A modified peak‐bagging technique for fitting low‐𝓁 solar p‐modes

We introduce a modified version of a standard power spectrum ‘peak‐bagging’ technique which is designed to gain some of the advantages that fitting the entire low‐degree p‐mode power spectrum simultaneously would bring, but without the problems involved in fitting a model incorporating many hundreds of parameters. Employing Monte‐Carlo simulations we show that by using this modified fitting code it is possible to determine the true background level in the vicinity of the p‐mode peaks. In addition to this we show how small biases in other mode parameters, which are related to inaccurate estimates of the true background, are also consequently removed. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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)     

Bayesian approach for g‐mode detection,or how to restrict our imagination

Nowadays, g‐mode detection is based upon a priori theoretical knowledge. By doing so, detection becomes more restricted to what we can imagine. De facto, the universe of possibilities ismade narrower. Such an approach is pertinent for Bayesian statisticians. Examples of how Bayesian inferences can be applied to spectral analysis and helioseismic power spectra are given. Our intention is not to give the full statistical framework (much too ambitious) but to provide an appetizer for going further in the direction of a proper Bayesian inference, especially for detecting gravity modes. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Peak asymmetry of solar p modes: a framework to explain the effects of the correlated noise from the acoustic source

It is well known that in the power spectrum solar p modes have asymmetric profiles, which depart from a Lorentzian shape. We present a framework to explain the contribution of correlated background noise, from the acoustic source, to this asymmetry. An important prediction is that observed peak asymmetry may differ depending on the way the p-mode observations are made, and on how the data are prepared. Furthermore, if valid, the proposed framework may provide the basis for separating the contribution of the correlated noise from that of the source location and properties.     

Modelling solar atmospheric gravity oscillation modes

Solar oscillations are investigated in a one‐dimensional hydrodynamic plane‐parallel model with an atmosphere. Besides the acoustic pressure (p) modes, the fundamental (f) and Lamb mode, another set of eigenmodes, a group of atmospheric gravity (g) modes, is found in the low‐frequency region of the spectrum. Their frequencies and spatial behaviour are studied. (© 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)     

Detection and temporal coherence of p‐modes below 1.4 mHz

Data collected recently by the helioseismic experiments aboard the SOHO spacecraft have allowed the detection of low degree p‐modes with increasingly lower order n. In particular, the GOLF experiment is currently able to unambiguously identify low degree modes with frequencies as low as 1.3 mHz. The detection of p‐modes with very low frequency (i.e., low n), is difficult due to the low signal‐to‐noise ratio in this spectral region and its contamination by solar signals that are not of acoustic origin. To address this problem without using any theoretical a priory, we propose a methodology that relies only on the inversion of observed values to define a spectral window for the expected locations of these low frequency modes. The application of this method to 2920‐day‐long GOLF observations is presented and its results discussed. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The statistical study of quasi‐periodic oscillations of the radio emission in solar quiet regions

In this study we discuss variations of the radio emission from the Quiet Sun Areas (QSA) at centimeter wavelength (1.76 cm). Data were obtained from Nobeyama Radioheliograph (NoRH). Oscillations of selected areas were studied carefully from data taken over one week. We try to find quasi‐periodic solar oscillations from the QSA. We used the traditional Fast Fourier Transform (FFT), Global Wavelet Spectrum (GWS) and Wavelet (Morlet) for studying signals in the frequency/time‐frequency domain. We used the Fisher randomization test to verify the significance of the observed signal. Instrumental and sky noises were studied using a cross‐correlation analysis. Additionally, a single pixel analysis were done. Wide ranges of solar oscillation periods were found from the Quiet Sun Area (QSA): 3–15, 35–70, and 90 minutes. Some physical explanations are suggested for these oscillations. However, it is not possible to give a conclusive statement about the origin of the long quasi‐periodic (>60 min) oscillations from the QSA (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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)     

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.     

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)     

On model predictions of the power spectral density of radial solar p modes

We investigate the frequency dependence of the power spectral density of low-degree solar p modes by comparing measurements with the results of a stochastic-excitation model. In the past it was common practice to use the total power in such investigations. Using the maximum of the power spectral density instead provides a direct comparison with the measured mode heights in the observed power spectrum. This method permits a more careful calibration of the adjustable parameters in the excitation model, a model which we present here, for the first time, in a format that precisely and unambiguously relates the amplitudes of the modes of oscillation to the Reynolds stress in the equilibrium model. We find that errors in the theory of the linear mode damping rates, particularly at low frequency, have a dramatic impact on the predictions of the mode heights in the spectral density, whereas parameter changes in the stochastic excitation model, within a plausible domain of parameter space, have a comparatively small effect.