Under the assumption that LS 5039 is a system composed by a pulsar rotating
around an O6.5V star in a $\sim 3.9$ day orbit, we present the results of a
theoretical modeling of the high energy phenomenology observed by the High
Energy Stereoscopy Array (H.E.S.S.). This model (including detailed account of
the system geometry, Klein-Nishina inverse Compton, $\gamma$-$\gamma$
absorption, and cascading) is able to describe well the rich observed
phenomenology found in the system at all timescales, both flux and
spectrum-wise.Comment: Figures and results are unchanged. Some new text and new reference

Sierpowska-Bartosik, Agnieszka

Torres, Diego F.

English

arXiv

Agnieszka Sierpowska-Bartosik

Diego F. Torres

MUCC (Crossref)

Pulsar Model of the High-Energy Phenomenology of LS 5039

4 pages.-- Printed version published on Dec 20, 2007.Under the assumption that LS 5039 is a system composed of a pulsar rotating around an O6.5 V star in a ~3.9 day orbit, we present the results of a theoretical modeling of the high-energy phenomenology observed by the High Energy Stereoscopy Array (H.E.S.S.). This model (including a detailed account of the system geometry, Klein-Nishina inverse Compton scattering, γ-γ absorption, and cascading) is able to describe well the rich observed phenomenology found in the system at all timescales, both flux- and spectrum-wise.We acknowledge support by grants AYA 2006-00530 and CSIC-PIE 200750I029.Peer reviewe

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DRAFT VERSION FEBRUARY 1, 2008Preprint typeset using LATEX style emulateapj v. 12/14/05PULSAR MODEL OF THE HIGH ENERGY PHENOMENOLOGY OF LS 5039AGNIESZKA SIERPOWSKA-BARTOSIK1 & DIEGO F. TORRES2,1Draft version February 1, 2008ABSTRACTUnder the assumption that LS 5039 is a system composed by a pulsar rotating around an O6.5V star in a∼ 3.9 day orbit, we present the results of a theoretical modeling of the high energy phenomenology observedby the High Energy Stereoscopy Array (H.E.S.S.). This model (including detailed account of the systemgeometry, Klein-Nishina inverse Compton, γ-γ absorption, and cascading) is able to describe well the richobserved phenomenology found in the system at all timescales, both flux and spectrum-wise.Subject headings: X-ray binaries (individual LS 5039), γ-rays: observations, γ-rays: theory1. INTRODUCTIONA few binaries have been identified as variable very-high-energy (VHE) γ-ray sources (Aharonian et al. 2005a,b; 2006,Albert et. al. 2006, 2007). For LS 5039, a periodicity in theγ-ray flux, consistent with the orbital timescale as determinedby Casares et al. (2005), was found with amazing precision(Aharonian et al. 2006). Short timescale variability displayedon top of this periodic behavior, both in flux and spectrum,was also reported. Indeed, the H.E.S.S. observations of LS5039 (∼ 70 hours distributed over many orbital cycles, Aha-ronian et al. 2006) constitute one of the most detailed datasetsof high energy astrophysics. Accordingly, it has been sub-ject of intense theoretical studies (e.g., Bednarek 2006, 2007;Bosch-Ramon et al. 2005; Bo¨ttcher 2007; Bo¨ttcher & Demer2005; Dermer & Bo¨ttcher 2006; Dubus 2006a,b; Paredes et al.2006; Khangulyan et al. 2007). However, the rich observedphenomenology of the system has precluded an unifying ex-planation.The discovery of a jet-like radio structure in LS 5039 andthe fact of it being the only radio/X-ray source co-localizedwith an EGRET detection, prompted a microquasar interpre-tation (Paredes et al. 2001). However, the current findings atradio and VHE γ-rays in the cases of LS I +61 303 (Dhawanet al. 2006, Albert et al. 2006) or PSR B1259-63 (Aharonianet al. 2005), gave the perspective that all three systems aredifferent realizations of the same scenario: a pulsar-massivestar binary. Dubus (2006a,b) has studied these similarities.He provided simulations of the extended radio emission in thecase of LS 5039, showing that the features found in high res-olution radio observations could also be interpreted as the re-sult of a pulsar wind. This result, the rest of similarities foundwith systems for which a pulsar companion is known, and theassessment of the low X-ray state (Martocchia et al. 2005),makes the pulsar hypothesis tenable. High energy emissionfrom pulsar binaries have been subject of study for a long time(e.g., Moskalenko et al. 1993, Moskalenko 1995; Arons &Tavani 1993; Maraschi & Treves 1981; Romero et al. 2001).But the dichotomy between pulsars or black hole binaries isnot settled (see, e.g., Mirabel 2006). Here, for testing whetherthe H.E.S.S. observations could be explained in a pulsar sce-1 Institut de Cie`ncies de l’Espai (IEEC-CSIC), Campus UAB, Torre C5,2a planta, 08193 Barcelona, Spain. Email: agni@ieec.uab.es2 Institucio´ Catalana de Recerca i Estudis Avanc¸ats (ICREA). Email: dtor-res@ieec.uab.esnario, we have assumed that the compact object in LS 5039is in fact a pulsar. Under this assumption, this Letter presentsthe results of a theoretical modeling of LS 5039 which is ableto describe reasonably well the phenomenology found in thesystem.2. THE MODELFollowing Sierpowska & Bednarek (2005) (see alsoBednarek 1997), we consider that the volume of the binarysystem is separated by a shock wave into two regions withdifferent properties, with the shock appearing as a result ofthe collision between the pulsar and the massive star winds.The position of the shock is defined by the parameter η =LSD/(M˙Vwc), where the wind velocity, Vw, depends on theradial distance from the massive star, M˙ is the star mass-lossrate, and LSD is the spin-down luminosity of the pulsar (Ball& Dodd, 2001). Note that for η < 1 the star wind domi-nates over the pulsar’s: the termination shock wraps aroundit. It is assumed that the pulsar and stellar winds are sym-metric. In the case of LS 5039 (see Table 1) the value of ηis between 0.5 (periastron) and 0.3 (apastron). Between thepulsar and the shock, inside the pulsar wind zone (PWZ), weassume that relativistic leptons are frozen in the magnetizedpulsar wind which propagate radially from the pulsar. There-fore, their synchrotron losses are neglected in our cascade cal-culations. We consider then (Klein Nishina) inverse Compton(IC) cascades in this PWZ, assuming that the thermal radia-tion from the massive star dominates in this region (see e.g.,Ball & Kirk 2000). Synchrotron emission are typically con-sidered in models where the γ-emission mainly comes fromthe shock region, especially applicable in the case of bina-ries with more eccentric orbits (e.g., Kirk, Ball & Skjaer-aasen 1999). In such very eccentric massive binaries withlarge separations the radiation field of the massive star doesnot dominate over the whole orbit and IC scattering is not ef-fective in the PWZ. We assume that the cascade initiated bya primary lepton in the PWZ develops in one dimension, i.e.in the direction of propagation of the primary particle. Thecharged products of this cascade arrive finally to the shock re-gion in the pulsar wind and follow the flow along the shocksurface. Due to the magnitude of the opacity to IC and γ-γ, most electrons effectively interact in the PWZ. Indeed, forinstance for inclination i = 30o, for 1 TeV (100 GeV) elec-trons, the opacity to IC is ∼ 1.5 (∼ 9) in the PWZ. The en-ergy carried by electrons that actually reach the shock to be2 A. SIERPOWSKA-BARTOSIK & D. F. TORREStrapped by the magnetic field is less than ∼ 10% of the pri-mary injected energy. The secondary γ-rays move into themassive star wind region (MSWR). Some of them escape thebinary system but a significant part can be absorbed due to γ-γ process. These cascades are followed by means of a MonteCarlo procedure (explained in general terms in Sierpowska &Bednarek 2005). The details of the LS 5039 implementationworked out for this paper (including the detailed account ofthe system geometry, the computation of opacities to the dif-ferent processes as a function of orbital phase, and many otherdetails specific to our study) will be presented elsewhere. Weassume that the pulsar-provided injected power in relativisticelectrons is a fraction of the spin-down power, and that theyare described by a power-law in energy. Table 1 presents thefew free parameters of the model.3 Additional model parame-ters are needed, but these are bound to fixed values (given alsoin Table 1) under multiwavelength observations (see, e.g., thepapers quoted at the introduction).3. RESULTSFigure 1 shows the phase folded H.E.S.S. data for the inte-gral flux above 1 TeV (Aharonian et al. 2006) and the resultsof our theoretical model. Casares et al.’s (2005) ephemeriswas used to fold the observational data. Each experimen-tal point represents a typical time span of observation of 28min. The corresponding phases for apastron, periastron, in-ferior (INFC), and superior (SUPC) conjunction are marked.Two periods and two different inclinations angles are shown.The trends in the H.E.S.S. datapoints are reproduced: orbitalperiodicity, a non-zero emission close to periastron, and themaximum of the fluxes is around INFC.VHE gamma-rays produced close to the star suffer se-vere absorption via pair production. The absorption processstrongly depends on the direction of propagation with respectto the massive star. Indeed, the cross-section for pair produc-tion depends on the angle θ between the VHE gamma-ray andoptical photons, and has an energy threshold∝ 1/(1− cosθ).The level of absorption therefore depends on geometry andleads to orbital modulation of the VHE gamma-ray flux. ForLS 5039, apastron and periastron are near INFC and SUPC.Absorption provides flux maxima at INFC, when γ-photonspropagate towards the observer outward the system, and opac-ities are the lowest (cos θ → 1). Flux minima happen atSUPC, when photons propagate toward the massive star (ab-sorption more effective, opacities the highest), as earlier dis-cussed, e.g., by Dubus (2006a). Absorption alone would how-ever produce strict modulation (zero flux) in the energy range0.2 to 2 TeV whereas the observations show that the fluxat ∼ 0.2 TeV is stable. Additional processes, i.e. cascad-ing, must be considered to explain the spectral modulation.Our model have these processes consistently included and thelightcurve details arise then as the interplay of the absorptionof γ-rays with the cascading process, in the framework of avarying geometry along the orbit of the system. It can be seenthat the differences between the two lightcurves correspond-ing to different inclinations are not large, but it is the detail atINFC what is worth noticing.The spectra for LS 5039 was presented in two broad or-bital phase intervals around INFC and SUPC (Aharonian etal. 2006). A clear tendency for a harder spectrum at higherflux level was found. This is reproduced by the theoreticalmodel herein presented. In order to compare with the broadphase-intervals spectra presented by H.E.S.S., we have alsocomputed the phase-average of our predictions, see Figure 1.We found an overall agreement. H.E.S.S. observations havealso provided the evolution of the normalization and slope ofa power-law fit to the 0.2–5 TeV data in 0.1 phase-binning(Aharonian et al. 2006). The variability of the spectral indexand normalization of these fits along the orbit is impressive.The use of a power-law fit has to do with low statistics insuch shorter sub-orbital intervals: higher-order functional fit-tings (such as a power-law with exponential cutoff) provide ano better fit and were not justified. We can directly comparewith these H.E.S.S. results fitting our spectral predictions inthe same way. However, we note that particularly for somephases close to periastron, the theoretical spectrum is badlymimicked by a power-law (see the examples of Figure 2). Us-ing these fits to each of the theoretically predicted spectra as afunction of phase along the orbit, we compare with H.E.S.S.observations in Figure 3. The overall similarity of the the-oretical and observational fittings is notable. Depending oninclination there are a few points around INFC for which theobservational data seem to be described by a harder spectrumthan what we obtain as a result of fitting the theoretical pre-dictions. This can be modeled with a slightly harder injectionspectrum for electrons. The normalization data point close toperiastron is missed by our predicted fitting ranges. This isthe result of our spectrum being badly fitted by a power-lawat these phases.4. CONCLUDING REMARKSA detailed modeling of LS 5039, under a pulsar scenario,accounting for the system geometry, Klein-Nishina IC, γ-γ absorption, and a Monte Carlo computation of cascading,describes well the phenomenology found in the system atall timescales, both flux and spectrum-wise. The predictivepower of the model is impressive: it is based on just a handfulof free parameters. The results shown here were not obtainedvarying these parameters searching for a best fit, but ratherexploring the predictions under minimal assumptions, whatenhances their value. The overall agreement found does nothowever constitute a proof that the system is indeed formedwith a pulsar companion (although contributes to circumstan-tial evidence in this direction). This agreement does providea framework in which the pulsar assumption can be preciselytested with future observations.We acknowledge W. Bednarek, J. Cortina, I. Ribas, J. Rico,and N. Sidro for comments, extended use of IEEC-CSIC par-allel computers cluster, and support by grants AYA 2006-00530 and CSIC-PIE 200750I029.3 The first two free parameters shown are obviously related. However,note that the spin-down power defines the position of the shock in the system, through η, which also relates the stellar mass-loss rate M˙ and LSD.REFERENCESAharonian F., et al. 2005a, A&A 442, 1Aharonian F., et al. 2005b, Science 309, 746Aharonian F., et al. 2006, A&A 460, 743Albert J. et al. 2006, Science 312, 1771PULSAR MODEL OF THE HIGH ENERGY PHENOMENOLOGY OF LS 5039 3TABLE 1MODEL PARAMETERSMeaning Symbol Adopted valueFree model parametersSpin-down power of assumed pulsar LSD 1037 erg s−1Fraction of spin-down power injected in relativistic electrons β 10−2Slope of the injected power-law description of the electron spectrum Γ −2.0VHE cutoff of the injection spectra (consistent with upper end of γ-spectrum in H.E.S.S. results) . . . 50 TeVInclination of the orbit of the system with respect to the line of sight (consistent with Casares et al. 2005) i 300, 600Most important additional parameters, fixed by multiwavelength observationsRadius of star R⋆ 9.3R⊙Mass of star M⋆ 23M⊙Temperature of star T⋆ 3.9× 104 KMass loss rate of star M˙ 10−7 M⊙ yr−1Stellar wind (SW) termination velocity V∞ 2400 km s−1SW initial velocity (SW velocity at radius r from the star: Vw(r) = V0 + (V∞ − V0)(1 −R⋆/r)1.5) V0 4 km s−1Distance to the system D 2.5 kpcEccentricity of the orbit ε 0.35Semimajor axis a 0.15AU ∼ 3.5R⋆Longitude of periastron ωp 226o0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 2,0012345   i = 30o   i = 60oINFCSUPCapastron  F > 1 TeV [ 10-12  ph cm-2 s-1 ]orbital phaseperiastronapastronSUPCINFC102 103 104 10510-1310-1210-11i = 30o INFC SUPCi = 60o INFC SUPC  E2  F(E) [ erg cm-2 s-1 ]E [GeV]FIG. 1.— Left: H.E.S.S. run-by-run folded observations of LS 5039 with the results of the theoretical model for two different inclination angles. Right:H.E.S.S. VHE spectra around INFC and SUPC together with theoretical predictions in equal phase intervals.Albert J. et al. 2007, ApJ Letters 665, 51Arons J., & Tavani M. 1993, ApJ, 403, 249Bednarek W. 1997, A&A 322, 523Bednarek W. 2006, MNRAS 368, 579Bednarek W. 2007, astro-ph/0611291Ball, L. & Dodd, J. 2001, PASA, 18, 98Bosch-Ramon, V., Paredes, J. M., Ribo´, M., et al. 2005, ApJ, 628, 388Bo¨ttcher, M. 2007, Astroparticle Physics 27, 278Bo¨ttcher, M., & Dermer, C. D. 2005, ApJ, 634, L81Dhawan V., Mioduszewski A. & Rupen M. 2006, Proceedings of Science(MQW06) 052, VI Microquasar Workshop, Sept. 18-22, 2006, Como,Italy.Dermer, C. D. & Bo¨ttcher, M. 2006, ApJ 644, 409Casares, J., Ribo´, M., Ribas, I., et al. 2005, MNRAS, 364, 899Dubus G. 2006a, A&A 451, 9Dubus G. 2006b, A&A 456, 801Khangulyan D., Aharonian F. A., Bosch-Ramon V. 2007, arXiv:0707.1689Kirk J. G., & Ball L., Astropart. Phys. 2000, 12, 335Kirk J. G., Ball L. & Skjaeraasen O., Astropart. Phys 1999, 10, 31Maraschi L., & Treves A. 1981, MNRAS, 194, 1Martocchia, A., Motch, C., Negueruela, I. 2005, A&A 430, 245Moskalenko, I.V., Karakula, S., Tkaczyk, W. 1993, MNRAS 260, 681Moskalenko, I.V. 1995, Space Science Rev. 72, 593Paredes, J. M., Martı´, J., Ribo´, M., & Massi, M. 2000, Science, 288, 2340Paredes, J. M., Bosch-Ramon, V., Romero, G. E. 2006, A&A 451, 259Romero G. E, Kaufman Bernado M. M., Combi J. A. & Torres D. F. 2001,A&A 376, 599Sierpowska A. & Bednarek W. 2005, MNRAS 356, 7114 A. SIERPOWSKA-BARTOSIK & D. F. TORRES102 103 104 10510-1310-1210-11i = 30o  = 0.00  = 0.72  E2 F(E) [ TeV cm-2 s-1 ]E [ GeV ]102 103 104 10510-1310-1210-11i = 60o  = 0.00  = 0.72  E2  F(E) [ TeV cm-2 s-1 ]E [ GeV ]FIG. 2.— Examples of the theoretical results, for different inclinations, for the spectrum of single phases fitted with a power law in the range 0.2–5 TeV.FIG. 3.— Parameters of power-law fittings to the spectra as a function of phase both for the observational H.E.S.S data and our theoretical curves. We showtwo sets of results corresponding to fitting in different energy ranges (0.2–1 TeV, 0.2–5 TeV), and inclination angles (top: i = 600, bottom: i = 300). The sizeof the shading represent the error in the parameter fitting of our model.

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Pulsar model of the high energy phenomenology of LS 5039

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Pulsar model of the high energy phenomenology of LS 5039

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