pseudo-Newtonian Potential Research Articles

Emergence of hot corona and truncated disc in simulations of accreting stellar mass black holes

ABSTRACT Stellar mass black holes in X-ray binaries (XRBs) are known to display different states characterized by different spectral and timing properties, understood in the framework of a hot corona coexisting with a thin accretion disc whose inner edge is truncated. There are several open questions related to the nature and properties of the corona, the thin disc, and dynamics behind the hard state. This motivated us to perform 2D hydrodynamical simulations of accretion flows onto a $10 \, \mathrm{M}_\odot$ black hole. We consider a two-temperature plasma, incorporate radiative cooling with bremmstrahlung, synchrotron, and Comptonization losses and approximate the Schwarzschild space–time via a pseudo-Newtonian potential. We varied the mass accretion rate in the range $0.02 \le \dot{M}/\dot{M}_{\rm Edd} \le 0.35$. Our simulations show the natural emergence of a colder truncated thin disc embedded in a hot corona, as required to explain the hard state of XRBs. We found that as $\dot{M}$ increases, the corona contracts and the inner edge of the thin disc gets closer to the event horizon. At a critical accretion rate $0.02 \le \dot{M}_{\text{crit }}/\dot{M}_{\rm Edd} \le 0.06$, the thin disc disappears entirely. We discuss how our simulations compare with XRB observations in the hard state.

Chaotic dynamics of off-equatorial orbits around pseudo-Newtonian compact objects with dipolar halos

In this paper, we implement a generalised pseudo-Newtonian potential to study the off-equatorial orbits inclined at a certain angle with the equatorial plane around Schwarzschild and Kerr-like compact object primaries surrounded by a dipolar halo of matter. The chaotic dynamics of the orbits are detailed for both non-relativistic and special-relativistic test particles. The dependence of the degree of chaos on the Kerr parameter a and the inclination angle i is established individually using widely used indicators, such as the Poincaré Maps and the Maximum Lyapunov Exponents. Although the orbits’ chaoticity has a positive correlation with i, the growth in the chaotic behaviour is not systematic. There is a threshold value of the inclination angle ic, after which the degree of chaos sharply increases. On the other hand, the chaoticity of the inclined orbits anti-correlates with a throughout its entire range. However, the negative correlation is systematic at lower values of the inclination angle. At higher values of i, the degree of chaos increases rapidly below a threshold value of the Kerr parameter, ac. Above this threshold value, the correlation becomes weak. Furthermore, we establish a qualitative correlation between the threshold values and the overall chaoticity of the system. The studies performed with different orbital parameters and several initial conditions reveal the intricate nature of the system.

Trajectory of massive particles around a static black hole in f(R) gravity

In this paper, we investigated the trajectory of the massive particle in the vicinity of a general spherical symmetric black hole. Also, in the framework of general sphericalily symmetric black hole, pseudo-Newtonian potential (PNP) and effective potentials have been investigated. As an example, static spherically symmetric black hole in f(R) gravity is considered and a brief discussion on the structure of spacetime and horizons is presented. We calculated energy and angular momentum in the framework of general relativity as well as in pseudo-Newtonian theory. A graphical comparison of angular momentum in both these frameworks has been studied.

Asymptotic Green’s function solutions of the general relativistic thin disc equations

ABSTRACT The leading order Green’s function solutions of the general relativistic thin disc equations are computed, using a pseudo-Newtonian potential and asymptotic Laplace mode matching techniques. This solution, valid for a vanishing innermost stable circular orbit (ISCO) stress, is constructed by ensuring that it reproduces the leading order asymptotic behaviour of the near-ISCO, Newtonian, and global Wentzel–Kramers–Brillouin limits. Despite the simplifications used in constructing this solution, it is typically accurate, for all values of the Kerr spin parameter a and at all radii, to less than a per cent of the full numerically calculated solutions of the general relativistic disc equations. These solutions will be of use in studying time-dependent accretion discs surrounding Kerr black holes.

Long-term 3D MHD simulations of black hole accretion discs formed in neutron star mergers

ABSTRACT We examine the long-term evolution of accretion tori around black hole (BH) remnants of compact object mergers involving at least one neutron star, to better understand their contribution to kilonovae and the synthesis of r-process elements. To this end, we modify the unsplit magnetohydrodynamic (MHD) solver in flash 4.5 to work in non-uniform three-dimensional spherical coordinates, enabling more efficient coverage of a large dynamic range in length scales while exploiting symmetries in the system. This modified code is used to perform BH accretion disc simulations that vary the initial magnetic field geometry and disc compactness, utilizing a physical equation of state, a neutrino leakage scheme for emission and absorption, and modelling the BH’s gravity with a pseudo-Newtonian potential. Simulations run for long enough to achieve a radiatively inefficient state in the disc. We find robust mass ejection with both poloidal and toroidal initial field geometries, and suppressed outflow at high disc compactness. With the included physics, we obtain bimodal velocity distributions that trace back to mass ejection by magnetic stresses at early times, and to thermal processes in the radiatively inefficient state at late times. The electron fraction distribution of the disc outflow is broad in all models, and the ejecta geometry follows a characteristic hourglass shape. We test the effect of removing neutrino absorption or nuclear recombination with axisymmetric models, finding ${\sim} 50{{\ \rm per\ cent}}$ less mass ejection and more neutron-rich composition without neutrino absorption, and a subdominant contribution from nuclear recombination. Tests of the MHD and neutrino leakage implementations are included.

Accretion onto a quintessence contaminated rotating black hole: violating the lower limit for eta over s

Viscous accretion flow around a rotating supermassive black hole sitting in a quintessence tub is studied in this article. To introduce such a dark energy contaminated black hole’s gravitational force, a new pseudo-Newtonian potential is used. This pseudo-Newtonian force can be calculated if we know the distance from the black hole’s center, spin of the black hole and equation of state of the quintessence inside which the black hole is considered to lie. This force helps us to avoid complicated nonlinearity of general relativistic field equations. Transonic, viscous, continuous and Keplerian flow is assumed to take place. Fluid speed, sonic speed profile and specific angular momentum to Keplerian angular momentum ratio are found out for different values of spin parameter and quintessence parameter. Density variation is built and tallied with observations. Shear viscosity to entropy density ratio is constructed for our model and a comparison with theoretical lower limit is done.

Orbit classification in a disk galaxy model with a pseudo-Newtonian central black hole

We numerically investigate the motion of stars on the meridional plane of an axially symmetric disk galaxy model, containing a central supermassive black hole, represented by the Paczyński-Wiita potential. By using this pseudo-Newtonian potential we can replicate important relativistic properties such as the existence of the Schwarzschild radius. After classifying extensive samples of initial conditions of trajectories, we managed to distinguish between collisional, ordered, and chaotic motion. Besides all starting conditions of regular orbits were further classified into families of regular orbits. Our results are presented via color-coded basin diagrams on several types of two-dimensional planes. Our analysis reveals that both the mass of the black hole (in direct relation with the Schwarzschild radius) as well as angular momentum play an important role in the character of the orbits of stars. More specifically, the trajectories of low angular momentum stars are highly affected by the mass of the black hole, while high angular momentum stars seem to be unaffected by the central black hole. A comparison with previous related outcomes, using Newtonian potentials for the central region of the galaxy, is also made.

Planetary orbital precession in pseudo-Newtonian potentials: reproduction of the general relativity orbital effect

In this paper, pseudo-Newtonian potentials are used to study the problem of orbital precession. The precession rates are found to have the same dependence on GM/cL, where M is the mass of the star and L the angular momentum per unit mass of the planet, comparable to the result obtained in Einstein’s general relativity (GR). Moreover, a specific form of pseudo-Newtonian potential (i.e. equation () in the text) is constructed to have the same precession rate with the GR result to the lowest order. Finally, we give a brief discussion for this potential form, as well.

Pseudo Newtonian potential for a rotating Kerr black hole embedded in quintessence

Pseudo-Newtonian potential has always been a useful tool to discuss the motion of a particle in space-time to avoid the tedious and nearly impossible nonlinear computations coming from the field equations of general relativity. Mukhopadhyay, in 2002, has introduced such a pseudo-Newtonian potential for rotating Kerr black hole which is efficient enough to replicate the scenario of the classical mechanics. But there was no such model to explain the dark energy realm. In 2016 Ghosh introduced a Lagrangian for such rotating black hole embedded in quintessence. in this article we obtained a pseudo-Newtonian force for this new black hole solution embedded quintessence. This paper introduces a simple computational scheme to evaluate a pseudo-Newtonian force for any space-time metric. This model possesses at most 4.95% error corresponding to general relativistic results. Since we took a popular agent of dark energy, i.e., quintessence into account, this is a general form of pseudo-Newtonian force to explain late time accelerating universe. In this paper, it also has been discussed about the difference between the pseudo-Newtonian force with and without dark energy effect. This paper also explains the natures of our present universe and its fate(locally around a black hole when repulsive negative pressure of dark energy is taken into account).

Effect of plasma composition on magnetized outflows

In this paper, we study magnetized winds described by variable adiabatic index equation of state in Paczyński & Wiita pseudo-Newtonian potential. We identify the flow solutions with the parameter space of the flow. We also confirm that the physical wind solution is the one which passes through the slow, Alfvén, and fast critical points. We study the dependence of the wind solution on the Bernoulli parameter E and the total angular momentum L. The adiabatic index, which is a function of temperature and composition, was found to be variable in all the outflow solutions. For the same values of the Bernoulli parameter and the total angular momentum, a wind in strong gravity is more accelerated, compared to a wind in Newtonian gravity. We show that flow variables such as the radial and azimuthal velocity components and temperature all depend on the composition of the flow. Unlike the outflow solutions in hydrodynamic regime, the terminal speed of a magnetically driven wind also depends on the composition parameter.

Properties of two-temperature dissipative accretion flow around black holes

We study the properties of two-temperature accretion flow around a non-rotating black hole in presence of various dissipative processes where pseudo-Newtonian potential is adopted to mimic the effect of general relativity. The flow encounters energy loss by means of radiative processes acted on the electrons and at the same time, flow heats up as a consequence of viscous heating effective on ions. We assumed that the flow is exposed with the stochastic magnetic fields that leads to Synchrotron emission of electrons and these emissions are further strengthen by Compton scattering. We obtain the two-temperature global accretion solutions in terms of dissipation parameters, namely, viscosity (α) and accretion rate (⁠|${\dot{m}}$|⁠), and find for the first time in the literature that such solutions may contain standing shock waves. Solutions of this kind are multitransonic in nature, as they simultaneously pass through both inner critical point (xin) and outer critical point (xout) before crossing the black hole horizon. We calculate the properties of shock-induced global accretion solutions in terms of the flow parameters. We further show that two-temperature shocked accretion flow is not a discrete solution, instead such solution exists for wide range of flow parameters. We identify the effective domain of the parameter space for standing shock and observe that parameter space shrinks as the dissipation is increased. Since the post-shock region is hotter due to the effect of shock compression, it naturally emits hard X-rays, and therefore, the two-temperature shocked accretion solution has the potential to explain the spectral properties of the black hole sources.

MHD simulations of oscillating cusp-filling tori around neutron stars – missing upper kHz QPO

Abstract We performed axisymmetric, grid-based, ideal magnetohydrodynamic simulations of oscillating cusp-filling tori orbiting a non-rotating neutron star. A pseudo-Newtonian potential was used to construct the constant angular momentum tori in equilibrium. The inner edge of the torus is terminated by a ‘cusp’ in the effective potential. The initial motion of the model tori was perturbed with uniform sub-sonic vertical and diagonal velocity fields. As the configuration evolved in time, we measured the mass accretion rate on the neutron star surface and obtained the power spectrum. The prominent mode of oscillation in the cusp torus is the radial epicyclic mode. It would appear that vertical oscillations are suppressed by the presence of the cusp. From our analysis, it follows that the mass accretion rate carries a modulation imprint of the oscillating torus, and hence so does the boundary layer luminosity.

Paczynski-Wiita-like potential for any static spherical black hole in metric theories of gravity

The pseudo-Newtonian potential of Paczynski and Wiita for particles orbiting a Schwarzschild black hole is generalized to arbitrary static and spherically symmetric spacetimes, including black hole solutions of alternative theories of gravity. In addition to being more general, our prescription differs substantially from a previous one in the literature, showing that even the association of a pseudo-Newtonian potential with a simple black hole metric is not unique.

Quasi-periodic oscillations of perturbed tori

We performed axisymmetric hydrodynamical simulations of oscillating tori orbiting a non-rotating black hole. The tori in equilibrium were constructed with a constant distribution of angular momentum in a pseudo-Newtonian potential (Klu{\'z}niak-Lee). Motions of the torus were triggered by adding sub-sonic velocity fields: radial, vertical and diagonal to the tori in equilibrium. As the perturbed tori evolved in time, we measured $L_{2}$ norm of density and obtained the power spectrum of $L_{2}$ norm which manifested eigenfrequencies of tori modes. The most prominent modes of oscillation excited in the torus by a quasi-random perturbation are the breathing mode and the radial and vertical epicyclic modes. The radial and the plus modes, as well as the vertical and the breathing modes will have frequencies in an approximate 3:2 ratio if the torus is several Schwarzschild radii away from the innermost stable circular orbit. Results of our simulations may be of interest in the context of high-frequency quasi-periodic oscillations (HF QPOs) observed in stellar-mass black hole binaries, as well as in supermassive black holes.

Outflows from accretion discs formed in neutron star mergers: effect of black hole spin

The accretion disk that forms after a neutron star merger is a source of neutron-rich ejecta. The ejected material contributes to a radioactively-powered electromagnetic transient, with properties that depend sensitively on the composition of the outflow. Here we investigate how the spin of the black hole remnant influences mass ejection on the thermal and viscous timescales. We carry out two-dimensional, time-dependent hydrodynamic simulations of merger remnant accretion disks including viscous angular momentum transport and approximate neutrino self-irradiation. The gravity of the spinning black hole is included via a pseudo-Newtonian potential. We find that a disk around a spinning black hole ejects more mass, up to a factor of several, relative to the non-spinning case. The enhanced mass loss is due to energy release by accretion occurring deeper in the gravitational potential, raising the disk temperature and hence the rate of viscous heating in regions where neutrino cooling is ineffective. The mean electron fraction of the outflow increases moderately with BH spin due to a highly-irradiated (though not neutrino-driven) wind component. While the bulk of the ejecta is still very neutron-rich, thus generating heavy r-process elements, the leading edge of the wind contains a small amount of Lanthanide-free material. This component can give rise to a ~1 day blue optical `bump' in a kilonova light curve, even in the case of prompt BH formation, which may facilitate its detection.

Dynamics of Charged Particles Around a Magnetized Black Hole with Pseudo—Newtonian Potential

The linear stability of equilibria of charged particles moving near a compact object with a dipole magnetic field and a pseudo-Newtonian potential is analyzed detailedly. An optimal fourth-order force gradient symplectic method, as a global symplectic integrator that can simultaneously solve both the equations of motion and the variational equations, is used to calculate fast Lyapunov indicators. In this way, dynamical structures are described, and parameter domains for causing chaos are found.

Finite, intense accretion bursts from tidal disruption of stars on bound orbits

We study accretion processes for tidally disrupted stars approaching supermassive black holes on bound orbits, by performing three dimensional Smoothed Particle Hydrodynamics simulations with a pseudo-Newtonian potential. We find that there is a critical value of the orbital eccentricity below which all the stellar debris remains bound to the black hole. For high but sub-critical eccentricities, all the stellar mass is accreted onto the black hole in a finite time, causing a significant deviation from the canonical $t^{-5/3}$ mass fallback rate. When a star is on a moderately eccentric orbit and its pericenter distance is deeply inside the tidal disruption radius, there can be several orbit crossings of the debris streams due to relativistic precession. This dissipates orbital energy in shocks, allowing for rapid circularization of the debris streams and formation of an accretion disk. The resultant accretion rate greatly exceeds the Eddington rate and differs strongly from the canonical rate of $t^{-5/3}$. By contrast, there is little dissipation due to orbital crossings for the equivalent simulation with a purely Newtonian potential. This shows that general relativistic precession is crucial for accretion disk formation via circularization of stellar debris from stars on moderately eccentric orbits.

PSEUDO-NEWTONIAN POTENTIALS FOR NEARLY PARABOLIC ORBITS

We describe a pseudo-Newtonian potential which, to within 1% error at all angular momenta, reproduces the precession due to general relativity of particles whose specific orbital energy is small compared to c^2 in the Schwarzschild metric. For bound orbits the constraint of low energy is equivalent to requiring the apoapsis of a particle to be large compared to the Schwarzschild radius. Such low energy orbits are ubiquitous close to supermassive black holes in galactic nuclei, but the potential is relevant in any context containing particles on low energy orbits. Like the more complex post-Newtonian expressions, the potential correctly reproduces the precession in the far-field, but also correctly reproduces the position and magnitude of the logarithmic divergence in precession for low angular momentum orbits. An additional advantage lies in its simplicity, both in computation and implementation. We also provide two simpler, but less accurate potentials, for cases where orbits always remain at large angular momenta, or when the extra accuracy is not needed. In all of the presented cases the accuracy in precession in low energy orbits exceeds that of the well known potential of Paczynski & Wiita (1980), which has ~30% error in the precession at all angular momenta.

Tidal disruption flares from stars on eccentric orbits

We study tidal disruption and subsequent mass fallback for stars approaching supermassive black holes on bound orbits, by performing three dimensional Smoothed Particle Hydrodynamics simulations with a pseudo-Newtonian potential. We find that the mass fallback rate decays with the expected -5/3 power of time for parabolic orbits, albeit with a slight deviation due to the self-gravity of the stellar debris. For eccentric orbits, however, there is a critical value of the orbital eccentricity, significantly below which all of the stellar debris is bound to the supermassive black hole. All the mass therefore falls back to the supermassive black hole in a much shorter time than in the standard, parabolic case. The resultant mass fallback rate considerably exceeds the Eddington accretion rate and substantially differs from the -5/3 power of time.

XMM-NEWTON , SWIFT , AND ROSAT OBSERVATIONS OF LBQS 0102-2713

We have analyzed the first XMM-Newton, Swift and archival ROSAT PSPC observations of the quasar LBQS 0102-2713.The object was selected from the ROSAT archive as being notable due to the steep soft X-ray photon index and due to the UV brightness based on HST and optical spectroscopic observations. The first XMM-Newton observations carried out in December 2009 and the first Swift observations from 2010 have confirmed the steepness of the soft X-ray photon index, which ranges between 3.35 and 4.41 for the different XMM-Newton and ROSAT detectors, the UV brightness of the source and the absence of significant absorption by neutral hydrogen. The new data allow a combined spectral fitting to the Swift UVOT and the XMM-Newton/ROSAT data which results in a huge luminosity of (6.2+-0.2)x10^47 erg s^(-1) and alpha_ox values ranging between (-1.87+-0.11) and (-2.11+-0.12). The nature of the soft X-ray emission can be explained as local Comptonized emission of the UV disc photons in the pseudo-Newtonian potential. The black hole mass is estimated from the Mg II line and translates into an Eddington ratio of L/L_edd = 18(+33)(-12). For the dimensionless electron temperature of the plasma cloud theta = kT_e/ (m_e c^2) we derive an upper limit of about 10 keV.