Adam Ingram

Low-frequency quasi-periodic oscillations spectra and Lense–Thirring precession

We show that the low frequency QPO seen in the power density sp ectra of black hole binaries (and neutron stars) can be explained by Lense-Thirring prec ession. This has been proposed many times in the past, and simple, single radius models can q u litatively match the observed increase in QPO frequency by decreasing a characteristic ra dius, as predicted by the truncated disc models. However, this also predicts that the frequency is strongly dependent on spin, and gives a maximum frequency at the last stable orbit which is ge nerally much higher than the remarkably constant maximum frequency at ∼ 10 Hz observed in all black hole binaries. The key aspect of our model which makes it match these observatio ns is that the precession is of a radially extended region of the hot inner flow. The outer r adius is set by the truncation radius of the disc as above, but the inner radius lies well out side of the last stable orbit at the point where numerical simulations show that the density dro ps ff sharply for a misaligned flow. Physically motivated analytic estimates for this inne r radius show that it increases with a∗, decreasing the expected frequency in a way which almost com pletely cancels the expected increase with spin, and ties the maximum predicted frequenc y to around 10 Hz for all a∗. This is the first QPO model which explains both frequencies and spe ctrum in the context of a well established geometry for the accretion flow.

A physical model for the continuum variability and QPO in accreting black holes

The power spectra of black hole binaries have been well studied for decades, giving a detailed phenomenological picture of the variability properties and their correlation with the energy spectrum (spectral state) of the source. Here we take the truncated disc/hot inner flow picture which can describe the spectral changes, and show that propagating mass accretion rate fluctuations in the hot flow can match the broad band power spectral properties seen in black hole binaries, i.e. give approximately band limited noise between a low and high frequency break. The low frequency break marks the viscous timescale at the outer edge of the hot inner flow, which is the inner edge of the truncated disc. The model also predicts the Lense-Thirring precession timescale of the hot flow, as this is set by the surface density of the flow which is self consistently calculated from the propagating fluctuations. We show that this naturally gives the observed relation between the low frequency break and QPO frequency as the outer radius of the flow moves inwards, and that this model predicts many of the observed QPO properties such as correlation of coherence with frequency, and of the recently discovered correlation of frequency with flux on short timescales. We fit this total model of the variability to a sequence of 5 observed power spectra from the bright black hole binary XTE J1550-564 as the source transitioned from a low/hard to very high state. This is the first time that a power spectrum from a black hole binary has been fit with a physical model for the variability. The data are well fit if the inner radius of the flow remains constant, while the outer radius sweeps inwards from ~60-12 Rg. This range of radii agrees with models of the energy spectral evolution, giving the first self consistent description of the evolution of both the spectrum and variability of BHB.

An exact analytic treatment of propagating mass accretion rate fluctuations in X-ray binaries

Many statistical properties of the aperiodic variability observed in X-ray radiation from accreting compact objects can be naturally explained by the propagating fluctuations model. This considers variations in mass accretion rate to be stirred up throughout the accretion flow. Variations from the outer regions of the accretion flow will propagate towards the central object, modulating the variations from the inner regions and eventually modulating the radiation, giving rise to the observed linear rms-flux relation and also Fourier frequency-dependent time lags. Previous treatments of this model have relied on computationally intensive Monte Carlo simulations which can only yield an estimate of statistical properties such as the power spectrum. Here, we find exact and analytic expressions for the power spectrum and lag spectrum predicted by the same model. We use our calculation to fit the model of Ingram & Done to a power spectrum of XTE J1550−564. The result we present here will apply to any treatment of the propagating fluctuations model and thus provides a very powerful tool for future theoretical modelling.

Modelling variability in black hole binaries: linking simulations to observations

Black hole accretion flows show rapid X-ray variability. The power spectral density (PSD) of this is typically fit by a phenomenological model of multiple Lorentzians for both the broad-band noise and quasi-periodic oscillations (QPOs). Our previous paper developed the first physical model for the PSD and fit this to observational data. This was based on the same truncated disc/hot inner flow geometry which can explain the correlated properties of the energy spectra. This assumes that the broad-band noise is from propagating fluctuations in mass accretion rate within the hot flow, while the QPO is produced by global Lense–Thirring precession of the same hot flow. Here we develop this model, making some significant improvements. First, we specify that the viscous frequency (equivalently, surface density) in the hot flow has the same form as that measured from numerical simulations of precessing, tilted accretion flows. Secondly, we refine the statistical techniques which we use to fit the model to the data. We re-analyse the PSD from the 1998 rise to outburst of XTE J1550−564 with our new model in order to assess the impact of these changes. We find that the derived outer radii of the hot flow (set by the inner radius of the truncated disc) are rather similar, changing from ∼68 to 13Rg throughout the outburst rise. However, the more physical assumptions of our new model also allow us to constrain the scaleheight of the flow. This decreases as the outer radius of the flow decreases, as expected from the spectral evolution. The spectrum steepens in response to the increased cooling as the truncation radius sweeps in, so gas pressure support for the flow decreases. The new model, propfluc, is publicly available within the xspec spectral fitting package.

A quasi-periodic modulation of the iron line centroid energy in the black hole binary H1743−322

Accreting stellar-mass black holes often show a ‘Type-C’ quasi-periodic oscillation (QPO) in their X-ray flux and an iron emission line in their X-ray spectrum. The iron line is generated through continuum photons reflecting off the accretion disc, and its shape is distorted by relativistic motion of the orbiting plasma and the gravitational pull of the black hole. The physical origin of the QPO has long been debated, but is often attributed to Lense–Thirring precession, a General Relativistic effect causing the inner flow to precess as the spinning black hole twists up the surrounding space–time. This predicts a characteristic rocking of the iron line between red- and blueshift as the receding and approaching sides of the disc are respectively illuminated. Here we report on XMM–Newton and NuSTAR observations of the black hole binary H1743−322 in which the line energy varies systematically over the ∼4 s QPO cycle (3.70σ significance), as predicted. This provides strong evidence that the QPO is produced by Lense–Thirring precession, constituting the first detection of this effect in the strong gravitation regime. There are however elements of our results harder to explain, with one section of data behaving differently than all the others. Our result enables the future application of tomographic techniques to map the inner regions of black hole accretion discs.

A Unified Lense-Thirring Precession Model for Optical and X-Ray Quasi-periodic Oscillations in Black Hole Binaries

Recent observations of accreting black holes reveal the presence of quasi-periodic oscillations (QPO) in the optical power density spectra. The corresponding oscillation periods match those found in X-rays, implying a common origin. Among the numerous suggested X-ray QPO mechanisms, some may also work in the optical. However, their relevance to the broadband—optical through X-ray—spectral properties have not been investigated. For the first time, we discuss the QPO mechanism in the context of the self-consistent spectral model. We propose that the QPOs are produced by Lense-Thirring precession of the hot accretion flow, whose outer parts radiate in optical wavelengths. At the same time, its innermost parts are emitting X-rays, which explains the observed connection of QPO periods. We predict that the X-ray and optical QPOs should be either in phase or shifted by half a period, depending on the observer position. We investigate the QPO harmonic content and find that the variability amplitudes at the fundamental frequency are larger in the optical, while the X-rays are expected to have strong harmonics. We then discuss the QPO spectral dependence and compare the expectations to the existing data.

Phase-resolved spectroscopy of low-frequency quasi-periodic oscillations in GRS 1915+105

X-ray radiation from black hole binary (BHB) systems regularly displays quasi-periodic oscillations (QPOs). In principle, a number of suggested physical mechanisms can reproduce their power spectral properties, thus more powerful diagnostics which preserve phase are required to discern between different models. In this paper, we first find for two Rossi X-ray Timing Explorer observations of the BHB GRS 1915+105 that the QPO has a well-defined average waveform. That is, the phase difference and amplitude ratios between the first two harmonics vary tightly around a well-defined mean. This enables us to reconstruct QPO waveforms in each energy channel, in order to constrain QPO phase-resolved spectra. We fit these phase-resolved spectra across 16 phases with a model including Comptonization and reflection (Gaussian and smeared edge components) to find strong spectral pivoting and a modulation in the iron line equivalent width. The latter indicates the observed reflection fraction is changing throughout the QPO cycle. This points to a geometric QPO origin, although we note that the data presented here do not entirely rule out an alternative interpretation of variable disc ionization state. We also see tentative hints of modulations in the iron line centroid and width which, although not statistically significant, could result from a non-azimuthally symmetric QPO mechanism.

The effect of frame dragging on the iron Kα line in X‐ray binaries

The clear characteristic time-scale picked out by the low-frequency quasi-periodic oscillations (QPOs) seen in many black hole and neutron star binaries has the potential to provide a very powerful diagnostic of the inner regions of the accretion flow. However, this potential cannot be realized without a quantitative model for the QPO. We have recently shown that the same truncated disc/hot inner flow geometry which is used to interpret the spectral transitions can also directly produce the QPO from Lense–Thirring (vertical) precession of the hot inner flow. This correctly predicts both the frequency and spectrum of the QPO, and the tight correlation of these properties with the total spectrum of the source via a changing truncation radius between the disc and hot flow. This model predicts a unique iron line signature as a vertically tilted flow illuminates different azimuths of the disc as it precesses. The iron line arising from this rotating illumination is blueshifted when the flow irradiates the approaching region of the spinning disc and redshifted when the flow irradiates the receding region of the disc. This gives rise to a characteristic rocking of the iron line on the QPO frequency which is a necessary (and probably sufficient) test of a Lense–Thirring origin. This is also an independent test of disc truncation models for the low/hard state, as vertical precession cannot occur if there is a disc in the midplane. We show that it may be possible to observe this effect using archival data from the Rossi X-ray Timing Explorer or XMM–Newton. However, a clean test requires a combination of moderate resolution and good statistics, such as would be available from a long XMM–Newton observation or with data from the proposed European Space Agency mission Large Observatory for X-ray Timing.

Low-frequency quasi-periodic oscillation from the 11 Hz accreting pulsar in Terzan 5: not frame dragging

We report on six RXTE observations taken during the 2010 outburst of the 11 Hz accreting pulsar IGR J17480-2446 located in the globular cluster Terzan 5. During these observations we find power spectra which resemble those seen in Z-type high-luminosity neutron star low-mass X-ray binaries, with a quasi-periodic oscillation (QPO) in the 35-50 Hz range simultaneous with a kHz QPO and broadband noise. Using well-known frequency-frequency correlations, we identify the 35-50 Hz QPOs as the horizontal branch oscillations, which were previously suggested to be due to Lense-Thirring (LT) precession. As IGR J17480-2446 spins more than an order of magnitude more slowly than any of the other neutron stars where these QPOs were found, this QPO cannot be explained by frame dragging. By extension, this casts doubt on the LT precession model for other low-frequency QPOs in neutron stars and perhaps even black hole systems.

POLARIZATION MODULATION FROM LENSE–THIRRING PRECESSION IN X-RAY BINARIES

It has long been recognized that quasi-periodic oscillations (QPOs) in the X-ray light curves of accreting black hole and neutron star binaries have the potential to be powerful diagnostics of strong field gravity. However, this potential cannot be fulfilled without a working theoretical model, which has remained elusive. Perhaps, the most promising model associates the QPO with Lense-Thirring precession of the inner accretion flow, with the changes in viewing angle and Doppler boosting modulating the flux over the course of a precession cycle. Here, we consider the polarization signature of a precessing inner accretion flow. We use simple assumptions about the Comptonization process generating the emitted spectrum and take all relativistic effects into account, parallel transporting polarization vectors toward the observer along null geodesics in the Kerr metric. We find that both the degree of linear polarization and the polarization angle should be modulated on the QPO frequency. We calculate the predicted absolute rms variability amplitude of the polarization degree and angle for a specific model geometry. We find that it should be possible to detect these modulations for a reasonable fraction of parameter space with a future X-ray polarimeter such as NASAs Polarization Spectroscopic Telescope Array (the satellite incarnation of the balloon experiment X-Calibur).