Magnetic flux in the internetwork quiet Sun

Abstract

We report a direct comparison of the amplitudes of Stokes spectra of the Fe i 630 nm and 1.56 $\mu$m lines produced by realistic MHD simulations with simultaneous observations in the same spectral regions. The Stokes spectra were synthesized in snapshots with a mixed polarity magnetic field having a spatially averaged strength, $\langle B \rangle$, between 10 and 30 G. The distribution of Stokes $V$ amplitudes depends sensitively on $\langle B \rangle$. A quiet inter-network region was observed at the German VTT simultaneously with TIP (1.56 $\mu$m) and POLIS (630 nm). We find that the Stokes $V$ amplitudes of both infrared and visible observations are best reproduced by the simulation snapshot with $\langle B \rangle = 20$ G. In observations with 1 resolution, up to 2/3 of the magnetic flux can remain undetected.

Full text

Page 1

A&A 436, L27–L30 (2005)
DOI: 10.1051/0004-6361:200500114
c ? ESO 2005
Astronomy
&
Astrophysics
Magnetic flux in the internetwork quiet Sun
E. V. Khomenko1,2, M. J. Martínez González1, M. Collados1, A. Vögler3, S. K. Solanki3,
B. Ruiz Cobo1, and C. Beck4
1Instituto de Astrofísica de Canarias, 38205 C/ vía Láctea, s/n, Tenerife, Spain
2Main Astronomical Observatory, NAS, 03680 Kyiv, Zabolotnogo Str. 27, Ukraine
e-mail: khomenko@iac.es
3Max-Planck-Institut für Sonnensystemforschung, 37191 Katlenburg-Lindau, Germany
4Kiepenheuer-Institut für Sonnenphysik, 79104 Freiburg, Germany
Received 1 March 2005 / Accepted 26 April 2005
Abstract. We report a direct comparison of the amplitudes of Stokes spectra of the Fe 630 nm and 1.56 µmlines produced by
realistic MHD simulations with simultaneous observations in the same spectral regions. The Stokes spectra were synthesized in
snapshots with a mixed polarity magnetic field having a spatially averaged strength, ?B?, between 10 and 30 G. The distribution
of Stokes V amplitudes depends sensitively on ?B?. A quiet inter-network region was observed at the German VTT simultane-
ously with TIP (1.56 µm) and POLIS (630 nm). We find that the Stokes V amplitudes of both infrared and visible observations
are best reproduced by the simulation snapshot with ?B? = 20 G. In observations with 1??resolution, up to 2/3 of the magnetic
flux can remain undetected.
Key words. Sun: MHD – Sun: magnetic fields – Sun: infrared – Sun: polarization
1. Introduction
Magnetic fields in inter-network regions of the quiet solar
atmosphere are difficult to accurately measure. As a conse-
quence, measurements of the magnetic flux based on obser-
vations with different sensitivity and spatial resolution some-
times contradict each other. Thus, Domínguez Cerdeña et al.
(2003) report a strong increase of the flux up to 17–21 G with
increasing resolution from 1??to 0.??5. At the same time, Lites
& Socas-Navarro (2004) do not find such an increase and mea-
sured fluxes of about 8 G at 0.??6 resolution.
The measurements by Zeeman effect using different spec-
tral lines also lead to different flux estimates. In the simultane-
ous observations in the visible and infrared Fe lines reported
by Sánchez Almeida et al. (2003b), the flux in both spectral
ranges is not the same and amounts to 11 G (630.2 nm) and
6 G (1.5648 µm); even the polarity of the field in the same spa-
tial point observed in the visible and infrared can be different.
The flux obtained in the visible is larger than in similar ASP
data (Lites & Socas-Navarro 2004) even though the resolution
of the former observations was significantly lower (about 1.??4).
Applyingthe Hanle effect, which is not affected by polarity
cancellations,Trujillo Buenoet al. (2004)reporta substantially
larger average magnetic field strength of 60 G (correspond-
ing to a longitudinal flux of about 35 G). The Hanle effect is
sensitive to weak turbulent fields, while the Zeeman effect is
not. This may cause an apparent contradictionbetween the two
techniques.
Here, we perform a direct comparison of the amplitudes of
simultaneously observed Stokes spectra of the Fe 630 nm and
1.56 µm lines with those produced by realistic MHD simula-
tions. By using simulation snapshots with different amounts of
unsigned magnetic flux we are able to determine the level of
flux best approximatingboth infrared and visible observations.
The simulations allow us to estimate the “true” magnetic flux
contained in the observed inter-network region even if the lim-
itedspatial resolutionoftheZeeman-basedobservationsallows
only a small part of the total flux to be directly detected.
2. Observations
On August 17, 2003, a very quiet inter-network region at disc
center was observed simultaneously in the infrared and visi-
ble spectral ranges using the polarimeters TIP (Martínez Pillet
et al. 1999) and POLIS (Schmidt et al. 2000) attached to the
Vacuum Tower Telescope at the Observatorio del Teide. The
Stokes spectra of the 1.5648, 1.5652 µm and 630.1, 630.2 nm
Fe lines were recorded by scanning a 33??× 42??region. The
image was stabilized using a Correlation Tracker (Ballesteros
et al. 1996), which also allowed accurate stepping perpendicu-
lar to the slit by 0.??4. The integration time at each slit position
wasaround27s,whichmadeit possibletoachievea noiselevel
of 1.9×10−4for TIP and 2.5×10−4for POLIS (in terms of the
Letter to the Editor
Article published by EDP Sciences and available at http://www.edpsciences.org/aa or http://dx.doi.org/10.1051/0004-6361:200500114

Page 2

L28E. V. Khomenko et al.: Magnetic flux in the internetwork quiet Sun
continuum intensity) and a spatial resolution of 1.??2 and 1.??3
respectively. The continuum contrast of granulation was 1.3%
(infrared) and 2.7% (visible).
Dark current, flat-field, cross-talk corrections and demodu-
lation were performed as usual. Continuum images were cor-
related to evaluate the differential displacement between the
visible and infrared data due to atmospheric refraction ef-
fects. After the standarddata reduction,a Principle Component
Analysis (PCA) technique was used to eliminate noise (Rees
et al. 2000). The filtered spectra have an extremely low noise
level that was never achieved before in spectropolarimetric
measurements with this spatial resolution (5 × 10−5Icfor TIP
and 6.5 × 10−5Icfor POLIS). In 80–90% of the field of view
we measured amplitudes of Stokes V above a 3-σ thresh-
old of 2 × 10−4. This threshold level corresponds to ?B? as
low as 0.3 G. For details on observations and calibration
see Martínez González et al. (2005) and Beck et al. (2005,
in preparation).
3. MHD simulations and synthetic spectra
We have used the MURAM code, a 3D MHD code which in-
cludes non-grey radiative transfer, full compressibility, and the
effects of partial ionization for the 11 most abundant chemical
elements (Vögler et al. 2005). The size of the computational
domain for the simulations considered here is 6000 × 6000 ×
1400 km3with 288 × 288 × 100 grid points. We consider here
a simulation run that has a bi-polar structure of the magnetic
field. The initial strengthof themagneticfield introducedin the
box was 200 G. Further details about the simulations can be
found elsewhere (Vögler et al. 2005; Khomenko et al. 2005).
The redistribution of the existing magnetic field by convec-
tive motions leads to the cancellationof elementswith different
polarities. This produces an almost exponential decrease with
time of the average unsigned magnetic flux in the computa-
tional box. The snapshots used in the present work were taken
when the average unsigned magnetic field strength in the box
reached 30, 20 and 10 G at logτ500= −1. In addition to that,
a snapshot of a unipolar simulation with ?B? = 10 G is also
considered (Shelyag et al. 2004).
The Stokes spectra of the Fe 630.25 nm and 1.5648 µm
lines formed at solar disc centre (µ = 1) were calculated for
every vertical column of the selected snapshots, under the as-
sumption of local thermodynamic equilibrium. The synthetic
spectra have a spatial grid resolutionof 20 km and a continuum
contrast of 9% (IR) and 16% (visible). In order to make these
parameters comparable with the observations, we performed
a convolution of the two-dimensional snapshots with a point-
spread function. We used a combination of an Airy function
appropriate for the VTT and a Lorentz function describing the
imagedegradationbyseeing(Shelyaget al.2004).Thecontrast
and the resolution of the smoothed images match the observa-
tions (Khomenko et al. 2005). After the smoothing, we added
noise comparable to the observations and selected for the anal-
ysis only Stokes V profiles with amplitudes above 2 × 10−4.
Fig.1. Histograms of the amplitudes of Stokes V of Fe 630.2 nm in
the ?B? = 20 G simulation snapshot. Solid line: original resolution;
dashed line: reduced resolution. Arrows indicate the mean values.
4. Original vs. reduced resolution
We verified that in the simulations, in most of the area, both
Fe lines are formedin the weak-field regime. Thus, the ampli-
tudes of Stokes V are proportionalto the longitudinalmagnetic
flux ?Bz? containedin a resolutionelement and the originalflux
and those inferred from the synthetic magnetograms in these
lines are nearly the same.
Figure 1 compares the distribution of Stokes V amplitudes
of Fe 630.2 nm with original and reduced resolution. The
smearing causes a decrease of the average Stokes V amplitude
inthe box.Thisdecreaseis causedbyseveraleffects. Up tohalf
of the average original amplitude can be lost by averaging pro-
files with significantly different displacements and splittings,
such as those in granules and intergranules. Another source of
loss is cancellation of elements with different polarities. While
the first effect is always present in granulation, the second one
dependson the spatial mixingof oppositepolarities. Inthe case
of the simulations, after reducing the resolution from 20 km to
700 km, the average polarization signal becomes about 3 times
lower in both lines in all considered snapshots. It means that
up to 2/3 of the original flux can remain undetected in 1??reso-
lution observations if one uses Stokes V amplitudes as a mea-
sure of the magnetic flux. In observations with 0.??5 resolution
about 1/2 of the flux can be lost.
5. Simulations vs. observations
Figures 2 and 3 show maps of V amplitude of the simulations
and observations, correspondingly.The stronger magnetic fea-
tures are very similar in the visible and the infrared maps, in
both Figs. 2 and 3. This demonstrates that both spectral lines
“see” the same strongmagneticfeatures.Strikingly,in bothfig-
ures, there are many weak-flux concentrations that are present
in the infrared and are absent in the visible. This is mainly a
manifestation of the different Zeeman saturation regimes for
the infrared and the visible lines.
Letter to the Editor
Article published by EDP Sciences and available at http://www.edpsciences.org/aa or http://dx.doi.org/10.1051/0004-6361:200500114

Page 3

E. V. Khomenko et al.: Magnetic flux in the internetwork quiet SunL29
Fig.2. Stokes V maps in the Fe 1.5648 µm and 630.2 nm lines in a
simulation snapshot with ?B? = 20 G. The grey scaling of both im-
ages is the same. The synthetic spectra are smoothed to the observed
resolution. The color contours surround areas of a given polarity.
Fig.3. Same as in Fig. 2 but now for the observations. Note the differ-
ence in spatial scale (bottom of right panel).
Sánchez Almeida et al. (2003b) found that 25% of the
V profiles in the visible and infraredshowedoppositepolarities
at the same spatial point. In our observations only 5.7% of the
profiles follow this behaviour. In the simulations, such profiles
make up1–2%of all consideredprofiles. Whereasourobserva-
tions were made under almost identical seeing conditions, they
were different for the two wavelength bands for the observa-
tions of Sánchez Almeida et al. (2003b). We conclude that the
appearance of the seemingly opposite polarities may be due to
the differencein the spatial smearing (see also Khomenkoet al.
2005).
Figure 4 shows a comparison between the observed and
simulated Stokes V amplitudes. It reveals that the amplitudes
resulting from the simulations are clearly too weak in the 10 G
case (leftpanels)andtoostrongforthe30Gcase(rightpanels).
The best approximationto the observed histograms is achieved
in the ?B? = 20 G case (central panels), suggesting that the
“true” ?B? contained in the observed inter-network region was
close to 20 G.
This conclusion depends on the scales on which the po-
larities are mixed in the simulations. If the field in the Sun is
mixed at smaller spatial scales than given by the simulations
then more cancellations would occur and more flux would be
needed to make the amplitudes in the simulations equal to the
observed ones (see for example the case of the turbulent dy-
namo simulations analyzed by Sánchez Almeida et al. 2003a,
where only 10% of the original flux remains at 1 arcsec res-
olution). However, the fact that almost the entire shape of the
histogram is matched and that the amplitudes of both lines can
be reproduced simultaneously supports the conclusion that the
field distribution in the simulations and observations should be
similar. The ratio between the amplitudes in the IR and visible
is an additional parameter constraining the magnetic field dis-
tribution and the flux level in the simulations. As follows from
Fig. 5, it depends on the magnetic field in the model and is al-
most independent of the spatial resolution. In the observations,
the average amplitudes of the infrared and the visible lines are
close (A6302/A15648≈ 1.2), which is clearly not the case for the
10 G unipolar simulation. In the bi-polar simulation, the ratio
oftheamplitudesincreaseswith ?B?andis equal0.9(for10G),
1.1 (for 20 G) and 1.5 (for 30 G) (Fig. 4). Thus, the ?B? = 20 G
case is, again, closest to the observations.
The case with a field strength of 20 G has an average
longitudinal flux ?|Bz|? of 11–15 G at logτ500 from −1 to 0.
Taking into account the flux loss due to smearing, a ?|Bz|?
of about 4–5 G should be detected in 1??resolution observa-
tions. In addition, because of the presence of noise, only the
highest-amplitude signals are detectable in observations (cov-
ering some 60% of the area). The longitudinal flux averaged
over these 60% of the highest-flux points in simulations at 1??
makes 6–9 G at logτ500from −1 to 0 and corresponds rather
well to most observations (see Sánchez Almeida et al. 2003b;
Khomenko et al. 2003; Lites & Socas-Navarro 2004). At 0.??5
resolutionthe lattervalueincreasesto 8–12G. Thus,ourresults
are in apparentcontradictionwith the high-resolution(0.??5) ob-
servations of Domínguez Cerdeña et al. (2003), who measured
flux of 17 G from the 60% of the area covered by the signal
above noise in Fe 630.2 nm.
6. Conclusions
A comparison is performed between the amplitudes of the
circular polarization signals in observations and realistic
magneto-convection simulations. The observations used here
are the first simultaneous observations in the visible and in-
frared Fe spectral lines obtained with the same telescope. The
extremely low noise in the observations allowed us to measure
signals down to 2 × 10−4in amplitude. These were found to
cover 80–90% of the observed area. We find that under similar
seeing conditions, Fe 630 nm and Fe 1.56 µm trace the same
magnetic structures within the resolution element. The infrared
line sees more weak-flux concentrations than the visible one.
The amplitudes observed in the inter-network are incompatible
with the amplitudes in a unipolarmagnetic field simulationand
are compatible with bi-polar simulations with an average mag-
netic field strength of ?B? = 20 G. Dependingon the technique,
upto 2/3of this valuecan remainundetectedin 1 arcsec resolu-
tion Zeeman observations. Further work (e.g. simulations with
higher resolution) is required to identify the cause of the
Letter to the Editor
Article published by EDP Sciences and available at http://www.edpsciences.org/aa or http://dx.doi.org/10.1051/0004-6361:200500114

Page 4

L30E. V. Khomenko et al.: Magnetic flux in the internetwork quiet Sun
Fig.4. Histograms of the amplitudes of Stokes V of Fe 1.5648 µm (top) and Fe 630.2 nm (bottom) lines. Blue and red line: simulations; black
line: observations. From left to right simulation snapshots with ?B? of 10 G, 20 and 30 G.
Fig.5. Average Stokes V amplitudes of the Fe 1.5648 µm (dashed)
and 630.2 nm (solid) lines in simulations with different ?B? as a func-
tion of the spatial resolution.
discrepancy between our results and the 3 times higher ?B?
value deduced by Trujillo Bueno et al. (2004).
Acknowledgements. This research was partially funded by INTAS
grant 00-00084 and by the Spanish Ministerio de Educación y Ciencia
through project AYA2004-05792.
References
Ballesteros, E., Collados, M., Bonet, J. A., et al. 1996, A&AS, 115,
353
Domínguez Cerdeña, I., Sánchez Almeida, J., & Kneer, F. 2003,
A&A, 407, 741
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, submitted
Lites, B., & Socas-Navarro, H. 2004, ApJ, 613, 600
Martínez Pillet, V., Collados, M., Sánchez Almeida, J., et al. 1999, in
High resolution solar physics: theory, observations and techniques,
ed. T. R. Rimmele, K. S. Balasubramaniam, & R. R. Radick, ASP
Conf. Ser., 183, 264
Rees, D. E., López Ariste, A., Thatcher, J., & Semel, M. 2000, A&A,
355, 759
Sánchez Almeida,J.,Domínguez Cerdeña,I.,&Kneer, F.2003b, ApJ,
597, L177
Sánchez Almeida, J., Emonet, T., & Cattaneo, F. 2003a, ApJ, 585, 536
Schmidt, W., Kentischer, T. J., & Lites, B. W. 2000, POLIS:
Instrument Description, HAO-KIS
Shelyag, S., Schüssler, M., Solanki, S. K., Berdyugina, S. V., &
Vögler, A. 2004, A&A, 427, 335
Trujillo Bueno, J., Shchukina, N. G., & Asensio Ramos, A. 2004,
Nature, 430, 326
Vögler, A., Shelyag, S., Schüssler, M., et al. 2005, A&A, 429, 335
Letter to the Editor
Article published by EDP Sciences and available at http://www.edpsciences.org/aa or http://dx.doi.org/10.1051/0004-6361:200500114