2,830 research outputs found
Helioseismology challenges models of solar convection
Convection is the mechanism by which energy is transported through the
outermost 30% of the Sun. Solar turbulent convection is notoriously difficult
to model across the entire convection zone where the density spans many orders
of magnitude. In this issue of PNAS, Hanasoge et al. (2012) employ recent
helioseismic observations to derive stringent empirical constraints on the
amplitude of large-scale convective velocities in the solar interior. They
report an upper limit that is far smaller than predicted by a popular
hydrodynamic numerical simulation.Comment: Printed in the Proceedings of the National Academy of Sciences (2
pages, 1 figure). Available at
http://www.pnas.org/cgi/doi/10.1073/pnas.120887510
Interpretation of Helioseismic Travel Times - Sensitivity to Sound Speed, Pressure, Density, and Flows
Time-distance helioseismology uses cross-covariances of wave motions on the
solar surface to determine the travel times of wave packets moving from one
surface location to another. We review the methodology to interpret travel-time
measurements in terms of small, localized perturbations to a horizontally
homogeneous reference solar model. Using the first Born approximation, we
derive and compute 3D travel-time sensitivity (Fr\'echet) kernels for
perturbations in sound-speed, density, pressure, and vector flows. While
kernels for sound speed and flows had been computed previously, here we extend
the calculation to kernels for density and pressure, hence providing a complete
description of the effects of solar dynamics and structure on travel times. We
treat three thermodynamic quantities as independent and do not assume
hydrostatic equilibrium. We present a convenient approach to computing damped
Green's functions using a normal-mode summation. The Green's function must be
computed on a wavenumber grid that has sufficient resolution to resolve the
longest lived modes. The typical kernel calculations used in this paper are
computer intensive and require on the order of 600 CPU hours per kernel.
Kernels are validated by computing the travel-time perturbation that results
from horizontally-invariant perturbations using two independent approaches. At
fixed sound-speed, the density and pressure kernels are approximately related
through a negative multiplicative factor, therefore implying that perturbations
in density and pressure are difficult to disentangle. Mean travel-times are not
only sensitive to sound-speed, density and pressure perturbations, but also to
flows, especially vertical flows. Accurate sensitivity kernels are needed to
interpret complex flow patterns such as convection
Generalization of the noise model for time-distance helioseismology
In time-distance helioseismology, information about the solar interior is
encoded in measurements of travel times between pairs of points on the solar
surface. Travel times are deduced from the cross-covariance of the random wave
field. Here we consider travel times and also products of travel times as
observables. They contain information about e.g. the statistical properties of
convection in the Sun. The basic assumption of the model is that noise is the
result of the stochastic excitation of solar waves, a random process which is
stationary and Gaussian. We generalize the existing noise model (Gizon and
Birch 2004) by dropping the assumption of horizontal spatial homogeneity. Using
a recurrence relation, we calculate the noise covariance matrices for the
moments of order 4, 6, and 8 of the observed wave field, for the moments of
order 2, 3 and 4 of the cross-covariance, and for the moments of order 2, 3 and
4 of the travel times. All noise covariance matrices depend only on the
expectation value of the cross-covariance of the observed wave field. For
products of travel times, the noise covariance matrix consists of three terms
proportional to , , and , where is the duration of the
observations. For typical observation times of a few hours, the term
proportional to dominates and , where the are arbitrary travel times. This
result is confirmed for travel times by Monte Carlo simulations and
comparisons with SDO/HMI observations. General and accurate formulae have been
derived to model the noise covariance matrix of helioseismic travel times and
products of travel times. These results could easily be generalized to other
methods of local helioseismology, such as helioseismic holography and ring
diagram analysis
Signal and noise in helioseismic holography
Helioseismic holography is an imaging technique used to study heterogeneities
and flows in the solar interior from observations of solar oscillations at the
surface. Holograms contain noise due to the stochastic nature of solar
oscillations. We provide a theoretical framework for modeling signal and noise
in Porter-Bojarski helioseismic holography. The wave equation may be recast
into a Helmholtz-like equation, so as to connect with the acoustics literature
and define the holography Green's function in a meaningful way. Sources of wave
excitation are assumed to be stationary, horizontally homogeneous, and
spatially uncorrelated. Using the first Born approximation we calculate
holograms in the presence of perturbations in sound-speed, density, flows, and
source covariance, as well as the noise level as a function of position. This
work is a direct extension of the methods used in time-distance helioseismology
to model signal and noise. To illustrate the theory, we compute the hologram
intensity numerically for a buried sound-speed perturbation at different depths
in the solar interior. The reference Green's function is obtained for a
spherically-symmetric solar model using a finite-element solver in the
frequency domain. Below the pupil area on the surface, we find that the spatial
resolution of the hologram intensity is very close to half the local
wavelength. For a sound-speed perturbation of size comparable to the local
spatial resolution, the signal-to-noise ratio is approximately constant with
depth. Averaging the hologram intensity over a number of frequencies above
3 mHz increases the signal-to-noise ratio by a factor nearly equal to the
square root of . This may not be the case at lower frequencies, where large
variations in the holographic signal are due to the individual contributions of
the long-lived modes of oscillation.Comment: Submitted to Astronomy and Astrophysic
Seismic probes of solar interior magnetic structure
Sunspots are prominent manifestations of solar magnetoconvection and imaging
their subsurface structure is an outstanding problem of wide physical
importance. Travel times of seismic waves that propagate through these
structures are typically used as inputs to inversions. Despite the presence of
strongly anisotropic magnetic waveguides, these measurements have always been
interpreted in terms of changes to isotropic wavespeeds and flow-advection
related Doppler shifts. Here, we employ PDE-constrained optimization to
determine the appropriate parameterization of the structural properties of the
magnetic interior. Seven different wavespeeds fully characterize helioseismic
wave propagation: the isotropic sound speed, a Doppler-shifting flow-advection
velocity and an anisotropic magnetic velocity. The structure of magnetic media
is sensed by magnetoacoustic slow and fast modes and Alfv\'{e}n waves, each of
which propagates at a different wavespeed. We show that even in the case of
weak magnetic fields, significant errors may be incurred if these anisotropies
are not accounted for in inversions. Translation invariance is demonstrably
lost. These developments render plausible the accurate seismic imaging of
magnetoconvection in the Sun.Comment: 4 pages, 4 figures, accepted Physical Review Letter
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