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Author name code: pietarila-graham
ADS astronomy entries on 2022-09-14
author:Pietarila Graham, Jonathan
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Title: Instrumental and Observational Artifacts in Quiet Sun Magnetic
Flux Cancellation Functions
Authors: Pietarila, A.; Pietarila Graham, J.
2013SoPh..282..389P Altcode: 2012arXiv1209.6388P
Under the assumption that the photospheric quiet Sun magnetic
field is turbulent, the cancellation function has previously been
used to estimate the true, resolution-independent mean, unsigned
vertical flux «|B<SUB>z</SUB>|»<SUB>true</SUB>. We show that
the presence of network elements, noise, and seeing complicate the
measurement of accurate cancellation functions and their power law
exponents κ. Failure to exclude network elements previously led
to estimates that were too low for both the cancellation exponent
κ and «|B<SUB>z</SUB>|»<SUB>true</SUB>. However, both κ and
«|B<SUB>z</SUB>|»<SUB>true</SUB> are overestimated due to noise
in magnetograms. While no conclusive value can be derived with
data from current instruments, our Hinode/SP results of κ⪅0.38
and «|B<SUB>z</SUB>|»<SUB>true</SUB>⪅270 gauss can be taken as
upper bounds.
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Title: Not much helicity is needed to drive large-scale dynamos
Authors: Pietarila Graham, Jonathan; Blackman, Eric G.; Mininni,
Pablo D.; Pouquet, Annick
2012PhRvE..85f6406P Altcode: 2011arXiv1108.3039P
Understanding the in situ amplification of large-scale magnetic fields
in turbulent astrophysical rotators has been a core subject of dynamo
theory. When turbulent velocities are helical, large-scale dynamos
that substantially amplify fields on scales that exceed the turbulent
forcing scale arise, but the minimum sufficient fractional kinetic
helicity f<SUB>h,C</SUB> has not been previously well quantified. Using
direct numerical simulations for a simple helical dynamo, we show that
f<SUB>h,C</SUB> decreases as the ratio of forcing to large-scale wave
numbers k<SUB>F</SUB>/k<SUB>min</SUB> increases. From the condition
that a large-scale helical dynamo must overcome the back reaction from
any nonhelical field on the large scales, we develop a theory that
can explain the simulations. For k<SUB>F</SUB>/k<SUB>min</SUB>⩾8 we
find f<SUB>h,C</SUB>≲3%, implying that very small helicity fractions
strongly influence magnetic spectra for even moderate-scale separation.
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Title: Universality of the Small-scale Dynamo Mechanism
Authors: Moll, R.; Pietarila Graham, J.; Pratt, J.; Cameron, R. H.;
Müller, W. -C.; Schüssler, M.
2011ApJ...736...36M Altcode: 2011arXiv1105.0546M
We quantify possible differences between turbulent dynamo action in
the Sun and the dynamo action studied in idealized simulations. For
this purpose, we compare Fourier-space shell-to-shell energy transfer
rates of three incrementally more complex dynamo simulations: an
incompressible, periodic simulation driven by random flow, a simulation
of Boussinesq convection, and a simulation of fully compressible
convection that includes physics relevant to the near-surface layers
of the Sun. For each of the simulations studied, we find that the
dynamo mechanism is universal in the kinematic regime because energy
is transferred from the turbulent flow to the magnetic field from
wavenumbers in the inertial range of the energy spectrum. The addition
of physical effects relevant to the solar near-surface layers, including
stratification, compressibility, partial ionization, and radiative
energy transport, does not appear to affect the nature of the dynamo
mechanism. The role of inertial-range shear stresses in magnetic
field amplification is independent from outer-scale circumstances,
including forcing and stratification. Although the shell-to-shell energy
transfer functions have similar properties to those seen in mean-flow
driven dynamos in each simulation studied, the saturated states of
these simulations are not universal because the flow at the driving
wavenumbers is a significant source of energy for the magnetic field.
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Title: Universality of the Small-Scale Dynamo Mechanism
Authors: Pietarila Graham, Jonathan; Moll, R.; Pratt, J.; Cameron,
R.; Mueller, W.; Schuessler, M.
2011SPD....42.1621P Altcode: 2011BAAS..43S.1621P
We quantify possible differences between turbulent dynamo action in
the Sun and the dynamo action studied in idealized simulation. For this
purpose we compare Fourier-space shell-to-shell energy transfer rates of
three incrementally more complex dynamo simulations: an incompressible,
periodic simulation driven by random flow, a simulation of Boussinesq
convection, and a simulation of fully compressible convection that
includes physics relevant to the near-surface layers of the Sun. For
each of the simulations studied, we find that energy is transferred
from the turbulent flow to the magnetic field from length-scales in the
inertial range of the energy spectrum. The addition of physical effects
relevant to the solar near-surface layers, including stratification,
compressibility, partial ionization, and radiative energy transport,
does not appear to affect the nature of the dynamo mechanism. The role
of inertial-range shear stresses in magnetic field amplification is
independent from outer-scale circumstances, including forcing and
stratification. Although shell-to-shell energy transfer functions
have similar properties in each simulation studied, the saturated
states of these simulations are not universal; the flow at the driving
scales is a significant source of energy for the magnetic field. The
mechanism of energy-transfer in kinematic small-scale dynamo simulations
exhibits universal properties. <P />This work has been supported by
the Max-Planck Society in the framework of the Interinstitutional
Research Initiative Turbulent transport and ion heating, reconnection
and electron acceleration in solar and fusion plasmas</u> of the
MPI for Solar System Research, Katlenburg-Lindau, and the Institute
for Plasma Physics, Garching (project MIF-IF-A-AERO8047).
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Title: Turbulent Small-Scale Dynamo Action in Solar Surface
Simulations
Authors: Pietarila Graham, Jonathan; Cameron, Robert; Schüssler,
Manfred
2010ApJ...714.1606P Altcode: 2010ApJ...714.1606G; 2010arXiv1002.2750P
We demonstrate that a magneto-convection simulation incorporating
essential physical processes governing solar surface convection exhibits
turbulent small-scale dynamo action. By presenting a derivation of
the energy balance equation and transfer functions for compressible
magnetohydrodynamics, we quantify the source of magnetic energy on a
scale-by-scale basis. We rule out the two alternative mechanisms for
the generation of the small-scale magnetic field in the simulations:
the tangling of magnetic field lines associated with the turbulent
cascade and Alfvénization of small-scale velocity fluctuations
("turbulent induction"). Instead, we find that the dominant source
of small-scale magnetic energy is stretching by inertial-range fluid
motions of small-scale magnetic field lines against the magnetic tension
force to produce (against Ohmic dissipation) more small-scale magnetic
field. The scales involved become smaller with increasing Reynolds
number, which identifies the dynamo as a small-scale turbulent dynamo.
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Title: The small-scale solar surface dynamo
Authors: Pietarila Graham, Jonathan; Danilovic, Sanja; Schuessler,
Manfred
2010arXiv1003.0347P Altcode:
The existence of a turbulent small-scale solar surface dynamo is likely,
considering existing numerical and laboratory experiments, as well as
comparisons of a small-scale dynamo in MURaM simulations with Hinode
observations. We find the observed peaked probability distribution
function (PDF) from Stokes-V magnetograms is consistent with a monotonic
PDF of the actual vertical field strength. The cancellation function
of the vertical flux density from a Hinode SP observation is found to
follow a self-similar power law over two decades in length scales down
to the ~200 km resolution limit. This provides observational evidence
that the scales of magnetic structuring in the photosphere extend
at least down to 20 km. From the power law, we determine a lower
bound for the true quiet-Sun mean vertical unsigned flux density of
~43 G, consistent with our numerically-based estimates that 80% or
more of the vertical unsigned flux should be invisible to Stokes-V
observations at a resolution of 200 km owing to cancellation. Our
estimates significantly reduce the order-of-magnitude discrepancy
between Zeeman- and Hanle-based estimates.
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Title: The Small-Scale Solar Surface Dynamo (Keynote)
Authors: Pietarila Graham, J.; Danilovic, S.; Schüssler, M.
2009ASPC..415...43P Altcode:
The existence of a turbulent small-scale solar surface dynamo is likely,
considering existing numerical and laboratory experiments, as well as
comparisons of a small-scale dynamo in MURaM simulations with Hinode
observations. We find the observed peaked probability distribution
function (PDF) from Stokes-V magnetograms is consistent with a monotonic
PDF of the actual vertical field strength. The cancellation function
of the vertical flux density from a Hinode SP observation is found
to follow a self-similar power law over two decades in length scales
down to the ≈200 km resolution limit. This provides observational
evidence that the scales of magnetic structuring in the photosphere
extend at least down to 20 km. From the power law, we determine a
lower bound for the true quiet-Sun mean vertical unsigned flux density
of ≈43 G, consistent with our numerically-based estimates that 80%
or more of the vertical unsigned flux should be invisible to Stokes-V
observations at a resolution of 200 km owing to cancellation. Our
estimates significantly reduce the order-of-magnitude discrepancy
between Zeeman- and Hanle-based estimates.
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Title: Lagrangian-averaged model for magnetohydrodynamic turbulence
and the absence of bottlenecks
Authors: Pietarila Graham, Jonathan; Mininni, Pablo D.; Pouquet, Annick
2009PhRvE..80a6313P Altcode: 2008arXiv0806.2054P
We demonstrate that, for the case of quasiequipartition between
the velocity and the magnetic field, the Lagrangian-averaged
magnetohydrodynamics (LAMHD) α model reproduces well both the
large-scale and the small-scale properties of turbulent flows;
in particular, it displays no increased (superfilter) bottleneck
effect with its ensuing enhanced energy spectrum at the onset of the
subfilter scales. This is in contrast to the case of the neutral
fluid in which the Lagrangian-averaged Navier-Stokes α model is
somewhat limited in its applications because of the formation of
spatial regions with no internal degrees of freedom and subsequent
contamination of superfilter-scale spectral properties. We argue
that, as the Lorentz force breaks the conservation of circulation and
enables spectrally nonlocal energy transfer (associated with Alfvén
waves), it is responsible for the absence of a viscous bottleneck in
magnetohydrodynamics (MHD), as compared to the fluid case. As LAMHD
preserves Alfvén waves and the circulation properties of MHD, there
is also no (superfilter) bottleneck found in LAMHD, making this method
capable of large reductions in required numerical degrees of freedom;
specifically, we find a reduction factor of ≈200 when compared to
a direct numerical simulation on a large grid of 1536<SUP>3</SUP>
points at the same Reynolds number.
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Title: Turbulent Magnetic Fields in the Quiet Sun: Implications of
Hinode Observations and Small-Scale Dynamo Simulations
Authors: Pietarila Graham, Jonathan; Danilovic, Sanja; Schüssler,
Manfred
2009ApJ...693.1728P Altcode: 2008arXiv0812.2125P
Using turbulent MHD simulations (magnetic Reynolds numbers up to
≈8000) and Hinode observations, we study effects of turbulence on
measuring the solar magnetic field outside active regions. First,
from synthetic Stokes V profiles for the Fe I lines at 6301 and
6302 Å, we show that a peaked probability distribution function
(PDF) for observationally derived field estimates is consistent
with a monotonic PDF for actual vertical field strengths. Hence, the
prevalence of weak fields is greater than would be naively inferred from
observations. Second, we employ the fractal self-similar geometry of the
turbulent solar magnetic field to derive two estimates (numerical and
observational) of the true mean vertical unsigned flux density. We also
find observational evidence that the scales of magnetic structuring in
the photosphere extend at least down to an order of magnitude smaller
than 200 km: the self-similar power-law scaling in the signed measure
from a Hinode magnetogram ranges (over two decades in length scales
and including the granulation scale) down to the ≈200 km resolution
limit. From the self-similar scaling, we determine a lower bound for
the true quiet-Sun mean vertical unsigned flux density of ~50 G. This
is consistent with our numerically based estimates that 80% or more of
the vertical unsigned flux should be invisible to Stokes V observations
at a resolution of 200 km owing to the cancellation of signal from
opposite magnetic polarities. Our estimates significantly reduce
the order-of-magnitude discrepancy between Zeeman- and Hanle-based
estimates.
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Title: Spectral Line Selection for HMI
Authors: Norton, A. A.; Pietarila Graham, J. D.; Ulrich, R. K.;
Schou, J.; Tomczyk, S.; Liu, Y.; Lites, B. W.; López Ariste, A.;
Bush, R. I.; Socas-Navarro, H.; Scherrer, P. H.
2006ASPC..358..193N Altcode:
We present information on two spectral lines, Fe I 6173 Å and Ni I 6768
Å, that were candidates for use in the Helioseismic and Magnetic Imager
(HMI) instrument. Both Fe I and Ni I profiles have clean continuum and
no blends that threaten performance. The higher Landé factor of Fe
I means its operational velocity range in regions of strong magnetic
field is smaller than for Ne I. Fe I performs better than Ni I for
vector magnetic field retrieval. Inversion results show that Fe I
consistently determines field strength and flux more accurately than
the Ni I line. Inversions show inclination and azimuthal errors are
recovered to ≈2° above 600 Mx/cm<SUP>2</SUP> for Fe I and above
1000 Mx/cm<SUP>2</SUP> for Ni I. The Fe I line was recommended, and
ultimately chosen, for use in HMI.
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Title: Inertial range scaling, Kármán-Howarth theorem,
and intermittency for forced and decaying Lagrangian averaged
magnetohydrodynamic equations in two dimensions
Authors: Pietarila Graham, J.; Holm, D. D.; Mininni, P.; Pouquet, A.
2006PhFl...18d5106P Altcode: 2005physics...8173P
We present an extension of the Kármán-Howarth theorem to the
Lagrangian averaged magnetohydrodynamic (LAMHD-α) equations. The
scaling laws resulting as a corollary of this theorem are studied
in numerical simulations, as well as the scaling of the longitudinal
structure function exponents indicative of intermittency. Numerical
simulations for a magnetic Prandtl number equal to unity are
presented both for freely decaying and for forced two-dimensional
magnetohydrodynamic (MHD) turbulence, solving the MHD equations
directly, and employing the LAMHD-α equations at 1/2 and 1/4
resolution. Linear scaling of the third-order structure function with
length is observed. The LAMHD-α equations also capture the anomalous
scaling of the longitudinal structure function exponents up to order 8.
