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)     

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)     

YAOPBM – yet another peak bagging method

I present and discuss the fitting methodology I developed for very‐long time series (2088‐day‐long). This new method was first used to fit low degree modes, 𝓁 ≤ 25. That time series was also sub‐divided in somewhat shorter segments (728‐daylong) and also fitted for these low degrees, in order to measure changes with the solar activity level. I have recently extended the fitting in several “directions”: 1) to substantially higher degrees (𝓁 ≤ 125), 2) to shorter time series (364‐ and 182‐day‐long), and, 3) to additional 728‐day‐long segments, covering now some 10 years of observations. I present and discuss issues related to this expansion, namely problems at low frequencies affecting the f and p₁ modes, and the inadequacy of the leakage matrix at higher degrees. I also present some of the characteristics of the observed temporal changes in the resulting frequencies. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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)     

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)     

Oscillatory Modes of a Prominence – PCTR – Corona Slab Model

Oscillations of magnetic structures in the solar corona have often been interpreted in terms of magnetohydrodynamic waves. We study the adiabatic magnetoacoustic modes of a prominence plasma slab with a uniform longitudinal magnetic field, surrounded by a prominence – corona transition region (PCTR) and a coronal medium. Considering linear small-amplitude oscillations, we deduce the dispersion relation for the magnetoacoustic slow and fast modes by assuming evanescentlike perturbations in the coronal medium. In the system without PCTR, a classification of the oscillatory modes according to the polarisation of their eigenfunctions is made to distinguish modes with fastlike or slowlike properties. Internal and external slow modes are governed by the prominence and coronal properties, respectively, and fast modes are mostly dominated by prominence conditions for the observed wavelengths. In addition, the inclusion of an isothermal PCTR does not substantially influence the mode frequencies, but new solutions (PCTR slow modes) are present.     

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)     

The effects of density stratification on standing fast body oscillations in coronal loops and dissipation

The standing magnetohydrodynamic (MHD) quasi-linear modes in a zero-β cylindrical magnetic flux tube that undergoes a longitudinal density stratification and radial density structuring are considered. The radial structuring is assumed to have a step-like density profile. The dispersion relation for the fast MHD body waves is derived and solved numerically to obtain the frequencies of the fundamental, first-overtone and second-overtone   k = 1, 2, 3  modes of both kink  ( m = 1)  and fluting  ( m = 2)  waves, where k and m are the longitudinal and azimuthal mode numbers, respectively. Damping rates due to both viscous and resistive dissipations in the presence of the density stratification are derived and solved numerically for the first three modes of both kink and fluting waves.     

Distribution of magnetic flux on the solar surface and low-degree p-modes

The frequencies of solar p-modes are known to change over the solar cycle. There is also recent evidence that the relation between frequency shift of low-degree modes and magnetic flux or other activity indicators differs between the rising and falling phases of the solar cycle, leading to a hysteresis in such diagrams. We consider the influence of the changing large-scale surface distribution of the magnetic flux on low-degree ( l ≤3) p-mode frequencies. To that end, we use time-dependent models of the magnetic flux distribution and study the ensuing frequency shifts of modes with different order and degree as a function of time. The resulting curves are periodic functions (in simple cases just sine curves) shifted in time by different amounts for the different modes. We show how this may easily lead to hysteresis cycles comparable to those observed. Our models suggest that high-latitude fields are necessary to produce a significant difference in hysteresis between odd- and even-degree modes. Only magnetic field distributions within a small parameter range are consistent with the observations by Jiménez-Reyes et al. Observations of p-mode frequency shifts are therefore capable of providing an additional diagnostic of the magnetic field near the solar poles. The magnetic distribution that is consistent with the p-mode observations also appears reasonable compared with direct measurements of the magnetic field.     

MHD waves at a spherical interface modelling EIT waves

Eruptive events such as flares and coronal mass ejections (CMEs) are known to generate global waves propagating over distances comparable to the solar radius in different layers of the solar atmosphere. Here we investigate the propagation of coronal EIT waves, modelled as fast magnetoacoustic modes propagating at a spherical interface in the presence of a purely radial magnetic field. Based on a simplified equilibrium we derive the dispersion relation of the waves. The generation and propagation of EIT waves at the spherical interface is studied numerically for different values of spherical degree and preliminary conclusions are reached regarding the properties of EIT waves. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of Gravity on the Fast Modes of a Horizontal Coronal Slab

Theoretical studies of the normal modes of a coronal slab often neglect gravity, as in Edwin and Roberts (Solar Phys. 71, 239, 1982). Here we study analytically the effect of gravity acting on a horizontal slab as a first step away from a homogeneous medium. Because of the inclusion of gravity, the symmetry of a homogeneous slab is lost, so the normal modes cannot be classified into kink and sausage modes. The presence of gravity also modifies the oscillatory frequencies of the slab, as well as the lower cutoff frequency, resulting in the possible transition between surface and body modes. For general coronal parameters, the dimensionless gravity term turns out to be small, so these effects are also small. A.J. Díaz’s current affiliation: Universitat de les Illes Balears, Palma, E-07122, Spain.     

Review of Hinode results

Hinode is an observatory‐style satellite, carrying three advanced instruments being designed and built to work together to explore the physical coupling between the photosphere and the upper layers for understanding the mechanism of dynam‐ ics and heating. The three instruments aboard are the Solar Optical Telescope (SOT), which can provide high‐precision photometric and polarimetric data of the lower atmosphere in the visible light (388–668 nm) with a spatial resolution of 0.2–0.3 arcseconds, the X‐Ray Telescope (XRT) which takes a wide field of full sun coverage X‐ray images being capable of diagnosing the physical condition of coronal plasmas, and the EUV Imaging Spectrometer (EIS) which observes the upper transition region and coronal emission lines in the wavelength ranges of 17–21 nm and 25–29 nm. Since first‐light observations in the end of October 2006, Hinode has been continuously providing unprecedented high‐quality solar data. We will present some new findings of the sun with Hinode, focusing on those from SOT (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

IR spectroscopy of COmosphere dynamics with the CO ?rst overtone band

We discuss observations of the weak ?rst overtone (Δν = 2) CO absorption band near 2300 nm with the U.S. National Solar Observatory Array Camera (NAC), a modern mid‐infrared detector. This molecular band provides a thermal diagnostic that forms lower in the atmosphere than the stronger fundamental band near 4600 nm. The observed center‐to‐limb increase in CO line width qualitatively agrees with the proposed higher temperature shocks or faster plasma motions higher in the COmosphere. The spatial extent of chromospheric shock waves is currently at or below the diffraction limit of the available CO lines at existing telescopes. Five minute period oscillations in line strength and measured Doppler shifts are consistent with the p‐mode excitation of the photospheric gas. We also show recent efforts at direct imaging at 4600 nm. We stress that future large‐aperture solar telescopes must be teamed with improved, dynamic mid‐infrared instruments, like the NAC, to capitalize on the features that motivate such facilities (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

An interpretation of rapid changes in the magnetic field associated with solar flares

The energy source of a flare is the magnetic field in the corona. A topological model of the magnetic field is used here for interpreting the recently discovered drastic changes in magnetic field associated with solar flares. The following observational results are self‐consistently explained: (1) the transverse field strength decreases at outer part of active regions and increases significantly in their centers; (2) the center‐of‐mass positions of opposite magnetic polarities converge towards the magnetic neutral line just after flares onset; (3) the magnetic flux of active regions decreases steadily during the course of flares. For X‐class flares, almost 50% events show such changes. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The effect of density stratification on the resonant absorption of MHD waves in coronal loops

The standing quasi-modes of the ideal magnetohydrodynamics (MHD) in a zero-β cylindrical magnetic flux tube that undergoes a longitudinal density stratification and radial density structuring are considered. The radial structuring is assumed to be a linearly varying density profile. Using the relevant connection formulae of the resonant absorption, the dispersion relation for the fast MHD body waves is derived and solved numerically to obtain both the frequencies and damping rates of the fundamental and first-overtone,   k = 1, 2  , modes of both the kink  ( m = 1)  and fluting  ( m = 2)  waves, where k and m are the longitudinal and azimuthal mode numbers, respectively.     

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)     

On the Excitation of Leaky Modes in Cylindrical Loops

The role of leaky waves in the coronal loop oscillations observed by TRACE is not yet clearly understood. In this work, the excitation of fast waves in solar coronal loops modelled as dense plasma cylindrical tubes in a uniform straight magnetic field is investigated. We study the trapped and especially leaky modes (whose energy escapes from the tube) that result from an initial disturbance by solving the time-dependent problem numerically. We find that the stationary state of the tube motion is given by the trapped normal modes. By contrast, the transient behaviour between the initial and the stationary phase is dominated by wave leakage. The so-called trig leaky modes are clearly identified since the transient behaviour shows periods and damping times that are in agreement with the values calculated from the normal-mode analysis. Consequently, these radiating modes have physical significance. However, we have not found any evidence for the excitation of other types of modes, such as the principal leaky kink mode. J. Andries is postdoctoral Fellow of the National Fund for Scientific Research – Flanders (Belgium) (F.W.O.-Vlaanderen).     

High resolution observations of white‐light emissions from the opacity minimum during an X‐class flare

Using high cadence, high resolution near infrared (NIR) observations of the X10 white‐light flare (WLF) on 2003 October 29, we investigated the evolution of the core‐halo structure of white‐light emission during the two‐second period flare peak. We found that size and intensity of the halo remained almost constant in the range of 10 Mm². However, the core area was very compact and expanded rapidly from about 1 Mm² to 4 Mm². At the same time, the total emission of the core increased nearly twenty times. This distinct behavior indicates that different heating mechanisms might be responsible for core and halo emissions. In addition to the temporal analysis, we compared the intensity enhancements of the flare core and halo. The result shows that the halo contrast increased by about 8% compared to the flare‐quiet region, which could be explained by a combination of direct‐heating and backwarming models (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Direct Propagation of Photospheric Acoustic <Emphasis Type="Italic">p</Emphasis> Modes into Nonmagnetic Solar Atmosphere

Solar p modes are one of the dominant types of coherent signals in Doppler velocity in the solar photosphere, with periods showing a power peak at five minutes. The propagation (or leakage) of these p-mode signals into the higher solar atmosphere is one of the key drivers of oscillatory motions in the higher solar chromosphere and corona. This paper examines numerically the direct propagation of acoustic waves driven harmonically at the photosphere, into the nonmagnetic solar atmosphere. Erdélyi et al. (Astron. Astrophys. 467, 1299, 2007) investigated the acoustic response to a single point-source driver. In the follow-up work here we generalise this previous study to more structured, coherent, photospheric drivers mimicking solar global oscillations. When our atmosphere is driven with a pair of point drivers separated in space, reflection at the transition region causes cavity oscillations in the lower chromosphere, and amplification and cavity resonance of waves at the transition region generate strong surface oscillations. When driven with a widely horizontally coherent velocity signal, cavity modes are caused in the chromosphere, surface waves occur at the transition region, and fine structures are generated extending from a dynamic transition region into the lower corona, even in the absence of a magnetic field.