Changes in convective properties over the solar cycle: effect on p-mode damping rates

Measurements of both solar irradiance and p-mode oscillation frequencies indicate that the structure of the Sun changes with the solar cycle. Balmforth, Gough & Merryfield investigated the effect of symmetrical thermal disturbances on the solar structure and the resulting pulsation frequency changes. They concluded that thermal perturbations alone cannot account for the variations in both irradiance and p-mode frequencies, and that the presence of a magnetic field affecting acoustical propagation is the most likely explanation of the frequency change, in the manner suggested earlier by Gough & Thompson and by Goldreich et al. Numerical simulations of Boussinesq convection in a magnetic field have shown that at high Rayleigh number the magnetic field can modify the preferred horizontal length scale of the convective flow.
Here, we investigate the effect of changing the horizontal length scale of convective eddies on the linewidths of the acoustic resonant mode peaks observed in helioseismic power spectra. The turbulent fluxes in these model computations are obtained from a time-dependent, non-local generalization of the mixing-length formalism. The modelled variations are compared with p-mode linewidth changes revealed by the analysis of helioseismic data collected by the Birmingham Solar-Oscillations Network (BiSON); these low-degree (low- l ) observations cover the complete falling phase of solar activity cycle 22. The results are also discussed in the light of observations of solar-cycle variations of the horizontal size of granules and with results from 2D simulations by Steffen of convective granules.     

Temporal and spatial distribution of the magnetic field and density of nonthermal electrons in the source of solar microwave bursts

The temporal and spatial distribution of the magnetic field and density of non-thermal electrons in the source of solar microwave bursts are studied by the gyrosynchrotron model, using the observations of the high-resolution spectrometer at the Owens Valley solar interferometer. The general results are consistent with the previous knowledge about these parameters. For example, the magnetic field decreases with increasing radio flux, and the distribution gradually flattens, so that the non-uniformity of the magnetic field decreases gradually, meanwhile the density increases, and the nonthermal electrons propagate from lower to higher levels. It is interesting that the oscillation of the density is detected at lower frequencies, and there is a correlation between the density and the energy index. The main purpose of this paper is to develop a diagnostic method for the basic plasma parameters in solar flares.     

Seismology of stellar envelopes: probing the outer layers of a star through the scattering of acoustic waves

The outer layers of Sun-like stars are regions of rapid spatial variation which modulate the p-mode frequencies by partially reflecting the constituent acoustic waves. With the accuracy that has been achieved by current solar observations, and that is expected from imminent stellar observations, this modulation can be observed from the spectra of the low-degree modes. We present a new and simple theoretical calculation to determine the leading terms in an asymptotic expansion of the outer phase of these modes, which is determined by the structure of the surface layers of the star. Our procedure is to compare the stellar envelope with a plane-parallel polytropic envelope, which we regard as a smooth reference background state. Then we can isolate a seismic signature of the acoustic phase and relate it to the stratification of the outer layers of the convection zone. One can thereby constrain theories of convection that are used to construct the convection zones of the Sun and Sun-like stars. The accuracy of the diagnostic is tested in the solar case by comparing the predicted outer phase with an exact numerical calculation.     

On the accuracy of the measurements of low-ℓ solar acoustic oscillations

Using a 1154 d long measurement of solar oscillations, obtained by the Global Oscillation Network Group from 1995 June 10 to 1998 August 6, we study the dependence of the accuracy of radial p-mode parameters on the duration of the observations. It is shown that relatively rare pulses of large power lead to the decrease of the accuracy achievable for a given duration of the observations and it is usually underestimated. The corresponding correction factor to the Libbrecht formula for a frequency accuracy estimation is provided. We have also investigated the influence of the solar activity on the mode parameters soon after the solar activity minimum. There is a clearly visible increase of the radial p-mode power in the beginning of the new solar cycle while the mode frequency variations are within the corresponding error bars.     

Probing sunspot magnetic fields with p-mode absorption and phase shift data

Long-standing observations of incoming and outgoing f- and p-modes in annuli around sunspots reveal that the spots partially absorb and substantially shift the phase of waves incident upon them. The commonly favoured absorption mechanism is partial conversion to slow magneto-acoustic waves that disappear into the solar interior channelled by the magnetic field of the sunspot. However, up until now, only f-mode absorption could be accounted for quantitatively by this means. Based on vertical magnetic field models, the absorption of p-modes was insufficient. In this paper, we use the new calculations of Crouch & Cally for inclined fields, and a simplified model of the interaction between spot interior and exterior. We find excellent agreement with phase shift data assuming field angles from the vertical in excess of 30° and Alfvén/acoustic equipartition depths of around 600–800 km. The absorption of f-modes produced by such models is considerably larger than is observed, but consistent with numerical simulations. On the other hand, p-mode absorption is generally consistent with observed values, up to some moderate frequency dependent on radial order. Thereafter, it is too large, assuming absorbing regions comparable in size to the inferred phase-shifting region. The excess absorption produced by the models is in stark contrast with previous calculations based on a vertical magnetic field, and is probably due to finite mode lifetimes and excess emission in acoustic glories. The excellent agreement of phase shift predictions with observational data allows some degree of probing of subsurface field strengths, and opens up the possibility of more accurate inversions using improved models. Most importantly, though, we have confirmed that slow mode conversion is a viable, and indeed the likely, cause of the observed absorption and phase shifts.     

Modeling helioseismic modes in the magnetic atmosphere of the Sun

The pulsation of the solar surface is caused by acoustic waves traveling in the solar interior. Thorough analyses of observational data indicate that these f and p helioseismic oscillation modes are not bounced back completely at the surface but they partially penetrate into the atmosphere. Atmospheric effects and their possible observational application are investigated in one‐dimensional magnetohydrodynamic models. It is found that f and p mode frequencies are shifted of the order of μHz due to the presence of an atmospheric magnetic field. This shift varies with the direction of the wave propagation.Resonant coupling of global helioseismic modes to local Alfvén and slow waves reduce the life time of the global modes. The resulting line width of the frequency line is of the order of nHz, and it also varies with propagation angle. These features enable us to use helioseismic observations in magnetic diagnostics of the lower atmosphere. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Rotation of the solar core from BiSON and LOWL frequency observations

Determination of the rotation of the solar core requires very accurate data on splittings for the low-degree modes which penetrate to the core, as well as for modes of higher degree to suppress the contributions from the rest of the Sun to the splittings of the low-degree modes. Here we combine low-degree data based on 32 months of observations with the BiSON network and data from the LOWL instrument. The data are analysed with a technique that specifically aims at obtaining an inference of rotation that is localized to the core. Our analysis provides what we believe is the most stringent constraint to date on the rotation of the deep solar interior.     

Effects of a gap-filling method on p-mode parameters

The quality of helioseismological ground-based data strongly depends on the presence of a gap in the observational window. In order to address that problem in the case of full-disc low-degree p-mode velocity measurements, Fossat et al. proposed a gap-filling method called 'Repetitive music'. The autocorrelation function of the velocity signal shows a correlation of more than 70 per cent at about 4 h because of the quasi-periodicity of p-mode peaks in the Fourier spectrum. The method then consists of filling gaps of the velocity signal with data, when they exist, located 4 h before or after.
By using Monte Carlo simulations, we assess the effects of the gap-filling method on p-mode parameters and their errors. A way to remove the modulation in the power spectrum resulting from the gap-filling method is proposed; its effects on p-mode frequencies, linewidths, amplitudes and asymmetries are discussed as a function of frequency and signal-to-noise ratio.     

Anomalous variations in low-degree helioseismic mode frequencies

We compare changes in the frequencies of solar acoustic modes with degree between 0 and 2, as derived from Global Oscillation Network Group (GONG), Birmingham Solar Oscillations Network (BiSON) and Michelson Doppler Imager (MDI) spectra obtained between 1995 and 2003. We find that, after the solar-activity dependence has been removed from the frequencies, there remain variations that appear to be significant, and are often well correlated between the different data sets. We consider possible explanations for these fluctuations, and conclude that they are likely to be related to the stochastic excitation of the modes. The existence of such fluctuations has possible relevance to the analysis of other low-degree acoustic mode spectra such as those from solar-type stars.     

Rigid rotation of the solar core? On the reliable extraction of low-ℓ rotational p-mode splittings from full-disc observations of the Sun

We present low-ℓ rotational p-mode splittings from the analysis of 8 yr of observations made by the Birmingham Solar-Oscillations Network (BiSON) of the full solar disc. These data are presented in the light of a thorough investigation of the fitting techniques used to extract them. Particular attention is paid to both the origin and magnitude of bias present in these estimates. An extensive Monte Carlo strategy has been adopted to facilitate this study – in all, several thousand complete, artificial proxies of the 96-month data set have been generated to test the analysis of real 'full-disc' data. These simulations allow for an assessment of any complications in the analysis which might arise from variations in the properties of the p modes over the 11-yr solar activity cycle.
The use of such an extended data set affords greater precision in the splittings, and by implication the rotation rate inferred from these data, and reduces bias inherent in the analysis, thereby giving a more accurate determination of the rotation. The grand, weighted sidereal average of the BiSON set is     , a value consistent with that expected were the deep radiative interior     to rotate at the same frequency, and in the same 'rigid' manner, as the more precisely and accurately studied outer part of the radiative zone.     

Solar p modes of high degree l: coupling by differential rotation

Accurate measurements of solar p-mode frequencies and frequency splittings at high degree l require an adequate theoretical knowledge of the effects of mode coupling, induced by the variation with latitude of the angular velocity of the solar internal rotation. Earlier results for expansion coefficients of composite solutions (coupling coefficients) are due to Woodard. In this paper, the analysis is extended to allow for the dependence of the differential rotation on depth, and the result is expressed in terms of measurable quantities (the rotational splitting coefficients), which makes it convenient for diagnostic purposes. The analysis is based on the approach of quasi-degenerate perturbation theory, and is extended further to address possible effects of mode coupling in the observational line profiles. It is shown, using approximations applicable at high degree l , that the expected line profiles of composite modes in the observational power spectra are not distorted by mode coupling.     

中尺度磁绳结构的行星际观测

由磁绳结构主导、平均尺度约二、三十个小时的行星际磁云是日冕物质抛射在行星际膨胀、传播的体现。最近，Moldwin等人报道在太阳风中还观测到一些尺度在几十分钟的小尺度磁绳结构，并认为太阳风中的磁绳结构在尺度分布上可能具有双峰特征，在全面检视了WIND卫星(1995年-2000年)和ACE卫星(1998年-2000年)的观测资料后，发现了在行星际太阳风中一些尺度为几个小时的中尺度磁绳结构，利用初步整理的其中28个中尺度磁绳结构事件，认为太阳风中的磁绳结构在尺度分布上可能是连续的，这对行星际太阳风中磁绳结构物理起源的研究可能提出重要的物理限制。     

Observation of hysteresis between solar activity indicators andp-mode frequency shifts for solar cycle 22

Using intermediate degreep-mode frequency data sets for solar cycle 22, we find that the frequency shifts and magnetic activity indicators show a “hysteresis” phenomenon. It is observed that the magnetic indices follow different paths for the ascending and descending phases of the solar cycle while for radiative indices, the separation between the paths are well within the error limits.     

What do the solar activity indices represent?

Sunspot number, sunspot area, and radio flux at 10.7 cm are the indices which are most frequently used to describe the long‐term solar activity. The data of the daily solar full‐disk magnetograms measured at Mount Wilson Observatory from 19 January 1970 to 31 December 2012 are utilized together with the daily observations of the three indices to probe the relationship of the full‐disk magnetic activity respectively with the indices. Cross correlation analyses of the daily magnetic field measurements at Mount Wilson observatory are taken with the daily observations of the three indices, and the statistical significance of the difference of the obtained correlation coefficients is investigated. The following results are obtained: (1) The sunspot number should be preferred to represent/reflect the full‐disk magnetic activity of the Sun to which the weak magnetic fields (outside of sunspots) mainly contribute, the sunspot area should be recommended to represent the strong magnetic activity of the Sun (in sunspots), and the 10.7 cm radio flux should be preferred to represent the full‐disk magnetic activity of the Sun (both the weak and strong magnetic fields) to which the weak magnetic fields mainly contribute. (2) On the other hand, the most recommendable index that could be used to represent/reflect the weak magnetic activity is the 10.7 cm radio flux, the most recommendable index that could be used to represent the strong magnetic activity is the sunspot area, and the most recommendable index that could be used to represent the full‐disk magnetic activity of the Sun is the 10.7cm radio flux. Additionally, the cycle characteristics of the magnetic field strengths on the solar disk are given. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Solar cycle according to mean magnetic field data

To investigate the shape of the solar cycle, we have performed a wavelet analysis of the large–scale magnetic field data for 1960–2000 for several latitudinal belts and have isolated the following quasi-periodic components: ∼22, 7 and 2 yr. The main 22-yr oscillation dominates all latitudinal belts except the latitudes of ±30° from the equator. The butterfly diagram for the nominal 22-yr oscillation shows a standing dipole wave in the low-latitude domain  (∣θ∣≤ 30°)  and another wave in the sub-polar domain  (∣θ∣≥ 35°)  , which migrates slowly polewards. The phase shift between these waves is about π. The nominal 7-yr oscillation yields a butterfly diagram with two domains. In the low-latitude domain  (∣θ∣≤ 35°)  , the dipole wave propagates equatorwards and in the sub-polar region, polewards. The nominal 2-yr oscillation is much more chaotic than the other two modes; however the waves propagate polewards whenever they can be isolated.
We conclude that the shape of the solar cycle inferred from the large-scale magnetic field data differs significantly from that inferred from sunspot data. Obviously, the dynamo models for a solar cycle must be generalized to include large-scale magnetic field data. We believe that sunspot data give adequate information concerning the magnetic field configuration deep inside the convection zone (say, in overshoot later), while the large-scale magnetic field is strongly affected by meridional circulation in its upper layer. This interpretation suggests that the poloidal magnetic field is affected by the polewards meridional circulation, whose velocity is comparable with that of the dynamo wave in the overshoot layer. The 7- and 2-yr oscillations could be explained as a contribution of two sub-critical dynamo modes with the corresponding frequencies.     

High-frequency modes in solar-like stars

p-mode oscillations in solar-like stars are excited by the outer convection zone in these stars and reflected close to the surface. The p modes are trapped inside an acoustic cavity, but the modes only stay trapped up to a given frequency [known as the acoustic cut-off frequency  (ν_ac)  ] as modes with larger frequencies are generally not reflected at the surface. This means that modes with frequency larger than the acoustic cut-off frequency must be travelling waves. The high-frequency modes may provide information about the physics in the outer layers of the stars and the excitation source and are therefore highly interesting as it is the estimation of these two phenomena that cause some of the largest uncertainties when calculating stellar oscillations.
High-frequency modes have been detected in the Sun, in β Hydri and in α Cen A and α Cen B by smoothing the so-called echelle diagram and the large frequency separation as a function of frequency has been estimated. The large frequency separation has been compared with a simple model of the acoustic cavity which suggests that the reflectivity of the photosphere is larger at high frequency than predicted by standard models of the solar atmosphere and that the depth of the excitation source is larger than what has been estimated by other models and might depend on the order n and degree l of the modes.     

Local Fractional Frequency Shifts Used as Tracers of Magnetic Activity

Using data from SOI-MDI (Haber et al., 2000), we compute the local frequencies of high-degree p modes and f modes. The frequencies are obtained through ring-diagram mode fitting. The Dense-Pack data set consists of a mosaic of 189 overlapping tiles, each tracked separately at the surface rotation rate over 1664-min time intervals during the Dynamics Programs. Each tile is 16° square and the tile centers are separated by 7.5° in latitude and longitude. For each sampling day and for each tile, we have computed the frequency shift measured relative to the temporal and spatial average of the entire set of frequencies. The motion of active regions as they rotate across the solar disk is vividly traced by these measurements. Active regions appear as locations of large positive frequency shifts. If the shifts are averaged over the solar disk and are scaled down to the appropriate wave number regime, the magnitude and frequency dependence of the shifts are consistent with the measured changes in global oscillation frequencies that occur over the solar cycle. As with the frequency shifts of low-degree global oscillations, the frequency dependence of the shifts indicates that the physical phenomena inducing the shifts is confined to the surface layers of the Sun.     

Spatially intermittent fields in photospheric magnetoconvection

Motivated by recent high-resolution observations of the solar surface, we investigate the problem of non-linear magnetoconvection in a three-dimensional compressible layer. We present results from a set of numerical simulations which model the situation in which there is a weak imposed magnetic field. This weak-field regime is characterized by vigorous granular convection and spatially intermittent magnetic field structures. When the imposed field is very weak, magnetic flux tends to accumulate at the edges of the convective cells, where it forms compact, almost 'point-like' structures which are reminiscent of those observed in the quiet Sun. If the imposed field is slightly stronger, there is a tendency for magnetic flux to become concentrated into 'ribbon-like' structures which are comparable to those observed in solar plages. The dependence of these simulations upon the strength of the imposed magnetic field is analysed in detail, and the concept of the fractal dimension is used to make a further, more quantitative comparison between these simulations and photospheric observations.     

On the measurement precision of solar p-mode eigenfrequencies

We make use of 3456 d of observations of the low-ℓ p-mode oscillations of the Sun in order to study the evolution over time of the measurement precision of the radial eigenfrequencies. These data were collected by the ground-based Birmingham Solar-Oscillations Network (BiSON) between 1991 January and 2000 June. When the power spectrum of the complete time series is fitted, the analysis yields frequency uncertainties that are close to those expected from the returned coherence times of the modes. The slightly elevated levels compared with the prediction appear to be consistent with a degradation of the signal-to-noise ratio in the spectrum that is the result of the influence of the window function of the observations (duty cycle 71 per cent). The fractional frequency precision reaches levels of a several parts in 10⁶ for many of the modes. The corresponding errors reported from observations made by the GOLF instrument on board the ESA/NASA SOHO satellite, when extrapolated to the length of the BiSON data set, are shown to be (on average) about ∼25 per cent smaller than their BiSON counterparts owing to the uninterrupted nature of the data from which they were derived.
An analysis of the BiSON data in contiguous segments of different lengths, T , demonstrates that the frequency uncertainties scale as T ^−1/2. This is to be expected in the regime where the coherence (life) times of the modes, τ _{n ℓ}, are smaller than the observing time T (the 'oversampled' regime). We show that mode detections are only now beginning to encroach on the 'undersampled' regime (where   T < τ _{n ℓ})  .