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1.
Owens  Mathew J. 《Solar physics》2020,295(10):1-28

Time–distance helioseismology is a set of powerful tools to study localized features below the Sun’s surface. Inverse methods are needed to robustly interpret time–distance measurements, with many examples in the literature. However, techniques that utilize a more statistical approach to inferences, and that are broadly used in the astronomical community, are less-commonly found in helioseismology. This article aims to introduce a potentially powerful inversion scheme based on Bayesian probability theory and Monte Carlo sampling that is suitable for local helioseismology. We first describe the probabilistic method and how it is conceptually different from standard inversions used in local helioseismology. Several example calculations are carried out to compare and contrast the setup of the problems and the results that are obtained. The examples focus on two important phenomena that are currently outstanding issues in helioseismology: meridional circulation and supergranulation. Numerical models are used to compute synthetic observations, providing the added benefit of knowing the solution against which the results can be tested. For demonstration purposes, the problems are formulated in two and three dimensions, using both ray- and Born-theoretical approaches. The results seem to indicate that the probabilistic inversions not only find a better solution with much more realistic estimation of the uncertainties, but they also provide a broader view of the range of solutions possible for any given model, making the interpretation of the inversion more quantitative in nature. The probabilistic inversions are also easy to set up for a broad range of problems, and they can take advantage of software that is publicly available. Unlike the progress being made in fundamental measurement schemes in local helioseismology that image the far side of the Sun, or have detected signatures of global Rossby waves, among many others, inversions of those measurements have had significantly less success. Such statistical methods may help overcome some of these barriers to move the field forward.

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2.
Migrating bands of weak, zonal flow, associated with the activity bands in the solar cycle, have been observed at the solar surface for some time. More recently, these flows have been probed deep within the convection zone using global helioseismology and examined in more detail close to the surface with the techniques of local helioseismology. We compare the near-surface results from global and local helioseismology using data from the Michelson Doppler Imager and the Global Oscillation Network Group with surface Doppler velocity measurements from the Mount Wilson 150-foot tower and find that the results are in reasonable agreement, with some explicable differences in detail. All of the data sets show zones of faster rotation approaching the equator from mid-latitudes during the solar cycle, with a variation at any given location that can be approximately, but not completely, described by a single sinusoid and an amplitude that does not drop off steeply below the surface.  相似文献   

3.
Solar active regions are distinguished by their strong magnetic fields. Modern local helioseismology seeks to probe them by observing waves which emerge at the solar surface having passed through their interiors. We address the question of how an acoustic wave from below is partially converted to magnetic waves as it passes through a vertical magnetic field layer where the sound and Alfvén speeds coincide (the equipartition level), and find that (i) there is no associated reflection at this depth, either acoustic or magnetic, only transmission and conversion to an ongoing magnetic wave; and (ii) conversion in active regions is likely to be strong, though not total, at frequencies typically used in local helioseismology, with lower frequencies less strongly converted. A simple analytical formula is presented for the acoustic-to-magnetic conversion coefficient.  相似文献   

4.
An important goal of helioseismology is to provide information about the basic physics and parameters that determine the structure of the solar interior. Here we discuss the procedures applied in such analyses, using as an example attempts to obtain significant constraints on the value of Newton's gravitational constant G from helioseismology. The analysis is based on complete direct and inverse helioseismic analysis of a set of accurate observed acoustic frequencies. We confirm, as found by previous investigations based on different approaches, that the actual level of precision of the helioseismic inferences does not allow us to constrain G with a precision better than that which can be reached with direct experimental measurements. The conclusion emphasizes the importance in helioseismic inferences of considering not only the accuracy with which solar oscillations are measured, but also the effect of uncertainties in other aspects of the model computation and helioseismic analysis.  相似文献   

5.
Sivaraman  K.R.  Sivaraman  Hari  Gupta  S.S.  Howard  Robert F. 《Solar physics》2003,214(1):65-87
We find from an analysis of the Kodaikanal sunspot group data that the rotation rates of spot groups increase with their age when the rotation rates are computed after sorting the spot groups life-span-wise. We confirm these findings from an analysis of the Mt. Wilson sunspot data set too. We show that this trend is in good agreement with the internal rotation profiles from helioseismology (GONG) observations and is also consistent with the concept that the footpoints of the magnetic loops of spot groups are initially anchored in the deeper layers in the solar interior and rise to shallower layers as the spots age, and that the spots reflect the rotation rates at the respective depths at which their footpoints are temporally located. We project the `first-day rotation rates' and the `daily rotation rates' of spot groups on the rotation profiles from the GONG observations and derive the initial anchoring depths of the footpoints of the magnetic loops of the spot groups and their rates of rise as the spot groups age. Our results of the rotation rates are in antithesis to the results reported by investigators from the Greenwich spot group data that show a deceleration in rotation rates as the spot groups age which are also inconsistent with the rotation profiles from helioseismology observations.  相似文献   

6.
Inversions for local helioseismology are an important and necessary step for obtaining three-dimensional maps of various physical quantities in the solar interior. Frequently, the full inverse problems that one would like to solve prove intractable because of computational constraints. Due to the enormous seismic data sets that already exist and those forthcoming, this is a problem that needs to be addressed. To this end, we present a very efficient linear inversion algorithm for local helioseismology. It is based on a subtractive optimally localized averaging (SOLA) scheme in the Fourier domain, utilizing the horizontal-translation invariance of the sensitivity kernels. In Fourier space the problem decouples into many small problems, one for each horizontal wave vector. This multichannel SOLA method is demonstrated for an example problem in time–distance helioseismology that is small enough to be solved both in real and Fourier space. We find that both approaches are successful in solving the inverse problem. However, the multichannel SOLA algorithm is much faster and can easily be parallelized.  相似文献   

7.
A major goal of helioseismology is to understand the mechanism of the solar cycle. In this paper, some results of helioseismic observations relevant to the cycle are briefly reviewed, the current state-of-the-art is discussed, and near-term future directions are sketched out. Topics covered include the internal rotation rate; activity-related parameter variations; the tachocline; far-side imaging; the torsional oscillation; and meridional flows.  相似文献   

8.
The purpose of deep-focusing time–distance helioseismology is to construct seismic measurements that have a high sensitivity to the physical conditions at a desired target point in the solar interior. With this technique, pairs of points on the solar surface are chosen such that acoustic ray paths intersect at this target (focus) point. Considering acoustic waves in a homogeneous medium, we compare travel-time and amplitude measurements extracted from the deep-focusing cross-covariance functions. Using a single-scattering approximation, we find that the spatial sensitivity of deep-focusing travel times to sound-speed perturbations is zero at the target location and maximum in a surrounding shell. This is unlike the deep-focusing amplitude measurements, which have maximum sensitivity at the target point. We compare the signal-to-noise ratio for travel-time and amplitude measurements for different types of sound-speed perturbations, under the assumption that noise is solely due to the random excitation of the waves. We find that, for highly localized perturbations in sound speed, the signal-to-noise ratio is higher for amplitude measurements than for travel-time measurements. We conclude that amplitude measurements are a useful complement to travel-time measurements in time–distance helioseismology.  相似文献   

9.
We review the impact of global helioseismology on key questions concerning the internal structure and dynamics of the Sun and consider the exciting challenges the field faces as it enters a fourth decade of science exploitation. We do so with an eye on the past, looking at the perspectives global helioseismology offered in its earlier phases, in particular the mid-to-late 1970s and the 1980s. We look at how modern, higher quality, longer datasets coupled with new developments in analysis have altered, refined, and changed some of those perspectives and opened others that were not previously available for study. We finish by discussing outstanding challenges and questions for the field.  相似文献   

10.
E. Mochizuki 《Solar physics》1992,142(2):395-398
The spherical harmonic analysis on hemisphere is reexamined to apply in helioseismology. New methods of mode identification are proposed to analyze the line-of-sight component which is expressed in terms of six spherical harmonics.  相似文献   

11.
The Sun's global oscillations, which are studied both in spatially unresolved ("Sun-as-a-star") and resolved observations of the solar disk, have enabled helioseismology to probe in detail the solar interior. I review first what is learned from the unresolved measurements, since this gives an idea of what we may in the not too distant future be able to learn about the interiors of other stars undergoing solar-type oscillations. I then look at the main results from resolved observations, which have begun to reveal the structure and dynamics of the interior of a star in exquisite detail. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

12.
Mechanisms of the formation and stability of sunspots are among the longest-standing and intriguing puzzles of solar physics and astrophysics. Sunspots are controlled by subsurface dynamics, hidden from direct observations. Recently, substantial progress in our understanding of the physics of the turbulent magnetized plasma in strong-field regions has been made by using numerical simulations and local helioseismology. Both the simulations and helioseismic measurements are extremely challenging, but it is becoming clear that the key to understanding the enigma of sunspots is a synergy between models and observations. Recent observations and radiative MHD numerical models have provided a convincing explanation for the Evershed flows in sunspot penumbrae. Also, they lead to the understanding of sunspots as self-organized magnetic structures in the turbulent plasma of the upper convection zone, which are maintained by a large-scale dynamics. Local helioseismic diagnostics of sunspots still have many uncertainties, some of which are discussed in this review. However, there have been significant achievements in resolving these uncertainties, verifying the basic results by new high-resolution observations, testing the helioseismic techniques by numerical simulations, and comparing results obtained by different methods. For instance, a recent analysis of helioseismology data from the Hinode space mission has successfully resolved several uncertainties and concerns (such as the inclined-field and phase-speed filtering effects) that might affect the inferences of the subsurface wave-speed structure of sunspots and the flow pattern. It is becoming clear that for the understanding of the phenomenon of sunspots it is important to further improve the helioseismology methods and investigate the whole life cycle of active regions, from magnetic flux emergence to dissipation. The Solar Dynamics Observatory mission has started to provide data for such investigations.  相似文献   

13.
Local helioseismology is providing new views of subphotospheric flows from supergranulation to global-scale meridional circulation and for studying structures and dynamics in the quiet Sun and active regions. In this short review we focus on recent developments, and in particular on a number of current issues, including the sensitivity of different measures of travel time and testing the forward modelling used in local helioseismology. We discuss observational and theoretical concerns regarding the adequacy of current analyses of waves in sunspots and active regions, and we report on recent progress in the use of numerical simulations to test local helioseismic methods.  相似文献   

14.
While sunspots are easily observed at the solar surface, determining their subsurface structure is not trivial. There are two main hypotheses for the subsurface structure of sunspots: the monolithic model and the cluster model. Local helioseismology is the only means by which we can investigate subphotospheric structure. However, as current linear inversion techniques do not yet allow helioseismology to probe the internal structure with sufficient confidence to distinguish between the monolith and cluster models, the development of physically realistic sunspot models are a priority for helioseismologists. This is because they are not only important indicators of the variety of physical effects that may influence helioseismic inferences in active regions, but they also enable detailed assessments of the validity of helioseismic interpretations through numerical forward modeling. In this article, we provide a critical review of the existing sunspot models and an overview of numerical methods employed to model wave propagation through model sunspots. We then carry out a helioseismic analysis of the sunspot in Active Region 9787 and address the serious inconsistencies uncovered by Gizon et al. (2009a, 2009b). We find that this sunspot is most probably associated with a shallow, positive wave-speed perturbation (unlike the traditional two-layer model) and that travel-time measurements are consistent with a horizontal outflow in the surrounding moat.  相似文献   

15.
Laurent Gizon 《Solar physics》2004,224(1-2):217-228
Flows in the upper convection zone are measured by helioseismology on a wide variety of scales. These include differential rotation and meridional circulation, local flows around complexes of magnetic activity and sunspots, and convective flows. The temporal evolution of flows through cycle 23 reveals connections between mass motions in the solar interior and the large-scale characteristics of the magnetic cycle. Here I summarize the latest observations and their implications. Observations from local helioseismology suggest that subsurface flows around active regions introduce a solar-cycle variation in the meridional circulation.  相似文献   

16.
Toutain  Thierry 《Solar physics》2001,200(1-2):353-360
The rotational splitting of low-degree p modes is still a controversial issue. There are small but nevertheless real discrepancies between the different measurements of splittings obtained with the existing helioseismology experiments from ground (BISON, IRIS, GONG, LOWL) or from space (VIRGO, GOLF, MDI). I review the current status of rotational splitting in the field of low-degree helioseismology and how we could explain the remaining discrepancies between the various sets of splittings.  相似文献   

17.
Birch  A.C.  Kosovichev  A.G. 《Solar physics》2000,192(1-2):193-201
We derive, following the standard first Born approximation approach used in the geophysics literature, an expression for the travel time perturbation caused by a perturbation to sound speed. In our simple model we employ a point source at one point and calculate the time taken for a wave packet created at the source to move to a second point. In the first Born approximation the travel time delay caused by a perturbation to the background model can be expressed as the integral over the whole sun of some function, called the travel time sensitivity kernel, multiplied by the perturbation. The sensitivity kernels are zero along the geometrical ray connecting the two points and have maximum weight in a tube around the ray; they are the solar equivalent of `the banana-doughnut' kernels discussed in the geophysics literature. Calculating sensitivity kernels that are more accurate than those derived from ray theory is important for the future of inversions done with time-distance helioseismology data as they will allow greater confidence in the results as well as increased resolution.  相似文献   

18.
We investigate the emergence of Active Region NOAA 10790 by means of time?–?distance helioseismology. Shallow regions of increased sound speed at the location of increased magnetic activity are observed, with regions becoming deeper at the locations of sunspot pores. We also see a long-lasting region of decreased sound speed located underneath the region of the flux emergence, possibly relating to a temperature perturbation due to magnetic quenching of eddy diffusivity, or to a dense flux tube. We detect and track an object in the subsurface layers of the Sun characterised by increased sound speed which could be related to emerging magnetic-flux and thus obtain a provisional estimate of the speed of emergence of around 1 km?s?1.  相似文献   

19.
In this presentation we briefly describe the Sun through large number of illustrations and pictures of the Sun taken from early times to the present day space missions. The importance of the study of the Sun is emphasized as it is the nearest star which presents unparallelled views of surface details and numerous phenomena. Our Sun offers a unique celestial laboratory where a large variety of phenomena take place, ranging in temporal domain from a few milliseconds to several decades, in spatial domain from a few hundred kilometers to thousands of kilometers, and in the temperature domain from a few thousand degrees to several million degrees. Its mass motion ranges from thousandths to thousands of kilometers per second. Such an object provides us with a unique laboratory to study the state of matter in the Universe. The existing solar ground-based and space missions have already revealed several mysteries of the outer environment of our Sun and much more is going to come in the near future from planned new sophisticated ground-based solar telescopes and Space missions. The new technique of helioseismology has unravelled many secrets of the solar interior and has put the Standard Solar Model (SSM) on firm footing. The long-standing problem of solar neutrinos has been recently sorted out, and even the ‘back side’ view of the Sun can be seen using the technique of holographic helioseismology.  相似文献   

20.
Surface gravity waves have been used to probe flows in the two megameters beneath the photosphere using the techniques of timedistance helioseismology. The results suggest that supergranule velocities are smaller than at the surface. The outward flow outside a sunspot penumbra (the moat) is observed, as is an inward flow in the region beyond the moat.  相似文献   

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