A precessing warped accretion disk around the X-ray pulsar Her X-1

0.22 MB·English

by  D. Klochkov

Proceedingsofthe363.WE-HeraeusSeminaron:“NeutronStars and Pulsars”(Postersand contributedtalks)
Physikzentrum BadHonnef, Germany,May.14−19,2006, eds.W.Becker,H.H.Huang, MPEReport291,pp.212-215
A precessing warped accretion disk around the X-ray pulsar
Her X-1
D. Klochkov1, N. Shakura2, K. Postnov2, R. Staubert1, and J. Wilms1,3
1 Institut fu¨r Astronomie undAstrophysik,University of Tu¨bingen, Sand1, 72076 Tu¨bingen, Germany
2 SternbergAstronomical Institute, 119992, Moscow, Russia
7 3 Department of Physics, Universityof Warwick, Coventry,CV8 1GA, UK
0
0
2

n Abstract. We have performed an analysis and interpre- Shakura et al. 1999 where dips are produced by the ac-
a tationoftheX-raylightcurveoftheaccretingneutronstar cretion stream and wobbling outer parts of the accretion
J
Her X-1 obtained with the ASM RXTE over the period disk.
9
1996 February to 2004 September. The averaged X-ray The analysis of Her X-1 observations obtained with

light curves are constructed by means of adding up light the All Sky Monitor (ASM) on board of the Rossi X-ray
2
v curves correspondingto different 35 day cycles.A numer- Timing Explorer (RXTE) satellite (see Bradt et al. 1993)
0 ical model is introduced to explain the properties of the which cover more than 90 35d cycles allowed to improve
9 averaged light curves. We argue that a change of the tilt the statistics ofthe averagedX-raylightcurveof HerX-1
7
of the accretion disk over the 35d period is necessary to with respect to previous analysis (Shakura et al. 1998a,
2
account for the observed features and show that our nu- Scott & Leahy 1999, Still & Boyd 2004). In addition to
1
6 mericalmodelcanexplainsuchabehaviorofthediskand well-known features (pre-eclipse dips and anomalous dips
0 reproduce the details of the light curve. duringthefirstorbitafterX-rayturn-on)theaveragedX-
/ raylightcurveshowsthatanomalousdipsandpost-eclipse
h
p recoveries are present for two successive orbits after the
- turn-on in the short-on state. These details have already
o 1. Introduction
been reported by Shakura et al. 1998a, but statistics was
r
t Her X-1/HZ Her is a close binary system with a 1.7d poorandtheauthorshavenotreproducedthemwiththeir
s
a orbital period containing an accretion powered 1.24s X- model.
:
v raypulsar(Giacconi et al. 1973,Tananbaum et al. 1972). In this work we substantially improve the numerical
i The X-ray flux of the source shows a ∼35d periodicity model presented by Shakura et al. 1999. Now it accounts
X
which is thought to be due to a counter-orbitallyprecess- for the dynamical time scale of the disk and includes ex-
r
a ing tilted accretion disk around the neutron star which plicit calculations of the precession rate at each phase of
mostlikelyhasatwistedform(Gerend & Boynron1976). the 35d period. The inclination of the disk is allowed to
The35dcyclecontainstwoonstates(highX-rayflux) change during the 35d cycle.
– the main-on and the short-on – separated by ∼7-8d With the improved model we reproduce all details of
interval of low X-ray flux – off state. the averaged light curves including those which were left
According to the generally accepted model the main- unexplained previously.
on state starts when the outer disk rim opens the line of
sight to the source.Subsequently, at the end of the main-
2. Observations
on state the inner part of the disk covers the source from
the observer. For the analysis of the X-ray light curve of Her X-1 we
An interesting feature of the X-ray light curve are the use data from the ASM (Levine et al. 1996). The archive
X-ray dips (Shakura et al. 1999 and references therein), contains X-ray flux measurements in the 2-12 keV band,
whichcanbeseparatedintothreegroups:pre-eclipse dips, averaged over ∼90 s. The monitoring began in February
which are observed in the first several orbits after X-ray 1996 and continues up to date. The archive is public and
turn-on, and march from a position close to the eclipse accessible on the Internet 1.
toward earlier orbital phase in successive orbits; anoma-
Preliminary processing of the X-ray light curve
lous dips, which are observed at φ = 0.45−0.65 and
orb was carried out by the method described by
post-eclipse recoveries, which areoccasionallyobservedas
Shakura et al. 1998a. The goals of this processing
ashortdelay(uptoafewhours)oftheegressfromtheX-
are the reduction of the dispersion of the flux through
rayeclipseinthefirstorbitafterturn-on.Ageneralmodel
explaining all types of X-ray dips has been suggested by 1 http://xte.mit.edu/asmlc/srcs/herx1.html
D. Klochkov et al.: A precessing warped accretion disk around theX-ray pulsar HerX-1 213
10
8 Post−eclipse recoveries
ec] 6
unts/s 4
o
ux [c 2
Fl
0
−2
Anomalous dips
8
ec] 6
unts/s 4
o
ux [c 2
Fl
0
−2
Fig.2. 3-20 keV PCA light curve of Her X-1 during a
0 5 10 15 20 25 30
Days short-on state.
Fig.1. Averaged X-ray light curves of Her X-1 cor-
responding to cycles with turn-ons near orbital phase
∼0.2 (top) and ∼0.7 (bottom). Vertical lines show X-ray 3. The model
eclipses.
As mentioned in the Introduction, it is believed that the
alternation of the On and Off states is caused through
shadowingby acounter-orbitallyprecessingtilted twisted
accretion disk. In our model (Shakura et al. 1999) pre-
rebinning, resulting in a smoothed light curve, and the
eclipse dips occur when the accretion stream crosses the
determination of the turn-on time of each individual
observer’s line of sight before entering the disk. This can
35day cycle, with the aim to classify the cycles into two
happen only if the stream is non-coplanar to the systems
classes: turn-on around orbital phase ∼ 0.2, and turn-on
orbital plane. The reason for the stream to move out of
aroundorbitalphase∼0.7(theyappearwithaboutequal
theorbitalplaneisnon-uniformX-rayheatingoftheopti-
probability).
calstarsatmosphereby the X-raysource,whichproduces
UsingtheRXTE/ASM(with∼5cts/sfromHerX-1in
a temperature gradient near the inner Lagrange point.
the main-on) details cannot be explored in individual 35
The non-uniformity of the heating comes from the par-
daycycles.However,if weconstructaveragedlightcurves
tial shadowingof the opticalstar surface by the accretion
through superposition of many 35d light curves common
disk. Furthermore, such a stream forces the outer parts
details (e.g. X-ray dips, post-eclipse recoveries) become
of the accretion disk to be tilted with respect to the or-
recognizable.
bital plane. The tidal torques cause the disk to precess in
This has been done e.g. by Shakura et al. 1998a, the direction opposite to the orbital motion. Due to tidal
Scott & Leahy 1999,Still & Boyd 2004.TheASMarchive torques and the dynamical action of the accretion stream
has grown considerably, allowing to construct averaged the outer parts of the disk develop a notable wobbling
light curves with smaller dispersion than in previous (nutational) motion twice the synodal period. For an ob-
works. server,theX-raysourcecanbescreenedbytheouterparts
Asmentionedabove,inmostcasesturn-onsoccurnear ofthediskforsometimeduringthefirstorbitaftertheX-
orbital phases 0.2 and 0.7. Thus all 35d cycles have been ray turn-on. This causes anomalous dips and post-eclipse
dividedintotwogroups–withtheturn-onnearφorb =0.2 recoveries.
and near φ = 0.7. Inside each group the light curves
orb
weresuperposedandaveraged,aftershiftingtheminsuch
3.1. Numerical calculations of the disk motion
a way that the eclipses coincided. The superposed light
curves are shown in Fig. 1. The method of calculation of the disk motion under the
In the short-on state complicated dip patterns can be actionoftidalforcesandtheaccretionstreamisdescribed
observed. Anomalous dips near orbital phase φ = 0.5 by Shakura et al. 1999. The disk was approximated by a
orb
and post-eclipse recoveries are present on two succes- solid ring with the radius equal to the outer radius of the
sive orbits after the beginning of the short-on state. This disk.Theinclinationofthediskwithrespecttotheorbital
can also be seen in one individual short-on observed by plane was assumed to be constant. Under these assump-
RXTE/PCA shown in Fig. 2 (see also Leahy et al. 2000, tions the dynamical time scale of the disk t = M /M˙
d d
Oosterbroek et al. 2000, Inam & Baykal 2005). (where M and M˙ are the mass of the disk and the ac-
d
214 D. Klochkov et al.: A precessing warped accretion disk around theX-ray pulsar HerX-1
cretion rate correspondingly) which characterizes the dy- features are observedonly during one orbit after turn-on.
namicalactionofthestreamturnedouttobesignificantly We failed to reproduce the observed behavior assuming
shorter than the viscous time scale which leads to incon- constantinclinationofthe disk.The observationsimply a
sistency. Also this model failed to explain some details generic asymmetry between the beginning of the main-on
of the averaged light curve, namely, anomalous dips and and short-on states. This asymmetry can take place only
post-eclipse recoveries on two orbits after the secondary if the disk tilt θ changes with precessional phase.
turn-on. The physical reason for this could be the periodic
In this work the model is substantially improved. In change of the mass transfer rate from the inner Lagrange
order to reconcile the dynamical and viscous time scales point into the disk. If free precession of the neutron
ofthediskweintroducetwocharacteristicradii:theouter star is ultimately responsible for the 35-day cycle in Her
radius of the disk r ∼ 0.3a which determines the tidal X-1 (Brecher 1972, Tru¨mper et al. 1986, Shakura 1995,
out
wobbling amplitude, and the effective radius r ∼ 0.18a Shakura et al. 1998b), the conditions of X-ray illumina-
eff
whichdetermines the meanprecessionmotionofthe disk. tion of the optical stars atmosphere will periodically
Thevalueofthiseffectiveradiusisfoundfromtherequire- change with precession phase. This in turn will lead to
ment that the net precession period of the entire disk be changes in the velocity components of the gas stream
equal to the observed value 20.5P and the dynamical in the vicinity of the inner Lagrangian point and hence
orb
time scale t = M /M˙ (which characterizes the dynam- in the matter supply rate to the accretion disk. Re-
d d
ical action of the stream) be 10 days. This value for the cently, X-ray pulse profiles evolution with the 35d phase
dynamicaltimeischosentobeoforderoftheviscoustime was successfully reproduced both in the main-on and
fromtheimpactradius∼0.1awhichisaround10daysand short-on states in the model of freely precessing neu-
scales as r−3/2. tron star with complex surface magnetic field structure
The inclination of the disk is allowed to change with (Ketsaris et al. 2000, Wilms et al. 2003).
the precessionalphase.It requires that the rate of preces-
sionwas calculatedfor eachprecessionalphase separately
4. Results
since it depends on the disk inclination.
It is important to note that the region of the disk be- Thephysicalpictureofthechangeofthediskstiltadopted
yondr ,whereisnomattersupply(calledthe“thestag- hereisasfollows.TherateofmasstransferM˙ suppliedby
imp
nationzone”)andwhichmediatestheangularmomentum HZ Her (which for a given moment can be different from
transfer outwards for accretion to proceed, can react to the accretionrate of the neutron star because the viscous
perturbations induced by the stream impact much faster timescaleformasstransportthroughthediskbothdelays
than on the viscous time scale. Indeed, in a binary sys- andsmoothesthemassflow)changesperiodicallyoverthe
tem, tidal-induced standing structures can appear in the precession cycle in response to changing illumination of
outerzoneoftheaccretiondisk(seee.g.Blondin 2000and the optical star atmosphere due to free precession of the
references therein) and perturbations of angular momen- neutron star. The streams action causes the outer disk to
tum can propagate through this region with a velocity precess slower than it would do if only tidal torque was
closeto the soundspeed(while the matter will accreteon acting, and it also changes the outer disk’s tilt on the
the much slower viscous time scale!). Recent analysis of dynamical time scale of about 10 days (see above), which
broad-band variability of SS 433 (Revnivtsev et al. 2005) issufficienttoexplainperiodicdisktiltvariationsoverthe
suggests that such a picture is realized in the accretion precessioncycle.The wobblingofthe outer diskis mainly
disk in that source. So the entire disk (inside and beyond due to tidal forces (the dynamical action of the stream
r ) reacts to changes in the mass transfer rate through providesminorcontribution).Theviscoustimescaleinthe
imp
the accretion stream on a time scale not longer than the “stagnation zone” is much longer, so the viscous torques
viscous time scale of the disk from the impact point (i. e. cannot smooth out the external disk variations.
∼10 days). Figure 3 shows the result of modeling of the disk mo-
tion.Theangleǫ(verticalaxis)istheanglebetweenthedi-
rectionfromthecenteroftheneutronstartotheobserver
3.2. Evidence for a change in the tilt of the disk
and to the outer parts of the accretion disk with non-
The fact that during the short-on state of Her X-1 more zero thickness. The complex shape of the disks wobbling
absorption dips appear on the averagedX-ray light curve is clearlyseen.The sine-likedashedcurveshowsschemat-
(the anomalous dips and post-eclipse recoveries during ically the same angle for the inner accretion disk regions
two successive orbits of the averaged short-on) as well as which eclipse the X-ray source at the end of on-states.
in an individual short-on observed by PCA (Fig. 2 and The horizontal line is the observer’s plane and the verti-
Inam & Baykal 2005) suggests that the angle ǫ between cal dashed lines mark centers of the binary eclipses. The
the disk and the line of sight remains close to zero dur- main-on and short-on states are indicated. The source is
ing the first two orbits after the turn-on in the short-on screenedbythediskwhentheobserverisinthe darkarea
state.This isincontrastto themain-onstate,wheresuch orbetweenthisareaandtheinnerdiskline.Itisseenthat
D. Klochkov et al.: A precessing warped accretion disk around theX-ray pulsar HerX-1 215
appearanceofthesefeaturesandtheobservedduration
of the main-on and short-on states.
Acknowledgements. In this research we used data obtained
through the High Energy Astrophysics Science Archive Re-
searchCenterOnlineService,providedbytheNASA/Goddard
SpaceFlightCenter.WethankA.Santangeloforusefuldiscus-
sion.TheworkwassupportedbytheDFGgrantSta173/31-2
and436RUS113/717/0-1 andthecorrespondingRBFRgrant
RFFI-NNIO-03-02-04003. KP also acknowledges partial sup-
port through RFBR grant 03-02-16110.
WegratefullyacknowledgethesupportbytheWE-Heraeus
foundation.
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