Gamma Ray Signal from the Pulsar Wind in the Binary Pulsar system PSR B1259-63/LS2883
Dmitry Khangulyan, Felix Aharonian, Sergey Bogovalov, Marc Ribó
aa r X i v : . [ a s t r o - ph . H E ] A p r Gamma Ray Signal from the Pulsar Wind in the Binary Pulsarsystem PSR B1259 − Dmitry Khangulyan , Felix A. Aharonian , Sergey V. Bogovalov , Marc Rib´o Institute of Space and Astronautical Science/JAXA, 3-1-1 Yoshinodai, Chuo-ku,Sagamihara, Kanagawa 252-5210, Japan [email protected] Dublin Institute for Advanced Studies, 31 Fitzwilliam Place, Dublin 2, Ireland [email protected] Max-Planck-Institut f¨ur Kernphysik, Saupfercheckweg 1, D-69117 Heidelberg, Germany National research nuclear university-MEPHI, Kashirskoe shosse 31, Moscow, 115409Russia [email protected] Departament d’Astronomia i Meteorologia, Institut de Ci`ences del Cosmos (ICC),Universitat de Barcelona (IEEC-UB), Mart´ı i Franqu`es 1, E-08028 Barcelona, Spain [email protected]
ABSTRACT
Binary pulsar systems emit potentially detectable components of gammaray emission due to Comptonization of the optical radiation of the companionstar by relativistic electrons of the pulsar wind, both before and after termi-nation of the wind. The recent optical observations of binary pulsar systemPSR B1259 − Fermi close to the periastronpassage, unless the pulsar wind is strongly anisotropic or the Lorentz factor ofthe wind is smaller than 10 or larger that 10 . The higher luminosity of theoptical star also has two important implications: (i) attenuation of gamma rays 2 –due to photon-photon pair production, and (ii) Compton drag of the unshockedwind. While the first effect has an impact on the lightcurve of VHE gammarays, the second effect may significantly decrease the energy available for particleacceleration after termination of the wind. Subject headings: binaries: close — gamma rays: stars — pulsars: individual(PSR B1259 −
1. Introduction
Three binary systems containing a massive star and a compact object – LS 5039,LS I +61 303 and PSR B1259 −
63– have been clearly detected in TeV energy band (see http://tevcat.uchicago.edu/ for the updated information). While the nature of the com-pact companion in LS 5039 and LS I +61 303 is not yet established (Casares et al. 2005a,b;Sarty et al. 2011), the detection of the pulsed radio emission from PSR B1259 −
63 indicatesthe presence of a 47.7 ms pulsar in the system (Johnston et al. 1992). The pulsar orbits aluminous star in a very eccentric orbit with the following orbital parameters: eccentricity e = 0 .
87, period P orb = 1237 d, and semi-major axis a = 6 . Fermi
LAT observations of periastron passage in December 2010 have shown that in general theGeV flux level from the system is quite low, although a short intensive flare was detected aswell (see e.g. Tam et al. 2011; Abdo et al. 2011).Recently, optical observations with VLT UT2 Kueyen discovered that the optical starLS 2883 corresponds to a late O-star and has a significantly higher luminosity of L ∗ =2 . × erg s − than previously thought (Negueruela et al. 2011). Because of fast rotationthe star is significantly oblated with equatorial radius of R eq = 9 . R ⊙ and the polar radiusof R pole = 8 . R ⊙ . This leads as well to a strong gradient of the star surface temperaturewith T eq = 27 500 K and T pole = 34 000 K. The star rotation axis is inclined by i ∗ ≃ ◦ in respect to the line-of-sight (Negueruela et al. 2011). The distance to the system is nowestimated to be 2 . ± . i ≃ ◦ , which is remarkably smaller than the previously obtained value of ∼ ◦ (Johnston et al. 1994). All these new parameters together should have an importantimpact on the multiwavelength properties of this system. 3 –The orbital separation distance, pulsar spindown luminosity and the lack of the accretionfeatures suggest a realization of the compactified nebula scenario, i.e. the source containstwo distinct regions: the relativistic pulsar wind and the terminated flow (Tavani & Arons1997; Bogovalov et al. 2008). The VHE emission is expected to originate in the post termi-nation shock region, and a number of models have been proposed invoking both hadronic(Kawachi et al. 2004; Neronov & Chernyakova 2007) and leptonic (Kirk et al. 1999; Khangulyan et al.2007) radiation mechanisms. In the framework of the hadronic scenario, the two humpedTeV lightcurve obtained with HESS in 2004 (Aharonian et al. 2005) have been interpretedas the enhancement of the production rate due to the pulsar passage through the densestellar disc. However, the recent report of a more complicated TeV gamma ray lightcurveby HESS with multiple humps and deeps disfavors, to a large extent, the hadronic scenario(Aharonian et al. 2009). In the case of leptonic origin of the emission, there is a numberof additional effects, which may significantly affect the production rate of the nonthermalemission in the post shock region (Khangulyan et al. 2007). Importantly, in the leptonicscenario, one expects a specific radiation component from the unshocked pulsar wind. Al-though, the pulsar wind region is not expected to produce VHE emission, a line-like bulkComptonization component from this region in HE band is predicted for isolated pulsars likeCrab pulsar (Bogovalov & Aharonian 2000) and for the binary pulsar system PSR B1259 − Fermi and
AGILE gamma ray telescopes close to the periastron passage are of great in-terest; any result (flux upper limit or detections of a signal) can greatly contribute to ourunderstanding of the physics of pulsar winds.Since the interaction of the pulsar wind with the stellar photon field does not occur inthe saturation regime , the production rate is very sensitive to the properties of the photonfield. In this paper we present new calculations of the radiation signal from the pulsar windtaking into account the new properties of the optical star (Negueruela et al. 2011) and usingresults of detailed hydrodynamical modeling of the interaction between the pulsar and stellarwinds in PSR B1259 −
2. Pulsar Wind in Binary Pulsar System
In the framework of the generally accepted paradigm (Kennel & Coroniti 1984), pulsarslaunch cold ultrarelativitic winds which are terminated due to external pressure. At the 4 –termination shock, the wind electrons can be accelerated to multi-TeV energies. The radi-ation of these electrons results in a phenomenon called pulsar wind nebula. Since the windis cold, i.e. particles remain at rest in the wind co-moving system, no synchrotron emissionis expected from the wind before its termination. On the other hand, the comptonization ofthe ultrarelativistic wind by external radiation fields, through which the wind propagates,can lead to detectable gamma ray emission. This effect is relatively weak in isolated pulsars,and can achieve a reasonable efficiency only in powerful pulsars, provided that the particledominated wind is formed close to the light cylinder (Bogovalov & Aharonian 2000). In bi-nary systems, the process operates with an enhanced efficiency thanks to the presence of thedense radiation field of the optical companion (Ball & Kirk 2000; Ball & Dodd 2001). Theinteraction rate in this channel depends on different parameters characterizing the system:(i) luminosity and temperature of the optical star; (ii) orbital separation and inclination;(iii) distance to the system; (iv) size of the region occupied by the pulsar wind; (v) pulsarwind bulk Lorentz factor.Remarkably, the recent optical observations of PSR B1259 −
63 have significantly revisedthe parameters (i), (ii) and (iii) in favor of higher temperature and luminosity, smallerinclination angle and further system location. Regarding the wind bulk Lorentz factor, itremains a highly uncertain parameter.The size of the region, where the pulsar wind can propagate depends on the ratio ofthe wind ram pressures, η (Bogovalov et al. 2008). Since the pulsar spindown luminosity isknown, one can estimate the ram pressure of the pulsar wind P pw = L sd πr c , (1)where L sd and r are the spindown luminosity of the pulsar and distance to the pulsar, re-spectively. It should be noted that this relation ignores the possible effects related to theanisotropy of the pulsar wind. Although, the level of the anisotropy may be quite high at largedistances from the pulsar, e.g. in the case of the Crab-like pulsars (Bogovalov & Khangoulyan2002), in this paper we limit our consideration by the case of an isotropic wind.To obtain the ram pressure of the stellar wind, one needs detailed information about theproperties of the optical star, including the mass-loss rate and wind velocity profile, whichare currently not firmly established. For the given optical star luminosity, the mass-lossrate can be estimated at the level of ˙ M = 6 × − M ⊙ yr − (Vink et al. 2000). Accountingfor the wind velocity at interaction point V w < V ∞ = 1350 ±
200 km s − (McCollum 1993),it is possible to estimate the expected value of the ratio of the momentum flux densities, 5 – η -parameter, as follows: η = L sd ˙ M cV w = 5 × − ˙ M × − M ⊙ yr − ! − (cid:18) V w − (cid:19) − . (2)We should note, however, that there are several factors which may introduce significantuncertainties in the η -parameter. In particular, the wind porosity may lead to an overes-timation of the mass-loss rate of the star (Owocki & Cohen 2006) and consequently to asignificant underestimate of the η parameter value. The opposite situation may occur if thepulsar wind interacts with the stellar wind close to the star equatorial plane, where a denseKeplerian disk is formed. Since the disk is expected to have a significantly higher densitythan the polar wind, and its typical velocity at distance r (i.e. Keplerian velocity) may beas high as v disk ≃ (cid:16) r cm (cid:17) − / km s − , (3)the disk effective ram pressure may significantly exceed the polar wind one, i.e. the η -parameter may be remarkably smaller than the estimate of Eq.(2). Moreover, because ofthe disk rotation and pulsar orbital velocity, the structure of the wind termination shock,in respect to the observer direction, may be rather different for two pulsar–disk interactionpoints. Because of these uncertainties related to the value of the η -parameter, below we willconsider a fairly broad range of the η parameter.In Figure 1 the shapes of the termination shock for three different values of the η parameter are shown. The points in the figure are from the results of numerical modelingperformed by Bogovalov et al. (2008), for η = 1 (squares), η = 0 .
05 (filled circles) and η = 1 . × − (open circles). Here the value of η = 1 roughly corresponds to the case ofthe interaction with the clumpy polar wind; η = 0 .
05 to the case of collision with the stellarwind; and η = 1 . × − is a lower limit value, which can be realized if e.g. pulsar windis significantly anisotropic at binary system scales; or if the stellar disk plays an importantrole in the interaction. To simplify the calculations we have approximated the terminationshock by the following analytical expressions:for η = 1 r = 3 . p ( z + 0 . z + 0 . , (4)for η = 0 . r = 0 . p ( z + 0 . z + 5 . , (5)for η = 1 . × − r = 0 . p ( z + 0 . . − z ) . (6)Here z is the coordinate along the axis joining the pulsar and the star (it is assumed thatthe pulsar is located at the point “0”, and the optical star is located at ( z = − , r = 0)), 6 –and r is the corresponding cylindrical radius (both coordinates are measured in the pulsar-star separation units, d p − s ). Eq.(6) shows non-smooth behavior at z ≃ . N d E γ d S d t = c πd Z pulsar d l Z d ǫ ph Z d E e (1 − cos θ ) e − τ d σ d E γ d N e d E e d l d N ph d ǫ ph d V . (7)Here d is the distance to the system; d σ/ d E γ is the differential anisotropic inverse Comp-ton cross-section (Aharonian & Atoyan 1981; Bogovalov & Aharonian 2000); τ is the energydependent optical depth due to gamma-gamma attenuation from the gamma ray creationpoint to the observer; and d N ph / d ǫ ph d V is the target photon density at the given location.The term representing the electron density in the cold pulsar wind has the following form:d N e d E e d l = L sd Γ mc δ E e − Γ mc − l Z d l ′ ˙ E/c , (8)where Γ and ˙ E are the initial wind bulk Lorentz factor and the electron energy loss rate.The integration of Eq.(7) is performed over the line of sight from the pulsar location tothe pulsar wind termination shock. Obviously, the integration path depends strongly on theorbital phase. In Figure 1, the lines of sight for three different orbital phases ( −
6, 0 and 6day from periastron passage) are shown by dashed lines.Another effect, which may lead to an additional orbital phase dependence, is the shapeof the optical star and temperature change between different regions of the star. To studythis effect we performed calculation for the precise properties of the star, i.e. assumingthe star to be an oblate spheroid with a linear gradient of the surface temperature as afunction of the zenith angel. The orientation of the star in respect to the observer is definedby inclination angle, i.e. angle between the star rotation axis and line-of-sight, which wasassumed to be i ∗ = 33 ◦ , as inferred by Negueruela et al. (2011). To fix the star orientationan additional angle is required, namely the angle which describes the turn in the plane ofthe sky. This angle was assumed to be a free parameter, and its influence was studied.Numerical calculations show (see Figures 2 and 3) that independently on this parameter,the emission is well described by a model with a spherical star of radius R ∗ = 6 . × cm 7 –and surface temperature T ∗ = 3 × K. Given the uncertainties related to the orientationof the star, in what follows we perform calculations for the spherical star with the inferredparameters.In Figure 2 we show the spectral energy distributions (SEDs) expected at the orbitalphase corresponding to the periastron passage for η = 1 (solid lines); η = 0 .
05 (dottedlines); η = 1 . × − (dashed line). In calculations we have adapted the following valuesof the initial wind Lorentz factors: Γ = 10 , . × , . × and 10 . In Figure 3 weshow a similar plot, but for the orbital phase corresponding to the epoch of 30 days beforethe periastron passage. For a rather broad range of the wind bulk Lorentz factors aroundΓ = 10 , the obtained flux level is above the Fermi sensitivity level (unless the η -parameteris small η ≪ . = 4 . × . In calculations weused two different values of the η -parameter: η = 1 (solid line) and η = 0 .
05 (dotted line).We note that this parameter may affect not only the flux level, but also the location of thelight-curve maximum: in the case of the small value the maximum is located close to theperiastron passage, while in the case of larger values of η the maximum is located a few daysbefore periastron passage.In the case of large bulk Lorentz factor, Γ ∼ − , the inverse Compton (IC) signalfrom the pulsar wind may appear at energies beyond the range of Fermi /LAT. In this energyband, the atmospheric Cherenkov telescope arrays are more appropriate tools for probingthe wind’s Lorentz factor (note that for this specific source, currently only the HESS arrayis able to monitor PSR B1259 − η -parameter η = 1 and for the bulk Lorentz factor of Γ = 10 .
3. Impact of the higher luminosity of the optical star
In addition to gamma-radiation of the unshocked pulsar wind, we expect gamma rays (athigher energies) from the Compton scattering of shock-accelerated electrons (Kennel & Coroniti1984). If the optical radiation density exceeds the density of the magnetic field, the IC gammaray production proceeds in the saturation regime, thus the increased luminosity of the optical 8 –star does not lead to amplification of the VHE gamma ray signal. On the other hand, for therecently reported luminosity of the optical star (Negueruela et al. 2011), the gamma-gammaopacity for VHE photons traveling from the pulsar to the observer, may be as large as 0 . E γ = 0 . .
15, 0 .
4, 1 and 5 TeV. Note that the gamma ray absorption is strongest at the energy of0.4 TeV, while at energies below 100 GeV and at multi-TeV energies it becomes negligible.We note however that the actual absorption level depends on the production region location,while the calculations in Figure 5 assume that the production occurs in the pulsar location.In particular, in Figure 4 two lightcurves for 0 . × erg s − , then the tendency ofreduction of the TeV flux observed by HESS (Aharonian et al. 2005) close to the periastronpassage may be explained by the reduction of the overall energy of the pulsar wind due to theCompton drag. The stellar luminosity reported by Negueruela et al. (2011) is remarkablyclose to the one speculated in Khangulyan et al. (2007), thus this effect now becomes morerelevant to the observed TeV lightcurve. To describe the effect quantitatively, we havecalculated the energy fraction lost by electrons emitted within the solid angle of π steradiantowards the optical star. The result are shown in Figure 6 for different values of the initialwind Lorentz factor: Γ = 10 (dash-dotted line), 4 . × (solid line), 2 . × (dashed line)and 10 (dotted lines). The η -parameter was assumed to be η = 1. The calculations showthat this effect may lead to a significant decrease of the pulsar wind energy transported tothe termination shock in the case of high values of the η -parameter, i.e. η ≥ .
1. This shouldlead to a proportional decrease of the VHE gamma ray production. Obviously, the Comptondrag can be important only if the GeV flux from the pulsar wind is high. This radiationshould be clearly detected by
Fermi /LAT, unless the pulsar wind is strongly anisotropic.The detection of the pulsar wind signal with
Fermi could allow a quantitative estimate of 9 –the expected decrease of the VHE gamma ray production.The Compton drag should lead as well to a decrease of the pulsar wind ram pressure inthe collision region. However, given a relatively weak dependence of the termination shockshape on the η -parameter, it is unlikely that the Compton drag would change significantlythe pulsar – optical star interaction regime.
4. Conclusion
Motivated by the recent revision of optical properties of LS 2883, the companion star ofPSR B1259 −
63 (Negueruela et al. 2011), we present new calculations of high energy gammaray fluxes using a realistic termination shock geometry as described in Bogovalov et al.(2008). Calculations show that the higher optical star luminosity is compensated, to alarge extent, by the new estimate of the distance to the source. Thus, the new calculationsof gamma ray fluxes are quite close to previous predictions based on the old gamma rayparameters of the optical star (see in Khangulyan et al. 2007). According to Figure 2, the0.1–10 GeV gamma ray fluxes calculated for epochs close to the periastron passage are belowthe current upper limits obtained with EGRET (Tavani et al. 1996), and above the mini-mum fluxes detectable by
Fermi /LAT for observation time of about 1 month. The pulsarwind radiation component can be identified by its distinct spectral shape. Another impor-tant feature of this emission is the expected modulation with the pulsar period on the topof the smooth orbital phase dependence. Indeed, since the emitting electrons move towardsthe observer almost with the speed of light, the gamma ray signal should have the secondmodulation reflecting the time structure of the striped pulsar wind. Although, a detailedshape of the fine lightcurve can be hardly obtained given a lack of any consistent descriptionof the striped pulsar wind, a detailed search for this effect looks quite important for a consis-tent interpretation of the results obtained with
Fermi /LAT Tam et al. (2011); Abdo et al.(2011).The most important implication of detection of this component of gamma radiationwould be the unique opportunity to measure the Lorentz factor of the pulsar wind. On theother hand, in the case of failure of detection of this component at GeV and/or TeV energies,the conclusions could be equally interesting and important. The possible reasons of non-detection of gamma rays from the unshocked wind could be: (i) an extremely powerful stellarwind, i.e. very low values of the η parameter; (ii) unconventional, i.e. very low (Γ ≪ )or very large (Γ ≥ ) values of the pulsar wind bulk Lorentz factor. The first conditionrequires the pulsar to interact with the stellar disc all over the orbit. This implies a veryspecific realization in the sense of orientation of the stellar disc (namely the orbital plane 10 –and the disc plane should almost coincide), which contradicts to the current expectations(Melatos et al. 1995; Bogomazov 2005; Bogovalov et al. 2008; Kerschhaggl 2010). However,we should note that one cannot exclude that the pulsar wind is strongly anisotropic. If so, thegamma ray signal should be anisotropic as well. This can be another reason for reduction ofthe gamma ray flux, which unfortunately would make the conclusions concerning the rangeof parameters Γ and η less robust. Finally, one should mention that if the pulsar wind is notabsolutely cold, electrons in the frame of the wind might have a rather broader distribution.This would make the gamma ray spectrum less distinct and smoother compared to the onesshown in Figures 2 and 3.Regarding VHE energy gamma rays produced after termination of the wind, the newoptical observations of Negueruela et al. (2011) imply a significant reduction of the flux of ICgamma rays produced by shock-accelerated electrons. All three main factors related to (1)the larger distance to the source, (2) the gamma-gamma attenuation, and (3) the Comptondrag of the pulsar wind work in the same (negative) direction reducing the gamma ray flux bya factor of up to 10. Given that the previous studies based on the old optical observationsalready have required a significant fraction of the spin-down luminosity (5%–10%) to bereleased in TeV gamma rays, the revised energy requirements become almost unbearable. Apossible solution to the energy budget crisis could be the Doppler boosting of radiation assuggested in Khangulyan et al. (2008). This important issues will be discussed elsewhere.The work of S.V.Bogovalov have been supported by the Federal Targeted Program”The Scientific and Pedagogical Personnel of the Innovative Russia” in 2009-2013 (the statecontract N 536 on May 17, 2010). M.R. acknowledges support by the Spanish Ministeriode Ciencia e Innovaci´on (MICINN) under grant FPA2010-22056-C06-02, as well as financialsupport from MICINN and European Social Funds through a Ram´on y Cajal fellowship.
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This preprint was prepared with the AAS L A TEX macros v5.2.
13 – r / d p - s z/d p-s ∆ t = - d ∆ t = d ∆ t = d Approximations η =1, Numerical Calculations η =0.05, Numerical Calculations η =0.0011, Numerical CalculationsLines of sight Fig. 1.— The geometry of interaction of pulsar and optical star winds: the pulsar isassumed to be located at the point with coordinates r = 0 , z = 0, the optical star at r = 0 , z/d p − s = −
1. The shapes of the termination shocks as obtained through the numeri-cal modeling (Bogovalov et al. 2008) are shown for the following values of the η -parameter: η = 1 (squares), η = 0 .
05 (filled circles) and η = 1 . × − (open circles). The analyticalapproximations Eq.(4-6) are shown with solid lines. The directions towards the observer areshown with dotted lines for three different epochs: −
6, 0 and 6 days to periastron passage. 14 – F l u x , e r g / c m / s E γ , GeV Γ =10 Γ =4.6x10 Γ =2.2x10 Γ =10 η w =1 η w =0.05 η w =0.0011Fermi Sensitivity Fig. 2.— Spectral energy distributions of IC radiation from the unshocked pulsar wind forthe epoch of periastron passage. The calculations were performed for different values of the η -parameter: η = 1 (solid lines), η = 0 .
05 (dotted lines) and η = 1 . × − (dashed lines).The initial pulsar wind bulk Lorentz factor was assumed to be Γ = 10 , 4 . × , 2 . × and 10 . The thick dashed line roughly corresponds to the expected Fermi sensitivity for0 . R ∗ = 6 . × cm and surface temperature T ∗ = 3 × K; the regions filled withgray correspond to calculations with oblate star for possible star orientations. 15 – F l u x , e r g / c m / s E γ , GeV Γ =10 Γ =4.6x10 Γ =2.2x10 Γ =10 η =1 η =0.05 η =0.0011Fermi Sensitivity Fig. 3.— The same as in Fig.2 but for the epoch of 30 days before periastron passage. 16 – F l u x , e r g / c m / s ∆ t, days 10GeV η =110GeV η =0.050.4TeV η =1 Fig. 4.— The solid and dotted lines show light-curves of 10GeV emission for two differentvalues of the η -parameter: η = 1 (solid lines), η = 0 .
05 (dotted lines) for the initial pulsarwind bulk Lorentz factor of Γ = 4 . × . Light curve of 0.4TeV gamma rays, calculatedfor η = 1 and the initial bulk Lorentz factor of Γ = 10 , is shown with thick dash-dotted line(accounting for gamma-gamma absorption) and with thin dash-dotted line without gamma-gamma attenuation. The calculations are performed for a spherical star with radius R ∗ =6 . × cm and surface temperature T ∗ = 3 × K. τ γγ ∆ t, days E γ =0.05TeVE γ =0.15TeVE γ = 0.4TeVE γ = 1TeVE γ = 5TeV Fig. 5.— The optical depth for gamma-gamma attenuation from the location of the pulsarto the observer for different energies of the gamma rays. The lines show model calculationsperformed for a spherical star with radius R ∗ = 6 . × cm and surface temperature T ∗ = 3 × K; the filled regions correspond to calculations with oblate star for possible starorientations. 17 – Γ / Γ ∆ t, days Γ = 10 Γ =4.6x10 Γ =2.2x10 Γ = 10 Fig. 6.— The averaged ratio of the electron Lorentz factor Γ at the termination shock to theinitial value Γ . The averaging is performed for electrons propagating within the angle of 60 ◦ towards the optical star. The ratio is calculated for the different values of the initial pulsarwind bulk Lorentz factor: Γ = 10 (dash-dotted line), 4 . × (solid line), 2 . × (dashedline) and 10 (dotted line). The η -parameter was assumed to be η = 1, and the calculationsare performed for a spherical star with radius R ∗ = 6 . × cm and surface temperature T ∗ = 3 ×4