arXiv subjects

Wlodek Kluzniak

Publications and source records attributed to Wlodek Kluzniak.

At least 19 recordsLinked to original sources

arXiv2026

Strange quark star II: the minimal and maximal gravitational mass and the Keplerian configuration

We employ the MIT bag model with density-dependent bag constant for the equation of state (EOS) to estimate the gravitational mass and Keplerian frequency of rapidly rotating strange quark stars (SQS). In a companion paper we discuss the structural parameters of such rotating stars under the influence of strong magnetic fields. We use the LORENE library to compute the structural parameters at different rotational frequencies in the range of 1100-1300~Hz for a non-magnetized SQS. While there is no minimum limit for the mass of slowly rotating self-bound stars, by computing the maximum rotational frequency, known as the mass-shedding limit, we show that SQS must have a minimum mass to sustain high rotational frequencies. The mass-shedding frequency in our EOS model is lower than that estimated from the MIT bag model EOS with a fixed bag constant. The Keplerian frequency in our model depends linearly on the gravitational mass at the mass-shedding limit (and similarly on the minimum mass) with the slope of 0.08~${\rm kHz}/M_\odot$. We obtain mass limits aligned with the observational data for both the heaviest and the lightest observed pulsars.

astro-ph.HE↗

arXiv2023

Energy distribution and substructure formation in astrophysical MHD simulations

During substructure formation in magnetized astrophysical plasma, dissipation of magnetic energy facilitated by magnetic reconnection affects the system dynamics by heating and accelerating the ejected plasmoids. Numerical simulations are a crucial tool for investigating such systems. In astrophysical simulations, the energy dissipation, reconnection rate and substructure formation critically depend on the onset of reconnection of numerical or physical origin. In this paper, we hope to assess the reliability of the state-of-the-art numerical codes, PLUTO and KORAL by quantifying and discussing the impact of dimensionality, resolution, and code accuracy on magnetic energy dissipation, reconnection rate, and substructure formation. We quantitatively compare results obtained with relativistic and non-relativistic, resistive and non-resistive, as well as two- and three-dimensional setups performing the Orszag-Tang test problem. We find the sufficient resolution in each model, for which numerical error is negligible and the resolution does not significantly affect the magnetic energy dissipation and reconnection rate. The non-relativistic simulations show that at sufficient resolution, magnetic and kinetic energies convert to internal energy and heat up the plasma. The results show that in the relativistic system, energy components undergo mutual conversion during the simulation time, which leads to a substantial increase in magnetic energy at 20\% and 90\% of the total simulation time of $10$ light-crossing times -- the magnetic field is amplified by a factor of five due to relativistic shocks. We also show that the reconnection rate in all our simulations is higher than $0.1$, indicating plasmoid-mediated regime. It is shown that in KORAL simulations magnetic energy is slightly larger and more substructures are captured than in PLUTO simulations.

astro-ph.HE↗

arXiv2023

Energy dissipation in astrophysical simulations: results of the Orszag-Tang test problem

The magnetic field through the magnetic reconnection process affects the dynamics and structure of astrophysical systems. Numerical simulations are the tools to study the evolution of these systems. However, the resolution, dimensions, resistivity, and turbulence of the system are some important parameters to take into account in the simulations. In this paper, we investigate the evolution of magnetic energy in astrophysical simulations by performing a standard test problem for MHD codes, Orszag-Tang. We estimate the numerical dissipation in the simulations using state-of-the-art numerical simulation code in astrophysics, PLUTO. The estimated numerical resistivity in 2D simulations corresponds to the Lundquist number $\approx 10^{4}$ in the resolution of $512\times512$ grid cells. It is also shown that the plasmoid unstable reconnection layer can be resolved with sufficient resolutions. Our analysis demonstrates that in non-relativistic magnetohydrodynamics simulations, magnetic and kinetic energies undergo conversion into internal energy, resulting in plasma heating.

physics.plasm-ph↗

arXiv2022

Observational properties of puffy disks: radiative GRMHD spectra of mildly sub-Eddington accretion

Numerical general relativistic radiative magnetohydrodynamic simulations of accretion disks around a stellar mass black hole with a luminosity above 0.5 of the Eddington value reveal their stratified, elevated vertical structure. We refer to these thermally stable numerical solutions as puffy disks. Above a dense and geometrically thin core of dimensionless thickness $h/r \sim 0.1$, crudely resembling a classic thin accretion disk, a puffed-up, geometrically thick layer of lower density and $h/r \sim 1.0$ is formed. We discuss the observational properties of puffy disks, in particular the geometrical obscuration of the inner disk by the elevated puffy region at higher observing inclinations, and collimation of the radiation along the accretion disk spin axis, which may explain the apparent super-Eddington luminosity of some X-ray objects. We also present synthetic spectra of puffy disks, and show that they are qualitatively similar to those of a Comptonized thin disk. We demonstrate that the existing xspec spectral fitting models provide good fits to synthetic observations of puffy disks, but cannot correctly recover the input black hole spin. The puffy region remains optically thick to scattering; in its spectral properties the puffy disk roughly resembles that of a warm corona sandwiching the disk core. We suggest that puffy disks may correspond to X-ray binary systems of luminosities above 0.3 of the Eddington luminosity in the intermediate spectral states.

astro-ph.HE↗

arXiv2018

Breathing Oscillations in a Global Simulation of a Thin Accretion Disk

We study the oscillations of an axisymmetric, viscous, radiative, general relativistic hydrodynamical simulation of a geometrically thin disk around a non-rotating, $6.62\,M_\odot$ black hole. The numerical setup is initialized with a Novikov-Thorne, gas-pressure-dominated accretion disk, with an initial mass accretion rate of $\dot{m} = 0.01\,L_\mathrm{Edd}/c^2$ (where $L_\mathrm{Edd}$ is the Eddington luminosity and $c$ is the speed of light). Viscosity is treated with the $α$-prescription. The simulation was evolved for about $1000$ Keplerian orbital periods at three Schwarzschild radii (ISCO radius). Power density spectra of the radial and vertical fluid velocity components, the total (gas $+$ radiation) midplane pressure, and the vertical component of radiative flux from the photosphere, all reveal strong power at the local breathing oscillation frequency. The first, second and third harmonics of the breathing oscillation are also clearly seen in the data. We quantify the properties of these oscillations by extracting eigenfunctions of the radial and vertical velocity components and total pressure. This confirms that these oscillations are associated with breathing motion.

astro-ph.HE↗

arXiv2018

Relativistic Viscous Radiation Hydrodynamic Simulations of Geometrically Thin Disks: I. Thermal and Other Instabilities

We present results from two-dimensional, general relativistic, viscous, radiation hydrodynamic numerical simulations of Shakura-Sunyaev thin disks accreting onto stellar mass Schwarzschild black holes. We consider cases on both the gas- and radiation-pressure-dominated branches of the thermal equilibrium curve, with mass accretion rates spanning the range from $\dot{M} = 0.01 L_\mathrm{Edd}/c^2$ to $10 L_\mathrm{Edd}/c^2$. The simulations directly test the stability of this standard disk model on the different branches. We find clear evidence of thermal instability for all radiation-pressure-dominated disks, resulting universally in the vertical collapse of the disks, which in some cases then settle onto the stable, gas-pressure-dominated branch. Although these results are consistent with decades-old theoretical predictions, they appear to be in conflict with available observational data from black hole X-ray binaries. We also find evidence for a radiation-pressure-driven instability that breaks the unstable disks up into alternating rings of high and low surface density on a timescale comparable to the thermal collapse. Since radiation is included self-consistently in the simulations, we are able to calculate lightcurves and power density spectra (PDS). For the most part, we measure radiative efficiencies (ratio of luminosity to mass accretion rate) close to 6%, as expected for a non-rotating black hole. The PDS appear as broken power laws, with a break typically around 100 Hz. There is no evidence of significant excess power at any frequencies, i.e. no quasi-periodic oscillations are observed.

astro-ph.HE↗

arXiv2017

Numerical simulations of oscillating tori in a pseudo-Newtonian potential

We have modeled hydrodynamical tori in the Klu{ź}niak-Lee pseudo-Newtonian potential. The tori in equilibrium were perturbed with uniform sub-sonic velocity fields: vertical, radial and diagonal respectively, and allowed to evolve in time. We identify the eigenmodes corresponding to those of slender tori. The results of our simulations are relevant to the investigation of high-frequency quasi-periodic oscillations observed in stellar-mass black hole binaries.

astro-ph.HE↗

arXiv2017

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

We performed axisymmetric, grid-based, ideal magnetohydrodynamic (MHD) 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.

astro-ph.HE↗

arXiv2017

Pulsing ULXs: tip of the iceberg?

We consider the three currently known pulsing ultraluminous X--ray sources (PULXs). We show that in one of them the observed spinup rate requires super--Eddington accretion rates at the magnetospheric radius, even if magnetar--strength fields are assumed. In the two other systems a normal--strength neutron star field implies super--Eddington accretion at the magnetosphere. Adopting super--Eddington mass transfer as the defining characteristic of ULX systems, we find the parameters required for self--consistent simultaneous fits of the luminosities and spinup rates of the three pulsed systems. These imply near--equality between their magnetospheric radii $R_M$ and the spherization radii $R_{\rm sph}$ where radiation pressure becomes important and drives mass loss from the accretion disc. We interpret this near--equality as a necessary condition for the systems to appear as pulsed, since if it is violated the pulse fraction is small. We show that as a consequence all PULXs must have spinup rates $\dotν\gtrsim 10^{-10}\, {\rm s^{-2}}$, an order of magnitude higher than in any other pulsing neutron--star binaries. The fairly tight conditions required for ULXs to show pulsing support our earlier suggestion that many unpulsed ULX systems must actually contain neutron stars rather than black holes.

astro-ph.HE↗

arXiv2016

Levitating atmospheres of Eddington-luminosity neutron stars

We construct models of static, spherically symmetric shells supported by the radiation flux of a luminous neutron star in the Schwarzschild metric. The atmospheres are disconnected from the star and levitate above its surface. Gas pressure and density inversion appear in the inner region of these atmospheres, which is a purely relativistic phenomenon. We account for the scattering opacity dependence on temperature and utilize the relativistic M1 closure scheme for the radiation tensor, hence allowing for a fully GR-consistent treatment of the photon flux and radiation tensor anisotropy. In this way we are able to address atmospheres of both large and moderate/low optical depths with the same set of equations. We discuss properties of the levitating atmospheres and find that they may indeed be optically thick, with the distance between star surface and the photosphere expanding as luminosity increases. These results may be relevant for the photosphereric radius expansion X-ray bursts.

astro-ph.HE↗

arXiv2016

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{ź}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.

astro-ph.HE↗

arXiv2015

An ultraluminous nascent millisecond pulsar

If the ultraluminous source (ULX) M82 X-2 sustains its measured spin-up value of $\dot ν= 10^{-10}\,{\rm s^{-2}}$, it will become a millisecond pulsar in less than $10^5\,$ years. The observed (isotropic) luminosity of $10^{40}\,$ erg/s also supports the notion that the neutron star will spin up to a millisecond period upon accreting about $0.1\,{\rm M_\odot}$---the reported hard X-ray luminosity of this ULX, together with the spin-up value, implies torques consistent with the accretion disk extending down to the vicinity of the stellar surface, as expected for low values of the stellar dipole magnetic field ($B\lesssim 10^9\,$G). This suggests a new channel of millisecond pulsar formation---in high-mass X-ray binaries (HMXBs)---and may have implications for studies of gravitational waves, and possibly for the formation of low-mass black holes through accretion-induced collapse.

astro-ph.SR↗

arXiv2015

High frequency oscillations in outbursts of Kerr-metric slim disks

We numerically investigate the thermally unstable accretion disks around black holes. We adopt an evolutionary viscous stress equation to replace the standard alpha-prescription based on the results of two MHD simulations. We find a kind of interesting oscillations on some running models in limit-cycle outburst state. The oscillations arise near the inner boundary and propagate radially outwards. We deem that they are the trapped $p$-mode oscillations excited by sonic-point instability. We directly integrate the local radiation cooling fluxes to construct the mimic bolometric light-curve. We find a series of overtones beside the fundamental harmonic on the power spectra of mimic light-curves. The frequency of the fundamental harmonic is very close to the maximum epicyclic frequency of the disk and the frequency ratio of the fundamental harmonic and overtones is a regular integer series. We suggest that the code for ray-tracing calculation must be time-dependent in virtual observation and point out the robustness of the black hole spin measurement with high frequency QPOs.

astro-ph.HE↗

arXiv2014

Numerical simulations of thin accretion discs with PLUTO

Our goal is to perform global simulations of thin accretion discs around compact bodies like neutron stars with dipolar magnetic profile and black holes by exploiting the facilities provided by state-of-the-art grid-based, high resolution shock capturing (HRSC) and finite volume codes. We have used the Godunov-type code PLUTO to simulate a thin disc around a compact object prescribed with a pseudo-Newtonian potential in a purely hydrodynamical (HD) regime, with numerical viscosity as a first step towards achieving our goal as mentioned above.

astro-ph.HE↗

arXiv2014

Epicyclic frequencies for rotating strange quark stars: the importance of stellar oblateness

Kilohertz QPOs can be used as a probe of the inner regions of accretion disks in compact stars and hence also of the properties of the central object. Most models of kHz QPOs involve epicyclic frequencies to explain their origin. We compute the epicyclic frequencies of nearly circular orbits around rotating strange quark stars. The MIT bag model is used to model the equation of state of quark matter and the uniformly rotating stellar configurations are computed in full general relativity. The vertical epicyclic frequency and the related nodal precession rate of inclined orbits are very sensitive to the oblateness of the rotating star. For slowly rotating stellar models of moderate and high mass strange stars, the sense of the nodal precession changes at a certain rotation rate. At lower stellar rotation rates the orbital nodal precession is prograde, as it is in the Kerr metric, while at higher rotation rates the precession is retrograde, as it is for Maclaurin spheroids. Thus, qualitatively, the orbits around rapidly rotating strange quark stars are affected more strongly by the effects of stellar oblateness than by the effects of general relativity. We show that epicyclic and orbital frequencies calculated numerically for small mass strange stars are in very good agreement with analytical formulae for Maclaurin spheroids.

astro-ph.SR↗

arXiv2013

Magnetic fields in Accretion Discs around Neutron Stars - Consequences for the change of spin

Accretion disks are ubiquitous in the universe and it is generally accepted that magnetic fields play a pivotal role in accretion-disk physics. The spin history of millisecond pulsars, which are usually classified as magnetized neutron stars spun up by an accretion disk, depends sensitively on the magnetic field structure, and yet highly idealized models from the 80s are still being used for calculating the magnetic field components. We present a possible way of improving the currently used models with a semi-analytic approach. The resulting magnetic field profile of both the poloidal and the toroidal component can be very different from the one suggested previously. This might dramatically change our picture of which parts of the disk tend to spin the star up or down.

astro-ph.SR↗

arXiv2011

Stability of radiation-pressure dominated disks. I. The dispersion relation for a delayed heating alpha-viscosity prescription

We derive and investigate the dispersion relation for accretion disks with retarded or advanced heating. We follow the alpha-prescription but allow for a time offset (τ) between heating and pressure perturbations, as well as for a diminished response of heating to pressure variations. We study in detail solutions of the dispersion relation for disks with radiation-pressure fraction 1 - β. For τ<0 (delayed heating) the number and sign of real solutions for the growth rate depend on the values of the time lag and the ratio of heating response to pressure perturbations, ξ. If the delay is larger than a critical value (e.g., if Ωτ<-125 for α=0.1, β=0 and ξ=1) two real solutions exist, which are both negative. These results imply that retarded heating may stabilize radiation-pressure dominated accretion disks.

astro-ph.HE↗

arXiv2011

Spinning up black holes with super-critical accretion flows

We study the process of spinning up black holes by accretion from slim disks in a wide range of accretion rates. We show that for super-Eddington accretion rates and low values of the viscosity parameter alpha (\lesssim 0.01) the limiting value of the dimensionless spin parameter a_* can reach values higher than a_*=0.9978 inferred by Thorne (1974) in his seminal study. For \mdot=10\mdot_{Edd} and alpha=0.01 spin equilibrium is reached at a_*=0.9994. We show that the equilibrium spin value depends strongly on the assumed value of alpha. We also prove that for high accretion rates the impact of captured radiation on spin evolution is negligible.

astro-ph.HE↗