arXiv subjects

Gabriel Török

Publications and source records attributed to Gabriel Török.

At least 19 recordsLinked to original sources

arXiv2026

Radiative GRMHD simulations of puffy accretion discs: Numerical versus analytical models of sub-Eddington accretion

A widely accepted picture of an accretion flow in the luminous soft spectral state of X-ray binary systems is a geometrically thin disc structure much like the classic analytic solution of Shakura& Sunyaev. Although the analytic models are troubled by instabilities and miss important aspects of physics, such as magnetic fields, they are successfully used as a framework for interpreting observational data. Here, we compare the results of general relativistic radiative magnetohydrodynamic (GRRMHD) simulations of optically thick, mildly sub-Eddington accretion on a stellar-mass black hole (the puffy disc) with established analytic and semi-analytic accretion models in the same regime. From the simulations, we find that the accretion flow is stabilised by the magnetic field, with a puffed-up, optically thick region resembling a warm corona surrounding a denser and cooler disc core. However, the stratified vertical structure of the disc significantly influences the observational picture of such a system. We analyse the inner disc structure, flow properties, effective viscosity, and inner edge position, and compare them to the predictions of standard models. We find that the simulated discs share some similarities with the models; however, they differ in several important aspects, most notably: the photosphere is geometrically thick, the inner edge is located closer to the central black hole than the analytic models assume, the surface density is significantly lower than analytically predicted, and the effective viscosity parameter is not constant but rises steeply in the innermost region.

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arXiv2026

Lense-Thirring precession of neutron-star accretion flows: Relativistic versus classical precession

The vertical (Lense-Thirring) precession of the innermost accretion flows has been discussed as a sensitive indicator of the rotational properties of neutron stars (NSs) and their equation of state because it vanishes for a non-rotating star. In this work, we apply the Hartle-Thorne spacetimes to study the frequencies of the precession for both geodesic and non-geodesic (fluid) flows. We build on previous findings on the effect of the NS quadrupole moment, which revealed the importance of the interplay between the relativistic and classical precession. Because of this interplay, the widely used Lense-Thirring metric, linear in the NS angular momentum, is insufficient to calculate the behaviour of the precession frequency across an astrophysically relevant range of NS angular momentum values. We find that even for a moderately oblate NSs, the dependencies of the precession frequency on the NS angular momentum at radii within the innermost accretion region have maxima that occur at relatively low values of the NS angular momentum. We conclude that very different groups of accreting NSs -- slow and fast rotators -- can display the same precession frequencies. This may explain the lack of evidence for a correlation between the frequencies of the observed low-frequency quasiperiodic oscillations and the NS spin. In our work, we provide a full, general description of precession behaviour, and also examples that assume specific NS and quark star (MIT bag) equation of state. Our calculations are reproducible using the associated Wolfram Mathematica notebook.

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arXiv2025

Modulation of X-ray flux by obscuration of neutron star boundary layer

The quasi-periodic oscillations (QPOs) observed in the X-ray variability of both black hole (BH) and neutron star (NS) systems provide a tool for probing strong gravity and dense matter equations of state. Nevertheless, the mechanism of QPO modulation in NS systems, where the amplitudes of QPOs with frequencies approaching kHz range are very high in comparison to BH high-frequency QPOs, remains an unsolved puzzle. Relativistic ray tracing of photons emitted from the immediate vicinity of compact objects has, to date, been used to investigate various mechanisms that explain the observed weak BH QPOs. However, it has not been applied to model the NS QPO signal, which requires incorporating the NS surface and a bright boundary layer (BL) on it. Here, we explore the QPO modulation mechanisms based on the BL obscuration. Using simplified models of axisymmetric oscillations of thick accretion discs (tori), we demonstrate that the disc oscillations drive the high NS QPO amplitudes through BL obscuration, which is relevant especially for vertical oscillations. We also demonstrate that obscuration effects enable the observability of the Keplerian frequency in the case of discs that decay due to instabilities.

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arXiv2024

Accretion tori around rotating neutron stars II: Oscillations and precessions

The four characteristic oscillation frequencies of accretion flows are, in addition to the Keplerian orbital frequency, often discussed in the context of the time variability of the black hole and neutron star (NS) low-mass X-ray binaries (LMXBs). These are namely the frequencies of the axisymmetric radial and vertical epicyclic oscillations, and the frequencies of non-axisymmetric oscillations corresponding to the periastron (radial) and Lense-Thirring (vertical) precessions. In this context, we investigate the effect of the quadrupole moment of a slowly rotating NS and provide complete formulae for calculating these oscillation and precession frequencies, as well as their convenient approximations. Simple formulae corresponding to the geodesic limit of a slender torus (and test particle motion) and the limit of a marginally overflowing torus (torus exhibiting a critical cusp) are presented, and furthermore, more general approximate formulae are included to allow calculations for arbitrarily thick tori. We provide the Wolfram Mathematica code used for our calculations together with C++ and PYTHON codes for calculations of the frequencies. Our formulae can be used for various calculations describing the astrophysical signatures of the NSs' superdense matter equation of state. For instance, we demonstrate that, even for a given fixed number of free parameters, a model accounting for fluid flow precession better matches the frequencies of twin-peak quasiperiodic oscillations observed in NS LMXBs than a model using geodesic precession.

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arXiv2024

Accretion tori around rotating neutron stars I: Structure, shape and size

We present a full general relativistic analytic solution for a radiation-pressure supported equilibrium fluid torus orbiting a rotating neutron star (NS). Previously developed analytical methods are thoroughly applied in the Hartle-Thorne geometry, including the effects of both the NS's angular momentum and quadrupole moment. The structure, size and shape of the torus are explored, focusing especially on the critically thick solution - the cusp tori. For the astrophysically relevant range of NS parameters, we examine how our findings differ from those obtained for the Schwarzschild spacetime. The solutions for rotating stars display signatures of the interplay between relativistic and Newtonian effects where the impact of NS angular momentum and quadrupole moment are almost counterbalanced at the given radius. Nevertheless, the spacetime parameters still strongly influence the size of tori, which can be shown in a coordinate-independent way. Finally, we discuss the importance of the size of the central NS, determining whether or not the surrounding torus may exist. We provide a set of tools in a Wolfram Mathematica code, which poses a basis allowing for a further investigation of the impact of the NSs' superdense matter equation of state on the spectral and temporal behaviour of accretion tori.

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arXiv2023

Oscillations of Fluid Tori around Neutron Stars

We examine the influence of quadrupole moment of a slowly rotating neutron star (NS) on the oscillations of a fluid accretion disk (torus) orbiting a compact object the spacetime around which is described by the Hartle-Thorne geometry. Explicit formulae for non-geodesic orbital epicyclic and precession frequencies, as well as their simplified practical versions that allow for an expeditious application of the universal relations determining the NS properties, are obtained and examined. We demonstrate that the difference in the accretion disk precession frequencies for NSs of the same mass and angular momentum, but different oblateness, can reach up to tens of percent. Even higher differences can arise when NSs with the same mass and rotational frequency, but different equations of state (EoS), are considered. In particular, the Lense-Thirring precession frequency defined in the innermost parts of the accretion region can differ by more than one order of magnitude across NSs with different EoS. Our results have clear implications for models of the LMXBs variability.

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arXiv2023

Spectra of Puffy Accretion Discs: the kynbb Fit

Puffy disc is a numerical model, expected to capture the properties of the accretion flow in X-ray black hole binaries in the luminous, mildly sub-Eddington state. We fit the kerrbb and kynbb spectral models in XSPEC to synthetic spectra of puffy accretion discs, obtained in general relativistic radiative magnetohydrodynamic simulations, to see if they correctly recover the black hole spin and mass accretion rate assumed in the numerical simulation. We conclude that neither of the two models is capable of correctly interpreting the puffy disc parameters, which highlights a necessity to develop new, more accurate, spectral models for the luminous regime of accretion in X-ray black hole binaries. We propose that such spectral models should be based on the results of numerical simulations of accretion.

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arXiv2022

Oscillations of non-slender tori in the external Hartle-Thorne geometry

We examine the influence of the quadrupole moment of a slowly rotating neutron star on the oscillations of non-slender accretion tori. We apply previously developed methods to perform analytical calculations of frequencies of the radial epicyclic mode of a torus in the specific case of the Hartle-Thorne geometry. We present here our preliminary results and provide a brief comparison between the calculated frequencies and the frequencies previously obtained assuming both standard and linearized Kerr geometry. Finally, we shortly discuss the consequences for models of high-frequency quasi-periodic oscillations observed in low-mass X-ray binaries.

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arXiv2022

Simple analytic formula relating the mass and spin of accreting compact objects to their rapid X-ray variability

Following the previous research on epicyclic oscillations of accretion disks around black holes (BHs) and neutron stars (NSs), a new model of high-frequency quasi-periodic oscillations (QPOs) has been proposed (CT model), which deals with oscillations of fluid in marginally overflowing accretion tori (i.e., tori terminated by cusps). According to preliminary investigations, the model provides better fits of the NS QPO data compared to the relativistic precession (RP) model. It also implies a significantly higher upper limit on the Galactic microquasars BH spin. A short analytic formula has been noticed to well reproduce the model's predictions on the QPO frequencies in Schwarzschild spacetimes. Here we derive an extended version of this formula that applies to rotating compact objects. We start with the consideration of Kerr spacetimes and derive a formula that is not restricted to a particular specific angular momentum distribution of the inner accretion flow, such as Keplerian or constant. Finally, we consider Hartle-Thorne spacetimes and include corrections implied by the NS oblateness. For a particular choice of a single parameter, our relation provides frequencies predicted by the CT model. For another value, it provides frequencies predicted by the RP model. We conclude that the formula is well applicable for rotating oblateness NSs and both models. We briefly illustrate application of our simple formula on several NS sources and confirm the expectation that the CT model is compatible with realistic values of the NS mass and provides better fits of data than the RP model.

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arXiv2021

Models of high-frequency quasi-periodic oscillations and black hole spin estimates in Galactic microquasars

We explore the influence of non-geodesic pressure forces that are present in an accretion disk on the frequencies of its axisymmetric and non-axisymmetric epicyclic oscillation modes. {We discuss its implications for models of high-frequency quasi-periodic oscillations (QPOs) that have been observed in the X-ray flux of accreting black holes (BHs) in the three Galactic microquasars, GRS 1915+105, GRO J1655$-$40 and XTE J1550$-$564. We focus on previously considered QPO models that deal with low azimuthal number epicyclic modes, $\lvert m \rvert \leq 2$, and outline the consequences for the estimations of BH spin, $a\in[0,1]$.} For four out of six examined models, we find only small, rather insignificant changes compared to the geodesic case. For the other two models, on the other hand, there is a fair increase of the estimated upper limit on the spin. Regarding the QPO model's falsifiability, we find that one particular model from the examined set is incompatible with the data. If the microquasar's spectral spin estimates that point to $a>0.65$ were fully confirmed, two more QPO models would be ruled out. Moreover, if two very different values of the spin, such as $a\approx 0.65$ in GRO J1655$-$40 vs. $a\approx 1$ in GRS 1915+105, were confirmed, all the models except one would remain unsupported by our results. Finally, we discuss the implications for a model recently proposed in the context of neutron star (NS) QPOs as a disk-oscillation-based modification of the relativistic precession model. This model provides overall better fits of the NS data and predicts more realistic values of the NS mass compared to the relativistic precession model. We conclude that it also implies a significantly higher upper limit on the microquasar's BH spin ($a\sim 0.75$ vs. $a\sim 0.55$).

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arXiv2019

Puffy accretion disks: sub-Eddington, optically thick, and stable

We report on a new class of solutions of black hole accretion disks that we have found through three-dimensional, global, radiative magnetohydrodynamic simulations in general relativity. It combines features of the canonical thin, slim and thick disk models but differs in crucial respects from each of them. We expect these new solutions to provide a more realistic description of black hole disks than the slim disk model. We are presenting a disk solution for a non-spinning black hole at a sub-Eddington mass accretion rate, $\dot M=0.6\,\dot M_{\rm Edd}$. By the density scale-height measure the disk appears to be thin, having a high density core near the equatorial plane of height $h_ρ \sim 0.1 \,r$, but most of the inflow occurs through a highly advective, turbulent, optically thick, Keplerian region that sandwiches the core and has a substantial geometrical thickness comparable to the radius, $H \sim r$. The accreting fluid is supported above the midplane in large part by the magnetic field, with the gas and radiation to magnetic pressure ratio $β\sim 1$, this makes the disk thermally stable, even though the radiation pressure strongly dominates over gas pressure. A significant part of the radiation emerging from the disk is captured by the black hole, so the disk is less luminous than a thin disk would be at the same accretion rate.

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arXiv2019

Timescale of twin-peak quasi-periodic oscillations and mass of accreting neutron stars

Einstein's general relativity predicts that orbital motion of accreted gas approaching a neutron star (NS) in a NS low-mass X-ray binary (LMXB) system occurs on a time scale proportional to the NS mass. Radiation of the gas accounts for most of the observed LMXBs variability. In more than a dozen of sources twin-peak quasi-periodic oscillations (QPOs) have been observed. Inspired by the expected proportionality between periods of orbital motion and NS mass we present a straightforward comparison among these sources. We investigate relations between QPO periods and their ratios and identify characteristic time scales of QPOs associated to individual sources. These timescales are likely determined by the relative mass of each NS. We show that the characteristic time scale of the millisecond pulsar XTE J1807.4-294 is longer than for most other NS LMXBs. Consequently, models of QPOs that consider geodesic orbital frequencies imply that the X-ray pulsars' mass has to be about 50 % higher than the average mass of other sources. Consideration of other X-ray pulsars indicates that the exceptionality of XTE J1807.4-294 cannot be related to NS magnetic field in any simple manner. We suggest that QPOs observed in this source can help to discriminate between the proposed versions of the NS equation of state.

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arXiv2019

Epicyclic oscillations in the Hartle-Thorne external geometry

The external Hartle-Thorne geometry, which describes the space-time outside a slowly-rotating compact star, is characterized by the gravitational mass $M$, angular momentum $J$ and quadrupole moment $Q$ of the star and gives a convenient description which, for the rotation frequencies of more than 95 % of known pulsars, is sufficiently accurate for most purposes. We focus here on the motion of particles in these space-times, presenting a detailed systematic analysis of the frequency properties of radial and vertical epicyclic motion and of orbital motion. Our investigation is motivated by X-ray observations of binary systems containing a rotating neutron star which is accreting matter from its binary companion. In these systems, twin high-frequency quasi-periodic oscillations are sometimes observed with a frequency ratio approaching $3:2$ or $5:4$ and these may be explained by models involving the orbital and epicyclic frequencies of quasi-circular geodesic motion. In our analysis, we use realistic equations of state for the stellar matter and proceed in a self-consistent way, following the Hartle-Thorne approach in calculating both the corresponding values of $Q$, $M$ and $J$ for the stellar model and the properties of the surrounding spacetime. Our results are then applied to a range of geodetical models for QPOs. A key feature of our study is that it implements the recently-discovered universal relations among neutron star parameters so that the results can be directly used for models with different masses $M$, radii $R$ and rotational frequencies $f_\mathrm{rot}$.

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arXiv2019

Mass of the active galactic nucleus black hole XMMUJ134736.6+173403

A recent study of the X-ray source XMMUJ134736.6+173403 has revealed a strong quasi-periodic modulation of the X-ray flux. The observation of two quasiperiodic oscillations (QPOs) that occur on a daily timescale and exhibit a 3:1 frequency ratio strongly supports the evidence for the presence of an active galactic nucleus black hole (AGN BH). Assuming the orbital origin of QPOs we calculate the upper and lower limit on AGN BH mass M arriving at $M\approx 10^7-10^9M_{\odot}$. Comparing that to mass estimates of other sources, MMUJ134736.6+173403 appears to be the most massive source with commensurable QPO frequencies, and its mass represents the current observational upper limit on AGN BH mass based on QPO observations. We note it will be crucial for the falsification of particular resonance models of QPOs whether only single QPO with frequency that completes the harmonic sequence 3:2:1 is found in this source, or whether there is a new different pair of QPOs with frequencies in the 3:2 ratio. The former case would agree with the prediction of the 3:2 epicyclic resonance model and black hole mass $M\approx(5a^2 + 8a + 8)\times 10^{7}M_{\odot}$, where a is a dimensionless BH spin.

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arXiv2018

Dense matter with eXTP

In this White Paper we present the potential of the Enhanced X-ray Timing and Polarimetry (eXTP) mission for determining the nature of dense matter; neutron star cores host an extreme density regime which cannot be replicated in a terrestrial laboratory. The tightest statistical constraints on the dense matter equation of state will come from pulse profile modelling of accretion-powered pulsars, burst oscillation sources, and rotation-powered pulsars. Additional constraints will derive from spin measurements, burst spectra, and properties of the accretion flows in the vicinity of the neutron star. Under development by an international Consortium led by the Institute of High Energy Physics of the Chinese Academy of Science, the eXTP mission is expected to be launched in the mid 2020s.

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arXiv2017

On one-parametric formula relating the frequencies of twin-peak quasi-periodic oscillations

Twin-peak quasi-periodic oscillations (QPOs) are observed in several low-mass X-ray binary systems containing neutron stars (NSs). Timing analysis of X-ray fluxes of more than dozen of such systems reveals remarkable correlations between the frequencies of two characteristic peaks present in the power density spectra. The individual correlations clearly differ, but they roughly follow a common individual pattern. High values of measured QPO frequencies and strong modulation of the X-ray flux both suggest that the observed correlations are connected to orbital motion in the innermost part of an accretion disc. Several attempts to model these correlations with simple geodesic orbital models or phenomenological relations have failed in the past. We find and explore a surprisingly simple analytic relation that reproduces individual correlations for a group of several sources through a single parameter. When an additional free parameter is considered within our relation, it well reproduces the data of a large group of 14 sources. The very existence and form of this simple relation supports the hypothesis of the orbital origin of QPOs and provides the key for further development of QPO models. We discuss a possible physical interpretation of our relation's parameters and their links to concrete QPO models.

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arXiv2017

Super-spinning compact objects and models of high-frequency quasi-periodic oscillations observed in Galactic microquasars. II. Forced resonances

In our previous work (Paper I) we applied several models of high-frequency quasi-periodic oscillations (HF QPOs) to estimate the spin of the central compact object in three Galactic microquasars assuming the possibility that the central compact body is a super-spinning object (or a naked singularity) with external spacetime described by Kerr geometry with a dimensionless spin parameter $a\equiv cJ/GM^2>1$. Here we extend our consideration, and in a consistent way investigate implications of a set of ten resonance models so far discussed only in the context of $a<1$. The same physical arguments as in Paper I are applied to these models, i.e. only a small deviation of the spin estimate from $a=1$, $a\gtrsim 1$, is assumed for a favoured model. For five of these models that involve Keplerian and radial epicyclic oscillations we find the existence of a unique specific QPO excitation radius. Consequently, there is a simple behaviour of dimensionless frequency $M\timesν_{U}(a)$ represented by a single continuous function having solely one maximum close to $a\gtrsim1$. Only one of these models is compatible with the expectation of $a\gtrsim 1$. The other five models that involve the radial and vertical epicyclic oscillations imply the existence of multiple resonant radii. This signifies a more complicated behaviour of $M\timesν_{U}(a)$ that cannot be represented by single functions. Each of these five models is compatible with the expectation of $a\gtrsim 1$.

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arXiv2016

Constraining models of twin peak quasi-periodic oscillations with realistic neutron star equations of state

Twin-peak quasi-periodic oscillations (QPOs) are observed in the X-ray power-density spectra of several accreting low-mass neutron star (NS) binaries. In our previous work we have considered several QPO models. We have identified and explored mass-angular-momentum relations implied by individual QPO models for the atoll source 4U 1636-53. In this paper we extend our study and confront QPO models with various NS equations of state (EoS). We start with simplified calculations assuming Kerr background geometry and then present results of detailed calculations considering the influence of NS quadrupole moment (related to rotationally induced NS oblateness) assuming Hartle-Thorne spacetimes. We show that the application of concrete EoS together with a particular QPO model yields a specific mass-angular-momentum relation. However, we demonstrate that the degeneracy in mass and angular momentum can be removed when the NS spin frequency inferred from the X-ray burst observations is considered. We inspect a large set of EoS and discuss their compatibility with the considered QPO models. We conclude that when the NS spin frequency in 4U 1636-53 is close to 580Hz we can exclude 51 from 90 of the considered combinations of EoS and QPO models. We also discuss additional restrictions that may exclude even more combinations. Namely, there are 13 EOS compatible with the observed twin peak QPOs and the relativistic precession model. However, when considering the low frequency QPOs and Lense-Thirring precession, only 5 EOS are compatible with the model.

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