Misalignment of the microquasar V4641 Sgr (SAX J1819.3--2525)
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Misalignment of the microquasar V4641 Sgr (SAX J1819.3–2525)
Rebecca G. Martin, Rubens C. Reis and J. E. Pringle
Institute of Astronomy, Madingley Road, Cambridge CB3 0HA
30 October 2018
ABSTRACT
In the microquasar V4641 Sgr the spin of the black hole is thought to be misaligned withthe binary orbital axis. The accretion disc aligns with the black hole spin by the Lense-Thirringeffect near to the black hole and further out becomes aligned with the binary orbital axis. Theinclination of the radio jets and the Fe Kα line profile have both been used to determinethe inclination of the inner accretion disc but the measurements are inconsistent. Using asteady state analytical warped disc model for V4641 Sgr we find that the inner disc regionis flat and aligned with the black hole up to about R g . Thus if both the radio jet andfluorescent emission originates in the same inner region then the measurements of the innerdisc inclination should be the same. Key words:
X-rays: Binaries– X-rays: individual V4641 Sgr – accretion, accretion discs
Microquasars are binary systems in which material is accreted froma normal star on to a compact object. They differ from typical X-ray binaries by the strong presence of a persistent or episodic ra-dio jet (Mirabel & Rodr´ıguez 1999). The compact object is usu-ally associated with a neutron star or a stellar mass black hole.To date there are over fifteen microquasars for which the com-pact object has been dynamically confirmed to be a stellar massblack hole (Orosz 2003). However, only four of these systems havewell resolved relativistic radio jets (XTE J1550–564, GRO J1655–40, GRS 1915+105 and V4641 Sgr, Garcia et al. 2003).It is usually assumed that the inclination of the jet axis isperpendicular to that of the orbital plane of the binary. However,it has been shown by Maccarone (2002) and more recently byMartin, Tout & Pringle (2008) that the alignment time-scale in mi-croquasars is usually a significant fraction of the lifetime of the sys-tem. If the black hole in such microquasars were formed with mis-aligned angular momentum, as expected from supernova-inducedkicks, then it would be likely that the system would remain mis-aligned for most of its lifetime.Precise measurements of both the orbital plane and jet in-clination are known for two systems. GRO J1655–40 is a micro-quasar thought to contain a rapidly rotating black hole (Zhang et al.1997; Reis et al. 2008a) with a mass constrained to be largerthan . ⊙ (Orosz & Bailyn 1997). Hjellming & Rupen (1995)measured a jet inclination of ◦ ± ◦ to the line-of-sight andit is thus misaligned by at least ◦ to the orbital plane, withan inclination of . ◦ ± . ◦ (Greene, Bailyn & Orosz 2001).Martin, Tout & Pringle (2008) presented a detailed investigation ofthe alignment timescale of this system and found that it is consis-tent with the lifetime of the secondary star. V4641 Sgr was discovered as an X-ray source independentlywith the Wide Field Cameras on BeppoSAX on 1999 February20 (in’t Zand et al. 1999) and with the Proportional Counter Ar-ray on the
Rossi X-ray Timing Explorer ( RXTE ) on 1999 Febru-ary 18 (Markwardt, Swank & Marshall 1999). Spectroscopic ob-servations made between 1999 September 17 and 1999 October16 led to a mass function f ( M ) = 2 . ± .
12 M ⊙ (Orosz et al.2001). From the lack of X-ray eclipses, combined with the largeamplitude of the folded light curve, they deduced an orbital in-clination angle in the range ◦ i orbit ◦ . and mass . M BH .
70 M ⊙ for the compact object. Radio obser-vations of V4641 Sgr (Hjellming et al. 2000) made during the 1999September outburst found the jet expanding at apparent superlumi-nal velocities with a proper motion ranging between . ′′ − ′′ per day. Based on the radio information, Orosz et al. (2001) sug-gested that that the jet must be highly beamed and have an inclina-tion along the line-of-sight of i jet ◦ . This differs significantlyfrom from the inclination of the binary orbital axis.X-ray spectral analysis made on BeppoSAX observations ofV4641 Sgr (in’t Zand et al. 2000) revealed the presence of a strongFe Kα emission with an equivalent width between 0.3 and 1 keV .They interpreted this as fluorescent emission using a photo-ionizedmedium. The presence of this Fe fluorescent emission was laterconfirmed by Revnivtsev et al. (2002) from a collection of RXTE data. They found an emission line at about . with an equiv-alent width of about
360 eV . A more recent analysis of the sourcewith
RXTE data obtained during the outburst of 2003 August 5–17 (Maitra & Bailyn 2006) showed the presence of both a strongFe Kα fluorescent emission line near 6.5 keV and a character-istic Compton hump at about
20 keV . If these features are at-tributed to the reprocessing of a hard X-ray (powerlaw) contin-uum by cold matter in an accretion disc (Reynolds & Nowak 2003; c (cid:13) R. G. Martin, R. C. Reis and J. E. Pringle
Reynolds & Fabian 2007) then the degree of broadening observedimplies that the emitting region is very close to the black hole. Theshape of the line profile can then give an indication of both the theradius of the emitting material from the black hole as well as the in-clination of the inner accretion disc (Fabian et al. 1989; Laor 1991).In this way Miller et al. (2002) obtained an estimate for the inclina-tion of the innermost part of the accretion disc of ◦ ± ◦ ( confidence). V4641 SgrThe orbit of V4641 Sgr is thought to be misaligned with the axis ofthe jet by about ◦ . The black hole was formed from a supernovawhich probably gave a kick to the black hole. Even a small veloc-ity kick can lead to a large misalignment between the spin axis ofthe black hole and the binary orbital axis (Brandt & Podsiadlowski1995).The intermediate inclination angle found from the Fe Kα line profile prompted the suggestion of a hierarchy of inclinations(Butt, Maccarone & Prantzos 2003) with i orbit = 65 ◦ ± ◦ greaterthan i innerdisc = 43 ◦ ± ◦ which is greater than i jet ◦ . TheBlandford & Znajek (1977) mechanism for jet formation uses therotational energy of a rapidly spinning black hole. Relativistic jetsare formed in the inner parts of the accretion disc at around R g (Nishikawa et al. 2005) and so must be perpendicular to the innerdisc. The gravitational radius is defined as R g = GM BH c = 1 . × „ M BH . ⊙ « cm . (1)Unless the mechanism for jet formation is very different, we expectthat the jet formation region of the inner disc is at an inclination ofless than ◦ .This is hard to reconcile even with the huge uncertainties inthe measurement of the inclination of the inner disc from the profileof the Fe Kα line (Miller et al. 2002). The inclinations as measuredby these two independent techniques, the Fe Kα and radio jets, arefound to differ by at least ◦ − ◦ − ◦ = 18 ◦ if we take thelower limit for the inner disc inclination. A warp in an accretion disc around a spinning black hole is drivenby Lense-Thirring precession. Evidence for this effect, that leadsto a warped accretion disc, can be seen in NGC 4258 where thedisc can be observed by maser emission (Martin 2008). How-ever, in the case of V4641 Sgr we cannot observe the disc di-rectly. The inner parts of the disc align with the black hole bythe Bardeen & Petterson (1975) effect and the outer parts arealigned with the binary orbit because of the angular momentumwith which they accrete as well as tidal effects. Scheuer & Feiler(1996) found a steady state solution for the inclination of adisc warped by the Bardeen-Petterson effect by solving the discequations of Pringle (1992) for a disc of constant surface den-sity. Martin, Pringle & Tout (2007) generalised this to a power-law density distribution. We note that it is possible to havea microquasar which is still misaligned (e.g. GRO J1655-40,Martin, Tout & Pringle 2008) and so we do not need to go into thedetails of the stellar evolution here for this system.The luminosity of the source is L = 6 × − L EDD = 7 . × „ M ⊙ M BH « erg s − (2) (Miller et al. 2002) where L EDD is the Eddington Luminosity andso we find L = 7 . × erg s − with M BH = 10 . ⊙ . Theaccretion rate is ˙ M = Lǫc = 1 . × − M ⊙ yr − (3)where we take the accretion efficiency ǫ = 0 . . We use asteady state disc model with surface density Σ ∝ R − / (Shakura & Sunyaev 1973), where R is the radius in the disc. Thisis the outermost region (region c) of the Shakura & Sunyaev disc.The middle region (b) has Σ ∝ R − / and the steady state shapeof this disc would be almost identical to that of a disc in region c(Martin, Pringle & Tout 2007). The transition radius from region bto c is at R bc = 960 R g . Note that we have a different definition of R g to Shakura & Sunyaev (1973). The inner most region (a) of theShakura & Sunyaev disc has Σ ∝ R / but the transition radiusdoes not exist here and so the disc in V4641 Sgr has only regionsb and c. We also take ν and ν ∝ R / (Wijers & Pringle 1999)as used by Martin, Pringle & Tout (2007), where ν is the viscositycorresponding to the azimuthal shear and ν to the vertical shear.Martin, Tout & Pringle (2008) find the radius up to which theLense-Thirring effect dominates the viscous effects in the disc tobe R warp = 1 . × “ a . ” “ α ” − „ M BH . ⊙ « × „ ˙ M . × − M ⊙ yr − « − / cm , (4)where a is the dimensionless spin of the black hole and α is the di-mensionless viscosity parameter associated with the vertical shearin the disc. For stellar mass black holes there are only a few sourceswith determined spins which vary from about . to that of a max-imally rotating black hole (McClintock, Narayan & Shafee 2007;Reis et al. 2008b; Miller et al. 2008). We choose a = 0 . in themiddle of this range.The ratio of the warp radius to the gravita-tional radius of the disc is R warp R g = 912 “ a . ” “ α ” − „ M BH . ⊙ « × „ ˙ M . × − M ⊙ yr − « − / . (5)We note that this radius is far from the inner edge of the disc asdefined by the innermost stable circular orbit.The direction of the angular momentum of a disc annulus isgiven by l = ( l x , l y , l z ) with | l | = 1 . We let W = l x + il y where i = √− and find the warped disc profile for this model to be W = 2 sin( i orbit − i jet )Γ (2 /
7) ( − i ) (7 / / „ R warp R « / × K / √
27 (1 − i ) „ RR warp « − ! (6)(Martin, Pringle & Tout 2007) in the frame of the black hole. Theinclination of the disc at radius R is θ ( R ) = cos − ( l z ) = cos − ( p − | W ( R ) | ) . (7)In Fig. 1 we plot the inclination of the disc in the frame of the blackhole in V4641 Sgr. We see that the disc is flat and aligned withthe black hole out to a radius of about R warp , which in the caseof V4641 Sgr is about R g (equation 5). The region where theFe Kα line is emitted is likely to be within the innermost R g c (cid:13) , 000–000 isalignment of the microquasar V4641 Sgr (SAX J1819.3–2525) Figure 1.
The inclination in the frame of the black hole of a steady stateaccretion disc warped by the Lense-Thirring effect with Σ ∝ R − / and ν , ν ∝ R / which has a misalignment of ◦ between the jet and thebinary orbital axis (Fabian 2006) so the inclination measured by the Fe Kα method(Miller et al. 2002) should be the same as that of the innermost partof the accretion disc and should thus be the same as the inclinationof the radio jets which are formed up to around R g . In view of the discrepancy between the measured inclination an-gles of the innermost parts of the accretion disc by Fe Kα pro-file fitting and that of the radio jet, Butt, Maccarone & Prantzos(2003) suggested a hierarchical system of inclinations of the jet,inner disc and binary orbit. We have shown here that if both the jetand iron fluorescent emission originate from within about R g then their measured inclination should be the same. This impliesthat either the measured value from the jet, Fe Kα or both areinaccurate. It was suggested by Chaty et al. (2001) and later byNarayan & McClintock (2005) that the the inclination of the radiojet could in fact be as high as that of the orbital inclination. Thisuncertainty comes about because the precise time of the radio out-burst is still unknown. However, the general consensus is that theradio outbursts started at the same time as those of the X-ray andthus we get the limit on the inclination of the jet of less than ◦ .The iron emission line seen at . has been generally in-terpreted as that originating from a cold accretion disc. In this wayMiller et al. (2002) obtained an inclination of about 43 ◦ . However,Maitra & Bailyn (2006) have argued that the emission could origi-nate in a varying, optically thick cloud enshrouding the black hole.The strong broadening of the line would thus be attributed to thehighly dynamical environment and outflows. If this interpretationis correct then the inclination as measured by Miller et al. (2002) isirrelevant.We found that the warp radius in V4641 Sgr is around R g for a black hole with moderate spin and the accretion disc is aligned with the black hole almost up to this radius. Given the similaritybetween the evolutionary state of this system and GRO J1655–40we expect the spin of the black hole to be large. Even if the spinof the black hole is as low as a = 0 . and the accretion rate isas high as the Eddington accretion rate we find that R warp = 184 and the disc would still be essentially flat in this region. If the jet isemitted within this radius, as is generally believed, then we wouldexpect an agreement between the inclination of the jet and that ofthe inner disc as obtained from the iron line profile. However it ispossible that the warp radius is very much closer to the black holein the unlikely event that the spin of the black hole, a , is very small.In that case, different values for the inclination of the warped innerdisc could be expected. We find that, in the accretion disc in V4641 Sgr, the region thoughtto be both the origin of the jets and the emission site of the Fe Kα line is flat and aligned with the central black hole. Thus we wouldexpect the inclinations measured for the jets and with the Fe Kα line to be similar. Because there is a significant difference betweenthe two measurements we conclude that one or both of them mustbe inaccurate or our model incorrect. It is important that this systembe observed in more detail to resolve this in the near future. ACKNOWLEDGEMENTS
RGM and RCR thank STFC for financial support.
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