735 research outputs found
Linear Sensitivity of Helioseismic Travel Times to Local Flows
Time-distance helioseismology is a technique for measuring the time for waves
to travel from one point on the solar surface to another. These wave travel
times are affected by advection by subsurface flows. Inferences of plasma flows
based on observed travel times depend critically on the ability to accurately
model the effects of subsurface flows on time-distance measurements. We present
a Born approximation based computation of the sensitivity of time distance
travel times to weak, steady, inhomogeneous subsurface flows. Three sensitivity
functions are obtained, one for each component of the 3D vector flow. We show
that the depth sensitivity of travel times to horizontally uniform flows is
given approximately by the kinetic energy density of the oscillation modes
which contribute to the travel times. For flows with strong depth dependence,
the Born approximation can give substantially different results than the ray
approximation.Comment: 6 pages, 6 figure
Time-distance helioseismology: Sensitivity of f-mode travel times to flows
Time-distance helioseismology has shown that f-mode travel times contain
information about horizontal flows in the Sun. The purpose of this study is to
provide a simple interpretation of these travel times. We study the interaction
of surface-gravity waves with horizontal flows in an incompressible,
plane-parallel solar atmosphere. We show that for uniform flows less than
roughly 250 m s, the travel-time shifts are linear in the flow
amplitude. For stronger flows, perturbation theory up to third order is needed
to model waveforms. The case of small-amplitude spatially-varying flows is
treated using the first-order Born approximation. We derive two-dimensional
Fr\'{e}chet kernels that give the sensitivity of travel-time shifts to local
flows. We show that the effect of flows on travel times depends on wave damping
and on the direction from which the observations are made. The main physical
effect is the advection of the waves by the flow rather than the advection of
wave sources or the effect of flows on wave damping. We compare the
two-dimensional sensitivity kernels with simplified three-dimensional kernels
that only account for wave advection and assume a vertical line of sight. We
find that the three-dimensional f-mode kernels approximately separate in the
horizontal and vertical coordinates, with the horizontal variations given by
the simplified two-dimensional kernels. This consistency between quite
different models gives us confidence in the usefulness of these kernels for
interpreting quiet-Sun observations.Comment: 34 pages, accepted to Astrophysical Journa
F-mode sensitivity kernels for flows
We compute f-mode sensitivity kernels for flows. Using a two-dimensional
model, the scattered wavefield is calculated in the first Born approximation.
We test the correctness of the kernels by comparing an exact solution (constant
flow), a solution linearized in the flow, and the total integral of the kernel.
In practice, the linear approximation is acceptable for flows as large as about
400 m/s.Comment: 4 pages, 3 figures. Proceedings of SOHO18/GONG 2006/HELAS I. Beyond
the Spherical Sun: A new era of helio- and asteroseismology. Sheffield,
England. August, 200
Spatially resolved vertical vorticity in solar supergranulation using helioseismology and local correlation tracking
Flow vorticity is a fundamental property of turbulent convection in rotating
systems. Solar supergranules exhibit a preferred sense of rotation, which
depends on the hemisphere. This is due to the Coriolis force acting on the
diverging horizontal flows. We aim to spatially resolve the vertical flow
vorticity of the average supergranule at different latitudes, both for outflow
and inflow regions. To measure the vertical vorticity, we use two independent
techniques: time-distance helioseismology (TD) and local correlation tracking
of granules in intensity images (LCT) using data from the Helioseismic and
Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO). Both maps
are corrected for center-to-limb systematic errors. We find that 8-h TD and LCT
maps of vertical vorticity are highly correlated at large spatial scales.
Associated with the average supergranule outflow, we find tangential (vortical)
flows that reach about 10 m/s in the clockwise direction at 40{\deg} latitude.
In average inflow regions, the tangential flow reaches the same magnitude, but
in the anti-clockwise direction. These tangential velocities are much smaller
than the radial (diverging) flow component (300 m/s for the average outflow and
200 m/s for the average inflow). The results for TD and LCT as measured from
HMI are in excellent agreement for latitudes between 60{\deg} and 60{\deg}.
From HMI LCT, we measure the vorticity peak of the average supergranule to have
a full width at half maximum of about 13 Mm for outflows and 8 Mm for inflows.
This is larger than the spatial resolution of the LCT measurements (about 3
Mm). On the other hand, the vorticity peak in outflows is about half the value
measured at inflows (e.g. 4/(10^6 s) clockwise compared to 8/(10^6 s)
anti-clockwise at 40{\deg} latitude). Results from MDI/SOHO obtained in 2010
are biased compared to the HMI/SDO results for the same period.Comment: 12 pages, 13 figures (plus appendix), accepted for publication in A&
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
SDO/HMI survey of emerging active regions for helioseismology
Observations from the Solar Dynamics Observatory (SDO) have the potential for
allowing the helioseismic study of the formation of hundreds of active regions,
which would enable us to perform statistical analyses. Our goal is to collate a
uniform data set of emerging active regions observed by the SDO/HMI instrument
suitable for helioseismic analysis up to seven days before emergence. We
restricted the sample to active regions that were visible in the continuum and
emerged into quiet Sun largely avoiding pre-existing magnetic regions. As a
reference data set we paired a control region (CR), with the same latitude and
distance from central meridian, with each emerging active region (EAR). We call
this data set, which is currently comprised of 105 emerging active regions
observed between May 2010 and November 2012, the SDO Helioseismic Emerging
Active Region (SDO/HEAR) survey. To demonstrate the utility of a data set of a
large number of emerging active regions, we measure the relative east-west
velocity of the leading and trailing polarities from the line-of-sight
magnetogram maps during the first day after emergence. The latitudinally
averaged line-of-sight magnetic field of all the EARs shows that, on average,
the leading (trailing) polarity moves in a prograde (retrograde) direction with
a speed of 121 +/- 22 m/s (-70 +/- 13 m/s) relative to the Carrington rotation
rate in the first day. However, relative to the differential rotation of the
surface plasma, the east-west velocity is symmetric, with a mean of 95 +/- 13
m/s. The SDO/HEAR data set will not only be useful for helioseismic studies,
but will also be useful to study other features such as the surface magnetic
field evolution of a large sample of EARs.Comment: Accepted by Astronomy and Astrophysics, 11 figures, one longtable;
update corrects units in Figure
Sensitivity Kernels for Flows in Time-Distance Helioseismology: Extension to Spherical Geometry
We extend an existing Born approximation method for calculating the linear
sensitivity of helioseismic travel times to flows from Cartesian to spherical
geometry. This development is necessary for using the Born approximation for
inferring large-scale flows in the deep solar interior. In a first sanity
check, we compare two mode kernels from our spherical method and from an
existing Cartesian method. The horizontal and total integrals agree to within
0.3 %. As a second consistency test, we consider a uniformly rotating Sun and a
travel distance of 42 degrees. The analytical travel-time difference agrees
with the forward-modelled travel-time difference to within 2 %. In addition, we
evaluate the impact of different choices of filter functions on the kernels for
a meridional travel distance of 42 degrees. For all filters, the sensitivity is
found to be distributed over a large fraction of the convection zone. We show
that the kernels depend on the filter function employed in the data analysis
process. If modes of higher harmonic degree () are
permitted, a noisy pattern of a spatial scale corresponding to
appears near the surface. When mainly low-degree modes are used
(), the sensitivity is concentrated in the deepest regions and it
visually resembles a ray-path-like structure. Among the different low-degree
filters used, we find the kernel for phase-speed filtered measurements to be
best localized in depth.Comment: 17 pages, 5 figures, 2 tables, accepted for publication in ApJ. v2:
typo in arXiv author list correcte
Sectoral r modes and periodic RV variations of Sun-like stars
Radial velocity (RV) measurements are used to search for planets orbiting
late-type main-sequence stars and confirm the transiting planets. The most
advanced spectrometers are approaching a precision of cm/s that
implies the need to identify and correct for all possible sources of RV
oscillations intrinsic to the star down to this level and possibly beyond. The
recent discovery of global-scale equatorial Rossby waves in the Sun, also
called r modes, prompted us to investigate their possible signature in stellar
RV measurements. R modes are toroidal modes of oscillation whose restoring
force is the Coriolis force and propagate in the retrograde direction in a
frame that corotates with the star. The solar r modes with azimuthal orders were identified unambiguously because of their dispersion
relation and their long e-folding lifetimes of hundreds of days. Here we
simulate the RV oscillations produced by sectoral r modes with assuming a stellar rotation period of 25.54 days and a maximum amplitude of
the surface velocity of each mode of 2 m/s. This amplitude is representative of
the solar measurements, except for the mode which has not yet been
observed. Sectoral r modes with azimuthal orders and would produce RV
oscillations with amplitudes of 76.4 and 19.6 cm/s and periods of 19.16 and
10.22 days, respectively, for a star with an inclination of the rotation axis
. Therefore, they may produce rather sharp peaks in the Fourier
spectrum of the radial velocity time series that could lead to spurious
planetary detections. Sectoral r~modes may represent a source of confusion in
the case of slowly rotating inactive stars that are preferential targets for RV
planet search. The main limitation of the present investigation is the lack of
observational constraint on the amplitude of the mode on the Sun.Comment: 7 pages; 4 figures; 1 table; accepted to Astronomy & Astrophysic
Prospects for the Detection of the Deep Solar Meridional Circulation
We perform helioseismic holography to assess the noise in p-mode travel-time
shifts which would form the basis of inferences of large-scale flows throughout
the solar convection zone. We also derive the expected travel times from a
parameterized return (equatorward) flow component of the meridional circulation
at the base of the convection zone from forward models under the assumption of
the ray and Born approximations. From estimates of the signal-to-noise ratio
for measurements focused near the base of the convection zone, we conclude that
the helioseismic detection of the deep meridional flow including the return
component may not be possible using data spanning an interval less than a solar
cycle
Tomography of the Solar Interior
Solar oscillations consist of a rich spectrum of internal acoustic waves and
surface gravity waves, stochastically excited by turbulent convection. They
have been monitored almost continuously over the last ten years with
high-precision Doppler images of the solar surface. The purpose of
helioseismology is to retrieve information about the structure and the dynamics
of the solar interior from the frequencies, phases, and amplitudes of solar
waves. Methods of analysis are being developed to make three-dimensional images
of subsurface motions and temperature inhomogeneities in order to study
convective structures and regions of magnetic activity, like sunspots.Comment: Brief Revie
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