Corotational damping of discoseismic c modes in black hole accretion discs

Discoseismic c modes in accretion discs have been invoked to explain low-frequency variabilities observed in black hole X-ray binaries. These modes are trapped in the innermost region of the disc and have frequencies much lower than the rotation frequency at the disc inner radius. We show that because the trapped waves can tunnel through the evanescent barrier to the corotational wave zone, the c modes are damped due to wave absorption at the corotation resonance. We calculate the corotational damping rates of various c modes using the Wentzel-Kramers-Brillouin (WKB) approximation. The damping rate varies widely depending on the mode frequency, the black hole spin parameter and the disc sound speed, and is generally much less than 10 per cent of the mode frequency. A sufficiently strong excitation mechanism is needed to overcome this corotational damping and make the mode observable.     

On the properties of strange modes

Properties of the so-called strange modes occurring in linear stability calculations of stellar models are discussed. The behaviour of these modes is compared for two different sets of stellar models, for very massive zero-age main-sequence stars and for luminous hydrogen-deficient stars, both with high luminosity-to-mass ratios. We have found that the peculiar behaviour of the frequencies of the strange modes with the change of a control parameter is caused by the pulsation amplitude of a particular eigenmode being strongly confined to the outer part of the envelope, around the density inversion zone. The frequency of a strange mode changes because the depth of the confinement zone changes with the control parameter. Weakly non-adiabatic strange modes tend to be overstable because the amplitude confinement quenches the effect of radiative damping. On the other hand, extremely non-adiabatic strange modes become overstable because the perturbation of radiation force (gradient of radiation pressure) provides a restoring force that can be out of phase with the density perturbation. We discuss this mechanism by using a plane-parallel two-zone model.     

Unstable non-radial modes in radial pulsators: theory and an example

We study the possibility of the excitation of non-radial oscillations in classical pulsating stars. The stability of an RR Lyrae model is examined through non-adiabatic non-radial calculations. We also explore stability in the presence of non-linear coupling between radial and non-radial modes of nearly identical frequency.   In our model, a large number of unstable low-degree (ℓ = 1,2) modes have frequencies in the vicinity of unstable radial mode frequencies. The growth rates of such modes, however, are considerably smaller than those of the radial modes. We also recover an earlier result that at higher degrees (ℓ = 6–12) there are modes trapped in the envelope with growth rates similar to those of radial modes.   Subsequently, monomode radial pulsation of this model is considered. The destabilizing effect of the 1:1 resonance between the radial mode and nearby non-radial modes of low degrees is studied, with the assumption that the excited radial mode saturates the linear instability of all other modes. The instability depends on the radial mode amplitude, the frequency difference, the damping rate of the non-radial mode, and the strength of the non-linear coupling between the modes considered. At the pulsation amplitudes typical for RR Lyrae stars, the instability of the monomode radial pulsation and the concomitant resonant excitation of some non-radial oscillation modes is found to be very likely.     

Peculiarities of the mode of oscillations in a floccule and its neighborhoods at different chromospheric levels

The behavior of oscillations in the quite solar chromosphere under a coronal hole at several heights has been investigated. The properties of oscillations in cell, network, and weak-floccule areas have been analyzed. A time series of spectrograms in three ionized calcium lines, the Ca II K and H resonance doublet lines and the infrared Ca II 849.8-nm triplet line, was used. The observations were carried out at the horizontal solar telescope of the Sayan Observatory. The goal of this study was to compare the distributions of spectral power in various frequency ranges and their variations for selected spatial areas at different heights of the chromosphere. Particular attention was paid to the weak floccule due to a noticeable difference in the central intensity distribution between the K and H lines and the 849.8-nm line. A spectral Fourier analysis was used. The central intensities of the observed spectral lines, the K-index, and the equivalent width (the latter for the 849.8-nm line) were chosen as oscillation parameters. The studies have shown that the main intensity oscillation power at both atmospheric levels is concentrated at frequencies below 9 mHz. In the distribution of intensity oscillation power at different chromospheric levels, there are differences clearly distinguishable in the floccule. Powerful five-minute oscillations whose main peak frequency decreases with height, while the amplitude increases have been detected in the central part of the floccule. This result confirms the assumptions recently pointed out in the literature that vertical magnetic field concentrations can serve as a channel for the passage of low-frequency oscillations from the photosphere to the chromosphere in faculae. The intensity oscillation power in the frequency ranges under consideration has turned out to decrease with height, on average, for the entire observed spatial area. This may be related to the loss of part of the wave energy through the reflection, dissipation, and transformation of wave modes in the magnetic canopy layer. An area with a low brightness but powerful oscillations at about 3.3 mHz covering a considerable range of heights probably pertaining to “magnetic flashers” has been isolated in the telescope’s field of view.     

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)     

Mixing-length theory and the excitation of solar acoustic oscillations

The stability of radial solar acoustic oscillations is studied using a time-dependent formulation of mixing-length theory. Though the radiation field is treated somewhat simplistically with the Eddington approximation, and we appreciate that any coupling of the pulsation to the radiation field is important, for the lower frequency radial modes that have been computed this should not produce too serious an error. Instead, we have concentrated upon treating the coupling with convection as accurately as is currently possible with generalized mixing-length theory in order to learn something about its pertinence. Our principal conclusion is that, according to this theory, solar radial acoustic oscillations are expected to be stable and generated by turbulence. Moreover, the theory predicts changes in mode frequency that may, in part, explain the discrepancy between solar observations and the adiabatic pulsation frequencies of theoretical models. We also compute the amplitudes of the modes using a theory of stochastic excitation. These are in good agreement with observed power spectra.     

Multi-Ridge Fitting for Ring-Diagram Helioseismology

Inferences of subsurface flow velocities using local domain ring-diagram helioseismology depend on measuring the frequency shifts of oscillation modes seen in acoustic power spectra. Current methods for making these measurements use maximum-likelihood fitting techniques to match a model of modal power to the spectra. The model typically describes a single oscillation mode, and each mode in a given power spectrum is fit independently. We present a new method that produces measurements with higher reliability and accuracy by fitting multiple modes simultaneously. We demonstrate that this method permits measuring sub-surface flows deeper into the Sun while providing higher uniformity in data coverage and velocity response closer to the limb of the solar disk. While the previous fitting method performs better for some measurements of low phase-speed modes, we find this new method to be particularly useful for high phase-speed modes and small spatial areas.     

Excitation and visibility of slow modes in rotating B-type stars

We use the traditional approximation to describe oscillations with frequencies comparable to the angular rotation rate. Validity of this approximation in application to main-sequence B stars is discussed. Numerical results regarding mode stability and visibility are presented for a model of the Be star HD 163868. For this object, Walker et al. detected a record number of mode frequencies using data from the small space telescope MOST . Our interpretation of these data differs from that of Walker et al. In particular, we interpret peaks in the lowest frequency range as retrograde g modes. We find instability in a large number of modes that remain undetectable because of unfavourable aspect and/or effect of cancellation. There is no clear preference to excitation of prograde modes.     

Non-linear effects of VLF noise generation by electron beams in the polar magnetosphere

A theory of VLF noise excitation by electron beams in the polar magnetosphere is proposed. Two modes of excited oscillations are considered: waves with frequencies in the vicinity of the lower hybrid resonance (LHR) from about 50 to 1000 kHz and whistler-mode waves in the frequency range of several kHz.The spectral distribution and the level of turbulent noise, having been excited by means of two counterstreaming electron beams, are deduced in magnetized plasma at the LHR frequency. It is also shown that the growth of noise up to the quasistationary level oscillates with time. Energy density of oscillations at the LHR frequency in the region of the dayside polar cusp agrees with the experimental data.The processes of whistler excitation by electron beams are discussed. The growth rate of excitation of whistler-mode by electrostatic oscillations at the LHR frequency is calculated.     

Global fits for the spectral index of the cosmological curvature perturbation

Best-fitting values of the spectral index of the curvature perturbation are presented, assuming the ΛCDM cosmology. Apart from the spectral index, the parameters are the Hubble parameter, the total matter density and the baryon density. The data points are intended to represent all measurements that are likely to affect the result significantly. The cosmic microwave anisotropy is represented by the COBE normalization, and heights of the first and second peaks are given by the latest Boomerang and Maxima data. The slope of the galaxy correlation function and the matter density contrast on the 8  h ⁻¹ Mpc scale are each represented by a data point, as are the expected values of the Hubble parameter and matter density. The 'low-deuterium' nucleosynthesis value of the baryon density provides a final data point, the fit giving a value higher by about one standard deviation. The reionization epoch is calculated from the model by assuming that it corresponds to the collapse of a fraction f ≳10⁻⁴ of matter. We consider the case of a scale-independent spectral index, and also the scale-dependent spectral index predicted by running mass models of inflation. In the former case, the result is compared with the prediction of models of inflation based on effective field theory, in which the field value is small on the Planck scale. A detailed comparison is made with other fits, and other approaches to the comparison with theory.     

Stochastic excitation of gravity modes in massive main-sequence stars

We investigate the possibility that gravity modes can be stochastically excited by turbulent convection in massive main-sequence (MS) stars. We build stellar models of MS stars with masses M=10?M _⊙,15?M _⊙, and 20?M _⊙. For each model, we then compute the power supplied to the modes by turbulent eddies in the convective core (CC) and the outer convective zones (OCZ). We found that, for asymptotic gravity modes, the major part of the driving occurs within the outer iron convective zone, while the excitation of low n order modes mainly occurs within the CC. We compute the mode lifetimes and deduce the expected mode amplitudes. We finally discuss the possibility of detecting such stochastically-excited gravity modes with the CoRoT space-based mission.     

Analysis of MDI High-Degree Mode Frequencies and their Rotational Splittings

We present a detailed analysis of solar acoustic mode frequencies and their rotational splittings for modes with degree up to 900. They were obtained by applying spherical harmonic decomposition to full-disk solar images observed by the Michelson Doppler Imager onboard the Solar and Heliospheric Observatory spacecraft. Global helioseismology analysis of high-degree modes is complicated by the fact that the individual modes cannot be isolated, which has limited so far the use of high-degree data for structure inversion of the near-surface layers (r>0.97R _⊙). In this work, we took great care to recover the actual mode characteristics using a physically motivated model which included a complete leakage matrix. We included in our analysis the following instrumental characteristics: the correct instantaneous image scale, the radial and non-radial image distortions, the effective position angle of the solar rotation axis, and a correction to the Carrington elements. We also present variations of the mode frequencies caused by the solar activity cycle. We have analyzed seven observational periods from 1999 to 2005 and correlated their frequency shift with four different solar indices. The frequency shift scaled by the relative mode inertia is a function of frequency alone and follows a simple power law, where the exponent obtained for the p modes is twice the value obtained for the f modes. The different solar indices present the same result.     

Constrained estimates of low-degree mode frequencies and the determination of the interior structure of the Sun

Low-degreep-modes penetrate to the solar centre and provide direct information about the core. However, the high observational accuracy that is required to resolve the details of the structure of the core is difficult to achieve because the oscillation power spectrum is significantly distorted by stochastic forcing of the oscillations, which appears as multiplicative noise. Here, an attempt is reported to reduce uncertainties of spectral parameter estimation by incorporating constraints imposed by smooth behaviour of some of the parameters (e.g., linewidths, background noise, rotational splitting) over a group of lines. Instead of estimating these parameters independently for each line, we determine them as smooth functions of frequency. It is expected that this procedure gives more accurate estimates of the average frequencies of any multiplet in the power spectrum, to which we have applied no constraints. We give some examples of the procedure for whole-disk measurements by the IPHIR space experiment. It is shown that the additional constraints do not result in significant changes in the frequency estimates, except for one mode whose peak in the power spectrum has the lowest signal-to-noise ratio. However, the uncertainty in the frequency of that mode does not influence substantially the results of the structure inversion in the core. Inversions of the IPHIR datasets are compared with corresponding inversions of data from the Birmingham Solar Oscillation Network (BISON). The IPHIR data indicate a sharp increase towards the centre of the deviation of the squared sound speed of the sun from that of a standard solar model, whereas the BISON data show a decrease. The difference between the IPHIR and BISON inversions is significant, preventing any definite conclusion about the deviation of the structure of the solar core from that of the model.     

The spherical infall model in a cosmological background density field

We discuss the influence of the cosmological background density field on the spherical infall model. The spherical infall model has been used in the PressSchechter formalism to evaluate the number abundance of clusters of galaxies, as well as to determine the density parameter of the Universe from the infalling flow. Therefore, the understanding of collapse dynamics plays a key role for extracting cosmological information. Here, we consider a modified version of the spherical infall model. We derive the mean field equations from the Newtonian fluid equations, in which the influence of cosmological background inhomogeneity is incorporated into the averaged quantities as the backreaction . By calculating the averaged quantities explicitly, we obtain simple expressions and find that, in the case of a scale-free power spectrum, density fluctuations with a negative spectral index make the infalling velocities slow. This suggests that we underestimate the density parameter when using the simple spherical infall model. In cases with the index n >0, the effect of background inhomogeneity could be negligible and the spherical infall model becomes a good approximation for infalling flows. We also present a realistic example with a cold dark matter power spectrum. In this case, the mean infall tends to be slow owing to the anisotropic random velocity.     

The visibility of low‐frequency solar acoustic modes

We make predictions of the detectability of low‐frequency p modes. Estimates of the powers and damping times of these low‐frequency modes are found by extrapolating the observed powers and widths of higher‐frequency modes with large observed signal‐to‐noise ratios. The extrapolations predict that the low‐frequency modes will have small signal‐to‐noise ratios and narrow widths in a frequency‐power spectrum. Monte Carlo simulations were then performed where timeseries containing mode signals and normally distributed Gaussian noise were produced. The mode signals were simulated to have the powers and damping times predicted by the extrapolations. Various statistical tests were then performed on the frequency‐amplitude spectra formed from these timeseries to investigate the fraction of spectra in which the modes could be detected. The results of these simulations were then compared to the number of p‐modes candidates observed in real Sun‐as‐a‐star data at low frequencies. The fraction of simulated spectra in which modes were detected decreases rapidly as the frequency of modes decreases and so the fraction of simulations in which the low‐frequency modes were detected was very small. However, increasing the signal‐to‐noise (S/N) ratio of the low‐frequency modes by a factor of 2 above the extrapolated values led to significantly more detections. Therefore efforts should continue to further improve the quality of solar data that is currently available. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Uncovering the Bias in Low-Degree p-Mode Linewidth Fitting

Obtaining reliable estimates of linewidths in the power spectra of low-degree p modes is problematic at low frequency. In this regime, the mode coherence time increases with decreasing frequency, often causing the modes to be unresolved in relatively long duration spectra. The signal-to-noise ratio is also less favourable at low frequency, resulting in fits to power spectra underestimating the true linewidth of the p modes owing to the tails of the Lorentzian peaks becoming dominated by the background noise. We use a numerical simulation approach to assess the effect of this bias on the fitted widths of p-mode peaks and calculate observational duration limits required to obtain an unbiased estimate of the p-mode linewidth as a function of frequency. This is done in four different cases, where the precision of the artificial data is set at 0.25, 0.50, 0.75, and 1.00 m?s^?1 by adding random?scatter to increase the sample standard deviation per 40-second measurement. In all cases, the observational duration required to accurately obtain width estimates increases beyond that required for sufficient spectral resolution below a certain threshold frequency. For modes at ≈?1500 μHz, with an amplitude of approximately ten times the background, observations of up to 972 days are required to obtain an unbiased estimate of the linewidth. This is equivalent to ≈?18 times the coherence time of the corresponding p modes.     

Drift anisotropy instability of a finite-β magnetospheric plasma

A unified theory of low frequency instabilities in a two component (cold and hot) finite-β magnetospheric plasma is suggested. It is shown that the low frequency oscillations comprise two wave modes : compressional Alfvén and drift mirror mode. No significant coupling between them is found in the long-wave approximation. Instabilities due to spontaneous excitation of these oscillations are considered. It is found that the temperature anisotropy significantly influences the instability growth rate at low frequency. A new instability due to the temperature anisotropy and density gradient appears when the frequency of compressional Alfvén waves is close to the drift mirror mode frequency. The theoretical predictions are compared in detail with the Pc5 event of 27 October 1978 observed simultaneously by the GEOS 2 satellite and the STARE radar facility. It is shown that the experimental results can be interpreted in terms of a compressional Alfvén wave driven by the drift anisotropy instability.     

Velocity oscillations in the solar atmosphere

From a series of long duration continuous Doppler records of selected spectral lines, characteristics of solar velocity oscillations have been studied. Statistical distribution of the durations of the bursts of oscillations has been estimated. From the nature of distortion of the waveforms of the oscillation, the presence of disturbing impulses has been speculated. Constancy and homogeneity of the oscillations have been examined from detailed spectral density plots. Duration indices for the oscillations at different heights in the solar atmosphere have been derived by estimating mean spectral densities of characteristic oscillation amplitudes during several individual bursts and comparing them with corresponding spectral densities from long records. The variation among experimental results has been explained as due to the limitations of the power spectral analysis method on short records.     

Investigation of Long-Period Oscillations of Sunspots with Ground-Based (Pulkovo) and SOHO/MDI Data

We applied special data-processing algorithms to the study of long-period oscillations of the magnetic-field strength and the line-of-sight velocity in sunspots. The oscillations were investigated with two independent groups of data. First, we used an eight-hour-long series of solar spectrograms, obtained with the solar telescope at the Pulkovo Observatory. We simultaneously measured Doppler shifts of six spectral lines, formed at different heights in the atmosphere. Second, we had a long time series of full-disk magnetograms (10 – 34 hour) from SOHO/MDI for the line-of-sight magnetic-field component. Both ground- and space-based observations revealed long-period modes of oscillations (40 – 45, 60 – 80, and 160 – 180 minutes) in the power spectrum of the sunspots and surrounding magnetic structures. With the SOHO/MDI data, one can study the longer periodicities. We obtained two new significant periods (> 3σ) in the power spectra of sunspots: around 250 and 480 minutes. The power of the oscillations in the lower frequencies is always higher than in the higher ones. The amplitude of the long-period magnetic-field modes shows magnitudes of about 200 – 250 G. The amplitude of the line-of-sight velocity periodicities is about 60 – 110 m s⁻¹. The absence of low-frequency oscillations in the telluric line proves their solar nature. Moreover, the absence of low-frequency oscillations of the line-of-sight velocity in the quiet photosphere (free of magnetic elements) proves their direct connection to magnetic structures. Long-period modes of oscillation observed in magnetic elements surrounding the sunspot are spread over the meso-granulation scales (10″ – 12″), while the sunspot itself oscillates as a whole. The amplitude of the long-period mode of the line-of-sight velocity in a sunspot decreases rapidly with height: these oscillations are clearly visible in the spectral lines originating at heights of approximately 200 km and fade away in lines originating at 500 km. We found a new interesting property: the low-frequency oscillations of a sunspot are strongly reduced when there is a steady temporal trend (strengthening or weakening) of the sunspot’s magnetic field. Another important result is that the frequency of long-period oscillations evidently depends on the sunspot’s magnetic-field strength.