Helioseismic Data Research Articles

Investigating the correlation between high-frequency global oscillations and solar flares

Global oscillations have been observed in the high-frequency spectrum in velocity and intensity measurements above the acoustic cutoff frequency of the solar atmosphere. In a recent work, strong correlation at high frequencies, determined between helioseismic spectra and soft x-ray flux has been cited as evidence that solar flares may be one of the mechanisms whereby these high-frequency oscillations are excited. We investigate the possible dependencies of the correlation coefficient, computed for helioseismic and soft x-ray data, on the pre-processing and data analysis, and the instruments used for data acquisition.

Internal magnetic fields inferred from helioseismic data

AbstractMeasuring the internal solar magnetic fields and how they change over the course of a solar cycle is one of the key aims of helioseismology. We present the results of attempts to model the global mode splitting coefficients over solar cycle 23, assuming that the frequency splitting is only due to rotation and a large‐scale magnetic field. The first results using only the a2 coefficients show that the data are best fit by a combination of a poloidal field and a double‐peaked near‐surface toroidal field. The toroidal fields are centered at r0 = 0.999 R⊙ and r0 = 0.996 R⊙ and are confined to the near‐surface layers. The poloidal field is a dipole field. The peak strength of the poloidal field is 124 ± 17 G. The toroidal field peaks at 380 ± 30 G and 1.4 ± 0.2 kG for the shallower and deeper fields, respectively. The field strengths are highly correlated with surface activity. We also examine the differences between the minima at the beginning and the end of solar cycle 23 (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A new code for Fourier‐Legendre analysis of large datasets: First results and a comparison with ring‐diagram analysis

AbstractFourier‐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 obtained from ring‐diagram analyis of the same time series (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

INFLUENCE OF ACOUSTIC SOURCE DENSITY ON CROSS-CORRELATED SIGNALS: IMPLICATIONS FOR AMPLITUDE-BASED TOMOGRAPHY IN HELIOSEISMOLOGY

We present new results from the numerical simulations of cross-correlated helioseismic data in a two-dimensional quiet non-magnetic solar subphotosphere for studying the effects of spatiotemporal density of solar acoustic sources on signal quality. Although the signal-to-noise level of helioseismic signals can be improved by data averaging, our results show that there exists a threshold above which this change in data quality is largely independent of the density of the acoustic sources. We also demonstrate that if the source density is below this threshold, significant data artifacts may arise depending on the source location relative to the two observation points at which cross-correlation is performed. Our numerical results therefore show that the density of the acoustic sources is a key, previously unidentified parameter that influences the quality and amplitude of cross-correlated helioseismic signals. We conclude that the identification of this source parameter is important for developing helioseismic tomography beyond travel-time-based methods, namely by modeling amplitudes.

CONSTRAINTS ON THE OPACITY PROFILE OF THE SUN FROM HELIOSEISMIC OBSERVABLES AND SOLAR NEUTRINO FLUX MEASUREMENTS

Motivated by the solar composition problem and by using the recently developed Linear Solar Model approach, we analyze the role of opacity and metals in the sun. After a brief discussion of the relation between the effects produced by a variation of composition and those produced by a modification of the radiative opacity, we calculate numerically the opacity kernels that, in a linear approximation, relate an arbitrary opacity variation to the corresponding modification of the solar observable properties. We use these opacity kernels to discuss the present constraints on opacity (and composition) provided by helioseismic and solar neutrino data.

SOLAR ROTATION RATE DURING THE CYCLE 24 MINIMUM IN ACTIVITY

The minimum of solar cycle 24 is significantly different from most other minima in terms of its duration as well as its abnormally low levels of activity. Using available helioseismic data that cover epochs from the minimum of cycle 23 to now, we study the differences in the nature of the solar rotation between the minima of cycles 23 and 24. We find that there are significant differences between the rotation rates during the two minima. There are differences in the zonal-flow pattern too. We find that the band of fast rotating region close to the equator bifurcated around 2005 and recombined by 2008. This behavior is different from that during the cycle 23 minimum. By auto-correlating the zonal-flow pattern with a time shift, we find that in terms of solar dynamics, solar cycle 23 lasted for a period of 11.7 years, consistent with the result of Howe et al. (2009). The autocorrelation coefficient also confirms that the zonal-flow pattern penetrates through the convection zone.

Helioseismic probing of the subsurface structure of sunspots

AbstractWe discuss recent progress in the helioseismic probing of the subsurface structure of solar magnetic regions. To simulate the interaction of helioseismic waves with magnetic fields and thermal perturbations we use a simple model that is translation invariant in the horizontal directions, has a realistic stratification in the vertical direction, and has physically consistent boundary conditions for the waves at the upper and lower boundaries of the computational domain. Using this model we generate synthetic helioseismic data and subsequently measure time-distance travel times. We evaluate a model for the wave-speed perturbation below sunspots that replaces the sound speed in a non-magnetic model by the fast-mode speed from a magnetic model; our results indicate that this approach is unlikely to be useful in modeling wave-speed perturbations in sunspots. We develop and test an inversion algorithm for inferring the sound-speed perturbation in magnetic regions. We show that this algorithm retrieves the correct sound-speed perturbation only when the sensitivity kernels employed account for the effects of the magnetic field on the waves and the subsurface structure.

UNUSUAL TRENDS IN SOLAR P -MODE FREQUENCIES DURING THE CURRENT EXTENDED MINIMUM

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 analyze the frequencies of individual oscillation modes from GONG data as a function of latitude and observe a signature of the onset of the solar cycle 24 in early 2009. Thus the intermediate degree modes do not confirm the onset of the cycle 24 during late 2007 as reported from the analysis of the low-degree GOLF frequencies. Further, both the GONG and MDI frequencies show a surprising anti-correlation between frequencies and activity proxies during the current minimum, in contrast to the behavior during the minimum between cycles 22 and 23.

Helioseismic Network Provides Valuable Data

[1] I read with interest the editorial in Space Weather entitled “The need for long-term solar-terrestrial data series” (7, S05006, doi:10.1029/2009SW000496). As discussed in the editorial, it can be difficult to convince funding agencies of the value of long-term observational programs with consistent instrumentation over decades. I would like to point out that one such program, the Global Oscillation Network Group (GONG), which operates a set of six sites around the world to obtain helioseismic data of the Sun's interior, has been providing solar data since 1995. GONG has achieved an average 24-hour observing fraction of 85–90% since its beginning. Continual solar magnetic field measurements are also being provided by GONG, and data on the hydrogen alpha emission line will be provided to the U.S. Air Force starting in summer of 2010.

Helioseismology as a diagnostic of the solar interior

Helioseismology has given us a unique window into the solar interior. Helioseismic data have enabled us to study the internal structure and dynamics with unprecedented detail. This has also allowed us to use the Sun as a laboratory to study the basic properties of stellar matter. We describe how helioseismology is used to determine solar structure and what we have learned about the Sun so far. We also describe how knowledge of the solar structure can be used to constrain the physics inputs.

SEISMIC DETECTION OF SOLAR MESOGRANULAR-SCALE FLOW

Helioseismic correlation data computed from the Solar and Heliospheric Observatory/Michelson Doppler Imager high-resolution Doppler images were inverted for solar flows of horizontal scale between 5 and 45 Mm. The photospheric Doppler velocity inferred from the inversions was compared with the original Doppler images at each scale. For horizontal scales greater than about 15 Mm, the seismically inferred and directly observed flow maps look similar, as has been seen in studies of supergranular flow. At smaller scales, the similarity disappears, but regression analysis reveals significant correlation between the maps, demonstrating that solar p- and f-mode oscillations contain useful information about these flows. The slope of the computed regression plots is close to unity, indicating that mesogranular-scale flows extend at least a megameter below the photosphere.

ON THE SOLAR ORIGIN OF THE SIGNAL AT 220.7 μHz: A POSSIBLE COMPONENT OF A g -MODE?

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 the Solar and Heliospheric Observatory (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 μHz 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 a component of a g-mode candidate detected in the GOLF Doppler velocity signal. The nature of this peak is studied in particular using the VIRGO/SPM instrument aboard SOHO. First we analyze all the available instrumental data of VIRGO and SOHO (housekeeping) to reject any possible instrumental origin. No relation was found, implying that the signal has a solar origin. Using Monte Carlo simulations, we find, with more than 99% confidence level, that the signal found in VIRGO/SPM is very unlikely to be due to pure noise.

Definitive Sun-as-a-star p-mode frequencies: 23 years of BiSON observations

Abstract We present a list of ‘best possible’ estimates of low-degree p-mode frequencies from 8640 days of observations made by the Birmingham Solar-Oscillations Network (BiSON). This is the longest stretch of helioseismic data ever used for this purpose, giving exquisite precision in the estimated frequencies. Every effort has been made in the analysis to ensure that the frequency estimates are also accurate. In addition to presenting the raw best-fitting frequencies from our ‘peak-bagging’ analysis, we also provide tables of corrected frequencies pertinent to the quiet-Sun and an intermediate level of solar activity.

HELIOSEISMIC DATA INCLUSION IN SOLAR DYNAMO MODELS

An essential ingredient in kinematic dynamo models of the solar cycle is the internal velocity field within the simulation domain—the solar convection zone (SCZ). In the last decade or so, the field of helioseismology has revolutionized our understanding of this velocity field. In particular, the internal differential rotation of the Sun is now fairly well constrained by helioseismic observations almost throughout the SCZ. Helioseismology also gives us some information about the depth dependence of the meridional circulation in the near-surface layers of the Sun. The typical velocity inputs used in solar dynamo models, however, continue to be an analytic fit to the observed differential rotation profile and a theoretically constructed meridional circulation profile that is made to match the flow speed only at the solar surface. Here, we take the first steps toward the use of more accurate velocity fields in solar dynamo models by presenting methodologies for constructing differential rotation and meridional circulation profiles that more closely conform to the best observational constraints currently available. We also present kinematic dynamo simulations driven by direct helioseismic measurements for the rotation and four plausible profiles for the internal meridional circulation—all of which are made to match the helioseismically inferred near-surface depth dependence, but whose magnitudes are made to vary. We discuss how the results from these dynamo simulations compare with those that are driven by purely analytic fits to the velocity field. Our results and analysis indicate that the latitudinal shear in the rotation in the bulk of the SCZ plays a more important role, than either the tachocline or surface radial shear, in the induction of the toroidal field. We also find that it is the speed of the equatorward counterflow in the meridional circulation right at the base of the SCZ, and not how far into the radiative interior it penetrates, that primarily determines the dynamo cycle period. Improved helioseismic constraints are expected to be available from future space missions such as the Solar Dynamics Observatory and through analysis of more long-term continuous data sets from ground-based instruments such as the Global Oscillation Network Group. Our analysis lays the basis for the assimilation of these helioseismic data within dynamo models to make future solar cycle simulations more realistic.

MEASUREMENTS OF ABSORPTION, EMISSIVITY REDUCTION, AND LOCAL SUPPRESSION OF SOLAR ACOUSTIC WAVES IN SUNSPOTS

The power of solar acoustic waves in magnetic regions is lower relative to the quiet Sun. Absorption, emissivity reduction, and local suppression of acoustic waves contribute to the observed power reduction in magnetic regions. We propose a model for the energy budget of acoustic waves propagating through a sunspot in terms of the coefficients of absorption, emissivity reduction, and local suppression of the sunspot. Using the property that the waves emitted along the wave path between two points have no correlation with the signal at the starting point, we can separate the effects of these three mechanisms. Applying this method to helioseismic data filtered with direction and phase-velocity filters, we measure the fraction of the contribution of each mechanism to the power deficit in the umbra of the leading sunspot of NOAA 9057. The contribution from absorption is 23.3 ± 1.3%, emissivity reduction 8.2 ± 1.4%, and local suppression 68.5 ± 1.5%, for a wave packet corresponding to a phase velocity of 6.98 × 10–5 rad s–1.

EFFICIENT PSEUDO-GLOBAL FITTING FOR HELIOSEISMIC DATA

Mode fitting or "peak-bagging" is an important procedure in helioseismology allowing one to determine the various mode parameters of solar oscillations. Here we describe a way of reducing the systematic bias in the fits of certain mode parameters that are seen when using "local" fitting techniques to analyse the sun-as-a-star p-mode power spectrum. To do this we have developed a new "pseudo-global" fitting algorithm designed to gain the advantages of fitting the entire power spectrum, but without the problems involved in fitting a model incorporating many hundreds of parameters. We have performed a comparative analysis between the local and pseudo-global peak-bagging techniques by fitting the "limit" profiles of simulated helioseismic data. Results show that for asymmetric modes the traditional fitting technique returns systematically biased estimates of the central frequency parameter. This bias is significantly reduced when employing the pseudo-global routine. Similarly, we show that estimates of the background returned from the pseudo-global routine match the input values much more closely than the estimates from the local fitting method. We have also used the two fitting techniques to analyse a set of real solar data collected by the Global Oscillations at Low Frequencies (GOLF) instrument on board the ESA/NASA Solar and Heliospheric Observatory (SOHO) spacecraft. Similar differences between the estimated frequencies returned by the two techniques are seen when fitting both the real and simulated data. We show that the background fits returned by the pseudo-global routine more closely match the estimate of the background one can infer from interpolating between fits to the high and low frequency ends of the p-mode power spectrum.

Large-scale horizontal flows in the solar photosphere IV. On the vertical structure of large-scale horizontal flows

In the recent papers, we introduced a method utilised to measure the flow field. The method is based on the tracking of supergranular structures. We did not precisely know, whether its results represent the flow field in the photosphere or in some subphotospheric layers. In this paper, in combination with helioseismic data, we are able to estimate the depths in the solar convection envelope, where the detected large-scale flow field is well represented by the surface measurements. We got a clear answer to question what kind of structures we track in full-disc Dopplergrams. It seems that in the quiet Sun regions the supergranular structures are tracked, while in the regions with the magnetic field the structures of the magnetic field are dominant. This observation seems obvious, because the nature of Doppler structures is different in the magnetic regions and in the quiet Sun. We show that the large-scale flow detected by our method represents the motion of plasma in layers down to ∼10Mm. The supergranules may therefore be treated as the objects carried by the underlying large-scale velocity field.

Phase Jumps in Local Helioseismology

Helioseismic rays trapped in a nonmagnetic acoustic cavity suffer a +90° phase jump at their lower (Lamb) turning point and −90° at the upper (acoustic cutoff) reflection point. That the two cancel allows helioseismologists to effectively assume that phase is locally continuous along a ray path joining two surface points. However, in strong surface magnetic field, as found in sunspots, it is shown – for an isothermal model with uniform magnetic field – that the phase jump for fast magnetoacoustic rays that penetrate the acoustic/Alfvenic equipartition level (c=a) is around −120°. Moreover, there are further negative phase jumps on the upgoing and downgoing legs at c=a that add to the net phase change. Neglecting these effects can lead to a misinterpretation of helioseismic data in terms of travel-time shifts.

Development of a new analysis technique to measure low radial-order p modes in spatially-resolved helioseismic data

In order to take full advantage of the long time series collected by the GONG and MDI helioseismic projects, we present here an adaptation of the rotation-corrected m-averaged spectrum technique in order to observe low radial-order solar p modes. Modeled profiles of the solar rotation demonstrated the potential advantage of such a technique [1, 2, 3]. Here we develop a new analysis procedure which finds the best estimates of the shift of each m of a given (n, ι) multiplet, commonly expressed as an expansion in a set of orthogonal polynomials, which yield the narrowest mode in the m-averaged spectrum. We apply the technique to the GONG data for modes with 1 ≤ ι ≤ 25 and show that it allows us to measure lower-frequency modes than with classic peak-fitting analysis of the individual-m spectra.

Modeling the excitation of acoustic modes inα Centauri A

From different seismic observations we infer the energy supplied per unit of time by turbulent convection to the acoustic modes of α Centauri A (HD 128620), a star that is similar but not identical to the Sun. The inferred rates of energy supplied to the modes (i.e. mode excitation rates) are found to be significantly higher than in the Sun. They are compared with those computed with an excitation model that includes two sources of driving, the Reynolds stress contribution and the advection of entropy fluctuations. The model also uses a closure model, the Closure Model with Plumes (CMP hereafter), that takes the asymmetry between the up- and down-flows (i.e. the granules and plumes, respectively) into account. Different prescriptions for the eddy-time correlation function are also compared to observational data. Calculations based on a Gaussian eddy-time correlation underestimate excitation rates compared with the values derived from observations for α Centauri A. On the other hand, calculations based on a Lorentzian eddy-time correlation lie within the observational error bars. This confirms results in the solar case. Compared to the helioseismic data, those obtained for α Centauri A constitute an additional support for our model of excitation. We show that mode masses must be computed taking turbulent pressure into account. Finally, we emphasize the need for more accurate seismic measurements in order to distinguish between the CMP closure model and the quasi-normal approximation in the case of α Centauri A, as well as to confirm or not the need to include the excitation by the entropy fluctuations.