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Helioseismology: A probe of the solar interior, atmosphere, and activity cycle

Helioseismology began in earnest in the mid 1970's. In the two decades which have elapsed since that time this branch of solar physics has become a mature field of research. Helioseismology has demonstrated that the solar convection zone is about twice as deep as was generally thought to be the case before 1977. Helioseismology has also provided measurements of the solar internal angular velocity over much of the sun's interior. Helioseismology has also ruled out models which would solve the solar neutrino problem by a lowering of the temperature of the core. Recently, some of the seismic properties of the sun have been demonstrated to vary with changing levels of solar activity. Also, helioseismology has recently provided evidence for helical flow patterns in the shallow, sub-photosphere layers. The techniques of helioseismology are also expanding to include seismic probes of solar active regions. Some work is also being conducted into the possible contributions of the solar acoustic models to the heating of the solar atmosphere. In this talk I will highlight a few of the above results and concentrate on current areas of research in the field.

Rhodes, E. J., Jr.

Time-Distance Helioseismology

Time-distance helioseismology is a method of ambient noise imaging using the solar oscillations. The basic realization that led to time-distance helioseismology was that the temporal cross correlation of the signals at two 'surface' (or photospheric) locations should show a feature at the time lag corresponding to the subsurface travel time between the locations. The temporal cross correlation, as a function of the location separation, is the Fourier transform of the spatio-temporal power spectrum of the solar oscillations, a commonly used function in helioseismology. It is therefore likely the characteristic ridge structure of the correlation function had been seen before without appreciation of its significance. Travel times are measured from the cross correlations. The times are sensitive to a number of important subsurface solar phenomena. These include sound speed variations, flows, and magnetic fields. There has been much interesting progress in the 17 years since the first paper on this subject (Duvall et al., Nature, 1993, 362, 430-432). This progress will be reviewed in this paper.

Duvall, Thomas L., Jr.

Implementation and Comparison of Acoustic Travel-Time Measurement Procedures for the Solar Dynamics Observatory-Helioseismic and Magnetic Imager Time-Distance Helioseismology Pipeline

The Helioseismic and Magnetic Imager (HMI) instrument onboard the Solar Dynamics Observatory (SDO) satellite is designed to produce high-resolution Doppler-velocity maps of oscillations at the solar surface with high temporal cadence. To take advantage of these high-quality oscillation data, a time - distance helioseismology pipeline (Zhao et al., Solar Phys. submitted, 2010) has been implemented at the Joint Science Operations Center (JSOC) at Stanford University. The aim of this pipeline is to generate maps of acoustic travel times from oscillations on the solar surface, and to infer subsurface 3D flow velocities and sound-speed perturbations. The wave travel times are measured from cross-covariances of the observed solar oscillation signals. For implementation into the pipeline we have investigated three different travel-time definitions developed in time - distance helioseismology: a Gabor-wavelet fitting (Kosovichev and Duvall, SCORE'96: Solar Convection and Oscillations and Their Relationship, ASSL, Dordrecht, 241, 1997), a minimization relative to a reference cross-covariance function (Gizon and Birch, Astrophys. J. 571, 966, 2002), and a linearized version of the minimization method (Gizon and Birch, Astrophys. J. 614, 472, 2004). Using Doppler-velocity data from the Michelson Doppler Imager (MDI) instrument onboard SOHO, we tested and compared these definitions for the mean and difference traveltime perturbations measured from reciprocal signals. Although all three procedures return similar travel times in a quiet-Sun region, the method of Gizon and Birch (Astrophys. J. 614, 472, 2004) gives travel times that are significantly different from the others in a magnetic (active) region. Thus, for the pipeline implementation we chose the procedures of Kosovichev and Duvall (SCORE'96: Solar Convection and Oscillations and Their Relationship, ASSL, Dordrecht, 241, 1997) and Gizon and Birch (Astrophys. J. 571, 966, 2002). We investigated the relationships among these three travel-time definitions, their sensitivities to fitting parameters, and estimated the random errors that they produce.

HMI

A co-ordinated and synergistic analysis strategy for future ground-based and space helioseismology

The variety of helioseismology observational programs planned for the mid-1990s represents an unprecedented opportunity to improve understanding of the solar interior. This review discusses the coordination of the GONG, IRIS, Birmingham and other ground-based observational programs with the space experiments on the SOHO mission: GOLF, VIRGO, and MDI. The integration and coordination of the different data streams in terms of the spatial and temporal coverage as well as the implications of the different spectral resolution and stability characteristics of each experiment are discussed. The study of the effect of active regions on various helioseismology signals is presented as an example of how ground-based and space experiments can be coordinated.

Ulrich, Roger K.

Test of a new theory for stellar convection using helioseismology

Two evolutionary models of the sun have been tested using helioseismological data. The two models use the same input microphysics (nuclear reaction rates, opacity, equation of state) and the same numerical evolutionary code, but differ in the treatment of turbulent convection. The first model employs the standard mixing - length theory of convection, while the second one employs a new turbulent convection model which overcomes some basic inconsistencies of the standard theory of convection. The test rests on the calculation of p-mode eigenfrequencies and on the comparison with the helioseismological data. The comparison shows an overall improvement of the eigenfrequencies calculated with the new model with respect to those calculated with the standard model, although it appears that both models still suffer from inaccuracies especially in the treatment of the surface layers.

Paterno, L.

Time-Distance Helioseismology with the MDI Instrument: Initial Results

In time-distance helioseismology, the travel time of acoustic waves is measured between various points on the solar surface. To some approximation, the waves can be considered to follow ray paths that depend only on a mean solar model, with the curvature of the ray paths being caused by the increasing sound speed with depth below the surface. The travel time is effected by various inhomogeneities along the ray path, including flows, temperature inhomogeneities, and magnetic fields. By measuring a large number of times between different locations and using an inversion method, it is possible to construct 3-dimensional maps of the subsurface inhomogeneities. The SOI/MDI experiment on SOHO has several unique capabilities for time-distance helioseismology. The great stability of the images observed without benefit of an intervening atmosphere is quite striking. It his made it possible for us to detect the travel time fo separations of points as small as 2.4 Mm in the high-resolution mode of MDI (0.6 arc sec 1/pixel). This has enabled the detection of the supergranulation flow. Coupled with the inversion technique, we can now study the 3-dimensional evolution of the flows near the solar surface.

Duvall, T. L., Jr.

Local Helioseismology: A New Window into the Sun

In recent years the focus of helioseismology has shifted from the classical measurements of global properties using normal mode frequencies to possibly a more difficult problem of measuring the three-dimensional, time-dependent structure of the solar interior, now called local helioseismology. Problems to be studed include the subsurface structure of observed surface features such as sunspots, convective flow patterns, and the magnetic field of the 1 1-year sunspot cycle. A variety of techniques have been developed to attack these problems, including a 'local' normal mode method, a method of measuring travel times between &stant locations, and a method for holographically reconstructing the acoustic signal in the solar interior. Recent results from the field will be reviewed.

Duvall, Thomas

Implementation and Comparison of Acoustic Travel-Time Measurement Procedures for the Helioseismic and Magnetic Imager Time-Distance Helioseismology Pipeline

The Helioseismic and Magnetic Imager (HMI) instrument on board the Solar Dynamics Observatory (SDO) satellite is designed to produce high-resolution Doppler velocity maps of oscillations at the solar surface with high temporal cadence. To take advantage of these high-quality oscillation data, a time-distance helioseismology pipeline has been implemented at the Joint Science Operations Center (JSOC) at Stanford University. The aim of this pipeline is to generate maps of acoustic travel times from oscillations on the solar surface, and to infer subsurface 3D flow velocities and sound-speed perturbations. The wave travel times are measured from cross covariances of the observed solar oscillation signals. For implementation into the pipeline we have investigated three different travel-time definitions developed in time-distance helioseismology: a Gabor wavelet fitting (Kosovichev and Duvall, 1997), a minimization relative to a reference cross-covariance function (Gizon and Birch, 2002), and a linearized version of the minimization method (Gizon and Birch, 2004). Using Doppler velocity data from the Michelson Doppler Imager (MDI) instrument on board SOHO, we tested and compared these definitions for the mean and difference travel-time perturbations measured from reciprocal signals. Although all three procedures return similar travel times in a quiet Sun region, the method of Gizon and Birch (2004) gives travel times that are significantly different from the others in a magnetic (active) region. Thus, for the pipeline implementation we chose the procedures of Kosovichev and Duvall (1997) and Gizon and Birch (2002). We investigated the relationships among these three travel-time definitions, their sensitivities to fitting parameters, and estimated the random errors they produce

Couvidat, S.

A Time-Distance Helioseismology Method for Quasi-Linear Geometries

Helioseismology is the study of the solar interior, through which we extract flow and wave-speed information from Doppler velocity observations at the surface. Local helioseismology involves the study of small regions on the solar disk and is used to create a detailed picture of the interior in that particular region. Perturbations in the flow and wave-speed results indicate, e.g. magnetic-flux or temperature variations. There are multiple methods used in local-helioseismic research, but all current local-helioseismic techniques assume a point-source perturbation. For this study, we develop a new time-distance (TD) helioseismic methodology that can exploit the quasi-linear geometry of an elongated feature, allowing us to i) improve the signal-to-noise ratio of the TD results, and ii) greatly decrease the number of calculations required and therefore the computing time of the TD analysis. Ultimately, the new method will allow us to investigate solar features with magnetic-field configurations previously unexplored. We validate our new technique using a simple F-mode wave simulation, comparing results of point-source and linear perturbations. Results indicate that local-helioseismic analysis is dependent on the geometry of the system and can be improved by taking the magnetic-field configuration into account.

Hess Webber, Shea A.

Helioseismology of a Realistic Magnetoconvective Sunspot Simulation

We compare helioseismic travel-time shifts measured from a realistic magnetoconvective sunspot simulation using both helioseismic holography and time-distance helioseismology, and measured from real sunspots observed with the Helioseismic and Magnetic Imager instrument on board the Solar Dynamics Observatory and the Michelson Doppler Imager instrument on board the Solar and Heliospheric Observatory. We find remarkable similarities in the travel-time shifts measured between the methodologies applied and between the simulated and real sunspots. Forward modeling of the travel-time shifts using either Born or ray approximation kernels and the sound-speed perturbations present in the simulation indicates major disagreements with the measured travel-time shifts. These findings do not substantially change with the application of a correction for the reduction of wave amplitudes in the simulated and real sunspots. Overall, our findings demonstrate the need for new methods for inferring the subsurface structure of sunspots through helioseismic inversions.

Sun-interior

Time-Distance Helioseismology Data-Analysis Pipeline for Helioseismic and Magnetic Imager Onboard Solar Dynamics Observatory (SDO-HMI) and Its Initial Results

The Helioseismic and Magnetic Imager onboard the Solar Dynamics Observatory (SDO/HMI) provides continuous full-disk observations of solar oscillations. We develop a data-analysis pipeline based on the time-distance helioseismology method to measure acoustic travel times using HMI Doppler-shift observations, and infer solar interior properties by inverting these measurements. The pipeline is used for routine production of near-real-time full-disk maps of subsurface wave-speed perturbations and horizontal flow velocities for depths ranging from 0 to 20 Mm, every eight hours. In addition, Carrington synoptic maps for the subsurface properties are made from these full-disk maps. The pipeline can also be used for selected target areas and time periods. We explain details of the pipeline organization and procedures, including processing of the HMI Doppler observations, measurements of the travel times, inversions, and constructions of the full-disk and synoptic maps. Some initial results from the pipeline, including full-disk flow maps, sunspot subsurface flow fields, and the interior rotation and meridional flow speeds, are presented.

Sun: helioseismology

Subsurface Supergranular Vertical Flows as Measured Using Large Distance Separations in Time-Distance Helioseismology

As large-distance rays (say, 10 - 24deg) approach the solar surface approximately vertically, travel times measured from surface pairs for these large separations are mostly sensitive to vertical flows, at least for shallow flows within a few Mm of the solar surface. All previous analyses of supergranulation have used smaller separations and have been hampered by the difficulty of separating the horizontal and vertical flow components. We find that the large-separation travel times associated with supergranulation cannot be studied using the standard phase-speed filters of time-distance helioseismology. These filters, whose use is based upon a refractive model of the perturbations, reduce the resultant travel time signal by at least an order of magnitude at some distances. More effective filters are derived. Modeling suggests that the center-annulus travel-time difference [outward-going time minus inward-going time] in the separation range delta= 10 - 24deg is insensitive to the horizontally diverging flow from the centers of the supergranules and should lead to a constant signal from the vertical flow. Our measurement of this quantity, 5.1+/-0.1 seconds, is constant over the distance range. This magnitude of the signal cannot be caused by the level of upflow at cell centers seen at the photosphere of 10 ms(exp−1) extended in depth. It requires the vertical flow to increase with depth. A simple Gaussian model of the increase with depth implies a peak upward flow of 240 ms(exp−1) at a depth of 2.3 Mm and a peak horizontal flow of 700 ms(exp−1) at a depth of 1.6 Mm.

convection

Inversion of helioseismology data

The paper presents an algorithm for performing an inversion of helioseismology data. The method is characterized by high speed, stability, and versatility. The existence of a method for producing an analog of the Backus-Gilbert optimal kernals is demonstrated. The method performs well, even when a moderate amount of observational noise is included.

Jeffrey, W.

The SOHO project - Helioseismology investigations

The helioseismology instruments on the payload of the planned Solar and Heliospheric Observatory (SOHO) mission are discussed. The SOHO mission and the experiments planned for the mission are described. The plans include the global oscillations at low frequencies experiment to perform uninterrupted velocity oscillations measurements of the full solar disk, the variability of irradiance and gravity oscillations experiment to study solar irradiance variability and oscillations, and the Michelson Doppler imager, a flight version of the Fourier Tachometer. The possible use of data from these studies to examine the radial stratification and longitudinal variation of the physical characteristics of the sun is discussed.

Domingo, V.

VIRGO: Experiment for helioseismology and solar irradiance monitoring

The scientific objectives of the variability of solar irradiance and gravity oscillations (VIRGO) experiment are as follows: to determine the characteristics of pressure and internal gravity oscillations by observing irradiance and radiance variations; to measure the solar total and spectral irradiance, and to quantify their variability. Helioseismological methods can be applied to these data in order to probe the solar interior. Certain convection characteristics and their interaction with magnetic fields will be studied from the results of the irradiance monitoring and from the comparison of the amplitudes and phases of the oscillations as observed from the brightness by VIRGO and from velocity by the global oscillations at low frequency (GOLF) experiment. The VIRGO experiment contains two active-cavity radiometers that monitor the solar constant, two three-channel sunphotometers that measure the spectral irradiance, and a low resolution imager with 12 pixels that measures the radiance distribution over the solar disk at 500 nm. The scientific objectives of VIRGO are presented, the instruments and the data acquisition and control system are described, and their measured performances are given.

Froehlich, Claus

Our Sun V: A Bright Young Sun Consistent with Helioseismology and Warm Temperatures on Ancient Earth and Mars

The relatively warm temperatures required on early Earth and Mars have been difficult to account for with warming from greenhouse gases. A slightly more massive young Sun would be brighter than predicted by the standard solar model, simultaneously resolving this problem for both Earth and Mars. We computed high-precision solar models with seven initial masses, from Mi = 1.01 to 1.07 solar mass - the latter being the maximum permitted if the early Earth is not to lose its water via a moist greenhouse effect. The relatively modest early mass loss that is required remains consistent with observational limits on mass loss from young stars and with estimates of the past solar wind obtained from lunar rocks. We considered three types of mass loss rates: (1) a reasonable choice of a simple exponential decline, (2) an extreme step-function case that gives the maximum effect consistent with observations, and (3) the radical case of a linear decline which is inconsistent with the solar wind mass loss estimates from lunar rocks. Our computations demonstrated that mass loss leaves a fingerprint oil the Sun's internal structure large enough to be detectable with helioseismic observations. All of our mass-losing solar models were consistent with the helioseismic observations; in fact, our preferred mass-losing cases were in marginally better agreement with the helioseismology than the standard solar model was, although this difference was smaller than the effects of other uncertainties in the input physics and in the solar composition. Mass loss has only a relatively minor effect on the predicted lithium depletion; the major portion of the solar lithium depletion must still be due to rotational mixing. Thus the modest mass loss cases considered here cannot be ruled out by observed lithium depletions. For the three mass loss types considered, the preferred initial masses were 1.07 solar mass for the exponential case and 1.04 solar mass for the step-function and linear cases; all of these provided high enough solar fluxes at Mars 3.8 Gyr ago to be consistent with the existence of liquid water. For a more massive early Sun, the planets would have had to be closer to the young Sun in order to end up in their present orbits; the orbital radii of the planets would vary inversely with the solar mass. Both of these effects contribute to the fact that the early solar flux at the planets would have been considerably higher than that of the standard solar model at that time. In fact, the 1.07 solar mass exponential case has a flux at birth 5% higher than the present solar flux, while the radical 1.04 solar mass linear case has a nearly constant flux over the first 3 Gyr only about 10% lower than at present. The early solar evolution would be in the opposite direction in the H-R diagram to that of the standard Sun.

Sackmann, I.-Juliana

Advances in Time-Distance Helioseismology

Time-distance helioseismology is a way to measure travel times between surface locations for waves traversing the solar interior. Coupling the travel with an extensive modeling effort has proven to be a powerful tool for measuring flows and other wave speed inhomogeneities in the solar interior. Problems receiving current attention include studying the time variation of the meridional circulation and torsional oscillation and active region emergence and evolution, current results on these topics will be presented.

Duvall, Thomas L., Jr.

Subsurface Supergranular Vertical Flows as Measured Using Large Distance Separations in Time-Distance Helioseismology

As large-distance rays (say, 10-24 deg) approach the solar surface approximately vertically, travel times measured from surface pairs for these large separations are mostly sensitive to vertical flows, at least for shallow flows within a few Mm of the solar surface. All previous analyses of supergranulation have used smaller separations and have been hampered by the difficulty of separating the horizontal and vertical flow components. We find that the large separation travel times associated with upergranulation cannot be studied using the standard phase-speed filters of time-distance helioseismology. These filters, whose use is based upon a refractive model of the perturbations,reduce the resultant travel time signal by at least an order of magnitude at some distances. More effective filters are derived. Modeling suggests that the center-annulus travel time difference in the separation range 10-24 deg is insensitive to the horizontally diverging flow from the centers of the supergranules and should lead to a constant signal from the vertical flow. Our measurement of this quantity for the average supergranule, 5.1 s, is constant over the distance range. This magnitude of signal cannot be caused by the level of upflow at cell centers seen at the photosphere of 10 m/s extended in depth. It requires the vertical flow to increase with depth. A simple Gaussian model of the increase with depth implies a peak upward flow of 240 m/s at a depth of 2.3 Mm and a peak horizontal flow of 700 m/s at a depth of 1.6 Mm.

Duvall, T. L., Jr.