Calculation of Spectral Darkening and Visibility Functions for Solar Oscillations

Calculations of spectral darkening and visibility functions for the brightness oscillations of the Sun resulting from global solar oscillations are presented. This has been done for a broad range of the visible and infrared continuum spectrum. The procedure for the calculations of these functions includes the numerical computation of depth-dependent derivatives of the opacity caused by p modes in the photosphere. A radiative-transport code was used for this purpose to get the disturbances of the opacities from temperature and density fluctuations. The visibility and darkening functions are obtained for adiabatic oscillations under the assumption that the temperature disturbances are proportional to the undisturbed temperature of the photosphere. The latter assumption is the only way to explore any opacity effects since the eigenfunctions of p-mode oscillations have not been obtained so far. This investigation reveals that opacity effects have to be taken into account because they dominate the violet and infrared part of the spectrum. Because of this dominance, the visibility functions are negative for those parts of the spectrum. Furthermore, the darkening functions show a wavelength-dependent change of sign for some wavelengths owing to these opacity effects. However, the visibility and darkening functions under the assumptions used contradict the observations of global p-mode oscillations, but it is beyond doubt that the opacity effects influence the brightness fluctuations of the Sun resulting from global oscillations.     

The influence of a finite conductivity on the spectrum of solar <Emphasis Type="Italic">p</Emphasis>-modes

We consider the influence of a finite conductivity on the spectrum of solar p-modes (by taking into account their absorption at cusp resonance levels) in a plane two-layer model that consists of an upper isothermal layer with a uniform horizontal magnetic field and a lower adiabatic layer with a linear increase in temperature with depth. We show that an allowance for the finite, but high conductivity of the medium is required only to calculate the eigenfrequencies of the p-modes for which the resonance levels are located almost at the interface between the layers.     

Effect of Wave Motions in the Active Region of the Solar Surface on Convection

The results of the observations of the active region (facula) near the center of the solar disk obtained with the German Vacuum Tower Telescope (VTT; Tenerife, Spain), are discussed. We have determined that the decrease in the contrast (brightness) of the facula with the magnetic field increasing from 130 to 160 mT is due to the fact that the V_V phase shift of waves in this range of magnetic field densities is close to zero (Φ _VV ≈ 0), i.e., the wave becomes stationary and does not transfer energy from the photosphere to the chromosphere. The sound waves that propagate from the chromosphere towards the photosphere significantly affect the temperature characteristics of turbulent vortices at the level of formation of the continuous spectrum. In particular, the contrast of granules under the influence of these waves can increase by 25%.     

Infrared photometry for two RV Tau stars and V1027 Cyg

We present and discuss the results of our long-term JHKLM photometry for two RV Tau stars (R Sge and RV Tau) and the yellow supergiant V1027 Cyg, a candidate for protoplanetary nebulae. The amplitude of the infrared brightness variations in R Sge and RV Tau over fourteen years of observations was 0 _. ^m 9?1 ^m ; the infrared brightness variations in V1027 Cyg over eighteen years did not exceed 0 _. ^m 25. The infrared brightness and color of R Sge fluctuated about their gradually changing mean values; the infrared brightness variations agree with a period of 70.77 days. The periodic J brightness and J-H color variations in R Sge can be explained by temperature pulsations with ΔT ≤ 200 K and radial pulsations with [ΔR/R] ≤ 0.2. From 1995 to 2008, the mean J brightness of RV Tau increased, while its mean J-H color index decreased; the variations in the mean J brightness can be associated mainly with stellar temperature variations; a periodic component with P = 78.73 days is observed in the infrared brightness and color fluctuations. The variations in the mean J brightness and J-H color index of the supergiant V1027 Cyg over eighteen years of observations did not exceed a few hundredths of a magnitude; both temperature and radial pulsations may be present in the observed J brightness variations. The most probable period of the infrared brightness fluctuations in V1027 Cyg is 237 ± 2 days. The dust shell of R Sge may consist of two layers with grain temperatures of ～1000 and ～700 K; the optical depth at 1.25 µm is ～0.02 and ～0.24, respectively. The grain temperatures in the circumstellar dust shells of the supergiants RV Tau and V1027 Cyg are ～600 K (RV Tau) and ～700 K (V1027 Cyg). Their optical depths at 1.25 µm are ～0.24 (RV Tau) and ～0.008 (V1027 Cyg).     

Oscillations of optical emission from flare stars and coronal loop diagnostics

Based on an analogy between stellar and solar flares, we investigate the ten-second oscillations detected in the U and B bands on the star EV Lac. The emission pulsations are associated with fast magnetoacoustic oscillations in coronal loops. We have estimated the magnetic field, B ≈ 320 G; the temperature, T ≈ 3.7 × 10⁷ K; and the plasma density, n ≈ 1.6 × 10¹¹ cm^?3, in the region of energy release. We provide evidence suggesting that the optical emission source is localized at the loop footpoints.     

Multicolor Photometry and Spectroscopy of the Yellow Supergiant with Dust Envelope HD 179821 = V1427 Aquilae

We present the results of multicolor (UBV JHKLM) photometry (2009–2017) and low-resolution spectroscopy (2016–2017) of the semi-regular variable V1427 Aql = HD 179821, a yellow supergiant with gas-dust envelope. The star displays low-amplitude (ΔV<0 _. ^m 2) semi-periodic brightness variations superimposed on a long-term trend. The light curve shape and timescale change from cycle to cycle. There are temperature variations characteristic for pulsations; brightness oscillations with no significant change of color are also observed. The UBV data for the 2009–2011 interval are well reproduced by a superposition of two periodic components with P = 170^d and 141^d (or P = 217^d—the one year alias of P = 141^d). The variation became less regular after 2011, the timescale increased and exceeded 250^d. Unusual photometric behavior was seen in 2015 when the star brightness increased by 0 _. ^m 25 in the V filter in 130 days and reached the maximum value ever observed in the course of our monitoring since 1990. In 2009–2016 the annual average brightness monotonically increased in V, J, K, whereas it decreased in U and B. The annual average U ? B, B ? V, and J ? K colors grew, the star was getting redder. The cooling and expanding of the star photosphere along with the increasing of luminosity may explain the long-term trend in brightness and colors. Based on our photometric data we suppose that the photosphere temperature decreased by ~400 K in the 2008–2016 interval, the radius increased by ~24%, and the luminosity grew by ~19%. We review the change of annual average photometric data for almost 30 years of observations. Low-resolution spectra in the λ4000?9000 Å wavelength range obtained in 2016–2017 indicate significant changes in the spectrum of V1427 Aql as compared with the 1994–2008 interval, i.e., the Ba II and near-infraredCa II triplet absorptions have gotten stronger while the OI λ7771-4 triplet blend has weakened that points out the decrease of temperature in the region where the absorptions are formed. The evolutionary stage of the star is discussed. We also compare V1427 Aql with post-AGB stars and yellow hypergiants.     

Properties of the noise storm source at wavelength 1 m from observations of the solar eclipse on March 29, 2006

Observations of the solar eclipse on March 29, 2006, at the Laboratory of Radio Astronomy of the CrAO showed that the radio radius of the Sun at a wavelength of 1 m in the direction of the first contact was R _d = 1.12 R _⊙ during solar activity minimum between cycles 23 and 24. The brightness temperature of the undisturbed Sun was T _d = (0.6 ± 0.06) × 10⁶ K. There was a noise storm source above the sunspot group NOAA 0865 whose bright nucleus had a size of 1′.3 and a brightness temperature T _b = 16 × 10⁶ K. The noise storm bursts were emitted from the region of the bright nucleus above the group NOAA 0865 and were absent during its covering by the disk of the Moon. Thermal radiation from a coronal condensation with a brightness temperature of (1?2) × 10⁶ K extending out from the visible solar disk to 2′.7 was observed during the eclipse above the eastern limb sunspot group NOAA 0866. The bright nucleus in this limb source appeared 42 min after eclipse termination and persisted in the ensuing days. This may be indicative of the time of its emergence from behind the radio horizon formed by regular refraction of radio waves in the corona. The refractive displacement was measured by comparison with the eclipse observations at a shorter wavelength of 12 cm. Its value of 0′.96 is close to the calculated value of 0′.8.     

The Intensity–Velocity Phase Spectra of Evanescent Oscillations and Acoustic Sources

There are three major issues in modeling solar evanescent oscillations: the variation of the intensity [I]–velocity [V] phase difference of p-modes close to the base of photosphere; the existence of a plateau of negative I–V phase differences below and between the ridges of the low-frequency p-modes; the explanation of the I–V cross-spectra of the evanescent oscillations. We present new interpretations for the first two issues, based on modeling intensity fluctuations taking steep temperature gradients, opacity, and non-adiabatic cooling into account. We also discuss consequences of our model for the explanation of power spectra and cross-power spectra of p-modes. In particular, we present evidence that the acoustic sources that generate evanescent waves produce a coherent background that explains the plateau–interridge regime of negative I–V phase difference.     

Variations of microwave emission from solar active regions

Based on observational data obtained with the RT-22 Crimean Astrophysical Observatory radio telescope at frequencies of 8.6 and 15.4 GHz, we investigate the quasi-periodic variations of microwave emission from solar active regions with periods T_p<10 min. As follows from our wavelet analysis, the oscillations with periods of 3–5 min and 10–40 s have the largest amplitudes in the dynamic power spectra, while there are virtually no oscillations with T_p<10 s. Our analysis shows that acoustic modes with T_p?1 min strongly dissipate in the lower solar corona due to thermal conduction losses. The oscillations with T_p=10–40 s are associated with Alfvén disturbances. We analyze the influence of acoustic and Alfvén oscillations on the thermal mechanisms of microwave emission in terms of the homogeneous model. We discuss the probable coronal heating sources.     

Analytical signal as a tool for studying solar p-modes

A technique for analyzing periodic processes based on the introduction of an analytical signal is described. This technique allows the instantaneous frequency, amplitude, and phase of oscillations to be obtained. The data on solar brightness fluctuations collected with the DIFOS multichannel photometer onboard the CORONAS-F satellite are processed. The p-mode spectral lines are broadened mainly by amplitude fluctuations, while the frequency stability appears to be high (～10^?4). A method for separating signals with close frequencies is developed. The p-mode with l = 0 and n = 21 is used as an example to show that the separation of signals with close frequencies is possible when the conventional spectral methods are inefficient. Analysis of the phase shifts between the oscillations observed in various optical channels of the DIFOS photometer has revealed that the five-minute oscillations travel from the upper and deep photospheric layers toward the middle photospheric layers. This effect directly proves that the evanescent p-modes in the photosphere are nonadiabatic.     

Instability of radial modes at the Wolf-Rayet evolutionary stage

The evolution of a Population-I star with an initial mass M _ZAMS = 60 M _⊙ has been calculated. At the stage when a red giant turns into an early-type helium star, the vast bulk of the stellar mass is concentrated in a compact core surrounded by an extended envelope that is unstable with respect to radial oscillations. The range of effective temperatures within which the instability arises extends to T _eff ? 10⁵ K. For the models corresponding to the Wolf-Rayet evolutionary stage (5 × 10⁴ K ≤ T _eff ≤ 1.05 × 10⁵ K), hydrodynamic calculations of self-exciting radial stellar pulsations have been performed. The pulsational instability develops in a time interval comparable to the dynamic timescale. Once the amplitude has ceased to grow, the pulsational motions are nonlinear traveling waves propagating from the core boundary to the stellar surface. The velocity amplitude of the outer layers is 500 km s^?1 < ΔU < 10³ km s^?1, depending on the effective temperature. During the evolution of a helium star, the mean ratio of the maximum expansion velocity of the outer layers to the local escape velocity decreases and lies within the range 0.25 < U _max/v _esc < 0.6 for the models considered. The nonlinearity of the stellar pulsations is responsible for the increase in the mean radius \(\bar r\) of the Lagrangian layers compared to the equilibrium radius r _eq. The effect of the increase in mean radius decreases with rising effective temperature from\(\bar r\)/r ～ 10 at T _eff = 7 × 10⁴ K to \(\bar r\)/r ≈ 2 at T _eff = 10⁵ K. The radial pulsation periods for the models considered lie within the range 0.1 day ≤ Π ≤ 1.6 day and the amplitude of the bolometric magnitude variations does not exceed 0 _. ^m 2.     

Structure of radio sources at wavelengths 10.5 and 12.0 cm from observations of the Solar eclipse on March 29, 2006

The eclipse observations were performed at the Laboratory of Radio Astronomy of the CrAO in Katsiveli with stationary instrumentation of the Solar Patrol at wavelengths of 10.5 and 12.0 cm. The data obtained were used to determine the brightness temperature of the undisturbed Sun at solar activity minimum between 11-year cycles 23 and 24: T _d10.5 = (43.7 ± 0.5) × 10³ K at 10.5 cm and T _d12.0 = (51.8 ± 0.5) × 10³ K at 12.0 cm. The radio brightness distribution above the limb group of sunspots NOAA 0866 was calculated. It shows that at both wavelengths the source consisted of a compact bright nucleus about 50 × 10³ km in size with temperatures T _b10.5 = 0.94 × 10⁶ K and T _b12.0 = 2.15 × 10⁶ K located, respectively, at heights h _10.5 = 33.5 × 10³ km and h _12.0 = 43.3 × 10³ km above the sunspot and an extended halo with a temperature T _b = (230–300) × 10³ K stretching to a height of 157 × 10³ km above the photosphere. The revealed spatial structure of the local source is consistent with the universally accepted assumption that the radiation from the bright part of the source is generated by electrons in the sunspot magnetic fields at the second-third cyclotron frequency harmonics and that the halo is the bremsstrahlung of thermal electrons in the coronal condensation forming an active region. According to the eclipse results, the electron density near the upper boundary of the condensation was N _e ≈ 2.3 × 10⁸ cm^?3, while the optical depth was τ ≈ 0.1 at an electron temperature T _e ≈ 10⁶ K. Thus, the observations of the March 29, 2006 eclipse have allowed the height of the coronal condensation at solar activity minimum to be experimentally determined and the physical parameters of the plasma near its upper boundary to be estimated.     

Variability and rapid evolution of the protoplanetary object IRAS 18062+2410=V886 her

We present our long-term photometric and spectroscopic observations of a high-latitude B supergiant with an infrared excess—the protoplanetary nebula IRAS 18062+2410. OurU BV observations in 2000–2006 have confirmed the rapid irregular photometric variability of the star with a maximum amplitude as high as 0 _. ^m 4 in V that we found previously. The B—V and U—B color indices vary with amplitudes as high as 0 _. ^m 10 and 0 _. ^m 25, respectively, and show no clear correlation with the brightness. Our V-band CCD observations on 11 nights in 2006 have revealed brightness trends during the night. The variability of IRAS18062+2410 is similar in pattern to the light variations in other hot post-AGB objects and some of the nuclei of young planetary nebulae. We assume that pulsations and a variable stellar wind can be responsible for the variability of these stars. In addition to the rapid variability, our 12-year-long observations have revealed a systematic decline in the mean brightness of IRAS 18062+2410. This may be related to a rise in the temperature of the star at constant luminosity as a result of its evolution. Low-resolution spectroscopic observations have shown a systematic increase in the equivalent widths of the Hα, Hβ, [NII]λ6584 Å, OI λ8446 Å, and [OII] λ7320–7330 Å emission lines. The changes in the star’s emission line spectrum are probably caused by an increase in the degree of ionization of the gas shell due to a rise in the temperature of the ionizing star. Our photometric and spectroscopic observations of IRAS 18062+2410 confirm the previously made assumptions that the star evolves very rapidly to the region of planetary nebulae.     

Stellar Mass—Halo Mass Relation and Star Formation Efficiency in High-Mass Halos

We study relation between stellar mass and halo mass for high-mass halos using a sample of galaxy clusters with accurate measurements of stellar masses from optical and ifrared data and total masses from X-ray observations. We find that stellar mass of the brightest cluster galaxies (BCGs) scales as M_*,BCG ∝ M ₅₀₀ ^αBCG with the best fit slope of α_BCG ≈ 0.4 ± 0.1. We measure scatter of M_*,BCG at a fixed M₅₀₀ of ≈0.2 dex. We show that stellar mass-halo mass relations from abundance matching or halo modelling reported in recent studies underestimate masses of BCGs by a factor of ～2?4. We argue that this is because these studies used stellar mass functions (SMF) based on photometry that severely underestimates the outer surface brightness profiles of massive galaxies. We show that M_*?M relation derived using abundance matching with the recent SMF calibration by Bernardi et al. (2013) based on improved photometry is in a much better agreement with the relation we derive via direct calibration for observed clusters. The total stellar mass of galaxies correlates with total mass M₅₀₀ with the slope of ≈0.6 ± 0.1 and scatter of 0.1 dex. This indicates that efficiency with which baryons are converted into stars decreases with increasing cluster mass. The low scatter is due to large contribution of satellite galaxies: the stellar mass in satellite galaxies correlates with M₅₀₀ with scatter of ≈0.1 dex and best fit slope of α_sat ≈ 0.8 ± 0.1. We show that for a fixed choice of the initial mass function (IMF) total stellar fraction in clusters is only a factor of 3?5 lower than the peak stellar fraction reached in M ≈ 10¹²M_⊙ halos. The difference is only a factor of ～1.5?3 if the IMF becomes progressively more bottom heavy with increasing mass in early type galaxies, as indicated by recent observational analyses. This means that the overall efficiency of star formation in massive halos is only moderately suppressed compared to L_* galaxies and is considerably less suppressed than previously thought. The larger normalization and slope of the M_*?M relation derived in this study shows that feedback and associated suppression of star formation in massive halos should be weaker than assumed in most of the current semi-analytic models and simulations.     

Velocity structure and variations in the region of quiet solar filaments

We study the velocity fields in the region of quiet solar filaments using spectral observations at the Sayan Solar Observatory (ISTP, Irkutsk). Once the series of spectral images have been processed, maps of the two-dimensional distribution of the velocity and its variations in the chromosphere (in the Hβ λ = 486.13 nm line) and the photosphere (in the Fe I λ = 486.37 nm line) are constructed. The motions in the filaments have been found to consist of steady and periodic components. Our analysis of the spatial distributions of various oscillation modes shows that the short-period (<10 min) oscillations propagate mainly vertically and are observed at the filament edges, on scales of several arcseconds. The quasi-hour (>40 min) oscillations propagate mostly along the filament at a small angle to its axis. The intensity in the Hβ core in individual fragments of some filaments varies with a period of about one hour. The observed velocity structures in the filaments and the imbalance of steady motions on the opposite sides of the filaments can be explained in terms of the model of a twisted fine-structure magnetic flux tube.     

Pulsations of microwave emission and flare plasma diagnostics

We consider the modulation of nonthermal gyrosynchrotron emission from solar flares by the ballooning and radial oscillations of coronal loops. The damping mechanisms for fast magnetoacoustic modes are analyzed. We suggest a method for diagnosing the plasma of flare loops that allows their main parameters to be estimated from peculiarities of the microwave pulsations. Based on observational data obtained with the Nobeyama Radioheliograph (17 GHz) and using a technique developed for the event of May 8, 1998, we determined the particle density n≈3.7×10¹⁰ cm^?3, the temperature T≈4×10⁷ K, and the magnetic field strength B≈220 G in the region of flare energy release. A wavelet analysis for the solar flare of August 28, 1999, has revealed two main types of microwave oscillations with periods P₁≈7, 14 s and P₂≈2.4 s, which we attribute to the ballooning and radial oscillations of compact and extended flare loops, respectively. An analysis of the time profile for microwave emission shows evidence of coronal loop interaction. We determined flare plasma parameters for the compact (T≈5.3×10⁷ K, n≈4.8≈10¹⁰ cm^?3, B≈280 G) and extended (T≈2.1≈10⁷ K, n≈1.2≈10¹⁰ cm^?3, B≈160 G) loops. The results of the soft X-ray observations are consistent with the adopted model.     

Nonlinear pulsations of red supergiants

Excitation of radial oscillations in population I (X = 0.7, Z = 0.02) red supergiants is investigated using the solution of the equations of radiation hydrodynamics and turbulent convection. The core helium burning stars with masses 8M _⊙ ≤ M ≤ 20M _⊙ and effective temperatures T _eff < 4000 K are shown to be unstable against radial pulsations in the fundamental mode. The oscillation periods range between 45 and 1180 days. The pulsational instability is due to the κ-mechanism in the hydrogen and heliumionization zones. Radial pulsations of stars with mass M < 15M _⊙ are strictly periodic with the light amplitude ΔM _bol ≤ 0?5. The pulsation amplitude increases with increasing stellar mass and for M > 15M _⊙ the maximum expansion velocity of outer layers is as high as one third of the escape velocity. The mean radii of outer Lagrangean mass zones increase due to nonlinear oscillations by ≤30% in comparison with the initial equilibrium. The approximate method (with uncertainty of a factor of 1.5) to evaluate the mass of the pulsating red supergiant with the known period of radial oscillations is proposed. The approximation of the pulsation constant Q as a function of the mass-to-radius ratio is given. Masses of seven galactic red supergiants are evaluated using the period-mean density relation.     

Spectropolarimetric investigation of an Ellerman bomb: 2. Photospheric models

Semiempirical models of the photosphere of an Ellerman bomb in the NOAA 11024 active region were obtained using profiles of Stokes parameters I, Q, U, and V of photospheric lines. Spectropolarimetric observations were conducted using the French–Italian THEMIS telescope (Tenerife, Spain). The SIR inversion code [28] was used in the modeling. The models have two components: a magnetic flux tube and nonmagnetic surroundings. The dependences of temperature, magnetic field strength, inclination of the magnetic field vector, and line-of-sight velocity in the tube on the optical depth were obtained. The models demonstrate that the thermodynamic parameters of the Ellerman bomb photosphere differ considerably from those of the quiet photosphere. The temperature in the tube model varied nonmonotonically with height and deviated by up to 700–900 K from its values for the quiet photosphere. Downflows were observed in the lower and the upper photospheric layers. The line-of-sight velocity in the upper layers of the photosphere was as high as 17 km/s. The magnetic field strength in the models varied from 0.1–0.13 T in the lower photospheric layers to 0.04–0.07 T in the upper ones. The physical state of the photosphere did change in the course of observations.     

Active zone of the nucleus of the quasar 3C 273

The superfine structure of the quasar 3C 273 has been investigated at wavelengths λ = 2 and 6 cm with angular resolutions up to φ = 20 μas for epochs 2005–2014. We have identified a nozzle and a bipolar outflow: a jet and a counterjet consisting of coaxial high- and low-velocity components. The separation between the nozzles in the plane of the sky is Δρ = 0.84 ± 0.16 pc; the flow ejection velocity is v ≤ 0.1c. The nozzle brightness temperature reaches T _b ≈ 45 × 10¹² K, φ = 20 μas, λ = 2 cm. The ejected electrons radiatively cool at a distance up to ≤4 pc. However, the jet afterglow is observed at a 8% level at a distance up to ρ ≈ 16 pc; the acceleration compensates for the radiative losses. The reduction in the emission level of the central flow at large distances determines the jet bifurcation. The counterjet shape is a mirror reflection of the initial part of the jet, suggesting a symmetry and identity of the ejected flows. The counterjet and jet nozzles are in the near and remote parts of the active region, respectively. The emission from the nozzles is absorbed by a factor of 2 and 15, respectively. The absorption decreases with increasing distance and the brightness of the jet fragments rises to its maximum at 0.5 pc from the nozzle. Arclike structures, arm fragments, are observed in the region of the nozzles. The relativistic plasma comes to the nozzles and is ejected. The brightness temperature of the arclike structures reaches 10% of the peak value, which is determined by the a smaller optical depth, the visibility in the transverse direction. The central high-velocity flow is surrounded by low-velocity components, hollow tubes being ejected as an excess angular momentum is accumulated. The remainder of the material flows along the arms toward the disk center until the next accumulation of an excess angular momentum and the process is repeated. The diameter of the outer nozzle is Ø = 25 pc and, further out, decreases exponentially; Ø _n ≈ 80 exp(?1.15n) pc. The flow kinematics, collimation, and acceleration have a vortical nature. Ring currents producing magnetic fields, which accelerate and stabilize the processes, are generated in the rotating flows (tubes). The tangential directions of the currents are observed as parallel chains of components.