Role of primordial black holes in the direct collapse scenario of supermassive black hole formation at high redshifts

In this paper, we explore the possibility of accreting primordial black holes as the source of heating for the collapsing gas in the context of the direct collapse black hole scenario for the formation of super-massive black holes (SMBHs) at high redshifts, \(z\sim \) 6–7. One of the essential requirements for the direct collapse model to work is to maintain the temperature of the in-falling gas at \(\approx \)10\(^4\) K. We show that even under the existing abundance limits, the primordial black holes of masses \(\gtrsim \)10\(^{-2}M_\odot \), can heat the collapsing gas to an extent that the \(\mathrm{H}_2\) formation is inhibited. The collapsing gas can maintain its temperature at \(10^4\) K till the gas reaches a critical density \(n_{{c}} \,{\approx }\, 10^3~\hbox {cm}^{-3}\), at which the roto-vibrational states of \(\mathrm{H}_2\) approaches local thermodynamic equilibrium and \(\mathrm{H}_2\) cooling becomes inefficient. In the absence of \(\mathrm{H}_2\) cooling, the temperature of the collapsing gas stays at \(\approx \)10\(^4\) K even as it collapses further. We discuss scenarios of subsequent angular momentum removal and the route to find collapse through either a supermassive star or a supermassive disk.     

The extreme initial kinetic energy allowed by a collapsing turbulent core

We present high-resolution hydrodynamical simulations aimed at following the gravitational collapse of a gas core, in which a turbulent spectrum of velocity is implemented only initially. We determine the maximal value of the ratio of kinetic energy to gravitational energy, denoted here by \((\frac{E_{\mathrm{kin}} }{E_{\mathrm{grav}}} )_{\max}\), so that the core (i) will collapse around one free-fall time of time evolution or (ii) will expand unboundedly, because it has a value of \(\frac{E_{\rm kin}}{E_{\mathrm{grav}}}\) larger than \(( \frac{E_{\mathrm{kin}}}{E_{\mathrm{grav}}} )_{\mathrm{max}}\). We consider core models with a uniform or centrally condensed density profile and with velocity spectra composed of a linear combination of one-half divergence-free turbulence type and the other half of a curl-free turbulence type. We show that the outcome of the core collapse are protostars forming either (i) a multiple system obtained from the fragmentation of filaments and (ii) a single primary system within a long filament. In addition, some properties of these protostars are also determined and compared with those obtained elsewhere.     

GeV-TeV $\gamma $-ray energy spectral break of BL Lac objects

In this paper, we compile the very-high-energy and high-energy spectral indices of 43 BL Lac objects from the literature. Based on a simple math model, \(\Delta \Gamma_{obs}= \alpha {{{z}}}+\beta \), we present evidence for the origin of an observed spectral break that is denoted by the difference between the observed very-high-energy and high-energy spectral indices, \(\Delta \Gamma_{obs}\). We find by linear regression analysis that \(\alpha \ne 0\) and \(\beta \ne 0\). These results suggest that the extragalactic background light attenuation and the intrinsic curvature dominate on the GeV-TeV \(\gamma \)-ray energy spectral break of BL Lac objects. We argue that the extragalactic background light attenuation is an exclusive explanation for the redshift evolution of the observed spectral break.     

Collapsing stellar structures in f(R) gravity using Karmarkar condition

Our study illuminates the effects of gravitational collapse by considering heat flux anisotropic matter sources within the framework of the $f\left(R\right)$ theory of gravity. We assume the non-static spherically symmetric configuration to narrate the nature of the interior spacetime and match it with the Vaidya exterior geometry. Further, we employ the well-known Karmarkar condition, as it reduces the solution-generating method of field equations to a single metric potential. To ensure the viability of our collapsing system, a comprehensive graphical analysis is presented in the context of the Logarithmic-corrected $R^2$ gravity model. Our investigation argues that there are no traces of trapped surfaces in the collapsing procedure. Thus, naked singularity and black hole are not the final fate of the gravitational collapse.     

Coronal Magnetic Field Lines and Electrons Associated with Type III–V Radio Bursts in a Solar Flare

We recently investigated some of the hitherto unreported observational characteristics of the low frequency (85–35 MHz) type III–V bursts from the Sun using radio spectropolarimeter observations. The quantitative estimates of the velocities of the electron streams associated with the above two types of bursts indicate that they are in the range \({\gtrsim }0.13c\)–0.02c for the type V bursts, and nearly constant (\({\approx }0.4c\)) for the type III bursts. We also find that the degree of circular polarization of the type V bursts vary gradually with frequency/heliocentric distance as compared to the relatively steeper variation exhibited by the preceding type III bursts. These imply that the longer duration of the type V bursts at any given frequency (as compared to the preceding type III bursts) which is its defining feature, is due to the combined effect of the lower velocities of the electron streams that generate type V bursts, spread in the velocity spectrum, and the curvature of the magnetic field lines along which they travel.     

Nature of Coherent Radio Emission from Pulsars

The pulsar radio emission originates from regions below 10% of the light cylinder radius. This requires a mechanism where coherent emission is excited in relativistic pair plasma with frequency \(\nu _{\mathrm{cr}}\) which is below the plasma frequency \(\nu _{\circ }\) i.e. \(\nu _{\mathrm{cr}} < \nu _{\circ }\). A possible model for the emission mechanism is charged bunches (charged solitons) moving relativistically along the curved open dipolar magnetic field lines capable of exciting coherent curvature radio emission. In this article, we review the results from high quality observations in conjunction with theoretical models to unravel the nature of coherent curvature radio emission in pulsars.     

Collapsing supra-massive magnetars: FRBs,the repeating FRB121102 and GRBs

Fast Radio Bursts (FRBs) last for \(\sim \) few milli-seconds and, hence, are likely to arise from the gravitational collapse of supra-massive, spinning neutron stars after they lose the centrifugal support (Falcke & Rezzolla 2014). In this paper, we provide arguments to show that the repeating burst, FRB 121102, can also be modeled in the collapse framework provided the supra-massive object implodes either into a Kerr black hole surrounded by highly magnetized plasma or into a strange quark star. Since the estimated rates of FRBs and SN Ib/c are comparable, we put forward a common progenitor scenario for FRBs and long GRBs in which only those compact remnants entail prompt \(\gamma \)-emission whose kick velocities are almost aligned or anti-aligned with the stellar spin axes. In such a scenario, emission of detectable gravitational radiation and, possibly, of neutrinos are expected to occur during the SN Ib/c explosion as well as, later, at the time of magnetar implosion.     

Resonance tongues in the linear Sitnikov equation

In this paper, we deal with a Hill’s equation, depending on two parameters \(e\in [0,1)\) and \(\varLambda >0\), that has applications to some problems in Celestial Mechanics of the Sitnikov type. Due to the nonlinearity of the eccentricity parameter e and the coexistence problem, the stability diagram in the \((e,\varLambda )\)-plane presents unusual resonance tongues emerging from points \((0,(n/2)^2),\ n=1,2,\ldots \) The tongues bounded by curves of eigenvalues corresponding to \(2\pi \)-periodic solutions collapse into a single curve of coexistence (for which there exist two independent \(2\pi \)-periodic eigenfunctions), whereas the remaining tongues have no pockets and are very thin. Unlike most of the literature related to resonance tongues and Sitnikov-type problems, the study of the tongues is made from a global point of view in the whole range of \(e\in [0,1)\). Indeed, an interesting behavior of the tongues is found: almost all of them concentrate in a small \(\varLambda \)-interval [1, 9 / 8] as \(e\rightarrow 1^-\). We apply the stability diagram of our equation to determine the regions for which the equilibrium of a Sitnikov \((N+1)\)-body problem is stable in the sense of Lyapunov and the regions having symmetric periodic solutions with a given number of zeros. We also study the Lyapunov stability of the equilibrium in the center of mass of a curved Sitnikov problem.     

Reduction and relative equilibria for the two-body problem on spaces of constant curvature

We consider the two-body problem on surfaces of constant nonzero curvature and classify the relative equilibria and their stability. On the hyperbolic plane, for each \(q>0\) we show there are two relative equilibria where the masses are separated by a distance q. One of these is geometrically of elliptic type and the other of hyperbolic type. The hyperbolic ones are always unstable, while the elliptic ones are stable when sufficiently close, but unstable when far apart. On the sphere of positive curvature, if the masses are different, there is a unique relative equilibrium (RE) for every angular separation except \(\pi /2\). When the angle is acute, the RE is elliptic, and when it is obtuse the RE can be either elliptic or linearly unstable. We show using a KAM argument that the acute ones are almost always nonlinearly stable. If the masses are equal, there are two families of relative equilibria: one where the masses are at equal angles with the axis of rotation (‘isosceles RE’) and the other when the two masses subtend a right angle at the centre of the sphere. The isosceles RE are elliptic if the angle subtended by the particles is acute and is unstable if it is obtuse. At \(\pi /2\), the two families meet and a pitchfork bifurcation takes place. Right-angled RE are elliptic away from the bifurcation point. In each of the two geometric settings, we use a global reduction to eliminate the group of symmetries and analyse the resulting reduced equations which live on a five-dimensional phase space and possess one Casimir function.     

Turbulent Gravito-Electrostatic Sheath (GES) Structure with Kappa-Distributed Electrons for Solar Plasma Characterization

We report on new characteristic features of the plasma-based gravito-electrostatic sheath (GES) model for solar plasma equilibrium characterization through nonthermal (\(\kappa\)-distributed) electrons composed of both a thermal halo (low-speed) and a suprathermal (high-speed) energy tail. The constituent ions are treated collectively as inertial species. The presence of intrinsic fluid turbulence is included with the help of a proper logatropic equation of state in the ionic momentum conservation law. The analysis is based on the basic physics of space-charge polarization effects, collectively evolving as a plasma sheath, but previously known only for laboratory plasma-scales. We show that the radial location of the solar surface boundary (SSB, inner boundary, diffused), formed by the counteracting GES force balancing, becomes slightly enhanced (by 0.5 on the Jeans scale). The net electric current densities, in both the solar interior and exterior, confirm the universal law of total charge conservation in the presence of geometrical curvature effects. The relevant properties of the new \(\kappa\)-modified equilibrium GES structure are numerically illustrated and discussed. The results are finally compared in the light of existing reports based on the Maxwell–Boltzmann electron distribution. The new outcomes can be extensively expanded to analyze the realistic thermostatistical dynamics of the Sun and its ambient atmosphere, as predicted earlier from various space-based observations.     

Relative equilibria of the restricted three-body problem in curved spaces

We use a formulation of the N-body problem in spaces of constant Gaussian curvature, \({\kappa }\in \mathbb {R}\), as widely used by A. Borisov, F. Diacu and their coworkers. We consider the restricted three-body problem in \(\mathbb {S}^2\) with arbitrary \({\kappa }>0\) (resp. \(\mathbb {H}^2\) with arbitrary \({\kappa }<0\)) in a formulation also valid for the case \({\kappa }=0\). For concreteness when \({\kappa }>0\) we restrict the study to the case of the three bodies at the upper hemisphere, to be denoted as \(\mathbb {S}^2_+\). The main goal is to obtain the totality of relative equilibria as depending on the parameters \({\kappa }\) and the mass ratio \(\mu \). Several general results concerning relative equilibria and its stability properties are proved analytically. The study is completed numerically using continuation from the \({\kappa }=0\) case and from other limit cases. In particular both bifurcations and spectral stability are also studied. The \(\mathbb {H}^2\) case is similar, in some sense, to the planar one, but in the \(\mathbb {S}^2_+\) case many differences have been found. Some surprising phenomena, like the coexistence of many triangular-like solutions for some values \(({\kappa },\mu )\) and many stability changes will be discussed.     

Thin-shell wormholes in non-linear f(R) gravity with variable scalar curvature

The present paper explores a thin-shell wormhole (TSW) developed by employing the cut and paste method to two copies of the black hole. It develops TSW in modified $f\left(R\right)$ theory of gravity with variable scalar curvature. The effects of the model parameters on the wormhole solutions are tested, the regions of linear stability are analyzed and stable wormhole solutions have been obtained.     

FRB Event Rate Predictions for the Ooty Wide Field Array

We developed a generic formalism to estimate the event rate and the redshift distribution of Fast Radio Bursts (FRBs) in our previous publication (Bera et al. 2016), considering FRBs are of an extragalactic origin. In this paper, we present (a) the predicted pulse widths of FRBs by considering two different scattering models, (b) the minimum total energy required to detect events, (c) the redshift distribution and (d) the detection rates of FRBs for the Ooty Wide Field Array (OWFA). The energy spectrum of FRBs is modelled as a power law with an exponent ?α and our analysis spans a range ?3≤α≤5. We find that OWFA will be capable of detecting FRBs with α≥0. The redshift distribution and the event rates of FRBs are estimated by assuming two different energy distribution functions; a Delta function and a Schechter luminosity function with an exponent ?2≤γ≤2. We consider an empirical scattering model based on pulsar observations (model I) as well as a theoretical model (model II) expected for the intergalactic medium. The redshift distributions peak at a particular redshift z _p for a fixed value of α, which lie in the range 0.3≤z _p ≤1 for the scattering model I and remain flat and extend up to high redshifts (z?5) for the scattering model II.     

The Sitnikov problem for several primary bodies configurations

In this paper we address an \(n+1\)-body gravitational problem governed by the Newton’s laws, where n primary bodies orbit on a plane \(\varPi \) and an additional massless particle moves on the perpendicular line to \(\varPi \) passing through the center of mass of the primary bodies. We find a condition for the described configuration to be possible. In the case when the primaries are in a rigid motion, we classify all the motions of the massless particle. We study the situation when the massless particle has a periodic motion with the same minimal period as the primary bodies. We show that this fact is related to the existence of a certain pyramidal central configuration.     

A viable dark fluid model

We consider a cosmological model based on a generalization of the equation of state proposed by Nojiri and Odintsov (2004) and ?tefan?i? (2005, 2006). We argue that this model works as a dark fluid model which can interpolate between dust equation of state and the dark energy equation of state. We show how the asymptotic behavior of the equation of state constrained the parameters of the model. The causality condition for the model is also studied to constrain the parameters and the fixed points are tested to determine different solution classes. Observations of Hubble diagram of SNe Ia supernovae are used to further constrain the model. We present an exact solution of the model and calculate the luminosity distance and the energy density evolution. We also calculate the deceleration parameter to test the state of the universe expansion.     

High-resolution Observations of H$\alpha$ Spectra with a Subtractive Double Pass

High-resolution imaging spectroscopy in solar physics has relied on Fabry–Pérot interferometers (FPIs) in recent years. FPI systems, however, become technically challenging and expensive for telescopes larger than the 1 m class. A conventional slit spectrograph with a diffraction-limited performance over a large field of view (FOV) can be built at much lower cost and effort. It can be converted into an imaging spectro(polari)meter using the concept of a subtractive double pass (SDP). We demonstrate that an SDP system can reach a similar performance as FPI-based systems with a high spatial and moderate spectral resolution across a FOV of \(100^{\prime\prime} \times100^{\prime \prime}\) with a spectral coverage of 1 nm. We use H\(\alpha\) spectra taken with an SDP system at the Dunn Solar Telescope and complementary full-disc data to infer the properties of small-scale superpenumbral filaments. We find that the majority of all filaments end in patches of opposite-polarity fields. The internal fine-structure in the line-core intensity of H\(\alpha\) at spatial scales of about 0\(.\!\!^{\prime \prime }\)5 exceeds that in other parameters such as the line width, indicating small-scale opacity effects in a larger-scale structure with common properties. We conclude that SDP systems in combination with (multi-conjugate) adaptive optics are a valid alternative to FPI systems when high spatial resolution and a large FOV are required. They can also reach a cadence that is comparable to that of FPI systems, while providing a much larger spectral range and a simultaneous multi-line capability.     

High energy power-law tail in X-ray binaries and bulk Comptonization due to an outflow from a disk

We study the high energy power-law tail emission of X-ray binaries (XRBs) by a bulk Comptonization process which is usually observed in the very high soft (VHS) state of black hole (BH) XRBs and the high soft (HS) state of the neutron star (NS) and BH XRBs. Earlier, to generate the power-law tail in bulk Comptonization framework, a free-fall converging flow into BH or NS had been considered as a bulk region. In this work, for a bulk region we consider mainly an outflow geometry from the accretion disk which is bounded by a torus surrounding the compact object. We have two choices for an outflow geometry: (i) collimated flow and (ii) conical flow of opening angle \(\theta _b\) and the axis is perpendicular to the disk. We also consider an azimuthal velocity of the torus fluids as a bulk motion where the fluids are rotating around the compact object (a torus flow). We find that the power-law tail can be generated in a torus flow having large optical depth and bulk speed (>0.75c), and in conical flow with \(\theta _b\) > \(\sim 30^\circ \) for a low value of Comptonizing medium temperature. Particularly, in conical flow the low opening angle is more favourable to generate the power-law tail in both the HS state and the VHS state. We notice that when the outflow is collimated, then the emergent spectrum does not have power-law component for a low Comptonizing medium temperature.