Hard X-ray Quiescent Emission in Magnetars via Resonant Compton Upscattering
TTo appear in Proc. “Physics of Neutron Stars – 2017,” Journal of Physics: Conference Series, eds. G. G.Pavlov, J. A. Pons, P. S. Shternin, D. G. Yakovlev, held in Saint Petersburg, Russia, 10–14 July, 2017
Hard X-ray Quiescent Emission in Magnetars viaResonant Compton Upscattering
M. G. Baring , Z. Wadiasingh , P. L. Gonthier , A. K. Harding Department of Physics and Astronomy, Rice University, Houston, TX 77251, U.S.A. Centre for Space Research, North-West University, Potchefstroom, South Africa Hope College, Department of Physics, 27 Graves Place, Holland, MI 49423, U.S.A Astrophysics Science Division, Code 663 NASA’s Goddard Space Flight Center, Greenbelt,MD 20771, U.S.A.E-mail: [email protected]
Abstract.
Non-thermal quiescent X-ray emission extending between 10 keV and around 150keV has been seen in about 10 magnetars by RXTE, INTEGRAL, Suzaku, NuSTAR and Fermi-GBM. For inner magnetospheric models of such hard X-ray signals, inverse Compton scatteringis anticipated to be the most efficient process for generating the continuum radiation, becausethe scattering cross section is resonant at the cyclotron frequency. We present hard X-rayupscattering spectra for uncooled monoenergetic relativistic electrons injected in inner regionsof pulsar magnetospheres. These model spectra are integrated over bundles of closed field linesand obtained for different observing perspectives. The spectral turnover energies are criticallydependent on the observer viewing angles and electron Lorentz factor. We find that electronswith energies less than around 15 MeV will emit most of their radiation below 250 keV, consistentwith the turnovers inferred in magnetar hard X-ray tails. Electrons of higher energy still emitmost of the radiation below around 1 MeV, except for quasi-equatorial emission locales for selectpulse phases. Our spectral computations use a new state-of-the-art, spin-dependent formalismfor the QED Compton scattering cross section in strong magnetic fields.
1. Introduction
A topical subset of the neutron star population is defined by magnetars. They are highly-magnetized stars that have historically been divided into two observational groups: Soft-GammaRepeaters (SGRs) and Anomalous X-ray Pulsars (AXPs). Their extreme fields, which generallyexceed the quantum critical value of B cr = m e c / ( e ¯ h ) ≈ . × Gauss (where the electroncyclotron and rest mass energies are equal), are inferred from their X-ray timing properties,presuming that their rapid rotational spin down is due to magnetic dipole torques (e.g. [1]).Such a class of neutron stars with superstrong fields was postulated for SGRs by [2], and forAXPs by [3]. For recent reviews of magnetar science, see [4, 5, 6].SGRs are transient sources that undergo repeated hard X-ray outbursts. Most of theirephemeral activity consists of short flares of subsecond duration in the 10 erg/sec < L < erg/sec range, often somewhat isolated in time, and sometimes occurring in storms. Yet threemagnetars have exhibited giant supersecond flares of energies exceeding 10 ergs: SGR 0525-66in 1979, as mentioned above, SGR 1900+14 on August 27th, 1998 (e.g. see [7]), and SGR 1806-20 on December 27, 2004 (see [8]). SGRs also exhibit quiescent X-ray emission below 10 keV, ofperiods P in the range 2–12 sec. (e.g. [1, 9]). The AXPs are bright X-ray sources with periods a r X i v : . [ a s t r o - ph . H E ] O c t n the same range. Their quiescent signals below 10 keV are mostly thermal with steep power-law tails, and possess luminosities L X ∼ − × erg s − [10]. As with the SGRs, these L X values far exceed their rotational power, perhaps being powered by their internal magneticenergy. Observations of outburst activity in AXP 1E 2259+586 [11], in AXP 1E1841-045 [12]and in others suggest that AXPs and SGRs are indeed very similar. This “unification paradigm”has garnered widespread support within the magnetar community over the last decade. Thereare also highly-magnetized pulsars that exhibit periods of magnetar-like bursting activity. Theobservational status quo of magnetars is summarized in the McGill Magnetar Catalog [13]. An additional element of the magnetar phenomenon emerged following the discovery byINTEGRAL and RXTE of hard, non-thermal pulsed spectral tails in three AXPs [14, 15]. Theseluminous tails are extremely flat, extending up to 150 - 200 keV. Similar quiescent emission tailsare seen in SGRs [16, 17]. In various magnetars, a turnover around 500 - 750 keV is impliedby constraining pre-2000 upper limits obtained by the COMPTEL instrument on the
ComptonGamma-Ray Observatory . The need for such a spectral turnover is reinforced above 100 MeV byupper limits in
Fermi -LAT data for around 20 magnetars [18, 19]. Magnetic inverse Comptonscattering of thermal atmospheric soft X-ray seed photons by relativistic electrons is expectedto be extremely efficient in magnetars, and thus is a prime candidate for generating the hardX-ray tails [20, 21]. This paper explores this model, highlighting some recent results from ourongoing program of modeling the resonant Compton hard X-ray emission in magnetars.
2. Hard X-rays in Magnetars from Magnetic Inverse Compton Scattering
The scenario for the generation hard X-ray tails considered in this paper is magnetic inverseCompton scattering of thermal atmospheric soft X-ray seed photons by relativistic electrons.This is extremely efficient in highly-magnetized pulsars because the scattering process is resonantat the electron cyclotron frequency and its harmonics, so that there the cross section in theelectron rest frame exceeds the classical Thomson value of σ T ≈ . × − cm by ∼ − cm, for high speed electrons traversing a magnetar magnetosphere [24]. Providedthere is a source of electrons with Lorentz factors γ e (cid:29)
1, single inverse Compton scatteringevents can readily produce the general character of hard X-ray tails [20, 21]. In particular,Baring & Harding [20] employed QED scattering cross sections in uniform fields, extendingcollision integral formalism for non-magnetic Compton upscattering that was developed by [25].The spectra presented in [20] were characteristically flat, a consequence of the resonantcyclotron kinematics. These do not match observations, nor are they expected to since theyintegrate over all lines of sight in the uniform B . Non-uniform fields offer a different weightingof angular geometries, and when combined with cooling can steepen the spectrum considerably:see the magnetic Thomson investigation of [26]. In [20], we discerned that kinematic constraintscorrelating the directions and energies of upscattered photons yielded Doppler boosting andblueshifting along the local magnetic field direction. Therefore, the strong angular dependenceof spectra computed for the uniform field case must extend to more complex magnetospheric fieldconfigurations. Consequently, emergent inverse Compton spectra in more complete models ofhard X-ray tails will depend critically on an observer’s perspective and the sampled localesof resonant scattering, both of which vary with the rotational phase of a magnetar. Theconstruction of the resonant Compton upscattering model whose results are presented here isa geometrical extension of the work of [20] to dipolar magnetic field morphologies. Directedemission spectra have been generated for an array of observer perspectives and magneticinclination angles α to the rotation axis; they serve as a basis for future calculations that See also the neutron star cooling site http://neutronstarcooling.info/ for magnetars in a broader context. An on-line version can be found at ill treat Compton cooling of electrons self-consistently. The scattering physics employs thestate-of-the-art, spin-dependent magnetic Compton formalism developed by us in Gonthier etal. [27] that uses the preferred Sokolov and Ternov eigenstates of the Dirac equation. For detailsof the model, its kinematics and geometry and spectral characteristics, and their connection toobserver perspectives, the reader is referred to the full exposition in Wadiasingh et al. [28]. B p = r max = - - - - - Log ϵ f L og ( / n e dn γ / d t d ϵ f ) - - - - - - - L og c m - s - k e V - γ e T = × θ v = ° ϕ * = B p = r max = - - - - - - - Log ϵ f L og ( / n e dn γ / d t d ϵ f ) - - - - - - - L og c m - s - k e V - Figure 1.
Spectra generated for meridional field loops, those where the line of sight to anobserver is coplanar ( φ ∗ = 0) with the loops. The viewing angle of the observer is θ v = 30 ◦ from the magnetic dipole axis. Results for various electron Lorentz factors are depicted. Theleft panel illustrates higher-altitude and lower-field directed spectra computed for B p = 10 and r max = 4 where the resonant interactions are readily sampled for Lorentz factors γ e > . Forthe right panel with r max = 2 and B p = 100, the local field is much higher, precluding resonantinteractions near equatorial regions unless Lorentz factors are much higher. Overlaid on thecomputed spectra are observational data points for AXP 4U 0142+61 (den Hartog et al. 2008b)along with a schematic ε − / f power-law with a 250 keV exponential cutoff (black dotted curve).Two elements of the extensive work in [28] are highlighted here. The first consists of selectedbut informative spectra, depicted in Fig. 1, computed for electrons of fixed Lorentz factorstraversing individual field lines. They correspond to viewing angles coplanar with the field loops(meridional cases) that readily sample the Doppler boosting and beaming. The combinationof γ e and local field B ∼ B p /r ∼ γ e ε f (1 + cos Θ B n ) essentially controls access to resonantinteractions [20], and the value of the spectral index. Here ε f is the upscattered photon energyin units of m e c , and Θ B n is the observer’s angle relative to B at the point of scattering. Thecoupling B ∼ γ e ε f (1 + cos Θ B n ) controls the directionality of emitted photons, with higherenergies ε f being beamed closer to the field lines. For much of the range in ε f , the spectrathat sample resonant interactions possess a characteristic scaling dn/ ( dtdε f ) ∼ ε / f , i.e. areextremely flat, even harder than the uniform field results in [20]. This approximate power-lawdependence is a consequence of kinematics and magnetospheric geometry [28]. Bracketing thesequasi-power-law bands are distinctive “horns” or cusps, distinguishing when resonant scatteringsare and are not accessed. These appear both at low values ε f in the soft X-rays/EUV, wherethey would be dominated by the surface emission signal (not shown), and also in the hardX-ray and gamma-ray domains. The narrow peaks of the horns are weighted images of theresonant differential cross section, enhanced by the beaming. Not all spectra possess frequencyranges where resonant interactions are accessible: for values of local B that are large, resonantinteractions in the Wien peak are often not fully sampled, as is evident from computed spectrapresented in the right panel of Fig. 1, and the γ e = 10 example in the left panel.lso illustrated in Fig. 1 are renormalized hard X-ray spectral data for one magnetar,to illustrate how the monoenergetic electron model from single field loops does not matchobservations. Modeling of hot thermal surface emission seeded by electron bombardment atloop footpoints is not undertaken. The computed spectra extend beyond the COMPTEL upperlimits (green points) when γ e > ∼
30 . Therefore, lower Lorentz factors γ e ∼
10 are desirable, andthese a naturally generated by electron cooling [24]. High-energy attenuation mechanisms likephoton splitting or magnetic pair creation may also be operating. In [28] we also exhibit spectrafrom integrations over field line azimuths, encompassing the non-meridional loops that dominatethe contribution from a toroidal surface comprising dipolar field lines. These demonstrate steeper dn/ ( dtdε f ) ∼ ε f power-laws because the loops that do not provide tangents (i.e. B directions)at scattering locales that point toward an observer soften the spectrum. Even more interestingly,[28] illustrate that spectral arrays over such toroidal surfaces that span a range of altitudes yieldan envelope that approximately matches the 4U0142+61 spectrum displayed in Fig. 1, providedthat γ e ∼
10 . This suggests that models with more complete volumetric integrations andelectron cooling incorporated will match the spectroscopy of hard X-ray tails.
Figure 2.
Normalized photon flux ζ − Ω t/ π phase space maps for resonant Comptonupscattering. These represent the logarithmically-scaled (base 10) intensity at energies 16 keV(top row) and 100 keV (bottom row), color coded according to the legend, as a function ofspin phase Ω t/ π for each value of ζ on the ordinate. The intensity maps are for uncooledelectrons with γ e = 10 , and a uniform surface temperature T = 5 × K. They are obtainedfor azimuthally-integrated bundles of field lines, i.e. a toroidal surface, with B p = 10 , and stellarmagnetic inclination α = 15 ◦ , and depict maps for maximum loop altitudes r max = 2 , , , ζ are represented by horizontal cuts of the maps.The spectral view so far has been for an instantaneous viewing perspective, i.e. fixed pulsephases. Another element delivered in [28] was the representation of how pulse profiles generatedfor spectra from toroidal surfaces vary with photon energy ε f and the maximum surface altitude r max (in units of R NS ). These were expressed as sky maps in the ζ − Ω t/ π plane, and anexample is depicted in Fig. 2. The intensity scale is logarithmic, and is normalized so thatthe maximum in each row of panels is set to unity. Here, ζ is the angle between the viewer’sdirection and the magnetar spin axis, and for a particular choice of this angle, horizontal sectionswithin each panel define an intensity trace with pulse phase. Generally, the pulsation profilesare of smooth, single-peaked character. Yet a symmetric double-peak structure of the profilesn domains ζ ≈ α is evident, being manifested as sections of the red rings: these are realizedwhen quasi-polar viewing is possible at select phases. The phase separation of this double-peakstructure in domains α ≈ ζ shrinks at higher r max and larger ε f . This identifies a potentiallypotent observational diagnostic: comparing theoretical energy-dependent pulse profiles withobservational ones can infer values for α and ζ in magnetars, an analogous protocol to thatwidely used in gamma-ray pulsar studies. To this end, [28] applied this to the observed phaseseparation of 0.4 between the two peaks in the pulse profile of 1E 1841-045 within the energyrange of 20-35 keV. We found that for γ e ∼
10 that would result from strong cooling, thissuggests that α < ∼ ◦ , an estimate that is quite similar to the value of α ∼ ◦ inferred in theanalysis of [29]. This determination would change if toroidal components to the equatorial field(scattering locales that dominate the spectral signal) yield twist angles ∆ φ ∼ θ > ◦ in MHD simulations of field untwisting [30].In summary, the sample results presented here provide an idea of the constraints imposedupon our model, and a taste of the promise of the resonant Compton upscattering picture inexplaining the phenomenon of the hard X-ray tails in magnetar quiescent emission. They alsosuggest the usefulness of the model in probing the magnetic angle α , thus aiding in reducinguncertainties in the determination of magnetar field strengths using spin-down information. Acknowledgments
M.G.B. acknowledges support by the NASA Astrophysics Theory (ATP) and
Fermi
GuestInvestigator Programs through grants NNX13AQ82 and NNX13AP08G. Z.W. is supported bythe South African National Research Foundation. P.L.G. thanks the Michigan Space GrantConsortium, the National Science Foundation (grant AST-1009731), and NASA ATP throughgrant NNX13AO12G. A.K.H. also acknowledges support through the NASA ATP program.
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