Variations of the low‐degree solar p‐mode frequencies for 10 years of GOLF observations

We experiment with a method of measuring the frequency of solar p modes, intended to extend the passband for the variations of the frequency spectrum as high as possible. So far this passband is limited to a fraction of μ Hz for the classical analysis based on numerical fits of a theoretical line profile to a power spectrum averaged over periods lasting at least several weeks. This limit for the present analysis can be shifted to the mHz range, corresponding to some of the “5 min” oscillations, but in this range we use a lower resolution which allows us to separate odd and even p modes. We show an example of the results for long term variations and apply this analysis to search for a modulation of the p‐mode frequency spectrum by asymptotic series of solar g modes. A faint signal is found in the analysis of 10 years of GOLF data. This very preliminary result possibly indicates the detection of a small number of g modes of degree l = 1. A tentative determination of an observational value of the parameter P₀ follows. P₀ is the scaling factor of the asymptotic series of g modes and is a key data for solar core physics. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

p‐mode power variation with solar atmosphere as observed in the Na D1 and K spectral lines

In this work we investigate p‐mode power variation with solar atmosphere. To this aim, we use THÉMIS observations of the Na D1 (λ 5896 Å) and K (λ 7699 Å) spectral lines. While the formation heights of the K spectral line are essentially located in the photospheric layer, the formation heights of the Na D1 line span a much wider region: from photosphere up to chromosphere. Hence, we had the opportunity to infer p‐mode power variation up to the chromospheric layer. By analyzing power spectra obtained by temporal series at different points of the Na D1 and K spectral lines, we confirm and quantify the increase in p‐mode power towards higher atmospheric layers. Furthermore, the large span in formation heights of the Na D1 line induces a larger enhancement of p‐mode power with solar atmosphere compared to the K spectral line. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Seismology of the solar convection zone

An attempt is made to infer the structure of the solar convection zone from observedp-mode frequencies of solar oscillations. The differential asymptotic inversion technique is used to find the sound speed in the solar envelope. It is found that envelope models which use the Canuto-Mazzitelli (CM) formulation for calculating the convective flux give significantly better agreement with observations than models constructed using the mixing length formalism. This inference can be drawn from both the scaled frequency differences and the sound speed difference. The sound speed in the CM envelope model is within 0.2% of that in the Sun except in the region withr > 0.99R _⊙. The envelope models are extended below the convection zone, to find some evidence for the gravitational settling of helium beneath the base of the convection zone. It turns out that for models with a steep composition gradient below the convection zone, the convection zone depth has to be increased by about 6 Mm in order to get agreement with helioseismic observations.     

The heating of the solar transition region

The temperature curve in the solar chromosphere has puzzled astronomers for a long time.Referring to the structure of supergranular cells,we propose an in ductive heating model.It mainly includes the following three steps.(1) A small-scale dynamo exists in the supergranulation and produces alternating small-scale magnetic fluxes;(2) The supergranular flow distributes these small-scale fluxes according to a regular pattern;(3) A skin effect occurs in the alternating and regularly-distributed magnetic fields.The induced current is concentrated near the transition region and heats it by resistive dissipation.     

Probing solar convection

In the solar convection zone, acoustic waves are scattered by turbulent sound speed fluctuations. In this paper the scattering of waves by convective cells is treated using Rytov's technique. Particular care is taken to include diffraction effects, which are important, especially for high-degree modes that are confined to the surface layers of the Sun. The scattering leads to damping of the waves and causes a phase shift. Damping manifests itself in the width of the spectral peak of p-mode eigenfrequencies. The contribution of scattering to the linewidths is estimated and the sensitivity of the results to the assumed spectrum of the turbulence is studied. Finally, the theoretical predictions are compared with recently measured linewidths of high-degree modes.     

Propagation of acoustic waves in the non‐isothermal solar atmosphere

The acoustic cutoff frequency was originally introduced by Lamb in the study of the propagation of acoustic waves in a stratified, isothermal medium. In this paper, we use a new method to generalize Lamb's result for a stratified, non‐isothermal medium and obtain the local acoustic cutoff frequency, which describes the propagation of acoustic waves in such a medium. The main result is that the cutoff frequency is a local quantity and that its value at a given atmospheric height determines the frequency acoustic waves must have in order to propagate at this height. Application of this result to specific physical problems like the solar atmosphere is discussed. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The anomalous intensities of helium lines in the quiet solar transition region

Previous studies using observations made at low spatial and spectral resolution showed that the resonance lines of He  i and He  ii are anomalously strong in the quiet Sun when compared with other transition region lines formed at similar temperatures. Here, the higher spatial and spectral resolution provided by the Coronal Diagnostic Spectrometer ( cds ) instrument on board the Solar and Heliospheric Observatory ( SOHO ) is used to re-examine the behaviour of the He  i and He  ii lines and other transition region lines, in quiet regions near Sun centre. Supergranulation cell boundaries and cell interiors are examined separately. Near-simultaneous observations with the sumer instrument provide information on the lower transition region and the electron pressure. While the lines of He  i and He  ii have a common behaviour, as do the other transition region lines, the behaviour of the helium lines relative to the other transition region lines is significantly different. The emission measure distributions that account for all transition region lines, except those of helium, fail to produce sufficient emission in the He  i and He  ii resonance lines by around an order of magnitude, in both supergranulation cell boundary and cell interior regions. The electron pressure appears to be higher in the cell interiors than in the average cell boundaries, although the uncertainties are large. While the VAL-D model gives a closer match to the He  i 584.3-Å line, it does not successfully reproduce other transition region lines.     

Testing turbulent convection theory in solar models – I. Structure of the solar convection zone

Turbulent convection models (TCMs) based on hydrodynamic moment equations are compared with the classical mixing-length theory (MLT) in solar models. The aim is to test the effects of some physical processes on the structure of the solar convection zone, such as the dissipation, diffusion and anisotropy of turbulence that have been ignored in the MLT. Free parameters introduced by the TCMs are also tested in order to find appropriate values for astrophysical applications. It is found that the TCMs usually give larger convective heat fluxes than the MLT does, and the heat transport efficiency is sensitively related to the dissipation parameters used in the TCMs. As a result of calibrating to the present solar values, our solar models usually have rather smaller values of the mixing length to local pressure scaleheight ratio than the standard solar model. The turbulent diffusion is found to have important effects on the structure of the solar convection zone. It leads to significantly lowered and expanded profiles for the Reynolds correlations, and a larger temperature gradient in the central part of the superadiabatic convection region but a smaller one near the boundaries of the convection zone. It is interesting to note that, due to a careful treatment of turbulence developing towards isotropic state, our non-local TCM results in radially dominated motion in the central part and horizontally dominated motion near the boundaries of the convection zone, just as what has been observed in many 3D numerical simulations. Our solar models with the TCMs give small but meaningful differences in the temperature and sound speed profiles compared with the standard solar model using the MLT.     

Brightness fluctuations of the Sun and p‐mode oscillations: The inverse problem and nonadiabatic waves in the photosphere

Using photometric observations of the Sun as a star (DIFOS, SoHO) we were able to solve the inverse heloiseismic problem and determine the global time‐dependent relative temperature fluctuations as functions of the geometric height. This was done under the adiabatic assumption. A mathematical tool was developed to solve the inverse problem, which is ill‐posed. The calculations were done using the numerical software Matlab 7. The adiabatic solution shows signs of temperature waves in the lower photosphere, which agrees with calculations done by Rodríguez Hidalgo et al. (2001) and Stodilka (2011). (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Influence of the anomalous thermal conductivity on the structure of the solar atmosphere transition region

The generalized Wiedemann-Franz law for a nonisothermal quasi-neutral plasma with developed ion-acoustic turbulence and Coulomb collisions has been proven. The results obtained are used to explain the anomalously low thermal conductivity in the chromosphere-corona transition region of the solar atmosphere. Model temperature distributions in the lower corona and the transition region that correspond to well-known experimental data have been determined. The results obtained are useful for explaining the abrupt change in turbulent-plasma temperature at distances smaller than the particle mean free path.     

Magneto‐seismology of the solar atmosphere

Magnetohydrodynamic (MHD) waves in solar coronal loops, which were previously only predicted by theory have actually been detected with space‐borne instruments. These observations have given an important and novel tool to measure fundamental parameters in the magnetically embedded solar corona. This paper will illustrate how information about the magnetic and density structure along coronal loops can be determined by measuring the frequency or amplitude profiles of standing fast kink mode oscillations. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Intermediate‐term variations in solar radius during solar cycle 23

In this study, we look for the mid‐term variations in the daily average data of solar radius measurements made at the Solar Astrolabe Station of TUBITAK National Observatory (TUG) during solar cycle 23 for a time interval from 2000 February 26 to 2006 November 15. Due to the weather conditions and seasonal effect dependent on the latitude, the data series has the temporal gaps. For spectral analysis of the data series, thus, we use the Date Compensated Discrete Fourier Transform (DCDFT) and the CLEANest algorithm, which are powerful methods for irregularly spaced data. The CLEANest spectra of the solar radius data exhibit several significant mid‐term periodicities at 393.2, 338.9, 206.5, 195.2, 172.3 and 125.4 days which are consistent with periods detected in several solar time series by several authors during different solar cycles. The knowledge relating to the origin of solar radius variations is not yet present. To see whether these variations will repeat in next cycles and to understand how the amplitudes of such variations change with different phases of the solar cycles, we need more systematic efforts and the long‐term homogeneous data. Since most of the periodicities detected in the present study are frequently seen in solar activity indicators, it is thought that the physical mechanisms driving the periodicities of solar activity may also be effective in solar radius variations (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

Dynamo action in simulations of penetrative solar convection with an imposed tachocline

We summarize new and continuing three-dimensional spherical shell simulations of dynamo action by convection allowed to penetrate downward into a tachocline of rotational shear. The inclusion of an imposed tachocline allows us to examine several processes believed to be essential in the operation of the global solar dynamo, including differential rotation, magnetic pumping, and the stretching and organization of fields within the tachocline. In the stably stratified core, our simulations reveal that strong axisymmetric magnetic fields (of ∼ 3000 G strength) can be built, and that those fields generally exhibit a striking antisymmetric parity, with fields in the northern hemisphere largely of opposite polarity to those in the southern hemisphere. In the convection zone above, fluctuating fields dominate over weaker mean fields. New calculations indicate that the tendency toward toroidal fields of antisymmetric parity is relatively insensitive to initial magnetic field configurations; they also reveal that on decade-long timescales, the magnetic fields can briefly enter (and subsequently emerge from) states of symmetric parity.We have not yet observed any overall reversals of the field polarity, nor systematic latitudinal propagation. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)