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Author name code: woodard
ADS astronomy entries on 2022-09-14
author:"Woodard, Martin"
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Title: Towards realistic estimates of solar global oscillation
mode-coupling measurement noise
Authors: Woodard, M. F.
2021MNRAS.505.3433W Altcode:
Time series of the medium-l spherical-harmonic decomposition of SOHO/MDI
Doppler images were used to investigate the noise of solar-oscillation
mode-coupling measurements and to reveal the coupling signatures of
global-scale Rossby-waves and magnetic activity. A theoretical model
of mode-coupling noise was developed starting from the assumption
that the Doppler oscillation signal obeys Gaussian statistics. The
measured coupling noise was found to agree with the model noise at
the level of 20 per cent. The noise of mode-coupling measurements
obtained from MDI data turns out to be considerably larger than that
of hypothetical, 'ideal' measurements, which could only be obtained
from observations with more coverage of the Sun's surface than current
instruments provide. The noise analysis was carried out for a simple
suboptimal mode-coupling estimation procedure which is described
in some detail. A more rigorous, maximum-likelihood, approach to
mode-coupling measurement, which generalizes a method currently used
to extract global oscillation mode information, is also described and
its relationship to the simple mode-coupling analysis is discussed.
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Title: Inferring Solar Differential Rotation through Normal-mode
Coupling Using Bayesian Statistics
Authors: Kashyap, Samarth G.; Das, Srijan Bharati; Hanasoge, Shravan
M.; Woodard, Martin F.; Tromp, Jeroen
2021ApJS..253...47K Altcode: 2021arXiv210108933K
Normal-mode helioseismic data analysis uses observed solar oscillation
spectra to infer perturbations in the solar interior due to global and
local-scale flows and structural asphericity. Differential rotation,
the dominant global-scale axisymmetric perturbation, has been tightly
constrained primarily using measurements of frequency splittings via
"a-coefficients." However, the frequency-splitting formalism invokes
the approximation that multiplets are isolated. This assumption is
inaccurate for modes at high angular degrees. Analyzing eigenfunction
corrections, which respect cross-coupling of modes across multiplets,
is a more accurate approach. However, applying standard inversion
techniques using these cross-spectral measurements yields a-coefficients
with a significantly wider spread than the well-constrained results from
frequency splittings. In this study, we apply Bayesian statistics to
infer a-coefficients due to differential rotation from cross-spectra
for both f-modes and p-modes. We demonstrate that this technique
works reasonably well for modes with angular degrees ℓ = 50-291. The
inferred a<SUB>3</SUB>-coefficients are found to be within 1 nHz of
the frequency-splitting values for ℓ > 200. We also show that
the technique fails at ℓ < 50 owing to the insensitivity of
the measurement to the perturbation. These results serve to further
establish mode-coupling as an important helioseismic technique with
which to infer internal structure and dynamics, both axisymmetric
(e.g., meridional circulation) and non-axisymmetric perturbations.
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Title: Sensitivity of helioseismic measurements of normal-mode
coupling to flows and sound-speed perturbations
Authors: Hanasoge, Shravan M.; Woodard, Martin; Antia, H. M.; Gizon,
Laurent; Sreenivasan, Katepalli R.
2017MNRAS.470.1404H Altcode: 2017arXiv170508204H
In this article, we derive and compute the sensitivity of measurements
of coupling between normal modes of oscillation in the Sun to underlying
flows. The theory is based on first-born perturbation theory, and the
analysis is carried out using the formalism described by Lavely &
Ritzwoller (1992). Albeit tedious, we detail the derivation and compute
the sensitivity of specific pairs of coupled normal modes to anomalies
in the interior. Indeed, these kernels are critical for the accurate
inference of convective flow amplitudes and large-scale circulations in
the solar interior. We resolve some inconsistencies in the derivation
of Lavely & Ritzwoller (1992) and reformulate the fluid-continuity
condition. We also derive and compute sound-speed kernels, paving the
way for inverting for thermal anomalies alongside flows.
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Title: Helioseismic Constraints on the Depth Dependence of Large-Scale
Solar Convection
Authors: Woodard, Martin F.
2017SPD....4811304W Altcode:
A recent helioseismic statistical waveform analysis of subsurface flow
based on a 720-day time series of SOHO/MDI Medium-l spherical-harmonic
coefficients has been extended to cover a greater range of
subphotospheric depths. The latest analysis provides estimates of
flow-dependent oscillation-mode coupling-strength coefficients
b(s,t;n,l) over the range l = 30 to 150 of mode degree (angular
wavenumber) for solar p-modes in the approximate frequency range 2
to 4 mHz. The range of penetration depths of this mode set covers
most of the solar convection zone. The most recent analysis measures
spherical harmonic (s,t) components of the flow velocity for odd s in
the angular wavenumber range 1 to 19 for t not much smaller than s at a
given s. The odd-s b(s,t;n,l) coefficients are interpreted as averages
over depth of the depth-dependent amplitude of one spherical-harmonic
(s,t) component of the toroidal part of the flow velocity field. The
depth-dependent weighting function defining the average velocity
is the fractional kinetic energy density in radius of modes of the
(n,l) multiplet. The b coefficients have been converted to estimates
of root velocity power as a function of l0 = nu0*l/nu(n,l), which is
a measure of mode penetration depth. (nu(n,l) is mode frequency and
nu0 is a reference frequency equal to 3 mHz.) A comparison of the
observational results with simple convection models will be presented.
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Title: Possible signature of solar oblateness in the Sun's oscillation
frequency splittings
Authors: Woodard, M. F.
2016AdSpR..58.1464W Altcode:
Departures from spherical symmetry split the frequencies of the Sun's
normal oscillation modes. In addition to the well-studied, dominant
splitting of the mode frequencies, due to the first-order advection
of internal wave motion, a number of second-order effects of rotation
on the frequency splittings, predominantly the solar oblateness,
are expected. Whereas the largest rotational frequency splittings
have an odd dependence on the azimuthal order, m, of the modes, the
second-order effects should have an even dependence. The biggest,
and thus far the only well-studied, even-m effect on splittings,
is due to the solar-cycle variations in magnetic activity near the
Sun's surface, which need to be modeled with some care to bring
out the signature of solar oblateness. A crude analysis of the even
mode-frequency splittings, obtained from approximately 15 years of
SOHO/MDI spherical-harmonic time series, was undertaken. To extract
the small even-m splittings of interest from the dominant, solar-cycle
effects, which have a strong mode-frequency dependence, the former
were assumed to depend only weakly on mode frequency and to have no
time dependence. Perhaps the most important finding of the study is
that the MDI data are capable of yielding statistically significant
estimates of solar oblateness. Indeed the oblateness estimates obtained
from the analysis presented here appear to be roughly consistent
with both theoretical expectations and with direct measurements of
the oblateness. There is also a hint of a pole-equator temperature
difference in the seismic measurements, at the level recently suggested
by Miesch and Hindman.
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Title: Evidence for large-scale subsurface convection in the Sun
Authors: Woodard, M. F.
2016MNRAS.460.3292W Altcode: 2016arXiv160506192W
A helioseismic statistical waveform analysis of subsurface flow was
performed on two 720-day time series of SOHO/Michelson Doppler Imager
medium-l spherical-harmonic coefficients. The time series coincide with
epochs of high and low solar activity. Time-dependent coupling-strength
coefficients b^t_s(n,l) of modes of the same radial order n and degree
l, but different azimuthal order m, were inferred from the waveform
analysis. These coefficients are sensitive to flows and general
aspherical structure. For odd values of s ≪ l, the coefficient
b^t_s(n,l) measures an average over depth of the amplitude of one
spherical-harmonic (s, t) component of the toroidal flow velocity
field. The depth-dependent weighting function defining the average
velocity is the fractional kinetic energy density in radius of modes of
the (n, l) multiplet. A mean-square (n, l)-dependent flow velocity was
inferred from the b-coefficients for s in the range 5 through 35 for
each n and l in the respective ranges 1 through 5 and 120 through 149
for the epochs of high and low activity. A further averaging, over l,
yielded a root-mean-square flow velocity as a function of n for each
epoch, which increases from about 20 m s<SUP>-1</SUP> at n = 1 to 35 m
s<SUP>-1</SUP> at n = 5. The inferred velocities are consistent with
(though perhaps do not demand) a cellular pattern of flow extending
over the vertical range of mode sensitivity, estimated to be about 4
per cent of the solar radius below the photosphere.
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Title: Helioseismic Evidence for Large-Scale Solar Subsurface
Turbulence
Authors: Woodard, Martin F.
2016SPD....47.0722W Altcode:
A statistical waveform analysis of subsurface flow was performed
on two 720-day time series of SOHO/MDI Medium-l spherical-harmonic
coefficients. The time series coincide with epochs of high and low solar
activity.Time-dependent coupling-strength coefficients b(s,t;n,l) of
modes of the same radial order n and degree l, but different azimuthal
order m, were inferred from the waveform analysis. These coefficients
are sensitive to flows and general aspherical structure. For odd values
of s ≪ l, the coefficient b(s,t;n,l) measures an average over depth of
the amplitude of one spherical-harmonic (s,t) component of the toroidal
flow velocity field. The depth-dependent weighting function defining
the average velocity is the fractional kinetic energy density in radius
of modes of the (n,l) multiplet. A mean-square (n,l)-dependent flow
velocity was inferred from the b-coefficients for s in the range 5
through 35 for each n and l in the respective ranges 1 through 5 and
120 through 149 for the epochs of high and low activity. A further
averaging, over l, yielded a root mean square flow velocity as a
function of n for each epoch, which average increases from about 20 m/s
at n=1 to 35 m/s at n=5. The inferred velocities are consistent with
(though perhaps do not demand) a cellular pattern of flow extending
over the vertical range of mode sensitivity, estimated to be a few
percent of the solar radius below the photosphere.
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Title: Detectability of Large-Scale Solar Subsurface Flows
Authors: Woodard, M.
2014SoPh..289.1085W Altcode:
The accuracy of helioseismic measurement is limited by the stochastic
nature of solar oscillations. In this article I use a Gaussian
statistical model of the global seismic wave field of the Sun to
investigate the noise limitations of direct-modeling analysis of
convection-zone-scale flows. The theoretical analysis of noise is based
on hypothetical data that cover the entire photosphere, including the
portions invisible from the Earth. Noise estimates are derived for
measurements of the flow-dependent couplings of global-oscillation
modes and for combinations of coupling measurements that isolate
vector-spherical-harmonic components of the flow velocity. For
current helioseismic observations, which sample only a fraction of
the photosphere, the inferred detection limits are best regarded as
optimistic limits. The flow-velocity fields considered in this work are
assumed to be decomposable into vector-spherical-harmonic functions
of degree less than five. The problem of measuring the general
velocity field is shown to be similar enough to the well-studied
problem of measuring differential rotation to permit rough estimates
of flow-detection thresholds to be gleaned from past helioseismic
analysis. I estimate that, with existing and anticipated helioseismic
datasets, large-scale flow-velocity amplitudes of a few tens of should
be detectable near the base of the convection zone.
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Title: Global-Oscillation Eigenfunction Measurements of Solar
Meridional Flow
Authors: Woodard, M.; Schou, J.; Birch, A. C.; Larson, T. P.
2013SoPh..287..129W Altcode: 2012SoPh..tmp..179W
We describe and apply a new helioseismic method for measuring solar
subsurface axisymmetric meridional and zonal flow. The method is
based on a theoretical model of the response of global-oscillation
eigenfunctions to the flow velocity and uses cross spectra of the
time-varying coefficients in the spherical-harmonic expansion of
the photospheric Doppler-velocity field. Eigenfunction changes
modify the leakage matrix, which describes the sensitivity of the
spherical-harmonic coefficients to the global-oscillation modes. The
form of the leakage matrix in turn affects the theoretically expected
spherical-harmonic cross spectra. Estimates of internal meridional and
zonal flow were obtained by fitting the theoretical flow-dependent cross
spectra to spherical-harmonic cross spectra computed from approximately
500 days of full-disk Dopplergrams from the Helioseismic and Magnetic
Imager (HMI) on the SDO spacecraft. The zonal-flow measurements,
parameterized in the form of "a" coefficients, substantially agree
with measurements obtained from conventional global-mode-frequency
analysis. The meridional-flow estimates, in the form of depth-weighted
averages of the flow velocity, are similar to estimates obtained from
earlier analyses, for oscillation modes that penetrate the outermost
one-third of the convection zone. For more deeply penetrating modes,
the inferred flow velocity increases significantly with penetration
depth, indicating the need for either a modification of the simple
conveyor-belt picture of meridional flow or improvement in the
cross-spectral model.
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Title: Using Distortion of Global Mode Eigenfunctions to Estimate
Large Scale Flows
Authors: Schou, J.; Woodard, M. F.; Baldner, C. S.; Larson, T. P.
2013enss.confE.103S Altcode:
The accurate measurement of large scale flows, such as differential
rotation and meridional flow, throughout the solar interior is important
for understanding the solar interior and the processes relevant for
the solar dynamo. Ordinarily normal modes would be expected to give
more accurate measurement of large scale flows than local helioseismic
techniques. Unfortunately, mode frequencies are not sensitive to the
meridional flow and so traditional methods do not work. Here we describe
our progress on using the distortion of the eigenfunctions to measure
flows. In particular on identifying the source of the large systematic
errors previously reported and determining the effect of light travel
time, center to limb phase variations and other physical effects.
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Title: Meridional Circulation From Normal Mode Analysis
Authors: Schou, Jesper; Woodard, M. F.; Larson, T. P.
2012AAS...22020505S Altcode:
We have recently been able to make significant progress in the
determining the solar meridional flow from the perturbations it causes
to the eigenfunctions of normal modes. In this poster we will describe
some of our recent progress and show that it will likely be possible to
determine the flow over a substantial part of the solar interior with
a precision sufficient <P />to address important questions. However,
we also see what appears to be significant systematic errors and will
describe our efforts at understanding those.
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Title: Measuring Meridional Flow Using Global Modes
Authors: Schou, J.; Woodard, M. F.; Birch, A. C.; Larson, T. P.
2011sdmi.confE..71S Altcode:
In the past the meridional flow has been determined near the photosphere
by direct observations and below the solar surface using local
helioseismic methods. To first order normal mode frequencies are not
sensitive to the meridional flow, and so they are not useful for this
purpose. However, the eigenfunctions are sensitive to the meridional
flow to first order. Here we describe our progress on a project to
measure the eigenfunction perturbations and infer the meridional flow
with depth.
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Title: Helioseismic Measurement of Large-Scale Solar Flows
Authors: Woodard, M. F.
2009ASPC..416...15W Altcode:
Large-scale flows in the deep convection zone, differential rotation
and meridional circulation in particular, are relatively accessible to
seismic probing and provide observational constraints on convection-zone
dynamics and structure. Flows and other aspherical perturbations
dynamically couple the Sun's normal oscillation modes. Mode coupling
produces signatures in power spectra of time series of coefficients in
the spherical harmonic decomposition of the photospheric velocity field,
the outstanding signature being the consequence of azimuthal-order (m)
dependence of the mode frequencies due to differential rotation. Mode
coupling also produces a signature in cross spectra of distinct
spherical-harmonic time series. In this paper I discuss the problem of
using helioseismic cross-spectra to map large-scale flow in the Sun and
prospects for measuring deep meridional flow. Some preliminary estimates
of meridional and zonal flow from MDI and GONG spherical-harmonic time
series are presented.
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Title: Seismic Detection of Solar Mesogranular-Scale Flow
Authors: Woodard, M. F.
2009ApJ...706L..62W Altcode:
Helioseismic correlation data computed from the Solar and Heliospheric
Observatory/Michelson Doppler Imager high-resolution Doppler images
were inverted for solar flows of horizontal scale between 5 and 45
Mm. The photospheric Doppler velocity inferred from the inversions was
compared with the original Doppler images at each scale. For horizontal
scales greater than about 15 Mm, the seismically inferred and directly
observed flow maps look similar, as has been seen in studies of
supergranular flow. At smaller scales, the similarity disappears, but
regression analysis reveals significant correlation between the maps,
demonstrating that solar p- and f-mode oscillations contain useful
information about these flows. The slope of the computed regression
plots is close to unity, indicating that mesogranular-scale flows
extend at least a megameter below the photosphere.
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Title: Large Scale Flows From Eigenfunction Fitting
Authors: Schou, Jesper; Woodard, M. F.; Birch, A. C.
2009SPD....40.0705S Altcode:
It is well known that the eigenfunctions, as well as the
eigenfrequencies, of normal modes are perturbed by flows and other
asphericities. In the case of meridional flows, it is known that
while the perturbations to the frequencies are second order, the
eigenfunctions are perturbed at first order in the strength of the
meridional flow. This leads to the question of whether one might be
able to measure meridional flows using the observed eigenfunction
perturbations. Here we discuss how well we expect to be able to do
this and show some preliminary analysis of MDI data.
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Title: Helioseismic Detection of Mesogranular Flow
Authors: Woodard, Martin F.
2009SPD....40.0701W Altcode:
Helioseismic correlation data computed from a sequence of SOHO/MDI high
resolution Doppler images were inverted for subphotospheric flow on
horizontal scales ranging from 45 Mm down to 5 Mm. The measurements are
sensitive to flows over a depth range of roughly one Mm. The resulting
seismically-reconstructed and directly-observed photospheric Doppler
velocity maps are similar for horizontal scales less than about 15 Mm,
as was seen in previous studies of supergranulation-scale flow. <P
/>For smaller scales it becomes difficult to see directly-observed
Doppler features in the seismic maps. But regression analysis of
the maps does reveal a component of subsurface flow which correlates
with the photospheric flow. The ratio of the seismically-inferred to
directly-observed Doppler velocity is typically 0.7 to 0.8, indicating a
slight decrease in the flow velocity with depth in the first megameter
below the photosphere. This finding is consistent with the results of
the recent convection simulations of Benson, Stein, and Nordlund. <P
/>This work is supported by NASA contract NNH07CD06C.
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Title: Probing Supergranular Flow in the Solar Interior
Authors: Woodard, M. F.
2007ApJ...668.1189W Altcode:
Helioseismic correlation data computed from SOHO MDI high-resolution
Doppler images were inverted for solar subsurface supergranular flow,
using an improved forward model. The statistical error of the inversion
is set by the stochastic nature of solar wave excitation, which limits
the detection of supergranular flow with these data to the first 4 or
5 Mm below the photosphere. The photospheric supergranulation pattern,
averaged over the ~34 hour duration of the data set, is found to persist
over the detectable depth range. Contrary to some recent findings,
there is no indication of a flow reversal at a depth between 5 and 6
Mm. However, since the depth of the putative reversal is at the edge
of the detectable range for these data, the discrepancy is probably
not significant.
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Title: Inferring subsurface supergranular flow directly from
helioseismic correlation data
Authors: Woodard, M. F.
2006ESASP.624E..51W Altcode: 2006soho...18E..51W
No abstract at ADS
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Title: The Seismic Correlation Signature of Moderate-Scale Flow in
the Sun
Authors: Woodard, M. F.
2006ApJ...649.1140W Altcode:
Flows in the solar convection zone introduce correlation between
distinct horizontal-wavevector and frequency components of wave
motion in the Sun. We derive expressions for the linear sensitivity of
helioseismic correlation data to subphotospheric supergranular-scale
flow, for use in helioseismic inversions. The sensitivity calculations
are based on a model of randomly excited p- and f-mode oscillations
in a plane-parallel solar envelope with flows. Woodard described
a simple inversion of helioseismic correlation data for depth- and
time-independent supergranular flow. The sensitivity calculations
presented in this paper generalize previous calculations to the
case of a flow velocity that depends on depth and varies slowly with
time. We describe a method of estimating the data sensitivity kernel
from helioseismic observations. The observed and theoretical kernels
agree to within ~20%.
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Title: Meridional flow measurements with statistical waveform analysis
Authors: Mitra-Kraev, U.; Thompson, M. J.; Woodard, M. F.
2006ESASP.624E..57M Altcode: 2006soho...18E..57M
No abstract at ADS
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Title: Cross-Spectral Signatures in Global Helioseismology Data of
Large-Scale Flow in the Sun
Authors: Woodard, M. F.
2005AGUSMSP11B..12W Altcode:
Large-scale flows in the Sun's interior have been studied
using a variety of helioseismic techniques, including spectral
analysis of spherical harmonic time series of photospheric velocity
oscillations. Detailed maps of differential rotation have been obtained
from measurements of the frequencies of resonance peaks in the power
spectra. Flows can also affect power spectra in subtler ways, e.g.,
by their influence on the widths of resonance peaks. In addition to
their spectral signature, flows and other aspherical perturbations
also produce cross-spectral signatures, via the mode-coupling effect
of a flow. Cross power spectra of time series of coefficients in the
spherical-harmonic decomposition of SOHO/MDI medium-ℓ velocity
images have been computed and are being compared with theoretical
predictions. The results of a preliminary comparison of observed and
theoretically predicted cross spectra for differential rotation and
meridional circulation will be presented. A program to systematically
map large-scale solar internal flow using cross-spectral data will be
described. The author acknowledges useful discussions with colleagues,
especially Doug Braun, Yuhong Fan, Aaron Birch, and Jesper Schou. He is
also grateful to Jesper Schou for help in acquiring MDI data products
and to NASA for support under contract NAS5-3114. The Solar Oscillations
Investigation- Michelson Doppler Imager experiment on SOHO is supported
by NASA contract NAG5-3077 at Stanford University. SOHO is a project
of international cooperation between ESA and NASA.
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Title: Depth Dependence of Solar Supergranular Flow
Authors: Woodard, M. F.
2005AGUSMSP11C..04W Altcode:
Helioseismic inversions for subsurface supergranular motion have been
performed using spectral-domain covariance estimates of the surface
wave field as input data. The surface wave measurements used in this
study were obtained from a 34-hr sequence of SOHO/MDI high-resolution
Doppler images covering an approximately 210 Mm x 210 Mm corotating
patch of the photosphere near disk center. The utilized signal, derived
by filtering the Doppler sequence, is dominated by p- and f-modes in
the frequency range 2.5 - 5.5 mHz and the range 600 - 1800 of angular
degree. The helioseismic forward model used for the inversions is
based on a wave equation which includes a stochastic driving term and
a damping term. The effect of subsurface flows on wave propagation is
treated in the single-scattering Born approximation. Several approaches
to inverting helioseismic covariance data were used, including the
method of optimally-localized averages. The inversions provide evidence
for supergranular-scale motion to a detection depth of 6 Mm beneath the
photosphere. The measured correlation coefficient between the surface
motion and the motion at depth is observed to decrease with depth,
but, contrary to some previous findings, does not change sign over
the detectable depth range. The author is indebted to Yuhong Fan and
Aaron Birch for extensive discussions about the theoretical aspects
of wave propagation in flows and to the former for vital solar model
outputs. The study was supported by NSF grant ATM-0223127.
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Title: Origin of irradiance variations from disk photometer data
Authors: Woodard, Martin F.; Libbrecht, Ken G.
2003ESASP.517..117W Altcode: 2003soho...12..117W
No abstract at ADS
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Title: Spatial and temporal variations in the solar brightness
Authors: Woodard, M. F.; Libbrecht, K. G.
2003SoPh..212...51W Altcode:
We have investigated long-term variations of solar brightness as
a function of both time and solar latitude using eight years of
ground-based photometric data in conjunction with space-based irradiance
data. In particular, we have examined whether the combination of sunspot
brightness deficits and facular brightness excesses is sufficient to
explain the solar cycle irradiance variations. After correcting for
the contribution from sunspots, we find that the irradiance data can
be adequately explained by a model in which the remaining brightness
variations are due entirely to facular contributions confined to
the magnetically active latitudes. Thus we find no support for the
hypothesis that there are convectively driven hot bands in the active
latitudes, and our data show brightness variations that are well
described by a facular contrast function.
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Title: Inferring Inhomogeneous Structure in the Sun Directly from
Correlations in the Seismic Signal
Authors: Woodard, M. F.
2002AAS...200.8902W Altcode: 2002BAAS...34..791W
A program for probing inhomogeneous subsurface structure in the Sun
based on the direct modeling of correlations in the seismic signal
will be outlined and some preliminary results presented. The method
has been applied , for instance, to the detection of subsurface
supergranular-scale flow using helioseismology datasets from the
Michelson Doppler Interferometer on the SOHO satellite. Strategies
for studying flow fields on both larger and smaller size and time
scales will be discussed. This effort is supported by NASA under
grant NAG5-8485.
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Title: Seismic Investigation of Solar Convection
Authors: Woodard, Martin
2002smra.progE..26W Altcode:
No abstract at ADS
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Title: Solar Subsurface Flow Inferred Directly from
Frequency-Wavenumber Correlations in the Seismic Velocity Field
Authors: Woodard, M. F.
2002ApJ...565..634W Altcode:
We describe a general strategy for inverting helioseismic data
for laterally inhomogeneous (aspherical) structure, in which the
physical state of the solar interior is compared directly with
inhomogeneity-induced correlations in the observable seismic wave
field. The method was used to invert for subsurface supergranular-scale
flow using Solar and Heliospheric Observatory Michelson Doppler
Imager high spatial resolution Doppler images. Although many
approximations were made in carrying out the inversion, general
agreement (a correlation coefficient of 0.68) was found between the
Doppler component of the seismically inferred flow in the photosphere
and the directly observed surface Doppler signal.
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Title: Evolution of the sun's near-surface asphericities over the
activity cycle
Authors: Goode, P. R.; Didkovsky, L. V.; Libbrecht, K. G.; Woodard,
M. F.
2002AdSpR..29.1889G Altcode:
Solar oscillations provide the most accurate measures of cycle dependent
changes in the sun, and the Solar and Heliospheric Observatory/Michelson
Doppler Imager (MDI) data are the most precise of all. They give us
the opportunity to address the real challenge — connecting the MDI
seismic measures to observed characteristics of the dynamic sun. From
inversions of the evolving MDI data, one expects to determine the nature
of the evolution, through the solar cycle, of the layers just beneath
the sun's surface. Such inversions require one to guess the form of
the causal perturbation — usually beginning with asking whether
it is thermal or magnetic. Matters here are complicated because the
inversion kernels for these two are quite similar, which means that we
don't have much chance of disentangling them by inversion. However,
since the perturbation lies very close to the solar surface, one can
use synoptic data as an outer boundary condition to fix the choice. It
turns out that magnetic and thermal synoptic signals are also quite
similar. Thus, the most precise measure of the surface is required. We
argue that the most precise synoptic data come from the Big Bear
Solar Observatory (BBSO) Solar Disk Photometer (SDP). A preliminary
analysis of these data implies a magnetic origin of the cycle-dependent
sub-surface perturbation. However, we still need to do a more careful
removal of the facular signal to determine the true thermal signal.
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Title: Energy Distribution of Solar Oscillation Modes Inferred from
Space-Based Measurements
Authors: Woodard, M. F.; Korzennik, S. G.; Rabello-Soares, C.; Kumar,
P.; Tarbell, T. D.; Acton, S.
2001AGUSM..SP21C05W Altcode:
We have measured the energy distribution of solar p- and f-mode
oscillations of angular degree and temporal frequency in the range
100<l<800 and 2<ν (mHz)<4 using helioseismology data from
the SOI/MDI instrument on the SOHO satellite. At temporal frequency ν
≈ 3 mHz, the surface velocity power per oscillation mode increases
slightly with angular degree between l = 100 and l=200, but decreases
rather steeply with l above l=200, in approximate agreement with
earlier findings from ground-based measurements. From this we infer
that the time-averaged energy per mode, which is theoretically related
to the modal surface velocity power, decreases steeply with l at fixed
frequency, over the entire observed l range. Specifically, at ν =3.1
mHz the energy per mode drops by a factor of ≈ 10 between l=150 and
l=650, a circumstance not quantitatively understood at present. This
research was supported by NASA and Stanford University.
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Title: Energy Distribution of Solar Oscillation Modes Inferred from
Space-based Measurements
Authors: Woodard, M. F.; Korzennik, S. G.; Rabello-Soares, M. C.;
Kumar, P.; Tarbell, T. D.; Acton, S.
2001ApJ...548L.103W Altcode:
We have measured the energy distribution of solar p- and f-mode
oscillations of angular degree and temporal frequency in the range
100<l<800 and 2<ν(mHz)<4 using helioseismology data
from the Solar Oscillations Investigation-Michelson Doppler Imager
instrument on the Solar and Heliospheric Observatory satellite. At
temporal frequency ν~3 mHz, the surface velocity power per oscillation
mode increases slightly with angular degree between l=100 and l=200 but
decreases rather steeply with l above l=200, in approximate agreement
with earlier findings from ground-based measurements. From this we
infer that the time-averaged energy per mode, which is theoretically
related to the modal surface velocity power, decreases steeply with l,
at fixed frequency, over the entire observed l-range. Specifically, at
ν=3.1 mHz, the energy per mode drops by a factor of ~10 between l=150
and l=650, a circumstance not quantitatively understood at present.
---------------------------------------------------------
Title: Theoretical Signature of Solar Meridional Flow in Global
Seismic Data
Authors: Woodard, Martin F.
2000SoPh..197...11W Altcode:
Approximate expressions are derived for the perturbations in solar p-
and f-mode oscillation eigenfunctions, due to large-scale, meridional
flows which are symmetric about the equator. The essential signature
of the perturbed eigenfunctions in global helioseismic data is derived
and the prospects for detecting meridional flow using global seismic
techniques are discussed.
---------------------------------------------------------
Title: Photometric measurements of the solar disk at BBSO.
Authors: Woodard, M. F.; Libbrecht, K. G.
2000BAAS...32..803W Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Photometric Measurements of the Solar Disk at BBSO
Authors: Woodard, M. F.; Libbrecht, K. G.
2000SPD....31.0112W Altcode:
Precise photometric measurements of the Sun have been obtained with the
BBSO Solar Disk Photometer (SDP) since 1993. We describe our program
to characterize sunspot, facular, and non-facular contributions to
the spatial and temporal variations in solar irradiance using these
data. This work is supported by NSF and NASA.
---------------------------------------------------------
Title: Solar Differential Rotation Derived from H-alpha Full Disk
Images by Means of Local Correlation Tracking
Authors: Woodard, M. F.; Denker, C.; Strous, L. H.; BBSO Collaboration;
LMSAL Collaboration
1999AAS...19410007W Altcode: 1999BAAS...31..997W
We present the application of Local Correlation Tracking (LCT)
techniques to time series of contrast-enhanced H-alpha full disk images
taken as part of the synoptic observing program at Big Bear Solar
Observatory (BBS0) during the summer of 1998. A typical set of daily
H-alpha full disk images consists of 600 to 800 individual frames,
taken 30 to 60 s apart, with a 2k x 2k pixel Kodak 4.2 MegaPlus CCD
camera at BBSO's Singer telescope. For each pair of successive images,
we compute displacement vectors over a 64 x 64 element cartesian
grid covering the solar disk. The resulting daily-averaged flow maps
show predominantly solar differential rotation and proper motions in
active regions. We remap the flow maps to heliographic coordinates and
determine a Legendre polynomial expansion of the daily differential
rotation profile. We present preliminary findings regarding differential
rotation based on different types of features seen in H-alpha, such as
quiet-sun fibrils, plages, and dark filaments. We discuss the relation
of our differential rotation profiles to profiles derived by other
methods and address the question of time variability. The work at
BBSO is supported by ONR under grant N00014-97-1-1037, by NSF under
grant ATM 97-14796, and by NASA under grant NAG 5-4919. Louis Strous
is supported by NASA NAG5-3077 to Stanford University.
---------------------------------------------------------
Title: Evidence for non-potential magnetic fields in the quiet Sun
Authors: Woodard, M. F.; Chae, Jongchul
1999SoPh..184..239W Altcode:
A comparison of BBSO Hα centerline filtergrams and videomagnetograms
was made to investigate the existence of non- potential magnetic fields
in the quiet Sun near magnetic network. We use the fibril structure
in the Hα images as a proxy for the horizontal chromospheric magnetic
field which we compare with the horizontal field obtained by potential
extrapolation of the observed, line-of-sight photospheric field. The
quiet-Sun field was found to be consistently and significantly
non-potential in each of the three fields of view studied. A
transient extreme ultraviolet (EUV) brightening, known as a blinker,
occurred during the observations of a region where the field is highly
non-potential, suggesting a connection between magnetic reconnection
and non-potentiality.
---------------------------------------------------------
Title: Effect of Subsurface Inhomogeneities on the Statistics of
Solar Oscillation Power Spectra
Authors: Woodard, M. F.
1998SoPh..180...19W Altcode:
We characterize the statistical properties of the frequency-wave number
periodogram of randomly-driven waves in a hypothetical, one-dimensional,
spatially inhomogeneous, stationary medium. The derived properties are
used to formulate a conceptually simple test of solar oscillation power
spectra to estimate the separate contributions of true dissipation
and inhomogeneous structure to the linewidths of high-degree p- and
f-mode oscillations.
---------------------------------------------------------
Title: Spatial Dependence of Solar-Cycle Changes in the Sun's
Luminosity
Authors: Taylor, S. F.; Varsik, J. R.; Woodard, M. F.; Libbrecht, K. G.
1998SoPh..178....1T Altcode:
We report observations of the large-scale spatial dependence of the
Sun's luminosity variations over the period 1993-1995. The measurements
were made using a new scanning disk solar photometer at Big Bear Solar
Observatory, specially designed to measure large-scale brightness
variations at the 10<SUP>−4</SUP> level. Since the level of solar
activity was very low for the entire observation period, the data
show little solar cycle variation. However, the residual brightness
signal ΔI/I (after subtracting the mean, first, and second harmonics)
does show a strong dependence on heliocentric angle, peaking near the
limb. This is as one would expect if the residual brightness signal
(including the excess brightness coming from the active latitudes)
were primarily facular in origin. Additional data over the next few
years, covering the period from solar minimum to maximum, should
unambiguously reveal the large-scale spatial structure of the solar
cycle luminosity variations.
---------------------------------------------------------
Title: Implications of Localized, Acoustic Absorption for
Heliotomographic Analysis of Sunspots
Authors: Woodard, M. F.
1997ApJ...485..890W Altcode:
Acoustic tomography is emerging as an important tool for mapping the
three-dimensional structure of the Sun. Widely used in seismic studies
of the Earth, tomography is being applied to probe the structure of
magnetically active regions (e.g., sunspots), large-scale convective
motions, and the structure of the solar atmosphere. By interpreting
solar tomographic data by analogy with terrestrial tomographic data,
namely in terms of acoustic travel times, Duvall et al. (1996)
argue that strong downflows of matter are present beneath sunspots,
a conclusion that lends support to the idea that convective downdrafts
play a role in forming and maintaining sunspots. <P />Helioseismic
waves are thought to be generated continuously, in a turbulent
layer beneath the solar photosphere. This circumstance and the fact
that sunspots absorb acoustic energy make heliotomographic data more
difficult to interpret than their terrestrial counterpart. Therefore,
the seismic evidence for strong downflows below sunspots should be
viewed with skepticism. <P />We perform a theoretical analysis of
waves in a simple absorbing medium, which explicitly deals with both
the generation and propagation of waves. The results of the analysis
suggest that localized acoustic absorption can qualitatively mimic the
effect of a travel time perturbation. However, absorption (by itself,
or in combination with flows) appears to be incapable of quantitatively
reproducing the sunspot observations, indicating the operation of some
as yet unidentified mechanism.
---------------------------------------------------------
Title: Distributiong Flight Dynamics Products via the World-Wide Web
Authors: Woodard, M.; Matusow, D.
1996ESASP.394.1382W Altcode: 1996smog.conf.1382W
No abstract at ADS
---------------------------------------------------------
Title: Doppler Acoustic Diagnostics of Subsurface Solar Magnetic
Structure
Authors: Lindsey, C.; Braun, D. C.; Jefferies, S. M.; Woodard, M. F.;
Fan, Y.; Gu, Y.; Redfield, S.
1996ApJ...470..636L Altcode:
We used the Bartol-NSO-NASA South Pole helioseismic observations of 1991
January to probe the subsurface structure of active regions to depths
of ∼15,000 km. The helioseismic signature we particularly examine is
intended to register acoustic Doppler effects caused by horizontal flows
associated with the active region. We propose to show that the Doppler
acoustic signature of horizontal flows is particularly well suited
for deep subsurface diagnostics in terms of vertical discrimination
of the structure. This study is based primarily on observations of
NOAA Active Regions 6431, 6432, 6440, and 6442 between 1991 January
1 and January 8. We interpret the acoustic signatures we find in
terms of a general outflow of the solar medium surrounding the active
region. The acoustic signatures are strongly dependent on wavenumber,
which suggests an outflow that is quite weak near the surface, the upper
4000 km of the subphotosphere, but which increases strongly with depth
to velocities of several hundred meters per second at 15,000 km. This
depth profile evolves rapidly as the active region matures. Young
active regions show a strong outflow signature for waves that explore
depths between 4000 and 8000 km. As the active region matures, the
outflow vacates these intermediate layers and submerges to depths
mostly below 8000 km. <P />We examine the location of AR 6442 for a
possible preemergence signature. We also show evidence for extended,
relatively superficial flows in the quiet Sun between the active region
bands directed roughly into the active region bands.
---------------------------------------------------------
Title: Advances in Helioseismology
Authors: Libbrecht, K. G.; Woodard, M. F.
1994snft.book..428L Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Observations of Time Variation in the Sun's Rotation
Authors: Woodard, M. F.; Libbrecht, K. G.
1993Sci...260.1778W Altcode:
Observations of solar p-mode frequency splittings obtained at Big
Bear Solar Observatory in 1986 and during 1988-90 reveal small (~1
percent) changes in the sun's subsurface angular velocity with solar
cycle. An asymptotic inversion of the splitting data yields the latitude
dependence of the rotation rate and shows that the largest changes in
the angular velocity, ≈4 nanohertz, occurred between 1986 and the
later years, at high (≈60^circ) solar latitudes. Earlier helioseismic
observations suggest that solar cycle changes in the ratio of magnetic
to turbulent pressure in the solar convection zone are large enough to
account for the magnitude of the observed angular velocity variations
but a detailed model of the phenomenon does not exist.
---------------------------------------------------------
Title: Seismic evidence of modulation of the structure and angular
velocity of the Sun associated with the solar cycle
Authors: Gough, D. O.; Kosovichev, A. G.; Sekii, T.; Libbrecht, K. G.;
Woodard, M. F.
1993ASPC...40...93G Altcode: 1993IAUCo.137...93G; 1993ist..proc...93G
No abstract at ADS
---------------------------------------------------------
Title: The Form of the Angular Velocity in the Solar Convection Zone
Authors: Gough, D. O.; Kosovichev, A. G.; Sekii, T.; Libbrecht, K. G.;
Woodard, M. F.
1993ASPC...42..213G Altcode: 1993gong.conf..213G
No abstract at ADS
---------------------------------------------------------
Title: Solar Activity and Oscillation Frequency Splittings
Authors: Woodard, M. F.; Libbrecht, K. G.
1993ApJ...402L..77W Altcode:
Solar p-mode frequency splittings, parameterized by the coefficients
through order N = 12 of a Legendre polynomial expansion of the mode
frequencies as a function of m/L, were obtained from an analysis
of helioseismology data taken at Big Bear Solar Observatory during
the 4 years 1986 and 1988-1990 (approximately solar minimum to
maximum). Inversion of the even-index splitting coefficients confirms
that there is a significant contribution to the frequency splittings
originating near the solar poles. The strength of the polar contribution
is anti correlated with the overall level or solar activity in the
active latitudes, suggesting a relation to polar faculae. From an
analysis of the odd-index splitting coefficients we infer an upper limit
to changes in the solar equatorial near-surface rotatinal velocity of
less than 1.9 m/s (3 sigma limit) between solar minimum and maximum.
---------------------------------------------------------
Title: Advances in Helioseismology
Authors: Libbrecht, K. G.; Woodard, M. F.
1991Sci...253..152L Altcode:
Globally coherent oscillation modes were discovered in the sun about
a decade ago, providing a unique seismological probe of the solar
interior. Current observations detect modes that are phase-coherent for
up to 1 year, with surface velocity amplitudes as low as 2 millimeters
per second, and thousands of mode frequencies have been measured
to accuracies as-high as 1 part in 10^5. This article discusses the
properties of these oscillation modes and the ways in which they are
adding to our understanding of the structure and dynamics of the sun.
---------------------------------------------------------
Title: Is There an Acoustic Resonance in the Solar Chromosphere?
Authors: Woodard, M. F.; Libbrecht, K. G.
1991ApJ...374L..61W Altcode:
By comparing helioseismology data from 1986, 1988, and 1989, it was
found that the frequecy dependence of the frequency perturbation
of solar p-modes caused by solar activity drops abruptly for modes
of frequency above approximately 3.9 mHz. The drop in the frequency
dependence of the frequency shift may result from solar cycle changes
in the chromosphere, provided that the chromosphere acts as a cavity
in which p-modes are trapped (Goldreich et al.). No evidence is found
in the temporal power spectrum of a time series of narrow-band Ca II
K-line filtergrams of a resonance which would reveal the existence
of a chromospheric cavity. This circumstance constrains the possible
physical explanations of the frequency shifts.
---------------------------------------------------------
Title: Short-Term Changes in Solar Oscillation Frequencies and
Solar Activity
Authors: Woodard, M. F.; Kuhn, J. R.; Murray, N.; Libbrecht, K. G.
1991ApJ...373L..81W Altcode:
It is shown that the frequencies of solar rho-mode oscillations
change significantly over periods as short as one month. These changes
correlate significantly with variations in the strength of surface solar
activity as measured by the average, over the sun's visible surface,
of the magnitude of the line-of-sight magnetic field component from
magnetograms. The frequency and mean magnetic variations are found to
obey a linear relationship. It is seen that the mean frequency shift at
any time depends on the history of solar activity over an interval of,
at most, several months prior to the measurement and conclude that the
dominant mechanism of the frequency shift is correlated with surface
magnetic activity.
---------------------------------------------------------
Title: Frequencies of Solar Oscillations
Authors: Libbrecht, K. G.; Woodard, M. F.; Kaufman, J. M.
1990ApJS...74.1129L Altcode:
Solar oscillations have been observed at three different spatial scales
at Big Bear Solar Observatory during 1986-1987 and, using three data
sets, a new and more accurate table of solar oscillation frequencies
has been compiled. The oscillations, which are presented as functions
of radial order n and spherical harmonic degree l, are averages over
azimuthal order and therefore approximate the normal mode frequencies
of a nonrotating, spherically symmetric sun, near solar minimum. The
table contains frequencies for most of the solar p and f modes with l
between 0 and 1860, n between 0 and 26, and oscillation mode frequencies
between 1.0 and 5.3.
---------------------------------------------------------
Title: Solar-cycle effects on solar oscillation frequencies
Authors: Libbrecht, K. G.; Woodard, M. F.
1990Natur.345..779L Altcode:
Measurements of solar oscillations taken in 1986 and 1988 show
systematic changes in the Sun's acoustic-mode frequencies of the order
of 1 part in 10,000. These data reveal that the frequency shifts are
the result of latitude-dependent changes in the structure of the Sun
which are correlated with the Sun's magnetic-activity cycle.
---------------------------------------------------------
Title: Depth and Latitude Dependence of the Solar Internal Angular
Velocity
Authors: Rhodes, Edward J., Jr.; Cacciani, Alessandro; Korzennik,
Sylvain; Tomczyk, Steven; Ulrich, Roger K.; Woodard, Martin F.
1990ApJ...351..687R Altcode:
One of the design goals for the dedicated helioseismology observing
state located at Mount Wilson Observatory was the measurement of the
internal solar rotation using solar p-mode oscillations. In this paper,
the first p-mode splittings obtained from Mount Wilson are reported
and compared with those from several previously published studies. It
is demonstrated that the present splittings agree quite well with
composite frequency splittings obtained from the comparisons. The
splittings suggest that the angular velocity in the solar equatorial
plane is a function of depth below the photosphere. The latitudinal
differential rotation pattern visible at the surface appears to persist
at least throughout the solar convection zone.
---------------------------------------------------------
Title: Observations of Solar Cycle Variations in Solar p_Mode
Frequencies and Splittings
Authors: Libbrecht, K. G.; Woodard, M. F.
1990LNP...367..145L Altcode: 1990psss.conf..145L
We discuss here two sets of helioseismology data acquired at Big Bear
Solar Observatory during the summers of 1986 and 1988. Each data
set consists of roughly 60,000 fulldisk Doppler images of the sun,
accumulated over a four-month time span. These data clearly show
that solar p-mode frequencies change with time, and that the measured
frequency shifts v = v 88 - v 86 depend strongly on frequency and only
weakly on for 5 60. The frequency dependence is well described by v ∞
M-1(v), where M(v) is the mode mass for low-ℓ modes. Such a frequency
dependence is expected if the effective sound speed perturbation is
located predominantly near the solar surface. It should be possible to
invert the frequency shift measurements to determine some aspects of the
structure of solar activity as a function of depth. The data also show
that the even-index splitting coefficients depend strongly on frequency,
again being well described by α2j (v) ∞ M-1(v). This functional
form is expected if the sound speed perturbation responsible for Δv is
localized in solar latitude. Latitude inversions of the time-dependent
splitting and Δv measurements show that the perturbation is strongest
in the active latitudes, but includes a weak polar component.
---------------------------------------------------------
Title: Distortion of High-Degree Solar p-Mode Eigenfunctions by
Latitudinal Differential Rotation
Authors: Woodard, Martin F.
1989ApJ...347.1176W Altcode:
The eigenfunctions of nonradial oscillation of the sun depart from
their customarily assumed spherical harmonic form as a result
of solar rotation. This paper treats the effect on oscillation
eigenfunctions of slow, axisymmetric differential rotation which
is also mirror symmetric across the solar equatorial plane. A given
oscillation eigenfunction, perturbed by rotation, can be expressed
as a superposition of eigenfunctions of a (hypothetical) nonrotating
state of the sun. The assumption of axialsymmetry implies that each
of the superposed functions has the same azimuthal order, m, while
mirror symmetry dictates that the values of l, the spherical harmonic
degree, involved in the superposition be either all odd or all even. The
treatment here is further specialized to the case of high-degree p- and
f-mode oscillations, on which the effect of the Coriolis acceleration
is small. It is shown that, by ignoring the Coriolis effect and making
other sensible approximations, an analytic expression can be obtained
for the rotationally distorted mode eigenfunctions, which is expected
to be a good approximation for typical solar oscillations of degree
l greater than 100. The effect of the calculated mode distortion on
the measurement of solar rotation is explored.
---------------------------------------------------------
Title: On the measurement of solar rotation using high-degree p-mode
oscillations.
Authors: Woodard, Martin F.; Libbrecht, Ken G.
1988ESASP.286...67W Altcode: 1988ssls.rept...67W
The authors describe the progress made and some of the difficulties
encountered in measuring the solar rotation rate with p-modes
of degree 100 ⪉ l ⪉ 400, using a set of high-resolution solar
images taken at Big Bear Solar Observatory. The main conclusion drawn
from an analysis of one day of data is that the equatorial angular
velocity is essentially equal to the observed surface rate over the
radius range 0.87 ⪉ r/R ⪉ 0.99 to within a few percent. Because
of likely systematic errors at the 1% level these data do not allow
us to distinguish between a surrface rotation rate equal to that
measured using magnetic tracers and that based on the Doppler shift
of photospheric spectral lines.
---------------------------------------------------------
Title: Radial and latitudinal gradients in the solar internal
angular velocity.
Authors: Rhodes, Edward J., Jr.; Cacciani, Alessandro; Korzennik,
Sylvain G.; Tomczyk, Steven; Ulrich, Roger K.; Woodard, Martin F.
1988ESASP.286...73R Altcode: 1988ssls.rept...73R
The authors recently presented the results of an analysis of the
frequency splittings of intermediate-degree (3 < degree ≤ 170)
p-mode oscillations which were obtained from a 16-day subset of our 1984
Mt. Wilson 60-foot tower observations. These results showed evidence
for both radial and latitudinal gradients in the solar internal
angular velocity. In particular, the results indicated that, from
0.6 R<SUB><SUB>sun</SUB></SUB> to 0.95 R<SUB><SUB>sun</SUB></SUB>,
the solar internal angular velocity increases systematically from
440 to 463 nHz, corresponding to a positive radial gradient of ≍66
nHz/R<SUB><SUB>sun</SUB></SUB> for that portion of the solar interior. A
previous analysis indicated that the latitudinal differential rotation
gradient which is seen at the solar surface persists throughout
the convection zone, although there was some indication that the
differential rotation might disappear entirely below the base of the
convection zone. Here the authors extend their previous analysis to
include comparisons with additional observational studies and they
also present comparisons between our earlier results and the results
of additional inversions of several of the observational datasets. All
of these comparisons reinforce the previous conclusions regarding
the existence of radial and latitudinal gradients in the internal
angular velocity.
---------------------------------------------------------
Title: On the Constancy of Intermediate-Degree p-Mode Frequencies
during the Declining Phase of Solar Cycle 21
Authors: Rhodes, Edward J., Jr.; Woodard, Martin F.; Cacciani,
Alessandro; Tomczyk, Steven; Korzennik, Sylvain G.; Ulrich, Roger K.
1988ApJ...326..479R Altcode:
A comparison of two sets of frequencies of intermediate-degree (6 ≤ l
≤ 89) solar p-mode oscillations obtained in late 1981 and in mid-1984
shows agreement at the level of 0.02 μHz, or better than one part in
10<SUP>5</SUP>. In particular, the frequencies of 573 modes obtained
at the South Pole during 1981 December 24 - 25, (reported by Duvall,
Harvey, and Pomerantz in 1987) were compared with the frequencies of
the same modes as observed at the Mount Wilson Observatory 60 foot
Solar Tower from 1984 July 29 through August 13. It is concluded that
the data are consistent with no change in intermediate-degree p-mode
frequencies between late 1981 and mid-1985.
---------------------------------------------------------
Title: Frequencies of low-degree solar acoustic oscillations and
the phase of the solar cycle
Authors: Woodard, Martin F.
1988SoPh..114...21W Altcode:
A study of the solar total irradiance data of the Active Cavity
Radiometer Irradiance Monitor (ACRIM) on the Solar Maximum Mission
(SMM) satellite shows a small but formally significant shift in the
frequencies of solar acoustic (p-mode) oscillations between the epochs
of maximum and minimum solar activity. Specifically, the mean frequency
of the strongest p-mode resonances of low spherical-harmonic degree
(l = 0-2) is approximately 1.3 parts in 10<SUP>4</SUP> higher in
1980, near the time of sunspot maximum, than in ∼1985, near sunspot
minimum. The observed frequency shift may be an 11-yr effect but the
precise mechanism is not clear.
---------------------------------------------------------
Title: Time Variations of the Frequencies of Low-Degree Solar P-Modes
Authors: Woodard, M. F.; Noyes, R. W.
1988IAUS..123..197W Altcode:
A comparison of three separate years (1980, 1984, 1985) of SMM/ACRIM
solar total irradiance data reveals small but significant changes in
the frequencies of low-degree solar p-modes.
---------------------------------------------------------
Title: Measurements of Solar Internal Rotation Obtained with the
Mt-Wilson 60-FOOT Solar Tower
Authors: Rhodes, E. J., Jr.; Cacciani, A.; Woodard, M.; Tomczyk, S.;
Korzennik, S.; Ulrich, R. K.
1988IAUS..123...41R Altcode:
The authors have obtained estimates of the solar internal rotational
velocity from measurements of the frequency splittings of p-mode
oscillations. Specifically, they have analyzed a 10-day time series
of full-disk Dopplergrams obtained during July and August 1984 at the
60-Foot Tower Telescope of the Mt. Wilson Observatory.
---------------------------------------------------------
Title: Constancy of Intermediate-degree p-Mode Frequencies During
the Declining Phase of Solar Cycle 21
Authors: Rhodes, E. J., Jr.; Woodard, M. F.; Cacciani, A.; Tomczyk,
S.; Korzennik, S.; Ulrich, R. K.
1987BAAS...19Q.933R Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Angular Velocity of the Solar Interior Obtained by an
Asymptotic Inversion of P-Mode Frequency Shifts
Authors: Woodard, M. F.; Rhodes, E. J., Jr.; Tomczyk, S.; Korzennik,
S.; Cacciani, A.; Ulrich, R. K.
1987BAAS...19..934W Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Estimates of the solar internal angular velocity obtained
with the Mt. Wilson 60-foot solar tower
Authors: Rhodes, Edward J., Jr.; Cacciani, Alessandro; Woodard,
Martin; Tomczyk, Steven; Korzennik, Sylvain; Ulrich, R. K.
1987ASSL..137...75R Altcode: 1987isav.symp...75R
Estimates are obtained of the solar internal angular velocity from
measurements of the frequency splittings of p-mode oscillations. A
16-day time series of full-disk Dopplergrams obtained during July and
August 1984 at the 60-foot tower telescope of the Mt. Wilson Observatory
is analyzed. Power spectra were computed for all of the zonal, tesseral,
and sectoral p-modes from l = 0 to 89 and for all of the sectoral
p-modes from l = 90 to 200. A mean power spectrum was calculated for
each degree up to 89. The frequency differences of all of the different
nonzonal modes were calculated for these mean power spectra.
---------------------------------------------------------
Title: Frequencies of low-degree solar acoustic oscillations and
the phase of the solar cycle
Authors: Woodard, Martin F.
1987SoPh..114...21W Altcode:
A study of the solar total irradiance data of the Active Cavity
Radiometer Irradiance Monitor (ACRIM) on the Solar Maximum Mission
(SMM) satellite shows a small but formally significant shift in the
frequencies of solar acoustic (p-mode) oscillations between the epochs
of maximum and minimum solar activity. Specifically, the mean frequency
of the strongest p-mode resonances of low spherical-harmonic degree
(l = 0-2) is approximately 1.3 parts in 10<SUP>4</SUP> higher in
1980, near the time of sunspot maximum, than in ≡1985, near sunspot
minimum. The observed frequency shift may be an 11-yr effect but the
precise mechanism is not clear.
---------------------------------------------------------
Title: Evidence for Radial Gradients in the Solar Internal Rotational
Velocity
Authors: Rhodes, E. J., Jr.; Tomczyk, S.; Woodard, M. F.; Cacciani,
A.; Korzennik, S.; Ulrich, R. K.
1986BAAS...18Q1010R Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Change of solar oscillation eigenfrequencies with the solar
cycle
Authors: Woodard, M. F.; Noyes, R. W.
1986ASIC..169..303W Altcode: 1986ssds.proc..303W
No abstract at ADS
---------------------------------------------------------
Title: Extraterrestrial Evidence Regarding the Frequency of
Collisional Events in the Solar System
Authors: Lavielle, B.; Regnier, S.; Simonoff, G. N.; Marti, K.;
Woodard, M.
1985Metic..20Q.692L Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Change of solar oscillation eigenfrequencies with the solar
cycle
Authors: Woodard, Martin F.; Noyes, Robert W.
1985Natur.318..449W Altcode:
Solar acoustic eigenfrequencies depend on the internal structure of the
Sun, which may change during the 11-yr cycle of magnetic activity as a
result of various effects associated with the solar dynamo. Observations
of low-degree acoustic frequencies were made, using the ACRIM instrument
on the Solar Maximum Mission (SMM) satellite, in 1980 (near solar
maximum) and 1984 (near solar minimum). The analysis of these data,
presented here, indicates that the frequencies of l = 0 and l = 1
acoustic modes in the 5-min band have decreased from 1980 to 1984,
by ~0.42 µHz or 1.3 parts in 10<SUP>4</SUP>. This finding may have
important implications for our understanding of the mechanism of the
solar activity cycle.
---------------------------------------------------------
Title: Clusters and Cycles in the Cosmic Ray Age Distributions
of Meteorites
Authors: Woodard, M. F.; Marti, K.
1985ICRC....5..402W Altcode: 1985ICRC...19e.402W
Statistically significant clusters in the cosmic ray exposure age
distributions of some groups of iron and stone meteorites are observed,
suggesting epochs of enhanced collisions and breakups. Fourier analyses
of the age distribution of chondrites reveal no significant periods,
nor does the same analysis when applied to iron meteorite clusters.
---------------------------------------------------------
Title: Observations of low-degree modes from the Solar Maximum
Mission.
Authors: Woodard, M.
1984sses.nasa..195W Altcode: 1984sss..conf..195W
Mean frequencies, amplitudes, and linewidths for the solar 5 min p mode
oscillations of degree 0, 1, and 2 have been obtained from approx. 280
days of SMM-ACRIM total irradiance data. The frequencies are in good
agreement with measurements obtained from velocity data. The amplitudes
of the modes lie along a well defined envelope of power vs. frequency,
which peaks at 3.1 mHz and has a width of 0.7 mHz (FWHM). The
r.m.s. amplitude of the highest peak in the spectrum (n=21, l=1) is
approx. 3 ppm of the total flux. The linewidths of the narrowest l=O
modes are approx. 1 micro Hz (FWHM). A broad continuum of power caused
both by solar surface granulation and by instrumental noise interferes
with the analysis of 5 min modes. The continuum spectral power in a 1
micro Hz band near 3 mHz corresponds to an apparent r.m.s. variation
of approx. 0.5 parts per million of the mean solar flux.
---------------------------------------------------------
Title: Total irradiance observations of low degree p-modes
Authors: Woodard, M.; Hudson, H.
1984MmSAI..55...67W Altcode:
A spectral analysis of 10 months of brightness data from the
Active Cavity Radiometer Irradiance Monitor on the SMM satellite has
revealed new information about the low-degree (l = 0,1, and 2) p-mode
oscillations of the Sun. The mean frequencies, irradiance amplitudes,
and line widths of the largest amplitude modes have been determined
with previously unattained accuracy.
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Title: The Inconstant Solar Constant
Authors: Willson, R. C.; Hudson, H.; Woodard, M.
1984S&T....67..501W Altcode:
The Active Cavity Radiometer Irradiance Monitor (ACRIM) of the Solar
Maximum Mission satellite measures the radiant power emitted by the sun
in the direction of the earth and has worked flawlessly since 1980. The
main motivation for ACRIM's use to measure the solar constant is the
determination of the extent to which this quantity's variations affect
earth weather and climate. Data from the solar minimum of 1986-1987 is
eagerly anticipated, with a view to the possible presence of a solar
cycle variation in addition to that caused directly by sunspots.
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Title: Upper limit on solar interior rotation
Authors: Woodard, M.
1984Natur.309..530W Altcode:
The power spectrum of solar total irradiance (flux) variations front the
Active Cavity Radiometer Irradiance Monitor (ACRIM) on the Solar Maximum
Mission (SMM) spacecraft shows individual 5-min p- mode oscillations
<SUP>1,2</SUP>of spherical harmonic degree l= 0-2 and radial order n=
16-26. An m-state splitting analysis based on the widths of the (n,l)
multiplets in the spectrum of ACRIM data yields a mean (sidereal)
interior rotation rate between 0 and 2.2 times the observed 0.456-
µHz equatorial surface rate, consistent with the rapid rotation
rate originally claimed by Claverie et al.<SUP>3</SUP>based on a
(controversial) splitting interpretation of the these 5-min modes seen
in line-of-sight velocity. Rotationally split p- and g- and f-modes have
been identified in the temporal power spectrum of the limb-darkening
data of Bos and Hill<SUP>4</SUP>, and from these splittings two internal
rotation curves<SUP>5,6</SUP> have been deduced which imply a solar
gravitational quadrupole moment J<SUB>2</SUB>large enough to spoil
the precise agreement between general relativity and observations of
planetary motion. The splitting of the low- l 5-min p- modes implied
by these curves is inconsistent with the upper limit derived here, and
the reported conflict with einsteinian theory, is therefore, premature.
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Title: Short-Period Oscillations in the Total Solar Irradiance.
Authors: Woodard, Martin Frederic
1984PhDT........34W Altcode: 1985DiAbI..45.2582W
This dissertation deals with normal-mode vibrations of the Sun, as
measured by their effect on the solar total irradiance. I have studied
"5-minute" p-mode oscillations of radial order n (TURNEQ) 16 - 26 and
degree l = 0 - 2 in the 1980 data from the Active Cavity Radiometer
Irradiance Monitor (ACRIM) on the Solar Maximum Mission satellite
(SMM). The frequencies of separate (n,l) peaks in the spectrum
of ACRIM data agree with those of previous observers to within
('(TURN))3 parts in 10('4). For the oscillatory peaks of highest
signal quality the frequency error is estimated to be less than
one part in 10('4). Discrepancies between observed and theoretical
frequencies are already much greater than discrepancies among observed
frequencies. Quasi -degenerate m states, of which the (n,l) peaks
are in principle comprised, cannot be distinguished in the ACRIM
power spectrum, contrary to previous claims. The mean amplitudes of
individual (n,l) peaks have been established with 10 - 20% accuracy;
r.m.s. fractional irradiance variations of up to 3 parts per million
occur. The observed amplitude ratio of 5-min modes in velocity and
intensity agrees roughly with preliminary theoretical estimates,
but more theory and observation are required. The 5-min oscillation
data from the ACRIM have been interpreted in terms of a theoretically
motivated picture in which the modes behave like independently and
randomly excited harmonic oscillators. The relative frequency width of
the most prominent l = 0 modes is about one part in 2000, implying an
oscillator time constant (e-folding time for energy decay) of 1 to 2
days. This lifetime is approximately confirmed by direct observations
of amplitude variations in these modes. The lifetime of these modes
was previously a matter of controversy. Solar rotation will split
the m states belonging to a given (n,l) multiplet, making the l >
1 peaks broader than they would otherwise be. From the widths of the
l = 1 peaks I deduce an upper limit on the separation of adjacent m
states of 1.0 (mu)Hz with ('(TURN))99% confidence. This is 2.2 times
the splitting that solid-body rotation at the observed ('(TURN))1/25-day
sidereal equatorial surface rate would imply. . . . (Author's abstract
exceeds stipulated maximum length. Discontinued here with permission
of author.) UMI.
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Title: Frequencies, amplitudes and linewidths of solar oscillations
from total irradiance observations
Authors: Woodard, M.; Hudson, H. S.
1983Natur.305..589W Altcode:
Ten months of solar total irradiance data from the Solar Maximum Mission
satellite have generated accurate frequencies, amplitudes and linewidths
for individual ~5-min solar p-mode ocillations of low degree. The modes
can be described as independent and chaotically excited oscillators,
and provide no evidence for the fine structure taken to imply rapid
internal rotation of the Sun.
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Title: Upper Limits on the Internal Rotation Rate of the Sun
Authors: Woodard, M. F.; Hudson, H. S.
1983BAAS...15..951W Altcode:
No abstract at ADS
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Title: Solar Surface Granulation and Variations of Total Irradiance
Authors: Hudson, H. S.; Woodard, M. F.
1983BAAS...15R.715H Altcode:
No abstract at ADS
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Title: Solar Oscillations Observed in the Total Irradiance
Authors: Woodard, M.; Hudson, H.
1983SoPh...82...67W Altcode: 1983IAUCo..66...67W
The total solar irradiance measurements obtained by the active-cavity
radiometer on board the Solar Maximum Mission have been analyzed
for evidence of global oscillations. We find that the most energetic
low-degree p-mode oscillations in the five-minute band have amplitudes
of a few parts per million of the total irradiance, and we positively
detect modes with l = 0, 1, and 2. The distribution in l differs from
that of the velocity spectrum, with relatively more power at lower l
values. The individual modes have narrow line widths, corresponding
to values of Q greater than a few thousand, or lifetimes of at least a
week. We do not detect the 160-min oscillation in the power spectrum,
and place an upper limit of 5 parts per million (99.9% confidence)
on its amplitude.
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Title: What are Solar Irradiance Observations of Global Oscillations
Telling Us?
Authors: Woodard, M. F.; Hudson, H. S.
1982BAAS...14..864W Altcode:
No abstract at ADS
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Title: The Effects of Sunspots on Solar Irradiance
Authors: Hudson, H. S.; Silva, S.; Woodard, M.; Willson, R. C.
1982SoPh...76..211H Altcode:
Sunspots have an obvious direct effect upon the visible radiant
energy falling upon the Earth. We show how to estimate this effect and
compare it quantitatively with recent observations of the solar total
irradiance (Willson et al., 1981). The sunspots explain about half of
the total observed variance of one-day averages. Since the sunspot
effect on irradiance produces an asymmetry of the solar radiation,
rather than (necessarily) a variation of the total luminosity, we have
also estimated the sunspot population on the invisible hemisphere. This
extrapolation allows us to estimate the true luminosity deficit produced
by sunspots, in a manner that tends toward the correct long-term average
value. We find no evidence for instantaneous global re-emission to
compensate for the sunspot flux deficit.
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Title: Observations of p-mode Oscillations in the Total Solar
Irradiance
Authors: Woodard, M.; Hudson, H.; Willson, R. C.
1981BAAS...13..858W Altcode:
No abstract at ADS
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Title: Variability of Total Solar Irradiance: the Flux Deficit
of Sunspots
Authors: Hudson, H. S.; Woodard, M.; Willson, R. C.
1980BAAS...12Q.898H Altcode:
No abstract at ADS
