Variability of Solar Five-Minute Oscillations in the Corona as Observed by the Extreme Ultraviolet Spectrophotometer (ESP) on the Solar Dynamics Observatory/Extreme Ultraviolet Variability Experiment (SDO/EVE)

Solar five-minute oscillations have been detected in the power spectra of two six-day time intervals from soft X-ray measurements of the Sun observed as a star using the Extreme Ultraviolet Spectrophotometer (ESP) onboard the Solar Dynamics Observatory (SDO)/Extreme Ultraviolet Variability Experiment (EVE). The frequencies of the largest amplitude peaks were found to match the known low-degree (?=0?–?3) modes of global acoustic oscillations within 3.7 μHz and can be explained by a leakage of the global modes into the corona. Due to the strong variability of the solar atmosphere between the photosphere and the corona, the frequencies and amplitudes of the coronal oscillations are likely to vary with time. We investigated the variations in the power spectra for individual days and their association with changes of solar activity, e.g. with the mean level of the EUV irradiance, and its short-term variations caused by evolving active regions. Our analysis of samples of one-day oscillation power spectra for a 49-day period of low and intermediate solar activity showed little correlation with the mean EUV irradiance and the short-term variability of the irradiance. We suggest that some other changes in the solar atmosphere, e.g., magnetic fields and/or inter-network configuration may affect the mode leakage to the corona.     

Velocity fields in the solar atmosphere

Observations of velocity fields in the solar atmosphere made with the Mount Wilson solar magnetograph are analyzed. These observations, which were made with very high velocity sensitivity, cover nearly 250 hours and were made with apertures of several sizes and at various parts of the solar disk, and in strong and weak magnetic fields. The amplitudes of the 300-sec oscillations are about 25% weaker in regions where the magnetic field is greater than 80 gauss than where the field is less than 10 gauss. No difference in the frequencies of the oscillations could be found between strong-field and field-free regions. It is suggested that the oscillations occur only where the field is absent and the lower amplitude in a strong field represents the fraction of the magnetograph aperture occupied by a magnetic field. The element sizes for the 300-sec oscillations are probably at least 5–10 arc seconds.Observations made simultaneously with two lines formed at different depths in the solar atmosphere showed small phase differences in the 5-min oscillations. The upper level showed shorter period oscillations when the lower level oscillations underwent phase changes.A short period oscillation is found superposed on the 300-sec oscillation. These SPOs come in bursts that last for a minute or two and have average amplitudes that fall in the range 0.05–0.10 km/sec peak to peak. All attempts to explain them as instrumental or seeing effects have failed. Their periods fall in the range 1–5 seconds. The horizontal scale of these oscillations is smaller than that of the 300-sec oscillations, and the SPOs are more nearly isotropic oscillations than are these around 300 seconds. They do not represent a high-frequency tail of the latter. These observations did not have a digitizing interval short enough to analyze the SPOs for power spectra, but it is clear from the tracings that they are not a nearly monochromatic oscillation as are the longer waves. The amplitudes of the SPOs in the solar atmosphere must be very large and they contribute greatly to the non-radiative energy flux. It is suggested that they represent a large microturbulence line-broadening effect.     

Detection of Periodic Oscillations in Sunspot-Associated Radio Sources

Using microwave observations made with the Nobeyama radioheliograph (=1.76 cm), we have studied temporal variations of sunspot-associated sources in the circularly polarized component. For all three cases of well-developed and rather stable sunspots we found nearly harmonic oscillations with periods in a range of 120–220 s. In one case of an unstable and quickly devolving active region, the fluctuations appear to be irregular with no dominant period. Sunspot-associated solar radio sources are known to be generated by cyclotron radiation of thermal electrons in magnetic tubes of sunspots at the level of the lower solar corona or chromosphere–corona transition region (CCTR). At the wavelength of 1.76 cm, the polarized emission arises in a layer where the magnetic field is B=2000 G (assuming the emission generated at the third harmonic of electron gyrofrequency). We suggest that the observed effect is a manifestation of the well-known 3-min oscillations observed in the chromosphere and photosphere above sunspots. The observed effects are believed to be a result of resonance oscillation of MHD waves inside a magnetic tube. Radio observations of this phenomenon open a new tool for studying regions of reflection of MHD waves near CCTR level. The method is very sensitive both to the height of the CCTR and magnetic fields above sunspots. Thus, detection of oscillations of the height of the transition region even with an amplitude of a few km are possible. The use of a spectrum of one of the observed sources obtained with the radio telescope RATAN-600 allows us to conclude that oscillations in magnetic field strength of about 4 G could be responsible for the effect and are reliably registered. The appearance of the famous 5-min oscillations in the solar atmosphere was also registered in some spectra of radio oscillations.     

MAG Waves in Sunspots Umbrae: Slow Waves Leaking to the Corona

The linear oscillations of a stratified atmosphere embedded in a uniform vertical magnetic field are studied here. We use a simple theoretical model, formed by the superposition of two isothermal layers, representing, respectively, i) the photosphere and the chromosphere, and ii) the corona. The bottom layer behaves, for some modes, as a resonant cavity where MAG waves are semi-trapped. We find the existence of two types of modes: 1) Fast modes which are trapped below the transition layer, 2) Mixed modes which are resonant modes in the first layer and leak part of the energy to the corona. These mixed modes have been found to be damped in the horizontal direction and can explain the observed slow modes in the corona.     

Heat flux as a source of ion-acoustic oscillations in the transition region of the solar atmosphere

Based on model calculations, we show that ion-acoustic oscillations can be excited by heat fluxes in a plasma. We discuss the probable effect of ion-acoustic oscillations on the formation of temperature gradients at critical heat fluxes. The local critical heat flux in the transition region of the solar atmosphere is close to the well-known experimental heat flux from the corona into the chromosphere.     

Magnetar corona

Persistent high-energy emission of magnetars is produced by a plasma corona around the neutron star, with total energy output of ～10³⁶ erg/s. The corona forms as a result of sporadic starquakes that twist the external magnetic field of the star and induce electric currents in the closed magnetosphere. Once twisted, the magnetosphere cannot untwist immediately because of its self-induction. The self-induction electric field lifts particles from the stellar surface, accelerates them, and initiates avalanches of pair creation in the magnetosphere. The created plasma corona maintains the electric current demanded by curl B and regulates the self-induction e.m.f. by screening. This corona persists in dynamic equilibrium: it is continually lost to the stellar surface on the light-crossing time ～10^?4 s and replenished with new particles. In essence, the twisted magnetosphere acts as an accelerator that converts the toroidal field energy to particle kinetic energy. The voltage along the magnetic field lines is maintained near threshold for ignition of pair production, in the regime of self-organized criticality. The voltage is found to be about ～1 GeV which is in agreement with the observed dissipation rate ～10³⁶ erg/s. The coronal particles impact the solid crust, knock out protons, and regulate the column density of the hydrostatic atmosphere of the star. The transition layer between the atmosphere and the corona is the likely source of the observed 100 keV emission. The corona also emits curvature radiation up to 10¹⁴ Hz and can supply the observed IR-optical luminosity.     

Oscillatory Response of the 3D Solar Atmosphere to the Leakage of Photospheric Motion

The direct propagation of acoustic waves, driven harmonically at the solar photosphere, into the three-dimensional solar atmosphere is examined numerically in the framework of ideal magnetohydrodynamics. It is of particular interest to study the leakage of 5-minute global solar acoustic oscillations into the upper, gravitationally stratified and magnetised atmosphere, where the modelled solar atmosphere possesses realistic temperature and density stratification. This work aims to complement and bring further into the 3D domain our previous efforts (by Erdélyi et al., 2007, Astron. Astrophys. 467, 1299) on the leakage of photospheric motions and running magnetic-field-aligned waves excited by these global oscillations. The constructed model atmosphere, most suitable perhaps for quiet Sun regions, is a VAL IIIC derivative in which a uniform magnetic field is embedded. The response of the atmosphere to a range of periodic velocity drivers is numerically investigated in the hydrodynamic and magnetohydrodynamic approximations. Among others the following results are discussed in detail: i) High-frequency waves are shown to propagate from the lower atmosphere across the transition region, experiencing relatively low reflection, and transmitting most of their energy into the corona; ii) the thin transition region becomes a wave guide for horizontally propagating surface waves for a wide range of driver periods, and particularly at those periods that support chromospheric standing waves; iii) the magnetic field acts as a waveguide for both high- and low-frequency waves originating from the photosphere and propagating through the transition region into the solar corona. Electronic Supplementary Material  The online version of this article () contains supplementary material, which is available to authorized users.     

Neutrino Tomography – Learning About The Earth’s Interior Using The Propagation Of Neutrinos

Because the propagation of neutrinos is affected by the presence of Earth matter, it opens new possibilities to probe the Earth’s interior. Different approaches range from techniques based upon the interaction of high energy (above TeV) neutrinos with Earth matter, to methods using the MSW effect on the oscillations of low energy (MeV to GeV) neutrinos. In principle, neutrinos from many different sources (sun, atmosphere, supernovae, beams etc.) can be used. In this talk, we summarize and compare different approaches with an emphasis on more recent developments. In addition, we point out other geophysical aspects relevant for neutrino oscillations.     

Radiative Cooling in MHD Models of the Quiet Sun Convection Zone and Corona

We present a series of numerical simulations of the quiet-Sun plasma threaded by magnetic fields that extend from the upper convection zone into the low corona. We discuss an efficient, simplified approximation to the physics of optically thick radiative transport through the surface layers, and investigate the effects of convective turbulence on the magnetic structure of the Sun’s atmosphere in an initially unipolar (open field) region. We find that the net Poynting flux below the surface is on average directed toward the interior, while in the photosphere and chromosphere the net flow of electromagnetic energy is outward into the solar corona. Overturning convective motions between these layers driven by rapid radiative cooling appears to be the source of energy for the oppositely directed fluxes of electromagnetic energy.     

Oscillations in a Magnetized Model Atmosphere with Non-Constant Coefficient of Thermal Conductivity

This paper extends previous investigations of non-adiabatic, oscillatory motions in plane-parallel, gravitationally stratified, magnetized atmospheres by replacing the simple polytropic equilibrium atmosphere with the detailed umbral model atmosphere of Thomas and Scheuer (1982). A normal mode analysis is performed on three cavities defined within the vertical extent of the model. For this work, the coefficient of thermal conductivity is taken to be a function of the temperature and the constant magnetic field is aligned with the direction of gravity. This significantly alters the structure of the eigenspectrum from that of the simpler models using a constant coefficient of thermal conductivity. When evaluated with physical parameters relevant to sunspot umbrae, 5-min and several 3-min oscillations are detected in the cavity from the upper photosphere to the temperature minimum whereas only 3-min oscillations are found in the spatially larger cavity from the upper photosphere to the chromosphere/corona transition region.     

Multilevel Analysis of Oscillation Motions in Active Regions of the Sun

The nature of the three-minute and five-minute oscillations observed in sunspots is considered to be an effect of propagation of magnetohydrodynamic (MHD) waves from the photosphere to the solar corona. However, the real modes of these waves and the nature of the filters that result in rather narrow frequency bands of these modes are still far from being generally accepted, in spite of a large amount of observational material obtained in a wide range of wave bands. The significance of this field of research is based on the hope that local seismology can be used to find the structure of the solar atmosphere in magnetic tubes of sunspots. We expect that substantial progress can be achieved by simultaneous observations of the sunspot oscillations in different layers of the solar atmosphere in order to gain information on propagating waves. In this study we used a new method that combines the results of an oscillation study made in optical and radio observations. The optical spectral measurements in photospheric and chromospheric lines of the line-of-sight velocity were carried out at the Sayan Solar Observatory. The radio maps of the Sun were obtained with the Nobeyama Radioheliograph at 1.76 cm. Radio sources associated with the sunspots were analyzed to study the oscillation processes in the chromosphere – corona transition region in the layer with magnetic field B=2000 G. A high level of instability of the oscillations in the optical and radio data was found. We used a wavelet analysis for the spectra. The best similarities of the spectra of oscillations obtained by the two methods were detected in the three-minute oscillations inside the sunspot umbra for the dates when the active regions were situated near the center of the solar disk. A comparison of the wavelet spectra for optical and radio observations showed a time delay of about 50 seconds of the radio results with respect to the optical ones. This implies an MHD wave traveling upward inside the umbral magnetic tube of the sunspot. For the five-minute oscillations the similarity in spectral details could be found only for optical oscillations at the chromospheric level in the umbral region or very close to it. The time delays seem to be similar. Besides three-minute and five-minute ones, oscillations with longer periods (8 and 15 minutes) were detected in optical and radio records. Their nature still requires further observational and theoretical study for even a preliminary discussion.     

Intensity Oscillation in the Corona as Observed during the Total Solar Eclipse of 29 March 2006

We obtained the images of the eastern part of the solar corona in the Fe xiv 530.3 nm (green) and Fe x 637.4 nm (red) coronal emission lines during the total solar eclipse of 29 March 2006 at Manavgat, Antalya, Turkey. The images were obtained using a 35 cm Meade telescope equipped with a Peltier-cooled 2k × 2k CCD and 0.3 nm pass-band interference filters at the rates of 2.95 s (exposure times of 100 ms) and 2.0 s (exposure times of 300 ms) in the Fe xiv and Fe x emission lines, respectively. The analysis of the data indicates intensity variations at some locations with period of strongest power around 27 s for the green line and 20 s for the red line. These results confirm earlier findings of variations in the continuum intensity with periods in the range of 5 to 56 s by Singh et al. (Solar Phys. 170, 235, 1997). The wavelet analysis has been used to identify significant intensity oscillations at all pixels within our field of view. Significant oscillations with high probability estimates were detected for some locations only. These locations seem to follow the boundary of an active region and in the neighborhood, rather than within the loops themselves. These intensity oscillations may be caused by fast magneto-sonic waves in the solar corona and partly account for heating of the plasma in the corona.     

Oscillations in the Umbral Atmosphere

The results of simultaneous observations of oscillations in the chromosphere, transition region, and corona above nine sunspots are presented. The data are obtained through coordinated observing with the Solar and Heliospheric Observatory — SOHO and the Transition Region And Coronal Explorer — TRACE. Oscillations are detected above each umbra. The power spectra show one dominant frequency corresponding to a period close to 3 min. We show that the oscillations in the sunspot transition region can be modeled by upwardly propagating acoustic waves. In the corona the oscillations are limited to small regions that often coincide with the endpoints of sunspot coronal loops. Spectral observations show that oscillations in the corona contribute to the observed oscillations in the TRACE 171 Å channel observations. We show that a recent suggestion regarding a connection between sunspot plumes and 3-min oscillations conflicts with the observations.     

Observation of multiple sausage oscillations in cool post-flare loop

Using simultaneous high spatial (1.3 arcsec) and temporal (5 and 10 s) resolution Hα observations from the 15 cm Solar Tower Telescope at Aryabhatta Research Institute of Observational Sciences (ARIES), we study the oscillations in the relative intensity to explore the possibility of sausage oscillations in the chromospheric cool post-flare loop. We use the standard wavelet tool, and find the oscillation period of ≈587 s near the loop apex, and ≈349 s near the footpoint. We suggest that the oscillations represent the fundamental and the first harmonics of the fast-sausage waves in the cool post-flare loop. Based on the period ratio   P ₁/ P ₂∼1.68  , we estimate the density scaleheight in the loop as ∼17 Mm. This value is much higher than the equilibrium scaleheight corresponding to Hα temperature, which probably indicates that the cool post-flare loop is not in hydrostatic equilibrium. Seismologically estimated Alfvén speed outside the loop is  ∼300–330  km s⁻¹  . The observation of multiple oscillations may play a crucial role in understanding the dynamics of lower solar atmosphere, complementing such oscillations already reported in the upper solar atmosphere (e.g. hot flaring loops).     

On the sunspot transition region

The EUV line emission and relative line-of-sight velocity in the transition region between the chromosphere and corona of 36 sunspot regions are investigated, based on observations with the Coronal Diagnostic Spectrometer – CDS and the Solar Ultraviolet Measurements of Emitted Radiation – SUMER on the Solar and Heliospheric Observatory – SOHO. The most prominent features in the transition-region intensity maps are the sunspot plumes. In the temperature range between log T=5.2 and log T=5.6 we find that 29 of the 36 sunspots contain one or two sunspot plumes. The relative line-of-sight velocity in sunspot plumes is high and directed into the Sun in the transition region, for 19 of the sunspots the maximum velocity exceeds 25 km s^?1. The velocity increases with increasing temperature, reaches a maximum close to log T=5.5 and then decreases abruptly.

Attention is given to the properties of oscillations with a period of 3 min in the sunspot transition region, based on observations of six sunspots. Comparing loci with the same phase we find that the 3-min oscillations affect the entire umbral transition region and part of the penumbral transition region. Above the umbra the observed relation between the oscillations in peak line intensity and line-of-sight velocity is compatible with the hypothesis that the oscillations are caused by upward-propagating acoustic waves. Information about intensity oscillations in the low corona is obtained from observations of one sunspot in the 171 Å channel with the Transition Region And Coronal Explorer – TRACE. We conclude that we observe the 3-min sunspot oscillations in the chromosphere, the transition region and the low corona. The oscillations are observable over a wider temperature range than the sunspot plumes, and show a different spatial distribution than that of the plumes.

     

The solution for seasonal variations in the Earth's rate of rotation

New physical principles for an explanation of seasonal variations in the Earth's rate of rotation are proposed. It is thought that the variations are caused by a variation of the total energy of the Earth's atmosphere in the course of the planet's revolution about the Sun in elliptic orbit. Jacobi's virial equation for the Earth's atmosphere is derived from the Eulerian equations. The virial theorem is obtained. The existence of the relationship between Jacobi's function and potential energy of the atmosphere is confirmed. In the framework of this relationship, Jacobi's equation is reduced to the equation of unperturbed virial oscillations. The solution of the above-mentioned equation expresses the periodic virial oscillations of Jacobi's function (moment of inertia) of the Earth's atmosphere with time. The solution of the perturbed virial oscillation problem of the atmosphere-solid Earth system is obtained. The perturbation term in Jacobi's virial equation regards, in explicit form, the energy changes occurring in the atmosphere in the course of the planet's revolution about the Sun in elliptic orbit. The annual and semi-annual periodic variations in the Earth's rate of rotation can be considered as an astrometrical result following from the obtained solution. A satisfactory accord of the theoretical results with experimental data is shown.     

Transverse oscillations in solar spicules induced by propagating Alfvénic pulses

The excitation of Alfvénic waves in solar spicules by localized Alfvénic pulses is investigated. A set of incompressible MHD equations in the two-dimensional x–z plane with steady flows and sheared magnetic fields is solved. Stratification due to gravity and transition region between chromosphere and corona is taken into account. An initially localized Alfvénic pulse launched below the transition region can penetrate from transition region into the corona. We show that the period of the transversal oscillations is in agreement with those observed in spicules. Moreover, it is found that the excited Alfvénic waves spread during propagation along the spicule length, and suffer efficient damping of the oscillations amplitude. The damping time of the transverse oscillations increased with decreasing k _b values.     

The heating of the solar corona

The heating of the solar corona has been a fundamental astrophysical issue for over sixty years. Over the last decade in particular, space-based solar observatories (Yohkoh, SOHO and TRACE) have revealed the complex and often subtle magnetic-field and plasma interactions throughout the solar atmosphere in unprecedented detail. It is now established that any energy release mechanism is magnetic in origin - the challenge posed is to determine what specific heat input is dominating in a given coronal feature throughout the solar cycle. This review outlines a range of possible magnetohydrodynamic (MHD) coronal heating theories, including MHD wave dissipation and MHD reconnection as well as the accumulating observational evidence for quasi-periodic oscillations and small-scale energy bursts occurring in the corona. Also, we describe current attempts to interpret plasma temperature, density and velocity diagnostics in the light of specific localised energy release. The progress in these investigations expected from future solar missions (Solar-B, STEREO, SDO and Solar Orbiter) is also assessed.Received: 6 February 2003, Published online: 14 November 2003 Correspondence to: R. W. Walsh     

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.     

Comptonization and QPO origins in accreting neutron star systems

We develop a simple, time-dependent Comptonization model to probe the origins of spectral variability in accreting neutron star systems. In the model, soft 'seed photons' are injected into a corona of hot electrons, where they are Compton upscattered before escaping as hard X-rays. The model describes how the hard X-ray spectrum varies when the properties of either the soft photon source or the Comptonizing medium undergo small oscillations. Observations of the resulting spectral modulations can determine whether the variability is due to (i) oscillations in the injection of seed photons, (ii) oscillations in the coronal electron density, or (iii) oscillations in the coronal energy dissipation rate. Identifying the origin of spectral variability should help clarify how the corona operates and its relation to the accretion disc. It will also help in finding the mechanisms underlying the various quasi-periodic oscillations (QPOs) observed in the X-ray outputs of many accreting neutron star and black hole systems. As a sample application of our model, we analyse a kilohertz QPO observed in the atoll source 4U 1608–52. We find that the QPO is driven predominantly by an oscillation in the electron density of the Comptonizing gas.