Issue |
A&A
Volume 509, January 2010
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|
---|---|---|
Article Number | A76 | |
Number of page(s) | 9 | |
Section | The Sun | |
DOI | https://doi.org/10.1051/0004-6361/200912283 | |
Published online | 21 January 2010 |
Magnetic field intensification: comparison of 3D MHD simulations with Hinode/SP results
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,
Yongin, Gyeonggi, 446-701, Korea
Received 6 April 2009 / Accepted 9 October 2009
Abstract
Context. Recent spectro-polarimetric observations have
provided detailed measurements of magnetic field, velocity and
intensity during events of magnetic field intensification in the solar
photosphere.
Aims. By comparing with synthetic observations derived from MHD
simulations, we investigate the physical processes underlying the
observations, as well as verify the simulations and the interpretation
of the observations.
Methods. We consider the temporal evolution of the relevant
physical quantities for three cases of magnetic field
intensification in a numerical simulation. In order to compare with
observations, we calculate Stokes profiles and take into account the
spectral and spatial resolution of the spectropolarimeter (SP) on board
Hinode. We determine the evolution of the intensity, magnetic flux
density and zero-crossing velocity derived from the synthetic Stokes
parameters, using the same methods as applied to the Hinode/SP
observations to derive magnetic field and velocity information from the
spectro-polarimetric data.
Results. The three events considered show a similar evolution:
advection of magnetic flux to a granular vertex, development of a
strong downflow, evacuation of the magnetic feature, increase of the
field strength and the appearance of the bright point. The magnetic
features formed have diameters of 0.1-0.2
.
The downflow velocities reach maximum values of 5-10 km s-1 at
.
In the largest feature, the downflow reaches supersonic speed in the
lower photosphere. In the same case, a supersonic upflow develops
approximately 200 s after the formation of the flux concentration.
We find that synthetic and real observations are qualitatively
consistent and, for one of the cases considered, also agree very
well quantitatively. The effect of finite resolution (spatial smearing)
is most pronounced in the case of small features, for which the
synthetic Hinode/SP observations miss the bright point formation and
also the high-velocity downflows during the formation of the smaller
magnetic features.
Conclusions. The observed events are consistent with the process
of field intensification by flux advection, radiative cooling, and
evacuation by strong downflow found in MHD simulations. The
quantitative agreement of synthetic and real observations indicates the
validity of both the simulations and the interpretations of the
spectro-polarimetric observations.
Key words: Sun: photosphere - Sun: granulation - magnetic fields
1 Introduction
Magnetic field is ubiquitously present in the solar photosphere
(de Wijn et al. 2008). On granular scales, it undergoes
continual deformation and displacement. It is swept by the
horizontal flows and concentrated in the intergranular lanes.
Flows are able to compress the field so that the magnetic energy
density
approaches the kinetic energy density
of the flow (Weiss 1966; Parker 1963). This results
in a magnetic field strength of a few hundred Gauss at the solar
surface. Further intensification to kG strength is driven by the
mechanism referred to as: superadiabatic effect
(Parker 1978), convective collapse
(Webb & Roberts 1978; Spruit & Zweibel 1979) or
convective intensification
(Grossmann-Doerth et al. 1998).
The first two concepts are a theoretical idealization of the process. The superadiabatic effect contains the basic idea. Parker (1978) pointed out that a thermally isolated dowflowing gas within the flux tube in a superadiabatically stratified environment will be accelerated, which would lead to evacuation of the flux tube. Because of the resulting pressure deficit, the gas inside the flux tube will then be pressed together (together with the frozen-in magnetic field) by the surrounding gas, causing the magnetic pressure to increase until a balance of total pressure (magnetic + gas) is reached.
The convective collapse extends the concept to the convective instability. It starts with a flux tube in thermal and mechanical equilibrium with the surrounding hydrostatically superadiabaticly stratified plasma. Since external stratification is convectively unstable, any vertical motion within the flux tube can be amplified. Downward flow will grow in amplitude and drain the material from the flux tube. The process continues until a new equilibrium with a strong field is reached. Different aspects of the concept have been the subject of extensive research (see Schüssler 1990; Steiner 1999, for reviews).
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Figure 1:
Maps of the whole simulation domain at t=140 s.
Normalized continuum intensity at 630 nm ( left), the vertical component of the magnetic field ( middle) and velocity ( right) at a geometrical height roughly corresponding
to the level of
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The term convective intensification is used for magnetic field intensification in realistic MHD simulations, where the process occurs in its full complexity. It is driven by the thermal effect in the surface layer of the magnetic concentration. There, due to the presence of the magnetic field, heat transport by convection is reduced. The material inside the concentration radiates more that it receives. This leads to cooling of material which thus starts to sink and partial evacuation of the concentration occurs. Contraction of the magnetic concentration by the surroundings (a result of the pressure imbalance) leads to an increase in magnetic field strength. Thus, the simulations (Gadun et al. 2001; Vögler et al. 2005; Grossmann-Doerth et al. 1998; Cheung et al. 2008; Nordlund 1983) bear out the basic properties described by idealized concepts, such as: the downflow, the evacuation of the magnetic structure, the field increase and, in some cases, establishment of a new equilibrium. The 3D MHD simulations show that the strong magnetic concentrations form as the horizontal flows in the intergranular lanes advect the weak, nearly vertical field and concentrate it at the vertices of granular and mesogranular downflow lanes (Stein & Nordlund 1998,2006). Larger magnetic structures form at sites where a granule submerges and the surrounding field is pushed into the resulting dark region. Whether the concentration formed appears dark or bright in the continuum intensity depends on whether the vertical cooling is compensated or not by the lateral heating due to horizontal energy exchange (Vögler et al. 2005; Bercik et al. 2003). This formation scenario is consistent with the observations described by Muller (1983) and Muller & Roudier (1992). Their observations show that network bright points form in intergranular spaces, at the junction of converging granules as the magnetic field becomes compressed by the converging granular flow.
The 2D simulations by Grossmann-Doerth et al. (1998) revealed that magnetic flux concentrations formed by convective intensification can evolve in different ways. They present two possible outcomes. Depending on the initial magnetic flux, a magnetic concentration can reach a stable state after the process, or can be dispersed due to an upflow that develops as high speed downflowing material rebounds from the dense bottom of the tube. Similar results were presented by Takeuchi (1999) and Sheminova & Gadun (2000).
Observational evidence was found for both cases. Bello González et al. (2008) reported on the formation of a magnetic feature at the junction of intergranular lanes, without any significant upflow observed. Bellot Rubio et al. (2001), on the other hand, detected a strongly blueshifted Stokes V profile originating in a upward propagating shock, 13 minutes after the amplification of the magnetic field. Socas-Navarro & Manso Sainz (2005) found that supersonic upflows are actually quite common.
Events that are interpreted as convective collapse were detected also with the spectropolarimeter (SP) (Lites et al. 2001) of the Solar Optical telescope (Tsuneta et al. 2008) on board Hinode (Kosugi et al. 2007). Shimizu et al. (2008) and Nagata et al. (2008) show cases of high speed downflows followed by magnetic field intensification and bright point appearance. The event described by Nagata et al. (2008) shows stronger field strength and upflow in the final phase of evolution.
In this paper we give three examples of magnetic field intensification from MURaM simulations and perform a detailed comparison with the results of Nagata et al. (2008) and Shimizu et al. (2008).
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Figure 2:
Evolution of the continuum intensity at 630 nm and the magnetic field in a
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2 Simulation data and spectral synthesis
We use 3D radiative MHD simulations of a thin layer containing the
solar surface carried out with the MURaM code (Vögler et al. 2005; Vögler 2003) in a
Mm domain with
non-grey radiative transfer included. Vertical and horizontal
spatial resolution is 10 km and 14 km respectively. The bottom and
top boundaries are open, permitting free in and outflow of matter.
The initial magnetic field of
G is
introduced in a checkerboard-like
pattern, with
opposite polarity in adjacent parts. As the field is redistributed
by convective motion, opposite polarities are pushed together and
dissipated, so that the unsigned magnetic flux decreases with
time. In this way, the run simulates the decay of the magnetic
field in a mixed polarity region. Local dynamo action
(Vögler & Schüssler 2007) does not occur since the magnetic Reynolds
number is below the threshold for dynamo action. We do not expect
that the intensification process would be significantly different
at higher Reynolds numbers (smaller grid cells). The simulated
magnetic flux concentrations considered here are well resolved.
The main effect of an increased resolution would be a decrease in
the width of the boundary layers between the flux concentration
and the surrounding downflows.
We examined a 30 min sequence of simulation snapshots with a
cadence of approximately 90 s. The snapshots shown in this paper
have
G at
.
In
Fig. 1, we show the continuum image and maps of the
vertical components of the magnetic field and velocity for a
snapshot at time t=140 s (t=0 s corresponds to the first
snapshot considered in this paper).
In order to synthesize the Stokes profiles, the physical
parameters from the simulation are used as an input for the 1D LTE
radiative transfer code, SPINOR (Frutiger et al. 2000). A
spectral range that contains Fe I lines 630.15 and 630.25 nm is
sampled in steps of 7.5 mÅ. The Fe abundance used for the
synthesis has been taken from Thevenin (1989) and the values
of the oscillator strengths from the VALD database
(Piskunov et al. 1995). Before comparing with Hinode/SP
(Lites et al. 2001) observations, the synthetic line profiles
have been treated to bring them to the same resolution as Hinode
data. Firstly, a realistic point spread function (PSF,
Danilovic et al. 2008) was applied to the synthesized Stokes
profiles. The PSF takes into account the basic optical properties
of the Hinode SOT/SP system and a slight defocus which brings the
continuum contrast of the simulation to the observed value of
7.5%. Secondly, to take into account the spectral resolution of
the spectropolarimeter, the profiles are convolved with a Gaussian
function of 25 mÅ FWHM and resampled to a wavelength spacing
of 21.5 mÅ. Thirdly, noise of
is added.
Velocities are determined from the shift between the Stokes Vzero-crossing wavelength and the line core position of the Stokes
I profile averaged over pixels with polarization signal
amplitudes less than
.
We correct these velocities
for convective blueshift by subtracting 150 m s-1. Finally,
the procedure by Lites et al. (2008) is used to calculate the
longitudinal apparent magnetic flux density (shown in
Fig. 2).
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Figure 3:
Enlargement of the regions, having a size of
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3 Results
Figure 2 shows the evolution of the continuum intensity
and the magnetic field in a
Mm subdomain of the
simulation, over approximately 7 min. Maps at the original
resolution of the simulation (left-hand side) and at the spatial
resolution of Hinode (right-hand side) are shown. For the original
resolution, we show the vertical component of the magnetic field
from the simulations (right column on the left-hand side). The
longitudinal apparent flux density (Lites et al. 2008)
retrieved from synthetic Stokes profiles is shown at the Hinode
resolution (right column on the right-hand side). During the
period shown, three bright points appear near the coordinates
,
and
,
in the regions outlined by yellow
squares. We refer to them here as cases I, II and III,
respectively. They are identified in the top left frame.
3.1 Horizontal flows
In all three cases, the magnetic field is advected by the flow to
the junction of multiple granules, where it is confined and
concentrated. The evolution of magnetic concentrations is examined
more closely in Fig. 3, where the regions
outlined by yellow squares in Fig. 2 are enlarged.
Horizontal velocities at approximately 80 km above
are represented by arrows in continuum maps
and magnetograms. Regions with a strong vertical component of
vorticity are also outlined.
Vortex flows around strong downflows are quite common in simulations of granulation (Nordlund 1986). They are formed at the vertices between multiple granules, where flows converge and angular velocities with respect to the center of downflow increase due to angular momentum conservation. The lifetime of vortex flows depends on the dynamical behavior of the neighboring granules. In a 30 min run that we examined, they lasted from less then 90 s to approximately 10 min. The ones shown in Fig. 3 are short-lived. In case II, the swirling motion persists for at least 150 s, until the shape of the neighboring granules is changed. The flux concentration formed is then squeezed between two granules and stretched into a flux-sheet-like feature. Later, as the granules evolve, the magnetic feature is advected to the left and trapped again in the junction between newly formed granules. In case III, a strong preexisting flux sheet is carried by the flow toward the junction of the granules. There, the field is caught in a vortex flow that lasts for at least 100 s. The flow becomes disturbed and then starts to swirl in the opposite direction. The vortex axes are inclined, in both cases II and III, with respect to the vertical direction. Also in both cases, there is a spatial and temporal coincidence between the existence of vortex flows and the formation of high speed downflows near the surface layer.
The vortices shown in Fig. 3 are less than
in diameter, much smaller then the ones found in
observations (Bonet et al. 2008). The size of the observed
vortex flows is of the order of 1
and the average
lifetime is around 5 min. They seem to outline supergranulation
and mesogranulation cells. As the authors of the observational
study suggest, most vortices could have been missed because of the
limited spatial resolution (Swedish Solar Telescope) and the
method used (tracking the motion of bright points in G band). A
short-lived vortex flow preceding formation of a network bright
point has been observed by Roudier et al. (1997).
No vortex is detected during the formation of flux concentration in the case I. In this case, a strong downflow and later upflow develops inside the flux concentration, whose shape and contrast in the intensity map is greatly affected by the convective motion. Spatial and temporal fluctuations across the magnetic feature make it difficult to define its center. The bright points, visible in continuum maps, form where fragments of flux concentrations become narrow so that lateral heating becomes important, as well as in the regions with higher field strength, i.e. higher evacuation.
During their further evolution after the intensification phase (t
> 420 s), the flux concentrations in cases I, II and III have
different fates. In case II, it meets a magnetic feature of
opposite polarity and vanishes in 3 min. The feature
formed in case I is gradually stretched by the flow and fragmented
after approximately 9 min. A few minutes after that, the
larger fragment encounters the opposite-polarity flux
concentration from case III. The cancellation continues for
12 min until both features disappear. The smaller fragment of
the feature from case I is caught in a granular vortex flow
approximately 5 min later which leads to further
intensification.
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Figure 4:
Time sequence of vertical cuts through the magnetic concentration
corresponding to case (positions of the cuts are marked by yellow
horizontal lines in right-hand images in Fig. 2). The plotted cuts correspond to the same instants as sampled in
Fig. 2. From left to right: density excess with respect to the the mean density at every
height, vertical component of magnetic field, vertical component of velocity (overplotted arrows show the
components of the velocity field in the x-z plane), and radiative heating rate. Horizontal solid lines follow the levels of
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Figure 5:
Height profiles of various quantities in the flux concentration
corresponding to the case I (magnetic field, vertical component of
velocity, density and temperature) at the positions marked by dashed
lines in Fig. 4 at different times. Thick vertical lines mark the positions of the optical depth
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3.2 Field intensification
The evolution of the magnetic structures formed during the studied time interval can be followed in more detail by taking vertical slices through the regions marked by horizontal lines in Fig. 3. We will examine three cases.
3.2.1 Case I
Vertical cuts through the regions corresponding to this case are
given in Fig. 4. The density excess (relative to the
mean density at each geometrical height), the vertical components
of magnetic field and velocity, and the radiative heating rate are
shown. Cuts at the instant t=0 show the fluctuation in density
outlining the granulation structure, with less dense, hotter
granules and a cooler intergranular lane, where magnetic field of
a few hundred G is accumulated and a downflow of a few km/s is
present. The fluctuation in radiative heating rate is highest in
the thin layer near an optical depth unity, where upflowing
granular material cools most strongly. The regions along the
intergranular lane seems to undergo cooling in the layers above
.
In the next instant, 140 s later, a strong magnetic
concentration has already formed. Variations in magnetic field
strength at a given geometrical height are accompanied by
variations in the gas pressure. Regions with increased field
strength have lower density, which in turn shifts the level of
optical depth unity downwards relative to neighboring regions with
weaker field. The depression of the visible surface inside the
magnetic structure gives rise to radiative heating through the
sidewalls from the hot neighboring material. The downflow velocity
is significantly increased from t=0 to t=140 s, becoming
supersonic in the layer between 100 km above and 350 km below the
surface. By t=280 s it is greatly diminished again inside the
flux concentration. The diameter and the shape of the flux
concentration continuously evolves and does not reach a stationary
state. At t=280 s strong radiative heating is present inside the
concentration. This is also the moment when the continuum
intensity is the highest, as shown later
(Fig. 9).
In the last two sets of snapshots shown in Fig. 4, an upflow is visible inside the flux concentration, extending almost from the bottom of the simulation domain. It reaches supersonic velocities in the upper layers of the photosphere. Its direction is inclined with respect to the vertical. The upflowing material inside the concentration exhibits strong cooling at the surface. As the material refills the region inside the flux concentration, the level of optical depth unity shifts upwards and the magnetic field strength decreases. However, the upflow does not lead to a complete dispersal of the field, as described in the last paragraph of Sect. 3.1.
The evolution of this flux concentration is further illustrated by
the vertical profiles given in Fig. 5. Three phases
before and after the field intensification are shown. The
horizontal positions of the profiles are marked by vertical dashed
lines in Fig. 4. The profiles of magnetic field
strength, the vertical component of velocity, the density and the
temperature for each phase are shown, together with the
corresponding level of optical depth unity, marked by thick
vertical lines. The level h=0 corresponds to the level of the
mean optical depth unity
for the
whole snapshot. Thin vertical lines in the upper plots mark the
position of the average height of formation of the Fe I 630.25 nm
line, which is defined by calculating the centroid of the
contribution function (CF) for line intensity depression
(Solanki & Bruls 1994), at the wavelength of the line core.
The definition gives only a rough estimate of the heights sampled,
since the lines are formed over a large portion of the photosphere
and the CFs are asymmetric in wavelength due to the presence of
high velocity gradients.
The figure shows that, in the interval from t=0 s to t=140 s,
the downflow extends to deeper layers and increases in amplitude,
reaching 10 km s-1 at 200 km below the surface. The magnetic field
strength increases from a few hundred to more than 2000 G at the
level of
.
The significant reduction in density
results in a shift of 200 km in the optical depth unity level. As
a result of radiative heating, the temperature gradient is flatter
and the temperature is around 400 K higher at h=0. The
temperature difference at equal optical depth is even greater,
exceeding 1000 K at
.
The estimated height of
formation of Fe I 6302 shifts from roughly 300 km to 150 km above
the surface when magnetic field concentration forms, which is in
agreement with Khomenko & Collados (2007). This effect
contributes to the increase of observed magnetic field strength in
the first two phases.
In the third phase, the upflow leads to a density enhancement and
a weakening of the magnetic field by a few hundred Gauss in the
lower photosphere. The level of
shifts upward by
100 km. No discontinuity is visible in the vertical component of
velocity, in contrast to the event studied by
Grossmann-Doerth et al. (1998).
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Figure 6: The same as Fig. 4 but for cases II and III. Each frame is subdivided into a left part displaying case II and a right part showing case III. Vertical lines mark the positions of the height profiles given in Figs. 7 and 8. |
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3.2.2 Cases II and III
Vertical cuts through the regions corresponding to these cases are shown in Fig. 6. The positions of the cuts are marked by horizontal lines in Fig. 3. The parameters shown are the same as in Fig. 4.
At t=0, weak magnetic structures in the intergranular lanes are
already present in both cases. Strong downflows along the magnetic
field lines persist over the entire time interval shown. They
reach supersonic velocities in some instances, but only in the
layers below .
In case II, the downflow is strongest at
t=140 s, just before the vortex flow becomes deformed owing to
evolution of the neighboring granule. Then it becomes somewhat
reduced at t=280 s, as the structure is squeezed between the
granules. Later, at t=380 s, a strong downflow is present again
in the newly formed granular junction, to which the flux
concentration is carried and where it is confined again. The
rightmost columns show strong cooling of the layers above the
level of
in both cases. At t=420 s, the interior
of the flux concentrations reaches radiative equilibrium. At that
moment, the flux concentrations in both cases are almost vertical,
with diameters of approximately
at
.
Figures 7 and 8 show height profiles
along the positions marked by the dashed lines in
Fig. 6. Since the flux concentrations are
inclined, the choice of curved lines along the axes of magnetic
structures would be more logical here. However, we are interested
in what would be observed at the disc center and the observables
(i.e. the Stokes profiles) depend on the vertical profiles of the
physical parameters which are shown here. In the case II, we
choose to show profiles at instants t=0, 280 and 420 s
(solid, dotted, dashed respectively). For the case III, profiles
at the last three instants in Fig. 6 are shown.
Both cases exhibit a similar behavior: there is a significant
evacuation of the magnetic concentration due to the strong
downflow and an increase of the magnetic field strength from a few
hundred G to kG values in the process. There is a persistent
dowflow that reaches 5 km s-1 (in the vertical direction) at
and a decrease in density with a corresponding
shift in the height of
.
In both cases, the shift in
reaches 150 km and the magnetic field strength
increases to 2000 G at that depth. The height of formation of the
Fe I 630.25 nm line shifts to deeper layers as the magnetic field
strength increases. In the last instant, the Fe I 630.25 nm line
probes layers with kG fields and a vertical velocity of 5 km s-1 in
both cases.
3.3 Comparison with synthetic Hinode observations
The intensity contrast is considerably reduced at Hinode spatial resolution, as can be seen in Fig. 2 (note that the color scales are adjusted). The maps of longitudinal apparent magnetic flux density are shown for comparison with the magnetograms at the original resolution. Fine structure in both maps, continuum and magnetograms, is lost due to smearing. The bright points that correspond to cases II and III are barely discernible.
3.3.1 Case I
In order to compare case I with the results of Shimizu et al. (2008), we calculate the parameter they refer to as signal excess (SE). It is defined as the Stokes Vprofile integrated over the spectral range of 250-400 mÅ redward from the nominal line center. This wavelength range corresponds to dowflows of 7-14 km s-1, so that high values of SE indicate the presence of hight-speed downflows. The red contour in the right-hand side of Fig. 2 outlines a region with an SE of 0.01 pm, which is a factor of 10 higher than in the surroundings. It fits the location and time of the strong downflows visible at the original resolution (left hand-side of Fig. 2). Both synthesized (here) and observed (Shimizu et al. 2008) SE occur simultaneously with the appearance of the bright point and the intensification of the magnetic field. However, the event described by Shimizu et al. (2008) (Fig. 8) lasts at least 6 min, while in our simulations it is present for less than 4 min.
Figure 9 compares the observable parameters with
the corresponding values at original resolution. The locations
chosen for the plots are marked by yellow crosses in
Fig. 2. The pixels are selected such that regions of
downflow and upflow are covered, as well as the evolution of the
bright point. The plots show the temporal change of normalized
intensity, longitudinal apparent flux density
(Lites et al. 2008), and zero-crossing velocity retrieved from
Stokes V profiles of the Fe I 630.25 nm line, so that a direct
comparison with the results of Nagata et al. (2008) can be
made. Overplotted (stars/solid lines) are the normalized intensity
at the original resolution, the vertical component of the magnetic
field and velocity at
.
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Figure 7: The same as Fig. 5, but for case II. |
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Figure 8: The same as Fig. 5, but for case III. |
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Figure 9:
Temporal change of normalized continuum intensity ( left), the vertical component of magnetic field ( middle) and the vertical component of velocity
( right), for cases I ( top row), II ( middle row) and III ( bottom row) at original (stars/solid line) and Hinode resolution (crosses/dashed line).
The vertical component of the magnetic field and velocity at log
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Figure 10: Synthetic Stokes I ( left) and V ( right) profiles at original ( upper row) and Hinode resolution ( lower row) for the times t=0,140 and 420 s marked by dotted, solid and dashed lines, respectively. The intensity is normalized to the mean continuum intensity in the full snapshot domain. |
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3.3.2 Cases II and III
The middle and bottom rows in Fig. 9 show the
temporal evolution for cases II and III, respectively. We find a
simultaneous increase in all parameters (continuum intensity,
apparent flux density and zero-crossing velocity). In both cases,
the downflow is suppressed at t=280 s, possibly because of the
evolution of the surrounding granules. The velocity at
reaches 6 and 4 km s-1 for case II and III,
respectively. As the magnetic field strength increases, the
intensity follows and, in both cases, the intensity contrast
reaches 50% with respect to the mean at original resolution.
The influence of spatial smearing is on the whole similar, although a few differences relative to case I are noteworthy. Firstly, due to the small size of the features, the correlation of the magnetic and brightness signals is largely destroyed. Although the magnetic signals are comparable to the values in case I, the brightness is lower, so that the features are inconspicuous in continuum images. The increase in magnetic flux density is followed by only a small fluctuation in intensity. Secondly, although the magnetic field strengths and diameters of the features are comparable for cases II and III at the original resolution, the case II shows lower magnetic flux density after convolution. Thirdly, the signature of the strong dowflow in case II is lost due to spatial smearing.
4 Summary
Our case study of three examples of magnetic field intensification
has shown that in all three cases, the field is advected to the
junction of several granules. There, it is confined by converging
granular flows, which, in two cases, form a vortex. Due to the
presence of the magnetic field, the thermal effect (radiative
cooling) induces evacuation of the flux concentration. The
evacuation leads to a downward shift of the optical depth scale
within the flux concentrations. The shift is smaller for the
smaller features due to the lateral radiative heating, which
inhibits further evacuation (Venkatakrishnan 1986). As a
result, the magnetic field at ,
in the smaller features,
is weaker than in the case of the feature with more flux. This is
in accordance with recent numerical (Cheung et al. 2007) and
observational (Rüedi et al. 1992; Solanki et al. 1996) results.
During the evacuation, the dowflow velocities reach maximum values
of 5-10 km s-1 at .
In the case of the largest feature, the
downflow extends from the upper boundary of the simulation domain
and becomes supersonic in the lower photosphere. The magnetic
features formed have diameters of 0.1-0.2
.
In the case of
the largest feature, a supersonic upflow develops approximately
200 s after the formation of the flux concentration. The upflow
does not lead to a complete dispersal of the field, but the
feature persists until 9 min later when it undergoes a
fragmentation. The disappearance of the features in all three
cases occurs when they meet opposite polarity features, between 3
and 20 min after their formation.
We also show what happens with the observables when the effects of smearing to observational spatial resolution is taken into account. An important result is that, in the case of small features, Hinode/SP would miss the bright point formation and, in some cases, also the high velocity downflows that develop in the process. On the other hand, the signatures of the evolution of large features are detectable even after the spatial smearing. We show that this case can be quantitatively compared with Hinode/SP observations (Shimizu et al. 2008; Nagata et al. 2008) and exhibits a very similar evolution. This suggests that the magnetic field intensification process in the MURaM simulations is a faithful description of the process taking place on the Sun. Furthermore, our study indicates that the analysis and interpretation of the observations in terms of the convective intensification process is well-founded.
AcknowledgementsHinode 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). We thank R. Cameron for valuable suggestions. This work was partially supported by WCU grant No. R:31-0016 funded by the Korean Ministry of Education, Science and Technology. This research has been partly supported by the Ministry of Science and Technological Development of the Republic of Serbia (Project No 146003 ``Stellar and Solar Physics'').
References
- Bello González, N., Okunev, O., & Kneer, F. 2008, A&A, 490, L23 [Google Scholar]
- Bellot Rubio, L. R., Rodríguez Hidalgo, I., Collados, M., et al. 2001, ApJ, 560, 1010 [NASA ADS] [CrossRef] [Google Scholar]
- Bercik, D. J., Nordlund, A., & Stein, R. F. 2003, In Proceedings of SOHO 12 / GONG+ 2002. Local and global helioseismology: the present and future, ed. H. Sawaya-Lacoste, 201 [Google Scholar]
- Bonet, J. A., Márquez, I., Sánchez Almeida, J., et al. 2008, ApJ, 687, L131 [NASA ADS] [CrossRef] [Google Scholar]
- Cheung, M. C. M., Schüssler, M., & Moreno-Insertis, F. 2007, A&A, 467, 703 [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 [Google Scholar]
- Frutiger, C., Solanki, S. K., Fligge, M., & Bruls, J. H. M. J. 2000, A&A, 358, 1109 [Google Scholar]
- Gadun, A. S., Solanki, S. K., Sheminova, V. A., & Ploner, S. R. O. 2001, Sol. Phys., 203, 1 [NASA ADS] [CrossRef] [Google Scholar]
- Grossmann-Doerth, U., Schüssler, M., & Steiner, O. 1998, A&A, 337, 928 [Google Scholar]
- Jeong, J., & Hussain, F. 1995, J. Fluid Mechanics, 285, 69 [Google Scholar]
- Khomenko, E., & Collados, M. 2007, ApJ, 659, 1726 [NASA ADS] [CrossRef] [Google Scholar]
- Kosugi, T., Matsuzaki, K., Sakao, T., et al. 2007, Sol. Phys., 243, 3 [NASA ADS] [CrossRef] [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., Kubo, M., Socas-Navarro, H., et al. 2008, ApJ, 672, 1237 [NASA ADS] [CrossRef] [Google Scholar]
- Muller, R. 1983, Sol. Phys., 85, 113 [NASA ADS] [CrossRef] [Google Scholar]
- Muller, R., & Roudier, T. 1992, Sol. Phys., 141, 27 [NASA ADS] [CrossRef] [Google Scholar]
- Nagata, S., Tsuneta, S., Suematsu, Y., et al. 2008, ApJ, 677, L145 [NASA ADS] [CrossRef] [Google Scholar]
- Nordlund, Å. 1983, Solar and Stellar Magnetic Fields: Origins and Coronal Effects, 102, 79 [Google Scholar]
- Nordlund, Å. 1986, Small Scale Magnetic Flux Concentrations in the Solar Photosphere, 83 [Google Scholar]
- Parker, E. N. 1963, ApJ, 138, 552 [NASA ADS] [CrossRef] [Google Scholar]
- Parker, E. N. 1978, ApJ, 221, 368 [NASA ADS] [CrossRef] [Google Scholar]
- Piskunov, N. E., Kupka, F., Ryabchikova, T. A., et al. 1995, A&AS, 112, 525 [Google Scholar]
- Roudier, T., Malherbe, J. M., November, L., et al. 1997, A&A, 320, 605 [Google Scholar]
- Rüedi, I., Solanki, S. K., Livingston, W., & Stenflo, J. O. 1992, A&A, 263, 323 [Google Scholar]
- Schüssler, M. 1990, in Solar Photosphere: Structure, Convection and Magnetic Fields, ed. J. O. Stenflo (Dordrecht: Kluwer), IAU Symp., 138, 161 [Google Scholar]
- Sheminova, V. A., & Gadun, A. S. 2000, Astron. Rep., 44, 701 [NASA ADS] [CrossRef] [Google Scholar]
- Shimizu, T., Lites, B. W., Katsukawa, Y., et al. 2008, ApJ, 680, 1467 [NASA ADS] [CrossRef] [Google Scholar]
- Socas-Navarro, H., & Manso Sainz, R. 2005, ApJ, 620, L71 [NASA ADS] [CrossRef] [Google Scholar]
- Solanki, S. K., & Bruls, J. H. M. J. 1994, A&A, 286, 269 [Google Scholar]
- Solanki, S. K., Zufferey, D., Lin, H., et al. 1996, A&A, 310, L33 [Google Scholar]
- Spruit, H. C., & Zweibel, E. G. 1979, Sol. Phys., 62, 15 [NASA ADS] [CrossRef] [Google Scholar]
- Stein, R. F., & Nordlund, A. 1998, ApJ, 499, 914 [Google Scholar]
- Stein, R. F., & Nordlund, Å. 2006, ApJ, 642, 1246 [NASA ADS] [CrossRef] [Google Scholar]
- Steiner, O. 1999, Third Advances in Solar Physics Euroconference: Magnetic Fields and Oscillations, ASP Conf. Ser., 184, 38 [Google Scholar]
- Takeuchi, A. 1999, ApJ, 522, 518 [NASA ADS] [CrossRef] [Google Scholar]
- Thevenin, F. 1989, A&AS, 77, 137 [Google Scholar]
- Tsuneta, S., Ichimoto, K., Katsukawa, Y., et al. 2008, Sol. Phys., 249, 167 [NASA ADS] [CrossRef] [Google Scholar]
- Venkatakrishnan, P. 1986, Nature, 322, 156 [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 [Google Scholar]
- Vögler, A., Shelyag, S., Schüssler, M., et al. 2005, A&A, 429, 335 [Google Scholar]
- Webb, A. R., & Roberts, B. 1978, Sol. Phys., 59, 249 [NASA ADS] [CrossRef] [Google Scholar]
- Weiss, N. O. 1966, R. Soc. London Proc. Ser. A, 293, 310 [NASA ADS] [CrossRef] [Google Scholar]
- de Wijn, A. G., Stenflo, J. O., Solanki, S. K., & Tsuneta, S. 2008, Space Sci. Rev., 144, 275 [Google Scholar]
All Figures
![]() |
Figure 1:
Maps of the whole simulation domain at t=140 s.
Normalized continuum intensity at 630 nm ( left), the vertical component of the magnetic field ( middle) and velocity ( right) at a geometrical height roughly corresponding
to the level of
|
Open with DEXTER | |
In the text |
![]() |
Figure 2:
Evolution of the continuum intensity at 630 nm and the magnetic field in a
|
Open with DEXTER | |
In the text |
![]() |
Figure 3:
Enlargement of the regions, having a size of
|
Open with DEXTER | |
In the text |
![]() |
Figure 4:
Time sequence of vertical cuts through the magnetic concentration
corresponding to case (positions of the cuts are marked by yellow
horizontal lines in right-hand images in Fig. 2). The plotted cuts correspond to the same instants as sampled in
Fig. 2. From left to right: density excess with respect to the the mean density at every
height, vertical component of magnetic field, vertical component of velocity (overplotted arrows show the
components of the velocity field in the x-z plane), and radiative heating rate. Horizontal solid lines follow the levels of
|
Open with DEXTER | |
In the text |
![]() |
Figure 5:
Height profiles of various quantities in the flux concentration
corresponding to the case I (magnetic field, vertical component of
velocity, density and temperature) at the positions marked by dashed
lines in Fig. 4 at different times. Thick vertical lines mark the positions of the optical depth
|
Open with DEXTER | |
In the text |
![]() |
Figure 6: The same as Fig. 4 but for cases II and III. Each frame is subdivided into a left part displaying case II and a right part showing case III. Vertical lines mark the positions of the height profiles given in Figs. 7 and 8. |
Open with DEXTER | |
In the text |
![]() |
Figure 7: The same as Fig. 5, but for case II. |
Open with DEXTER | |
In the text |
![]() |
Figure 8: The same as Fig. 5, but for case III. |
Open with DEXTER | |
In the text |
![]() |
Figure 9:
Temporal change of normalized continuum intensity ( left), the vertical component of magnetic field ( middle) and the vertical component of velocity
( right), for cases I ( top row), II ( middle row) and III ( bottom row) at original (stars/solid line) and Hinode resolution (crosses/dashed line).
The vertical component of the magnetic field and velocity at log
|
Open with DEXTER | |
In the text |
![]() |
Figure 10: Synthetic Stokes I ( left) and V ( right) profiles at original ( upper row) and Hinode resolution ( lower row) for the times t=0,140 and 420 s marked by dotted, solid and dashed lines, respectively. The intensity is normalized to the mean continuum intensity in the full snapshot domain. |
Open with DEXTER | |
In the text |
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