magnetic topology,
especially to the possible existence of a magnetic canopy
(McIntosh et al. 2003; Vecchio et al. 2006). The region
observed here was less oscillatory than average but still
not exceptionally quiet.
Both the simulated profiles and observed network pro-
files (Fig. 13) show time varying patterns where the
Stokes I and V amplitudes change periodically. In the
simulation the wave propagation manifests itself in the
Stokes I profiles most clearly as a shift of the line core
and the saw-tooth shape of the time series. In the ob-
servations, waves cause the lines’ periodically varying
self-reversals that result in alternating bright and dark
phases. There are indications of diagonal structures in
the observed Stokes I images, but they are not nearly
as clear as in the simulation. In the simulation the up-
ward propagating waves cause the blue and red lobes of
the Stokes V profiles to disappear alternately. In con-
trast, the observed time varying pattern in Stokes V
looks more complicated: there is much more structure
in the observed profiles, especially in the line cores, than
in the simulation. This is related to the simulated pro-
files not exhibiting strong self-reversals as seen in the
observations.
In the simulation, because of radiative cooling and ex-
pansion of the falling material, the down flows are in
general cooler than the up flows. In the synthesized pro-
files this manifests itself by the red wings of the Stokes
I profiles showing less variations, though the difference
with the blue wing is quite small. Similar behavior is also
seen in the observations: the self-reversals are in general
larger in the blue wing of the Stokes I profiles and the red
lobes of the Stokes V profiles show clearly less variation.
4.2. Comparison of statistics and Stokes V
morphologies
In the simulation the magnetic field decays exponen-
tially with height and therefore the Ca II Stokes V am-
plitudes are significantly lower than the Fe I 8497 Å am-
plitude. In the observations the Ca and Fe line Stokes V
profiles have roughly the same amplitudes. This may be
explained by the field decaying much slower with height
in the observations, or by the filling factor in the ob-
servations being smaller in the photosphere than in the
chromosphere.
Both Ca II lines’ observed Stokes V profiles have a sig-
nificant amount of signal in the wings. In the simulations
only the 8498 Å line Stokes V has extended wings with
large amplitudes (Fig. 4 in P06). The amount of signal
in the wings depends on the atmospheric magnetic field
Fig. 16.— Time evolution of Stokes I and V profiles in the high-β simulation (P06). The Stokes V signal in wavelength range -1.2 to -0.6
Å in the 8498 Å image is scaled down with factor 7.5 in order to display both the Ca II 8498 Å and Fe I 8497 Å lines in the same panel.
gradient. If there is no gradient the wings of all three
Ca lines have very little signal. Whereas a model atmo-
sphere with a constant field gradient produces profiles
where all lines, 8498 Å the most, have some signal in
the line wings and an exponential field produces profiles
with the largest wings. Depending on where the gradi-
ent is located and how strong the field is, the Ca lines
may or may not have similar Stokes V profiles. Based
on the profile shapes and relative amplitudes, it is ob-
vious that the magnetic topology in the observations is
different from the simulation.
Formation of area and amplitude asymmetries in the
simulation is coupled. The correlation is especially
strong in the 8542 Å line (upper row of Fig. 17). In
the 8498 Å Stokes V profiles the strong wings affect
the asymmetries, and the correlation is weaker. The
observed area and amplitude asymmetries of both lines
show less correlation. This is at least partly because the
observed profiles have more complex shapes than in the
simulation.
The lower panels in Figure 17 show the Stokes V asym-
metry histograms for the simulation. The observed his-
tograms are re-plotted to enable direct comparison. In
the simulation both lines’ amplitude and asymmetry his-
tograms are centered roughly around zero (percentage-
wise there are a couple of percent more negative than
positive asymmetries). This was not the case in the ob-
servations where all the asymmetries, except the 8542 Å
area asymmetry, have clearly more positive than nega-
tive values, i.e. the blue lobe is larger in area/amplitude
than the red lobe.
The observed 8498 Å profiles are more dynamic than
the simulated ones. Consequently the observed 8498 Å
asymmetry histograms are clearly wider than the simu-
lated. Because there is very little signal in the simulated
8542 Å Stokes V profile wings, when an upward propa-
gating wave causes a Stokes V lobe to disappear, there is
no signal in the line wing to contribute to the amplitude.
This leads to the extreme amplitude asymmetries in the
simulations and in the additional lobes at large values
in the simulated 8542 Å line area asymmetry histogram.
Since the observed profiles have a significant amount of
signal in the wings, the extreme amplitude asymmetries
are moderated, and no lobes at large values are seen in
the histogram.
5. CONCLUSIONS AND DISCUSSION
So far most spectropolarimetric studies using the
Ca II IR triplet lines have focused on active regions
(e.g., Socas-Navarro, Trujillo Bueno, & Ruiz Cobo
2000a; López Ariste, Socas-Navarro, & Molodij
2001; Socas-Navarro 2005;
Uitenbroek, Balasubramaniam, & Tritschler 2006).
The observations presented here show that these lines
are also promising candidates for studying the magnetic
chromosphere outside of active regions. Interpreting the
observations, however, is not straight forward.
The main results of the analysis presented here are:
• Classification of Stokes V profile shapes.
Asymmetric line profiles are very common and that
the two lines, despite being formed fairly close in a
geometrical sense, often do not have similar shapes.
Furthermore, the edges of the network patches ex-
hibit profile shapes different from those seen in the
center of the patches. The cluster analysis results,
as expected, in a qualitative, not quantitative, de-
scription of the profile shapes.
• Statistics of the line profiles.
The 8542 Å area asymmetry is predominantly neg-
ative; while the 8498 Å area asymmetry and the
amplitude asymmetries are usually positive.
• Time dependent behavior.
The enhanced network has very different dynamic
behavior compared with the internetwork. It is
more dynamic and the oscillation period, as seen
in both Stokes I and V , is greater than in the in-
ternetwork.
• Comparison with high-β simulation.
Oscillations are present in both the observations
and the simulation. The simulated profiles are
more dynamic than the observed internetwork pro-
files. The opposite is true for network profiles.
In the simulation, the formation of asymmetries is
more tightly coupled than what is seen in the ob-
servations. Except for the 8542 Å amplitude asym-
metry the observed profiles show a wider range of
asymmetries. And lastly, the peculiar negative area
asymmetries seen in the observed 8542 Å line and
the tendency of the other asymmetries to be posi-
tive are not reproduced by the simulation.
The tendency of large Stokes V asymmetries to de-
crease with an increasing signal amplitude has also been
observed in photospheric lines (Grossmann-Doerth et al.
1996). In the photosphere a magnetic canopy is one pos-
sible explanation: the canopy gives rise to asymmetries
in the lines, and as a flux tube diameter increases, the
relative contribution from the canopy to the Stokes V
signal decreases. In the photosphere the scatter in an
amplitude vs. asymmetry plot is significantly larger in
the area than in the amplitude. No large difference is
seen in the area and amplitude asymmetry scatters of
the Ca II lines.
In the quiet Sun photosphere, more positive
than negative Stokes V asymmetries are found
(Grossmann-Doerth et al. 1996). In contrast with 8498
Å line (where there is no large difference in the mean area
and amplitude asymmetries) the photospheric mean area
asymmetries are significantly smaller (4 % in the Fe I
6302 Å line) than the mean amplitude asymmetries (15
% in the Fe I 6302 Å line). The photospheric asymme-
tries are often attributed to multiple atmospheric compo-
nents within a resolution element. In the chromosphere,
however, gradients have to play a dominant role since
the formation of area asymmetries require them. An-
other piece of evidence of the importance of gradients
in the chromosphere is that Milne-Eddington inversions,
which include the Paschen-Back effect of the He I 10830
Å triplet, are not able to reproduce the observed area
asymmetries (Sasso & Solanki 2006).
Fig. 17.— Stokes V asymmetries of the simulated and observed profiles. Upper 4 panels show the correlation of amplitude and area
asymmetries in the simulated and observed Ca lines. The Pearson correlation coefficient for each case is given. The asterisk symbols show
the mean for each 0.1 wide bin and the error bars show the standard deviation. The lower panels are histograms of observed and simulated
amplitude and area asymmetries.
Khomenko et al. (2005) used a 3-dimensional magne-
toconvection model to synthesize photospheric magneti-
cally sensitive lines in the visible and IR. There are more
positive than negative Stokes V asymmetries in their syn-
thetic profiles. They found that reducing the spatial res-
olution increases the number of irregular stokes V pro-
files (though the number of strongly asymmetric profiles
decreases). They conclude that the asymmetries reflect
more inhomogeneities in the horizontal direction than in
the vertical. In the chromosphere large velocity gradients
are more common and variation in the vertical direction
are likely to be more important than variation in the hor-
izontal direction. When these two factors are combined
with the observed area asymmetries, one concludes that
the chromospheric asymmetries mainly reflect the line-of-
sight inhomogeneities, and not variations in the horizon-
tal direction. Despite the apparent similarities between
the photospheric and chromospheric Stokes V profiles,
the underlying mechanism causing the asymmetries does
not appear to be the same. Drawing parallels between
the chromosphere and photosphere is problematic since
the two regions exist in very different physical regimes.
The discrepancy between the Stokes V asymmetry his-
tograms of the observations and the simulation may be
related to the self-reversals. The simulated profiles ex-
hibit only small self-reversals. The observations show
large self-reversals in the Stokes I profiles and accompa-
nying emission features in the Stokes V profiles. These
features are stronger on the blue side of the line cores.
Another effect that contributes to the imbalance is that
that the down flow phase lasts longer. Our observations,
especially with a 5 second exposure time, sample more
profiles with red-shifts and positive asymmetries (since
there will be more emission on the blue side). However,
inspection of Fig. 16 shows the same to be true of the
simulations. If this is the case, why are there not more
positive than negative asymmetries in the simulation as
well?
The sample of these observations is limited because the
majority of the profiles are drawn from the same three
slit positions which sample the same local magnetic field
configuration. It would not be surprising if histograms
made of profiles from a variety of quiet-Sun magnetic
field topologies would have somewhat different shapes.
The complexity of the observed profiles makes the inter-
pretation of the area and amplitude asymmetries diffi-
cult. Because of multiple lobes and the strong signal in
the line wings, the asymmetries are not necessarily good
proxies for the overall complexity of the Stokes V pro-
files. This is especially true if the two asymmetries are
viewed separately.
It is a well known result that the network intensity
oscillations have a longer period than the internetwork
(e.g. Orrall 1966, Lites et al. 1993, Banerjee et al. 2001).
This has also been observed before in the Ca II IR
lines (Deubner & Fleck 1990). Why do the intermedi-
ate flux regions in our observations appear to be more
dynamic than the stronger flux regions? It may be re-
lated to a more complex magnetic topology at the edges
of the network patches. The observations show no sig-
nal above the noise in Stokes Q and U , so we can-
not draw any conclusions of possible horizontal fields.
Any signal would be affected by atomic polarization
(Manso Sainz & Trujillo Bueno 2003) making the inter-
pretation exceedingly complex. The filling factor in the
network is not likely to be very large, and is likely smaller
at the edges than in the center of the network patch. In-
versions by Bellot Rubio et al. (2000) of average Stokes
profiles in a plage region gave a filling factor of 0.5 a
z = 0 km. The filling factor in the photospheric net-
work can safely be assumed to be lower than this. In
fact, in recent inversions by Domı́nguez Cerdeña et al.
(2006), which included a small patch of network, the pho-
tospheric filling factor in the patch center was as small
as 0.1. The network magnetic fields must expand with
height and consequently the chromospheric filling fac-
tor must exceed photospheric values. Results of com-
paring photospheric and chromospheric magnetograms,
however, Zhang & Zhang (2000) suggest that the sizes
of the network magnetic elements are not very different
at the two heights . The chromospheric magnetograms in
the comparison are based on the Hβ line. Its interpreta-
tion is complicated by the magnetically sensitive blends
close to the line core, and the line may suffer from same
problems as the Hα line when used as a proxy for chro-
mospheric magnetic fields, namely that the photospheric
contribution to the polarization signal is not insignificant
(Socas-Navarro & Uitenbroek 2004). Lastly, the size of
network patches is not directly linked with the filling fac-
tor. We see some expansion of the network with height in
the magnetograms of the map (Fig. 2), especially when
comparing the Ca II 8498 Å and 8542 Å magnetograms.
But since the magnetograms were constructed by using
the weak field formula, and the network fields have gra-
dients and are not necessarily weak, the magnetograms
are not accurate. Also the choice of color scaling of the
images affects the comparison. However, the apparent
expansion is not necessarily an artifact, since expansion
of network seen in magnetograms has also been reported
by Giovanelli (1980).
Obviously we need to understand better the topology
of the network magnetic fields. To do this we plan to
perform nLTE inversions of these data in the near fu-
ture. The inversions will help further in understanding
the formation dynamics of the Ca II IR lines in the quiet
Sun, and hopefully reveal how the underlying atmosphere
differs from that used in the simulation. An important
question to answer is why the two Ca lines behave as
differently as they do. Having a time series taken during
good seeing would be helpful. Also in order to expand the
analysis to internetwork regions, better spatial resolution
is required. Another interesting question is how much
variation there is in dynamics in different internetwork
regions, and how well the differences can be explained in
terms of the surrounding magnetic fields as has been sug-
gested by Vecchio et al. (2006) based on imaging data of
Ca II 8542 Å Stokes I. To fully investigate this in detail
high quality data of the full Stokes vector are needed.
TABLE 1
Observed Stokes V asymmetries
8498 Å 8498 Å 8498 Å 8542 Å 8542 Å 8542 Å
< 0 (%) > 0 (%) mean (%) < 0 (%) > 0 (%) mean (%)
σa 43.2 55.7 3.1 36.6 61.4 6.3
σA 35.5 64.5 3.3 69.7 30.3 -6.8
Note. — Percentages of observed Ca II 8498 Å and 8542 Å Stokes V
amplitude and area asymmetries with negative (i.e. red lobe larger) and
positive (i.e. blue lobe larger) signs.
Thanks to Doug Gilliam, Joe Elrod and Mike Bradford for all their invaluable help during the observing run.
REFERENCES
Andretta, V. & Jones, H. P. 1997, ApJ, 489, 375
Banerjee, D., O’Shea, E., Doyle, J. G., & Goossens, M. 2001,
A&A, 371, 1137
Bel,N. & Leroy, B. 1977, A&A, 55, 239
Bellot Rubio, L. R. 2006, ArXiv Astrophysics e-prints
Bellot Rubio, L. R., Ruiz Cobo, B., & Collados, M. 2000, ApJ,
535, 489
Carlsson, M. & Stein, R. F. 1997, ApJ, 481, 500
Deubner, F.-L. & Fleck, B. 1990, A&A, 228, 506
Domı́nguez Cerdeña, I., Almeida, J. S., & Kneer, F. 2006, ApJ,
646, 1421
Giovanelli, R. G. 1980, Solar Phys., 68, 49
Grossmann-Doerth, U., Keller, C. U., & Schuessler, M. 1996,
A&A, 315, 610
Judge, P. G., Carlsson, M., & Stein, R. F. 2003, ApJ, 597, 1158
Keller, C. U. & The Solis Team. 2001, in ASP Conf. Ser. 236:
Advanced Solar Polarimetry – Theory, Observation, and
Instrumentation, ed. M. Sigwarth, 16–+
Khomenko, E. V., Collados, M., Solanki, S. K., Lagg, A., &
Trujillo Bueno, J. 2003, A&A, 408, 1115
Khomenko, E. V., Shelyag, S., Solanki, S. K. & Vögler, A. 2005,
A&A, 442, 1059
Lagg, A. 2005, in ESA SP-596: Chromospheric and Coronal
Magnetic Fields, ed. D. E. Innes, A. Lagg, & S. A. Solanki
Landi Degl’Innocenti,E. 1992, in Solar Observations: Techniques
and Interpretation, First Canary Islands Winter School of
Astrophysics, ed. F. Sanchez, M. Collados & M. Vazquez
Lites, B. W., Chipman, E. G., & White, O. R. 1982, ApJ, 253, 367
Lites, B. W., Rutten, R. J., & Kalkofen, W. 1993, ApJ, 414, 345
López Ariste, A., Socas-Navarro, H., & Molodij, G. 2001, ApJ,
552, 871
MacQueen, J. 1967, in Proceedings Fifth Berkeley Symposium on
Math. Stat. and Prob., ed. L. M. LeCam & J. Neyman, 281–+
Manso Sainz, R. & Trujillo Bueno, J. 2003, Physical Review
Letters, 91, 111102
Mart́ınez Pillet, V., L. B. W. . S. A. 1997, ApJ, 474, 810
McIntosh, S. W., Fleck, B., & Judge, P. G. 2003, A&A, 405, 769
McIntosh, S. W. & Judge, P. G. 2001, ApJ, 561, 420
Neckel, H. & Labs, D. 1984, Solar Phys., 90, 205
Noyes, R. W. 1967, in IAU Symp. 28: Aerodynamic Phenomena
in Stellar Atmospheres, ed. R. N. Thomas, 293–+
Orrall, F. Q. 1966, ApJ, 143, 917
Paletou, F. & Molodij, G. 2001, in ASP Conf. Ser. 236: Advanced
Solar Polarimetry – Theory, Observation, and Instrumentation,
ed. M. Sigwarth, 9–+
Pietarila, A., Socas-Navarro, H., Bogdan, T., Carlsson, M., &
Stein, R. F. 2006, ApJ, 640, 1142
Rees, D. E., López Ariste, A., Thatcher, J., & Semel, M. 2000,
A&A, 355, 759
Rimmele, T. R. 2000, in Proc. SPIE Vol. 4007, p. 218-231,
Adaptive Optical Systems Technology, Peter L. Wizinowich;
Ed., ed. P. L. Wizinowich, 218–231
Sánchez Almeida, J. & Lites, B. W. 2000, ApJ, 532, 1215
Sasso, C., Lagg, A. & Solanki, S. 2006, A&A, 456, 367
Scharmer, G. B., Bjelksjo, K., Korhonen, T. K., Lindberg, B., &
Petterson, B. 2003, in Innovative Telescopes and
Instrumentation for Solar Astrophysics. Edited by Stephen L.
Keil, Sergey V. Avakyan . Proceedings of the SPIE, Volume
4853, pp. 341-350 (2003)., ed. S. L. Keil & S. V. Avakyan,
341–350
Shimizu, T. 2004, in ASP Conf. Ser. 325: The Solar-B Mission and
the Forefront of Solar Physics, ed. T. Sakurai & T. Sekii, 3–+
Socas-Navarro, H. 2005, ApJ, 631, L167
Socas-Navarro, H., López Ariste, A., & Lites, B. W. 2001, ApJ,
553, 949
Socas-Navarro, H., Trujillo Bueno, J., & Landi Degl’Innocenti, E.
2004, ApJ, 612, 1175
Socas-Navarro, H., Trujillo Bueno, J., & Ruiz Cobo, B. 2000a,
Science, 288, 1398
—. 2000b, ApJ, 530, 977
Socas-Navarro, H. & Uitenbroek, H. 2004, ApJ, 603, L129
Socas-Navarro, H. et al. 2006, Solar Physics, 235, 55
Stein, R. F. & Nordlund, Å. 2006, ApJ, 642, 1246
Uitenbroek, H., Balasubramaniam, K. S., & Tritschler, A. 2006,
ApJ, 645, 776
Vecchio, A., Cauzzi, G., Reardon, K. P., Janssen, K. & Rimmele,
T. 2006, astro-ph/0611206
Wikstøl, Ø., Hansteen, V., Carlsson, M., & Judge, P. G. 2000,
Astrophys. J., 531, 1150
Zhang, H. & Zhang, M. 2000, Solar Phys., 196, 269
http://arxiv.org/abs/astro-ph/0611206
