GIANT OUTBURSTS IN Be/X-RAY BINARIES

Be stars are early main-sequence stars that have shown Hα emission at least once (e.g., Porter & Rivinius 2003). They are rapidly rotating close to their break up velocity (Slettebak 1982; Porter 1996). The stars are surrounded by decretion disks (Pringle 1991) formed from ejected material which settles into a Keplerian disk and spreads outward through viscous diffusion (Lee et al. 1991; Hanuschik 1996; Carciofi 2011). The mechanism for ejection is uncertain (rotation alone is insufficient) with magnetic fields (e.g., Underhill 1987; Smith et al. 1994) and stellar pulsation (Rivinius et al. 2001) being candidates. The disk and its associated emission appears and disappears on a timescale of a few months to a few years (e.g., Bjorkman et al. 2002).

Gas from the decretion disk of the Be star can be captured and accreted by a companion in Be/X-ray binaries. These systems contain a Be star in a relatively wide orbit (an orbital period of tens to hundreds of days) of significant eccentricity (e ≳ 0.1) with a compact object, often a neutron star (Reig 2011) or less commonly a black hole (Munar-Adrover et al. 2014). Typically, the orbital angular momentum of the binary is misaligned to the spin of the Be star with a relative inclination of i ≳ 25° (see Table 1 in Martin et al. 2011, and references therein). The misalignment and the orbital eccentricity are both plausibly the result of kicks imparted during the supernova that formed the compact object (e.g., Martin et al. 2009, 2010).

In this Letter, we investigate how the interaction of the misaligned disk and eccentric binary may give rise to the observed X-ray phenomenology of Be/X-ray binaries. Two types of X-ray outbursts are produced in such systems (Stella et al. 1986; Negueruela et al. 1998). Type I X-ray outbursts are periodic and coincide with periastron passage with a typical luminosity of L_X = 10³⁶–10³⁷ erg s⁻¹ which lasts for a few days. Type II X-ray outbursts occur much less frequently but have a larger luminosity of L_X > 10³⁷ erg s⁻¹ and last weeks to months, showing no orbital modulation. The majority of giant outbursts are finished in less than one orbital period, but some may last up to five orbital periods (Kretschmar et al. 2013). Several suggestions as to the origin of these outbursts have been made (Negueruela et al. 2001; Okazaki & Negueruela 2001; Moritani et al. 2013; Okazaki et al. 2013), all of which involve as a central element the tilted and warped disks which have been observed before and during the outbursts (Negueruela et al. 2001; Reig et al. 2007; Moritani et al. 2011). Most recently, Kato (2014), presented analytic arguments suggesting that simultaneous growth of eccentric and tilt modes could occur on timescales relevant to the giant outbursts. However, it remains unclear exactly how a warped (and potentially eccentric) disk causes a long duration accretion event onto the neutron star.

The outline of the Letter is as follows. In Section 2, we present results from three-dimensional numerical simulations of accretion in Be/X-ray binaries. Type I outbursts can be produced when the neutron star captures a small fraction of low angular momentum gas from the disk at closest approach. We show that Type II outbursts can be explained as a consequence of eccentricity growth within the Be star disk. Capture of larger amounts of gas from the eccentric disk generates a Type II outburst, and in Section 3 we show that the long duration of these events can be due to the increased viscous time when the material circularizes around the compact object. We discuss our results in Sections 4 and 5.

Previous work on misaligned Be star systems mainly focused on coplanar systems or those with a small misalignment angle, i ≲ 45° (e.g., Okazaki 2006, 2007; Okazaki & Hayasaki 2007). They found that the resonant truncation radius for the Be star disk is the same for the inclined case unless i > 60° (i is the angle between the spin of the Be star and the binary orbital axis). In this work, we use the smoothed particle hydrodynamics (SPH) code Phantom (Price & Federrath 2010; Lodato & Price 2010) to model highly misaligned systems. Phantom has been used to model misaligned disks in other binary systems (Nixon 2012; Nixon et al. 2013) and we use the same method here. The simulations have two sink particles: one representing a Be star with mass M_⋆ = 18 M_☉ and the other a neutron star of mass M_NS = 1.4 M_☉. The binary has an orbital period of P_orb = 24 days (thus the orbit has semi-major axis a = 95 R_☉) and eccentricity e = 0.34, to target the Be/X-ray binary 4U 0115+63, although our results are more generally applicable. The parameters of the simulation are summarized in Table 1. Figures 1–3 show the overall evolution of the calculation.

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The accretion radius of the Be star is equal to its stellar radius of R_⋆ = 8 R_☉. For the neutron star, we take the accretion radius to be 1 R_☉ (the Bondi–Hoyle accretion radius at periastron is about 3.3 R_☉). Thus, we do not model the inner parts of the accretion disk around the neutron star (if it forms). Figure 1 shows the initial flat but tilted disk with an inclination of i = 70° to the x-axis. The disk has a mass of M_di = 10⁻⁸ M_☉ distributed with a surface density power law Σ∝R⁻¹ between R_in = R_⋆ and R_out = 50 R_☉ with 10⁶ SPH particles. Varying the outer disk radius, we find little difference in the disk behavior for smaller disk radii once the disk has expanded to the tidal truncation radius. The disk is isothermal with an aspect ratio of H/R = 0.01 at the inner edge, where R = R_⋆ and the Shakura & Sunyaev (1973) α parameter varies in the range 0.2–0.4 (e.g., King et al. 2007) over the disk (we implement the disk viscosity in the usual manner by adapting the SPH artificial viscosity according to the procedure described in Lodato & Price 2010, using α_AV = 6.0 and β_AV = 2.0). ⁶

The left-hand panel of Figure 4 shows the mass flow rate through the neutron star accretion radius as a function of time. Initially small (Type I) accretion outbursts occur every orbital period. Figure 2 shows the disk structure during a Type I outburst at a time of 6.1 P_orb. These outbursts occur when the disk is close to circular and the neutron star passes close to the spiral arm of the Be star disk. A small amount of material is pulled from the spiral arm onto the neutron star.

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Figure 4 shows that the accretion changes phase at a time of around 21 P_orb. The peak accretion rate is about an order of magnitude higher than during the Type I phase and the accretion does not subside between the periastron passages. We suggest that this is a giant Type II outburst. This can be seen clearly in the right panel of Figure 4 where we show the total mass accreted onto the neutron star as a function of time. The mass increases slowly during the Type I phase and then dramatically during the Type II phase before returning to the Type I phase. The top row of panels in Figure 3 shows the disk structure during the Type II outburst at a time of 22.1 P_orb. The Be star disk is highly eccentric and it is this that causes the Type II outburst where a large amount of material is transferred to the neutron star. The bottom row of panels show the end of the outburst and the neutron star disk. The precession of the eccentric Be star disk can also be seen by comparing the disk structures at different times.

We bin the particles in (instantaneous) radius (from the Be star) and calculate properties of the Be star disk. Initially, the disk is misaligned by i = 70°. Just before the Type II outburst, the disk has aligned to i ≈ 60°. The disk remains approximately flat during this process with the outer parts aligning only a few degrees more than the inner parts. This is in agreement with the analytic estimates for the alignment timescale for the Be star disk with a binary orbit of the order of a few years (Martin et al. 2011). Furthermore, we find that the eccentricity grows first at large radius in the disk. Just before the Type II outburst, the eccentricity of the disk is approximately constant with radius at e = 0.6. During and after the giant outburst, the eccentricity decays.

2.1. Eccentricity Growth in the Be Star Disk

Here, we consider the properties of the accretion disk that forms around the neutron star. Due to the misalignment between the Be star disk and the neutron star orbit, it is likely that accretion onto the neutron star proceeds through an initially misaligned disk (see Nixon & Salvesen 2014). For numerical tractability, we cannot model the neutron star disk in its entirety and it remains under-resolved even during the peak of the Type II outburst. This will be investigated in more detail in a future publication. However, we have run several SPH simulations with a much smaller neutron star accretion radius. We do not find significant evidence for a neutron star accretion disk during the Type I activity, only during the Type II. There is much less material and its circularization radius is much smaller during the Type I outburst phase and thus it accretes more rapidly (see also Okazaki et al. 2002).

The viscous timescale in the neutron star disk is $\tau _{\nu _{\rm NS}}=R_{\rm NS}^2/\nu _{\rm NS}$, where R_NS is the distance from the neutron star, the viscosity is $\nu _{\rm NS}=\alpha _{\rm NS} c_{\rm s,NS}^2/\Omega _{\rm NS}$, α_NS is the Shakura & Sunyaev (1973) parameter, and the sound speed is $c_{\rm s,NS}=\sqrt{{\cal R}T/\mu }$, where $\cal R$ is the gas constant and μ is the gas mean molecular weight. The temperature of the disk surface is found by assuming a steady profile:

$$\begin{equation} \sigma T^4=\frac{3 \dot{M}_{\rm NS}}{8 \pi }\Omega _{\rm NS}^2 \end{equation} \tag{ 1 }$$

(Pringle 1981). Thus, the accretion timescale of the disk scaled by the orbital period is

$$\begin{eqnarray} \frac{\tau _{\nu _{\rm NS}}}{P_{\rm orb}} &=& 4.7 \, \left(\frac{\alpha _{\rm NS}}{0.3}\right)^{-1} \left(\frac{M_{\rm NS}}{1.4\,M_\odot }\right)^{\frac{1}{4}} \left(\frac{\dot{M}_{\rm NS}}{10^{-8}\, M_\odot \,{\rm yr}^{-1}}\right)^{-\frac{1}{4}}\nonumber\\ &&\times \left(\frac{R_{\rm NS}}{0.5\,R_\odot }\right)^\frac{3}{4}. \end{eqnarray} \tag{ 2 }$$

If the disk is significantly optically thick, then this is an overestimate. While a radially extended neutron star disk is present, the accretion onto the neutron star is smoothed on a timescale of several orbital periods. This explains why there is no orbital modulation observed during a Type II X-ray outburst. We do not expect smoothing on this timescale to take place during the Type I activity because the accreting material has lower initial angular momentum and therefore a smaller circularization radius (≲ 0.5 R_☉) and viscous time. These numbers are approximate and tend to over-predict the viscous time compared to observations as we assume a steady disk. Time-dependent processes, such as tides or interactions of the neutron star disk with streams from the Be star disk, could shorten the viscous timescale.

The corresponding X-ray luminosity of the disk is $L_{\rm X}=GM_{\rm NS} \dot{M}_{\rm NS}/r_{\rm NS}$, where r_NS is the radius of the neutron star, and thus

$$\begin{eqnarray} L_{\rm X} &=& 1.2\times 10^{38} \left(\frac{M_{\rm NS}}{1.4\,M_\odot }\right)\left(\frac{\dot{M}_{\rm NS}}{10^{-8} M_\odot \,{\rm yr}^{-1}}\right) \nonumber\\ &&\times \left(\frac{r_{\rm NS}}{10^6\,\rm cm}\right)^{-1}\,\rm erg\,s^{-1}. \end{eqnarray} \tag{ 3 }$$

Thus, for the accretion rates to agree with observations of the X-ray luminosities, we require an initial disk mass of around 10⁻⁸ M_☉ or smaller. This agrees well with the Be star mass loss rates that are in the range 10⁻⁸ to 10⁻¹⁰ M_☉ yr⁻¹ (e.g., Snow 1981; Porter & Rivinius 2003) and the lifetimes of the Be star disks (of a few years).

The simulations presented here model a warped, eccentric, precessing Be star disk. The ejection mechanism for material from the Be star to the disk is poorly understood, and thus we have considered only the evolution following disk formation. Thus, the disk is an accretion rather than a decretion disk, but over the timescales we simulate this should not affect our conclusions. The ejection of material from the Be star surface in a circular orbit at the inner edge of the disk could affect the eccentricity growth and inclination of the disk. However, because eccentricity growth is driven more strongly in the outer parts of the disk, this should not affect the Type II outburst mechanism.

During the Type II outburst in our simulation, the Be star disk becomes significantly depleted. About 40% of the initial disk mass is accreted onto the Be star. This depletion could explain the cycles observed in the optical light curves of Be/X-ray binaries (e.g., Rajoelimanana et al. 2011). With mass ejection from the Be star included, the disk would build up again and we would expect the Type II outbursts to recur. The recurrence timescale would depend on the accretion rate onto the Be star disk. Parameters such as the eccentricity, misalignment, and binary separation could be varied to model other Be/X-ray binary systems and predict the types of outbursts that may occur.

Observations suggest that the Type II outbursts occur when the disk becomes warped. However, we have found that this is not a sufficient condition. It is necessary for the disk to become eccentric. An inclined circular disk, which can expand freely as the tidal torques are smaller, becomes eccentric before it becomes large enough for a neutron star encounter. If there are no outbursts observed in a Be binary system, then the binary must have small eccentricity and misalignment. Conversely, if Type II outbursts are observed, then the system must be highly misaligned. We find that eccentricity may also be driven in counter-rotating disks. The frequency of outbursts in Be/X-ray binary systems will be investigated in the future with a disk model including mass injection into the disk from the Be star in order to determine the critical inclination angles required for outbursts. The tidal torque aligns the disk with the binary orbital plane on a timescale of years (Martin et al. 2011). In a long-term disk simulation, this alignment may also play a role in ending the outburst cycle.

We have performed three-dimensional SPH simulations of a moderately eccentric and highly misaligned Be/X-ray binary. We find that for a binary with an orbital period of 24 days and eccentricity 0.34, Type I outbursts occur for all misalignments, including the aligned case. If the disk is sufficiently misaligned, i ≳ 60°, then the disk is much larger because the tidal torque is weaker. This allows strong eccentricity growth in the outer parts of the disk from the gravitational forcing of the eccentric companion. Thus, the disk becomes eccentric on a timescale of around 10 binary orbital periods. We suggest that the eccentric disk causes a Type II X-ray outburst as a large amount of material is transferred to the neutron star.

R.G.M.'s support was provided under contract with the California Institute of Technology (Caltech) funded by NASA through the Sagan Fellowship Program. Support for C.J.N. was provided by NASA through the Einstein Fellowship Program, grant PF2-130098. P.J.A. acknowledges support from NASA's ATP program under awards NNX11AE12G and NNX14AB42G. D.J.P. is supported by Future Fellowship FT130100034 from the Australian Research Council. We acknowledge the use of SPLASH (Price 2007) for the rendering of the figures. This work utilized the Janus supercomputer, which is supported by the National Science Foundation (award No. CNS-0821794), the University of Colorado Boulder, the University of Colorado Denver, and the National Center for Atmospheric Research. The Janus supercomputer is operated by the University of Colorado Boulder.