Confronting the models of 3:2 quasiperiodic oscillations with the rapid spin of the microquasar GRS 1915+105

Török, Gabriel; Kotrlová, Andrea; Šrámková, Eva; Stuchlík, Zdeněk

doi:10.1051/0004-6361/201015549

Cited by 106 publications

(119 citation statements)

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“…Thus, the above result is justified, except when very large non-geodesic corrections are taken into account. Only the RP1 model can survive with corrections of |∆ν| up to ∼ 20%, but the present physical interpretation of this model is unclear (see Török et al, 2011 for references). Török et al (2005) pointed out that since the 3 : 2 QPO frequencies in microquasars scale roughly as ν U .…”

Section: Discussionmentioning

confidence: 96%

“…Analysis including the influence of non-geodesic effects would require a very detailed study. A rough estimate of their possible relevance can be done assuming the relative non-geodesic correction ∆ν (Török et al, 2011), which is needed to match the observations of GRS 1915+105 with a given model for a certain spin. For a ∈ (0.9, 1) and the RP model, it changes from −40% to −60%.…”

Section: Discussionmentioning

confidence: 99%

“…The mass ranges implied by combinations of the fundamental discoseismic modes overlap with those observationally determined only for the model relating the 3 : 2 QPOs to the c-mode (corrugation 2 A. Kotrlová et al Table 1. Frequency relations corresponding to individual QPO models examined by Török et al (2011) and the resulting ranges of spin implied by the 3 : 2 QPOs in GRS 1915+105.…”

Section: The Spin Implied By Individual Modelsmentioning

confidence: 99%

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confidence: 99%

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Confronting the Models of 3 : 2 QPOs with the Evidence of Near Extreme Kerr Black Hole

Kotrlová¹,

Török²,

Šrámková³

et al. 2012

Proc. IAU

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Abstract.The black hole mass and spin estimates assuming various specific models of the 3 : 2 high frequency quasi-periodic oscillations (HF QPOs) have been carried out in Török et al. (2005Török et al. ( , 2011. Here we briefly summarize some current points. Spectral fitting of the spin a ≡ cJ/GM 2 in the microquasar GRS 1915+105 reveals that this system can contain a near extreme rotating black hole (e.g., McClintock et al., 2011). Confirming the high value of the spin would have significant consequences for the theory of the HF QPOs. The estimate of a > 0.9 is almost inconsistent with the relativistic precession (RP), tidal disruption (TD), and the warped disc (WD) model. The epicyclic resonance (Ep) and discoseismic models assuming the c-and g-modes are instead favoured. However, consideration of all three microquasars that display the 3 : 2 HF QPOs leads to a serious puzzle because the differences in the individual spins, such as a = 0.9 compared to a = 0.7, represent a generic problem almost for any unified orbital 3:2 QPO model.Keywords. accretion, accretion disks; X-rays: binaries; black hole physics The spin implied by individual modelsAssuming the Kerr geometry, the Keplerian and epicyclic orbital frequencies (ν K , ν r and ν θ ) for a given radius depend only on mass M and spin a of the black hole. It is therefore possible to infer the black hole spin or mass from the observed 3 : 2 frequencies and concrete orbital QPO models.The 3 : 2 QPO frequencies in GRS 1915+105 are given byAssuming relation (1.1) and the well known formulae for the orbital frequencies, we calculate the implied mass-spin functions for the models associating the 3 : 2 QPOs with common radii by means of the definition relations given in Table 1. Following Török et al. (2005) and taking into account the estimated range of the mass of GRS 1915+105,we infer the expected ranges of the spin. The results are presented in Table 1.The above considered models assume that both of the observed 3 : 2 frequencies are produced by the same mechanism and excited at a certain (common) preferred radius. For the discoseismic modes the individual observed QPOs correspond to different modes located at different radii. The frequencies of these modes depend on the black hole spin and the speed of sound in the accreted gas, and scale as 1/M . The mass ranges implied by combinations of the fundamental discoseismic modes overlap with those observationally determined only for the model relating the 3 : 2 QPOs to the c-mode (corrugation 1

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Section: Discussionmentioning

confidence: 96%

Section: Discussionmentioning

confidence: 99%

Section: The Spin Implied By Individual Modelsmentioning

confidence: 99%

“…

…”

mentioning

confidence: 99%

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Confronting the Models of 3 : 2 QPOs with the Evidence of Near Extreme Kerr Black Hole

Kotrlová¹,

Török²,

Šrámková³

et al. 2012

Proc. IAU

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“…In such situations, the ratio of the triples of the resonant frequencies is directly related to the black hole spin, independently of the black hole mass. The related possibility of directly measuring the black hole spin is very important because of relatively high uncertainties in observational estimates of the black hole mass that are necessary for determining the black hole spin in general resonant phenomena (Török et al , 2011, or in black hole spin determinations based on the measurements of profiled spectral lines (Laor 1991;Karas et al 1992;Dovčiak et al 2004;Fabian & Miniutti 2005;Zakharov 2003;Zakharov & Repin 2006;Zakharov et al 2012;Fanton et al 1997;Čadež et al 2003;Čadež & Calvani 2005).…”

Section: Discussionmentioning

confidence: 99%

Multi-resonance orbital model of high-frequency quasi-periodic oscillations: possible high-precision determination of black hole and neutron star spin

Stuchlík

Kotrlová

Török

2013

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129

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Context. Using known frequencies of the twin-peak high-frequency quasiperiodic oscillations (HF QPOs) and known mass of the central black hole, the black-hole dimensionless spin a can be determined by assuming a concrete version of the resonance model. However, a wide range of observationally limited values of the black hole mass implies low precision of the spin estimates. Aims. We discuss the possibility of higher precision for the black hole spin a measurements in the framework of a multi-resonance model inspired by observations of more than two HF QPOs in the black hole systems, which are expected to occur at two (or more) different radii of the accretion disc. This framework is also applied in a modified form to the neutron star systems. Methods. We determine the spin and mass dependence of the twin-peak frequencies with a general rational ratio n:m, assuming a non-linear resonance of oscillations with the epicyclic and Keplerian frequencies or their combinations. In the multi-resonant model, the twin-peak resonances are combined properly to give the observed frequency set. For the black hole systems we focus on the special case of duplex frequencies, when the top, bottom, or mixed frequency is common at two different radii where the resonances occur giving triple frequency sets. Results. The sets of triple frequency ratios and the related spin a are given. The resonances are considered up to n = 5 since excitation of higher order resonances is improbable. The strong resonance model for "magic" values of the black hole spin means that two (or more) versions of resonance could occur at the same radius, allowing cooperative effects between the resonances. For neutron star systems we introduce a resonant switch model that assumes switching of oscillatory modes at resonant points. Conclusions. In the case of doubled twin-peak HF QPOs excited at two different radii with common top, bottom, or mixed frequency, the black hole spin a is given by the triple frequency ratio set. The spin is determined precisely, but not uniquely, because the same frequency set could correspond to more than one concrete spin a. The black hole mass is given by the magnitude of the observed frequencies. The resonant switch model puts relevant limits on the mass and spin of neutron stars, and we expect a strong increase in the fitting procedure precision when different twin oscillatory modes are applied to data in the vicinity of different resonant points. We expect the multi-resonance model to be applicable to data from the planned LOFT or similar X-ray satellite observatory.

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Statistical properties of twin kilohertz quasi‐periodic oscillations in neutron star low‐mass X‐ray binaries

et al. 2014

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We collect the data of twin kilohertz quasi-periodic oscillations (kHz QPOs) published before 2012 from 26 neutron star (NS) low-mass X-ray binary (LMXB) sources, then we analyze the centroid frequency (ν) distribution of twin kHz QPOs (lower frequency ν1 and upper frequency ν2) both for Atoll and Z sources. For the data without shift-and-add, we find that Atoll and Z sources show the different distributions of ν1, ν2 and ν2/ν1, but the same distribution of ∆ν (difference of twin kHz QPOs), which indicates that twin kHz QPOs may share the common properties of LXMBs and have the same physical origins. The distribution of ∆ν is quite different from constant value, so is ν2/ν1 from constant ratio. The weighted mean values and maxima of ν1 and ν2 in Atoll sources are slightly higher than those in Z sources. We also find that shift-and-add technique can reconstruct the distribution of ν1 and ∆ν. The K-S test results of ν1 and ∆ν between Atoll and Z sources from data with shift-and-add are quite different from those without it, and we think that this may be caused by the selection biases of the sample. We also study the properties of the quality factor (Q) and the root-mean-squared (rms) amplitude of 4U 0614+09 with the data from the two observational methods, but the errors are too big to make a robust conclusion. The NS spin frequency (νs) distribution of 28 NS-LMXBs show a bigger mean value (∼ 408 Hz) than that (∼ 281 Hz) of the radio binary millisecond pulsars (MSPs), which may be due to the lack of the spin detections from Z sources (systematically lower than 281 Hz). Furthermore, on the relations between the kHz QPOs and NS spin frequency νs, we find the approximate correlations of the mean values of ∆ν with NS spin and its half, respectively.

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Confronting the models of 3:2 quasiperiodic oscillations with the rapid spin of the microquasar GRS 1915+105

Cited by 106 publications

References 85 publications

Confronting the Models of 3 : 2 QPOs with the Evidence of Near Extreme Kerr Black Hole

Confronting the Models of 3 : 2 QPOs with the Evidence of Near Extreme Kerr Black Hole

Multi-resonance orbital model of high-frequency quasi-periodic oscillations: possible high-precision determination of black hole and neutron star spin

Statistical properties of twin kilohertz quasi‐periodic oscillations in neutron star low‐mass X‐ray binaries

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