Models of the non-thermal emission from early-type binaries
aa r X i v : . [ a s t r o - ph . H E ] M a y High Energy Phenomena in Massive StarsASP Conference Series, Vol. XX, c (cid:13) Models of the non-thermal emission from early-typebinaries
J. M. Pittard
The University of Leeds, Leeds, LS2 9JT, U.K.
Abstract.
The powerful wind-wind collision in massive star binaries createsa region of high temperature plasma and accelerates particles to relativistic en-ergies. I briefly summarize the hydrodynamics of the wind-wind interaction andthe observational evidence, including recent γ -ray detections, of non-thermalemission from such systems. I then discuss existing models of the non-thermalemission and their application to date, before concluding with some futureprospects. The winds of O and WR stars couple high mass-loss rates of ∼ − to a fewtimes 10 − M ⊙ yr − with fast velocities typically ∼ − − . Theram pressure balance between the hypersonic winds determines the position ofthe wind-wind collision region (WCR). Shocks are formed either side of theWCR which thermalize the plasma, heating it to ∼ − K. The proper-ties (e.g. density) of the WCR can span a very large range (see e.g. Table 2in Pittard et al. 2005), reflecting the diversity of the underlying binary popu-lation. In systems where the orbital period is only a few days, the shocks arecollisional, and the WCR displays a large aberration and downstream curvaturedue to the coriolis force. Cooling of the shocked gas is also likely to be signifi-cant. In addition, the presence of the companion star’s radiation field may havesignificant influence on the driving and dynamics of the winds. In contrast, insystems with longer orbital periods the shocks may be collisionless, orbital andradiation-field-induced effects on the dynamics and geometry of the WCR aremuch smaller, and the hot shocked gas may only cool adiabatically as it flowsdownstream. Particle acceleration at the shocks (but also possibly within theWCR - see Pittard & Dougherty (2006) for a detailed review) is likely to occurin these wider systems. Systems with (highly) eccentric orbits are particularlyinteresting since the changing separation of the stars is useful as a probe of thephysics which takes place. Colliding wind binaries (CWBs) are also useful assimpler, less complicated, analogues of the multiple wind-wind collisions whichoccur throughout the volume of clusters of massive stars.The collision of the winds is best studied using hydrodynamical simulations.A seminal paper by Stevens, Blondin & Pollock (1992) was the first to self-consistently include cooling, and it focussed on the dynamical instabilities and X-ray emission which arise from the WCR. Other works since then have examinedthe influence of the companion star’s radiation field (Stevens & Pollock 1994;Gayley et al. 1997), the effects of thermal conduction (Myasnikov & Zhekov1
J. M. Pittard − to 1630 km s − ), which leadsto significantly higher (lower) postshock temperatures (densities), resulting ina largely adiabatic WCR. The higher wind speeds and reduced orbital veloci-ties also diminishes the aberration and downstream curvature of the WCR dueto coriolis forces (note the difference in spatial scale between the two systemspresented in Fig. 1). Direct evidence for non-thermal emission from relativistic particles within aWCR was presented by Williams et al. (1997). Here, radio images were overlaidon UKIRT shift-and-add IR images of WR 147. When the southern (thermal) ra-dio source was aligned with the southern (WR) star, the northern (non-thermal)radio source was found to lie just south of the northern (O) star, in a positionconsistent with the point of ram-pressure balance between the winds . Directimaging of the WCR in WR 146 and WR 140 have provided further supportfor this interpretation (Dougherty, Williams & Pollacco 2000; Dougherty et al.2005). See Dougherty (these proceedings) for further details.WR 146 and WR 147 are both very wide, and the non-thermal radio emis-sion from the WCR escapes easily from the system. This contrasts with WR 140(the best studied of any WR+O binary), where the stars are very much closertogether, and which displays dramatic, phase-repeatable, variations in its ra-dio emission over the course of every 7.94 yr orbit (see White & Becker 1995; WR 147 is the only CWB to date which also has spatially resolved X-ray emission - seePittard et al. (2002). on-thermal emission models of early-type binaries Figure 1. Density and temperature plots through the orbital plane of hy-drodynamic models of the wind-wind collision in short period O6V+O6Vbinaries. In the left plots the orbital period is 3 days, and the winds collideat relatively low speeds. Hence, the WCR is highly radiative and is stronglydistorted by the orbital motion of the stars. In the right plots the orbitalperiod is 10 days, the winds collide at higher speeds, and the WCR is largelyadiabatic. The top panels display the density and the bottom panels the tem-perature. The left panels have sides of length 240 R ⊙ , while the right panelshave sides of length 570 R ⊙ . See Pittard (2009) for further details. J. M. Pittard
Dougherty et al. 2005). The high eccentricity of the orbit causes the stellarseparation to vary between ≈ −
28 AU. While the radio lightcurve has defiedsatisfactory explanation to date, it is likely that at least part of its variationis caused by variable circumstellar extinction to the source of the non-thermalemission as the O star orbits in and out of the radio photosphere in the denseWR wind. More recently, this system has been imaged with the VLBA, yieldinga full orbit definition, including, most importantly, the inclination of the system(Dougherty et al. 2005). While this study has helped to provide some of the bestmodelling constraints of any system, relatively little is known about the wind ofthe O star, and the wind momentum ratio of the system remains ill-constrained.In the hard X-ray and γ -ray regimes there has been many false dawns con-cerning potential emission from CWBs. However, definitive evidence for non-thermal X-ray and γ -ray emission from CWBs has finally been presented inrecent years, with an especially exciting period in just the last few months. Us-ing INTEGRAL, Leyder, Walter & Rauw (2008) presented a clear detection ofMeV γ -ray emission from η Carinae (a lower spatial resolution observation withBeppoSAX was previously presented by Viotti et al. 2004, though some of theemission attributed to η Carinae was shown by Leyder et al. (2008) to be asso-ciated with other nearby sources). This detection has since been confirmed witha Suzaku observation (Sekiguchi et al. 2009). And in just the last few months, η Carinae has been associated with an AGILE source (Tavani et al. 2009), and ison the FERMI bright source list. Upper limits have also been placed on the MeVemission from WR 140, WR 146, and WR 147 (De Becker et al. 2007), and onthe TeV emission from WR 146 and WR 147 (Aliu et al. 2008). Finally, a greatdeal of effort has gone into searching for non-thermal X-ray emission from CWBswith known non-thermal radio emission (e.g. Rauw et al. 2002; De Becker et al.2004, 2006). However, the lack of success in this undertaking appears to showthat the physical conditions necessary to produce observable emission at radioand hard X-ray energies are mutually incompatible.There are many possible mechanisms for accelerating particles in CWBs.Most works assume that diffusive shock acceleration (DSA) is the dominantprocess, though reconnection and turbulent processes are other possibilities.Each mechanism differs in its efficiency, and in the properties of the non-thermalparticles which it produces, such as their spectral index. A detailed discussionof the many possibilities can be found in Pittard & Dougherty (2006).
Some notes on the key physics of particle acceleration in CWBs were presentedby Eichler & Usov (1993). Early models of the non-thermal radio emission werevery simple, with the observed flux ( S obs ν ) assumed to be a combination of thefree-free flux from the spherically symmetric winds ( S ff ν ), plus the flux froma point-like non-thermal source located at the stagnation point of the winds( S nt ν ), the latter being attenuated by free-free absorption (opacity τ ff ν ) throughthe surrounding winds: S obs ν = S ff ν + S nt ν e − τ ff ν . (1) on-thermal emission models of early-type binaries γ -ray domain was, until a fewyears ago, even more rudimentary. With no firm detections at γ -ray energies,theoreticians were reduced to estimating the inverse Compton (IC) luminosity, L ic , by the following simple formula: L ic = U ph U B L sync , (2)where L sync is the synchrotron luminosity, and U ph and U B are the photon andmagnetic field energy densities, respectively. A fundamental problem with theuse of the above formula is that the predicted value of L ic is highly sensitive tothe assumed magnetic field ( B = √ πU B ). Varying B results in a wide rangeof predictions for L ic , as shown in Benaglia & Romero (2003). The magneticfield in the WCR is highly uncertain, even when the surface magnetic fields areknown (which is very rare), because one cannot necessarily extrapolate these toobtain their strength in the WCR, since there are the possibilities of large-scalemagnetic reconnection within the WCR on the one hand, and magnetic fieldamplification by non-linear DSA on the other. Finally, observed rather than intrinsic values have been used for L sync . This may be of little consequence inthe wider systems where the attenuation of non-thermal emission through thecircumstellar envelope surrounding the stars may be negligible, but for a givenset of parameters, L ic could be underestimated in closer systems.While there are many problems and uncertainties associated with the earlymodelling work of the non-thermal radio and γ -ray emission from CWBs, thesesimple models nevertheless paved the way for the more sophisticated modellingwhich has since followed, as we now describe. A major step along the path towards improved models of the radio emission fromcolliding wind binaries was taken by Dougherty et al. (2003). This work removedthe assumptions of a point-like source of non-thermal emission, and a spheri-cally symmetric, single temperature, surrounding envelope. Instead, models ofthe thermal and non-thermal radio emission were based on 2D, axisymmetric hy-drodynamical simulations. This approach provided a much better description of
J. M. Pittard the density and temperature distribution in the the system, allowing sight-linesto the observer to pass through regions of both high and low opacity. The non-thermal emission was treated in a phenomenological way: accelerated electronswere assumed to be present within the WCR, with an energy density ( U rel , e )proportional to the local thermal energy density ( U th ) i.e. U rel , e = ζ rel , e U th . Themagnetic field energy density was specified in a similar manner: U B = ζ B U th .The non-thermal electrons were further assumed to have a power-law distribu-tion, N ( γ ) dγ = Cγ − p dγ , where γ is the Lorentz factor and C is proportional to ζ rel , e . The non-thermal electrons were assumed to arise from test particle DSA,where p = 2 for strong shocks of adiabatic index 5 / D − / ν − / , where D is the separation of thestars (for comparison, the X-ray emission in the optically thin, adiabatic limit,scales as D − ). This work also highlighted the importance of IC cooling, whichwas noted to be important even in wide systems. Indeed, neglect of IC coolingof the non-thermal electrons in this model led to an overestimation of the highfrequency synchrotron flux in a model of WR 147.This failing was addressed in a follow-up paper (Pittard et al. 2006). Here,the non-thermal electrons were assumed to be accelerated by DSA at the global shocks confining the WCR, and to cool once they flowed downstream. Sincethe amount of cooling is dependent on the “exposure” time of the non-thermalelectrons to the radiation fields of the stars, this assumption led to those elec-trons suffering the most severe cooling to concentrate along the contact surfacebetween the winds, and thus to a dearth of emission from this region (see Fig. 2).This addition significantly improved the fit between models and observations ofWR 147. It also modified the scaling relation for the total synchrotron luminos-ity noted in Dougherty et al. (2003) - now, the intrinsic luminosity was observedto decline with stellar separation as IC cooling became increasingly strong. Inaddition, it was noted that the thermal radio emission from the WCR scales as D − , in an identical way to the thermal X-ray emission. Since this emission isoptically thin (on account of the high temperatures within the WCR), it canmimic a synchrotron component. Therefore, one needs to cautiously interpretdata with a spectral index − . ∼ < α ∼ < .
5, where S ν ∝ ν α (more negative valuesof α , e.g. α ≈ − .
5, clearly indicate a bona-fide synchrotron component). X -ray and γ -ray emission The dramatic sensitivity gains made by arrays of Cerenkov telescopes have ledin recent years to a new interest in the level of non-thermal X-ray and γ -rayemission from colliding wind binaries. Bednarek (2005) calculated the expected γ -ray emission from WR 20a, a WR+WR binary. The short orbital period meansthat the optical depth to electron-positron pair creation is high enough to initi-ate electromagnetic cascades in this system. Particle acceleration by magnetic on-thermal emission models of early-type binaries Figure 2. The impact of IC cooling on the intensity distribution of a CWBmodel (see Pittard et al. 2006, for details), for a viewing angle of 0 ◦ and at1.6 GHz (top) and 22 GHz (bottom). The images on the left do not includeIC cooling, while those on the right do. Each image has the same intensityscale and contours. J. M. Pittard
Figure 3. a) Geometry of the 2-zone model in Reimer et al. (2006). b)Evolution of the non-thermal electron spectrum from the inner accelerationzone (solid) line as a function of downstream distance in the advection zone.At low energies adiabatic/expansion losses dominate, while at high energiesIC losses dominate. c) As b) but for nucleons. Only adiabatic losses occur.See Reimer et al. (2006) for further details. reconnection and DSA was considered, and it was concluded that detectableneutrino fluxes should be produced. Due to the high optical depth to TeV pho-tons within this system, WR 20a cannot be directly responsible for nearby TeVemission (Aharonian et al. 2007), which more likely is the result of accelerationprocesses within the collective wind of the nearby cluster Westerlund 2.Following on from this work, Reimer, Pohl & Reimer (2006) developed atwo-zone model of the non-thermal emission. Particles are accelerated in an innerzone where their spatial diffusion exceeds their motion due to advection withthe background fluid. Their energy distribution is self-consistently computedby considering all relevant gain and loss mechanisms. Particles are assumed tobe resident within this region until their timescales for advection and diffusionare comparable, after which they are assumed to move into the advection regionwhere they suffer further losses as they flow downstream. Fig. 3 shows theassumed geometry and the resultant non-thermal energy spectra of the electronsand nucleons.Consideration is also given to the anisotropic nature of the IC process,where the emitted power is dependent on the scattering angle. Fig. 4 shows thepredicted IC emission from WR 140 as a function of orbital phase. Reimer et al.(2006) conclude that while WR 140 should be easily detected with GLAST/Fermi,the change in the IC flux with viewing angle due to anisotropic scattering is likelyto be obscured by large variations in the energy density of the stellar radiationfields resulting from the high orbital eccentricity. However, the latest work byReimer & Reimer (2009) demonstrates that it is possible to use the property ofnonisotropic IC emission to constrain the orbital inclination of colliding windsystems.Another model of the X-ray and γ -ray emission, which is in many ways com-plementary to that of Reimer et al. (2006), was presented by Pittard & Dougherty(2006). This built on the phenomenological model developed previously byDougherty et al. (2003) and Pittard et al. (2006) to explore the non-thermalradio emission. Although the energy spectrum is assumed rather than calcu-lated, and so in this sense is weaker than the model in Reimer et al. (2006), thisapproach benefits from a realistic description of the density and temperature dis-tribution within the system, and constraints placed on the key parameters (e.g. on-thermal emission models of early-type binaries Figure 4. Predicted IC spectra for WR 140 at phases 0.2, 0.671, 0.8 and0.955 from Reimer et al. (2006). γ -ray absorption is not included. mass-loss rates) by fits made to the X-ray data. Pittard & Dougherty (2006)showed that other uncertainities, such as the particle acceleration efficiency andthe spectral index of their energy distribution (both of which unfortunately re-main ill-constrained from fits to radio data), have at least as much influence onthe predicted flux as the angle-dependence of the IC emission.Fig. 5 shows a predicted spectral energy distribution for WR 140 from oneof the models presented in Pittard & Dougherty (2006). Large differences inthe predicted γ -ray emission occur depending on whether the low frequencyturndown in the radio spectrum results from free-free absorption through thesurrounding stellar winds, or from the Razin effect. Furthermore, satisfactoryfits to the radio spectrum at orbital phase 0.837 could be achieved in one of twoways: either with a standard p = 2 index, or with a harder index (e.g. p ≈ . γ -ray detectionswill determine the γ -ray flux and spectral index, and thus will also distinguishthe nature of the low-frequency turndown. The acceleration efficiency of thenon-thermal electrons and the strength of the magnetic field will then both berevealed.0 J. M. Pittard
Figure 5. The radio and non-thermal UV, X-ray and γ -ray emission cal-culated from model B in Pittard & Dougherty (2006), together with the ob-served radio and X-ray flux (both at orbital phase 0.837). The model IC (longdash), relativistic bremsstrahlung (short dash), and neutral pion decay (dot-ted) emission components are shown, along with the total emission (solid).See Pittard & Dougherty (2006) for more details. Work is also continuing on fits to the radio spectra of WR 140 at otherphases around its orbit. Preliminary results indicate that there is significantevolution of key parameters in the model (such as the acceleration efficiencyand magnetic field). Finally, the non-thermal emission from the short periodO+O binary models in Pittard (2009) is being investigated. One area of inter-est concerns the ease with which non-thermal radio emission can escape thesesystems, despite the orbital-induced curvature preventing lines-of-sight to thenon-thermal emission from existing purely within the low opacity, hot WCR.
In recent years there has been a steady improvement in theoretical model pre-dictions of the non-thermal emission from CWBs, in both the radio and γ -raydomains. This work is being driven by corresponding advances on the obser-vational front. In the past, CWBs have played a poor second role to SNRs interms of investigations of the physics of high Mach number shocks and cosmicray acceleration. However, they provide access to higher mass densities, radia-tion backgrounds, and magnetic field energy densities than found for supernovaremnants, thus enabling studies in previously unexploited regimes, and due torecent observational detections of non-thermal emission at hard X-ray and γ -ray energies are slowly gaining popularity in the community. Future high energyobservational prospects with Fermi and CTA, etc., look very good. An exciting on-thermal emission models of early-type binaries Acknowledgments.
I gratefully acknowledge the invitation of the SOCto present a review at this conference, and would like to especially thank Dr.Josep Mart´ı for his tireless organization and enthusiasm which made, I believe, avery successful meeting. I would also like to thank collaborators and colleaguesfor their interesting discussions and input over the years, especially Drs. SeanDougherty and Don Ellison, and my PhD student Ross Parkin. Finally, I wouldlike to thank the Royal Society for funding a Research Fellowship.