Identification of Relativistic Effects in X-Ray Astrophysical Source

0.22 MB·English

by  Costantino Sigismondi

IL NUOVOCIMENTO Vol. ?, N. ? ?
Identification ofRelativistic EffectsinX-RayAstrophysicalSources
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0 Costantino Sigismondi( )
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( ) ICRA,InternationalCenterforRelativisticAstrophysics,andUniversityofRomeLaSapienza,
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Piazzale Aldo Moro 5 00185 Roma, Italy.
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Summary.—PreciseknowledgeofthefeaturesofseveralX-raysourcesfromcom-
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pactbinarysourcestogalacticnucleiisgraduallyunveilingthephysicalparameters
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ofrelativisticneutronstarsandblackholestherein. Recentdevelopmentsintheory,
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3 astrophysical models and experiments are reviewed.
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PACS 98.70.Q – X-ray Astronomy.
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PACS 95.30.S – General Relativity.
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PACS 97.60.Cf – Black Holes.
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s 1. – Introduction
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:
v InthelastyearsappearedseveralworksdealingwithinterpretationsofX-raysources’
Xi observations, mainly made with Rossi XTE satellite [1], and following the main streams
of the debate on the identification of Lense-Thirring frequency in QPOs [2] or the clas-
r
a sification of “Z and atoll sources” [3].
2. – Observational phenomena of “Z” and “atoll” sources
The presence of neutron stars in low-mass X-ray binaries (LMXBs) is revealed by
the occurrenceof X-ray bursts or pulsations in these systems. The brigthest LMXBs, as
CygnusX-2(observedwithBeppoSAX[4])andScoX-1,werecalled“Zsources”because
of the Z pattern in the X-ray color-color diagram: horizontal branch; top stroke of the
Z; normal branch (middle stroke) and flaring branch (end stroke). The “Z Sources”
were thought to have a mass accretion rate near the Eddington limit. [5] Thanks to the
microsecond accuracy of the Rossi X-ray Timing Explorer launched in 1995 it has been
possibletoprogresslargelyintheinterpretationofthenatureofLMXBs[6]andnowthe
entire catalogue of observations is available online. [7]
In figure 1 there is the explanation about “Z sources” denomination.
HasingerandVanderKlis[8]foundinEXOSATdata(timeresolutionofmilliseconds)
the evidence of a new class of sources with a different pattern of correlated timing and
spectral behaviour. Because of their fragmented color-color diagram they called them
(cid:13)c Societa`ItalianadiFisica 1
2 COSTANTINOSIGISMONDI
S = 1
a
S = 2
a
Fig.1.–X-raycolor-colordiagramoftheatollsource4U1608−52. Massaccretionrateisinferred
to increase counterclockwise, approximately along the drawn curve. kHz QPO detections are
indicated with filled symbols (credit: Van derKlis [1]). A Z source traces a complete Z on this
diagram.
“atollsources”. Zsourcestendtobemoreluminousthanatollsources. [10]Thepatterns
whichatollsourcestraceinX-raycolor-colordiagramsaresimilartotheshapesforwhich
the more-luminous Z sources are named.
.
21. Quasi-periodic oscillators: QPOs. – Quasi-periodic oscillations QPOs have been
discovered also in atoll sources with Rossi XTE. Analyses of those sources have been
published until now, and compared with theoretical models. Timing properties of the
bursting atoll source 4U 1728-34 have been studied as a function of its position in the
X-ray color-color diagram. [9] A detailed discussion of the different components of the
signal (as very low frequency noise below 1 Hz, low-frequency QPO between 20-40 Hz)
is also present.
IDENTIFICATIONOFRELATIVISTICEFFECTSINX-RAYASTROPHYSICALSOURCES 3
Fig.2.–Twin kHzpeaksinScoX-1(credit: VanderKlis[1]). ItisaZsourceshowingkilohertz
QPOs.
3. – Different models of QPO
Several models in addition to those related to Lense-Thirring precession [2, 12] have
been used to explainsuchobservationalfeatures: QPOsdue to orbitalmotionofclumps
[16]; epicyclic motions in the accretion disk [17]; transonic disk accretion flows [19, 24],
stellar oblateness [15], photospheric radius expansion[23], and beaming oscillations[21].
Homan et al. [18] compare the behavior of GX 17+2 and other Z sources with that of
blackhole sourcesandconsiderthe possibility thatthe massaccretionratemightnotbe
driving force behind all spectral and variability changes.
.
31. Transition layer model. – Wu [22] compared the theoretical predictions for neu-
tron stars X-ray binaries of the transition layer model with some observational features
4 COSTANTINOSIGISMONDI
of QPOs and suggested that similar transition layer oscillations may be responsible for
the observed QPOs in accretion-powered millisecond X-ray pulsars and galactic black
hole candidates.
.
32.The role of stellar magnetic field.–Theinnerregionsofaccretiondisksofweakly
magnetizedneutronstarsareaffectedbygeneralrelativisticgravityandstellarmagnetic
fields. Lai [20] posed an upper limit to the surface magnetic field B can be obtained,
o
i.e., Bo ≤3·107(M˙17/β)1/2 G, where M˙17 =M˙ /(1017 g·s−1), in order to produce kHz
orbital frequency at the sonic radius. An accretion disk around a rotating magnetized
star is subjected to magnetic torques that induce disk warping and precession. General
studies on thin disks have been recently published [26], and around weakly magnetized
neutron stars. [25] These torques arise generically from interactions between the stellar
field and induced surface currents on the disk. Applying these new effects to weakly
magnetized (B ∼107−109 G) neutron stars in low-mass X-ray binaries, Shirakawa and
Lai [28] studied the global hydrodynamical warping/precessionmodes of the disk under
the combined influences of relativistic frame dragging, classical precession due to the
oblateness of the neutron star, and the magnetic torques. The modes are confined to
the inner region of the disk and have frequencies equal to 0.3÷0.95 (depending on the
mass accretion rate M˙ ) times the Lense-Thirring frequency. The magnetically driven
precession is retrograde (opposite to the Lense-Thirring precession). This may account
for several observed features of low-frequency (10-60 Hz) quasi-periodic oscillations in
LMXBs. Interactions with neutron stars magnetic fields have been invoked in other
papers [27, 25] The magnetospheric beat-frequency [29] QPO is the model proposed to
explain the signal of 4U 1735-44 and Z sources in Wijnands et al. [30].
4. – Lense-Thirring effect on warped accretion disks
AmongtheeffectsaroundarapidlyrotatingcompactobjectistheBardeen-Petterson
effect[11]whichcausesatiltedaccretiondisktowarpintotheequatorialplaneofthero-
tatingbody. Viscousforcescausetheaccretionflowtodivideintotwodistinctregions-an
inner aligned accretion disk and an outer tilted accretion disk. The transition between
these two regimes occurs at a characteristic radius that depends on the mass and angu-
lar momentum of the centralobject andpossibly onthe accretionrate throughthe disk.
Fragile et al. [31] propose that the accreting material passing through the transition
regionmay generate quasi-periodic brightness oscillations suchas have been observedin
a number of X-ray binaries. QPO frequency range predicted by this model is consistent
with observed QPO frequencies in both black hole and neutron star low-mass X-ray bi-
naries. Armitage and Natarajan [13] studied the Lense-Thirring and Bardeen-Petterson
effect acting upon warped accretion disks. Sibgatullin gave compact approximation for-
mulas for the nodal precession frequency of the marginally stable circular orbits around
black holes [32] and around rapidly rotating neutron stars. [33]
5. – Gravitomagnetism around neutron stars and black holes
The main processes that produce the variability are the same for black holes and
neutron stars [34]. The distinction amongthem is suggestedstudying Fourier spectra at
high frequencies [36]. Galloway et al. [37] studying the discovery of a highly coherent
oscillationin atype I X-rayburstobservedfrom4U1916-053by the RossiXTE guessed
the neutron star spin period to be around 3.7 milliseconds. Begelman [35] also agrees
IDENTIFICATIONOFRELATIVISTICEFFECTSINX-RAYASTROPHYSICALSOURCES 5
that observational techniques and theoretical ideas are enabling us to find black holes
andmeasuretheirmasseswithincreasingprecision,andwemaysoonbeabletomeasure
black hole’s spins.
6. – Galactic black holes
Meliaetal. [38]suggestedthatsubmillimetertimingobservationscouldyieldasignal
correspondingtotheperiodP0 ofthemarginallystableorbitandthereforepointdirectly
to the black hole’s spin ~s. Sgr A*’s mass is now known to be 2.6±0.2×106 M⊙ (an
unusually accurate value for supermassive black hole candidates), for which 2.7 min-
utes ≤ P0 ≤ 36 minutes, depending on the value of ~s and whether the Keplerian flow
is prograde or retrograde. A Schwarzschild black hole (~s = 0) should have P0 ∼ 20
minutes. The identification of the orbital frequency with the innermost stable circular
orbit is made feasible by the transition from optically thick to thin emission at submil-
limeter wavelengths. By analogy with low-mass X-ray binaries and Galactic black hole
candidates, Sgr A* may also display quasi-periodic oscillations. Other authors studied
matter flows onto galactic black holes in the same perspective of X-ray binaries or grav-
itomagnetism [14]. Alternative derivations of Lense-Thirring effect [39], as well as some
derivations of the “clock effect” related to the non static part of the metric in General
Relativity [40,41, 42, 43]like time delay in gravitationallensing due to the rotationof a
foreground galaxy [44, 45] have been proposed.
7. – Experiments around Earth
Waiting for GP-B data, the satellite has been launched in april 2004[51], and consid-
ering all space experiments already done on this topic [1], the dramatic improvement of
this field it is expected from two years after the launch (end of 2006). C. La¨mmerzahl
coedited with C.W.F. Everitt and F. W. Hehl a volume dedicated to tests of General
Relativity in Space [46].
About measurements of Lense-Thirring effect around Earth there are the studies
on the influence of Earth tides [40, 41], Earth’s penumbra [47], non gravitational per-
turbations modeling [48] and the use of clocks. [49] Pascual-Sa´nchez [50] proposes a
measurement of gravitomagnetismin a terrestrial laboratory.
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