Issue |
A&A
Volume 513, April 2010
|
|
---|---|---|
Article Number | A1 | |
Number of page(s) | 8 | |
Section | The Sun | |
DOI | https://doi.org/10.1051/0004-6361/200913379 | |
Published online | 09 April 2010 |
Probing quiet Sun magnetism using MURaM simulations and Hinode/SP results: support for a local dynamo
S. Danilovic1,2 - M. Schüssler1 - S. K. Solanki1,3
1 - Max-Planck-Institut für Sonnensystemforschung, Max-Planck-Straße 2,
37191 Katlenburg-Lindau, Germany
2 - Astronomical Observatory, Volgina 7, 11160 Belgrade 74, Serbia
3 - School of Space Research, Kyung Hee University, Yougin, Gyeonggi
446-701, Korea
Received 30 September 2009 / Accepted 23 December 2009
Abstract
Context. Owing to the limited spatial resolution and
the weak polarization signal coming from the quietest regions on the
Sun, the organization of the magnetic field on the smallest scales is
largely unknown.
Aims. We obtain information about the magnetic flux
present in the quiet Sun by comparing radiative MHD simulations with
observations, with particular emphasis on the role of surface dynamo
action.
Methods. We synthesized Stokes profiles on the basis
of the MHD simulation results. The profiles are degraded by taking the
properties of the spectropolarimeter (SP) into account onboard the
Hinode satellite. We used simulation runs with different magnetic
Reynolds numbers ()
and observations at different heliocentric angles with different levels
of noise.
Results. Simulations with an imposed mixed-polarity
field and
below the threshold for dynamo action reproduce the observed vertical
flux density, but do not display a high enough horizontal flux density.
Surface dynamo simulations at the highest
feasible at the moment yield a ratio of the horizontal and vertical
flux density consistent with observational results, but the overall
amplitudes are too low. Based on the properties of the local dynamo
simulations, a tentative scaling of the magnetic field strength by a
factor 2-3 reproduces the signal observed in the internetwork
regions.
Conclusions. We find agreement with observations at
different heliocentric angles. The mean field strength in internetwork
implied by our analysis is roughly 170 G at the optical depth
unity. Our study shows that surface dynamo could be responsible for
most of the magnetic flux in the quiet Sun outside the network, given
that the extrapolation to higher
is valid.
Key words: Sun: granulation - Sun: photosphere
1 Introduction
The origin of the small-scale magnetic flux found in the quiet Sun is uncertain (de Wijn et al. 2008). The estimated order of magnitude for the magnetic Reynolds number of the granulation flow indicates that a substantial part of the magnetic field in the quiet Sun could be generated locally through dynamo action driven by near-surface convective flows (Petrovay & Szakaly 1993; Vögler & Schüssler 2007; Cattaneo 1999). The simulations suggest that the magnetic field could be organized in mixed-polarity structures down to very small spatial scales. The simulations exhibit a mostly horizontal field in the photospheric layers in the form of low-lying loops connecting nearby opposite polarities (Schüssler & Vögler 2008).
Substantial observational evidence has been gathered showing that internetwork flux is dominated by strongly inclined, almost horizontal magnetic fields (Orozco Suárez et al. 2007a; Lites et al. 2008; Orozco Suárez et al. 2007b). The validity of the deduced properties has been questioned by Asensio Ramos (2009), who argues that the influence of noise has not been adequately taken into account in such studies. Nevertheless, several authors report loop-like horizontal field structures of different sizes (Harvey et al. 2007; Ishikawa et al. 2008; Martínez González et al. 2007; Centeno et al. 2007; Martin 1988). Such structures could be due to local dynamo action, but small-scale flux emergence (Cheung et al. 2008) or flux expulsion of a pre-existing field by granular flows (Steiner et al. 2008) probably also contribute to the horizontal flux.
Another open question concerns the amount of magnetic flux
contained in the internetwork. The observations give a wide range
of values that vary with the spatial resolution and the diagnostic
technique used (e.g,
Khomenko
et al. (2003); Berdyugina & Fluri
(2004); Asensio Ramos
et al. (2007); Domínguez Cerdeña
et al. (2003)).
From the many results (see Solanki 2009; de Wijn
et al. 2008, for
overviews), we mention here only
those that directly concern the work presented in this paper.
Comparing the center-to-limb observations of the scattering
polarization in the
Sr I 4607 Å line with the signal
synthesized from the 3D hydrodynamical simulations,
Trujillo Bueno
et al. (2004) infer that the mean strength of the
internetwork field is G,
under the
assumption that the magnetic field is isotropically tangled at
subresolution scales and that it fills the whole resolution
element. Khomenko
et al. (2005a), on the other hand, compared
the observed Stokes V amplitudes of the
visible and infrared Fe I lines with the profiles
synthesized from 3D radiative MHD simulations, and conclude
that
G
(see also Bello González
et al. 2009). Sánchez Almeida
et al. (2003) used
Boussinesq 3D simulations of local dynamo action to suggest that a
snapshot with mean longitudinal magnetic field of 50 G can
reproduce both the observed Hanle and Zeeman signals. However, the
simulations used by these authors are somewhat idealized and the
solar atmospheric structure is arbitrarily introduced for
comparison with the observational data.
Table 1: Details of the three Hinode/SP data sets used.
In this paper, we use 3D radiative MHD simulations of the
solar
photosphere to obtain an estimate of the true magnetic flux
density in the quiet Sun. Our approach differs from that of
Khomenko et al.
(2005a) by considering also fields produced by
a local dynamo action. In addition, the synthesized polarization
signals are compared with the higher resolution data, obtained
with the spectropolarimeter (Lites
et al. 2001) of the Solar
Optical telescope (Tsuneta
et al. 2008) on board of the Hinode
satellite (Kosugi
et al. 2007). The comparison with the
simulations at the highest
feasible at the moment allows
us to gain insight into the role of the local dynamo action for
the quiet Sun magnetism.
2 Observations
We consider three data sets obtained with the spectropolarimeter
(SP) onboard Hinode. Details are given in Table 1.
Data sets I and II were recorded near disk center,
while data set III was obtained closer to the limb. Data
sets I and III were
obtained in the scan mode of the Hinode/SP, with an exposure time
of 9.6 s per slit position. They cover quiet Sun regions at
the
disk center and a region near the south solar pole, respectively.
In the case of data set III, we used a
wide strip
perpendicular to the scan direction that corresponds to
(
being the cosine of the heliocentric angle). Corrections
for various instrumental effects were made using the procedure
sp_prep, included in the
SolarSoft
package.
The procedure gives the longitudinal and transversal magnetic flux
density maps (Lites
et al. 2008) shown in Fig. 1.
The mean values are given in Table 1. The rms
continuum contrast values for data sets I and III are 7.5%
and 5.1% respectively.
Data set II is a time series recorded with fixed slit position. It consists of 103 scans at solar disk center, each with an exposure time of 9.6 s. After applying a temporal running mean, the effective exposure time becomes 67.2 s, which gives a significantly lower level of noise. This data set has been used previously by Lites et al. (2008) and Orozco Suárez et al. (2007b).
![]() |
Figure 1:
Maps of longitudinal (
|
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3 Simulation data
We used results from 3D radiative MHD simulations of a layer containing the solar surface, carried out with the MURAM code (Vögler et al. 2005; Vögler 2003). Non-gray LTE radiative transfer and partial ionization are taken into account. We compared snapshots from several simulation runs. The basic properties of the computational domains are given in Table 2. In all runs, the top of the simulation box is located about 500 km above the average height level of optical depth unity. The side boundaries are periodic, whereas the bottom boundary is open, permitting free in and outflow of matter. The magnetic field is vertical at the top and bottom boundaries.
The first run, henceforth referred to as the ``mixed
polarity'' run,
simulates the decay of the magnetic field in a mixed polarity
region. In this run, local dynamo action
(Vögler &
Schüssler 2007) does not occur since the magnetic
Reynolds number is below the threshold for dynamo action. The run
starts with a vertical magnetic field of |B| =
200 G, in a
checkerboard-like
pattern, with opposite polarities in
adjacent parts. The field is concentrated and redistributed by the
convective motions, and the opposite polarities are pushed
together, which results in flux cancellation and an almost
exponential decrease in the mean magnetic field strength. The
snapshots with
G
and
G
averaged over the surface
were used in our study.
The same snapshots were used by
Khomenko
et al. (2005b,a).
The second and third groups of snapshots were taken from the
runs
with a magnetic Reynolds number of the flow sufficiently high for
small-scale turbulent dynamo action to take place. A seed field of
|B0|=10 mG
grows exponentially in time until the saturation
level is reached. In the dynamo run C, described in
Vögler &
Schüssler (2007), the mean magnetic field strength
at this phase is G
at
.
In the
case of the dynamo run G, the higher magnetic Reynolds number
leads to a saturation level of the magnetic energy that is a
factor of 1.7 higher than in run C. Figure 2
shows the mean magnetic field strength (averaged over surfaces of
constant
)
as a function of the optical depth for one
snapshot from each run. The field from dynamo C run is multiplied
by a factor 1.5, to illustrate the similarity of the scaled
optical depth profiles in the dynamo runs. This factor differs
only by
15%
from
,
the square root of the
corresponding total magnetic energy ratio. This indicates that a
tentative scaling of the dynamo-generated field to represent
higher Reynolds numbers is not completely unreasonable.
Figure 2
shows the optical depth profiles of the horizontal magnetic field,
i.e.,
and the average vertical field
.
The dynamo runs have a significantly larger
than
.
Their
ratio reaches values between 2 and 4 in the optical depth interval
.
The mixed polarity snapshot, on the other hand,
has a
and
of
similar magnitude over all heights.
![]() |
Figure 2: Average total (solid), horizontal (dashed), and vertical (dotted) mean magnetic field strength from MURaM simulations as a function of the optical depth. Snapshots from different runs are indicated by line color: mixed polarity (blue), dynamo G (red), dynamo C multiplied by factor of 1.5 (black), and dynamo C with background unipolar field (green). |
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The last group of snapshots is taken from a simulation run that
continues dynamo run C with a superposed unipolar vertical
field.
Such a superposition might be a way of describing a weak network
region. The mean vertical field strength is thereby increased to
around 36 G at
and the strength of the horizontal
field to around 50 G at
(Fig. 2).
Table 2:
The simulation parameters with the size of computational
domain and vertical ()
and horizontal (
)
grid spacing.
4 Spectral synthesis
The simulation results have been used as input for the LTE
radiative transfer code SPINOR (Frutiger
et al. 2000) to
synthesize the Stokes profiles for the heliocentric angles
and
(corresponding to
and
,
respectively). The spectral range that contains the
Fe I lines at 630.15 and 630.25 nm is sampled in
steps of
7.5 mÅ. The Fe abundance used in the synthesis has been taken
from Thevenin (1989)
and the values of the oscillator
strengths from the VALD database (Piskunov
et al. 1995). We
then applied a realistic point spread function
(PSF, Danilovic
et al. 2008) to the maps of synthesized
Stokes profiles. The PSF takes the basic optical properties of the
Hinode SOT/SP system and a small defocus into account. Applying an
ideal PSF without defocus reduces the original rms contrast values
of the simulated continuum map from 14.5% to 8.5%
(
)
and 11.2% to 5.5%
(
), respectively. For the
comparison with the
observations at
,
we used a defocus of
-1.5 mm, which degrades the continuum contrast of the
simulation
to the observed value of 7.5%. A value of -0.75 mm is used
for the synthesized data at
in order to match
the continuum contrast of 5.1% deduced from dataset III. The
difference in the focus of the SOT between data sets I and III
amounts to approximately 2 steps of the SOT focus mechanism.
![]() |
Figure 3:
Histograms of the mean horizontal ( left), the
unsigned vertical ( middle) and the signed vertical (
right) magnetic flux density calculated for |
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The appropriate PSF is applied to the 2D maps at each
wavelength
position for every Stokes parameter. The degraded maps are then
rebinned to the pixel size of the Hinode/SP detector. To take the
spectral resolution of the spectropolarimeter into account, the
profiles are convolved with a Gaussian function of
25 mÅ FWHM
and resampled to a wavelength spacing of 21.5 mÅ. Next, a
noise level corresponding to the observations is added, and
finally the procedure by Lites
et al. (2008) is used to
calculate the longitudinal and transversal apparent magnetic flux
densities,
and
.
5 Results
We present our results in the following sequence: (1) snapshots
from the simulation runs are compared with the disk center
observations in terms of the mean values of
and
;
(2) the spatial distribution of the magnetic
features in the observed and in the synthesized maps is compared;
(3) a comparison of the probability density functions (PDFs) from
the simulations and from the low-noise data set II is presented.
Finally, we show how the mean magnetic flux density changes with
the heliocentric angle and compare the synthesized and observed
signal at a heliocentric angle of
.
5.1 Comparison with the observations at disk center
Table 3: Mean apparent magnetic flux densities from observations and simulations.
When comparing the observational signals with the ones
synthesized
from the simulations, one has to take into account that the solar
surface area covered by the observations of data set I is much
larger than that for the simulations. The small squares in
Fig. 1
indicate the actual size of the simulation
snapshots. To take this proportion into account, we divided the
region covered by the observations into subdomains of
.
For each of these, we calculated the
mean transversal
,
the mean unsigned
longitudinal
and the mean signed
longitudinal
apparent magnetic flux
densities. The histograms of these quantities are shown in
Fig. 3.
By considering the contribution of each
subdomain separately, we could exclude the contribution of the
network, which extends the wings of the histograms towards higher
values of
and
.
The maxima of the distributions, on the
other hand, give an estimate of the typical magnetic flux density
value in the internetwork regions. Consequently, when the whole
observed region is considered, the mean values (marked by the
vertical lines in Fig. 3)
are higher than the values
retrieved from the maxima. The mean values over the whole FOV
agree with the values obtained by Lites
et al. (2008) and show
a ratio of
.
The values retrieved from the distribution maxima are given in
the
first row of Table 3.
The other numbers are the
results obtained from the synthesized Stokes profiles from the
simulation snapshots, with the values determined from the
snapshots at their original resolution given in parenthesis. They
roughly correspond to the mean vertical and horizontal field
strengths near
(cf. Fig. 2).
Thus, the
ratio
obtained
from the simulations at the original resolution reflects
the ratio of the underlying magnetic fields at
.
The
values are close to unity for the mixed-polarity run and about 3for the
dynamo snapshots. For the dynamo snapshots, the values
after spatial smearing and
application of noise are considerably reduced compared to the
noise-free, unsmeared case owing to the presence of mixed
polarities on very small scales. On the other hand,
is increased for all groups of snapshots,
except for the dynamo run C with unipolar background field.
This
is the result of the noise added to the Stokes profiles in order
to simulate the Hinode/SP observations. The row labeled ``noise'' in
Table 3
gives values determined from pure white
noise with a standard deviation corresponding to the noise level
of data set I. We give the mean values from 100 realizations. The
value of
determined from pure noise
is almost as high as the values retrieved from the dynamo
snapshots, with the exception of the dynamo run C with a
unipolar
background field. This means that hardly any signal of
remained above the noise after spatial smearing and
introduction of noise. Dynamo C run with a unipolar field is a
special case because it has a much higher mean field (cf.
Fig. 2).
The more magnetic flux introduced, the
more the field can be tangled by the turbulent flows, so that
noticeably more horizontal field is generated.
The last two rows of Table 3 show the
results of the
attempt to estimate how much field the dynamo simulations would
have to contain to reproduce the observed
and
values.
Multiplying the magnetic field strengths by factors of 2 and
3(everywhere in the simulation box) in the case of the dynamo run G
and dynamo run C, respectively, gives a mean total magnetic
field
strength of 170 G and 67 G at the levels of
and
,
respectively. The strength of the mean vertical
magnetic field at the same levels becomes 84 G and
27 G,
respectively. These values are consistent with the extrapolation
by Pietarila Graham
et al. (2009)on the basis of Hinode data. Also, as
we have seen in Fig. 2,
the average mean field
strength distribution of run G can be reproduced by multiplying
run C result by a factor roughly corresponding to the square
root
of the ratio of the total magnetic energies. This suggests that
such a simple scaling might extend somewhat into the
regime that
is not covered by the simulations. The necessary
scaling factor of 2 for run G is not unreasonably large.
Figure 4
shows one snapshot from the dynamo
run C with the field multiplied by a factor of 3, before and
after
spatial smearing, together with an observed region of the same
size. Maps of the longitudinal
and transversal
magnetic flux density are shown. The granular
pattern is indicated by white contours of normalized continuum
intensity equal to 1.05. Vertical fields with mixed polarities
on scales of less than a third of an arcsec are smeared into
unipolar ``tube'' or ``sheet''-shaped patches (yellow and blue in the
central frame). The bundles of horizontal field, composed of loops
of different sizes, are molded into patches with higher
values. These can occur on the edges of granules or
between patches with vertical field of opposite polarity (see, for
instance, the feature at
).
Similar
features can be seen in the Hinode maps, e.g. in the two lower
frames on the right (see
also Lites
et al. 2008; Ishikawa et al. 2008)).
At the position
[
]
in the central frame, a vertical field of
Mx/cm2
is located inside a granule. A
similar case has been observed by Orozco
Suárez et al. (2008).
Figure 5
shows a different region on the Sun,
with more vertical flux (outlined by the yellow square in
Fig. 1)
compared with a snapshot from the dynamo run C
with a unipolar background field. No scaling of the dynamo field
has been carried out here. The maps based on the simulation show
features that are very similar to the structures present in the
observed weak network region, although the
signal is
somewhat weaker than in the observations. Small patches of
horizontal field correspond to small loops that are visible
between concentrations of the vertical flux at the original
resolution of the simulations.
![]() |
Figure 4: Comparison of a snapshot from dynamo run C with magnetic field scaled by a factor 3 at original ( left column) and Hinode ( middle column) resolution, with Hinode observations ( right column). From top to bottom: normalized intensity, longitudinal and transversal apparent magnetic flux density. The observed region is outlined by a white square in Fig. 1. White lines outline the contours of normalized continuum intensity equal to 1.05. |
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5.2 Comparison with the data set II
Pietarila Graham
et al. (2009) demonstrated how different effects can
influence the probability density function (PDF) of magnetic field
derived from Stokes V spectra, such that it differs
from the PDF
of the underlying magnetic field. In particular, the effect of
noise leads to a PDF with a peak at the position that corresponds
to the noise level. Here we compare the PDFs of (lefthand
panels) and
(righthand panels) determined
from the synthesized Stokes profiles with those from observations.
Figure 6
shows, from top to bottom, PDFs computed for
the mixed polarity (20 G) snapshot, a snapshot from the dynamo
run C without scaling, and from the dynamo run C
after scaling by
a factor of 3. Overplotted are the results calculated from
pure
noise with a standard deviation corresponding to the noise level
of the observations and the PDFs obtained from data set II.
The figure shows that all the PDFs from the simulation
snapshots
at Hinode resolution are strongly influenced by the noise at the
lowest field strengths, which is also the case for the PDF based
on the Hinode data. The noise-induced maxima lie at approximately
G
and
G.
Due to the
mixed polarity field on small scales, dynamo run C shows
significant loss of stronger signals after spatial smearing. The
mixed-polarity simulation snapshot, on the other hand, contains
larger unipolar patches so that it retains a considerable amount
of the stronger vertical field. Its PDF for
has an
extended tail of stronger field, which corresponds to the observed
distribution. In the observations, this extended tail is a result
of the contribution of the network flux concentrations. The
distributions of both mixed-polarity and dynamo C
run snapshots follow closely the distribution generated from the
pure noise, which means that the signature of the horizontal field
is mostly lost in the noise. Only a low percentage of the pixels
show a
signal above the noise level. However, after
scaling the original field values by a factor 3, the PDF for
(bottom row of the Fig. 6)
agrees well
with the observed one. Small discrepancies at the weakest signals
result from poor sampling (a consequence of the small region
covered by the simulations). The corresponding synthesized
distribution of
follows the observed distribution up
to approximately 10 Mx/cm2. Pixels with
signals
higher than 40 Mx/cm2 are very rare for
the maps
resulting from dynamo run C.
![]() |
Figure 5: Same as Fig. 4 but for the dynamo run C with a background unipolar field and a different region from the observed map (outlined by a yellow square in Fig. 1). |
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![]() |
Figure 6:
Probability density function (PDFs) for the longitudinal (
left column) and transversal ( right column)
apparent magnetic flux density. PDFs from synthetic |
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5.3 Changes with the heliocentric angle
The variation in the apparent magnetic flux density at different
heliocentric angles was determined using a snapshot from the
dynamo run C. The magnetic field strength was scaled by a
factor
of 3 in keeping with the findings from the previous sections. The
upper panels of Fig. 7
show height profiles of the
mean transversal (right) and mean absolute longitudinal (left)
field in the simulation at different heliocentric angles. Since
the transversal component of the magnetic field becomes
increasingly dominant in the layers above optical depth unity, the
mean absolute longitudinal (line-of-sight) component of the field
increases as the line of sight becomes inclined with respect to
the surface normal. However, the polarization signals in spectral
lines reflect the component of magnetic field averaged over the
line formation heights. The lower left panel of
Fig. 7
shows the PDF of ,
the vertical
component of magnetic field averaged over the height range that
corresponds to
at different heliocentric
angles. The PDFs at
follow the PDF at
closely,
with a discrepancy at the strong field end. This discrepancy
increases with the heliocentric angle.
As illustrated by Pietarila Graham
et al. (2009),
and
are well correlated, which explains the similar
trend of
with the heliocentric angle, as shown in
the lower right panel of Fig. 7. Plotted are the
mean
values of
and
as functions of the
heliocentric angle. The mean value of
stays
roughly constant until
and then gradually decreases when
moving further away from disk center. The mean value of
decreases monotonically.
5.4
Comparison with observations at
= 0.4 (
= 66
)
![]() |
Figure 7:
Simulated change with heliocentric angle retrieved from a dynamo
run C snapshot. Upper panels: the mean
absolute longitudinal ( left) and transversal (
right) components of the magnetic field as a function of
height in the simulation box at different heliocentric angles. Vertical
lines indicate the level of optical depth unity. Lower left:
PDFs for the signed longitudinal field (averaged over the line
formation height) at different heliocentric angles. Lower
right: change of the mean absolute longitudinal (
|
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![]() |
Figure 8:
PDFs for the longitudinal ( left column) and
transversal ( right column) apparent magnetic flux
density. Upper row: |
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In this section, we compare the synthesized signals at Hinode
resolution with the observations. The upper panel of
Fig. 8
shows PDFs of the field proxies,
and
,
retrieved from the observations
at disk center and
(data sets I and III),
respectively. The maxima of the PDFs are displaced with respect to
each other, because of the difference in the noise level
(Table 1)
as indicated by the overplotted PDFs
resulting from the pure noise. The probability that the
signals are stronger than 30 Mx/cm2
decreases
at
,
while the probability of the
signals
being more than 200 Mx/cm2 increases.
This effect
results from the strong magnetic concentrations present in the
field of view. When a strong magnetic tube-like structure with a
vertical field of kG strength is observed under an angle, then the
signal decreases, while
signal
displays a corresponding increase relative to the value at the
disk center. This is because, projected onto the line of sight,
the strong vertical component of the magnetic field gives rise to
a significant transversal component, leading to a strong
signal. Note, however that more pixels has values in
the range
Mx/cm2
where
PDF(
)
decreases towards the limb. Hence the mean
value of
decreases with heliocentric angle, in
agreement with the result obtained from local dynamo simulations
at original resolution (shown in lower right frame of
Fig. 7).
The lower panels of Fig. 8 show the PDFs
retrieved
from the dynamo run C snapshot at Hinode resolution. Their
trends
correspond to the ones at original resolution, showing a small
difference only for the strong signals. The PDF of the synthesized
signal follows the observations at both heliocentric
angles up to
Mx/cm2.
The synthesized
PDF matches the observations at
up
to approximately 20 Mx/cm2.
6 Discussion
We based our comparison between MHD simulations and observational results upon the magnetic proxies, the longitudinal and transversal apparent magnetic flux density introduced by Lites et al. (2008). It was shown that these proxies are prone to the influence of the non-magnetic properties of the atmosphere (Beck & Rezaei 2009) and do not correctly reflect the properties of the underlying field (Pietarila Graham et al. 2009). However, if we take that realistic MHD simulations represent the solar atmosphere properly (supported by numerous studies, e.g., Danilovic et al. (2010); Schüssler et al. (2003); Shelyag et al. (2004,2007)) and that our forward modeling of the instrumental effects and the noise is correct, we introduce the same assumption as in the case of the observations, allowing us to make a relatively unbiased comparison with the findings of Lites et al. (2008).
The magnetic proxies obtained from the synthesized data were
compared with observations of the internetwork region. The mixed
polarity simulations (which have a magnetic Reynolds number below
the threshold for dynamo action) reproduce the observed vertical
flux density, as was previously shown by
Khomenko et al.
(2005a). However, they do not contain enough
horizontal field to be consistent with the Hinode data.
Simulations of the surface dynamo give a ratio of the horizontal
to the vertical flux density consistent with the observational
results (Schüssler
& Vögler 2008), but the overall
amplitudes are too low, at least for the simulations with the
magnetic Reynolds number that are feasible at the moment. A simple
scaling of the field in the simulation domain by a fixed factor
brings the magnetic flux density from the dynamo snapshots at
Hinode resolution close to the observed ones. Some justification
for this tentative procedure comes from comparing simulations with
different magnetic Reynolds numbers. The resulting mean magnetic
field strength is 70 G
at
and
170 G
at the solar surface. This is roughly consistent with the
estimates given by Trujillo Bueno
et al. (2004), since the line they
consider samples the middle photosphere, and with extrapolations
based on the cancellation coefficient (Pietarila Graham
et al. 2009).
The contribution of the surface dynamo dominates in the
regions
with Mx/cm2
and
Mx/cm2
at Hinode spatial resolution.
Everything stronger than that could imply: (1) flux emergence with
kG horizontal fields (Cheung
et al. 2008) or (2) strong
network fields, which have a different source from those in the
internetwork, a possibility supported by studies of ephemeral
active regions (Harvey
1993; Hagenaar et al. 1999).
The synthesized magnetic proxies exhibit a decrease from the
disk
center to the limb. This agrees qualitatively with the
observations by Lites
et al. (2008). The PDFs show little
dependence for the low values of the magnetic proxies, in
accordance with the results of Martínez González
et al. (2008). In
contrast, Steiner
et al. (2009) could not reproduce the
observed simultaneous decrease towards the limb of the
longitudinal and transversal field proxies on the basis of
MHD simulations assuming a prescribed vertical magnetic flux
or a
transport of horizontal flux into the computational box from
below.
Our results support the presence of local dynamo action in the
quiet Sun. They also suggest that the magnetic field is dominantly
horizontal. The ratio of the mean horizontal and vertical
component of the dynamo-generated magnetic field reaches values
between 2 and 4 in the optical depth interval .
This gives the observed ratio of the transversal and longitudinal
apparent magnetic flux densities at the Hinode resolution when an
adequate noise level is considered.
We note, however, that the conclusions drawn here are based on a simple assumption drawn from the properties of magnetic field in the simulations with different magnetic Reynolds numbers. The increase in the field strength by a factor of 2 or 3 would result in a change of physical parameters, as well as the dynamics of the plasma, since the strong field is much less susceptible to the influence of the turbulent motions. These effects are not considered in our scaling procedure. Thus, we consider our work to be a step towards revealing the role of the surface dynamo in the quiet Sun magnetism until more realistic simulations, as well as higher resolution observation of the solar photosphere become available.
AcknowledgementsWe thank Jonathan Pietarila Graham for the valuable help with the PDFs and Anna Pietarila for a critical reading of the paper. Hinode is a Japanese mission developed and launched by ISAS/JAXA, with NAOJ as domestic partner and NASA and STFC (UK) as international partners. It is operated by these agencies in co-operation with ESA and NSC (Norway). This work was partly supported by the Ministry of Science and Technological Development of the Republic of Serbia (Project No 146003 ``Stellar and Solar Physics'') and by WCU grant No. R31-100016 from the Korean Ministry of Education, Science and Technology.
References
- Asensio Ramos, A. 2009, ApJ, 701, 1032 [NASA ADS] [CrossRef] [Google Scholar]
- Asensio Ramos, A., Martínez González, M. J., López Ariste, A., et al. 2007, ApJ, 659, 829 [NASA ADS] [CrossRef] [Google Scholar]
- Beck, C., & Rezaei, R. 2009, A&A, 502, 969 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
- Bello González, N., Yelles Chaouche, L., Okunev, O., & Kneer, F. 2009, A&A, 494, 1091 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
- Berdyugina, S. V., & Fluri, D. M. 2004, A&A, 417, 775 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
- Cattaneo, F. 1999, ApJ, 515, L39 [NASA ADS] [CrossRef] [Google Scholar]
- Centeno, R., Socas-Navarro, H., Lites, B., et al. 2007, ApJ, 666, L137 [NASA ADS] [CrossRef] [Google Scholar]
- Cheung, M. C. M., Schüssler, M., Tarbell, T. D., & Title, A. M. 2008, ApJ, 687, 1373 [NASA ADS] [CrossRef] [Google Scholar]
- Danilovic, S., Gandorfer, A., Lagg, A., et al. 2008, A&A, 484, L17 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
- Danilovic, S., Schüssler, M., & Solanki, S. K. 2010, A&A, 509, A76 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
- Domínguez Cerdeña, I., Sánchez Almeida, J., & Kneer, F. 2003, A&A, 407, 741 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
- Frutiger, C., Solanki, S. K., Fligge, M., & Bruls, J. H. M. J. 2000, A&A, 358, 1109 [NASA ADS] [Google Scholar]
- Hagenaar, H. J., Schrijver, C. J., Title, A. M., & Shine, R. A. 1999, ApJ, 511, 932 [NASA ADS] [CrossRef] [Google Scholar]
- Harvey, K. L. 1993, Ph.D. Thesis, Utrecht University [Google Scholar]
- Harvey, J. W., Branston, D., Henney, C. J., & Keller, C. U. 2007, ApJ, 659, L177 [NASA ADS] [CrossRef] [Google Scholar]
- Ishikawa, R., Tsuneta, S., Ichimoto, K., et al. 2008, A&A, 481, L25 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
- Kosugi, T., Matsuzaki, K., Sakao, T., et al. 2007, Sol. Phys., 243, 3 [NASA ADS] [CrossRef] [Google Scholar]
- Khomenko, E. V., Collados, M., Solanki, S. K., et al. 2003, A&A, 408, 1115 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
- Khomenko, E. V., Martínez González, M. J., Collados, M., et al. 2005a, A&A, 436, L27 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
- Khomenko, E. V., Shelyag, S., Solanki, S. K., & Vögler, A. 2005b, A&A, 442, 1059 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
- Lites, B. W., Elmore, D. F., & Streander, K. V. 2001, in Advanced Solar Polarimetry - Theory, Observation, and Instrumentation, ed. M. Sigwarth, ASP Conf. Ser., 236, 33 [Google Scholar]
- Lites, B. W., et al. 2008, ApJ, 672, 1237 [NASA ADS] [CrossRef] [Google Scholar]
- Martin, S. F. 1988, Sol. Phys., 117, 243 [NASA ADS] [CrossRef] [Google Scholar]
- Martínez González, M. J., Collados, M., Ruiz Cobo, B., & Solanki, S. K. 2007, A&A, 469, L39 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
- Martínez González, M. J., Asensio Ramos, A., López Ariste, A., & Manso Sainz, R. 2008, A&A, 479, 229 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
- Orozco Suárez, D., Bellot Rubio, L. R., del Toro Iniesta, J. C., et al. 2007a, ApJ, 670, L61 [NASA ADS] [CrossRef] [Google Scholar]
- Orozco Suárez, D., Bellot Rubio, L. R., Del Toro Iniesta, J. C., et al. 2007b, PASJ, 59, 837 [Google Scholar]
- Orozco Suárez, D., Bellot Rubio, L. R., del Toro Iniesta, J. C., & Tsuneta, S. 2008, A&A, 481, L33 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
- Pietarila Graham, J., Danilovic, S., & Schüssler, M. 2009, ApJ, 693, 1728 [Google Scholar]
- Petrovay, K., & Szakaly, G. 1993, A&A, 274, 543 [Google Scholar]
- Sánchez Almeida, J., Emonet, T., & Cattaneo, F. 2003, ApJ, 585, 536 [NASA ADS] [CrossRef] [Google Scholar]
- Schüssler, M., Shelyag, S., Berdyugina, S., et al. 2003, ApJ, 597, L173 [NASA ADS] [CrossRef] [Google Scholar]
- Shelyag, S., Schüssler, M., Solanki, S. K., & Vögler, A. 2007, A&A, 469, 731 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
- Solanki, S. K. 2009, ASP Conf. Ser., 405, 135 [NASA ADS] [Google Scholar]
- Shelyag, S., Schüssler, M., Solanki, S. K., et al. 2004, A&A, 427, 335 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
- Steiner, O., Rezaei, R., Schaffenberger, W., & Wedemeyer-Böhm, S. 2008, ApJ, 680, L85 [NASA ADS] [CrossRef] [Google Scholar]
- Steiner, O., Rezaei, R., Schlichenmaier, R., et al. 2009 [arXiv:0904.2030] [Google Scholar]
- Piskunov, N. E., Kupka, F., Ryabchikova, T. A., et al. 1995, A&AS, 112, 525 [Google Scholar]
- Thevenin, F. 1989, A&AS, 77, 137 [Google Scholar]
- Trujillo Bueno, J., Shchukina, N., & Asensio Ramos, A. 2004, Nature, 430, 326 [Google Scholar]
- Tsuneta, S., Ichimoto, K., Katsukawa, Y., et al. 2008, Sol. Phys., 249, 167 [NASA ADS] [CrossRef] [Google Scholar]
- Vögler, A. 2003, Ph.D. Thesis, University of Göttingen, Germany, http://webdoc.sub.gwdg.de/diss/2004/voegler [Google Scholar]
- Vögler, A., & Schüssler, M. 2007, A&A, 465, L43 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
- Vögler, A., Shelyag, S., Schüssler, M., et al. 2005, A&A, 429, 335 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
- Schüssler, M., & Vögler, A. 2008, A&A, 481, L5 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
- de Wijn, A. G., Stenflo, J. O. Solanki, S. K., & Tsuneta, S. 2008, Space Sci. Rev., 144, 275 [Google Scholar]
Footnotes
- ...
SolarSoft
- http://www.lmsal.com/solarsoft/
All Tables
Table 1: Details of the three Hinode/SP data sets used.
Table 2:
The simulation parameters with the size of computational
domain and vertical ()
and horizontal (
)
grid spacing.
Table 3: Mean apparent magnetic flux densities from observations and simulations.
All Figures
![]() |
Figure 1:
Maps of longitudinal (
|
Open with DEXTER | |
In the text |
![]() |
Figure 2: Average total (solid), horizontal (dashed), and vertical (dotted) mean magnetic field strength from MURaM simulations as a function of the optical depth. Snapshots from different runs are indicated by line color: mixed polarity (blue), dynamo G (red), dynamo C multiplied by factor of 1.5 (black), and dynamo C with background unipolar field (green). |
Open with DEXTER | |
In the text |
![]() |
Figure 3:
Histograms of the mean horizontal ( left), the
unsigned vertical ( middle) and the signed vertical (
right) magnetic flux density calculated for |
Open with DEXTER | |
In the text |
![]() |
Figure 4: Comparison of a snapshot from dynamo run C with magnetic field scaled by a factor 3 at original ( left column) and Hinode ( middle column) resolution, with Hinode observations ( right column). From top to bottom: normalized intensity, longitudinal and transversal apparent magnetic flux density. The observed region is outlined by a white square in Fig. 1. White lines outline the contours of normalized continuum intensity equal to 1.05. |
Open with DEXTER | |
In the text |
![]() |
Figure 5: Same as Fig. 4 but for the dynamo run C with a background unipolar field and a different region from the observed map (outlined by a yellow square in Fig. 1). |
Open with DEXTER | |
In the text |
![]() |
Figure 6:
Probability density function (PDFs) for the longitudinal (
left column) and transversal ( right column)
apparent magnetic flux density. PDFs from synthetic |
Open with DEXTER | |
In the text |
![]() |
Figure 7:
Simulated change with heliocentric angle retrieved from a dynamo
run C snapshot. Upper panels: the mean
absolute longitudinal ( left) and transversal (
right) components of the magnetic field as a function of
height in the simulation box at different heliocentric angles. Vertical
lines indicate the level of optical depth unity. Lower left:
PDFs for the signed longitudinal field (averaged over the line
formation height) at different heliocentric angles. Lower
right: change of the mean absolute longitudinal (
|
Open with DEXTER | |
In the text |
![]() |
Figure 8:
PDFs for the longitudinal ( left column) and
transversal ( right column) apparent magnetic flux
density. Upper row: |
Open with DEXTER | |
In the text |
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