Fast variability from X-ray binaries
aa r X i v : . [ a s t r o - ph . H E ] J u l Fast variability from X-ray binaries
Tomaso M. Belloni ∗ INAF - Osservatorio Astronomico di BreraVia E. Bianchi 46, I-23807 Merate, ItalyE-mail: [email protected]
The X-ray emission from accreting black-holes and neutron stars features strong variability onsub-second time scales, with very complex and broad phenomenology. From high-frequencyquasi-periodic oscillations to rapidly changing X-ray burst oscillations to millisecond pulsations,these are weak signals immersed in strong noise and their study is pushing instrument capabilitiesto their limit. The scientific significance of fast time variability studies are both astronomical(properties of accretion flows, nature and evolution of sources) and physical (effects of GeneralRelativity, equation of state of degenerate matter). I first review the main observational properties,then discuss the future prospects and observational needs.
High Time Resolution Astrophysics IV - The Era of Extremely Large Telescopes - HTRA-IV,May 5-7, 2010Agios Nikolaos, Crete, Greece ∗ Speaker. c (cid:13) Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlikeLicence. http://pos.sissa.it/ ast variability from X-ray binaries
Tomaso M. Belloni
1. The Promise of X-ray Binaries
X-ray binaries are systems made of a compact object and a non-collapsed star. When dealingwith high-energy emission however, it is more correct to say that they are made of a compact objectand matter orbiting around it and falling onto/into it. They therefore constitute an ideal laboratoryfor studying two separate phenomena: accretion onto the compact object and General relativity inthe strong field regime. Matter orbiting a few kilometers from a neutron star or a black hole ispart of a complex accretion flow and is located in the deepest part of the gravitational well. Thebest way to study a gravitational field is to make use of a test particle and here we have many suchtest particles right where we would like to have them. While active galactic nuclei also provide acomparable gravitational potential, the field curvature is much smaller than in galactic systems (seeFig. 1, from [27]). Therefore, X-ray binaries appear as the best space laboratories.The main problem with these approaches is that they are entangled: we want to understand theproperties of accretion close to a compact object making use of the fact that they are in a stronggravitational field, while at the same time we want to study the same gravitational field making useof the accreting matter. Accretion onto a compact object is a very complex and messy phenomenon:it provides not a test particle, but a stream of magnetized plasma that moves towards the compactobject forming a very complex object. This intrinsic difficulty has not yet been overcome, but thefield remains very promising.In addition to probing General Relativity, neutron-star binaries are systems where we candetect strong high-energy emission from the surface of the neutron star and its surroundings. Thisprovides a potential instrument to put limits on the equation of state of neutron matter, in particularas it offers the possibility of measuring mass and radius of the central object.Both these goals have still to be reached. They are approached from two separate directions:the spectral distribution of the X-ray emission and the fast time variability. As continuum energyspectra of neutron-star Low-Mass X-Ray Binaries (LMXB) are very complex and do not offera simple and unique interpretation, the attention has been concentrated on the shape of the ironemission fluorescence line due to reflection of X-ray radiation off the accretion disk in the system.Since the expected line is narrow, the effects of relativity (such as gravitational redshift, transversedoppler shift and beaming) on the orbiting gas, smeared by the complex motion in the accretiondisk, can be studied. The alternative approach is through fast timing. Timing signals are the mostdirect way of studying the motion of matter around a compact object and there are plenty of thesesignals observed. However, in this case the theoretical modeling is still not able to interpret thecomplex phenomenology observed in this variability. Below, I briefly outline the current standpointand the its future prospects.
2. Fast variability
When dealing with time variability, it is important to consider the possible characteristic timescales that we can expect from the system. In addition to the spin period of the neutron star in thecase of a pulsar, an obvious frequency that could be (but is not always) observed, we have all thetime scales associated to the accretion flow (see e.g. [5, 23, 24]). Important quantities are e.g. the2 ast variability from X-ray binaries
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Figure 1:
Tests of General Relativity placed on an appropriate parameter space. The x -axis measures thepotential e ≡ GM / rc and the y -axis measures the spacetime curvature x ≡ GM / r c of the gravitationalfield at a radius r away from a central object of mass M . The long-dashed line represents the event horizonof Schwarzschild black holes (from [27]) time scales for radial light-crossing, radial sound-crossing, free-fall, viscous and thermal diffusion.The identification of these time scales in the data would provide important insights on the processof accretion (see e.g. [6]). In addition, there are the time scales associated to General Relativity:a particle orbiting around a compact object with angular momentum, in addition to its Keplerianorbital period, is also subject to nodal and frame-dragging precessions. The identification of oneor more of these characteristic time scales in the emitted radiation and its firm identification is themost promising path to the discovery of relativistic effects. However, the situation is very complexand it is difficult to disentangle the various components. Although X-ray pulsars are known since the dawn of X-ray astronomy, the “normal” systemsof this type have magnetic fields so high that they do not allow the formation of an inner accretionflow and start channeling matter onto the neutron star at a large distance. However, since 1999we have discovered a few systems with low-mass companion showing millisecond pulsations (see[34]). The discovery of these pulsations has been a goal for decades, when people looked into theemission of bright sources, where no detection was obtained. As it happens, pulsations are detectedfrom faint transients and are associated to very compact binaries. More recently, intermittent pul-3 ast variability from X-ray binaries
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Figure 2:
Spectrogram of a RXTE observation of the intermittent pulsar SAX J1748.9–2021. The contoursshow the pulsation, whose frequency drifts due to orbital modulation. Superimposed is the light curve, whichshows the presence of X-ray bursts (from [1]). sations have been detected from a few systems, including the bright transient Aql X-1 ([13, 1]). InAql X-1, the pulsation appeared for a mere 150 seconds over a total exposure time of 1.3 × s.Another example where more pulsation intervals were detected is shown in Fig. 2. It is not yetclear what leads to these intermittency and what prevents the detection of pulsations in other brightsystems (for which we know the pulse period nevertheless, see below). Neutron-star low-mass X-ray binaries (LMXB) at low accretion rate often show thermonu-clear X-ray bursts. They are powerful strong surges in X-ray emission caused by the ignition of athermonuclear reaction in the material accreted onto the surface of the neutron star (see e.g. [15]).With the RossiXTE satellite, transient highly coherent (although drifting in frequency) oscillationswere observed during some bursts in a number of sources and it was soon realized that the oscilla-tion frequency was the same for all bursts of each source, suggesting that what was seen was thepulse frequency. This was later confirmed with the detection of pulsations and burst oscillationsat the same frequency in the same source. This not only allows to enlarge the sample of sourcesfor which we know the pulse period, but offers a very interesting window onto processes that takeplace on the very surface of the neutron star (see [31]). These signals, in the range ∼ When in their low-luminosity states, both black-hole and neutron-star X-ray binaries, in ad-dition to a rather hard energy spectrum, are characterized by very strong aperiodic variability,with an integrated fractional rms that can reach 40-50% (see [4, 16]). In the Fourier domain,this variability can be interpreted as the sum of a small number of Lorentzian-shaped components([25, 26, 22, 7, 4], see Fig. 4). These components move in frequency hand-in-hand, positivelycorrelated with the source flux ([26, 7]). At higher fluxes, their fractional rms decreases and Quasi-Periodic Oscillations appear (see below). This strong variability is associated to very clear signa-tures in the phase-lag spectrum, providing a complex but important set of constraints to theoretical4 ast variability from X-ray binaries
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Figure 3:
Spectrogram for an X-ray burst of 4U 702—429, plotted over the RXTE/PCA light curve (solidhistogram). The best fit frequency evolution is shown as a thick solid line (from [31]). models, whether they involve themal/hybrid Comptonization or contributions from a jet component([23, 16]). In other states, where the emission is dominated by a thermal optically thick accretiondisk, the variability is reduced and can be of the order of 1% (see Fig. 5).
Quasi-periodic Oscillations (QPO) peaked components in the power-density spectra, offer amore direct way to measure frequencies, as their centroid is unambiguous, unlike the case of broadnoise components (see [7]). Since the first discovery in 1985, low-frequency (0.1-20 Hz) QPOhave been detected in both classes of sources and classified in a complex way (see [12]). There arestrong indications that here too we are observing the same phenomenon across classes of sources.Their typical quality factor Q (defined as the ration between the frequency and the width of a PDSpeak) is around ∼
10, their fractional rms increases with energy and can be as high as ∼
20% above10 keV. In black-hole binaries, one of these QPOs (type-B) is found not to be associated to thepresence of a strong noise component, which is consistent with being the evolution to higher fluxesof those shown before, and appears to be connected to the intervals of ejection of relativistic jetsfrom the system (see [14, 4]). During the evolution of a transient source, this QPO appears in a veryspecific high-flux state and is of transient nature itself. Whether and how this feature is associateddirectly to the jet formation or ejection we do not know, but the association with the time of jetejection, although not exact, indicates that major changes take place in the accretion flow aroundthat time. This is also confirmed by spectral analysis ([21]).The most common type (called horizontal-branch QPO for NS and type-C QPO for BH), hasa frequency that correlates extremely well with those of the broad-band noise components, which5 ast variability from X-ray binaries
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RXTE/PCA Cygnus X-1Fractional rms = 29% P o w e r -5 -4 -3 -2 -1 Frequency (Hz)0.01 0.1 1 10 100
Figure 4:
Typical power-density spectrum of Cyg X-1 in its low/hard state. Three broad Lorentzian compo-nents (red) are overplotted.
Cygnus X-1 Hard State C oun t r a t e GX 339-4 Soft State C oun t r a t e Figure 5:
Left panel: a RXTE/PCA observation of Cygnus X-1 in the low-hard state; Right panel: aRXTE/PCA observation of GX 339-4 in the high-soft state. The tow panels have the same dynamical rangein count rate. The difference in total variability is evident. ast variability from X-ray binaries Tomaso M. Belloni
Figure 6:
Left panel: sketch of a hardness-intensity diagram of an outburst of an X-ray transient (theequivalent of a color-magnitude diagram) with the four source states marked (see [4]). Right panel: twotypes of QPO (intentionally selected to have the same frequency) corresponding to two high-flux states.At the top type-C QPO, associated to strong noise, at the botton type-B QPO, with reduced noise. TheHIMS-SIMS transition is marked by the sudden change between these two QPOs. suggests a common origin (see [35]). These low-frequency features have received less attentionthan high-frequency QPOs in the past decade, but are strongly connected to them and offer aninsight on the accretion phenomenon, while being possibly associated to fundamental relativisticfrequencies.
The major fast time variability features are without doubt kilohertz QPOs in neutron-starLMXB. They are quasi-periodic signals in the range 200-1200 Hz. Although their full phenomenol-ogy is rather complex (see [34] and references therein), we can identify the following basic features: • Often, two separate peaks are observed simultaneously (see Fig. 7), usually with differentcoherence. The Q value can reach values as high as 200. • Both peaks change frequency as a function of time in a random-walk fashion, i.e. withoutjumps. There are no special frequencies in the 200-1200 Hz range ([8, 10, 11]). • Their frequency correlates positively with source luminosity, but there is no one-to-one over-all correlation. In other words, during each observation this correlation is observed, but thefrequencies always cover the same range ([33]). • The frequency separation between the two peaks is not constant, but for single sources isobserved to decrease at high and low QPO frequencies. However, the distribution of observedseparations is a rough Gaussian with average 300 Hz (see right panel in Fig. 8 [18]).7 ast variability from X-ray binaries
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Figure 7:
Left panel: kHz QPOs observed from the brightest LMXB Sco X-1 (from [32]). Right panel:two high-frequency QPOs from the black-hole binary GRS 1915+105, with centroid frequencies in 3:4 ratio(from [30]). • A correlation between frequency separation and pulse frequency has been suggested, inwhich
D n is equal to n spin if n spin <
400 Hz and to half of it if n spin >
400 Hz. This is incontrast to the previous statement of a Gaussian distribution in
D n values across all sources,which suggests that there is no connection with n spin . In the left panel of Fig. 8 one cansee the plot of D n vs. n spin for all published values, to be compared with a constant value(solid line) and the “step” model described above. Notice that for each source, and hence foreach spin frequency, there can be a number of measurements of D n which are statisticallyinconsistent with each other, so that neither of these lines can be considered a fit to the data. • kHz QPO correlate linearly with low-frequency QPOs (of the type-C/horizontal branch fla-vor). The correlation between the first kHz QPO (lower) and the low-frequency QPO hasbeen extended to low-luminosity systems and black-hole binaries, provided noise frequen-cies are used for those ([28, 7]).Given the high frequencies, it is clear that these signals come from the innermost regions ofthe space-time around the neutron star. Although the basic phenomenology outlined above is ratherclear, theoretical models are still not able to reproduce it.One important point is whether we can use these signals to find direct evidence of the presenceof an innermost stable circular orbit (ISCO) around the neutron star. If the highest-frequency QPOobserved in a system is associated to a Keplerian frequency at the ISCO, we can use it to measurethe ISCO itself. Recently, effects related to the ISCO have been claimed, although there is stilldebate on possible alternatives ([3, 17]).Since another approach to this measurement is through the analysis of relativistically broad-ened iron fluorescence lines, it is interesting to compare the results of the two methods on simul-taneous data. Obtaining such data is not simple, but (quasi)-simultaneous RXTE/Chandra/XMM8 ast variability from X-ray binaries Tomaso M. Belloni Δ ν ( H z ) spin (Hz)150 200 250 300 350 400 450 500 550 600 6500 20 40 Figure 8:
Left panel: separation of the two kHz QPO frequencies
D n versus the NS spin frequency forall published measurements. The white circles represent two millisecond X-ray pulsars. The solid line is aconstant at y = D n values, which are more than the points in the left panel since there are sourcesfor which the spin frequency is not (yet) known. data exist for the source 4U 1636–53. From these data, it appears that the two measurements can bereconciled only with a massive neutron star ( > M ⊙ or > M ⊙ depending on the line model used),indicating that more observational data are needed in order to obtain a robust comparison (see [2]). For black-hole binaries, the situation at high frequencies (above 30 Hz) is very different. De-spite the extremely large base of data covering outbursts of transient sources and monitoring ofpersistent sources, only very few detection of high-frequency features have been obtained (see [9]).In all seven sources where narrow peaks were found (and only in few observations), the frequencyseems to be constant. Moreover, in four sources two peaks have been detected simultaneously,although not always in the same energy band. In three of these cases their frequencies are in ratio2:3, in the fourth in ratio 3:4 (see Fig. 7). There is an indication that the highest of the two QPOfrequency is anti-correlated with the mass of the black hole, as expected if it was a Keplerian fre-quency at the ISCO. Thee features are observed in or close to a particular source state, the sameone when type-B LFQPO are observed. However, even within this state only a few observationsyield a detection. There seems to be no correlation with the frequency of low-frequency features,9 ast variability from X-ray binaries
Tomaso M. Belloni although a comparative statistical study has not been done yet.
3. Theoretical models
All the observables described above need to find a physical explanation. QPOs provide veryprecise frequencies to compare with models, but it is becoming clear now that other variables, suchas the quality factor and the fractional rms of the peaks must be considered in order to understandthe origin of the oscillations (see [3, 17]).The original class of models for QPOs was based on the beat between the neutron star rotationfrequency and the Keplerian frequency of accreting matter at a special radius (see [19, 34]). Abouta decade ago, the relativistic frequencies were introduced by the Relativistic Precession Model(citestellavietri). The LFQPO (of type-C) and two kHz QPO are identified with Lense-Thirringprecession, nodal precession and Keplerian motion respectively. In the model, only the basic iden-tification with fundamental relativistic frequencies is made, but the comparison with observationsis rather successful and indicates that this direction is very promising for a more thorough under-standing.For high-frequency QPOs in black-hole binaries, the relativistic resonance models interpretthe fixed frequencies in terms of resonance between orbital and epicyclic frequencies at a particularradius, yielding special ratios between the frequencies (see [34] for a discussion). More detectionsare needed to confirm this model, at variance with the case of neutron stars, where more modelsare needed to explain the large set of observational data.In addition to probing accretion and General Relativity, kHz QPOs can be used to put usefullimits on the equation of state of neutron matter (see [20]). The fact that matter is orbiting withperiod P at a radius R around the neutron star puts a limit to the relation between mass and radiusof the star, which should be smaller than R . In addition, R cannot be smaller than the ISCO. Withthe highest QPO frequency, limits can already be put, but the observability of a higher frequencywould make these limits very stringent. Unfortunately, although the instrumental sensitivity wouldallow to detect signals well above ∼
4. The future
The space mission that brought all advancements in fast timing for X-ray binaries is the RossiX-Ray Timing Explorer. After 15 years of service, the satellite will soon cease operations. Thereare a number of proposed instruments and missions devoted to fast timing, such as AXTAR andthe HTRS on board the International X-ray Observatory, all on medium to long time scales. Otherpapers in these proceedings deal with them. However, in the spring of 2011 the indian satellitefor astronomy ASTROSAT will be launched . Among other instruments covering a wide energyrange from the ultraviolet to hard X-rays, ASTROSAT will carry a large high-pressure proportionalcounter (LAXPC) which will provide a response similar to that of the RXTE/PCA below 10 keVand much higher at higher energies (see Fig. 9). This constitutes a unique possibility to continue http://meghnad.iucaa.ernet.in/~astrosat/ ast variability from X-ray binaries Tomaso M. Belloni
ASTROSAT/LAXPCRXTE/PCA E ff e c t i v e a r ea ( c m ) Figure 9:
Comparison between the effective areas of the ASTROSAT/LAXPC (black) and the RXTE/PCA(five PCU elements, blue). timing studies, the major advantage that the collecting area, which even below 10 keV is betterthan that of the current PCA, where obtaining a 5-unit observation is very unlikely, resulting ina considerable increase in area. Moreover, most of the timing features shown before are moreintense at high energies, where the increased area of the LAXPC will bring a higher sensitivity.In particular, it will be possible to study black-hole high-frequency QPOs with higher sensitivity,hopefully bringing the necessary increase in observational wealth to compare them in details withtheoretical models.
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