X-ray mapping of the stellar wind in the binary PSR J2032+4127/MT91 213

X-ray mapping of the stellar wind in the binary PSR J2032+4127/MT91 213 Abstract PSR J2032+4127 is a young and rapidly rotating pulsar on a highly eccentric orbit around the high-mass Be star MT91 213. X-ray monitoring of the binary system over an ∼4000 d period with Swift has revealed an increase of the X-ray luminosity which we attribute to the synchrotron emission of the shocked pulsar wind. We use Swift X-ray observations to infer a clumpy stellar wind with r−2 density profile and constrain the Lorentz factor of the pulsar wind to 105 < γw < 106. We investigate the effects of an axisymmetric stellar wind with polar gradient on the X-ray emission. Comparison of the X-ray light curve hundreds of days before and after the periastron can be used to explore the polar structure of the wind. radiation mechanisms: non-thermal, stars: massive, pulsars: individual: PSR J2032+4127, X-rays: binaries 1 INTRODUCTION PSR J2032+4127/MT91 213 is a γ-ray binary system (Lyne et al. 2015) and associated with the source TeV J2032+4130 (Camilo et al. 2009). The compact object of the binary is PSR J2032+4127 (Abdo et al. 2009), a young (∼0.2 Myr) pulsar with spin-down luminosity Lsd ≃ 1.7 × 1035 erg s−1 and spin period P = 143 ms yielding a magnetic field strength of ∼2 × 1012 G. The companion is most likely a Be star (MT91 213; Massey & Thompson 1991) that belongs to the Cygnus OB2 association at a distance d = 1.33 ± 0.60 kpc (Kiminki et al. 2015). The pulsar is on a highly eccentric orbit (e ∼ 0.93–0.99) around its companion with an orbital period of Porb ∼ 44–49 yr (Ho et al. 2017). The long Porb and short spin period make the system an outlier of the P–Porb diagram for Be X-ray binaries (Corbet 1984). However, we note many similarities between this system and PSR B1259-63/LS 2883 (Chernyakova et al. 2014). X-ray monitoring of the system with Swift has revealed a gradual increase of the X-ray luminosity combined with episodes of flaring activity (Ho et al. 2017; Li et al. 2017). The enhancement of the X-ray emission is believed to arise from the interaction between the relativistic wind of the pulsar and the outflowing wind of the companion Be star. Within this scenario, Takata et al. (2017) have recently argued that the Swift X-ray light curve (LC) can be explained by either a variation in the momentum ratio of the two winds along the orbit or with a pulsar wind magnetization that depends on the distance from the pulsar. In this letter, we provide analytical expressions connecting the X-ray luminosity of the binary system with properties of the stellar wind and the relativistic wind of the pulsar. We assume that the observed X-ray emission results from synchrotron emitting pairs which are accelerated at the termination shock formed in the relativistic wind of the pulsar. We search for deviations from the typical r−2 density profile of the companion Be star and also provide model X-ray LCs for scenarios where the stellar wind properties have polar and radial dependences. The upcoming periastron, occurring in 2017 mid-November, provides a unique opportunity to observe variations in the emission of the system from X-rays up to TeV γ-rays. Follow-up X-ray observations after the periastron passage will allow us to explore anisotropies in the wind properties of a massive star. 2 MODEL SET-UP We adopt the scenario where the observed X-ray emission from PSR J2032+4127/MT91 213 is attributed to the synchrotron radiation from relativistic electrons and positrons (i.e. pairs). These are accelerated at the termination shock formed by the interacting winds. The shock terminates at a distance rt from the neutron star, which can be derived by balancing the ram pressures of the pulsar and stellar winds (e.g. Lipunov et al. 1994; Tavani, Arons & Kaspi 1994):   \begin{equation} r_{\rm t}=\sqrt{\frac{L_{\rm sd}}{4\pi c \rho _{\rm w} v_{\rm r}^2}}\approx \sqrt{\frac{L_{\rm sd}}{4\pi c p_{\rm w}}}, \end{equation} (1)where $$p_{\rm w}=\rho _{\rm w} v_{\rm w}^2$$ is the ram pressure of the stellar wind and vr ≈ vw is the relative velocity of the two winds along the orbit.1 The shocked pulsar wind moves with a mildly relativistic speed (∼c/2), while it may accelerate to superfast magnetosonic speeds due to sideways expansion (Bucciantini, Amato & Del Zanna 2005). The relevant expansion time-scale is:   \begin{equation} t_{\rm exp}\sim \frac{2r_{\rm t}}{c}. \end{equation} (2)In general, pw is expected to vary with radial distance, thus leading to changes of rt and texp along the pulsar’s orbit. The magnetic field of the shocked pulsar wind can also be expressed in terms of pw as follows:   \begin{equation} B \approx \sqrt{8\pi \epsilon _{\rm B}p_{\rm w}}, \end{equation} (3)where the dimensionless parameter εB is related to the wind magnetization σ (Kennel & Coroniti 1984) as εB = 4σ. At the termination shock, pairs are expected to accelerate and obtain a non-thermal energy distribution typically described by a power law with slope p > 2. The pair injection rate into the shocked pulsar wind region can be written as (e.g. Christie et al. 2017):   \begin{equation} Q(\gamma ) \simeq \epsilon _{\rm e}\frac{L_{\rm sd} (p-2)}{\gamma _{\min }^2 m_{\rm e}c^2}\left(\frac{\gamma }{\gamma _{\min }} \right)^{-p}, \,\quad \gamma \ge \gamma _{\min }, \end{equation} (4)where εe ≤ 1 is the fraction of the pulsar’s spin-down power transferred to relativistic pairs and γmin  is the minimum Lorentz factor of the pairs, γmin  = γw(p − 2)/(p − 1). Among the free parameters of the model, γw is the most uncertain one with values in the range 102–106 (e.g. Montani & Bernardini 2014; Porth, Komissarov & Keppens 2014). Henceforth, we assume equipartition between particles and magnetic fields in the downstream region of the shock, i.e. εe = εB = 0.5 (e.g. Porth et al. 2014). Synchrotron photons of energy εx will be produced by pairs with Lorentz factor:   \begin{equation} \gamma _{\rm x} \simeq 3\times 10^6 \ p_{\rm w,-4}^{-1/4}\left(\frac{\epsilon _{\rm x}}{5 \ {\rm keV}}\right)^{1/2} \left( \frac{\epsilon _{\rm B}}{0.5}\right)^{-1/4}, \end{equation} (5)where pw = 10−4pw, -4 g cm−1 s−2. As long as the synchrotron cooling time-scale of the X-ray emitting pairs is longer than texp (slow cooling regime), the X-ray synchrotron luminosity emitted over a frequency range [νx1, νx2] will be given by:   \begin{equation} L_{\rm x}= \mathcal {C}f_{\rm x} L_{\rm sd}^{3/2} \gamma _{\min }^{p-2} \epsilon _{\rm e}\epsilon _{\rm B}^{\frac{p+1}{4}} p_{\rm w}^{\frac{p-1}{4}}, \end{equation} (6)where $$f_{\rm x} = (\nu _{\rm x1}^{-\beta +1}-\nu _{\rm x2}^{-\beta +1} )/(\beta -1)$$, β = (p − 1)/2, and $$\mathcal {C}=\sigma _{\rm T}(8\pi )^{\frac{p+1}{4}}\left( 2\pi m_{\rm e}c/e\right)^{\frac{3-p}{2}}(p-2)/(6\pi m_{\rm e}c^2\sqrt{4\pi c} )$$. For the derivation of equation (6), we used the δ-function approximation for the synchrotron emissivity, the relation N(γ) = Q(γ)texp, and equations (1)–(4). A transition from the slow cooling to the fast cooling regime can result in a softening of the X-ray spectrum and in the saturation of the system’s X-ray luminosity, seen as a plateau in the LC, at a fraction of εeLsd, namely:   \begin{eqnarray} L_{\rm x, s} & \approx & 2\times 10^{34} \ {\rm erg \ s^{-1}} \ p_{\rm w, -4}^{1/4} \frac{L_{\rm sd}}{10^{35} {\rm erg \ s^{-1}}} \nonumber\\ &&\times \, \left(\frac{\gamma _{\rm w}}{10^6}\right) \left(\frac{\epsilon _{\rm e}}{0.5}\right) \left(\frac{\epsilon _{\rm B}}{0.5}\right)^{1/4} \left(\frac{\epsilon _{\rm x}}{1 \ {\rm keV}}\right)^{-1/2}, \end{eqnarray} (7)where equation (5) and p = 3 were used. 3 X-RAY OBSERVATIONS Swift /XRT observations can provide a detailed X-ray LC of the system while available XMM–Newton , Chandra , and NuSTAR observations can be used to derive accurate spectral properties. We note that all available observations yield compatible spectral properties within errors, apart from a single combined XRT/NuSTAR spectrum that appears to be much softer (Ho et al. 2017; Li et al. 2017). The Swift/XRT LC (up to MJD 58033.4) was produced following the instructions described in the Swift data analysis guide (http://www.swift.ac.uk/analysis/xrt/). We used xrtpipeline to generate the Swift/XRT products, and extracted events by using xselect (HEASoft FTOOLS; Blackburn 1995). The LC was also compared for consistency with the automated Swift/XRT online products (Evans et al. 2007). None of the Swift/XRT observations during the monitoring campaign of the system yielded sufficient statistics to allow a meaningful study of the spectrum. We therefore used fixed spectral parameters for converting the XRT count rates to flux. In particular, to transform the Swift/XRT rates to unabsorbed luminosities, we assumed a distance of 1.3 kpc and a power-law spectrum with photon index Γ = 2 and column density NH = 7.7 × 1021 cm−2 (see table 4 in Ho et al. 2017). 4 SPHERICAL STELLAR WIND The X-ray luminosity depends on the following model parameters: p, εe, εB, γw, and pw, see equation (6). We benchmark the power-law index of the pair distribution to p = 2Γ − 1 (see Section 3), assuming that the pairs emitting in the Swift energy band (0.3–10 keV) are slow cooling. The validity of our assumption will also be checked by comparing a posteriori the synchrotron cooling and shock expansion time-scales. If energy is shared equally between particles and magnetic fields (i.e. εe = εB = 0.5), we can derive pw by matching equation (6) to the unabsorbed Swift X-ray luminosity for different values of γw. In Fig. 1, we show the results for γw = 106, although these can be scaled accordingly for other parameter values using the analytical expressions of Section 2. Figure 1. View largeDownload slide Plotted (from top to bottom) as a function of time till periastron (MJD 58069): the unabsorbed 0.3–10 keV Swift X-ray LC of the binary, the ram pressure of the stellar wind, the mass-loss rate of the stellar wind for vw = 103 km s−1, and the ratio of the synchrotron to expansion time-scales for pairs emitting at 10 keV. The 1/r2 dependence of the wind’s ram pressure is shown with a dashed magenta line. The horizontal blue dashed lines indicate the typical range of values for the mass-loss rate of B stars (Martins et al. 2008; Krtička 2014). Figure 1. View largeDownload slide Plotted (from top to bottom) as a function of time till periastron (MJD 58069): the unabsorbed 0.3–10 keV Swift X-ray LC of the binary, the ram pressure of the stellar wind, the mass-loss rate of the stellar wind for vw = 103 km s−1, and the ratio of the synchrotron to expansion time-scales for pairs emitting at 10 keV. The 1/r2 dependence of the wind’s ram pressure is shown with a dashed magenta line. The horizontal blue dashed lines indicate the typical range of values for the mass-loss rate of B stars (Martins et al. 2008; Krtička 2014). The first two panels from the top show, respectively, the Swift X-ray LC and the inferred ram pressure of the stellar wind, $$p_{\rm w} \propto L_{\rm x}^2 \gamma _{\rm w}^{-2} \epsilon _{\rm e}^{-2} \epsilon _{\rm B}^{-2}$$. The magnetic field, which can be derived by equation (3), can be as high as ∼0.1 G in agreement with Takata et al. (2017). The temporal variability of pw may originate from changes in the wind’s velocity and/or density. Simulations of line-driven winds from massive stars have shown that both their velocity and density are strongly variable close to the stellar surface (e.g. Feldmeier 1995; Lobel & Blomme 2008). The wind velocity is typically less variable than the density, which may vary more than two orders of magnitude (see Fig. 1; Bozzo et al. 2016). In addition, at the distances of interest (i.e. r ≫ R⊙), the stellar wind is expected to move with its terminal velocity. As a zeroth-order approximation, we thus attribute the changes of pw (second panel from top) to changes of the wind’s density and assume that vw is constant with radius and equal to its terminal value (∼103 km s−1). Assuming spherical symmetry, the mass-loss rate of the wind can be estimated as $$\dot{M}= 4 \pi r^2 p_{\rm w}/v_{\rm w}$$, where r is the separation distance of the binary members. The mass-loss rate fluctuates around an average value of ∼10−9 M⊙ yr−1 that falls within the value range for B stars (Martins et al. 2008; Krtička 2014). Interestingly, the inferred mass-loss rate is compatible with ρw ∝ r−2 (magenta dashed line in Fig. 1), while density enhancements giving rise to X-ray flares (top panel in Fig. 1) can be explained by a clumpy wind (e.g. Oskinova, Feldmeier & Kretschmar 2012). Because of the scaling $$p_{\rm w}\propto \gamma _{\rm w}^{-2}$$, the inferred mass-loss rate could be as high as 10−7 M⊙ yr−1 for a slower pulsar wind with γw = 105. Unless the Be star of the binary has an uncommonly high mass-loss rate, then we can set a lower limit on the γw by requiring that $$\langle \dot{M} \rangle \lesssim 10^{-7}$$ M⊙ yr−1:   \begin{equation} \gamma _{\rm w}\gtrsim 10^5 \left(\frac{0.5}{\epsilon _{\rm e}}\right)\left(\frac{0.5}{\epsilon _{\rm B}}\right)\left(\frac{10^3 \ {\rm km \ s^{-1}}}{v_{\rm w}}\right)^{1/2}. \end{equation} (8)Equation (8) also suggests that neither εB nor εe can be much smaller than unity, as very large values of the pulsar wind’s Lorentz factor (γw ≫ 105) or the star’s mass-loss rate ($$\dot{M} \gg 10^{-7}$$ M⊙ yr−1) would be necessary to explain the observed Lx. The synchrotron cooling time-scale of pairs emitting at energy εx is $$t_{\rm syn} \propto \epsilon _{\rm x}^{-1/2} L_{\rm x}^{-3/2} \epsilon _{\rm B}^{3/4} \left(\gamma _{\rm w} \epsilon _{\rm e}\right)^{3/2}$$ (see equations 3 and 5) and is longer than texp for the adopted parameters (bottom panel in Fig. 1). Transition to the fast cooling regime during the period of Swift observations would be relevant for γw < 105, which would, in turn, imply very high mass-loss rates in contradiction to the expected values for B stars as discussed above (see also equation 8). Although synchrotron cooling is not relevant for the X-ray emitting pairs during the period of Swift observations, we discuss the possibility of inverse Compton (IC) cooling in Section 6. 5 AXISYMMETRIC STELLAR WIND WITH POLAR GRADIENT The extended atmosphere of a Be star can, in general, be divided into two regions: the equatorial (decretion) disc region and the wind region (Okazaki et al. 2011). The former is described by a geometrically thin Keplerian disc with high plasma density (for a review, see Porter & Rivinius 2003), whereas the wind region is composed of low density plasma moving with ∼103 km s−1. Here, we consider a toy model for the description of the wind structure. We assume that the stellar wind is axisymmetric (i.e. no azimuthal dependence) and model the ram pressure of the stellar wind as (e.g. Petrenz & Puls 2000; Ignace & Brimeyer 2006):   \begin{equation} p_{\rm w}(r, \theta ) = p_0 \ r^{-n} \left(1+ G \left|\cos \theta \right|^m\right), \end{equation} (9)where the distance r is measured from the focus of the ellipse where the Be star is located, the polar angle θ ∈ [0, 2π] is measured from the Be equator, and n, m > 0. The constant G is the equator-to-pole density contrast, the power-law index m determines the confinement of the wind to the equatorial plane, and p0 is a normalization constant. The latter is determined by requiring pw = 10−5 g cm−1 s−2 when the binary separation is 4 × 1014 cm about 1000 d before periastron for the same parameters used in Fig. 1. We consider the case where the pulsar’s orbital plane is perpendicular to the Be’s equatorial plane (see Fig. 2), since we have no knowledge of the system’s orientation at the time of writing. The pulsar’s orbit can be then expressed in terms of θ as rNS(θ) = a(1 − e2)/[1 + e cos (θ − θod)], where e is the eccentricity of the orbit and θod is the angle between the equator of the star and the orbit’s semimajor axis a. Figure 2. View largeDownload slide Sketch of the Be wind structure. The properties of the wind depend on the distance from the star and on the polar angle θ. The product of the plasma density and velocity becomes lower as we move from the equatorial plane (θ = 0) to the pole (θ = π/2), as indicated with the colour gradient. The Be disc (red coloured region) is Keplerian and geometrically thin with high plasma density. Two possible orientations of the pulsar’s orbit through the wind structure are shown. The pulsar’s orbital plane is perpendicular to the Be star’s equatorial plane (objects are not in scale). Figure 2. View largeDownload slide Sketch of the Be wind structure. The properties of the wind depend on the distance from the star and on the polar angle θ. The product of the plasma density and velocity becomes lower as we move from the equatorial plane (θ = 0) to the pole (θ = π/2), as indicated with the colour gradient. The Be disc (red coloured region) is Keplerian and geometrically thin with high plasma density. Two possible orientations of the pulsar’s orbit through the wind structure are shown. The pulsar’s orbital plane is perpendicular to the Be star’s equatorial plane (objects are not in scale). The effect of different wind structures on the X-ray LCs is exemplified in Fig. 3. For the displayed cases, we keep n = 2 (see previous section) while varying θod, G, and m separately – see panels (a) to (c) in Fig. 3. The LC shape can be symmetric around periastron only for specific orientations; for θod = 0°, the LC shows a major peak at periastron, while it exhibits two symmetric peaks for θod = 90° as the pulsar crosses the dense equatorial wind twice. All other configurations result in anisotropic LCs. Although the binary separation does not change much close to periastron, the polar variation of the wind becomes stronger for larger G values. This results in LCs with sharp features (dips or peaks) close to the periastron. The duration of these features is determined by the pulsar’s speed as it passes through regions with different wind properties along its orbit. Additionally, the G parameter can mimic the effect of different angles between the pulsar’s orbital plane and the Be disc plane. The parameter m determines the confinement of the wind to the equatorial plane of the star. Changes in m do not strongly affect the LC close to periastron, but have an impact on the LC shape hundreds of days before or after. A radial wind profile that deviates from the standard one (i.e. r−2) may masquerade an axisymmetric stellar wind with polar variations, namely n = 2 and m > 0 (see equation 9), but cannot explain asymmetric LCs around periastron. Figure 3. View largeDownload slide X-ray LCs from the interaction of the pulsar wind with different wind structures modelled by equation (9). (a) We vary the angle θod (inset legend) for fixed m = 3 and G = 10. The LC obtained for a stellar wind without polar dependence (i.e. G = 0) is also shown for a comparison (magenta dashed line). Swift data (MJD 58019.9) and their symmetric ones with respect to the periastron time are overplotted with black and grey symbols, respectively. (b) We vary the equator-to-pole density contrast G (inset legend) for fixed θod = 30° and m = 3. (c) We vary the confinement of wind to the equatorial plane by changing the power-law index m (inset legend) for fixed θod = 30° and G = 10. In all panels, we used n = 2 and pw = 10−5 g cm−1 s−2 at ∼1000 d before periastron. Figure 3. View largeDownload slide X-ray LCs from the interaction of the pulsar wind with different wind structures modelled by equation (9). (a) We vary the angle θod (inset legend) for fixed m = 3 and G = 10. The LC obtained for a stellar wind without polar dependence (i.e. G = 0) is also shown for a comparison (magenta dashed line). Swift data (MJD 58019.9) and their symmetric ones with respect to the periastron time are overplotted with black and grey symbols, respectively. (b) We vary the equator-to-pole density contrast G (inset legend) for fixed θod = 30° and m = 3. (c) We vary the confinement of wind to the equatorial plane by changing the power-law index m (inset legend) for fixed θod = 30° and G = 10. In all panels, we used n = 2 and pw = 10−5 g cm−1 s−2 at ∼1000 d before periastron. 6 DISCUSSION The Swift X-ray data indicate the presence of a clumpy stellar wind whose density scales, on average, as ∼r−2. The latter can explain the gradual increase of the X-ray luminosity as the pulsar approaches periastron, while the X-ray flares are attributed to clumps of dense matter (Section 4). Relativistic hydrodynamic simulations of an inhomogeneous stellar wind interacting with a pulsar wind show that the two-wind interaction region can be perturbed by clumps (see e.g. Paredes-Fortuny et al. 2015). These perturbations may enhance the energy dissipation of the pulsar wind at the termination shock, strengthen the post-shock magnetic field, or change the direction of motion of the shocked pulsar wind, thus giving rise to X-ray flares (de la Cita et al. 2017). Synchrotron cooling is not relevant for X-ray emitting pairs in the 0.3–10 keV band during the period of Swift observations, as shown in Fig. 1. This holds also for more energetic pairs that emit in the NuSTAR energy band (i.e. up to 50 keV). It seems therefore unlikely that the softening of the NuSTAR X-ray spectrum in 2016 is caused by synchrotron cooling (Li et al. 2017), unless γw < 103. IC scattering of stellar photons can also be a potential source of pair cooling. For a typical Be star with T* = 3 × 104 K, pairs radiating at $$\epsilon _{\rm x} \propto B \gamma _{\rm x}^2$$ will Thomson up-scatter stellar photons from the Rayleigh–Jeans part of the spectrum with ν < νT ≡ 3mec2/hγx and energy density $$u_{\rm T}\simeq 2\pi k T_* \nu _{\rm T}^3 (10 R_{{\odot }})^2/(3 c^3 r^2)$$. For the same parameters as in Fig. 1, we find that the shortest IC cooling time-scale for pairs emitting at 0.3 keV is ≳ texp at periastron. A two-wind interaction is expected for the largest part of the pulsar’s orbit, whereas the interaction of the pulsar wind with the Be disc may become relevant only close to the periastron (for a detailed study, see Takata et al. 2017). In principle, the Be disc/pulsar wind interaction can be studied with equation (9), since the X-ray luminosity depends on the product of the density and relative velocity of the interacting plasma flows. Takata et al. (2017) derived ∼0.2 g cm−1 s−2 close to periastron, by adopting a specific model for the Be disc with ρ = 10−10 g cm−3 on the stellar surface and rotational velocity ∼107 cm s−1 at r ∼ 1 au (see equations 8–9 therein). We obtain similar values using equation (9) for large m and G values (e.g. m = 27, G = 100). Current Hα measurements suggest a Be disc with size ∼0.2–0.5 au (Ho et al. 2017). It is well known that the Hα emission only arises in an inner portion of the disc and the actual size of decretion discs can be many times larger. Thus, as the pulsar approaches periastron, it may interact with stellar material. This can be then captured by the neutron star, if the termination shock lies within its gravitational sphere of influence. For vr = 100 km s−1, this requires ρ ≳ 3 × 10−16 g cm−3 at periastron. Still, accretion on to the rapidly rotating neutron star will be halted by the propeller effect (Illarionov & Sunyaev 1975), unless the accretion rate is extremely high, i.e. $$\dot{M}_{\rm a}=(2\text{--}20)\times 10^{18}$$ g s−1 corresponding to Lx = (5–50) × 1038 erg s−1 (Campana et al. 2002). Although a type-I outburst is unlikely to happen close to periastron (see e.g. Okazaki & Negueruela 2001), further phenomenology is expected. The pulsar spins down due to electromagnetic torque NEM = −μ2Ω3/c3, where Ω and μ are the pulsar’s angular spin frequency and magnetic moment, respectively. Close to the periastron, the pulsar may experience an additional spin-down due to the propeller effect on the plasma ‘held’ outside the corotation radius (e.g. Illarionov & Sunyaev 1975; Ghosh 1995). We adopt the conservative expression of Illarionov & Sunyaev (1975) for the propeller torque (for details, see Papitto, Torres & Rea 2012): $$N_{\rm prop}=-\dot{M}_{\rm a}\sqrt{GMR_{\rm m}}\Omega _{\rm K}(R_{\rm m})/\Omega$$, where ΩK is the Keplerian velocity, $$R_{\rm m} =\xi \left(\mu ^4/2\, G M_{\rm NS} \dot{M}_{\rm a}^2\right)^{1/7}$$ is the magnetospheric radius, and ξ ≃ 0.5–1 (see Chashkina, Abolmasov & Poutanen 2017, and references therein). The total spin-down torque acting upon the pulsar will be at least doubled, if $$\dot{M}_{\rm a}\gtrsim 4\times 10^{17}$$ g s−1. Assuming that the propeller torque acts upon the pulsar for ∼10 d, we expect a spin-frequency change of −4 × 10−6 Hz, i.e. an antiglitch (Şaşmaz Muş, Aydın & Göğüş 2014). The predicted effect could be detectable by Fermi –LAT which has already measured a pulsar glitch with Δν = 1.9 × 10−6 Hz (Lyne et al. 2015). The upcoming periastron passage of PSR J2032+4127 offers a unique opportunity to observe the system across the electromagnetic spectrum. In this letter, we focused on the non-thermal X-ray emission of the system and showed how it can be used to map the wind properties of the stellar companion. Comparison of the X-ray LC hundreds of days before and after the periastron will allow us to explore the polar structure of the wind while changes in the pulsar’s spin-down rate close to the periastron may probe the rate of mass captured by the neutron star. Acknowledgements We thank the anonymous referee for the report. We acknowledge support from NASA through the grant NNX17AG21G issued by the Astrophysics Theory Program. We acknowledge the use of publicly available data from the Swift satellite. 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M., 1994, ApJ , 433, L37 CrossRef Search ADS   © 2017 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical Society http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Monthly Notices of the Royal Astronomical Society: Letters Oxford University Press

X-ray mapping of the stellar wind in the binary PSR J2032+4127/MT91 213

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Abstract

Abstract PSR J2032+4127 is a young and rapidly rotating pulsar on a highly eccentric orbit around the high-mass Be star MT91 213. X-ray monitoring of the binary system over an ∼4000 d period with Swift has revealed an increase of the X-ray luminosity which we attribute to the synchrotron emission of the shocked pulsar wind. We use Swift X-ray observations to infer a clumpy stellar wind with r−2 density profile and constrain the Lorentz factor of the pulsar wind to 105 < γw < 106. We investigate the effects of an axisymmetric stellar wind with polar gradient on the X-ray emission. Comparison of the X-ray light curve hundreds of days before and after the periastron can be used to explore the polar structure of the wind. radiation mechanisms: non-thermal, stars: massive, pulsars: individual: PSR J2032+4127, X-rays: binaries 1 INTRODUCTION PSR J2032+4127/MT91 213 is a γ-ray binary system (Lyne et al. 2015) and associated with the source TeV J2032+4130 (Camilo et al. 2009). The compact object of the binary is PSR J2032+4127 (Abdo et al. 2009), a young (∼0.2 Myr) pulsar with spin-down luminosity Lsd ≃ 1.7 × 1035 erg s−1 and spin period P = 143 ms yielding a magnetic field strength of ∼2 × 1012 G. The companion is most likely a Be star (MT91 213; Massey & Thompson 1991) that belongs to the Cygnus OB2 association at a distance d = 1.33 ± 0.60 kpc (Kiminki et al. 2015). The pulsar is on a highly eccentric orbit (e ∼ 0.93–0.99) around its companion with an orbital period of Porb ∼ 44–49 yr (Ho et al. 2017). The long Porb and short spin period make the system an outlier of the P–Porb diagram for Be X-ray binaries (Corbet 1984). However, we note many similarities between this system and PSR B1259-63/LS 2883 (Chernyakova et al. 2014). X-ray monitoring of the system with Swift has revealed a gradual increase of the X-ray luminosity combined with episodes of flaring activity (Ho et al. 2017; Li et al. 2017). The enhancement of the X-ray emission is believed to arise from the interaction between the relativistic wind of the pulsar and the outflowing wind of the companion Be star. Within this scenario, Takata et al. (2017) have recently argued that the Swift X-ray light curve (LC) can be explained by either a variation in the momentum ratio of the two winds along the orbit or with a pulsar wind magnetization that depends on the distance from the pulsar. In this letter, we provide analytical expressions connecting the X-ray luminosity of the binary system with properties of the stellar wind and the relativistic wind of the pulsar. We assume that the observed X-ray emission results from synchrotron emitting pairs which are accelerated at the termination shock formed in the relativistic wind of the pulsar. We search for deviations from the typical r−2 density profile of the companion Be star and also provide model X-ray LCs for scenarios where the stellar wind properties have polar and radial dependences. The upcoming periastron, occurring in 2017 mid-November, provides a unique opportunity to observe variations in the emission of the system from X-rays up to TeV γ-rays. Follow-up X-ray observations after the periastron passage will allow us to explore anisotropies in the wind properties of a massive star. 2 MODEL SET-UP We adopt the scenario where the observed X-ray emission from PSR J2032+4127/MT91 213 is attributed to the synchrotron radiation from relativistic electrons and positrons (i.e. pairs). These are accelerated at the termination shock formed by the interacting winds. The shock terminates at a distance rt from the neutron star, which can be derived by balancing the ram pressures of the pulsar and stellar winds (e.g. Lipunov et al. 1994; Tavani, Arons & Kaspi 1994):   \begin{equation} r_{\rm t}=\sqrt{\frac{L_{\rm sd}}{4\pi c \rho _{\rm w} v_{\rm r}^2}}\approx \sqrt{\frac{L_{\rm sd}}{4\pi c p_{\rm w}}}, \end{equation} (1)where $$p_{\rm w}=\rho _{\rm w} v_{\rm w}^2$$ is the ram pressure of the stellar wind and vr ≈ vw is the relative velocity of the two winds along the orbit.1 The shocked pulsar wind moves with a mildly relativistic speed (∼c/2), while it may accelerate to superfast magnetosonic speeds due to sideways expansion (Bucciantini, Amato & Del Zanna 2005). The relevant expansion time-scale is:   \begin{equation} t_{\rm exp}\sim \frac{2r_{\rm t}}{c}. \end{equation} (2)In general, pw is expected to vary with radial distance, thus leading to changes of rt and texp along the pulsar’s orbit. The magnetic field of the shocked pulsar wind can also be expressed in terms of pw as follows:   \begin{equation} B \approx \sqrt{8\pi \epsilon _{\rm B}p_{\rm w}}, \end{equation} (3)where the dimensionless parameter εB is related to the wind magnetization σ (Kennel & Coroniti 1984) as εB = 4σ. At the termination shock, pairs are expected to accelerate and obtain a non-thermal energy distribution typically described by a power law with slope p > 2. The pair injection rate into the shocked pulsar wind region can be written as (e.g. Christie et al. 2017):   \begin{equation} Q(\gamma ) \simeq \epsilon _{\rm e}\frac{L_{\rm sd} (p-2)}{\gamma _{\min }^2 m_{\rm e}c^2}\left(\frac{\gamma }{\gamma _{\min }} \right)^{-p}, \,\quad \gamma \ge \gamma _{\min }, \end{equation} (4)where εe ≤ 1 is the fraction of the pulsar’s spin-down power transferred to relativistic pairs and γmin  is the minimum Lorentz factor of the pairs, γmin  = γw(p − 2)/(p − 1). Among the free parameters of the model, γw is the most uncertain one with values in the range 102–106 (e.g. Montani & Bernardini 2014; Porth, Komissarov & Keppens 2014). Henceforth, we assume equipartition between particles and magnetic fields in the downstream region of the shock, i.e. εe = εB = 0.5 (e.g. Porth et al. 2014). Synchrotron photons of energy εx will be produced by pairs with Lorentz factor:   \begin{equation} \gamma _{\rm x} \simeq 3\times 10^6 \ p_{\rm w,-4}^{-1/4}\left(\frac{\epsilon _{\rm x}}{5 \ {\rm keV}}\right)^{1/2} \left( \frac{\epsilon _{\rm B}}{0.5}\right)^{-1/4}, \end{equation} (5)where pw = 10−4pw, -4 g cm−1 s−2. As long as the synchrotron cooling time-scale of the X-ray emitting pairs is longer than texp (slow cooling regime), the X-ray synchrotron luminosity emitted over a frequency range [νx1, νx2] will be given by:   \begin{equation} L_{\rm x}= \mathcal {C}f_{\rm x} L_{\rm sd}^{3/2} \gamma _{\min }^{p-2} \epsilon _{\rm e}\epsilon _{\rm B}^{\frac{p+1}{4}} p_{\rm w}^{\frac{p-1}{4}}, \end{equation} (6)where $$f_{\rm x} = (\nu _{\rm x1}^{-\beta +1}-\nu _{\rm x2}^{-\beta +1} )/(\beta -1)$$, β = (p − 1)/2, and $$\mathcal {C}=\sigma _{\rm T}(8\pi )^{\frac{p+1}{4}}\left( 2\pi m_{\rm e}c/e\right)^{\frac{3-p}{2}}(p-2)/(6\pi m_{\rm e}c^2\sqrt{4\pi c} )$$. For the derivation of equation (6), we used the δ-function approximation for the synchrotron emissivity, the relation N(γ) = Q(γ)texp, and equations (1)–(4). A transition from the slow cooling to the fast cooling regime can result in a softening of the X-ray spectrum and in the saturation of the system’s X-ray luminosity, seen as a plateau in the LC, at a fraction of εeLsd, namely:   \begin{eqnarray} L_{\rm x, s} & \approx & 2\times 10^{34} \ {\rm erg \ s^{-1}} \ p_{\rm w, -4}^{1/4} \frac{L_{\rm sd}}{10^{35} {\rm erg \ s^{-1}}} \nonumber\\ &&\times \, \left(\frac{\gamma _{\rm w}}{10^6}\right) \left(\frac{\epsilon _{\rm e}}{0.5}\right) \left(\frac{\epsilon _{\rm B}}{0.5}\right)^{1/4} \left(\frac{\epsilon _{\rm x}}{1 \ {\rm keV}}\right)^{-1/2}, \end{eqnarray} (7)where equation (5) and p = 3 were used. 3 X-RAY OBSERVATIONS Swift /XRT observations can provide a detailed X-ray LC of the system while available XMM–Newton , Chandra , and NuSTAR observations can be used to derive accurate spectral properties. We note that all available observations yield compatible spectral properties within errors, apart from a single combined XRT/NuSTAR spectrum that appears to be much softer (Ho et al. 2017; Li et al. 2017). The Swift/XRT LC (up to MJD 58033.4) was produced following the instructions described in the Swift data analysis guide (http://www.swift.ac.uk/analysis/xrt/). We used xrtpipeline to generate the Swift/XRT products, and extracted events by using xselect (HEASoft FTOOLS; Blackburn 1995). The LC was also compared for consistency with the automated Swift/XRT online products (Evans et al. 2007). None of the Swift/XRT observations during the monitoring campaign of the system yielded sufficient statistics to allow a meaningful study of the spectrum. We therefore used fixed spectral parameters for converting the XRT count rates to flux. In particular, to transform the Swift/XRT rates to unabsorbed luminosities, we assumed a distance of 1.3 kpc and a power-law spectrum with photon index Γ = 2 and column density NH = 7.7 × 1021 cm−2 (see table 4 in Ho et al. 2017). 4 SPHERICAL STELLAR WIND The X-ray luminosity depends on the following model parameters: p, εe, εB, γw, and pw, see equation (6). We benchmark the power-law index of the pair distribution to p = 2Γ − 1 (see Section 3), assuming that the pairs emitting in the Swift energy band (0.3–10 keV) are slow cooling. The validity of our assumption will also be checked by comparing a posteriori the synchrotron cooling and shock expansion time-scales. If energy is shared equally between particles and magnetic fields (i.e. εe = εB = 0.5), we can derive pw by matching equation (6) to the unabsorbed Swift X-ray luminosity for different values of γw. In Fig. 1, we show the results for γw = 106, although these can be scaled accordingly for other parameter values using the analytical expressions of Section 2. Figure 1. View largeDownload slide Plotted (from top to bottom) as a function of time till periastron (MJD 58069): the unabsorbed 0.3–10 keV Swift X-ray LC of the binary, the ram pressure of the stellar wind, the mass-loss rate of the stellar wind for vw = 103 km s−1, and the ratio of the synchrotron to expansion time-scales for pairs emitting at 10 keV. The 1/r2 dependence of the wind’s ram pressure is shown with a dashed magenta line. The horizontal blue dashed lines indicate the typical range of values for the mass-loss rate of B stars (Martins et al. 2008; Krtička 2014). Figure 1. View largeDownload slide Plotted (from top to bottom) as a function of time till periastron (MJD 58069): the unabsorbed 0.3–10 keV Swift X-ray LC of the binary, the ram pressure of the stellar wind, the mass-loss rate of the stellar wind for vw = 103 km s−1, and the ratio of the synchrotron to expansion time-scales for pairs emitting at 10 keV. The 1/r2 dependence of the wind’s ram pressure is shown with a dashed magenta line. The horizontal blue dashed lines indicate the typical range of values for the mass-loss rate of B stars (Martins et al. 2008; Krtička 2014). The first two panels from the top show, respectively, the Swift X-ray LC and the inferred ram pressure of the stellar wind, $$p_{\rm w} \propto L_{\rm x}^2 \gamma _{\rm w}^{-2} \epsilon _{\rm e}^{-2} \epsilon _{\rm B}^{-2}$$. The magnetic field, which can be derived by equation (3), can be as high as ∼0.1 G in agreement with Takata et al. (2017). The temporal variability of pw may originate from changes in the wind’s velocity and/or density. Simulations of line-driven winds from massive stars have shown that both their velocity and density are strongly variable close to the stellar surface (e.g. Feldmeier 1995; Lobel & Blomme 2008). The wind velocity is typically less variable than the density, which may vary more than two orders of magnitude (see Fig. 1; Bozzo et al. 2016). In addition, at the distances of interest (i.e. r ≫ R⊙), the stellar wind is expected to move with its terminal velocity. As a zeroth-order approximation, we thus attribute the changes of pw (second panel from top) to changes of the wind’s density and assume that vw is constant with radius and equal to its terminal value (∼103 km s−1). Assuming spherical symmetry, the mass-loss rate of the wind can be estimated as $$\dot{M}= 4 \pi r^2 p_{\rm w}/v_{\rm w}$$, where r is the separation distance of the binary members. The mass-loss rate fluctuates around an average value of ∼10−9 M⊙ yr−1 that falls within the value range for B stars (Martins et al. 2008; Krtička 2014). Interestingly, the inferred mass-loss rate is compatible with ρw ∝ r−2 (magenta dashed line in Fig. 1), while density enhancements giving rise to X-ray flares (top panel in Fig. 1) can be explained by a clumpy wind (e.g. Oskinova, Feldmeier & Kretschmar 2012). Because of the scaling $$p_{\rm w}\propto \gamma _{\rm w}^{-2}$$, the inferred mass-loss rate could be as high as 10−7 M⊙ yr−1 for a slower pulsar wind with γw = 105. Unless the Be star of the binary has an uncommonly high mass-loss rate, then we can set a lower limit on the γw by requiring that $$\langle \dot{M} \rangle \lesssim 10^{-7}$$ M⊙ yr−1:   \begin{equation} \gamma _{\rm w}\gtrsim 10^5 \left(\frac{0.5}{\epsilon _{\rm e}}\right)\left(\frac{0.5}{\epsilon _{\rm B}}\right)\left(\frac{10^3 \ {\rm km \ s^{-1}}}{v_{\rm w}}\right)^{1/2}. \end{equation} (8)Equation (8) also suggests that neither εB nor εe can be much smaller than unity, as very large values of the pulsar wind’s Lorentz factor (γw ≫ 105) or the star’s mass-loss rate ($$\dot{M} \gg 10^{-7}$$ M⊙ yr−1) would be necessary to explain the observed Lx. The synchrotron cooling time-scale of pairs emitting at energy εx is $$t_{\rm syn} \propto \epsilon _{\rm x}^{-1/2} L_{\rm x}^{-3/2} \epsilon _{\rm B}^{3/4} \left(\gamma _{\rm w} \epsilon _{\rm e}\right)^{3/2}$$ (see equations 3 and 5) and is longer than texp for the adopted parameters (bottom panel in Fig. 1). Transition to the fast cooling regime during the period of Swift observations would be relevant for γw < 105, which would, in turn, imply very high mass-loss rates in contradiction to the expected values for B stars as discussed above (see also equation 8). Although synchrotron cooling is not relevant for the X-ray emitting pairs during the period of Swift observations, we discuss the possibility of inverse Compton (IC) cooling in Section 6. 5 AXISYMMETRIC STELLAR WIND WITH POLAR GRADIENT The extended atmosphere of a Be star can, in general, be divided into two regions: the equatorial (decretion) disc region and the wind region (Okazaki et al. 2011). The former is described by a geometrically thin Keplerian disc with high plasma density (for a review, see Porter & Rivinius 2003), whereas the wind region is composed of low density plasma moving with ∼103 km s−1. Here, we consider a toy model for the description of the wind structure. We assume that the stellar wind is axisymmetric (i.e. no azimuthal dependence) and model the ram pressure of the stellar wind as (e.g. Petrenz & Puls 2000; Ignace & Brimeyer 2006):   \begin{equation} p_{\rm w}(r, \theta ) = p_0 \ r^{-n} \left(1+ G \left|\cos \theta \right|^m\right), \end{equation} (9)where the distance r is measured from the focus of the ellipse where the Be star is located, the polar angle θ ∈ [0, 2π] is measured from the Be equator, and n, m > 0. The constant G is the equator-to-pole density contrast, the power-law index m determines the confinement of the wind to the equatorial plane, and p0 is a normalization constant. The latter is determined by requiring pw = 10−5 g cm−1 s−2 when the binary separation is 4 × 1014 cm about 1000 d before periastron for the same parameters used in Fig. 1. We consider the case where the pulsar’s orbital plane is perpendicular to the Be’s equatorial plane (see Fig. 2), since we have no knowledge of the system’s orientation at the time of writing. The pulsar’s orbit can be then expressed in terms of θ as rNS(θ) = a(1 − e2)/[1 + e cos (θ − θod)], where e is the eccentricity of the orbit and θod is the angle between the equator of the star and the orbit’s semimajor axis a. Figure 2. View largeDownload slide Sketch of the Be wind structure. The properties of the wind depend on the distance from the star and on the polar angle θ. The product of the plasma density and velocity becomes lower as we move from the equatorial plane (θ = 0) to the pole (θ = π/2), as indicated with the colour gradient. The Be disc (red coloured region) is Keplerian and geometrically thin with high plasma density. Two possible orientations of the pulsar’s orbit through the wind structure are shown. The pulsar’s orbital plane is perpendicular to the Be star’s equatorial plane (objects are not in scale). Figure 2. View largeDownload slide Sketch of the Be wind structure. The properties of the wind depend on the distance from the star and on the polar angle θ. The product of the plasma density and velocity becomes lower as we move from the equatorial plane (θ = 0) to the pole (θ = π/2), as indicated with the colour gradient. The Be disc (red coloured region) is Keplerian and geometrically thin with high plasma density. Two possible orientations of the pulsar’s orbit through the wind structure are shown. The pulsar’s orbital plane is perpendicular to the Be star’s equatorial plane (objects are not in scale). The effect of different wind structures on the X-ray LCs is exemplified in Fig. 3. For the displayed cases, we keep n = 2 (see previous section) while varying θod, G, and m separately – see panels (a) to (c) in Fig. 3. The LC shape can be symmetric around periastron only for specific orientations; for θod = 0°, the LC shows a major peak at periastron, while it exhibits two symmetric peaks for θod = 90° as the pulsar crosses the dense equatorial wind twice. All other configurations result in anisotropic LCs. Although the binary separation does not change much close to periastron, the polar variation of the wind becomes stronger for larger G values. This results in LCs with sharp features (dips or peaks) close to the periastron. The duration of these features is determined by the pulsar’s speed as it passes through regions with different wind properties along its orbit. Additionally, the G parameter can mimic the effect of different angles between the pulsar’s orbital plane and the Be disc plane. The parameter m determines the confinement of the wind to the equatorial plane of the star. Changes in m do not strongly affect the LC close to periastron, but have an impact on the LC shape hundreds of days before or after. A radial wind profile that deviates from the standard one (i.e. r−2) may masquerade an axisymmetric stellar wind with polar variations, namely n = 2 and m > 0 (see equation 9), but cannot explain asymmetric LCs around periastron. Figure 3. View largeDownload slide X-ray LCs from the interaction of the pulsar wind with different wind structures modelled by equation (9). (a) We vary the angle θod (inset legend) for fixed m = 3 and G = 10. The LC obtained for a stellar wind without polar dependence (i.e. G = 0) is also shown for a comparison (magenta dashed line). Swift data (MJD 58019.9) and their symmetric ones with respect to the periastron time are overplotted with black and grey symbols, respectively. (b) We vary the equator-to-pole density contrast G (inset legend) for fixed θod = 30° and m = 3. (c) We vary the confinement of wind to the equatorial plane by changing the power-law index m (inset legend) for fixed θod = 30° and G = 10. In all panels, we used n = 2 and pw = 10−5 g cm−1 s−2 at ∼1000 d before periastron. Figure 3. View largeDownload slide X-ray LCs from the interaction of the pulsar wind with different wind structures modelled by equation (9). (a) We vary the angle θod (inset legend) for fixed m = 3 and G = 10. The LC obtained for a stellar wind without polar dependence (i.e. G = 0) is also shown for a comparison (magenta dashed line). Swift data (MJD 58019.9) and their symmetric ones with respect to the periastron time are overplotted with black and grey symbols, respectively. (b) We vary the equator-to-pole density contrast G (inset legend) for fixed θod = 30° and m = 3. (c) We vary the confinement of wind to the equatorial plane by changing the power-law index m (inset legend) for fixed θod = 30° and G = 10. In all panels, we used n = 2 and pw = 10−5 g cm−1 s−2 at ∼1000 d before periastron. 6 DISCUSSION The Swift X-ray data indicate the presence of a clumpy stellar wind whose density scales, on average, as ∼r−2. The latter can explain the gradual increase of the X-ray luminosity as the pulsar approaches periastron, while the X-ray flares are attributed to clumps of dense matter (Section 4). Relativistic hydrodynamic simulations of an inhomogeneous stellar wind interacting with a pulsar wind show that the two-wind interaction region can be perturbed by clumps (see e.g. Paredes-Fortuny et al. 2015). These perturbations may enhance the energy dissipation of the pulsar wind at the termination shock, strengthen the post-shock magnetic field, or change the direction of motion of the shocked pulsar wind, thus giving rise to X-ray flares (de la Cita et al. 2017). Synchrotron cooling is not relevant for X-ray emitting pairs in the 0.3–10 keV band during the period of Swift observations, as shown in Fig. 1. This holds also for more energetic pairs that emit in the NuSTAR energy band (i.e. up to 50 keV). It seems therefore unlikely that the softening of the NuSTAR X-ray spectrum in 2016 is caused by synchrotron cooling (Li et al. 2017), unless γw < 103. IC scattering of stellar photons can also be a potential source of pair cooling. For a typical Be star with T* = 3 × 104 K, pairs radiating at $$\epsilon _{\rm x} \propto B \gamma _{\rm x}^2$$ will Thomson up-scatter stellar photons from the Rayleigh–Jeans part of the spectrum with ν < νT ≡ 3mec2/hγx and energy density $$u_{\rm T}\simeq 2\pi k T_* \nu _{\rm T}^3 (10 R_{{\odot }})^2/(3 c^3 r^2)$$. For the same parameters as in Fig. 1, we find that the shortest IC cooling time-scale for pairs emitting at 0.3 keV is ≳ texp at periastron. A two-wind interaction is expected for the largest part of the pulsar’s orbit, whereas the interaction of the pulsar wind with the Be disc may become relevant only close to the periastron (for a detailed study, see Takata et al. 2017). In principle, the Be disc/pulsar wind interaction can be studied with equation (9), since the X-ray luminosity depends on the product of the density and relative velocity of the interacting plasma flows. Takata et al. (2017) derived ∼0.2 g cm−1 s−2 close to periastron, by adopting a specific model for the Be disc with ρ = 10−10 g cm−3 on the stellar surface and rotational velocity ∼107 cm s−1 at r ∼ 1 au (see equations 8–9 therein). We obtain similar values using equation (9) for large m and G values (e.g. m = 27, G = 100). Current Hα measurements suggest a Be disc with size ∼0.2–0.5 au (Ho et al. 2017). It is well known that the Hα emission only arises in an inner portion of the disc and the actual size of decretion discs can be many times larger. Thus, as the pulsar approaches periastron, it may interact with stellar material. This can be then captured by the neutron star, if the termination shock lies within its gravitational sphere of influence. For vr = 100 km s−1, this requires ρ ≳ 3 × 10−16 g cm−3 at periastron. Still, accretion on to the rapidly rotating neutron star will be halted by the propeller effect (Illarionov & Sunyaev 1975), unless the accretion rate is extremely high, i.e. $$\dot{M}_{\rm a}=(2\text{--}20)\times 10^{18}$$ g s−1 corresponding to Lx = (5–50) × 1038 erg s−1 (Campana et al. 2002). Although a type-I outburst is unlikely to happen close to periastron (see e.g. Okazaki & Negueruela 2001), further phenomenology is expected. The pulsar spins down due to electromagnetic torque NEM = −μ2Ω3/c3, where Ω and μ are the pulsar’s angular spin frequency and magnetic moment, respectively. Close to the periastron, the pulsar may experience an additional spin-down due to the propeller effect on the plasma ‘held’ outside the corotation radius (e.g. Illarionov & Sunyaev 1975; Ghosh 1995). We adopt the conservative expression of Illarionov & Sunyaev (1975) for the propeller torque (for details, see Papitto, Torres & Rea 2012): $$N_{\rm prop}=-\dot{M}_{\rm a}\sqrt{GMR_{\rm m}}\Omega _{\rm K}(R_{\rm m})/\Omega$$, where ΩK is the Keplerian velocity, $$R_{\rm m} =\xi \left(\mu ^4/2\, G M_{\rm NS} \dot{M}_{\rm a}^2\right)^{1/7}$$ is the magnetospheric radius, and ξ ≃ 0.5–1 (see Chashkina, Abolmasov & Poutanen 2017, and references therein). The total spin-down torque acting upon the pulsar will be at least doubled, if $$\dot{M}_{\rm a}\gtrsim 4\times 10^{17}$$ g s−1. Assuming that the propeller torque acts upon the pulsar for ∼10 d, we expect a spin-frequency change of −4 × 10−6 Hz, i.e. an antiglitch (Şaşmaz Muş, Aydın & Göğüş 2014). The predicted effect could be detectable by Fermi –LAT which has already measured a pulsar glitch with Δν = 1.9 × 10−6 Hz (Lyne et al. 2015). The upcoming periastron passage of PSR J2032+4127 offers a unique opportunity to observe the system across the electromagnetic spectrum. In this letter, we focused on the non-thermal X-ray emission of the system and showed how it can be used to map the wind properties of the stellar companion. Comparison of the X-ray LC hundreds of days before and after the periastron will allow us to explore the polar structure of the wind while changes in the pulsar’s spin-down rate close to the periastron may probe the rate of mass captured by the neutron star. Acknowledgements We thank the anonymous referee for the report. We acknowledge support from NASA through the grant NNX17AG21G issued by the Astrophysics Theory Program. We acknowledge the use of publicly available data from the Swift satellite. 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Monthly Notices of the Royal Astronomical Society: LettersOxford University Press

Published: Feb 1, 2018

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