Quasi-periodic Oscillations Frequency Research Articles

A Geometric Origin for Quasi-periodic Oscillations in Black Hole X-Ray Binaries

Abstract We expand the relativistic precession model to include nonequatorial and eccentric trajectories and apply it to quasi-periodic oscillations (QPOs) in black hole X-ray binaries (BHXRBs) and associate their frequencies with the fundamental frequencies of the general case of nonequatorial (with Carter's constant, ) and eccentric ( ) particle trajectories, around a Kerr black hole. We study cases with either two or three simultaneous QPOs and extract the parameters {e, r p , a, Q}, where r p is the periastron distance of the orbit, and a is the spin of the black hole. We find that the orbits with should have e ≲ 0.5 and r p ∼ 2–20 for the observed range of QPO frequencies, where a ∈ [0, 1], and that the spherical trajectories {e = 0, } with Q = 2–4 should have r s ∼ 3–20. We find nonequatorial eccentric solutions for both M82 X-1 and GROJ 1655-40. We see that these trajectories, when taken together, span a torus region and give rise to a strong QPO signal. For two simultaneous QPO cases, we found equatorial eccentric orbit solutions for XTEJ 1550-564, 4U 1630-47, and GRS 1915+105, and spherical orbit solutions for BHXRBs M82 X-1 and XTEJ 1550-564. We also show that the eccentric orbit solution fits the Psaltis–Belloni–Klis correlation observed in BHXRB GROJ 1655-40. Our analysis of the fluid flow in the relativistic disk edge suggests that instabilities cause QPOs to originate in the torus region. We also present some useful formulae for trajectories and frequencies of spherical and equatorial eccentric orbits.

A Relativistic Orbit Model for Temporal Properties of AGN

We present a unified model for X-ray quasi-periodic oscillations (QPOs) seen in Narrow-line Seyfert 1 (NLSy1) galaxies, γ-ray and optical band QPOs that are seen in Blazars. The origin of these QPOs is attributed to the plasma motion in corona or jets of these AGN. In the case of X-ray QPOs, we applied the general relativistic precession model for the two simultaneous QPOs seen in NLSy1 1H 0707-945 and deduce orbital parameters, such the radius of the emission region, and spin parameter a for a circular orbit; we obtained the Carter’s constant Q, a, and the radius in the case of a spherical orbit solution. In other cases where only one X-ray QPO is seen, we localized the orbital parameters for NLSy1 galaxies REJ 1034+396, 2XMM J123103.2+110648, MS 2254.9-3712, Mrk 766, and MCG-06-30-15. By applying the lighthouse model, we found that a kinematic origin of the jet based γ-ray and optical QPOs, in a relativistic MHD framework, is possible. Based on the inbuilt Hamiltonian formulation with a power-law distribution in the orbital energy of the plasma consisting of only circular or spherical trajectories, we show that the resulting Fourier power spectral density (PSD) has a break corresponding to the energy at ISCO. Further, we derive connection formulae between the slopes in the PSD and that of the energy distribution. Overall, given the preliminary but promising results of these relativistic orbit models to match the observed QPO frequencies and PSD at diverse scales in the inner corona and the jet, it motivates us to build detailed models, including a transfer function for the energy spectrum in the corona and relativistic MHD jet models for plasma flow and its polarization properties.

Orbital mechanics and quasiperiodic oscillation resonances of black holes in Einstein-Æther theory

In this paper, we study the motion of test particles around two exact charged black-hole solutions in Einstein-{\AE}ther theory. Specifically, we first consider the quasi-periodic oscillations (QPOs) and their resonances generated by the particle moving in the Einstein-{\AE}ther black hole and then turn to study the periodic orbits of the massive particles. For QPOs, we drop the usually adopted assumptions $\nu_U=\nu_\theta$, $\nu_L=\nu_r$, and $\nu_U/\nu_L=3/2$ with $\nu_U$ ($\nu_L$) and $\nu_r$ ($\nu_\theta$) being the upper (lower) frequency of QPOs and radial (vertical) epicyclic frequency of the orbiting particles, respectively. Instead, we put-forward a new working ansatz for which the Keplerian radius is much closer to that of the innermost stable circular orbit and explore in detail the effects of the {\ae}ther field on the frequencies of QPOs. We then realize good curves for the frequencies of QPOs, which fit to data of three microquasars very well by ignoring any effects of rotation and magnetic fields. The innermost stable circular orbits (isco) of timelike particles are also analyzed and we find the isco radius increases with increasing $c_{13}$ for the first type black hole while decreases with increasing $c_{14}$ for the second one. We also obtain several periodic orbits and find that they share similar taxonomy schemes as the periodic equatorial orbits in the Schwarzschild/Kerr metrics, in addition to exact solutions for certain choices of the Einstein-\AE ther parameters. The equations for null geodesics are also briefly considered, where we study circular photon orbits and bending angles for gravitational lensing.

The parallel tracks of kHz QPOs in low-mass X-ray binary 4U 1728−34: explorer of the bimodal accretion modes

ABSTRACT Parallel tracks in the relation between the lower kilohertz quasi-periodic oscillation (kHz QPO) frequency ν1 and the X-ray intensity I have been observed in the neutron star low-mass X-ray binary (NS-LMXB) 4U 1728−34, and we try to ascribe these phenomena to the bimodal accretion modes, i.e. the disc accretion and radial accretion. For the source with one constant radial accretion rate $\dot{M}_{\rm r}$, as the increase of the disc accretion rate $\dot{M}_{\rm d}$, the NS magnetosphere-disc radius can shrink from ∼18 to ∼16 km, while ν1 increases from ∼670 to ∼870 Hz. Then, due to the increase of the kHz QPO frequency and total X-ray intensity Itot, the source will trace out an oblique track in ν1–I relation. While, if the source enters another constant radial accretion rate due to the variation of the accretion environment, the increase of the disc accretion rate can arise another parallel track in ν1–I relation. Finally, the reliability of the theoretical assumptions, the variability of the accretion radius and accretion rate, as well as the dependence of the two accretion modes, are also investigated and discussed.

Time-domain variability properties of XTE J1650−500 during its 2001 outburst: evidence of disc–jet connection

ABSTRACT The evolution of variability properties of Galactic transient sources is a diagnostic tool to understand various regimes of the accretion flow and its dynamics close to the central black hole. In this paper, we concentrate on the variability properties of the X-ray transient XTE J1650−500 and investigate the evolution of viscous delay, time lag, quasi-periodic oscillation (QPO) frequency, and their energy dependence throughout the rising phase as observed by Rossi X-ray Timing Explorer(RXTE) during its outburst in 2001. Our analysis reveals (1) a delay of 12 ± 1 d between 1 d-averaged hard (5–12 keV) and soft (1.5–3 keV) photon light curves as observed by RXTE/ASM; (2) QPOs with high rms values are observed in lower energy (4–8 keV) range; (3) the QPO frequencies and associated time lags were anticorrelated during the initial days of the rising phase, and later on, they were found to be correlated; (4) the time lags of Fe-line photons with respect to hard and soft photons remained almost constant during the initial days of hard state and the lag magnitude increased during the state transition. We perform comparative studies with outbursts of GX 339−4 and XTE J1550−564. We find the evolution of time lags associated with the QPO characteristics during the outburst – stronger QPOs at low energy and constant lags of broad Fe-line photons present a unique nature of outburst profile in XTE J1650−500. The possible cause of such variabilities is explained by considering disc–jet geometry closer to the central black hole.

A New Method to Constrain Neutron Star Structure from Quasi-periodic Oscillations

Abstract We develop a new method to measure neutron star (NS) parameters and derive constraints on the equation of state (EoS) of dense matter by fitting the frequencies of simultaneous quasi-periodic oscillation (QPO) modes observed in the X-ray flux of accreting NSs in low-mass X-ray binaries. To this aim, we calculate the fundamental frequencies of geodesic motion around rotating NSs based on an accurate general-relativistic approximation for their external spacetime. Once the fundamental frequencies are related to the observed frequencies through a QPO model, they can be fit to the data to obtain estimates of the three parameters describing the spacetime, namely the NS mass, angular momentum and quadrupole moment. From these parameters we derive information on the NS structure and EoS. We present a proof of principle of our method applied to pairs of kHz QPO frequencies observed from three systems (4U1608-52, 4U0614+09, and 4U1728-34). We identify the kHz QPOs with the azimuthal and the periastron precession frequencies of matter orbiting the NS, and via our Bayesian inference technique we derive constraints on the neutrons stars’ masses and radii. This method is applicable to other geodesic-frequency-based QPO models.

Time lags of the type-B quasi-periodic oscillation in MAXI J1348−630

ABSTRACT The fast variability observed in the X-ray emission from black hole binaries has a very complex phenomenology, but offers the possibility to investigate directly the properties of the inner accretion flow. In particular, type-B oscillations in the 2–8 Hz range, observed in the soft-intermediate state, have been associated with the emission from a relativistic jet. We present the results of the timing and spectral analysis of a set of observations of the bright transient MAXI J1348−630 made with the NICER (Neutron Star Interior Composition Explorer) telescope. The observations are in the brightest part of the outburst and all feature a strong type-B quasi-periodic oscillation (QPO) at ∼4.5 Hz. We compute the energy dependence of the fractional rms and the phase lags at the QPO frequency, obtaining high signal-to-noise data and sampling for the first time at energies below 2 keV. The fractional rms decreases from more than 10 per cent at 9 keV to 0.6 per cent at 1.5 keV, and is constant below that energy. Taking the 2–3 keV band as reference, photons at all energies show a hard lag, increasing with the distance from the reference band. The behaviour below 2 keV has never been observed before, due to the higher energy bandpass of previous timing instruments. The energy spectrum can be fitted with a standard model for this state, consisting of a thin disc component and a harder power law, plus an emission line between 6 and 7 keV. We discuss the results, concentrating on the phase lags, and show that they can be interpreted within a Comptonization model.

Estimating the masses of three neutron stars by twin kilohertz quasi-periodic oscillations and innermost stable circular orbits: constraining equations of state

ABSTRACT We test the magnetohydrodynamics (MHD) model derived by Shi, Zhang and Li by the like-standard deviations of the twin kilohertz (kHz) quasi-periodic oscillation (QPO) frequencies when the modes of the MHD waves in the MHD model are recalculated. A group of approximate equations derived from the MHD equations in the MHD model are proposed. Consequently, the dependence of the twin kHz QPO frequencies on several neutron star (NS) parameters is determined by the approximate equations. Based on the selection criterion that NS parameters corresponding to the minimum like-standard deviation are the most reasonable parameters, the masses of the three NSs in 4U 0614+09, 4U 1636–53 and 4U 1608–52 are estimated as M < 2.60 M⊙, 2.00 M⊙ < M < 2.31 M⊙ and 2.17 M⊙ < M < 2.62 M⊙, respectively. According to these NS masses, some equations of state for the nuclear matter in compact stars can be ruled out.

Evidence for Disk Truncation at Low Accretion States of the Black Hole Binary MAXI J1820+070 Observed by NuSTAR and XMM-Newton

Abstract We present results from NuSTAR and XMM-Newton observations of the new black hole X-ray binary MAXI J1820+070 at low accretion rates (below 1% of the Eddington luminosity). We detect a narrow Fe Kα emission line, in contrast to the broad and asymmetric Fe Kα line profiles commonly present in black hole binaries at high accretion rates. The narrow line, with weak relativistic broadening, indicates that the Fe Kα line is produced at a large disk radius. Fitting with disk reflection models assuming standard disk emissivity finds a large disk truncation radius (a few tens to a few hundreds of gravitational radii, depending on the disk inclination). In addition, we detect a quasi-periodic oscillation (QPO) varying in frequency between 11.6 ± 0.2 mHz and 2.8 ± 0.1 mHz. The very low QPO frequencies suggest a large size for the optically thin Comptonization region according to the Lense–Thirring precession model, supporting that the accretion disk recedes from the innermost stable circular orbit and is replaced by advection-dominated accretion flow at low accretion rates. We also discuss the possibility of an alternative accretion geometry that the narrow Fe Kα line is produced by a lamppost corona with a large height illuminating the disk.

A systematic analysis of the phase lags associated with the type-C quasi-periodic oscillation in GRS 1915+105

ABSTRACT We present a systematic analysis of the phase lags associated with the type-C quasi-periodic oscillations (QPOs) in GRS 1915+105 using RXTE data. Our sample comprises 620 RXTE observations with type-C QPOs ranging from ∼0.4 to ∼6.3 Hz. Based on our analysis, we confirm that the QPO phase lags decrease with QPO frequency, and change sign from positive to negative at a QPO frequency of ∼2 Hz. In addition, we find that the slope of this relation is significantly different between QPOs below and above 2 Hz. The relation between the QPO lags and QPO rms can be well fitted with a broken line: as the QPO lags go from negative to positive, the QPO rms first increases, reaching its maximum at around zero lag, and then decreases. The phase-lag behaviour of the subharmonic of the QPO is similar to that of the QPO fundamental, where the subharmonic lags decrease with subharmonic frequency and change sign from positive to negative at a subharmonic frequency of ∼1 Hz; on the contrary, the second harmonic of the QPO shows a quite different phase-lag behaviour, where all the second harmonics show hard lags that remain more or less constant. For both the QPO and its (sub)harmonics, the slope of the lag–energy spectra shows a similar evolution with frequency as the average phase lags. This suggests that the lag–energy spectra drive the average phase lags. We discuss the possibility for the change in lag sign, and the physical origin of the QPO lags.

Identification of QPO Frequency of GRS 1915+105 as the Relativistic Dynamic Frequency of a Truncated Accretion Disk

Abstract We have analyzed AstroSat observations of the galactic microquasar system GRS 1915+105, when the system exhibited C-type quasi-periodic oscillations (QPOs) in the frequency range of 3.4–5.4 Hz. The broadband spectra (1–50 keV) obtained simultaneously from the Large Area X-ray Proportional Counter and Soft X-ray Telescope can be well described by a dominant relativistic truncated accretion disk along with thermal Comptonization and reflection. We find that while the QPO frequency depends on the inner radii with a large scatter, a much tighter correlation is obtained when both the inner radii and accretion rate of the disk are taken into account. In fact, the frequency varies just as the dynamic frequency (i.e., the inverse of the sound crossing time) does as predicted decades ago by the relativistic standard accretion disk theory for a black hole with a spin parameter of ∼0.9. We show that this identification has been possible due to the simultaneous broadband spectral coverage with temporal information as obtained from AstroSat.

Quasi-periodic oscillations around Kerr-MOG black holes

The study of the quasi-periodic oscillations (QPOs) of X-ray flux observed in the stellar-mass black hole (BH) binaries can provide a powerful tool for testing the phenomena occurring in strong gravity regime. We thus present and apply to three known microquasars the model of epicyclic oscillations of Keplerian discs orbiting rotating BHs governed by the modified theory of gravity (MOG). We show that the standard geodesic models of QPOs can explain the observationally fixed data from the three microquasars, GRO 1655-40, XTE 1550-564, and GRS 1915+105. We perform a successful fitting of the high frequency (HF) QPOs observed in these microquasars, under assumption of MOG BHs, for epicyclic resonance and its variants, relativistic precession and its variants, tidal disruption, as well as warped disc models and discuss the corresponding constraints of parameters of the model, which are the mass and spin and parameter alpha of the BH.

Spectral and Timing Properties of the Galactic X-Ray Transient Swift J1658.2–4242 Using Astrosat Observations

Abstract We present the X-ray timing and spectral analysis of the new Galactic X-ray transient Swift J1658.2–4242 observed with the Large Area X-ray Proportional Counter and Soft X-ray Telescope instruments on board Astrosat. We detect prominent C-type quasi-periodic oscillations (QPOs) of frequencies varying from ∼1.5 to ∼6.6 Hz along with distinct second harmonics and subharmonics. The QPO detected at ∼1.56 Hz drifts to a higher centroid frequency of ∼1.74 in the course of the observation, while the QPO detected at ∼6.6 Hz disappeared during hard flarings. The fractional rms at the QPO and the subharmonic frequencies increases with photon energy, while at the second harmonic frequencies the rms seems to be constant. In addition, we have observed soft time lag at QPO and subharmonic frequencies up to a timescale of ∼35 ms; however, at the second harmonic frequencies there is weak/zero time lag. We attempt spectral modeling of the broadband data in the 0.7–25 keV band using the doubly absorbed disk plus thermal Comptonization model. Based on the spectral and timing properties, we identified the source to be in the hard-intermediate state of black hole X-ray binaries. To quantitatively fit the energy- and frequency-dependent fractional rms and time lag, we use a single-zone fluctuation propagation model and discuss our results in the context of that model.

Discovery of an Accretion-rate Independent Absolute RMS Amplitude of Millihertz Quasi-periodic Oscillations in 4U 1636-53

Abstract We investigate the frequency and amplitude of the millihertz quasi-periodic oscillations (mHz QPOs) in the neutron-star low-mass X-ray binary 4U 1636–53 using Rossi X-ray Timing Explorer observations. We find that no mHz QPOs appear when the source is in the hard spectral state. We also find that there is no significant correlation between the frequency and the fractional RMS amplitude of the mHz QPOs. Notwithstanding, for the first time, we find that the absolute rms amplitude of the mHz QPOs is insensitive to the parameter S a , which measures the position of the source in the color–color diagram and is usually assumed to be an increasing function of mass accretion rate. This finding indicates that the transition from marginally stable burning to stable burning or unstable burning could happen very rapidly since, before the transition, the mHz QPOs do not gradually decay as the rate further changes.

Timing analysis of Swift J1658.2–4242's outburst in 2018 with Insight-HXMT, NICER and AstroSat

We present the observational results from a detailed timing analysis of the black hole candidate Swift J1658.2–4242 during its 2018 outburst with the observations of Hard X-ray Modulation Telescope (Insight-HXMT), Neutron Star Interior Composition Explorer (NICER) and AstroSat in 0.1–250keV. The evolution of intensity, hardness and integrated fractional root mean square (rms) observed by Insight-HXMT and NICER are presented in this paper. Type-C quasi-periodic oscillations (QPOs) observed by NICER (0.8–3.5Hz) and Insight-HXMT (1–1.6Hz) are also reported in this work. The features of the QPOs are analyzed with an energy range of 0.5–50keV. The relations between QPO frequency and other characteristics such as intensity, hardness and QPO rms are carefully studied. The timing and spectral properties indicate that Swift J1658.2–4242 is a black hole binary system. Besides, the rms spectra of the source calculated from the simultaneous observation of Insight-HXMT, NICER and AstroSat support the Lense-Thirring origin of the QPOs. The relation between QPO phase lag and the centroid frequency of Swift J1658.2–4242 reveals a near zero constant when <4Hz and a soft phase lag at 6.68Hz. This independence follows the same trend as the high inclination galactic black hole binaries such as MAXI J1659–152.

Disk–Jet Coupling in the 2017/2018 Outburst of the Galactic Black Hole Candidate X-Ray Binary MAXI J1535–571

Abstract MAXI J1535−571 is a Galactic black hole candidate X-ray binary that was discovered going into outburst in 2017 September. In this paper, we present comprehensive radio monitoring of this system using the Australia Telescope Compact Array, as well as the MeerKAT radio observatory, showing the evolution of the radio jet during its outburst. Our radio observations show the early rise and subsequent quenching of the compact jet as the outburst brightened and then evolved toward the soft state. We constrain the compact jet quenching factor to be more than 3.5 orders of magnitude. We also detected and tracked (for 303 days) a discrete, relativistically moving jet knot that was launched from the system. From the motion of the apparently superluminal knot, we constrain the jet inclination (at the time of ejection) and speed to ≤45° and ≥0.69 c, respectively. Extrapolating its motion back in time, our results suggest that the jet knot was ejected close in time to the transition from the hard intermediate state to soft intermediate state. The launching event also occurred contemporaneously with a short increase in X-ray count rate, a rapid drop in the strength of the X-ray variability, and a change in the type-C quasi-periodic oscillation (QPO) frequency that occurs &gt;2.5 days before the first appearance of a possible type-B QPO.

Exploring the X-ray universe via timing: mass of the active galactic nucleus black hole XMMUJ134736.6+173403

AbstractA strong quasi-periodic modulation has recently been revealed in the X-ray flux of the X-ray source XMMUJ134736.6+173403. The two observed twin-peak quasiperiodic oscillations (QPOs) exhibit a 3:1 frequency ratio and strongly support the evidence for the presence of an active galactic nucleus black hole (AGN BH). It has been suggested that detections of twin-peak QPOs with commensurable frequency ratios and scaling of their periods with BH mass could provide the basis for a method intended to determine the mass of BH sources, such as AGNs. Assuming the orbital origin of QPOs, we calculate the upper and lower limit on the AGN BH mass M, reaching M ≍ 107–109M⊙. Compared to mass estimates of other sources, XMMUJ134736.6+173403 appears to be the most massive source with commensurable QPO frequencies, and its mass represents the current observational upper limit on the AGN BH mass obtained from the QPO observations.

MAXI J1820+070 with NuSTAR I. An increase in variability frequency but a stable reflection spectrum: coronal properties and implications for the inner disc in black hole binaries

ABSTRACT MAXI J1820+070 (optical counterpart ASASSN-18ey) is a black hole candidate discovered through its recent very bright outburst. The low extinction column and long duration at high flux allow detailed measurements of the accretion process to be made. In this work, we compare the evolution of X-ray spectral and timing properties through the initial hard state of the outburst. We show that the inner accretion disc, as measured by relativistic reflection, remains steady throughout this period of the outburst. Nevertheless, subtle spectral variability is observed, which is well explained by a change in coronal geometry. However, characteristic features of the temporal variability – low-frequency roll-over and quasi-periodic oscillation frequency – increase drastically in frequency, as the outburst proceeds. This suggests that the variability time-scales are governed by coronal conditions rather than solely by the inner disc radius. We also find a strong correlation between X-ray luminosity and coronal temperature. This can be explained by electron pair production with a changing effective radius and a non-thermal electron fraction of $\sim 20$ per cent.

The Lense–Thirring timing-accretion plane for ULXs

ABSTRACT Identifying the compact object in ultraluminous X-ray sources (ULXs) has to date required detection of pulsations or a cyclotron resonance scattering feature (CRSF), indicating a magnetized neutron star. However, pulsations are observed to be transient and it is plausible that accretion on to the neutron star may have suppressed the surface magnetic field such that pulsations and CRSFs will be entirely absent. We may therefore lack direct means to identify neutron star systems whilst we presently lack an effective means by which to identify black hole ULXs. Here we present a possible method for separating the ULX population by assuming the X-ray, mHz quasi-periodic oscillations (QPOs), and day time-scale periods/QPOs are associated with Lense–Thirring precession of the inflow and outflowing wind, respectively. The precession time-scales combined with the temperature of the soft X-ray component produce planes where the accretor mass enters as a free parameter. Depending on the properties of the wind, use of these planes may be robust to a range in the angular momentum (spin) and, for high accretion rates, essentially independent of the neutron star’s surface dipole field strength. Our model also predicts the mHz QPO frequency and magnitude of the phase lag imprinted due to propagation through the optically thick wind; in the case of NGC 5408 X-1 we subsequently infer a black hole mass and moderate-to-high spin. Finally, we note that observing secular QPO evolution over sufficient baselines may indicate a neutron star, as the precession responds to spin-up which is not readily observable for black hole primaries.

Re-awakening of GRS 1716–249 after 23 yr, observed by Swift/XRT and NuSTAR

In this work, we present a spectral and temporal analysis of {\it Swift}/XRT and {\it NuSTAR} observations of GRS 1716--249 during its recent 2016--2017 outburst. This low mass X-ray binary underwent an extraordinary outburst after a long quiescence of 23 years, since its last major outburst in 1993. The source was observed over two different epochs during 2017 April, 07 and 10. The best fit joint spectral fitting in the energy range 0.5 $-$ 79.0 keV indicates that the spectrum is best described by relatively cold, weak disk blackbody emission, dominant thermal Comptonization emission, and a relativistically broadened fluorescent iron K$\alpha$ emission line. We observed a clear indication of a Compton hump around 30 keV. We also detected an excess feature of $\sim1.3$ keV. Assuming a lamp-post geometry of the corona, we constrained the inner disk radius for both observations to 11.92$^{+8.62}_{-11.92}$ R$_{ISCO}$ (i.e., an upper limit) and 10.39$^{+9.51}_{-3.02}$ R$_{ISCO}$ (where R$_{ISCO}\equiv$ radius of the innermost stable circular orbit) for the first epoch (E1) and second epoch (E2), respectively. A significant ($\sim5\sigma$) type$-$C quasi-periodic oscillation (QPO) at $1.20\pm0.04$ Hz is detected for the first time for GRS 1716--249, which drifts to $1.55\pm0.04$ Hz ($\sim6\sigma$) at the end of the second observation. The derived spectral and temporal properties show a positive correlation between the QPO frequency and the photon index.