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 $M\times\nu_{U}(a)$ 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 $M\times\nu_{U}(a)$ that cannot be represented by single functions. Each of these five models is compatible with the expectation of $a\gtrsim 1$.Comment: 8 pages, 4 figures, accepted for publication in Astronomy & Astrophysic

QPOs in microquasars: the spin problem

In the Galactic microquasars with double peak kHz quasi-periodic oscillations (QPOs), the ratio of the two frequencies is 3:2. This supports the suggestion that double peak kHz QPOs are due to a non-linear resonance between two modes of accretion disk oscillations. For the microquasars with known mass, we briefly compare the black hole spin estimates based on the orbital resonance model with the recently reported spin predictions obtained by fitting the spectral continua. Results of these two approaches are not in good agreement. We stress that if the spectral fit estimates are accurate and can be taken as referential (which is still questionable), the disagreement between the predicted and referential values would represent a rather generic problem for any relativistic QPO model, as no spin influence would appear in the observed 1/M scaling of the QPO frequencies. The epicyclic frequencies relevant in these models are often considered to be equal to those of a test particle motion. However modifications of the frequencies due to the disc pressure or other non-geodesic effects may play an important role, and the inaccuracy introduced in the spin estimates by the test particle approximation could be crucial.Comment: 3 pages, proceedings of the IAU XXVIth General Assembl

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, $a>0.99979$.Comment: 9 pages, 7 figure

RESONANT SWITCH MODEL OF HF QPOS AND EQUATIONS OF STATE OF NEUTRON STARS AND QUARK STARS

The mass and spin estimates of the 4U 1636−53 neutron star obtained by the Resonant Switch (RS) model of high-frequency quasi-periodic oscillations (HF QPOs) are tested by a large variety of equations of state (EoS) governing the structure of neutron stars. Neutron star models are constructed under the Hartle–Thorne theory of slowly rotating neutron stars calculated using the observationally given rotational frequency frot = 580 Hz (or alternatively frot = 290 Hz) of the neutron star at 4U 1636−53. It is demonstrated that only two variants of the RS model are compatible with the parameters obtained by modelling neutron stars for the rotational frequency frot = 580 Hz. The variant giving the best fit with parameters M ~ 2.20Mʘ and a ~ 0.27 agrees with high precision with the prediction of one of the Skyrme EoS [1]. The variant giving the second best fit with parameters M ~ 2.12Mʘ and a ~ 0.20 agrees with lower precision with the prediction of the Gandolfi EoS [2]

On mass-constraints implied by the relativistic precession model of twin-peak quasi-periodic oscillations in Circinus X-1

Boutloukos et al. (2006) discovered twin-peak quasi-periodic oscillations (QPOs) in 11 observations of the peculiar Z-source Circinus X-1. Among several other conjunctions the authors briefly discussed the related estimate of the compact object mass following from the geodesic relativistic precession model for kHz QPOs. Neglecting the neutron star rotation they reported the inferred mass M_0 = 2.2 +/- 0.3 M_\sun. We present a more detailed analysis of the estimate which involves the frame-dragging effects associated with rotating spacetimes. For a free mass we find acceptable fits of the model to data for (any) small dimensionless compact object angular momentum j=cJ/GM^2. Moreover, quality of the fit tends to increase very gently with rising j. Good fits are reached when M ~ M_0[1+0.55(j+j^2)]. It is therefore impossible to estimate the mass without the independent knowledge of the angular momentum and vice versa. Considering j up to 0.3 the range of the feasible values of mass extends up to 3M_\sun. We suggest that similar increase of estimated mass due to rotational effects can be relevant for several other sources.Comment: 10 pages, 9 figures (in colour

How to Choose and When to Start Best ITS Projects That Enhance Logistic Performance?

This paper is dealing with the evolvement of operational research in logistics related to ITS projects. Basically a static model has been introduced by the authors. The model is an extended assigned method. There are more and more quasi-real-time data existing on the changing properties of real world elements and processes due to the less and less cycle time of data collecting. On the other hand volume of the data mapping the real world in more details increased significantly. Therefore ITS projects in logistic has been examined. Later on the model has been partly dynamited

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.Comment: 12 pages, 9 figures, 3 tables, accepted for publication in The Astrophysical Journa

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.Comment: 6 pages, 4 figures, submitted to the AN as proceedings of XMM-Newton 2022 Science Worksho