Bardeen-Petterson Effect and Quasi-Periodic Oscillations in X-Ray Binaries

6 Pages·0.14 MB·

by  P. Chris Fragile

DraftversionFebruary1,2008
PreprinttypesetusingLATEXstyleemulateapjv.16/07/00
BARDEEN-PETTERSON EFFECT AND QUASI-PERIODIC OSCILLATIONS IN X-RAY
BINARIES
P. Chris Fragile, Grant J. Mathews, and James R. Wilson1
CenterforAstrophysics,UniversityofNotreDame,NotreDame,IN46556
Draft version February 1, 2008
ABSTRACT
TheBardeen-Pettersoneffectaroundarapidly-rotatingcompactobjectcausesatiltedaccretiondiskto
warpintotheequatorialplaneoftherotatingbody. Viscousforcescausetheaccretionflowtodivideinto
1 two distinct regions - an inner aligned accretion disk and an outer tilted accretion disk. The transition
0 betweenthesetwooccursatacharacteristicradiusthatdepends onthemassandangularmomentumof
0 thecentralobjectandpossiblyontheaccretionratethroughthedisk. Weproposethataccretingmaterial
2 passing through the transition region may generate quasi-periodic brightness oscillations (QPOs) such

n as have been observed in a number of X-ray binaries. We show that this effect may be present in the
a black-hole X-ray binary GRO J1655-40. We also argue that the QPO frequency range predicted by this
J model is consistent with observedQPO frequencies in both black-hole and neutron-star low-mass X-ray

7 binaries.
1 Subject headings: accretion, accretion disks—stars: neutron—black hole physics—X-rays: stars—stars:

individual(GRO J1655-40)
2
v
8 1. introduction Lapidus, & Muslimov 1998), and various beat-frequency
7 interpretations (e.g. Alpar & Shaham 1985; Lamb et al.
Sincetheirdiscoveryinthemid-1980s(vanderKlisetal.
4 1985; Miller, Lamb, & Psaltis 1998). Some of these mod-
7 1985), quasi-periodic oscillations (QPOs) have been ob-
els depend explicitly on the existence of a stellar surface
0 served in the X-ray brightness of a number of neutron-
and/or a large-scale magnetic field and are therefore only
0 star(NS)andblack-hole(BH)X-raybinaries. Inso-called
valid for QPOs in NS systems. Furthermore, none of the
0 Z-sources, which are high-luminosity NS low-mass X-ray
models proposed thus far has been able to simultaneously
/ binaries (LMXBs), there are typically four distinct QPO
h explain all of the QPOs observed in individual systems.
frequencies observed: 1) The ≃ 5−20 Hz normal/flaring
p Most recent theoretical attention has focused on the
- branchoscillation;2) The ≃15−60 Hz horizontal-branch
o oscillation; 3) & 4) Two “kilohertz” QPOs in the range high-frequency kHz QPOs. In this paper, however, we
r ≃200−1200 Hz (van der Klis et al. 1996). Atoll sources, wishtoinsteadaddressmoderate-frequency(∼1−300Hz)
st which are less luminous NS LMXBs, typically display two QPOs. Specifically, we propose the Bardeen-Pettersonef-
a fect(Bardeen&Petterson1975)asapotentialmechanism
kHz QPOs in the range ∼ 500−1330 Hz as well as low
: for generating such QPOs in X-ray binaries. This new
v frequency (∼ 20−60 Hz) QPOs and broad noise compo-
Xi nents (Strohmayer et al. 1996). Not as many detections mechanism derives from the possible existence of a well-
defined transition radius in tilted accretion disks around
exist for QPOs in BH X-ray binaries. However, several
r rapidly-rotatingcompactobjects. Thistransitionradiusis
a low-frequency (∼0.1−50 Hz) QPOs have been observed,
a result of the Bardeen-Petterson effect which will be ex-
and higher-frequency QPO components have been identi-
plained further in Section 2. In Section 3 we consider the
fiedinthespectraofatleastthreeBHcandidates[≃67Hz
likelihood that this effect is present in BH and NS X-ray
in GRS 1915+105 (Morgan, Remillard, & Greiner 1997);
binaries. We also discuss mechanisms by which accreting
≃300 Hz in GRO J1655-40 (Remillard et al. 1999b); and
material passing through this transition radius may gen-
∼160−280HzinXTEJ1550-564(Remillardetal.1999a;
erate observable quasi-periodic brightness oscillations. In
Homan et al. 2000)]. (See, e.g. van der Klis 1995,van der
Section 4 we discuss the BH X-ray binary GRO J1655-40.
Klis 2000,and Wijnands 2000 for recent summaries.)
We find that our estimated QPO frequency range is con-
These QPOs may provide a useful probe into the in-
sistent with wither of two QPOs observedin that system.
ner accretion flows around neutron stars and black holes.
In Section 5 we consider neutron-star LMXBs and argue
Consequently, a number of theoretical models have been
that our model is consistent with the ∼ 100 Hz peaked-
proposedto explainthe observations. For example,QPOs
noise component seen in some of these systems.
have been modeled as general relativistic Lense-Thirring
precession (e.g. Stella & Vietri 1998; Morsink & Stella
2. the bardeen-petterson effect
1999), geodesic motion of gas clumps (e.g. Stella & Vi-
etri 1999; Stella, Vietri, & Morsink 1999; Karas 1999), The Bardeen-Petterson effect is illustrated schemati-
trapped oscillation modes in the disk (e.g. Markovi´c & cally inFigure 1. This effect causesa tilted accretiondisk
Lamb 1998; Nowak & Wagoner 1991, 1992), interruption aroundarapidly-rotatingcompactobjecttowarpintothe
of the gas flow at the centrifugal barrier (e.g. Titarchuk, equatorial plane of the central object (Bardeen & Petter-
son 1975; Kumar & Pringle 1985;Scheuer & Feiler 1996).
1
LawrenceLivermoreNationalLaboratory,Livermore,CA94550
1
2
The effect is the combined result of differential Lense- In the present work we will adopt the following expres-
Thirring precession and internal viscosity. The Lense- sionfortheBardeen-Pettersontransitionradiusmotivated
Thirring precession causes the disk to “twist up.” Damp- largely by equation 3 and the numerical results of Nelson
ing of the fluid motion by viscosity limits this twisting. & Papaloizou(2000):
Close to the accreting black hole or neutron star, where
theLense-Thirringprecessionisstrongest,viscosityallows RBP =Aa2∗/3RGR , (4)
the misalignedangularmomentum of the tilted disk to be where the scaling parameter A lies in the range 10.A.
transported outward. This allows the inner region to set- 300. The corresponding Keplerian orbital frequency is
tle into the rotation plane of the BH or NS. Further out, therefore:
the disk remains in its original plane because the Lense-
c3
Thirring precession rate drops off rapidly with increasing ν = . (5)
radial distance [∼r−3 (Lense & Thirring 1918)]. Internal Kep,BP 2πGA3/2a∗M
pressure and viscous stress in the outer regions are thus
3. bardeen-petterson effect in x-ray binaries
able to limit its effects. The end result, as shown in Fig-
ure1,isanalignedinneraccretiondisk(region2),atilted As noted above, the Bardeen-Petterson effect requires
outeraccretiondisk(region4),anda transitionregion(3) a tilted accretion disk around a rapidly-rotating compact
between the two. object. In the context of our present study, we must eval-
uate the likelihood that this condition is met in observed
2.1. Transition Radius
X-ray binaries. To do this, we must consider the likeli-
The Bardeen-Pettersontransition radius is expected to hood that tilted-disk systems are formed and how long
occur approximately where the rate of twisting up by dif- they last relative to the overall lifetime of X-ray binaries.
ferentialprecessionisbalancedbytherateatwhichwarps These factors are not well known, but we can make some
of the disk are diffused or propagated away by viscosity. estimates.
Using thindisk theory,inwhichthe effects ofpressureare
neglected and an isotropic viscosity is assumed, the tran- 3.1. X-Ray Binary Formation
sition radius was first estimated as (Bardeen & Petterson
X-raybinariescanpossiblyforminoneoffourways(e.g.
1975; Hatchett, Begelman, & Sarazin 1981):
Canal, Isern, & Labay 1990; Verbunt & van den Heuvel
6a∗ 2/3 1995). The mostlikely paradigmsfor Galacticsourcesare
RBP = αδ2 RGR . (1) core-collapseof a massive star in a binary or accretionin-
(cid:20) (cid:21) ducedcollapseofawhitedwarforneutronstarinabinary.
Hereαisthestandardviscosityparameterassociatedwith
Less likely possibilities (except perhaps in dense globular
theradialaccretion(Shakura&Sunyaev1973),δistheas-
clusters)arebinarycapture orbinaryreplacement. Inthe
pectratioofthedisk,a∗isthedimensionlessspecificangu- first two mechanisms one member of a preexisting binary
larmomentumparameteroftheBHorNS(a∗ =Jc/GM2 mustexplodeasasupernovainordertoformtherequired
where J is the angular momentum), and R = GM/c2,
GR NS or BH. During this violent event even a small asym-
where M is the gravitationalmass of the BH or NS.
metry in the explosionwill impartsubstantialmomentum
Ivanov & Illarionov (1997) obtained an alternative
to the newly-formedremnant (e.g. Dewey & Cordes 1987;
expression for a characteristic radius analogous to the
Bailes et al. 1989). Even if an initially aligned system re-
Bardeen-Petterson transition radius by considering the
mains bound, it is unlikely that the two stellar spin axes
scale of oscillations in a twisted accretion disk around a
will remain aligned with the orbital spin axis after the
Kerr BH:
supernova. Detailed Monte Carlo modeling by Brandt &
384a∗ 2/5 Podsiadlowski(1995)ofthisevolutionarypathforLMXBs
RBP = 25δ2 RGR . (2) indicates that only ∼ 20% of the progenitor systems re-
(cid:20) (cid:21) main bound after a supernova explosion. Furthermore,
Most recently, Nelson & Papaloizou (2000) obtained a
the resultant median of tilt angle for the systems that re-
slightlydifferentestimatebyconsideringseparatehorizon- main bound is approximately 20◦, with roughly 60% of
tal and vertical shear components of viscosity. Their ex- them having tilt angles in the range of 5◦−45◦. Hence, a
pression for the transition radius depends on the relative
large fraction (∼ 1/2) of such systems should be born as
strength of the dimensionless vertical shear viscosity pa-
candidates for the Bardeen-Pettersoneffect.
rameter, α :
1 In the other two mechanisms,which areunlikely except
24α1a∗ 2/3R , if α >δ, perhaps in globular clusters, a NS or BH must pass close
RBP =((cid:2)24δaδ∗2 2/(cid:3)3RGRGR, if α11 .δ. (3) eitnaotuiognhaltloyabnooutnhder. stHaerroertbhienacroyllasypssteedmsttaorbaencodmietsgnraevw-
Typical values for the viscosity parameters α and α , companion evolved separately until the time of their en-
(cid:2) (cid:3) 1
and the aspect ratio δ, are 0.04 . α . 0.2, α ∼ α, and counter. There is therefore no preferred orientation for
1
0.03 . δ . 0.3. These are based on numerical calcula- the angular momenta of the stars relative to the angular-
tions (e.g.Nelson& Papaloizou1999;Brydenetal.1999). momentum axis of the forming binary. Hence the major-
In hydrodynamic simulations Nelson & Papaloizou(2000) ityofsuchsystemswouldalsobeBardeen-Pettersoneffect
foundthetransitionradiustolieconsistentlybelowthean- candidates.
alytic estimates in equation3 by a factor of ∼2−3. This Thus, it appears likely that many, if not most, X-ray
correction is included in the following analysis, although binariesformwithmisalignedangularmomenta(one such
it does not qualitatively change the results. observed system is discussed in Section 4).
Bardeen-PettersonEffect in X-Ray Binaries 3
3.2. Alignment Timescale The black-hole binary GRO J1655-40 is a very impor-
tant target for studies such as this one since many of
Since the Bardeen-Petterson effect causes the accretion
therelevantsystemparametershavebeenmeasuredorin-
flowtolieintheequatorialplaneoftheaccretingbodyout
ferred. Thereisalsoevidencethattheangular-momentum
to a disk radius of R , the materialactually accretedby
BP axisoftheblackholeinthissystemisnotalignedwiththe
the stellar remnant will not change the orientation of the
angular momentum of the binary.
remnant’s angular momentum. However, as pointed out
The observational constraints on the orientation of this
by Rees (1978), the torque exerted by the BH or NS as it
systemaresummarizedinFigure2. Orosz&Bailyn(1997)
aligns the disk withits ownspinaxis alsohas the effect of
found the inclination of the binary orbit of this partially
aligningthe BHorNSwiththe angularmomentumofthe
eclipsing system to be i=69◦.5±0◦.1 (measured from the
disk. A number of authors have addressed this issue (e.g.
planeofthesky). Thismeansthattheangular-momentum
Rees 1978; Scheuer & Feiler 1996; Natarajan & Pringle
axis of the binary, J , is tilted by the same amount
1998), particularly with respect to misaligned accretion binary
from the line-of-sight of an observer. However, the ori-
disks around black holes. The alignment angle decreases
entation of the binary orbit (i.e. position angle) in the
exponentially with a characteristictimescale, t , given
align sky is not known. Thus, J is only constrained to
by (Scheuer & Feiler 1996): binary
lie somewhere on a 69◦.5 cone about the line-of-sight as
M 2R 1/2 shown in Figure 2. Hjellming & Rupen (1995) observed
talign ≈3a∗M˙ (cid:18) RBGPR(cid:19) , (6) tpwoositheigshidlyescoolflitmhaistesdourreclaetdivuisrtinicgjaetspeerxipoadnodfinhgarfrdomX-orapy-
where M˙ is the mass accretion rate through the disk. For activity (Harmon et al. 1995). The position angle on the
illustration, we consider a 1.4 M⊙ NS and a 7 M⊙ BH, skyofthe approachingjetwas47◦±1◦ andits inclination
each with a∗ = 0.1 and A = 100. We derive a lower was i=5◦±2◦ (i.e. almost in the plane of the sky). This
limit for talign by setting M˙ at the respective Eddington means that the axis through the center of the radio jets
accretion limits. These values give minimum alignment was tilted with respect to J by between 15◦.5 and
binary
timescales of3×106 yr and7×106 yr,respectively. How- 90◦ as illustrated in Figure 2. Depending on the model
ever, a more realistic long-termaccretionrate for LMXBs used to describe the radio jets, their orientation should
is M˙ = 0.01M˙ (van der Klis 1995). This gives align- reflect the angular momentum axis of either the BH or
Edd
ment timescales comparable to the estimated lifetime of the inner accretion disk. On the other hand, the orien-
X-ray binaries [108 −109 yr (Verbunt & van den Heuvel tation of the binary orbit should define the orientation of
1995)]. These long timescales for alignment imply that the outer accretion disk. Altogether this implies that the
the typicaldistribution of tilt angles in LMXBs should be outer accretion disk is probably tilted with respect to the
close to the distribution estimated by Brandt & Podsiad- equatorial plane of the black hole by between 15◦.5 and
lowski(1995)forLMXB formation. Thus, alargefraction 90◦. ThismakesGROJ1655-40astrongcandidateforthe
(∼ 1/2) of LMXBs may be candidates for observation of occurrence of the Bardeen-Pettersoneffect.
the Bardeen-Pettersoneffect. In order to estimate the Bardeen-Petterson transition
radius using equation 4, we need to know the mass and
3.3. X-Ray Modulation Mechanism angular momentum of the BH. Optical investigations of
We nowwishto considerpossible mechanismsby which the binary give a mass of MBH = 6.7±1.2M⊙ (Orosz &
Bailyn 1997; Shahbaz et al. 1999). Modeling of the X-
the Bardeen-Petterson effect could generate observable
ray spectra from this system (Sobczak et al. 1999) gives
QPOs. WebeginwiththefindingsofNelson&Papaloizou
(2000) that for moderate angles (θ & 30◦) between the a probable angular momentum of a∗ ≈ 0.5, with an up-
disk mid-planes, the inner and outer accretion disks are per limit of a∗ <0.7. Other authors, however,give values
nearly disconnected. For larger angles, the separation be- as high as a∗ = 0.95 (Cui, Zhang, & Chen 1998). More-
tween the two disks becomes even more pronounced. In over, the exact value of a∗ is not critical to our conclu-
sions. We simply require an upper limit, which we take
such cases, accretion between the outer and inner disks
presumably occurs along a tenuous bridge of material or as a∗ . 0.95. This gives us an upper limit on the tran-
sition radius of R . 290R , based on our adopted
in the form of gas clumps that periodically break off from BP GR
constraintsonthescalingparameterA. The physicalcon-
the outer disk and collide with the inner disk. Whether
straintthatthetransitionregionlieoutsidethe innermost
accretiontakes place alonga bridge or in discrete clumps,
stablecircularorbitgivesusafirmlowerlimitonthetran-
there is likely to be significant shock heating at the point
sition radius of R &6R for a non- or slowly-rotating
where this accreting material impacts the inner disk. As BP GR
BH. The resultant range is 6R .R .290R or 60
the shock-heated gas continues to orbit the BH or NS, it GR BP GR
km . R . 2900 km. We caution, however, that these
maygenerateperiodicbrightnessoscillationsattheorbital BP
frequencyforthatradius. Weexpectthisradiustoliejust estimatesofMBH anda∗ derivefrommodelsthathaveas-
sumedasinglecontinuousaccretiondisk,whereaswehave
insidetheBardeen-Pettersontransitionradius,sothatthe
shown that the Bardeen-Petterson effect creates an inner
QPO frequency should be very close to the Keplerian or-
bital frequency given in equation 5. Using θ & 30◦ as a andouterdiskcomponentinclinedrelativetooneanother.
This point may require further analysis, however the size
guide, we may expect ∼ 30% of LMXBs to be suscepti-
ofthe inner accretiondisk is extremelysmallcomparedto
ble to this mechanism based on the tilt-angle distribution
theestimatedsizeoftheouteraccretiondisk[4.2×106km
predicted by Brandt & Podsiadlowski(1995).
(Orosz & Bailyn 1997)],so that this correctionis likely to
4. gro j1655-40 be small.
4
TherangeofKeplerianfrequenciescorrespondingtoour it is only present during some observations but is mostly
derived range of R is 1 Hz . ν . 300 Hz. This absent. This transient behavior is presumably related to
BP Kep,BP
range of frequencies is consistent with three of the four the accretiondynamics,e.g. in our model, whether or not
QPOsobservedinGROJ1655-40(Remillardetal.1999b): clumps happen to be crossing the transition region dur-
the variable 14-28 Hz QPO and the relatively stable 9 ing an observation. Hopefully this aspect can be better
and 300 Hz QPOs. However, identification of the 300 Hz understood with future hydrodynamic simulations.
QPO with the Bardeen-Pettersontransition radius would AmongNSLMXBs,low-coherencyQPOsarefairlycom-
require that the transition region lie just outside the in- mon. However, the combination of low coherency and
nermost stable circular orbit, which would make it diffi- count-rateindependence seemstobemostconsistentwith
cult for an inner, aligned disk to form. It seems more the∼100Hzpeaked-noiseorLorentziancomponent. This
likely that the Bardeen-Petterson effect might be associ- 100 Hz feature was first identified in 4U 1728-34 (Ford &
ated with either the 9 Hz or the 14-28 Hz QPO. This vanderKlis1998). IthasbeenextensivelystudiedinSAX
conclusion seems to be supported by the spectral model- J1808.4-3658 by Wijnands & van der Klis (1998). These
ing of Remillard et al. (1999b), who identified the 300 Hz authors were also the first to identify a similar feature
andthe 14-28Hz QPOswiththe power-lawcomponentof in 4U 0614+09 (based on observations by M´endez et al.
their model rather than the disk component. Only the 9 1997)and4U1705-44(basedonobservationsbyFordetal.
Hz QPO appeared to have the X-ray spectral characteris- 1998). Similar features have also been found in 4U 1820-
ticsexpectedforapurelydisk-basedoscillation(Remillard 30 (Wijnands, van der Klis, & Rijkhorst 1999), Terzan 2
etal.1999b). Hence,wetentativelyidentifythe9HzQPO (Sunyaev&Revnivtsev2000),andGS1826-24(Sunyaev&
in GRO J1655-40 as perhaps the best potential observa- Revnivtsev2000). These observationsmayimply thatthe
tionoftheBardeen-PettersontransitionradiusinanX-ray 100 Hz feature is fairly common in LMXBs. This might,
binary. However,thereisanongoingdebateastowhether however,become aconcernifthis featureprovesto be too
the9HzQPOisdefintelydisk-relatedandtheotherQPOs common to be consistent with the likely occurence of the
are not. Hence, it is premature to definitively exclude the Bardeen-Pettersoneffect.
14-28 or the 300 Hz QPOs as possible candidates. Irrespective of all this, we argue that the Bardeen-
PettersonmechanismshouldproduceQPOsofsimilarfre-
5. neutron star x-ray binaries quency in all NS LMXBs since all NS systems are charac-
teristically very similar. We have already argued that the
For neutron-star X-ray binaries, the parameter space NS masses are similar (MNS ≈1.4M⊙). Furthermore, in-
available is much narrower than for black-hole binaries. terpretationofthenearly-coherentoscillationsseenduring
Both the mass and the angular momentum of NSs are Type I X-raybursts in ten NSLMXBs arguefor anarrow
tightly constrained by theory and observation. Models range of angular momenta for the NSs in these systems
for the NS equation of state give the following upper (see, e.g. Strohmayer 2001). The two remaining parame-
limits (Salgado et al. 1994, Cook, Shapiro, & Teukol- ters in the estimates of the Bardeen-Petterson transition
sky 1994): MNS . 2.6M⊙ and a∗,NS . 0.7. Observed radius, the viscosity and the disk aspect ratio, are pre-
radio pulsars in binary systems are all consistent with sumably similar in all LMXBs since the accretion mech-
1.35M⊙ ≤ MNS ≤ 1.45M⊙ (Thorsett & Chakrabarty anism (Roche-lobe overflow) is assumed to be the same.
1999). If we consider these upper limits of MNS, a∗,NS, In this context, it is interesting that ∼100 Hz QPOs may
and the parameter A, then we can use equation 5 to be quite common among NS LMXBs. This frequency is
set a lower limit for the Bardeen-Petterson orbital fre- alsocomfortablywithintherange(3-1700Hz)expectedfor
quency in NSs: νKep,BP & 3 Hz. The upper limit for the the Bardeen-Petterson effect in NSs, as calculated above.
Bardeen-Pettersonorbitalfrequencyisfixedbytheorbital Therefore,allofthe parameterscanassumetypicalvalues
frequency at the inner edge of the accretion disk. For a if the 100 Hz QPO is triggered by the Bardeen-Petterson
putative 1.4 M⊙ NS with a∗ = 0.1, the orbital frequency effect.
at the innermost stable circular orbit is ≈ 1700 Hz. This For now, the association of the 100 Hz feature in NS
range of frequencies (3−1700Hz) is consistent with most LMXBs with the 9 Hz QPO in GRO J1655-40 is just a
of the QPOs observed in NS LMXBs. In Z-sources, it is suggestion. Other authors have suggested different asso-
consistent with the normal/flaring and horizontal branch ciations. For instance, based on a possible correlationbe-
oscillations and kHz QPOs. In atoll sources, it is con- tween the 9 Hz and the 300 Hz QPO in GRO J1655-40,
sistent with the low frequency QPOs, the peaked noise Psaltis, Belloni, & van der Klis (1999) suggest that these
components, and the kHz QPOs. two QPOs are similar to the following QPO pairs seen in
However, in order for the Bardeen-Petterson effect to othersystems: the ≃10−50Hz andthe lowerkHz QPOs
be a consistent interpretation, we should expect all the in 4U 1728-34 and 4U 1608-52 and the ∼ 0.08−13 Hz
QPOs associated with this effect to show similar proper- and ∼ 160−220 Hz QPOs in XTE J1550-564. However,
ties. Tentatively adopting the 9 Hz QPO in GRO J1655- these authors acknowledge that these identifications are
40as ourmostlikelyexample,we canuseit asa template very tentative and must be scrutinized carefully.
with which to identify other Bardeen-Pettersongenerated
QPOs. Toward this end, this QPO has at least two note-
6. discussion
worthy features: It has a relatively low coherence param-
eter (Q = ν/∆ν < 3) and its frequency appears to be Positive association of a QPO in a LMXB with the or-
independent of the count rate in the detector (Remillard bitalfrequencyattheBardeen-Pettersontransitionradius
etal.1999b),thoughthisconclusionisbasedononlyafew could provide important constraints on the mass and an-
observations. Anotherpeculiarfeatureofthe QPOis that gular momentum of the accreting body and possibly the
Bardeen-PettersonEffect in X-Ray Binaries 5
thickness and tilt of the accretion disk. Careful study of frequency QPO when applied to individual neutron-star
the properties of such a QPO could also provide informa- LMXBs.
tionaboutthegasdynamicsnearthetransitionradiusand We are currently undertaking the task of studying the
the role of the accretion rate in this model. Furthermore, Bardeen-Pettersoneffectnumericallytofollowthedynam-
identification of such QPOs in several LMXBs could pro- icsofthegasnearthetransitionradius. Theresultsofthis
vide information about the relative abundance of tilted studyshouldprovidefurtherinsightintothevalidityofthe
accretiondisk systems, whichis importantin understand- model we have proposed here.
ing their formation and evolution.
We have argued that the Bardeen-Petterson effect may
be a common phenomenon in LMXBs and that it pro- The authors wish to thank the referee for numerous
vides a plausible physical explanation for at least some helpfulsuggestionsandCharlesBailynforhishelpinclar-
observed quasi-periodic brightness oscillations. The esti- ifying the relative orientationof the radio jets and the bi-
matesofourmodelareconsistentwitha1-300HzQPOin nary orbitof GRO J1655-40. P. C. F. would like to thank
the black-hole X-ray binary GRO J1655-40. This system the Arthur J. Schmidt Foundation for fellowship support
is animportanttestsince itappearslikely tohaveatilted at the University of Notre Dame. This work was sup-
accretiondiskaroundarapidly-rotatingBH.Wehavealso ported in part by the National Science Foundation under
argued that this mechanism could generate a moderate- grant PHY-97-22086.
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6
1 2 3 4 5
Fig. 1.— Schematic diagram of the Bardeen-Petterson effect showing: (1) the central rotating black hole or neutron star; (2) the inner,
alignedaccretiondisk;(3)thetransitionregion;(4)theouter,tiltedaccretiondisk;and(5)thecompanionstar.
47ο ΝΕ
∆Dec
5o
47o
θ
J ∆RA
To 69.5o
Observer
Fig. 2.—Illustrationoftherelativeorientation between theradiojetsandthe binaryangularmomentum axis,J,ofGROJ1655-40. The
observed orientation of the radio jets is shown by the dashed cones (Hjellming & Rupen 1995). J is restricted to lie on either of two 69◦.5
conesaboutthelineofsightoftheobserver(Orosz&Bailyn1997),asshownbythesolidcones. Thetiltangle,θ,betweentheradiojetsand
J isbetween 15◦.5and90◦.