In this article, we provide a review of the current state of the research of the black hole shadow, focusing on analytical (as opposed to numerical and observational) studies. We start with particular attention to the definition of the shadow and its relation to the often used concepts of escape cone, critical impact parameter and particle cross-section. For methodological purposes, we present the derivation of the angular size of the shadow for an arbitrary spherically symmetric and static space-time, which allows one to calculate the shadow for an observer at arbitrary distance from the center. Then we discuss the calculation of the shadow of a Kerr black hole, for an observer anywhere outside of the black hole. For observers at large distances we present and compare two methods used in the literature. Special attention is given to calculating the shadow in space-times which are not asymptotically flat. Shadows of wormholes and other black-hole impostors are reviewed. Then we discuss the calculation of the black hole shadow in an expanding universe as seen by a comoving observer. The influence of a plasma on the shadow of a black hole is also considered.

One of the most interesting phenomena in the ultracold plasmas are multiple subharmonics of the electron emission observed after its irradiation by the monochromatic radiowaves. Unfortunately, the early interpretation of this phenomenon as the so-called Tonks-Dattner resonances (i.e., actually the standing Langmuir waves) encountered a number of serious obstacles, such as a lack of the adequate boundary conditions, an incorrect dependence on the electron temperature, and an insensitivity to the shape of the cloud. Here, we suggest an alternative interpretation based on the quasi-classical multiphoton ionization of the 'secondary' Rydberg atoms formed in the expanding and cooling plasma clouds. As follows from our numerical simulations, the efficiency of such ionization exhibits a series of well-expressed peaks. Moreover, this process is evidently irrelevant to the boundary conditions and global shape of the cloud. Therefore, this should be a viable alternative to the earlier idea of Tonks--Dattner resonances.

The exact time-dependent solution is obtained for a magnetic field growth during a spherically symmetric accretion into a black hole (BH) with a Schwarzschild metric. Magnetic field is increasing with time, changing from the initially uniform into a quasi-radial field. Equipartition between magnetic and kinetic energies in the falling gas is established in the developed stages of the flow. Estimates of the synchrotron radiation intensity are presented for the stationary flow. The main part of the radiation is formed in the region $r \leq 7 r_g$, here$r_g$ is a BH gravitational radius. The two-dimensional stationary self-similar magnetohydrodynamic solution is obtained for the matter accretion into BH, in a presence of a large-scale magnetic field, when the magnetic field far from the BH is homogeneous and does not influence the flow. At the symmetry plane perpendicular to the direction of the distant magnetic field, the quasi-stationary disk is formed around BH, which structure is determined by dissipation processes. Parameters of the shock forming due to matter infall onto the disk are obtained. The radiation spectrum of the disk and the shock are obtained for the $10\,\, M_\odot$ BH. The luminosity of such object is about the solar one, for a characteristic galactic gas density, with possibility of observation at distances less than 1 kpc. The spectra of a laminar and a turbulent disk structure around BH are very different. The turbulent disk emits a large part of its flux in the infrared. It may occur that some of the galactic infrared star-like sources are a single BH in the turbulent accretion state. The radiative efficiency of the magnetized disk is very high, reaching $\sim 0.5\,\dot M\,c^2$ so it was called recently as a magnetically arrested disk (MAD). Numerical simulations of MAD, and its appearance during accretion into neutron stars are considered and discussed.

Cosmic expansion influences the angular size of black hole shadow. The most general way to describe a black hole embedded into an expanding universe is to use the McVittie metric. So far, the exact analytical solution for the shadow size in the McVittie metric, valid for arbitrary law of expansion and arbitrary position of the observer, has not been found. In this paper, we present the first analytical solution for angular size of black hole shadow in McVittie metric as seen by observer comoving with the cosmic expansion. We use a method of matched asymptotic expansions to find approximate solution valid within the entire range of possible positions of observer. As two particular examples, we consider black hole in de Sitter and matter dominated universe.

Deflection angles of massive test particles moving along an unbound trajectory in the Schwarzschild metric are considered for the case of large deflection. We analytically consider the strong deflection limit, which is opposite to the commonly applied small deflection approximation and corresponds to the situation when a massive particle moves from infinity, makes several revolutions around a central object and goes to infinity. For this purpose we rewrite an integral expression for the deflection angle as an explicit function of the parameters determining the trajectory and expand it. Remarkably, in the limiting case of strong deflection, we succeed in deriving for the first time the analytical formulas for deflection angles as explicit functions of parameters at infinity. In particular, we show that in this case the deflection angle can be calculated as an explicit function of the impact parameter and velocity at infinity beyond the usual assumption of small deflection.

The influence of the medium on the gravitational deflection of light rays is widely discussed in literature for the simplest non-trivial case: cold non-magnetized plasma. In this article, we generalize these studies to the case of an arbitrary transparent dispersive medium with a given refractive index. We calculate the deflection angle of light ray moving in a general spherically symmetric metric in the presence of medium with the spherically symmetric refractive index. The equation for the radius of circular light orbits is also derived. We discuss in detail the properties of these results and various special cases. In particular, we show that multiplying the refractive index by a constant does not affect the deflection angle and radius of circular orbits. At the same time, the presence of dispersion makes the trajectories different from the case of vacuum even in spatially homogeneous medium. As one of the applications of our results, we calculate the correction to the angle of vacuum gravitational deflection for the case when a massive object is surrounded by homogeneous but dispersive medium. As another application, we present the calculation of the shadow of a black hole surrounded by medium with arbitrary refractive index. Our results can serve as a basis for studies of various plasma models beyond the cold plasma case.

The influence of the medium on the gravitational deflection of light rays is widely discussed in literature for the simplest non-trivial case: cold non-magnetized plasma. In this article, we generalize these studies to the case of an arbitrary transparent dispersive medium with a given refractive index. We calculate the deflection angle of light ray moving in a general spherically symmetric metric in the presence of medium with the spherically symmetric refractive index. The equation for the radius of circular light orbits is also derived. We discuss in detail the properties of these results and various special cases. In particular, we show that multiplying the refractive index by a constant does not affect the deflection angle and radius of circular orbits. At the same time, the presence of dispersion makes the trajectories different from the case of vacuum even in spatially homogeneous medium. As one of the applications of our results, we calculate the correction to the angle of vacuum gravitational deflection for the case when a massive object is surrounded by homogeneous but dispersive medium. As another application, we present the calculation of the shadow of a black hole surrounded by medium with arbitrary refractive index. Our results can serve as a basis for studies of various plasma models beyond the cold plasma case.

In most analytical studies of light ray propagation in curved spacetimes around a gravitating object surrounded by a medium, it is assumed that the medium is a cold nonmagnetized plasma. The distinctive feature of this environment is that the equations of motion of the rays are independent of the plasma velocity, which, however, is not the case in other media. In this paper, we consider the deflection of light rays propagating near a spherically symmetric gravitating object in a moving dispersive medium given by a general refractive index. The deflection is studied when the motion of the medium is defined either as a radially falling onto a gravitating object (e.g., black hole), or rotating in the equatorial plane. For both cases the deflection angles are obtained. These examples demonstrate that fully analytic expressions can be obtained if the Hamiltonian for the rays takes a rather general form as a polynomial in a given momentum component. The general expressions are further applied to three specific choices of refractive indices and these cases are compared. Furthermore, the light rays propagating around a gravitating object surrounded by a generally moving medium are further studied as a small perturbation of the cold plasma model. The deflection angle formula is hence expressed as a sum of zeroth and first order components, where the zeroth order term corresponds to the known cold plasma case and the first order correction can be interpreted as caused by small difference in the refractive index compared to the cold plasma. The results presented in this paper allow to describe the effects caused by the motion of a medium and thus go beyond cold nonmagnetized plasma model.

Multi-wavelength surveys covering large sky volumes are necessary to obtain an accurate census of rare objects such as high luminosity and/or high redshift active galactic nuclei (AGN). Stripe 82X is a 31.3 deg$^2$ X-ray survey with $Chandra$ and $XMM$-Newton observations overlapping the legacy Sloan Digital Sky Survey (SDSS) Stripe 82 field, which has a rich investment of multi-wavelength coverage from the ultraviolet to the radio. The wide-area nature of this survey presents new challenges for photometric redshifts for AGN compared to previous work on narrow-deep fields because it probes different populations of objects that need to be identified and represented in the library of templates. Here we present an updated X-ray plus multi-wavelength matched catalog, including $Spitzer$ counterparts, and estimated photometric redshifts for 5961 (96% of a total of 6181) X-ray sources, which have a normalized median absolute deviation, $\sigma_{\rm nmad}$ = 0.06 and an outlier fraction, $\eta$ = 13.7%. The populations found in this survey, and the template libraries used for photometric redshifts, provide important guiding principles for upcoming large-area surveys such as $eROSITA$ and 3$XMM$ (in X-ray) and the Large Synoptic Survey Telescope (LSST; optical).

We study the emission from the hot interstellar medium in a sample of nearby late type galaxies defined in Paper I. Our sample covers a broad range of star formation rates, from ~0.1 Msun/yr to ~17 Msun/yr and stellar masses, from ~3x10^8 Msun to ~6x10^10 Msun. We take special care of systematic effects and contamination from bright and faint compact sources. We find that in all galaxies at least one optically thin thermal emission component is present in the unresolved emission, with the average temperature of = 0.24 keV. In about ~1/3 of galaxies, a second, higher temperature component is required, with the = 0.71 keV. Although statistically significant variations in temperature between galaxies are present, we did not find any meaningful trends with the stellar mass or star formation rate of the host galaxy. The apparent luminosity of the diffuse emission in the 0.5-2 keV band linearly correlates with the star formation rate with the scale factor of Lx/SFR\approx 8.3x10^38 erg/s per Msun/yr, of which in average ~30-40% is likely produced by faint compact sources of various types. We attempt to estimate the bolometric luminosity of the gas and and obtained results differing by an order of magnitude, log(Lbol/SFR)\sim39-40, depending on whether intrinsic absorption in star-forming galaxies was allowed or not. Our theoretically most accurate, but in practice the most model dependent result for the intrinsic bolometric luminosity of ISM is Lbol/SFR\sim 1.5x10^40 erg/s per Msun/yr. Assuming that core collapse supernovae are the main source of energy, it implies that \epsilon_SN\sim5x10^-2 (E_SN/10^51)^-1 of mechanical energy of supernovae is converted into thermal energy of ISM.

Novae are the observational manifestations of thermonuclear runaways on the surface of accreting white dwarfs (WDs). Although novae are an ubiquitous phenomenon, their properties at low metallicity are not well understood. Using the publicly-available stellar evolution code Modules for Experiments in Stellar Astrophysics (MESA), we model the evolution of accreting carbon-oxygen WDs and consider models which accrete matter with metallicity Z=0.02 or $10^{-4}$. We consider both models without mixing and with matter enriched by CO-elements assuming that mixing occurs in the process of accretion (with mixing fraction 0.25). We present and contrast ignition mass, ejected mass, recurrence period and maximum luminosity of novae for different WD masses and accretion rates for these metallicities and mixing cases. We find that models with Z = 0.02 have ignition masses and recurrence periods smaller than models with low Z, while the ejected mass and maximum luminosity are larger. Retention efficiency during novae outbursts decreases with increasing metallicity. In our implementation, inclusion of mixing at the H/He interface reduces accreted mass, ejected mass and recurrence period as compared to the no-mixing case, while the maximum luminosity becomes larger. Retention efficiency is significantly reduced, becoming negative in most of our models. For ease of use, we provide a tabular summary of our results.

This work is a continuation of Paper I [Sharykin et al., 2018] devoted to analysis of nonthermal electron dynamics and plasma heating in the confined M1.2 class solar flare SOL2015-03-15T22:43 revealing energy release in the highly sheared interacting magnetic loops in the low corona, above the polarity inversion line (PIL). The scope of the present work is to make the first extensive quantitative analysis of the photospheric magnetic field and photospheric vertical electric current (PVEC) dynamics in the confined flare region near the PIL using new vector magnetograms obtained with the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO) with high temporal resolution of 135 s. Data analysis revealed sharp changes of the magnetic structure and PVEC associated with the flare onset near the PIL. It was found that the strongest plasma heating and electron acceleration were associated with the largest increase of the magnetic reconnection rate, total PVEC and effective PVEC density in the flare ribbons. Observations and non-linear force-free field (NLFFF) extrapolations showed that the magnetic field structure around the PIL is consistent with the tether-cutting magnetic reconnection (TCMR) geometry. We gave qualitative interpretation of the observed dynamics of the flare ribbons, magnetic field and PVEC, and electron acceleration, within the TCMR scenario.

The influence of plasma on different effects of gravitational lensing is reviewed. Using the Hamiltonian approach for geometrical optics in a medium in the presence of gravity, an exact formula for the photon deflection angle by a black hole (or another body with a Schwarzschild metric) embedded in plasma with a spherically symmetric density distribution is derived. The deflection angle in this case is determined by the mutual combination of different factors: gravity, dispersion, and refraction. While the effects of deflection by the gravity in vacuum and the refractive deflection in a nonhomogeneous medium are well known, the new effect is that, in the case of a homogeneous plasma, in the absence of refractive deflection, the gravitational deflection differs from the vacuum deflection and depends on the photon frequency. In the presence of a plasma nonhomogeneity, the chromatic refractive deflection also occurs, so the presence of plasma always makes gravitational lensing chromatic. In particular, the presence of plasma leads to different angular positions of the same image if it is observed at different wavelengths. It is discussed in detail how to apply the presented formulas for the calculation of the deflection angle in different situations. Gravitational lensing in plasma beyond the weak deflection approximation is also considered.

We analyse the spectra of black hole (BH) and neutron star (NS) X-ray binaries (XBs) in the hard state using archival RXTE observations. We find that there is a clear dichotomy in the strength of Comptonisation between NS and BH sources, as measured by both the Compton y-parameter and amplification factor A, with distinct groups of BH and NS XBs separated at y~0.9 and A~3. The electron temperature kTe can occupy a broad range in BH systems, from kTe~30-200 keV, whereas for NSs kTe is peaked at ~15-25 keV, but can extend to higher values. The difference between BHs and NSs in y implies that kTe is higher at a given optical depth for BH XBs. Our results also imply that for NS systems the accreting material loses ~1/2-2/3 of its energy through Comptonisation in the corona. The remaining energy is released on the surface of the neutron star, making it a powerful source of soft radiation, which alters the properties of the Comptonising corona. Finally, we find evidence at the 2.4 sigma confidence level that Comptonisation parameters may be correlated with the neutron star spin, whereas no correlation with the BH spin is found. Our results highlight a further observational distinction between BH and NS XBs that is a consequence of NSs possessing a physical surface.

Energetic neutral atom (ENA) models typically require post-processing routines to convert the distributions of plasma and H atoms into ENA maps. Here we investigate how two different kinetic-MHD models of the heliosphere (the BU and Moscow models) manifest in modeled ENA maps using the same prescription and how they compare with Interstellar Boundary Explorer (IBEX) observations. Both MHD models treat the solar wind as a single-ion plasma for protons, which include thermal solar wind ions, pick-up ions (PUIs), and electrons. Our ENA prescription partitions the plasma into three distinct ion populations (thermal solar wind, PUIs transmitted and ones energized at the termination shock) and models the populations with Maxwellian distributions. Both kinetic-MHD heliospheric models produce a heliotail with heliosheath plasma organized by the solar magnetic field into two distinct north and south columns that become lobes of high mass flux flowing down the heliotail, though in the BU model the ISM flows between the two lobes at distances in the heliotail larger than 300 AU. While our prescription produces similar ENA maps for the two different plasma and H atom solutions at the IBEX-Hi energy range (0.5 - 6 keV), the modeled ENA maps require a scaling factor of ~2 to be in agreement with the data. This problem is present in other ENA models with the Maxwellian approximation of multiple ion species and indicates that a higher neutral density or some acceleration of PUIs in the heliosheath is required.

Gravitational lensing of luminous matter that surrounds a black hole or some other sufficiently compact object produces an infinite sequence of images. Besides the direct (or primary) image, it comprises demagnified and deformed replicas of the original known as photon rings which are progressively nearing the boundary of the socalled shadow. In the present paper, we present analytical approximation formulas for higher-order photon rings for an asymptotically flat, static, spherically symmetric spacetime that admits a photon sphere. We consider a geometrically thin disk of light sources in the equatorial plane and an observer at arbitrary inclination far away from the center. Fixing the emission radius and leveraging the strong deflection limit, which provides an analytical logarithmic approximation for the deflection angle, we find the deformed shape of higher-order photon rings in the form of a polar equation on the observer's screen. It has been suggested by other authors to use the relative size of photon rings for characterizing the underlying spacetime. In particular, the relative separation between two neighboring photon rings, which we call "gap parameter", was considered. We analytically calculate the gap parameter of higher-order photon rings for metrics of the considered class that may depend on multiple parameters. The advantage of using this quantity is in the fact that, to within the assumed approximations, it is independent of the mass of the central object (or of some other characteristic parameter if the mass is zero) and of the distance of the observer. Measurements of the gap parameter, which may become possible in the near future, will restrict the spacetime models that are in agreement with the observations. Even without knowing the inner and outer radii of the shining disk, it will conclusively rule out some metrics. Some examples are provided.

The magnetotail current sheet's spatial configuration and stability control the onset of magnetic reconnection - the driving process for magnetospheric substorms. The near-Earth current sheet has been thoroughly investigated by numerous missions, whereas the midtail current sheet has not been adequately explored. This is especially the case for the long-term variation of its configuration in response to the solar wind. We present a statistical analysis of 1261 magnetotail current sheet crossings by the Acceleration, Reconnection, Turbulence and Electrodynamics of Moon's Interaction with the Sun (ARTEMIS) mission orbiting the moon (X~-60 RE), collected during the entirety of Solar Cycle 24. We demonstrate that the magnetotail current sheet typically remains extremely thin, with a characteristic thickness comparable to the thermal ion gyroradius, even at such large distances from Earth's dipole. We also find that a substantial fraction (~one quarter) of the observed current sheets have a partially force-free magnetic field configuration, with a negligible contribution of the thermal pressure and a significant contribution of the magnetic field shear component to the pressure balance. Further, we quantify the impact of the changing solar wind driving conditions on the properties of the midtail around the lunar orbit. During active solar wind driving conditions, we observe an increase in the occurrence rate of thin current sheets, whereas quiet solar wind driving conditions seem to favor the formation of partially force-free current sheets.

This work explores the use of big data technologies deployed in the cloud for processing of astronomical data. We have applied Hadoop and Spark to the task of co-adding astronomical images. We compared the overhead and execution time of these frameworks. We conclude that performance of both frameworks is generally on par. The Spark API is more flexible, which allows one to easily construct astronomical data processing pipelines.