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

As large-distance rays (say, 10?–?24°) 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 [δt _oi] in the separation range Δ=10?–?24^° 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 m?s^?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 m?s^?1 at a depth of 2.3 Mm and a peak horizontal flow of 700 m?s^?1 at a depth of 1.6 Mm.     

Helioseismic Travel-Time Definitions and Sensitivity to Horizontal Flows Obtained from Simulations of Solar Convection

We study the sensitivity of wave travel times to steady and spatially homogeneous horizontal flows added to a realistic simulation of the solar convection performed by Robert F. Stein, Ake Nordlund, Dali Georgobiani, and David Benson. Three commonly used definitions of travel times are compared. We show that the relationship between travel-time difference and flow amplitude exhibits a non-linearity depending on the travel distance, the travel-time definition considered, and the details of the time – distance analysis (in particular, the impact of the phase-speed filter width). For times measured using a Gabor wavelet fit, the travel-time differences become nonlinear in the flow strength for flows of about 300 m s⁻¹, and this non-linearity reaches almost 60% at 1200 m s⁻¹ (relative difference between actual travel time and expected time for a linear behavior). We show that for travel distances greater than about 17 Mm, the ray approximation predicts the sensitivity of travel-time shifts to uniform flows. For smaller distances, the ray approximation can be inaccurate by more than a factor of three.     

Helioseismic Holography of an Artificial Submerged Sound Speed Perturbation and Implications for the Detection of Pre-emergence Signatures of Active Regions

We use a publicly available numerical wave-propagation simulation of Hartlep et al. (Solar Phys. 268, 321, 2011) to test the ability of helioseismic holography to detect signatures of a compact, fully submerged, 5 % sound-speed perturbation placed at a depth of 50 Mm within a solar model. We find that helioseismic holography employed in a nominal “lateral-vantage” or “deep-focus” geometry employing quadrants of an annular pupil can detect and characterize the perturbation. A number of tests of the methodology, including the use of a plane-parallel approximation, the definition of travel-time shifts, the use of different phase-speed filters, and changes to the pupils, are also performed. It is found that travel-time shifts made using Gabor-wavelet fitting are essentially identical to those derived from the phase of the Fourier transform of the cross-covariance functions. The errors in travel-time shifts caused by the plane-parallel approximation can be minimized to less than a second for the depths and fields of view considered here. Based on the measured strength of the mean travel-time signal of the perturbation, no substantial improvement in sensitivity is produced by varying the analysis procedure from the nominal methodology in conformance with expectations. The measured travel-time shifts are essentially unchanged by varying the profile of the phase-speed filter or omitting the filter entirely. The method remains maximally sensitive when applied with pupils that are wide quadrants, as opposed to narrower quadrants or with pupils composed of smaller arcs. We discuss the significance of these results for the recent controversy regarding suspected pre-emergence signatures of active regions.     

Surface-Focused Seismic Holography of Sunspots: I. Observations

We present a comprehensive set of observations of the interaction of p-mode oscillations with sunspots using surface-focused seismic holography. Maps of travel-time shifts, relative to quiet-Sun travel times, are shown for incoming and outgoing p modes as well as their mean and difference. We compare results using phase-speed filters with results obtained with filters that isolate single p-mode ridges, and we further divide the data into multiple temporal frequency bandpasses. The f mode is removed from the data. The variations of the resulting travel-time shifts with magnetic-field strength and with the filter parameters are explored. We find that spatial averages of these shifts within sunspot umbrae, penumbrae, and surrounding plage often show strong frequency variations at fixed phase speed. In addition, we find that positive values of the mean and difference travel-time shifts appear exclusively in waves observed with phase-speed filters that are dominated by power in the low-frequency wing of the p ₁ ridge. We assess the ratio of incoming to outgoing p-mode power using the ridge filters and compare surface-focused holography measurements with the results of earlier published p-mode scattering measurements using Fourier?–?Hankel decomposition.     

Comparison of Travel-Time and Amplitude Measurements for Deep-Focusing Time–Distance Helioseismology

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.     

High-Resolution Mapping of Flows in the Solar Interior: Fully Consistent OLA Inversion of Helioseismic Travel Times

To recover the flow information encoded in travel-time data of time?–?distance helioseismology, accurate forward modeling and a robust inversion of the travel times are required. We accomplish this using three-dimensional finite-frequency travel-time sensitivity kernels for flows along with a (2+1)-dimensional (2+1D) optimally localized averaging (OLA) inversion scheme. Travel times are measured by ridge filtering MDI full-disk Doppler data and the corresponding Born sensitivity kernels are computed for these particular travel times. We also utilize the full noise-covariance properties of the travel times, which allow us to accurately estimate the errors for all inversions. The whole procedure is thus fully consistent. Because of ridge filtering, the kernel functions separate in the horizontal and vertical directions, motivating our choice of a 2+1D inversion implementation. The inversion procedure also minimizes cross-talk effects among the three flow components, and the averaging kernels resulting from the inversion show very small amounts of cross-talk. We obtain three-dimensional maps of vector solar flows in the quiet Sun at horizontal spatial resolutions of 7?10 Mm using generally 24 hours of data. For all of the flow maps we provide averaging kernels and the noise estimates. We present examples to test the inferred flows, such as a comparison with Doppler data, in which we find a correlation of 0.9. We also present results for quiet-Sun supergranular flows at different depths in the upper convection zone. Our estimation of the vertical velocity shows good qualitative agreement with the horizontal vector flows. We also show vertical flows measured solely from f-mode travel times. In addition, we demonstrate how to directly invert for the horizontal divergence and flow vorticity. Finally we study inferred flow-map correlations at different depths and find a rapid decrease in this correlation with depth, consistent with other recent local helioseismic analyses.     

Time – Distance Modelling in a Simulated Sunspot Atmosphere

In time?–?distance helioseismology, wave travel times are measured from the cross-correlation between Doppler velocities recorded at any two locations on the solar surface. However, one of the main uncertainties associated with such measurements is how to interpret observations made in regions of strong magnetic field. Isolating the effects of the magnetic field from thermal or sound-speed perturbations has proved to be quite complex and has yet to yield reliable results when extracting travel times from the cross-correlation function. One possible way to decouple these effects is by using a 3D sunspot model based on observed surface magnetic-field profiles, with a surrounding stratified, quiet-Sun atmosphere to model the magneto-acoustic ray propagation, and analyse the resulting ray travel-time perturbations that will directly account for wave-speed variations produced by the magnetic field. These artificial travel-time perturbation profiles provide us with several related but distinct observations: i) that strong surface magnetic fields have a dual effect on helioseismic rays?–?increasing their skip distance while at the same time speeding them up considerably compared to their quiet-Sun counterparts, ii) there is a clear and significant frequency dependence of both skip-distance and travel-time perturbations across the simulated sunspot radius, iii) the negative sign and magnitude of these perturbations appears to be directly related to the sunspot magnetic-field strength and inclination, iv) by “switching off” the magnetic field inside the sunspot, we are able to completely isolate the thermal component of the travel-time perturbations observed, which is seen to be both opposite in sign and much smaller in magnitude than those measured when the magnetic field is present. These results tend to suggest that purely thermal perturbations are unlikely to be the main effect seen in travel times through sunspots, and that strong, near-surface magnetic fields may be directly and significantly altering the magnitude and lateral extent of sound-speed inversions of sunspots made by time?–?distance helioseismology.     

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 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 (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.     

Phase-sensitive Holography of Solar Activity

Phase-correlation statistics comparing acoustic radiation coming out of a particular point on the solar photosphere with acoustic radiation going into it show considerably reduced sound travel times through the subphotospheres of active regions. We have now applied techniques in phase-sensitive seismic holography to data from the Solar Oscillations Investigation – Michelson Doppler Imager (SOI-MDI) on the Solar and Heliospheric Observatory (SOHO) spacecraft to obtain high resolution phase-correlation maps of a large, complex active region and the `acoustic moat' which surrounds it. We report the following new results: First, the reduced sound travel-time perturbations in sunspots, acoustic moats, and isolated plages increase approximately in proportion to the logarithm of the surface magnetic flux density, for flux densities above 10 G. This is consistent with an interpretation of the travel-time anomalies, observed with holographic and other local-helioseismic procedures, as caused by acoustic Wilson-like depressions in photospheres of magnetic regions. Second, we find that, compared with isolated plages, the acoustic moats have an additional sound travel-time reduction on the order of 3–5 s which may be explained by a thermal excess due to the blockage of convective transport by the sunspot photosphere. Third, the combined effect of the Wilson depression in plages, acoustic moats, and sunspots may explain the observed variation of global p-mode frequencies with the solar cycle. Fourth, we find that active regions, including sunspots, acoustic moats, and plages, significantly reflect p modes above the acoustic cut-off frequency, where the surface of the quiet Sun acts as a nearly perfect absorber of incident acoustic radiation.     

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.     

Travel Time Sensitivity Kernels

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.     

The Inversion Problem of Phase Travel Time Perturbations in Acoustic Imaging

The three-dimensional distribution of change in phase travel time of an active region below the solar surface can be constructed with the technique of acoustic imaging. The interpretation of the distribution of measured phase travel time perturbation suffers from the finite spatial resolution of the acoustic lenses. In the ray approximation, the phase travel time perturbation measured in acoustic imaging can be expressed as an integral of the product of the relative sound-speed perturbation and a kernel. Forward computations show that the vertical resolution of phase travel time perturbation is poor even in the ray approximation. In this study, we discuss the inversion of phase travel time perturbations to estimate the relative sound-speed perturbation with a regularized least-squares inversion method. The tests with model perturbations of sound speed show that the inversion reasonably recovers the distribution of the model perturbation. We also apply the inversion method to the measured phase travel time perturbation of active region NOAA 7981.     

Acoustic-Power Maps of Solar Active Regions with Direction Filters and Phase-Velocity Filters

We study the properties of power maps of solar acoustic waves filtered with direction filters and phase-velocity filters. A direction filter is used to isolate acoustic waves propagating in a narrow range of directions. The acoustic-power map of the waves filtered with a direction filter shows extended reduced-power features behind magnetic regions with respect to the wave direction. A phase-velocity filter is further applied to isolate waves with similar wave paths. In the power maps of the waves filtered with both a direction filter and a phase-velocity filter, a reduced-power image of a sunspot appears behind the sunspot with respect to the wave direction. The distance between the sunspot and the secondary image is consistent with the one-skip travel distance of the wave packet associated with the phase-velocity filter. The waves filtered with direction and phase-velocity filters at the location of the secondary image could be used to probe the sunspot. In the quiet Sun, spatial fluctuations exist in any acoustic-power map. These fluctuations are mainly caused by interference among modes with the same frequency. The fluctuations are random with two properties: They change rapidly with time, and their magnitude decreases with the square root of the number of frames used in computing the acoustic-power map.     

The visibility of low‐frequency solar acoustic modes

We make predictions of the detectability of low‐frequency p modes. Estimates of the powers and damping times of these low‐frequency modes are found by extrapolating the observed powers and widths of higher‐frequency modes with large observed signal‐to‐noise ratios. The extrapolations predict that the low‐frequency modes will have small signal‐to‐noise ratios and narrow widths in a frequency‐power spectrum. Monte Carlo simulations were then performed where timeseries containing mode signals and normally distributed Gaussian noise were produced. The mode signals were simulated to have the powers and damping times predicted by the extrapolations. Various statistical tests were then performed on the frequency‐amplitude spectra formed from these timeseries to investigate the fraction of spectra in which the modes could be detected. The results of these simulations were then compared to the number of p‐modes candidates observed in real Sun‐as‐a‐star data at low frequencies. The fraction of simulated spectra in which modes were detected decreases rapidly as the frequency of modes decreases and so the fraction of simulations in which the low‐frequency modes were detected was very small. However, increasing the signal‐to‐noise (S/N) ratio of the low‐frequency modes by a factor of 2 above the extrapolated values led to significantly more detections. Therefore efforts should continue to further improve the quality of solar data that is currently available. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

多通道双折射滤光器——Ⅲ.多通道头及多通道望远镜

本文讨论多通道滤光器的第三种型式——带多通道头的滤光器。在多通道头中设置较初级的滤光级次,分出各所需要的通道,使指定的工作谱线分别通过各通道,然后分别在各通道之后配置高级次的滤光级,构成整个多通道滤光器。这一结构:1)不需要将最热敏的最厚级置于滤光器最前部,避免了温敏引起的波带位置不稳定;2)各通道可根据工作需要各自选择带宽;3)有利于在其后配置众多的Fabry-Perot和Daystar等各种单通道滤光器;4)可将天文台中现存的所有滤光器,经过多通道头组合在一起,在一个镜筒中实现同时的多通道观测。 本文还讨论了与多通道滤光器相配合的多通道太阳望远镜的一些结构特点和设计方法。     

Surface-Focused Seismic Holography of Sunspots: II. Expectations from Numerical Simulations Using Sound-Speed Perturbations

Helioseismic observations of sunspots show that wave travel times, at fixed horizontal phase speed, depend on the temporal frequency of the waves employed in the data analysis. This frequency variation has been suggested to be consistent with near-surface (vertical length scales of order one Mm or smaller) changes in wave propagation properties relative to the quiet Sun. We investigate this suggestion by employing numerical simulations of acoustic-wave propagation through models with horizontally and vertically inhomogeneous structure. Standard methods of surface-focused helioseismic holography are applied to the resulting simulated wave fields. We find that the travel-time shifts measured using holography from the simulations with deep sound-speed perturbations (relative to a plane-parallel quiet-Sun model) do not show a systematic frequency dependence at phase speeds above about 20 km s⁻¹. However, shallow sound-speed perturbations, similar to those proposed to model the acoustic scattering properties of sunspots observed with Hankel analysis, produce systematic frequency dependence at these phase speeds. In both cases, positive travel-time shifts can be caused by positive sound-speed perturbations. The details of the travel-time shifts are, however, model dependent.     

A Search for Helioseismic Signature of Emerging Active Regions

Using SOHO/MDI and GONG observations we present time–distance deep-focusing measurements to examine the deeper layers of the solar convective zone. The constructed travel-time maps show 10?–?15 second perturbations at depths of 40?–?75 Mm around active region locations before their emergence to the solar surface. The majority of the active regions used in this study were the same as those used in the recent work published by Ilonidis, Zhao, and Kosovichev (Science 333, 993, 2011). In order to confirm the capability of time–distance measurements to detect emerging active regions, we used a technique similar to their time–distance scheme. Our measurements only in some cases show a similar travel-time anomaly. Additionally, we have shown that the technique utilized in our study can provide more spatial details of the emerging flux configurations.     

Limits on isocurvature perturbations from non-Gaussianity in WMAP temperature anisotropy

We study the effect of primordial isocurvature perturbations on non-Gaussian properties of cosmic microwave background (CMB) temperature anisotropies. We consider generic forms of the non-linearity of isocurvature perturbations which can be applied to a wide range of theoretical models. We derive analytical expressions for the bispectrum and the Minkowski Functionals for CMB temperature fluctuations to describe the non-Gaussianity from isocurvature perturbations. We find that the isocurvature non-Gaussianity in the quadratic isocurvature model, where the isocurvature perturbation S is written as a quadratic function of the Gaussian variable  σ,  S =σ²−〈σ²〉  , can give the same signal-to-noise ratio as   f _NL= 30  even if we impose the current observational limit on the fraction of isocurvature perturbations contained in the primordial power spectrum α. We give constraints on isocurvature non-Gaussianity from Minkowski Functionals using the Wilkinson Microwave Anisotropy Probe ( WMAP ) 5-year data. We do not find a significant signal of isocurvature non-Gaussianity. For the quadratic isocurvature model, we obtain a stringent upper limit on the isocurvature fraction  α < 0.070  (95 per cent CL) for a scale-invariant spectrum which is comparable to the limit obtained from the power spectrum.     

asmooth: a simple and efficient algorithm for adaptive kernel smoothing of two-dimensional imaging data

An efficient algorithm for adaptive kernel smoothing (AKS) of two-dimensional imaging data has been developed and implemented using the Interactive Data Language ( idl ). The functional form of the kernel can be varied (top-hat, Gaussian, etc.) to allow different weighting of the event counts registered within the smoothing region. For each individual pixel, the algorithm increases the smoothing scale until the signal-to-noise ratio (S/N) within the kernel reaches a pre-set value. Thus, noise is suppressed very efficiently, while at the same time real structure, that is, signal that is locally significant at the selected S/N level, is preserved on all scales. In particular, extended features in noise-dominated regions are visually enhanced. The asmooth algorithm differs from other AKS routines in that it allows a quantitative assessment of the goodness of the local signal estimation by producing adaptively smoothed images in which all pixel values share the same S/N above the background .
We apply asmooth to both real observational data (an X-ray image of clusters of galaxies obtained with the Chandra X-ray Observatory) and to a simulated data set. We find the asmooth ed images to be fair representations of the input data in the sense that the residuals are consistent with pure noise, that is, they possess Poissonian variance and a near-Gaussian distribution around a mean of zero, and are spatially uncorrelated.     

High-resolution imaging of the cosmic mass distribution from gravitational lensing of pre-galactic H i

Low-frequency radio observations of neutral hydrogen during and before the epoch of cosmic re-ionization will provide ∼1000 quasi-independent source planes, each of precisely known redshift, if a resolution of ∼1 arcmin or better can be attained. These planes can be used to reconstruct the projected mass distribution of foreground material. Structure in these source planes is linear and Gaussian at high redshift  (30 < z < 300)  but is non-linear and non-Gaussian during re-ionization. At both epochs, significant power is expected down to subarcsecond scales. We demonstrate that this structure can, in principle, be used to make mass images with a formal signal-to-noise ratio (S/N) per pixel exceeding 10, even for pixels as small as an arcsecond. With an ideal telescope, both resolution and S/N can exceed those of even the most optimistic idealized mass maps from galaxy lensing by more than an order of magnitude. Individual dark haloes similar in mass to that of the Milky Way could be imaged with high S/N out to   z ∼ 10  . Even with a much less ambitious telescope, a wide-area survey of 21-cm lensing would provide very sensitive constraints on cosmological parameters, in particular on dark energy. These are up to 20 times tighter than the constraints obtainable from comparably sized, very deep surveys of galaxy lensing, although the best constraints come from combining data of the two types. Any radio telescope capable of mapping the 21-cm brightness temperature with good frequency resolution (∼0.05 MHz) over a band of width ≳10 MHz should be able to make mass maps of high quality. The planned Square Kilometre Array may be able to map the mass with moderate S/N down to arcminute scales, depending on the re-ionization history of the universe and the ability to subtract foreground sources.