Oscillations In X-ray Binaries Research Articles

Modelling stochastic and quasi-periodic behaviour in stellar time-series: Gaussian process regression versus power-spectrum fitting

ABSTRACT As the hunt for an Earth-like exoplanets has intensified in recent years, so has the effort to characterize and model the stellar signals that can hide or mimic small planetary signals. Stellar variability arises from a number of sources, including granulation, supergranulation, oscillations, and activity, all of which result in quasi-periodic or stochastic behaviour in photometric and/or radial velocity observations. Traditionally, the characterization of these signals has mostly been done in the frequency domain. However, the recent development of scalable Gaussian process regression methods makes direct time-domain modelling of stochastic processes a feasible and arguably preferable alternative, obviating the need to estimate the power spectral density of the data before modelling it. In this paper, we compare the two approaches using a series of experiments on simulated data. We show that frequency-domain modelling can lead to inaccurate results, especially when the time-sampling is irregular. By contrast, Gaussian process regression results are often more precise, and systematically more accurate, in both the regular and irregular time-sampling regimes. While this work was motivated by the analysis of radial velocity and photometry observations of main-sequence stars in the context of planet searches, we note that our results may also have applications for the study of other types of astrophysical variability such as quasi-periodic oscillations in X-ray binaries and active galactic nuclei variability.

QPOML: a machine learning approach to detect and characterize quasi-periodic oscillations in X-ray binaries

ABSTRACT Astronomy is presently experiencing profound growth in the deployment of machine learning to explore large data sets. However, transient quasi-periodic oscillations (QPOs) that appear in power density spectra of many X-ray binary (XRB) system observations are an intriguing phenomena heretofore not explored with machine learning. In light of this, we propose and experiment with novel methodologies for predicting the presence and properties of QPOs to make the first ever detections and characterizations of QPOs with machine learning models. We base our findings on raw energy spectra and processed features derived from energy spectra using an abundance of data from the NICER and Rossi X-ray Timing Explorer space telescope archives for two black hole low-mass XRB sources, GRS 1915+105 and MAXI J1535−571. We advance these non-traditional methods as a foundation for using machine learning to discover global inter-object generalizations between – and provide unique insights about – energy and timing phenomena to assist with the ongoing challenge of unambiguously understanding the nature and origin of QPOs. Additionally, we have developed a publicly available python machine learning library, QPOML, to enable further machine learning aided investigations into QPOs.

A phase lag between disc and corona in GRMHD simulations of precessing tilted accretion discs

In the course of its evolution, a black hole (BH) accretes gas from a wide range of directions. Given a random accretion event, the typical angular momentum of an accretion disc would be tilted by ∼60∘ relative to the BH spin. Misalignment causes the disc to precess at a rate that increases with BH spin and depends on disc morphology. We present general-relativistic magnetohydrodynamic (GRMHD) simulations spanning a full precession period of highly tilted (60∘), moderately thin (h/r=0.1) accretion discs around a rapidly spinning (a≃0.9) BH. While the disc and jets precess in phase, we find that the disc wind/corona, sandwiched between the two, lags behind by ≳10°. For spectral models of BH accretion, the implication is that hard non-thermal (corona) emission lags behind the softer (disc) emission, thus potentially explaining some properties of the hard energy lags seen in Type-C low frequency quasi-periodic oscillations in X-ray binaries. While strong jets are unaffected by this disc-corona lag, weak jets can stall when encountering the lagging corona at distances r∼100 BH radii. This interaction may quench large-scale jet formation.

SOFT TIME LAGS IN THE X-RAY EMISSION OF Mrk 1040

Temporal analysis of X-ray binaries and Active Galactic Nuclei have shown that hard X-rays react to variation of soft ones after a time delay. The opposite trend, or soft lag, has only been seen in a few rare Quasi-periodic Oscillations in X-ray binaries and recently for the AGN, 1H 0707-495, on short timescales of ~ 10^3 secs. Here, we report analysis of a XMM-Newton observation of Mrk~1040, which reveals that on the dominant variability timescale of ~ 10^4 secs, the source seems to exhibit soft lags. If the lags are frequency independent, they could be due to reverberation effects of a relativistically blurred reflection component responding to a varying continuum. Alternatively, they could be due to Comptonization delays in the case when high energy photons impinge back on the soft photon source. Both models can be verified and their parameters tightly constrained, because they will need to predict the photon spectrum, the r.m.s variability and time lag as a function of energy. A successful application of either model will provide unprecedented information on the radiative process, geometry and more importantly the size of the system, which in turn may provide stringent test of strong general relativistic effects.

Constraining the mass and moment of inertia of neutron stars from quasi-periodic oscillations in X-ray binaries

Neutron stars are the densest objects known in the Universe. Being the final product of stellar evolution, their internal composition and structure is rather poorly constrained by measurements. It is the purpose of this paper to put some constrains on the mass and moment of inertia of neutron stars based on the interpretation of kHz quasi-periodic oscillations observed in low mass X-ray binaries. We use observations of high-frequency quasi-periodic observations (HF-QPOs) in low mass X-ray binaries (LMXBs) to look for the average mass and moment of inertia of neutron stars. This is done by applying our parametric resonance model to discriminate between slow and fast rotators. We fit our model to data from ten LMXBs for which HF-QPOs have been seen and the spin of the enclosed accreting neutron star is known. For a simplified analysis we assume that all neutron stars possess the same properties (same mass $M_*$ and same moment of inertia $I_*$). We find an average mass $M_* \approx 2.0-2.2\, M_{\odot}$. The corresponding average moment of inertia is then $I_* \approx 1-3 \times 10^{38}\;{\rm kg\,m^2} \approx 0.5-1.5 \, (10\;\textrm{ km})^2 \, M_\odot$ which equals to dimensionless spin parameter $\tilde{a} \approx 0.05-0.15$ for slow rotators (neutron stars with a spin frequency roughly about 300~Hz) respectively $\tilde{a} \approx 0.1-0.3$ for fast rotators (neutron stars with the spin frequency roughly about 600~Hz).

An analytic model of a rotating hotspot and kilohertz quasi-periodic oscillations in X-ray binaries

To explain kilohertz quasi-periodic oscillations (QPOs) in X-ray binaries, an analytic model of a rotating hotspot is proposed, which is based on the magnetic coupling of a rotating black hole (BH) with its surrounding accretion disc. The hotspot in the inner region of the disc is produced by energy transferred from a spinning BH with non-axisymmetric magnetic field. The frequency and energy band of the hotspot turn out to be related to six parameters, in terms of which the strength and the azimuthal angular region of the bulging magnetic field on the BH horizon, the mass and spin of the BH, and the power-law index of the magnetic field varying with the radial coordinate on the disc are described. In addition, the correlation of the fluctuation of the bulging magnetic field with the widths of QPO frequency is discussed.

Relativistic Hydrodynamics and Quasiperiodic Oscillations

We present preliminary numerical simulations of tilted-disk accretion around a rotating black hole. Our goal is to explore whether hydrodynamic instabilities near the Bardeen-Petterson radius could be responsible for generating moderate-frequency quasi-periodic oscillations in X-ray binaries. We review the relevant general relativistic hydrodynamic equations, and discuss preliminary results on the structure and dynamics of a thin, Keplerian disk.

Non-linear fluid dynamics of eccentric discs

A new theory of eccentric accretion discs is presented. Starting from the basic fluid-dynamical equations in three dimensions, I derive the fundamental set of one-dimensional equations that describe how the mass, angular momentum and eccentricity vector of a thin disc evolve as a result of internal stresses and external forcing. The analysis is asymptotically exact in the limit of a thin disc, and allows for slowly varying eccentricities of arbitrary magnitude. The theory is worked out in detail for a Maxwellian viscoelastic model of the turbulent stress in an accretion disc. This generalizes the conventional alpha viscosity model to account for the non-zero relaxation time of the turbulence, and is physically motivated by a consideration of the nature of magnetohydrodynamic turbulence. It is confirmed that circular discs are typically viscously unstable to eccentric perturbations, as found by Lyubarskij, Postnov & Prokhorov, if the conventional alpha viscosity model is adopted. However, the instability can usually be suppressed by introducing a sufficient relaxation time and/or bulk viscosity. It is then shown that an initially uniformly eccentric disc does not retain its eccentricity as had been suggested by previous analyses. The evolutionary equations should be useful in many applications, including understanding the origin of planetary eccentricities and testing theories of quasi-periodic oscillations in X-ray binaries.

The Global Normal Disk Oscillations and the Persistent Low-Frequency Quasi-periodic Oscillations in X-Ray Binaries

We suggest that persistent low-frequency quasi-periodic oscillations (QPOs) detected in the black hole (BH) sources XTE J1118+480, GRO J1655-40, and LMC X-1 at ~0.1 Hz, in HZ Her/Her X-1 at ~0.05 Hz, and in neutron star (NS) binaries 4U 1323-62, 4U 1746-31, and EXO 0748-76 at ~1 Hz are caused by the global disk oscillations in the direction normal to the disk (normal mode). We argue that these disk oscillations are a result of the gravitational interaction between the central compact object and the disk. A small displacement of the disk from the equatorial plane results in a linear gravitational restoring force opposite to this displacement. Our analysis shows that the frequency of this mode is a function of the mass of the central object and that it also depends on the inner and outer radii of the disk, which in turn are related to the orbital period of the binary system. We derive an analytical formula for the frequency of the normal disk mode and show that these frequencies can be related to the persistent lower QPO frequencies observed in the NS and BH sources. We offer a new independent approach to the BH mass determination by interpreting this low QPO frequency as the global disk oscillation frequency. The implementation of this method combined with the independent method recently developed by Shrader & Titarchuk that uses the X-ray energy spectra results in stringent constraints for the BH masses.

Rapidly Rotating Strange Stars for a New Equation of State of Strange Quark Matter

For a new equation of state of strange quark matter, we construct equilibrium sequences of rapidly rotating strange stars in general relativity. The sequences are the normal and supramassive evolutionary sequences of constant rest mass. We also calculate equilibrium sequences for a constant value of Ω corresponding to the most rapidly rotating pulsar PSR 1937+21. In addition, we calculate the radius of the marginally stable orbit and its dependence on Ω, relevant for modeling of kilohertz quasi-periodic oscillations in X-ray binaries.

δ-Invariant for Quasi-periodic Oscillations and Physical Parameters of the 4U 0614+09 Binary

The recently formulated two-oscillator (TO) model interprets the lowest of the kilohertz frequencies of the twin-peak quasi-periodic oscillations in X-ray binaries as the Keplerian frequency νK. The high twin frequency νh in this model holds the upper hybrid frequency relation to the rotational frequency of the neutron star's magnetosphere Ω: ν = ν + 4(Ω/2π)2. The vector Ω is assumed to have an angle δ with the normal to the disk. The first oscillator in the TO model allows one to interpret the horizontal branch observed below 100 Hz as the lower mode of the Keplerian oscillator under the influence of the Coriolis force, with frequency νL being dependent on νh, νK, and δ. For some stars such as 4U 0614+09, Scorpius X-1, and 4U 1702-42, νh, νK, and νL have been observed simultaneously, thus providing the opportunity to check the central prediction of the TO model, i.e., the constancy of δ for a particular source. Given the considerable variation of each of these three frequencies, the existence of an observational invariant with a clear physical interpretation as a global parameter of the neutron star magnetosphere is an important test of the TO model. Using the results of recent observations of 4U 0614+09, we verify the existence of this invariant and determine the angle δ = 156 ± 05 for this star. The second oscillator in the model deals with both a radial (presumably sound) oscillation and a diffuse process in the viscous layer surrounding the neutron star. Our analysis of the viscous oscillation frequency νV and the break frequency νb of the diffusion shows that the spin value of the inner boundary of the transition layer for 4U 0614+09 is at least 2 times more than the values for 4U 1728-34 and Sco X-1.

Implications of kHz quasi-periodic brightness oscillations in X-ray binaries for neutron star structure

Kilohertz quasi-periodic oscillations (QPOs) in low-mass X-ray binaries (LMXBs) may represent the orbital frequencies of the innermost Keplerian orbits around accreting neutron stars. Attempts have recently been made to derive constraints on the mass and the equation of state of the neutron star, by identifying the highest observed QPO frequency with the Keplerian frequency at the marginally stable orbit given by the general theory of relativity. These estimates have either neglected the effect of neutron star rotation or used an approximate treatment of rotation in general relativity. We rederive these constraints using a fully general relativistic formalism including the effect of rapid rotation. We also present constraints corresponding to the case where the innermost stable orbit touches the stellar surface.

The Evolution of Accretion Disks with Coronae: A Model for the Low-Frequency Quasi-periodic Oscillations in X-Ray Binaries

The global nonlinear time dependent evolution of accretion disk-corona systems in X-ray binary sources has been investigated to provide an understanding of the low frequency ($\sim 0.04$~Hz) quasi-periodic oscillations (QPOs) observed recently in the Rapid Burster MXB 1730-335 and in some black hole candidates sources (Cyg X--1 and GRO~J0422+32). We consider $\alpha$-viscosity models in which the viscous stress is proportional to the total pressure. In contrast to previous time dependent studies it is assumed that all mass accretion and angular momentum transport take place in an optically thick disk, but that a fraction of the gravitational energy that is released is dissipated in a corona. It is found that the coronal energy dissipation can effectively reduce the amplitudes of the mass flow variations generated from the thermal and viscous instabilities (in comparison to models without a corona) to a state in which the disk exhibits mild oscillatory nonsteady behavior. These oscillations are globally coherent in the unstable regions of the disk. A model for the high and low states of black hole candidate systems is also proposed. It is suggested that the low state, which is characterized by a hard X-ray spectrum, corresponds to a disk configuration in which the inner disk is in an advection dominated hot optically thin state whereas the high state corresponds to a configuration in which the inner disk is in an optically thick state surrounded by a corona. In this model, the mass accretion rate in the system is higher in the low state than in the high state. The hard X-ray spectrum of QPOs observed in the low state can be naturally explained by such a model.