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X-Ray Binaries X-Ray Binaries Basic Properties ² generic system: a Roche-lobe ¯lling star (low-mass, massive, white dwarf) transfers matter to a compact Literature: companion (neutron star, black hole, [white dwarf]) ² An Introduction to Modern Astronomy, Carroll & ² traditionally two main classes: high-mass X-ray bina- Ostlie, Chapter 17 (good basic source) ries (HMXBs; M2 »> 10 M¯) and low-mass X-ray bina- < ² Black Holes, White Dwarfs and Neutron Stars, ries (LMXBs; M2 » 1:5 M¯) Shapiro & Teukolsky (more advanced, but good . missing intermediate-mass systems? source) . probably not: most systems classi¯ed as LMXBs ² \The Formation and Evolution of Compact X-Ray almost certainly originate from intermediate-mass Sources", Tauris & van den Heuvel, Online review X-ray binaries (IMXBs, 1:5 M¯ »< M2 »< 5 M¯), but (google astro-ph/0303456), almost up-to-date have already lost most/transferred most of their mass I. Types and Basic Properties High-Mass X-Ray Binaries II. Formation Channels ² relatively hard X-ray spectra: kT »> 15 keV III. Mass Transfer and Accretion ² type of variability: regular X-ray pulsations; no X-ray IV. Variability, X-Ray Bursts bursts V. Do Black Holes Exist? ² concentrated towards the Galactic plane, young age »< 107 yr VI. Ultraluminous X-Ray Sources ² optical counterparts: O, B stars with Lopt=LX > 1 High−Mass X−Ray Binaries Centaurus X−3 (2.1 days) Low-Mass X-Ray Binaries ² softer X-ray spectra: (kT »< 15 keV) ² type of variability: often X-ray bursts, sometimes pul- sations (recent: ms pulsations!) ² not so concentrated to the Galactic plane; older? ² faint optical counterparts: Lopt=LX < 0:1 (usually un- detectable!) Orbital Period Distributions ² known periods only! Selection e®ects! Low−Mass X−Ray Binaries 1820−30 (11 min) Low-Mass X-Ray Binaries Formation Scenarios ² the present size of many XRB's (» 0:1 ¡ 10 R¯) is much smaller than the size of a blue/red supergiant, the progenitor of the compact object ! require drastic shrinkage of orbit ² common-envelope evolution . mass transfer for supergiant is often unstable (star ² neutron-star (black-hole) binaries with orbital periods expands when losing mass rapidly; Roche lobe of typically hours to less than a few days (for those shrinks) ! companion star cannot accrete all the » 30 % with known periods) transferred matter and is engulfed ! formation of a common envelope (CE) ! friction ! spiral-in ² the companion stars are \believed" to be low-mass . CE is ejected when ¢E > E , where ¢E objects: CE orb bind orb is the orbital energy released, Ebind the binding en- < P < 1 hr: degenerate stars (M2 » 0:1 M¯) ergy of the envelope and CE a generally poorly 3 hr < P »< 10 hr: main-sequence stars determined e±ciency factor P »> 10 hr: subgiants, giants (?) (Note: the modelling of CE evolution is one of the major uncertainties in binary stellar evolution) ² they are concentrated in the direction of the Galactic center (\Bulge Sources") and in globular clusters (old ² LMXBs are more frequent in globular clusters (GCs) population?) . Galaxy: » 100; GCs: » 10 LMXBs BUT: neutron stars receive a kick at birth but: globular clusters only contain 0:05 % of the mass (median: 200 { 250 km/s) of the Galaxy ¡1 ! LMXBs receive a kick of 180 § 80 km s (Brandt ! 20 times more frequent and Podsiadlowski 1994/95) ! di®erent formation mechanisms ! the LMXB distribution is consistent with a young . tidal capture, three-body interactions in GCs progenitor population Formation of Low-Mass X-Ray Binaries (I) wide binary with large mass ratio dynamical mass transfer common-envelope and spiral-in phase ejection of common envelope and subsequent supernova ² ² LMXBs are the progenitors of the majority of mil- LMXB/ms-pulsar statistics (e.g. in globular clusters lisecond pulsars [Fruchter]) . recycling scenario: spin-up of the neutron-star due # of LMXBs ' lifetime of LMXBs to accretion (requires \magnetic ¯eld decay") # of ms pulsars lifetime of ms pulsars » 5 £ 109 yr Problems with the standard Model for LMXBs N ¼ 10 (supplementary) LMXB binary correction ² the formation of LMXBs requires a very contrived evo- z(1 +}| ){ 4 NPSR ¼ 1500 ' 10 lution: f beaming factor |{z} . extreme initial mass ratio 7 ! tLMXB » 10 yr . ejection of a massive common envelope by a low- mass star . implied LMXB lifetime too short by a factor of 10 to 100 both in globular clusters and in the Galaxy . survival as a bound system after the supernova (eject < 1=2 of the total mass or supernova kick) Possible solutions ² 6 LMXBs are very rare objects (1 in 10 stars) ² X-ray irradiation ² standard theory cannot explain . irradiation-driven wind (Ruderman et al. 1988) . orbital period distribution: di®erent from CV dis- . irradiation-driven expansion (Podsiadlowski 1991) tribution . luminosity distribution: too many luminous sys- ² di®erent channel for the formation of ms pulsars tems . accretion-induced collapse ² the problem of the missing intermediate-mass X-ray . formation from intermediate-mass X-ray binary binaries (should be the most common) population in the past The Eddington Limit Mass-Transfer Driving Mechanisms ² De¯nition: the maximum luminosity for which the gravitational force on a fluid element exceeds the ra- ² mass transfer is driven either by the expansion of the diation pressure force (i.e. the maximum luminosity mass donor or because the binary orbit shrinks due to at which matter can be accreted) angular momentum loss from the system ∆A ² expansion of the donor: . fluid element with cross section A and ∆R height R at a distance R from the cen- . due to nuclear evolution (\evolutionary driven R tre of gravity of mass M, mass transfer"; then M_ » M=tnuclear) or . non-thermal-equilibrium evolution (\thermal ² the (inward) gravitational force on the element is timescale mass transfer"; then M_ » M=tKH) GM ¡ Fgrav = 2 ¡ A R conservative mass transfer: R mass | {z } . total angular momentum of binary: gra| {zvity} M1M2 ² the (outward) radiative force on the element (due to J = rG(M1 + M2) A M + M the deposition of momentum by photons absorbed or 1 2 speci¯c| angular{z momen} tum L (A: orbital separation) £ scattered): Frad = 2 A ¡ R 4 ¢ R c . if J, M + M conserved ! (M M )2 A = constant momen| {z tum} 1 2 1 2 |momen{z tum} \deposited" (implies minimum separation if M1 = M2) flow ² ² maximum luminosity: Fgrav + Frad = 0 and solving for angular momentum loss from the system: 4 ¢ GMc gravitational radiation: L then yields Ledd = £ . e®ective for Porb »< 12 hr ² for Thomson scattering in a solar-type plasma magnetic braking 2 ¡1 4 ( £ = 0:034 m kg ), Ledd ' 3:8 £ 10 L¯ (M= M¯) : . red dwarf loses angular Eddington accretion rate (maximum accretion rate) momentum in magnetic wind ² if the luminosity is due to accretion luminosity (i.e. gravitational energy release) Lgrav = GMM_ =R; where . tidal locking of R is the inner edge of the accretion flow, equating secondary 4 ¢ cR . extracts angular Ledd = Lgrav: M_ edd = £ momentum from orbit ¡8 ¡1 ² For a neutron star, M_ ' 1:8 £ 10 M¯ yr Accretion discs ² an accretion disc forms when the stream of material flowing from the secondary intersects with its own tra- jectory before hitting the surface of the accreting star (typically if Racc »< 0:1 A) M r ² in a Keplerian accretion disc: inflow of matter requires a source of viscosity so that angular momentum can . examples: accretion onto a neutron star (no mag- ¡8 ¡1 di®use outwards and matter inwards (not well under- netic ¯elds) with M_ ' 2 £ 10 M¯ yr , M = 1:4 M¯, stood, magnetorotational instability?) R = 10 km the disc temperature structure: T(r) ! R = 10km: T ' 1:5 £ 107 K ' 1:4 keV (X-rays) ¡1 8 . energy per unit mass in disc at radius r . for a massive black hole (M_ » 1 M¯ yr , M = 10 M¯, 1 GM GM 8 E = v2 ¡ = ¡ (virial theorem) R = 3Rs = 9 £ 10 km) 2 r 2r dE GM ! T ' 2:2 £ 105 K ' 20 eV (UV) ! = u, where u is the radial drift velocity; dt 2r2 . energy radiated by unit area ( (r) : surface density [mass/area]), assumed to be blackbody (the disc GM 4 has two sides!): u (r) = 2 ¡ T 2r2 . and using mass conservation 4 3 _ _ ¢ ¡ M = 2 ¢ ru (r) ! T = GMM=8 r . with proper viscous energy transport _ 4 3GMM T = 3 8 ¢ r ¡ Neutron Star Spin up by Accretion High-Mass X-Ray Binaries Alfven surface . ² M because of the large mass ratio, mass transfer gener- ally becomes unstable, leading to a common-envelope . M and spiral-in phase ² r mass transfer is either due to atmospheric Roche-lobe Alfven overflow (short-lived) or wind accretion (relatively low luminosity) ² when magnetic ¯elds are important, the accretion Bondi-Hoyle wind accretion flow near the neutron star becomes dominant and channels the mass towards the poles, making the . accretion from a stellar object a X-ray pulsar wind onto an object of mass Macc with ² » Alfv¶en radius: where kinetic energy magnetic velocity v occurs 1 B(r)2 wind 2 ' from a radius energy density,i.e. ¡ v 2 2 0 (Bondi-Hoyle accretion ² approximating the flow velocity v by the free-fall radius RBH) where 1=2 2GM 1 2 NS mv » GMacc=RBH velocity, i.e. v ' v® = 0 1 ; 2 wind @ RAlf A ² 2GM obtaining the density ¡ from mass conservation acc ! R ' M_ BH 2 ' vwind (quasi-spherical flow) ¡ 2 4 ¢ RAlf v® 2 _ ¢ . accretion rate: Macc = RBH vwind ¡ (A), ² and assuming a dipole magnetic ¯eld (B / r¡3) 3 . where the wind mass density ¡ at orbital separation B0R B(r) » NS (where B is the surface ¯eld strength) M_ R3 0 ' wind Alf A follows from mass conservation: ¡ (A) 2 ; 4 ¢ A vwind ¡2=7 B 4=7 M_ 2 ! ' £ 4 0 1 .
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