Weak nonlinear coupling between epicyclic modes in slender tori

Kotrlová

Šrámková

et al. 2011

A&A

105

116

Spectral fitting of the spin a ≡ cJ/GM 2 in the microquasar GRS 1915+105 estimate values higher than a = 0.98. However, there are certain doubts about this (nearly) extremal number. Confirming a high value of a > 0.9 would have significant concequences for the theory of high-frequency quasiperiodic oscillations (HF QPOs). Here we discuss its possible implications assuming several commonly used orbital models of 3:2 HF QPOs. We show that the estimate of a > 0.9 is almost inconsistent with two hot-spot (relativistic precession and tidal disruption) models and the warped disc resonance model. In contrast, we demonstrate that the epicyclic resonance and discoseismic models assuming the c-and g-modes are favoured. We extend our discussion to another two microquasars that display the 3:2 HF QPOs. The frequencies of these QPOs scale roughly inversely to the microquasar masses, and the differences in the individual spins, such as a = 0.9 compared to a = 0.7, represent a generic problem for most of the discussed geodesic 3:2 QPO models. To explain the observations of all the three microquasars by one unique mechanism, the models would have to accommodate very large non-geodesic corrections.

Section: Resonant Modelsmentioning

confidence: 99%

Section: Resonant Modelsmentioning

confidence: 99%

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

Kotrlová

Šrámková

et al. 2011

A&A

105

116

“…In our study, the location of the torus centre is empirically chosen using the observed twin peaks HF QPOs ratio. The resonant coupling of oscillation modes can prefer particular values of radial coordinate for amplification or excitation of QPOs (Horák 2008). Therefore, further important improvements in the simulations can incorporate mode-resonant coupling.…”

Section: Discussionmentioning

confidence: 99%

“…This setup corresponds to the often quoted epicyclic resonance (ER) HF QPOs model ) based on the presence of non-linear resonant phenomena between epicyclic disc oscillation modes Abramowicz et al 2003a,b;Horák 2008). The dual oscillation mode with such behaviour is related to wave number pair m r = 0, m θ = 0.…”

Section: Epicyclic Resonance Axisymmetric Setupmentioning

confidence: 99%

Twin peak high-frequency quasi-periodic oscillations as a spectral imprint of dual oscillation modes of accretion tori

Bakala

Goluchová

et al. 2015

A&A

Context. High-frequency (millisecond) quasi-periodic oscillations (HF QPOs) are observed in the X-ray power-density spectra of several microquasars and low-mass X-ray binaries. Two distinct QPO peaks, so-called twin peak QPOs, are often detected simultaneously exhibiting their frequency ratio close or equal to 3:2. A widely discussed class of proposed QPOs models is based on oscillations of accretion toroidal structures orbiting in the close vicinity of black holes or neutron stars. Aims. Following the analytic theory and previous studies of observable spectral signatures, we aim to model the twin peak QPOs as a spectral imprint of specific dual oscillation regime defined by a combination of the lowest radial and vertical oscillation mode of slender tori. We consider the model of an optically thick slender accretion torus with constant specific angular momentum. We examined power spectra and fluorescent Kα iron line profiles for two different simulation setups with the mode frequency relations corresponding to the epicyclic resonance HF QPOs model and modified relativistic precession QPOs model. Methods. We used relativistic ray-tracing implemented in the parallel simulation code LSDplus. In the background of the Kerr spacetime geometry, we analyzed the influence of the distant observer inclination and the spin of the central compact object. Relativistic optical projection of the oscillating slender torus is illustrated by images in false colours related to the frequency shift. Results. We show that performed simulations yield power spectra with the pair of dominant peaks that correspond to the frequencies of radial and vertical oscillation modes and with the peak frequency ratio equal to the proper value 3:2 on a wide range of inclinations and spin values. We also discuss exceptional cases of a very low and very high inclination, as well as unstable high spin relativistic precession-like configurations that predict a constant frequency ratio equal to 1:2. We demonstrate a significant dependency of broadened Kα iron line profiles on the inclination of the distant observer. Conclusions. This study presents a further step towards the proper model of oscillating accretion tori producing HF QPOs. More realistic future simulations should be based on incorporating the resonant coupling of oscillation modes, the influence of torus opacity, and the pressure effects on the mode frequencies and the torus shape.

“…Finding a proper QPO model may thus help us to test the strong field regime predictions of general relativity and, in the case of NS sources, also the models of highly dense matter (see van Abramowicz et al 2003a,b;Rebusco 2004;Horák 2008;Stuchlík et al 2008;Horák et al 2009, and others; see also Aliev &Galtsov 1981 andAliev 2007). These ideas have been widely discussed and adapted into numerous individual disc-oscillation models.…”

Section: Hf Qpo Interpretationmentioning

confidence: 99%

Disc-oscillation resonance and neutron star QPOs: 3:2 epicyclic orbital model

Urbanec

Šrámková

et al. 2010

A&A

The high-frequency quasi-periodic oscillations (HF QPOs) that appear in the X-ray fluxes of low-mass X-ray binaries remain an unexplained phenomenon. Among other ideas, it has been suggested that a non-linear resonance between two oscillation modes in an accretion disc orbiting either a black hole or a neutron star plays a role in exciting the observed modulation. Several possible resonances have been discussed. A particular model assumes resonances in which the disc-oscillation modes have the eigenfrequencies equal to the radial and vertical epicyclic frequencies of geodesic orbital motion. This model has been discussed for black hole microquasar sources as well as for a group of neutron star sources. Assuming several neutron (strange) star equations of state and Hartle-Thorne geometry of rotating stars, we briefly compare the frequencies expected from the model to those observed. Our comparison implies that the inferred neutron star radius R NS is larger than the related radius of the marginally stable circular orbit r ms for nuclear matter equations of state and spin frequencies up to 800 Hz. For the same range of spin and a strange star (MIT) equation of state, the inferrred radius is R NS ∼ r ms . The "Paczyński modulation" mechanism considered within the model requires that R NS < r ms . However, we find this condition to be fulfilled only for the strange matter equation of state, masses below 1 M , and spin frequencies above 800 Hz. This result most likely falsifies the postulation of the neutron star 3:2 resonant eigenfrequencies being equal to the frequencies of geodesic radial and vertical epicyclic modes. We suggest that the 3:2 epicyclic modes could stay among the possible choices only if a fairly non-geodesic accretion flow is assumed, or if a different modulation mechanism operates.