Magnetic flux emergence in the photosphere
M. Cheung (LMSAL, Palo Alto), M Schüssler, F. Moreno-Insertis (IAC, Tenerife/Spain)
Magnetic fields exist over a wide range of length- and time-scales on
the solar photosphere. We investigate the flux emergence process by
carrying out realistic simulations of emerging flux tubes in the
photosphere with the MURaM code. Since the effects of radiative transfer
is included in our MURaM code, we are able to compare our simulation
results with real photospheric observations of magnetic flux
emergence. The picture on the left shows a transient dark lane marking
the site of flux emergence. The properties of this dark lane are
different from those of normal granulation. The animation to the right
shows a synthetic greyscale `magnetogram' (white and black indicating
the two opposite magnetic polarities) from the simulated emergence of a
magnetic loop. The upper panel gives the original resolution of the
simulation while the lower panel results after smearing with a Gaussian
to be comparable with a typical ground-based observational result.
References
Magnetic flux emergence in granular convection: radiative MHD simulations and observational signatures, Cheung, M. C. M.; Schüssler, M.; Moreno-Insertis, F., Astron. Astrophys., 467, 703-719 (2007).
MURaM website
Spectro-polarimetric diagnostics near the solar limb: Simulations
versus high-resolution observations
L. Yelles Chaouche, S. K. Solanki
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| Figure 1: Simulated continuum image inclined at an angle of 67 degree |
Figure 2: Illustration of construction of inclined rays from a simulation box.
Left panel : Magnetic field strength at Tau=1, in the original (non-inclined) simulation
box. Right panel: Vertical cut at the location shown by the dark slit (left panel);
The inclined arrows shows the way the inclined rays are constructed. |
The aim of this investigation is to understand the detailed formation of
Stokes
profiles and thus to lay the foundation of the physical interpretation of
spectro-polarimetric
diagnostics in an active region plage near the limb. We use 3-D
radiation-MHD simulations with unipolar fields of an average
strength of 200G and 400G, which is distributed between weak fields
and flux tubes in which the field typically reaches Kilo-Gauss values.
We generate synthetic Stokes spectra by radiative transfer
calculations, then we smear the simulated Stokes signal to reproduce
observational conditions. The synthetic data
treated in this
manner statistically reproduce spectro-polarimetric high resolution
observations at mu=0.39 obtained by the SOUP
instrument with the
Swedish Solar Telescope in 2006 by L. Rouppe van
der Voort and M. van Noort (SST). After establishing the similarity
between observations and simulations, we investigate in more detail
individual features in the simulations corresponding to magnetic flux
concentrations,
and identify the properties and origin of their Stokes signatures.
Many properties of these concentrations turn out to be rather similar to
those of thin flux tubes, but with some important differences.
Wave propagation through a model sunspot
R. Cameron, in conjunction with L. Gizon and K. Daiffallah
We have written and tested a code for to numerically follow the
evolution of linear amplitude waves as they propagate through
the solar atmosphere. The modeled atmosphere can include large amplitude
magnetic fields, temperature, velocity, density and sound speed
inhomogeneities. The code has now been tested, and we are beginning to
use it to understand the real problems.
Caption: Shown is an f-mode (suface gravity) wave propagating through an
atmosphere containing a vertical flux tube. The wavefront is distorted
primarily due to the fact that the propagation through the tuber is
faster than through its non-magnetic surroundings. A second effect is
through mode-coupling which causes some of the energy to propagate
down the tube in the form of slow-mode waves.
Reference
SLiM: a code for the simulation of wave propagation through an inhomogenous,
magnetised solar atmosphere, R. Cameron, L. Gizon, and K. Daiffallah, Astron. Nachr. 328 313-318
Mesogranulation
L. Matloch, R. Cameron, D. Schmitt, M. Schüssler
Since their discovery in 1981, the origin of mesogranulation on the photosphere
has remained controversial. Evidence in recent years suggest that the origin of
mesogranulation maybe due to the self-arrangement of granules at the surface
instead of a convective effect rooted deeper in the convection zone. We persue
this idea by studying the evolution of cell systems, like the example in the figure
above (left panel). To capture the basic properties of granulation in the models, we set
appropriate rules for granule disappearance and birth. By comparing features of
the emerging mesogranular-like patterns (horizontal velocity divergence in the figure,
right panel) for different cell-interaction rules (e.g. size-induced pressure, random
walk, etc) with results from MHD simulations as well as observations, we attempt
to identify the cause of mesogranulation.
References
Solar mesogranulation as a cellular automaton effect, Matloch, L.; Cameron, R.; Schmitt, D.; Schüssler, M. in: "Modern solar facilities - advanced solar science", F. Kneer, K. G. Puschmann, A. D. Wittmann (eds.) p.339-342 (2007)
MURaM website
Reconstruction of the magnetic field in the inner heliosphere
J. Jiang, R. Cameron, D.Schmitt, M. Schüssler
We aim to model the heliospheric magnetic field, especially near the earth,
using the historical sunspot record. This will allow us to reconstruct the
heliospheric field back to the end of the Maunder minimum. The sunspot
record is used as input data, and is evolved using the Surface
Flux Transport model. The heliospheric field is then obtained using
the Current Sheet Source Surface model.
Upper panel: The temporal evolution of polar field, solar surface total flux
density and open flux density.
Lower panel: The temporal evolution of the solar surface field distribution
from the SFT simulation and the location of the open flux.
References
Magnetic flux transport on the Sun
I. Baumann, D.Schmitt, M. Schüssler, S.K. Solanki
Active regions emerge on the photosphere as bipolar magnetic regions in the
low-latitude sunspot-belts. The magnetic flux is dispersed by supergranular
convective motions and meridional circulation. The differential rotation rate of
the sun leads to a shearing of the flux pattern. The transport equation is
derived from the induction equation resulting from the MHD-Approximation.
Longitude averaged latitude-time diagram of a simulation over a few solar cycles. The emergence latitude of bipolar magnetic regions decreases with the ongoing cycle from higher latitudes towards the equator. The "poleward surges" result from a photospheric meridional flow. The change of leading and trailing polarities of the bipolar regions due to Hale's law results in the reversal of the polar fields during cycle maxima.
References
Modeling the Sun's open magnetic flux, Schüssler, M. & Baumann, I., Astron. Astrophys. 459, 945-953 (2006).
A necessary
extension of the surface flux transport model, Baumann, I., Schmitt, D. and
Schüssler, M., Astron. Astrophys., 446, 307-314 (2006).
Evolution of the large-scale magnetic field on the solar surface: a parameter study, I. Baumann, D. Schmitt, M. Schüssler, and S. K. Solanki, Astron. & Astrophys., 426, 1075-1091 (2004).
Turbulent solar magnetic fields
J. Pietarila Graham, S. Danilovic, M. Schüssler
Observations of small-scale magnetic fields fields from Hinode
and numerical simulations of dynamo action in the photospheric layers
of the Sun are compared. Using turbulence theory to motivate
self-similar scaling laws, a lower bound of 50G is derived for the
unsigned quiet-Sun vertical flux. This agrees with our MURaM
simulation-based estimate and (considering vector magnitudes) resolves
the discrepancy between Hanle and Zeeman observations.
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Figure 1. Left: Portion of magnetic flux remaining after averaging
over boxes of increasing size (from Hinode observation). A
self-similar power-law is abundantly clear for 2 decades of length
scales down to the resolution limit. Right: Flux remaining after
averaging over 200 km X 200 km boxes for MURaM as a function of
magnetic Reynolds number, ReM. Extrapolation to solar
ReM indicates at least 80% cancellation at 200 km
resolution.
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Figure 2. Probability distribution functions of magnetic field
strengths from the simulations (solid line), from the Hinode
observations (dashed lines), the inversions of synthetic
stokes-diagnostics created from the simulations (dash dot) and when an
observational noise level of 0.0011 is added (dotted line). The
observational peak that was previously considered solar is seen to be
solely due to noise.
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References
Turbulent Magnetic Fields in the Quiet Sun: Implications of Hinode Observations and Small-Scale Dynamo
Simulations, Pietarila Graham, J., Danilovic, S., Schüssler, M., ApJ, Volume 693, 1728-1735 (2009).
Dynamics of magnetic fields in the convection zone
Stability and dynamics of thin flux tubes in the solar convection zone
V. Holzwarth, E. Isik, M. Schüssler, D. Schmitt, A. Ferriz Mas (Univ. of Vigo)
The magnetic field permeating the solar atmosphere is expected to
originate from the bottom of the convection zone.
The field is amplified in the tachocline and stored in the stably
stratified overshoot region at the interface to the radiative core.
When the field strength is larger than a critical value, perturbations
lead to the formation of rising flux loops, which eventually emerge at
the surface.
The above figure shows the rise of a magnetic flux loop in the convection
zone, from the onset of the instability (left)
to its eruption at the stellar surface (right). The flux tube radius
is shown 5 times magnified. The animation can be seen upon clicking
on the figure. The initial flux tube is in mechanical equilibrium in mid-overshoot
region near the bottom of the convection zone. The initial latitude is 5 degrees, and
the initial magnetic field strength is 10 Tesla. The tube radius is 1000 km and is shown
5 times magnified for better visibility.
We also study the effects of transversal and longitudinal flows on a magnetic flux tube
near the bottom of the convection zone.
References
Flow instabilities of magnetic flux tubes. II. Longitudinal flow, Holzwarth, V.; Schmitt, D.; Schüssler, M., Astron. Astrophys., 469, 11-17 (2007).
Flow instabilities of magnetic flux tubes. I. Perpendicular flow, Schüssler, M. & Ferriz-Mas, A., Astron. Astrophys. 463, 23-29 (2007).
Dynamo theory
A solar surface dynamo
A. Vögler (Univ. of Utrecht), M. Schüssler
Various observations indicate the existence of significant amounts of
magnetic flux ubiquitous in the `quiet Sun', i.e., outside active
regions, with mixed polarity on small scales. Since idealized Boussinesq
closed-box simulations of Cattaneo (ApJ, 1999) showed dynamo action of
non-helical instationary convection, the existence of a similar process
based upon granular convection of the Sun has been discussed. Removing
the idealizations in a realistic simulation with the MURaM code, we have
found that solar surface convection seems indeed capable of supporting a
dynamo process: for sufficiently large magnetic Reynolds number, the
magnetic energy of an initial weak seed field grows exponentially and
saturates at levels consistent with the observational inferences. The
generated surface field has a small/scale structure with mixed polarity
(right panel: vertical field image near optical unity; the size of the
magnified inset is about 1200 km x 1200 km on the Sun) and shows an
association with the intergranular downflow lanes.
Reference
A solar surface dynamo, Vögler, A.; Schüssler, M., Astron. Astrophys., 465, L43-L46 (2007).
Identification of MURaM dynamo as a turbulent small-scale dynamo
J. Pietarila Graham, R. Cameron, M. Schüssler
Spectral transfer analysis of the MURaM dynamo rules out the tangling
of magnetic field lines (turbulent cascade) and Alfvénization
of turbulent velocity fluctuations ("turbulent induction") as sources
of small-scale magnetic field (see Figure 1). Rather, small-scale
fluid motions stretch small-scale magnetic field to produce more
small-scale magnetic field and the scales involved become smaller with
increasing Reynolds number. This is a small-scale turbulent dynamo.
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Figure 1. Transfer analysis of MURaM surface dynamo. Left: Work
against Lorentz force versus horizontal spatial frequency shows that
fluid motions at scales near 200 km stretch magnetic
field lines (dynamo). Right: Rate of magnetic energy production by
stretching (blue solid) and compression (blue dotted), magnetic energy
lost (red) and gained (black) from the turbulent cascade versus
horizontal spatial frequency. Magnetic field is produced predominantly
at scales near 65 km from stretching motions. Bottom: Triadic transfer
indicates the magnetic field that is stretched has scales near 75 km.
All scales are well below the 1000 km granulation scale, identifying
the dynamo mechanism as a turbulent small-scale dynamo.
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Figure 2. Vertical cuts of Top: Real-space analog of blue solid line
from Figure 1: rate of magnetic energy production by stretching and
Bottom: vertical velocity (dark for down-flows). Down-flow plumes are
the site of dynamo generation.
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Statistical properties of the multipole coefficients of the geomagnetic field
P. Hoyng (Utrecht), C. St-Jean, D. Schmitt, J. Wicht, U. Christensen
The Earth has had a magnetic field for several billion years. The main component is the dipole
which is variable on all time scales from a few 100 years and longer. A spectacular aspect of this
variability are sudden dipole polarity reversals which occur on average once every few times
105 years. The magnetic field is generated in the electrically conducting and convecting
fluid in the outer core by dynamo processes. Many features of the Earth's magnetic field, including
polarity reversals, can be reproduced by three-dimensional simulations of the magnetohydrodynamics
in the Earth's interior. Due to the very complicated nonlinear interaction of the flow and the
magnetic field, it is difficult to extract e.g. the conditions for polarity reversals. The object of
the present project is a systematic quantitative analysis of the output of these geodynamo
simulations.
We propose to compare the statistical properties of the first few multipole components of the
magnetic field extracted from the hydromagnetic simulations with theoretical predictions. The
statistical properties of the velocity field are supposed to be given. We expand the field in the
complete set of biorthogonal eigenfunctions of the dynamo operator and thus describe the physics of
the dynamo entirely in terms of interactions between global modes. The statistical properties of
the expansion coefficients such as rms values, the autocorrelation functions, the cross
correlations, the distribution of the mode coefficients, the mean reversal rate of the fundamental
mode etc are derived from the theory of stochastic differential equations.
First, the dynamo operator has to be derived from the velocity field of the numerical simulations
of a typical geodynamo model. This requires the determination of the dynamo coefficients alpha and
beta (see figure). Second, from the dynamo operator, the eigenfunctions have to be determined.
Third, the magnetic field of the numerical simulations is decomposed and the timeprofiles of the
first few multipole coefficients are obtained. The computation of the averages and correlation
functions from the time series is straightforward.
By comparing the numerical with the analytical results we can, on the one hand, refine our theory
as various approximations are involved and, on the other hand, make predictions on the outcome of
the dynamo model, e.g. about the mean reversal rate.
This project is following two past projects on "Magnetic
field reversals and secular variation in a
bistable geodynamo model" and "Mean-field
coefficients for geodynamo models". The work is made in colloboration with the "Planetary Dynamics Group"
at the MPS, whose numerical simulation results are used and
analysed.
Stellar magnetism
Coupled models of generation, emergence, and surface evolution of stellar magnetic flux
E. Isik, D. Schmitt, M. Schüssler
We develop a model which connects the missing link
between deep-seated dynamos and the evolving surface flux in cool stars.
The link, which is hitherto not included in any dynamo model,
is the buoyant rise of magnetic flux tubes
from the dynamo layer throughout the entire convection zone.
We choose toroidal flux tubes with a spatial probability distribution
determined by the mean toroidal magnetic field generated by a cyclic dynamo.
As a first example, we use a thin-layer
alpha-omega dynamo (Schüssler & Schmitt 1989) with Sun-like shear
in the convective overshoot region. We carry out numerical
simulations of the rise of Parker-unstable flux tubes (Caligari et al. 1995),
which in turn determine the latitudes
and the tilt angles of the emerging flux loops. This information is then
put into a surface flux transport model (Baumann et al. 2004, 2006) with
Sun-like differential rotation, meridional flow, and turbulent supergranular
diffusion. In this part, we simulate the evolution of bipolar magnetic
regions, which emerge with a Sun-like area distribution and with tilt angles
and emergence latitudes determined by rising flux tubes.
The figure on the left panel shows a comparison of the generated toroidal field pattern
in the overshoot region (contours) and the emerging flux tubes on the surface (dots),
for a star having solar internal structure but rotating 2.7 times faster than
the Sun, hence representing somewhat a "younger Sun". The time-latitude diagram
on the right-hand panel shows the surface evolution of longitudinally averaged
magnetic flux density. The polar fields are about 20-30 times stronger than in
the Sun, and the cyclic dynamo is no longer visible in the variation of
magnetic flux integrated over the entire surface.
Reference
A coupled model of magnetic flux generation and transport in stars, Isik, E.;
Schmitt, D.; Schüssler, M., Astron. Nachr., 328, 1111
Magnetic flux transport on active cool stars
E. Isik, M. Schüssler, S. K. Solanki
Rapidly rotating cool stars show signatures of magnetic activity, particularly
around their rotational poles, unlike the Sun. We have made numerical
simulations that give a possible explanation for the formation of polar
spots, besides depicting the effects of large-scale surface flows upon the
evolution of starspots. The above figure shows the magnetic field distribution
of isolated bipolar magnetic regions when the field strength is about to
fall under a detection threshold. Black and yellow show opposite magnetic
polarities. White regions covered by black contours indicate regions still
above the threshold. Panels a,b): solar-like magnetic regions with an initial
tilt with respect to the equator (a) and without tilt (b), 52 days and 45 days
after their emergence. c,d): Very large stellar magnetic regions - tilted (c)
and non-tilted (d), 218 and 123 days after their
emergence. A nonzero tilt angle lead to a longer spot lifetime, particularly
for a very large bipolar region (c), which eventually forms a long-living
polar cap.
Reference
Magnetic flux transport in active cool stars and starspot lifetimes,
E. Isik, M. Schüssler, S. K. Solanki, Astron. and Astrophys., 464, 1049-1057 (2007).
Theoretical mass loss rates of cool stars
V. Holzwarth, M. Jardine (Univ. of St. Andrews)
Figure: Comparison between empirical wind ram pressures (symbols, indicating
spectral type, from Wood et al. 2005, ApJ 628, L143) and theoretical wind ram
pressures (curves) of main-sequence stars. The cross marks the transition from
slow to fast magnetic rotators.
The stellar mass loss rate is important for the rotational evolution of
a star and for its interaction with the circumstellar environment.
The analysis of astrospheric absorption features enables an
empirical determination of mass loss rates of cool stars other than the
Sun.
In collaboration with M Jardine (St Andrews, Scotland), we have developed
a model for the wind properties of cool main-sequence stars, which
comprises their wind ram pressures, mass fluxes, and terminal wind
velocities.
The wind properties are determined through a polytropic magnetised wind
model, assuming power laws for the dependence of the thermal and
magnetic wind parameters on the stellar rotation rate.
We use the empirical data to constrain theoretical wind scenarios,
which are characterised by different rates of increase of the wind
temperature, wind density, and magnetic field strength.
Since the predicted mass loss rates of cool main-sequence stars do not
exceed about ten times the solar value, we expect the impact of stellar
winds on planetary atmospheres to be less severe and the detectability
of magnetospheric radio emission to be lower than suggested in previous
investigations.
Reference
Theoretical mass loss rates of cool main-sequence stars, Holzwarth, V.; Jardine, M., Astron. and Astrophys., 463, 11-21, 2007.
Magnetic flux emergence in fast rotating stars
V. Holzwarth, E. Isik, M. Schüssler
Fast rotating cool stars are characterised by high magnetic activity
levels and frequently show dark spots up to polar latitudes.
High latitudes of magnetic flux eruption are expected to be caused by
the influence of the Coriolis force on the dynamics of rising flux tubes,
which entails a strong poleward deflection of the tube's trajectory in
rapidly rotating stars.
Yet the formation of proper polar spots likely requires the assistance of
meridional flows, which increases the poleward transport of magnetic
flux both before and after its eruption on the stellar surface.
The above figure shows the poleward deflection (left) and tilt angle (right) of erupting
flux tubes. All flux tubes start with the same initial conditions
(Initial field strength 2 x 105 G, initial latitude 5 degrees, distance from
the centre of the star (of 1 solar radius), 5.07 x 1010 cm.
Reference
Magnetic flux emergence in fast rotating stars, Holzwarth, V.; Mem. Soc. Astron. It., 78, 271 (2007)
