arXiv subjects

G. Torok

Publications and source records attributed to G. Torok.

10 recordsLinked to original sources

arXiv2024

Timing of accreting neutron stars with future X-ray instruments: towards new constraints on dense matter equation of state

The Enhanced X-ray Timing and Polarimetry (eXTP) mission is a space mission to be launched in the late 2020s that is currently in development led by China in international collaboration with European partners. Here we provide a progress report on the Czech contribution to the eXTP science. We report on our simulation results performed in Opava (Institute of Physics of the Silesian University in Opava) and Prague (Astronomical Institute of the Czech Academy of Sciences), where the advanced timing capabilities of the satellite have been assessed for bright X-ray binaries that contain an accreting neutron star (NS) and exhibit the quasi-periodic oscillations. Measurements of X-ray variability originating in oscillations of fluid in the innermost parts of the accretion region determined by general relativity, such as the radial or Lense-Thirring precession, can serve for sensitive tests enabling us to distinguish between the signatures of different viable dense matter equations of state. We have developed formulae describing non-geodesic oscillations of accreted fluid and their simplified practical forms that allow for an expeditious application of the universal relations determining the NS properties. These relations, along with our software tools for studying the propagation of light in strong gravity and neutron star models, can be used for precise modeling of the X-ray variability while focusing on properties of the intended Large Area Detector (LAD). We update the status of our program and set up an electronic repository that will provide simulation results and gradual updates as the mission specifications progress toward their final formulation.

astro-ph.HE↗

arXiv2015

Black hole spin inferred from 3:2 epicyclic resonance model of high-frequency quasi-periodic oscillations

Estimations of black hole spin in the three Galactic microquasars GRS 1915+105, GRO J1655-40, and XTE J1550-564 have been carried out based on spectral and timing X-ray measurements and various theoretical concepts. Among others, a non-linear resonance between axisymmetric epicyclic oscillation modes of an accretion disc around a Kerr black hole has been considered as a model for the observed high-frequency quasi-periodic oscillations (HF QPOs). Estimates of spin predicted by this model have been derived based on the geodesic approximation of the accreted fluid motion. Here we assume accretion flow described by the model of a pressure-supported torus and carry out related corrections to the mass-spin estimates. We find that for dimensionless black hole spin a<0.9, the resonant eigenfrequencies are very close to those calculated for the geodesic motion. Their values slightly grow with increasing torus thickness. These findings agree well with results of a previous study carried out in the pseudo-Newtonian approximation. The situation becomes different for a>0.9, in which case the resonant eigenfrequencies rapidly decrease as the torus thickness increases. We conclude that the assumed non-geodesic effects shift the lower limit of the spin, implied for the three microquasars by the epicyclic model and independently measured masses, from a~0.7 to a~0.6. Their consideration furthermore confirms compatibility of the model with the rapid spin of GRS 1915+105 and provides highly testable predictions of the QPO frequencies. Individual sources with a moderate spin (a<0.9) should exhibit a smaller spread of the measured 3:2 QPO frequencies than sources with a near-extreme spin (a~1). This should be further examined using the large amount of high-resolution data expected to become available with the next generation of X-ray instruments, such as the proposed Large Observatory for X-ray Timing (LOFT).

astro-ph.HE↗

arXiv2014

Appearance of innermost stable circular orbits of accretion discs around rotating neutron stars

The innermost stable cicular orbit (ISCO) of an accretion disc orbiting a neutron star (NS) is often assumed a unique prediction of general relativity. However, it has been argued that ISCO also appears around highly elliptic bodies described by Newtonian theory. In this sense, the behaviour of an ISCO around a rotating oblate neutron star is formed by the interplay between relativistic and Newtonian effects. Here we briefly explore the consequences of this interplay using a straightforward analytic approach as well as numerical models that involve modern NS equations of state. We examine the ratio K between the ISCO radius and the radius of the neutron star. We find that, with growing NS spin, the ratio K first decreases, but then starts to increase. This non-monotonic behaviour of K can give rise to a neutron star spin interval in which ISCO appears for two very different ranges of NS mass. This may strongly affect the distribution of neutron stars that have an ISCO (ISCO-NS). When (all) neutron stars are distributed around a high mass M0, the ISCO-NS spin distribution is roughly the same as the spin distribution corresponding to all neutron stars. In contrast, if M0 is low, the ISCO-NS distribution can only have a peak around a high value of spin. Finally, an intermediate value of M0 can imply an ISCO-NS distribution divided into two distinct groups of slow and fast rotators. Our findings have immediate astrophysical applications. They can be used for example to distinguish between different models of high-frequency quasiperiodic oscillations observed in low-mass NS X-ray binaries.

astro-ph.HE↗

arXiv2014

Distinguishing between spot and torus models of high-frequency quasiperiodic oscillations

In the context of high-frequency quasi-periodic oscillation (HF QPOs) we further explore the appearance of an observable signal generated by hot spots moving along quasi-elliptic trajectories close to the innermost stable circular orbit in the Schwarzschild spacetime. The aim of our investigation is to reveal whether observable characteristics of the Fourier power-spectral density can help us to distinguish between the two competing models, namely, the idea of bright spots orbiting on the surface of an accretion torus versus the scenario of intrinsic oscillations of the torus itself. We take the capabilities of the present observatories (represented by the Rossi X-ray Timing Explorer, RXTE) into account, and we also consider the proposed future instruments (represented here by the Large Observatory for X-ray Timing, LOFT).

astro-ph.HE↗

arXiv2014

Power density spectra of modes of orbital motion in strongly curved spacetime: obtaining the observable signal

High frequency quasi-periodic oscillations (HF QPOs) appear in the X-ray variability of several accreting low-mass binaries. In a series of works it was suggested that these QPOs may have connection to inhomogeneities orbiting close to an inner edge of the accretion disc. In this paper we explore the appearance of an observable signal generated by small radiating circular hot spots moving along quasi-elliptic trajectories close to the innermost stable circular orbit in the Schwarzschild spacetime. Our consideration takes into account the capabilities of observatories that have been operating in the past two decades represented by the Rossi X-ray Timing Explorer (RXTE) and the proposed future instruments represented by the Large Observatory for X-ray Timing (LOFT). For these purposes we choose such model parameters that lead to lightcurves comparable to those observed in Galactic black hole sources, in particular the microquasar GRS 1915+105. We find that when a weak signal corresponding to the hot-spot Keplerian frequency is around the limits of the RXTE detectability, the LOFT observations can clearly reveal its first and second harmonics. Moreover, in some specific situations the radial epicyclic frequency of the spot can be detected as well. Finally, we also compare the signal produced by the spots to the signal produced by axisymmetric epicyclic disc-oscillation modes and discuss the key differences that could be identified via the proposed future technology. We conclude that the ability to recognize the harmonic content of the signal can help to distinguish between the different proposed physical models.

astro-ph.HE↗

arXiv2013

Quasi-periodic oscillations from Rossby Wave Instability

We study the Rossby wave instability model of high-frequency quasi-periodic oscillations (QPO) of microquasars. We show ray-traced light curves of QPO within this model and discuss perspectives of distinguishing alternative QPO models with the future Large Observatory For X-ray Timing (LOFT) observations.

astro-ph.HE↗

arXiv2009

Internal resonance in non-linear disk oscillations and the amplitude evolution of neutron star kilohertz QPOs

We explore some properties of twin kilohertz quasiperiodic oscillations (QPOs) in a simple toy-model consisting of two oscillation modes coupled by a general nonlinear force. We examine resonant effects by slowly varying the values of the tunable, and nearly commensurable, eigenfrequencies. The behavior of the actual oscillation frequencies and amplitudes during a slow transition through the 3:2 resonance is examined in detail and it is shown that both are significantly affected by the nonlinearities in the governing equations. In particular, the amplitudes of oscillations reflect a resonant exchange of energy between the modes, as a result the initially weaker mode may become dominant after the transition. We note that a qualitatively similar behavior has been recently reported in several neutron star sources by Torok (2008, arXiv:0812.4751), who found that the difference of amplitudes in neutron star twin peak QPOs changes sign as the observed frequency ratio of the QPOs passes through the value 3:2.

astro-ph.CO↗

arXiv2007

LNRF-velocity hump-induced oscillations of a Keplerian disc orbiting near-extreme Kerr black hole: A possible explanation of high-frequency QPOs in GRS 1915+105

At least four high-frequency quasiperiodic oscillations (QPOs) at frequencies 41Hz, 67Hz, 113Hz, and 167Hz were reported in a binary system GRS 1915+105 hosting near-extreme Kerr black hole with a dimensionless spin a>0.98. We use the idea of oscillations induced by the hump of the orbital velocity profile (related to locally non-rotating frames - LNRF) in discs orbiting near-extreme Kerr black holes, which are characterized by a "humpy frequency" f_h, that could excite the radial and vertical epicyclic oscillations with frequencies f_r, f_v. Due to non-linear resonant phenomena the combinational frequencies are allowed as well. Assuming mass M=14.8M_sun and spin a=0.9998 for the GRS 1915+105 Kerr black hole, the model predicts frequencies f_h=41Hz, f_r=67Hz, (f_h+f_r)=108Hz, (f_v-f_r)=170Hz corresponding quite well to the observed ones. For black-hole parameters being in good agreement with those given observationally, the forced resonant phenomena in non-linear oscillations, excited by the "hump-induced" oscillations in a Keplerian disc, can explain high-frequency QPOs in GRS 1915+105 within the range of observational errors.

astro-ph↗

arXiv2005

The correlations and anticorrelations in QPO data

Double peak kHz QPO frequencies in neutron star sources varies in time by a factor of hundreds Hz while in microquasar sources the frequencies are fixed and located at the line ν_2 = 1.5 ν_1 in the frequency-frequency plot. The crucial question in the theory of twin HFQPOs is whether or not those observed in neutron-star systems are essentially different from those observed in black holes. In black hole systems the twin HFQPOs are known to be in a 3:2 ratio for each source. At first sight, this seems not to be the case for neutron stars. For each individual neutron star, the upper and lower kHz QPO frequencies, ν_2 and ν_1, are linearly correlated, ν_2=A ν_1 + B, with the slope A < 1.5, i.e., the frequencies definitely are not in a 1.5 ratio. In this contribution we show that when considered jointly on a frequency-frequency plot, the data for the twin kHz QPO frequencies in several (as opposed to one) neutron stars uniquely pick out a certain preferred frequency ratio that is equal to 1.5 for the six sources examined so far.

astro-ph↗

arXiv2004

The Aschenbach effect: unexpected topology changes in motion of particles and fluids orbiting rapidly rotating Kerr black holes

Newton's theory predicts that the velocity $V$ of free test particles on circular orbits around a spherical gravity center is a decreasing function of the orbital radius $r$, $dV/dr < 0$. Only very recently, Aschenbach (A&A 425, p. 1075 (2004)) has shown that, unexpectedly, the same is not true for particles orbiting black holes: for Kerr black holes with the spin parameter $a>0.9953$, the velocity has a positive radial gradient for geodesic, stable, circular orbits in a small radial range close to the black hole horizon. We show here that the {\em Aschenbach effect} occurs also for non-geodesic circular orbits with constant specific angular momentum $\ell = \ell_0 = const$. In Newton's theory it is $V = \ell_0/R$, with $R$ being the cylindrical radius. The equivelocity surfaces coincide with the $R = const$ surfaces which, of course, are just co-axial cylinders. It was previously known that in the black hole case this simple topology changes because one of the ``cylinders'' self-crosses. We show here that the Aschenbach effect is connected to a second topology change that for the $\ell = const$ tori occurs only for very highly spinning black holes, $a>0.99979$.

gr-qc↗