Shock oscillation model for quasi-periodic oscillations in stellar mass and supermassive black holes

We numerically examine centrifugally supported shock waves in 2D rotating accretion flows around a stellar mass  (10 M_⊙)  and a supermassive  (10⁶ M_⊙)  black holes over a wide range of input accretion rates of     . The resultant 2D shocks are unstable with time and the luminosities show quasi-periodic oscillations (QPOs) with modulations of a factor of 2–3 and with periods of a tenth of a second to several hours, depending on the black hole masses. The shock oscillation model may explain the intermediate frequency QPOs with 1–10 Hz observed in the stellar mass black hole candidates and also suggest the existence of QPOs with the period of hours in active galactic nuclei. When the accretion rate     is low, the luminosity increases in proportion to the accretion rate. However, when     greatly exceeds the Eddington critical rate     , the luminosity is insensitive to the accretion rate and is kept constantly around  ∼3 L _E  . On the other hand, the mass-outflow rate     increases in proportion to     and it amounts to about a few per cent of the input mass-flow rate.     

A variable Quasi-Periodic Oscillation in M82 X-1. Timing and spectral analysis of XMM–Newton and RossiXTE observations

We report results from a spectral and timing analysis of M82 X-1, one of the brightest known ultraluminous X-ray sources. Data from a new 105-ks XMM–Newton observation of M82 X-1, performed in 2004 April, and of archival RossiXTE observations are presented. A very soft thermal component is present in the XMM spectrum. Although it is not possible to rule out a residual contamination from the host galaxy, modelling it with a standard accretion disc would imply a black hole (BH) mass of  ≈10³ M_⊙  . An emission line was also detected at an energy typical for fluorescent Fe emission. The power density spectrum of the XMM observation shows a variable Quasi-Periodic Oscillation (QPO) at frequency of 113 mHz with properties similar to those discovered by Strohmayer and Mushotzky. The QPO was also found in seven archival RXTE observations, that include those analysed by Strohmayer and Mushotzky, and Fiorito and Titarchuk. A comparison of the properties of this QPO with those of the various types of QPOs observed in Galactic black hole candidates strongly suggests an association with the type-C, low-frequency QPOs. Scaling the frequency inversely to the BH mass, the observed QPO frequency range (from 50 to 166 mHz) would yield a BH mass anywhere in the interval few tens to  1000  M_⊙  .     

kHz quasi-periodic oscillations in the low-mass X-ray binary 4U 0614+09

We report on a comprehensive analysis of the kilohertz (≥300 Hz) quasi-periodic oscillations (kHz QPOs) detected from the neutron star low-mass X-ray binary 4U 0614+09 with the Rossi X-ray Timing Explorer. With a much larger data set than previously analysed (all archival data from 1996 February up to 2007 October), we first investigate the reality of the 1330 Hz QPO reported by van-Straaten et al. This QPO would be of particular interest since it has the highest frequency reported for any source. A thorough analysis of the same observation fails to confirm the detection. On the other hand, over our extended data set, the highest QPO frequency we measure for the upper kHz QPO is at ∼1224 Hz; a value which is fully consistent with the maximum values observed in similar systems. Secondly, we demonstrate that the frequency dependence of the quality factor  ( Q =ν/Δν)  and amplitude of the lower and upper kHz QPOs follow the systematic trends seen in similar systems. In particular, 4U 0614+09 shows a drop of the quality factor of the lower kHz QPO above ∼700 Hz. If this is due to an approach to the innermost stable circular orbit, it implies a neutron star mass of  ∼1.9 M_⊙  . Finally, when analysing the data over fixed durations, we have found a gap in the frequency distribution of the upper QPO, associated with a local minimum of its amplitude. A similar gap is not present in the distribution of the lower QPO frequencies, suggesting some cautions when interpreting frequency ratio distributions, based on the occurrence of the lower QPO only.     

The correlations between the twin kHz quasi-periodic oscillation frequencies of low-mass X-ray binaries

We analyzed the recently published kHz quasi-period oscillaiton (QPO) data in the neutron star low-mass X-ray binaries (LMXBs), in order to investigate the different correlations of the twin-peak kHz QPOs in bright Z sources and in the less luminous Atoll sources. We find a power-law relation  ν₁∼ν ^b ₂  between the upper and the lower kHz QPOs with different indices: b ≃ 1.5 for the Atoll source 4U 1728-34 and b ≃ 1.9 for the Z source Sco X-1. The implications of our results for the theoretical models for kHz QPOs are discussed.     

Is there a link between the neutron-star spin and the frequency of the kilohertz quasi-periodic oscillations?

There is a general consensus that the frequencies of the kilohertz quasi-periodic oscillations (kHz QPOs) in neutron-star low-mass X-ray binaries are directly linked to the spin of the neutron star. The root of this idea is the apparent clustering of the ratio of the frequency difference of the kHz QPOs, and the neutron-star spin frequency,  Δν/ν_s  , at around 0.5 and 1 in 10 systems for which these two quantities have been measured. Here, we re-examine all available data of sources for which there exist measurements of two simultaneous kHz QPOs and spin frequencies, and we advance the possibility that Δν and  ν_s  are not related to each other. We discuss ways in which this possibility could be tested with current and future observations.     

Evidence of a decrease of kHz quasi-periodic oscillation peak separation towards low frequencies in 4U 1728–34 (GX 354–0)

We have produced the colour–colour diagram of all the observations of 4U 1728–34 available in the Rossi X-ray Timing Explorer public archive (from 1996 to 2002) and found observations filling in a previously reported 'gap' between the island and the banana X-ray states. We have made timing analysis of these gap observations and found, in one observation, two simultaneous kHz quasi-periodic oscillations (QPOs). The timing parameters of these kHz QPOs fit in the overall trend of the source. The 'lower' kHz QPO has a centroid frequency of ∼308 Hz. This is the lowest 'lower' kHz QPO frequency ever observed in 4U 1728–34. The peak frequency separation between the 'upper' and the 'lower' kHz QPO is  Δν= 274 ± 11 Hz  , significantly smaller than the constant value of  Δν∼ 350 Hz  found when the 'lower' kHz QPO frequency is between ∼500 and 800 Hz. This is the first indication in this source for a significant decrease of kHz QPO peak separation towards low frequencies. We compare the result briefly to theoretical models for kHz QPO production.     

Super-Eddington accretion discs around Kerr black holes

We calculate the structure of the accretion disc around a rapidly rotating black hole with a super-Eddington accretion rate. The luminosity and height of the disc are reduced by the advection effect. In the case of large viscosity parameter, α>0.03, the accretion flow deviates strongly from thermodynamic equilibrium and overheats in the central region. With increasing accretion rate, the flow temperature steeply increases, reaches maximum, and then falls off. The maximum is achieved in the advection-dominated regime of accretion. The maximum temperature in the disc around a massive black hole of M =10⁸ M⊙ with α=0.3 is of order 3×10⁸ K. The discs with large accretion rates can emit X-rays in quasars as well as in galactic black hole candidates.     

Are there three peaks in the power spectra of GX 339−4 and Cyg X-1?

Among the variability behaviours exhibited by neutron star systems are the so-called 'horizontal branch oscillations' (HBO, with frequencies ≈50 Hz), the 'lower-frequency kHz quasi-periodic oscillation' (QPO) and the 'upper-frequency kHz QPO', with the latter two features being separated in frequency by an amount comparable to, but varying slightly from, the suspected spin-frequency of the neutron star. Recently, Psaltis, Belloni & van der Klis have suggested that there exists a correlation between these three frequencies that, when certain identifications of variability features are made, even encompasses black hole sources. We consider this hypothesis by reanalysing a set of GX 339−4 observations. The power spectral density (PSD) constructed from a composite of seven separate, but very similar, observations shows evidence for three broad peaks in the PSD. If the peak frequencies of these features are identified with QPO, then their frequencies approximately fit the correlations suggested by Psaltis, Belloni, & van der Klis. We also reanalyse a Cyg X-1 observation and show that the suggested QPO correlation may also hold, but that complications arise when the QPOs (which, in reality, are fairly broad features) are considered as a function of energy band. These fits suggest the existence of at least three separate, independent physical processes in the accretion flow, a hypothesis that is also supported by consideration of the Fourier frequency-dependent time lags and coherence function between variability in different energy bands. If these variability features have a common origin in neutron star and black hole systems, then 'beat frequency models' of kHz QPO in neutron star systems are called into question.     

Dissipative accretion flows around a rotating black hole

We study the dynamical structure of a cooling dominated rotating accretion flow around a spinning black hole. We show that non-linear phenomena such as shock waves can be studied in terms of only three flow parameters, namely the specific energy     , the specific angular momentum (λ) and the accretion rate     of the flow. We present all possible accretion solutions. We find that a significant region of the parameter space in the     plane allows global accretion shock solutions. The effective area of the parameter space for which the Rankine–Hugoniot shocks are possible is maximum when the flow is dissipation-free. It decreases with the increase of cooling effects and finally disappears when the cooling is high enough. We show that shock forms further away when the black hole is rotating compared to the solution around a Schwarzschild black hole with identical flow parameters at a large distance. However, in a normalized sense, the flow parameters for which the shocks form around the rotating black holes are produced shocks closer to the black hole. The location of the shock is also dictated by the cooling efficiency in that higher the accretion rate     , the closer is the shock location. We believe that some of the high-frequency quasi-periodic oscillations may be due to the flows with higher accretion rate around the rotating black holes.     

Steady shocks around black holes produced by sub-Keplerian flows with negative energy

We discuss a special case of formation of axisymmetric shocks in the accretion flow of ideal gas on to a Schwarzschild black hole: when the total energy of the flow is negative. The result of our analysis enlarges the parameter space for which these steady shocks are exhibited in the accretion of gas rotating around relativistic stellar objects. Since Keplerian discs have negative total energy, we guess that, in this energy range, the production of the shock phenomenon might be easier than in the case of positive energy. So our outcome reinforces the view that sub-Keplerian flows of matter may significantly affect the physics of the high energy radiation emission from black hole candidates. We give a simple procedure to obtain analytically the position of the shocks. The comparison of the analytical results with the data of one-dimensional (1D) and two-dimensional (2D) axisymmetric numerical simulations confirms that the shocks form and are stable.     

Evolution of black hole intermediate-mass X-ray binaries: the influence of a circumbinary disc

We report the results of a systematic timing analysis of RXTE observations of GRS 1915+105 when the source was in its variability class θ, characterized by alternating soft and hard states on a time-scale of a few hundred seconds. The aim was to examine the high-frequency part of the power spectrum in order to confirm the hectohertz quasi-periodic oscillations (QPO) previously reported from observations from mixed variability behaviours. During the hard intervals (corresponding to state C in the classification of Belloni et al.), we find a significant QPO at a frequency of ∼170 Hz, although much broader (Q∼2) than previously reported. No other significant peak is observed at frequencies >30 Hz. A time-resolved spectral analysis of selected observations shows that the hard intervals from class θ show a stronger and steeper  (Γ= 2.8–3.0)  power-law component than hard intervals from other classes. We discuss these results in the framework of hectohertz QPOs reported from GRS 1915+105 and other black hole binaries.     

Accretion flow behaviour during the evolution of the quasi-periodic oscillation frequency of XTE J1550−564 in 1998 outburst

Low and intermediate frequency quasi-periodic oscillations (QPOs) are thought to be due to oscillations of Comptonizing regions or hot regions embedded in Keplerian discs. Observational evidence of evolutions of QPOs would therefore be very important as they throw lights on the dynamics of the hotter region. Our aim is to find systems in which there is a well-defined correlation among the frequencies of the QPOs over a range of time so as to understand the physical picture. In this paper, we concentrate on the archival data of XTE J1550−564 obtained during 1998 outburst, and study the systematic drifts during the rising phase from the 1998 September 7 to the 1998 September 19, when the QPO frequency increased monotonically from 81 mHz to 13.1 Hz. Immediately after that, QPO frequency started to decrease and on the 1998 September 26, the QPO frequency became 2.62 Hz. After that, its value remained almost constant. This frequency drift can be modelled satisfactorily with a propagatory oscillating shock solution where the post-shock region behaves as the Comptonized region. Comparing with the nature of a more recent 2005 outburst of another black hole candidate GRO 1655−40, where QPOs disappeared at the end of the rising phase, we conjecture that this so-called 'outburst' may not be a full-fledged outburst.     

黑洞双星的B型QPO频率与幂律通量的相关性的解释

观测表明, 黑洞双星的B型准周期振荡(Quasi-Periodic Oscillation, QPO)频率与幂律通量之间存在正相关性. 试图基于阿尔文波振荡模型定量解释该相关性. 标准薄吸积盘辐射通量极大值处的阿尔文波振荡产生QPO. 标准薄盘上的软光子与冕或喷流基部的热电子介质发生逆康普顿散射产生幂律通量. 通过吸积率的连续变化, 得到QPO频率与幂律通量关系的分析解和数值解. 模拟得到的相关性在合理的参数范围内与观测值相吻合. QPO频率与幂律通量的正相关性可以理解为, 较强的磁场导致较高的阿尔文波频率和较高的电子温度从而得到较高的幂律通量. 结果表明B型QPO可能与吸积盘或喷流中的环向磁场的活动有关.     

Where are the X-ray quasi-periodic oscillations in active galaxies?

In this paper, we address the question of whether existing X-ray observations of Seyfert galaxies are sufficiently sensitive to detect quasi-periodic oscillations (QPOs) similar to those observed in the X-ray variations of Galactic black holes (GBHs). We use data from XMM–Newton and simulated data based on the best Rossi X-ray Timing Explorer ( RXTE ) long-term monitoring light curves to show that if X-ray QPOs are present in Seyfert X-ray light curves – with similar shapes and strengths to those observed in GBHs, but at lower frequencies commensurate with their larger black hole masses – they would be exceedingly difficult to detect. Our results offer a simple explanation for the present lack of QPO detections in Seyferts. We discuss the improvements in telescope size and monitoring patterns needed to make QPO detections feasible. The most efficient type of future observatory for searching for X-ray QPOs in active Galactic nuclei (AGN) is an X-ray All-Sky Monitor (ASM). A sufficiently sensitive ASM would be ideally suited to detect low-frequency QPOs in nearby AGN. The detection of AGN QPOs would strengthen the AGN–GBH connection, and could serve as powerful diagnostics of the black hole mass and the structure of the X-ray emitting region in AGN.     

Discovery of drifting high-frequency quasi-periodic oscillations in global simulations of magnetic boundary layers

We report on the numerical discovery of quasi-periodic oscillations (QPOs) associated with accretion through a non-axisymmetric magnetic boundary layer in the unstable regime, when two ordered equatorial streams form and rotate synchronously at approximately the angular velocity of the inner disc. The streams hit the star's surface producing hotspots. Rotation of the spots leads to high-frequency QPOs. We performed a number of simulation runs for different magnetospheric sizes from small to tiny, and observed a definite correlation between the inner disc radius and the QPO frequency: the frequency is higher when the magnetosphere is smaller. In the stable regime, a small magnetosphere forms and accretion through the usual funnel streams is observed, and the frequency of the star is expected to dominate the light curve. We performed exploratory investigations of the case in which the magnetosphere becomes negligibly small and the disc interacts with the star through an equatorial belt. We also performed investigation of somewhat larger magnetospheres where one or two ordered tongues may dominate over other chaotic tongues. In application to millisecond pulsars, we obtain QPO frequencies in the range of 350–990 Hz for one spot. The frequency associated with rotation of one spot may dominate if spots are not identical or antipodal. If the spots are similar and antipodal, then the frequencies are twice as high. We show that variation of the accretion rate leads to drift of the QPO peak.     

Hot accretion discs with thermal Comptonization and advection in luminous black hole sources

We solve for the structure of a hot accretion disc with unsaturated thermal Comptonization of soft photons and with advection, generalizing the classical model of Shapiro et al. The upper limit on the accretion rate due to advection constrains the luminosity to ≲ 0.15 y^3/5 α^7/5 of the Eddington limit, where y and α are the Compton and viscosity parameters, respectively. The characteristic electron temperature and Thomson optical depth of the inner flow at accretion rates within an order of magnitude of that upper limit are ∼ 10⁹ K and ∼ 1, respectively. The resulting spectra are then in close agreement with the X-ray and soft γ-ray spectra from black hole binaries in the hard state and Seyferts. At low accretion rates, bremsstrahlung becomes the dominant radiative process.     

Gravitational wave emission from a companion black hole in the presence of an accretion disc around a super-massive Kerr black hole

Gravitational wave signal characteristics from a binary black hole system in which the companion moves through the accretion disc of the primary are studied. We chose the primary to be a super-massive  ( M = 10⁸ M_⊙)  Kerr black hole and the companion to be a massive black hole  ( M = 10⁵ M_⊙)  to clearly demonstrate the effects. We show that the drag exerted on the companion by the disc is sufficient to reduce the coalescence time of the binary. The drag is primarily due to the fact that the accretion disc on a black hole deviates from a Keplerian disc and becomes sub-Keplerian due to inner boundary condition on the black hole horizon. We consider two types of accretion rates on to the companion. The companion is deeply immersed inside the disc and it can accrete at the Bondi rate which depends on the instantaneous density of the disc. However, an accretion disc can also form around the smaller black hole and it can accrete at its Eddington rate. Thus, this case is also studied and the results are compared. We find that the effect of the disc will be significant in reducing the coalescence time and one needs to incorporate this while interpreting gravitational wave signals emitted from such a binary system.     

Sidebands to the lower kilohertz quasi-periodic oscillation in 4U 1636–53

In this paper we report on further observations of the third and fourth kilohertz quasi-periodic oscillations (QPOs) in the power spectrum of the low-mass X-ray binary (LMXB) 4U 1636−53. These kilohertz QPOs are sidebands to the lower kilohertz QPO. The upper sideband has a frequency  55.5 ± 1.7 Hz  larger than that of the contemporaneously measured lower kilohertz QPO. Such a sideband has now been measured at a significance  >6σ  in the power spectra of three neutron-star LMXBs (4U 1636−53, 1728−34 and 1608−52). We also confirm the presence of a sideband at a frequency ∼55 Hz less than the frequency of the lower kilohertz QPO. The lower sideband is detected at a 3.5σ level only when the lower kilohertz QPO frequency is between 800 and 850 Hz. In that frequency interval, the sidebands are consistent with being symmetric around the lower kilohertz QPO frequency. The upper limit to the rms amplitude of the lower sideband is significantly lower than that of the upper sideband for lower kilohertz QPO frequencies >850 Hz. Symmetric sidebands are unique to 4U 1636−53. This might be explained by the fact that lower kilohertz QPO frequencies as high as 800–850 Hz are rare for 4U 1728−34 and 1608−52. Finally, we also measured a low-frequency QPO at a frequency of ∼43 Hz when the lower kilohertz QPO frequency is between 700 and 850 Hz. A similar low-frequency QPO is present in the power spectra of the other two systems for which a sideband has been observed. We briefly discuss the possibility that the sideband is caused by Lense–Thirring precession.     

The coherence of kilohertz quasi-periodic oscillations in the X-rays from accreting neutron stars

We study in a systematic way the quality factor of the lower and upper kilohertz quasi-periodic oscillations (kHz QPOs) in a sample of low-luminosity neutron star X-ray binaries, showing both QPOs varying over a wide frequency range. The sample includes 4U 1636−536, 4U 1608−522, 4U 1735−44, 4U 1728−34, 4U 1820−303 and 4U 0614+09. We find that all sources except 4U 0614+09 show evidence of a drop in the quality factor of their lower kHz QPOs at high frequency. For 4U 0614+09 only the rising part of the quality factor versus frequency curve has been sampled so far. At the same time, in all sources but 4U 1728−34, the quality factor of the upper kHz QPO increases all the way to the highest detectable frequencies. We show that the high-frequency behaviours of both the lower and the upper kHz QPO quality factors are consistent with what is expected if the drop is produced by the approach of an active oscillating region to the innermost stable circular orbit: the existence of which is a key feature of general relativity in the strong field regime. Within this interpretation, our results imply gravitational masses around 2 M_⊙ for the neutron stars in those systems.