Be/X-Ray Binaries

  1. What are Be/X-Ray Binaries?
  2. What's Interesting in Be/X-Ray Binaries?
  3. Interaction between the Be Disk and the Neutron Star in Be/X-Ray Binaries
    1. Viscous Disks around Be Stars
    2. Resonant Truncation of Be Disks
    3. SPH Simulations of the Be Disk-Neutron Star Interactionnew-star.gif

1. What are Be/X-Ray Binaries?

The Be/X-ray binaries represent the largest subclass of high mass X-ray binaries. About 2/3 of the identified systems falls into this category. Each system consists of a Be star and a neutron star. The orbit is generally wide (a couple of ten days < Porb < several hundred days) and eccentric (0.1 < e < 0.9).

       Most of the Be/X-ray binaries show only transient X-ray activity due to transient accretion of the circumstellar matter of the Be star. Each Be/X-ray binary shows some (or all) of the following X-ray activities:

(Stella et al. 1986; see also Negueruela et al. 1998). The figure below shows how Type I and Type II X-ray outbursts look like.

Two types of X-ray outburts from 2S 1417-629 (Porb=42.1 d, e=0.45). This figure is taken from Bildsten et al. (1997) and modified a little bit.

       For more detailed explanation of Be/X-ray binaries (and other X-ray binaries), see http://xmm.u-strasbg.fr/staff/ignacio/xbinscience.html.

2. What's Interesting in Be/X-Ray Binaries?

The Be/X-ray binaries are worth studying in several aspects. First, most of them are transient X-ray sources. The mechanisms that cause the transient X-ray activity (i.e., Type I and Type II outbursts) is not known. ( The conventional model for the Type I outbursts, which assumes a big disk around the Be star, is wrong! Such a big disk can't exist in Be/X-ray binaries. See the part of disk truncation below.)

       Second, due to the resonant truncation, the Be disk in Be/X-ray binaries can't be steady. It grows, and then at some point it decays (disappears). In 4U0115+63, the Be disk becomes warped (probably via the interaction with the stellar radiation) before it disappears (Negueruela et al. 2001). The mechanism for the disk decay, which is related to the origin of the Type II outburst (Negueruela et al. 2001), is not known.

       Third, Be/X-ray binaries are interacting binaries. Usually, studies of interacting binaries are related to the interaction between an accretion disk around a compact star and a companion in a circular orbit. On the other hand, in a Be/X-ray binary, the interaction occurs between the Be disk, which is likely a viscous decretion disk, and the neutron star in an eccentric orbit. Few study has been done on the interaction between a viscous (decretion) disk and a (compact) star in an eccentric orbit.

       In summary, we have many reasons to study Be/X-ray binaries, whereas at present we know little about what's going on in these systems.

3. Interaction between the Be Star Disk and the Neutron Star in Be/X-Ray Binaries

3.1. Viscous Disks around Be Stars
3.2. Resonant Truncation of Be Disks
3.3. SPH Simulations of the Be Disk-Neutron Star Interactionnew-star.gif

3.1. Viscous Disks around Be Stars

       A Be star has two-component envelope, a polar wind and an equatorial disk. The former consists of a low-density, fast outflow emitting UV radiation, while the latter consists of a high density plasma rotating at near Keplerian speed. Optical emission lines and the infrared excess arise from the equatorial disk.

       Although there is no widely-accepted model for Be disks, the viscous decretion disk model proposed by Lee et al. (1991) seems promising (Porter 1999; Okazaki 2001). In this model, the matter supplied from the equatorial surface of the star drifts outward by viscosity and forms the disk. Basic equations for viscous decretion are the same as those for viscous accretion, except that the sign of the mass flow rate is opposite. Thus, viscous decretion produces a geometrically thin, near Keplerian disk around a Be star. The outflow in the viscous decretion disk is very subsonic (Okazaki 2001).

3.2. Resonant Truncation of Be Star Disks in Be/X-Ray Binaries

       It is well known that viscous accretion disks in close binaries are truncated by tidal/resonant torques from the companion. This naturally leads us to the idea that Be disks in Be/X-ray binaries would also be tidally/resonantly truncated. Observed correlation between the orbital period and the maximum value of the equivalent width of H$\alpha$ line supports this idea (Reig et al. 1997). On the other hand, the conventional view of the Be/X-ray binaries assumes that the Be disk is so large that it extends beyond the periastron distance. It is, therefore, important to study whether the truncation radius is larger than the periastron distance.

       In viscous disks in binary systems, the disk outer radius is the radius inside which the viscous torque Tvis is larger than the tidal/resonant torque Tres. In other words, the criterion of the tidal/resonant truncation is that Tvis+Tres < 0 at a given resonant radius (Artymowicz & Lubow 1994; Negueruela & Okazaki 2001). This criterion is met for $\alpha$ smaller than a critical value, $\alpha_{\rm crit}$. That is, the disk around a Be star is truncated at a given resonance if $\alpha$ < $\alpha_{\rm crit}$. For more details, see section 4.3 of Negueruela & Okazaki (2001) or this page.

       In order to evaluate the viscous torque in the disk, we adopt Shakura-Sunyaev's viscosity prescription and assume the Be disk to be isothermal of the temperature of 0.5Teff, where Teff is the effective temperature of the Be star. The tidal/resonant torque is averaged over the binary orbit.

$\alpha_{\rm crit}$ at the n:1 resonance radii for eight Be/X-ray binaries of which orbital parameters are known. Numbers on top indicate the locations of the n:1 commensurabilities of disk and binary orbital periods.

       The above figure shows $\alpha_{\rm crit}$ for Be disks in eight Be/X-ray binaries of which orbital parameters are known. From the figure, we find that the Be disk is truncated at a radius smaller than the periastron distance for plausible range of viscosity parameter $\alpha$. This means that the orbit of the neutron star would never intersect in the middle of a disk as has been supposed in the conventional view of the Be/X-ray binaries. As schematically shown in the figure below, there would be a gap between the disk and the neutron star orbit.

Schematic view of a Be/X-ray binary

       Since the gas is continually ejected from the star but the resonant torque prevents gas from going beyond the disk outer radius, the Be-disk structure in Be/X-ray binaries is inevitably time dependent. The gas supplied from the Be star will accumulate in the outer part of the disk. We expect that the accumulation of gas will finally make the disk unstable to radiation-driven warping.

3.3. SPH Simulations of the Be Disk-Neutron Star Interaction in Be/X-Ray Binaries

       The above result on the resonant truncation of the Be disks in Be/X-ray binaries is obtained by using a semi-analytical method. We have adopted an axisymmetric disk, decomposed the tidal potential into a double series, and averaged the phase dependence of the torques.

       It's interesting to see

under a more realistic situation (i.e., a time-dependent, non-axisymmetric disk + a full potential).

       For this purpose, we have done 3D SPH simulations of Be disk-neutron star interaction for some combinations of orbital parameters, viscosity parameter, and stellar parameters. The following page includes some of the latest results.

Be/X-simulation logo SPH Simulations of the Be Disk-Neutron Star Interaction in Be/X-Ray Binaries new.gif

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Last modified: 26 April 2001