Upper-twin-peak quasiperiodic oscillation in x-ray binaries and the energy from tidal circularization of relativistic orbits

High frequency quasiperiodic oscillations (HF QPOs) detected in the power spectra of low mass x-ray binaries (LMXBs) could unveil the fingerprints of gravitation in the strong field regime. Using the energy-momentum relation we calculate the energy a clump of plasma orbiting in the accretion disk releases during circularization of its slightly eccentric relativistic orbit. Following previous works, we highlight the strong tidal force as a mechanism to dissipate such energy. We show that tides acting on the clump are able to reproduce the observed coherence of the upper HF QPO seen in LMXBs with a neutron star (NS). The quantity of energy released by the clump and relativistic boosting might give a modulation amplitude in agreement with that observed in the upper HF QPO. Both the amplitude and coherence of the upper HF QPO in NS LMXBs could allow us to disclose, for the first time, the tidal circularization of relativistic orbits occurring around a neutron star.

Figure 1

Radius $R$ set by tides of a clump of plasma as a function of the periastron of the orbit $r_p$, around a $2M_{\odot }$ neutron star.

Figure 2

Tidal load ${\sigma }_T$ (4) over a clump of plasma $R=3000\mathrm{m}$ big as a function of the orbital radius. Each segment draws the variation of the load from periastron to apastron of the orbit.

Figure 3

Orbital energy released by a clump of plasma with $R$ as in Fig. 1 in order to circularize its orbit with initial $e=0.1$. The energy is plotted as a function of the frequency of the beat ${\nu }_k+{\nu }_r$ for a $2M_{\odot }$ compact object.

Figure 4

Simulated coherence $Q$ of the beat ${\nu }_k+{\nu }_r$ as a function of the frequency ${\nu }_k+{\nu }_r$ for a $2M_{\odot }$ compact object. The value of $Q$ is related to the time scale the tidal circularization of relativistic orbits takes place, for clumps of plasma of $R$ as in Fig. 1. Such behavior is typical of the $Q$ of the detected upper HF QPO. For a comparison with the data see Fig. 2 in Ref. [52].

Figure 5

Amplitude the beat ${\nu }_k+{\nu }_r$ would have in the observations after the energy release by tidal circularization of relativistic orbits (Fig. 3). The amplitude is in percent of the luminosity of an atoll NS LMXB ($\sim {10}^{37}\mathrm{erg}/\mathrm{s}$). The amplitude is plotted as a function of the frequency of the beat ${\nu }_k+{\nu }_r$. Such behavior is typical of the amplitude of the upper HF QPO. For a comparison with the data see Fig. 3 in Ref. [52].