Meridional flow is thought to play a very important role in the dynamics of the solar convection zone; however, because of its relatively small amplitude, precisely measuring it poses a significant challenge. Here we present a complete time-distance helioseismic analysis of about two years of ground-based GONG Doppler data to retrieve the meridional circulation profile for modest latitudes, in an attempt to corroborate results from other studies. We use an empirical correction to the travel times due to an unknown center-to-limb systematic effect. The helioseismic inversion procedure is first tested and reasonably validated on artificial data from a large-scale numerical simulation, followed by a test to broadly recover the solar differential rotation found from global seismology.
From GONG data, we measure poleward photospheric flows at all latitudes with properties that are comparable with earlier studies, and a shallow equatorward flow about $65$\,Mm beneath the surface, in agreement with recent findings from HMI data. No strong evidence of multiple circulation cells in depth nor latitude is found, yet the whole phase space has not yet been explored. Tests of mass flux conservation are then carried out on the inferred GONG and HMI flows and compared to a fiducial numerical baseline from models, and we find that the continuity equation is poorly satisfied.
While the two disparate data sets do give similar results for about the outer $15\%$ of the interior radius, the total inverted circulation pattern appears to be unphysical in terms of mass conservation when interpreted over modest time scales. We can likely attribute this to both the influence of realization noise and subtle effects in the data and measurement procedure.
We present an analysis of the variability of the solar oscillation spectrum during solar cycle 23 and its extended minimum. We use simultaneous observations of the low-degree solar p modes collected by the space-based, Sun-as-a-star GOLF (radial velocity) and VIRGO (intensity) instruments, and by the ground-based, multi-site network GONG. We investigate in particular the response of the p-mode eigenfrequencies to the observed peculiar deep solar minimum of surface activity of 2007-2009 as compared with the previous solar cycle 23. We study the different temporal variations of the p-mode freque…
We present and discuss results from time-distance helioseismic measurements of meridional circulation in the solar convection zone using 4 years of Doppler velocity observations by the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO). Using an in-built mass conservation constraint in terms of the stream function we invert helioseismic travel times to infer meridional circulation in the solar convection zone. We find that the return flow that closes the meridional circulation is possibly beneath the depth of $0.77 R_{\odot}$. We discuss the significance of thi…
Large-scale plasma flows in the Sun's convection zone likely play a major role in solar dynamics on decadal timescales. In particular, quantifying meridional motions is a critical ingredient for understanding the solar cycle and the transport of magnetic flux. Because the signal of such features can be quite small in deep solar layers and be buried in systematics or noise, the true meridional velocity profile has remained elusive. We perform time-distance helioseismology measurements on several years worth of GONG Doppler data. A spherical harmonic decomposition technique is applied to a subse…
The meridional flow in the Sun is an axisymmetric flow that is generally poleward directed at the surface, and is presumed to be of fundamental importance in the generation and transport of magnetic fields. Its true shape and strength, however, is debated. We present a numerical simulation of helioseismic wave propagation in the whole solar interior in the presence of a prescribed, stationary, single-cell, deep meridional circulation serving as a test-bed for helioseismic measurement techniques. A deep-focusing time-distance helioseismology technique is applied to the artificial data showing t…
We report on a systematic center-to-limb variation in measured helioseismic travel times, which must be taken into account for an accurate determination of solar interior meridional flows. The systematic variation, found in time-distance helioseismology analysis using SDO/HMI and SDO/AIA observations, is different in both travel-time magnitude and variation trend for different observables. It is not clear what causes this systematic effect. Subtracting the longitude-dependent east-west travel times, obtained along the equatorial area, from the latitude-dependent north-south travel times, obtai…
Steady meridional flow makes no first-order perturbation to the frequencies of helioseismic normal modes. It does, however, Doppler shift the local wavenumber, thereby distorting the eigenfunctions. For high-degree modes, whose peaks in a power spectrum are blended into continuous ridges, the effect of the distortion is to shift the locations of those ridges. From this blended superposition of modes, one can isolate oppositely directed wave components with the same local horizontal wavenumber and measure a frequency difference which can be safely used to infer the subsurface background flow. B…
Measuring the Sun's internal meridional flow is one of the key issues of helioseismology. Using the Fourier-Legendre analysis is a technique for addressing this problem. We validate this technique with the help of artificial helioseismic data. The analysed data set was obtained by numerically simulating the effect of the meridional flow on the seismic wave field in the full volume of the Sun. In this way, a 51.2-hour long time series was generated. The resulting surface velocity field is then analyzed in various settings: Two $360^\circ \times 90^\circ$ halfspheres, two $120^\circ \times 60^\c…
Using a 3D global solver of the linearized Euler equations, we model acoustic oscillations over background velocity flow fields of single-cell meridional circulation with deep and shallow return flows as well as double-cell meridional circulation with strong and weak reversals. The velocities are generated using a mean-field hydrodynamic and dynamo model -- moving through the regimes with minimal parameter changes; counter-rotation near the base of the tachocline is induced by sign inversion of the non-diffusive action of turbulent Reynolds stresses ($Λ$-effect) due to the radial inhomogeneity…
We use a novel global helioseismic analysis method to infer the meridional flow in the deep Solar interior. The method is based on the perturbation of eigenfunctions of Solar p modes due to meridional flow. We apply this method to time series obtained from Dopplergrams measured by the Michelson Doppler Imager aboard the Solar and Heliospheric Observatory (SOHO) covering the observation period 2004-2010. Our results show evidence that the meridional flow reaches down to the base of the convection zone. The flow profile has a complex spatial structure consisting of multiple flow cells distribute…
Oscillatory Phase and Acoustic Travel-Time Inconsistencies Measured between SDO/HMI and GONG Dopplergrams
Stanford University（斯坦福大学）；Indian Institute of Astrophysics（印度天体物理研究所）；National Solar Observatory（国家太阳观测台）；National Research University TIIAME（塔什干国立研究技术大学）
Accurate inference of solar meridional flow is of crucial importance for the understanding of solar dynamo process. Wave travel times, as measured on the surface, will change if the waves encounter perturbations e.g. in the sound speed or flows, as they propagate through the solar interior. Using functions called sensitivity kernels, we may image the underlying anomalies that cause measured shifts in travel times. The inference of large-scale structures e.g meridional circulation requires computing sensitivity kernels in spherical geometry. Mandal et al. (2017) have computed such spherical ker…
The form of the solar meridional circulation is a very important ingredient for mean field flux transport dynamo models. Yet a shroud of mystery still surrounds this large-scale flow, given that its measurement using current helioseismic techniques is challenging. In this work we use results from 3D global simulations of solar convection to infer the dynamical behavior of the established meridional circulation. We make a direct comparison between the meridional circulation that arises in these simulations and the latest observations. Based on our results we argue that there should be an equato…
Global hydrodynamic simulations of internal solar dynamics have focused on replicating the conditions for solar-like differential rotation and meridional circulation using the results of helioseismic inversions as a constraint. Inferences of meridional circulation, however, have provided controversial results showing the possibility of one, two, or multiple cells along the radius. To resolve this controversy and develop a more robust understanding of global flow regimes in the solar interior, we apply a "forward-modeling" approach to the analysis of helioseismic signatures of meridional circul…
A key component of solar interior dynamics is the meridional circulation (MC), whose poleward component in the surface layers has been well observed. Time-distance helioseismic studies of the deep structure of MC, however, have yielded conflicting inferences. Here, following a summary of existing results we show how a large center-to-limb systematics (CLS) in the measured travel times of acoustic waves affect the inferences through an analysis of frequency dependence of CLS, using data from the Helioseismic and Doppler Imager (HMI) onboard Solar Dynamics Observatory (SDO). Our results point to…
The Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO) provides a new tool for the systematic observation of white-light flares, including Doppler and magnetic information as well as continuum. In our initial analysis of the highly impulsive γ-ray flare SOL2010-06-12T00:57 (Mart'ınez Oliveros et al., Solar Phys., 269, 269, 2011), we reported the signature of a strong blueshift in the two footpoint sources. Concerned that this might be an artifact due to aliasing peculiar to the HMI instrument, we undertook a comparative analysis of Global Oscillations Network G…
We apply the helioseismic methodology of Legendre Function Decomposition to 88 months of Dopplergrams obtained by the Helioseismic and Magnetic Imager (HMI) as the basis of inferring the depth variation of the mean meridional flow, as averaged between 20 and 60 degrees latitude and in time, in both the northern and southern hemispheres. We develop and apply control procedures designed to assess and remove center-to-limb artifacts, using measurements obtained by performing the analysis with respect to artificial poles at the east and west limbs. Forward modeling is carried out, using sensitivit…
The south-north travel-time differences are measured by applying time-distance helioseismology to the MDI and HMI medium-degree Dopplergrams covering May 1996-April 2017. Our data analysis corrects for several sources of systematic effects: P-angle error, surface magnetic field effects, and center-to-limb variations. An interpretation of the travel-time measurements is obtained using a forward-modeling approach in the ray approximation. The travel-time differences are similar in the southern hemisphere for cycles 23 and 24. However, they differ in the northern hemisphere between cycles 23 and …
Today's picture of the internal solar rotation rate profile results essentially from helioseismic analyses of frequency splittings of resonant acoustic waves. Here we present another, complementary estimation of the internal solar rotation rate using the perturbation of the shape of the acoustic waves. For this purpose, we extend a global helioseismic approach developed previously for the investigation of the meridional flow \cite{schad11, schad12, schad13} to work on the components of the differential rotation. We discuss the effect of rotation on mode eigenfunctions and thereon based observa…
Mean-field hydrodynamics advanced to clear explanations for the origin and properties of the global meridional flow in stellar convection zones. Qualitative arguments and analysis of basic equations both show that the meridional circulation is driven by non-conservative centrifugal and buoyancy forces and results from a slight disbalance between these two drivers. The deviations from the thermal wind balance are relatively large near the boundaries of convection zones. Accordingly, the meridional flow attains its largest velocities in the boundary layers and decreases inside the convection zon…
The main object of the paper is to present the condition of the non-diffusive part of the Reynolds stress for driving the double-cell structure of the solar meridional circulation, which has been revealed by recent helioseismic observations. By conducting a set of mean-field hydrodynamic simulations, we confirm for the first time that the double-cell meridional circulation can be achieved along with the solar-like differential rotation when the Reynolds stress transports the angular momentum upward in the lower part and downward in the upper part of the convection zone. It is concluded that, i…
Meridional flow in the solar interior plays an important role in redistributing angular momentum and transporting magnetic flux inside the Sun. Although it has long been recognized that the meridional flow is predominantly poleward at the Sun's surface and in its shallow interior, the location of the equatorward return flow and the meridional flow profile in the deeper interior remain unclear. Using the first two years of continuous helioseismology observations from the Solar Dynamics Observatory / Helioseismic Magnetic Imager, we analyze travel times of acoustic waves that propagate through d…
Helioseismology provides important constraints for the solar dynamo problem. However, the basic properties and even the depth of the dynamo process, which operates also in other stars, are unknown. Most of the dynamo models suggest that the toroidal magnetic field that emerges on the surface and forms sunspots is generated near the bottom of the convection zone, in the tachocline. However, there is a number of theoretical and observational problems with justifying the deep-seated dynamo models. This leads to the idea that the subsurface angular velocity shear may play an important role in the …
Fourier-Legendre decomposition (FLD) of solar Doppler imaging data is a promising method to estimate the sub-surface solar meridional flow. FLD is sensible to low-degree oscillation modes and thus has the potential to probe the deep meridional flow. We present a newly developed code to be used for large scale FLD analysis of helioseismic data as provided by the Global Oscillation Network Group (GONG), the Michelson Doppler Imager (MDI) instrument, and the upcoming Helioseismic and Magnetic Imager (HMI) instrument. First results obtained with the new code are qualitatively comparable to those o…
The solar-activity-cycle minimum observed between Cycles 23 and 24 is generally regarded as being unusually deep and long. That minimum is being followed by one of the smallest amplitude cycles in recent history. We perform an in-depth analysis of this minimum with helioseismology. We use Global Oscillation Network Group (GONG) data to demonstrate that the frequencies of helioseismic oscillations are a sensitive probe of the Sun's magnetic field: The frequencies of the helioseismic oscillations were found to be systematically lower in the minimum following Cycle 23 than in the minimum precedin…
We investigate the behavior of the intermediate-degree mode frequencies of the sun during the current extended minimum phase to explore the time-varying conditions in the solar interior. Using contemporaneous helioseismic data from GONG and MDI, we find that the changes in resonant mode frequencies during the activity minimum period are significantly greater than the changes in solar activity as measured by different proxies. We detect a seismic minimum in MDI p-mode frequency shifts during 2008 July--August but no such signature is seen in mean shifts computed from GONG frequencies. We also a…
Solar sub-surface fluid topology provides an indirect approach to examine the internal characteristics of active regions (ARs). Earlier studies have revealed the prevalence of strong flows in the interior of ARs having complex magnetic fields. Using the Doppler data obtained by the Global Oscillation Network Group (GONG) project for a sample of 74 ARs, we have discovered the presence of steep gradients in meridional velocity at depths ranging from 1.5 to 5 Mm in flare productive ARs. The sample of these ARs is taken from the Carrington rotations 1980--2052 covering the period August 2001-Janua…
We present a 3-dimensional (3D) numerical solver of the linearized compressible Euler equations (GALE -- Global Acoustic Linearized Euler), used to model acoustic oscillations throughout the solar interior. The governing equations are solved in conservation form on a fully global spherical mesh ($0 \le ϕ\le 2π$, $0 \le θ\le π$, $0 \le r \le R_{\odot}$) over a background state generated by the standard Solar Model S. We implement an efficient pseudo-spectral computational method to calculate the contribution of the compressible material derivative dyad to internal velocity perturbations, comput…
We studied the effect of the perturbation of the meridional flow in the activity belts detected by local helioseismology on the development and strength of the surface magnetic field at the polar caps. We carried out simulations of synthetic solar cycles with a flux transport model, which follows the cyclic evolution of the surface field determined by flux emergence and advective transport by near-surface flows. In each hemisphere, an axisymmetric band of latitudinal flows converging towards the central latitude of the activity belt was superposed onto the background poleward meridional flow. …
Helioseismic inferences of large-scale flows in the solar interior necessitate accounting for the curvature of the Sun, both in interpreting systematic trends introduced in measurements as well as the sensitivity kernel that relates photospheric measurements to subsurface flow velocities. Additionally the inverse problem that relates measurements to model parameters needs to be well-posed to obtain accurate inferences, which necessitates a sparse set of parameters. Further, the sensitivity functions need to be computationally easy to evaluate. In this work we address these issues by demonstrat…
Context. In local helioseismology, the travel times of acoustic waves propagating in opposite directions along the same meridian inform us about horizontal flows in the north-south direction. The longitudinal averages of the north-south helioseismic travel-time shifts vary with the sunspot cycle. Aims. We aim to study the contribution of inflows into solar active regions to this solar-cycle variation. Methods. To do so, we identify the local flows around active regions in the horizontal flow maps obtained from correlation tracking of granulation in SDO/HMI continuum images. We compute the forw…
The results of determinations of the azimuthal and meridional velocities by time-distance helioseismology from Helioseismic and Magnetic Imager (HMI) onboard Solar Dynamics Observatory (SDO) from May 2010 to September 2020 at latitudes from -60° to +60° and depths to about 19 Mm below the photosphere are used to analyze spatiotemporal variations of the solar differential rotation and meridional circulation. The pattern of torsional oscillations, or latitudinal belts of alternating `fast' and `slow' zonal flows migrating from high latitudes towards the equator, is found to extend in the time--l…
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, Carring…
The frequency, $ν_{\rm max}$, at which the envelope of pulsation power peaks for solar-like oscillators is an important quantity in asteroseismology. We measure $ν_{\rm max}$ for the Sun using 25 years of Sun-as-a-Star Doppler velocity observations with the Birmingham Solar-Oscillations Network (BiSON), by fitting a simple model to binned power spectra of the data. We also apply the fit to Sun-as-a-Star Doppler velocity data from GONG and GOLF, and photometry data from VIRGO/SPM on the ESA/NASA SOHO spacecraft. We discover a weak but nevertheless significant positive correlation of the solar $…
The meridional circulation at high latitudes is crucial to the build-up and reversal of the Sun's polar magnetic fields. Here we characterize the axisymmetric flows by applying a magnetic feature cross-correlation procedure to high resolution magnetograms obtained by the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO). We focus on Carrington Rotations 2096-2107 (April 2010 to March 2011) - the overlap interval between HMI and the Michelson Doppler Investigation (MDI). HMI magnetograms averaged over 720 seconds are first mapped into heliographic coordinates. …
Helioseismic waves observable at the solar surface can be used to probe the properties of the Sun's interior. By measuring helioseismic travel times between different location on the surface, flows and other interior properties can be inferred using so-called sensitivity kernels which relate the amount of travel-time shift with variations in interior proporties. In particular, sensitivity kernels for flows have been developed in the past, using either ray or Born approximation, and have been used to infer solar interior flows such as the meridional circulation which is of particular interest f…
Meridional circulation is a crucial component of the Sun's internal dynamics, but its inference in the deep interior is complicated by a systematic center-to-limb effect in helioseismic measurement techniques. Previously, an empirical method, removing travel-time shifts measured for east-west traveling waves in the equatorial area from those measured for north-south traveling waves in the central meridian area, was used, but its validity and accuracy need to be assessed. Here we develop a new method to separate the center-to-limb effect, δτ_CtoL, and meridional-flow-induced travel-time shifts,…
We studied the solar surface flows (differential rotation and meridional circulation) using a magnetic element feature tracking technique by which the surface velocity is obtained using magnetic field data. We used the line-of-sight magnetograms obtained by the Helioseismic and Magnetic Imager aboard the Solar Dynamics Observatory from 01 May 2010 to 16 August 2017 (Carrington rotations 2096 to 2193) and tracked the magnetic element features every hour. Using our method, we estimated the differential rotation velocity profile. We found rotation velocities of $\sim$ 30 and -170 m s$^{-1}$ at la…
The solar cycle onset at mid-latitudes, the slow down of the sunspot drift toward the equator, the tail-like attachment and the overlap of successive cycles at the time of activity minimum are delicate issues in $αΩ$ dynamo wave and flux transport dynamo models. Very different parameter values produce similar results, making it difficult to understand the origin of these solar cycle properties. We use GONG helioseismic data to investigate the progression of the solar cycle as observed in intermediate-degree global $p$-mode frequency shifts at different latitudes and subsurface layers, from the…
We looked for signatures of Quasi-Biennial Periodicity (QBP) over different phases of solar cycle by means of acoustic modes of oscillation. Low-degree p-mode frequencies are shown to be sensitive to changes in magnetic activity due to the global dynamo. Recently have been reported evidences in favor of two-year variations in p-mode frequencies. Long high-quality helioseismic data are provided by BiSON (Birmingham Solar Oscillation Network), GONG (Global Oscillation Network Group), GOLF (Global Oscillation at Low Frequency) and VIRGO (Variability of Solar IRradiance and Gravity Oscillation) in…
The solar meridional flow is a crucial ingredient in modern dynamo theory. Seismic estimates of this flow have, however, been contradictory in deeper layers below about $0.9\,R_\odot$. Results from time-distance helioseismology have so far been obtained using the ray approximation. Here, we perform inversions using the Born approximation. The initial result is similar to the result previously obtained by Jackiewicz et al. (2015) using ray kernels while using the same set of GONG data and the SOLA inversion technique. However, we show that the assumption of uncorrelated measurements used in ear…
The solar-cyle variation of acoustic mode frequencies has a frequency dependence related to the inverse mode inertia. The discrepancy between model predictions and measured oscillation frequencies for solar and solar-type stellar acoustic modes includes a significant frequency-dependent term known as the surface term that is also related to the inverse mode inertia. We parametrize both the surface term and the frequency variations for low-degree solar data from Birmingham Solar-Oscillations Network (BiSON) and medium-degree data from the Global Oscillations Network Group (GONG) using the mode …
We present an adaptation of the rotation-corrected, m-averaged spectrum technique designed to observe low signal-to-noise-ratio, low-frequency solar p modes. The frequency shift of each of the 2l+1 m spectra of a given (n,l) multiplet is chosen that maximizes the likelihood of the m-averaged spectrum. A high signal-to-noise ratio can result from combining individual low signal-to-noise-ratio, individual-m spectra, none of which would yield a strong enough peak to measure. We apply the technique to GONG and MDI data and show that it allows us to measure modes with lower frequencies than those o…
We have calculated the effects of large scale solar flows like the meridional circulation, giant convection cells and solar rotation on the helioseismic splitting coefficients using quasi-degenerate perturbation theory (QDPT). Our investigation reveals that the effect of poloidal flows like the large scale meridional circulation are difficult to detect in observational data of the global acoustic modes since the frequency shifts are much less than the errors. However, signatures of large scale convective flows may be detected if their amplitude is sufficiently large by looking for frequency sh…
The Sun supports a rich spectrum of internal waves that are continuously excited by turbulent convection. The GONG network and the MDI/SOHO space instrument provide an exceptional data base of spatially-resolved observations of solar oscillations, covering an entire sunspot cycle (11 years). Local helioseismology is a set of tools for probing the solar interior in three dimensions using measurements of wave travel times and local mode frequencies. Local helioseismology has discovered (i) near-surface vector flows associated with convection (ii) 250 m/s subsurface horizontal outflows around sun…
Gravity modes in the Sun have been the object of a long and difficult search in recent decades. Thanks to the data accumulated with the last generation of instruments (BiSON, GONG and three helioseismic instruments aboard SoHO), scientists have been able to find signatures of their presence. However, the individual detection of such modes remains evasive. In this article, we study the signal at 220.7 microHz which is a peak that is present in most of the helioseismic data of the last 10 years. This signal has already been identified as being one component of a g-mode candidate detected in the …
Helioseismic observations have provided valuable datasets with which to pursue the detailed investigation of solar interior dynamics. Among various methods to analyse these data, normal-mode coupling has proven to be a powerful tool, used to study Rossby waves, differential rotation, meridional circulation, and non-axisymmetric multi-scale subsurface flows. Here, we invert mode-coupling measurements from Helioseismic Magnetic Imager (HMI) and Michelson Doppler Imager (MDI) to obtain mass-conserving toroidal convective flow as a function of depth, spatial wavenumber, and temporal frequency. To …
Near-surface flows measured by the ring-diagram technique of local helioseismology show structures that persist over multiple rotations. We examine these phenomena using data from the {\em Global Oscillation Network Group} (GONG) and the {\em Helioseismic and Magnetic Imager} (HMI) and show that a correlation analysis of the structures can be used to estimate the rotation rate as a function of latitude, giving a result consistent with the near-surface rate from global helioseismology and slightly slower than that obtained from a similar analysis of the surface magnetic field strength. At latit…
Large scale flows in the Sun play an important role in the dynamo process linked to the solar cycle. The important large scale flows are the differential rotation and the meridional circulation with an amplitude of km/s and few m/s , respectively. These flows also have a cycle related components, namely the torsional oscillations. Our attempt is to determine large-scale plasma flows on the solar surface by deriving horizontal flow velocities using the techniques of solar granule tracking, dopplergrams, and time distance helioseismology. Coherent structure tracking (CST) and time distance helio…
