Parametrizing the time-variation of the "surface term" of stellar p-mode frequencies: application to helioseismic data

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 inertia together with cubic and inverse frequency terms. We find that for the central frequency of rotationally split multiplets the cubic term dominates both the average surface term and the temporal variation, but for the medium-degree case the inverse term improves the fit to the temporal variation. We also examine the variation of the even-order splitting coefficients for the medium-degree data and find that, as for the central frequency, the latitude-dependent frequency variation, which reflects the changing latitudinal distribution of magnetic activity over the solar cycle, can be described by the combination of a cubic and an inverse function of frequency scaled by inverse mode inertia. The results suggest that this simple parametrization could be used to assess the activity-related frequency variation in solar-like asteroseismic targets.Comment: 13 pages, 11 figures. Accepted by MNRAS 13 October 201

The Sun in transition? Persistence of near-surface structural changes through Cycle 24

We examine the frequency shifts in low-degree helioseismic modes from the Birmingham Solar-Oscillations Network (BiSON) covering the period from 1985 - 2016, and compare them with a number of global activity proxies well as a latitudinally-resolved magnetic index. As well as looking at frequency shifts in different frequency bands, we look at a parametrization of the shift as a cubic function of frequency. While the shifts in the medium- and highfrequency bands are very well correlated with all of the activity indices (with the best correlation being with the 10.7 cm radio flux), we confirm earlier findings that there appears to have been a change in the frequency response to activity during solar cycle 23, and the low frequency shifts are less correlated with activity in the last two cycles than they were in Cycle 22. At the same time, the more recent cycles show a slight increase in their sensitivity to activity levels at medium and higher frequencies, perhaps because a greater proportion of activity is composed of weaker or more ephemeral regions. This lends weight to the speculation that a fundamental change in the nature of the solar dynamo may be in progress.Comment: 9 pages, 6 figures. Accepted by MNRAS 24 May 201

Solar-cycle variation of the sound-speed asphericity from GONG and MDI data 1995-2000

We study the variation of the frequency splitting coefficients describing the solar asphericity in both GONG and MDI data, and use these data to investigate temporal sound-speed variations as a function of both depth and latitude during the period from 1995-2000 and a little beyond. The temporal variations in even splitting coefficients are found to be correlated to the corresponding component of magnetic flux at the solar surface. We confirm that the sound-speed variations associated with the surface magnetic field are superficial. Temporally averaged results show a significant excess in sound speed around 0.92 solar radii and latitude of 60 degrees.Comment: To be published in MNRAS, accepted July 200

Subsurface Flows in and Around Active Regions with Rotating and Non-rotating Sunspots

The temporal variation of the horizontal velocity in subsurface layers beneath three different types of active regions is studied using the technique of ring diagrams. In this study, we select active regions (ARs) 10923, 10930, 10935 from three consecutive Carrington rotations: AR 10930 contains a fast-rotating sunspot in a strong emerging active region while other two have non-rotating sunspots with emerging flux in AR 10923 and decaying flux in AR 10935. The depth range covered is from the surface to about 12 Mm. In order to minimize the influence of systematic effects, the selection of active and quiet regions is made so that these were observed at the same heliographic locations on the solar disk. We find a significant variation in both components of the horizontal velocity in active regions as compared to quiet regions. The magnitude is higher in emerging-flux regions than in the decaying-flux region, in agreement with earlier findings. Further, we clearly see a significant temporal variation in depth profiles of both zonal and meridional flow components in AR 10930, with the variation in the zonal component being more pronounced. We also notice a significant influence of the plasma motion in areas closest to the rotating sunspot in AR 10930 while areas surrounding the non-rotating sunspots in all three cases are least affected by the presence of the active region in their neighborhood.Comment: Solar Physics (in press), includes 11 figure

A spatial and spectral maximum entropy method as applied to OVRO solar data

We present first results of applying a Maximum Entropy Method (MEM) algorithm that acts in both the spatial and spectral domains to data obtained with the frequency-agile solar interferometer at Owens Valley Radio Observatory (OVRO) taken at 45 frequencies in the range 1 – 18 GHz. The traditional MEM algorithm does not exploit the spatial information available at adjacent frequencies in the OVRO data, but rather applies separately to each frequency. We seek an algorithm that obtains a global solution to the visibilities in both the spatial and spectral domains. To simplify the development process, the algorithm is at present limited to the one-dimensional spatial case. We apply our 1-d algorithm to observations taken with the OVRO frequency-agile interferometer of active region AR 5417 near the solar limb on March 20, 1989 (vernal equinox). The interferometer's two 27 m antennas and 40 m antenna were arranged in a linear east-west array, which at the vernal equinox gives a good match to the 1-d algorithm. Our results show that including the spectral MEM term greatly improves the dynamic range of the reconstructed image compared with a reconstruction without using this information. The derived brightness temperature spectra show that for AR 5417 the dominant radio emission mechanism is thermal gyroresonance and we use this information to deduce the spatial variation of electron temperature and magnetic field strength in the corona above the active region

Energy loss of solar p modes due to the excitation of magnetic sausage tube waves: importance of coupling the upper atmosphere

We consider damping and absorption of solar p modes due to their energy loss to magnetic tube waves that can freely carry energy out of the acoustic cavity. The coupling of p modes and sausage tube waves is studied in a model atmosphere composed of a polytropic interior above which lies an isothermal upper atmosphere. The sausage tube waves, excited by p modes, propagate along a magnetic fibril which is assumed to be a vertically aligned, stratified, thin magnetic flux tube. The deficit of p-mode energy is quantified through the damping rate, Γ, and absorption coefficient, α. The variation of Γ and α as a function of frequency and the tube's plasma properties is studied in detail. Previous similar studies have considered only a subphotospheric layer, modeled as a polytrope that has been truncated at the photosphere. Such studies have found that the resulting energy loss by the p modes is very sensitive to the upper boundary condition, which, due to the lack of an upper atmosphere, have been imposed in a somewhat ad hoc manner. The model presented here avoids such problems by using an isothermal layer to model the overlying atmosphere (chromosphere, and, consequently, allows us to analyze the propagation of p-mode-driven sausage waves above the photosphere. In this paper, we restrict our attention to frequencies below the acoustic cut off frequency. We demonstrate the importance of coupling all waves (acoustic, magnetic) in the subsurface solar atmosphere with the overlying atmosphere in order to accurately model the interaction of solar f and p modes with sausage tube waves. In calculating the absorption and damping of p modes, we find that for low frequencies, below ≈3.5 mHz, the isothermal atmosphere, for the two-region model, behaves like a stress-free boundary condition applied at the interface (z = –z 0)

Deeply penetrating banded zonal flows in the solar convection zone

Helioseismic observations have detected small temporal variations of the rotation rate below the solar surface corresponding to the so-called `torsional oscillations' known from Doppler measurements of the surface. These appear as bands of slower and faster than average rotation moving equatorward. Here we establish, using complementary helioseismic observations over four years from the GONG network and from the MDI instrument on board SOHO, that the banded flows are not merely a near-surface phenomenon: rather they extend downward at least 60 Mm (some 8% of the total solar radius) and thus are evident over a significant fraction of the nearly 200 Mm depth of the solar convection zone.Comment: 4 pages, 4 figures To be published in ApJ Letters (accepted 3/3/2000

Multitaper Spectral Analysis and Wavelet Denoising Applied to Helioseismic Data

Estimates of solar normal mode frequencies from helioseismic observations can be improved by using Multitaper Spectral Analysis (MTSA) to estimate spectra from the time series, then using wavelet denoising of the log spectra. MTSA leads to a power spectrum estimate with reduced variance and better leakage properties than the conventional periodogram. Under the assumption of stationarity and mild regularity conditions, the log multitaper spectrum has a statistical distribution that is approximately Gaussian, so wavelet denoising is asymptotically an optimal method to reduce the noise in the estimated spectra. We find that a single m-upsilon spectrum benefits greatly from MTSA followed by wavelet denoising, and that wavelet denoising by itself can be used to improve m-averaged spectra. We compare estimates using two different 5-taper estimates (Stepian and sine tapers) and the periodogram estimate, for GONG time series at selected angular degrees l. We compare those three spectra with and without wavelet-denoising, both visually, and in terms of the mode parameters estimated from the pre-processed spectra using the GONG peak-fitting algorithm. The two multitaper estimates give equivalent results. The number of modes fitted well by the GONG algorithm is 20% to 60% larger (depending on l and the temporal frequency) when applied to the multitaper estimates than when applied to the periodogram. The estimated mode parameters (frequency, amplitude and width) are comparable for the three power spectrum estimates, except for modes with very small mode widths (a few frequency bins), where the multitaper spectra broadened the modest compared with the periodogram. We tested the influence of the number of tapers used and found that narrow modes at low n values are broadened to the extent that they can no longer be fit if the number of tapers is too large. For helioseismic time series of this length and temporal resolution, the optimal number of tapers is less than 10

A spatial and spectral maximum entropy method as applied to OVRO solar data

We present first results of applying a Maximum Entropy Method (MEM) algorithm that acts in both the spatial and spectral domains to data obtained with the frequency-agile solar interferometer at Owens Valley Radio Observatory (OVRO) taken at 45 frequencies in the range 1 – 18 GHz. The traditional MEM algorithm does not exploit the spatial information available at adjacent frequencies in the OVRO data, but rather applies separately to each frequency. We seek an algorithm that obtains a global solution to the visibilities in both the spatial and spectral domains. To simplify the development process, the algorithm is at present limited to the one-dimensional spatial case. We apply our 1-d algorithm to observations taken with the OVRO frequency-agile interferometer of active region AR 5417 near the solar limb on March 20, 1989 (vernal equinox). The interferometer's two 27 m antennas and 40 m antenna were arranged in a linear east-west array, which at the vernal equinox gives a good match to the 1-d algorithm. Our results show that including the spectral MEM term greatly improves the dynamic range of the reconstructed image compared with a reconstruction without using this information. The derived brightness temperature spectra show that for AR 5417 the dominant radio emission mechanism is thermal gyroresonance and we use this information to deduce the spatial variation of electron temperature and magnetic field strength in the corona above the active region

Rotation profiles of solar-like stars with magnetic fields

The aim of this work is to investigate rotation profile of solar-like stars with magnetic fields. A diffusion coefficient of magnetic angular momentum transport is deduced. Rotating stellar models with different mass are computed under the effect of the coefficient. Then rotation profiles are obtained from the theoretical stellar models. The total angular momentum of solar model with only hydrodynamic instabilities is about 13 times larger than that of the Sun at the age of the Sun, and this model can not reproduce quasi-solid rotation in the radiative region. However, not only can the solar model with magnetic fields reproduce an almost uniform rotation in the radiative region, but its total angular momentum is consistent with helioseismic result at the level of 3 $\sigma$ at the age of the Sun. The rotation of solar-like stars with magnetic fields is almost uniform in the radiative region. But there is an obvious transition region of angular velocity between the convective core and the radiative region of models with 1.2 - 1.5 $M_{\odot}$, where angular velocity has a sharp radial change, which is different from the rotation profile of the Sun and massive stars with magnetic fields. Moreover the changes of the angular velocity in the transition region increase with the increasing in the age and mass.Comment: Accepted for publication in ChjA