1.2 High-mass X-ray Binaries
1.2.5 The relationship between neutron star spin and the binary orbit
A significant number of the HMXBs in the Milky Way and Magellanic Clouds have both their orbital and spin periods known. The orbital periods are usually derived in two distinct ways: from the timing analysis of long-term X-ray and optical light curves that bear evidence of periodic Type I outbursts, or from X-ray pulse arrival time analysis. The latter is the focus of Chapter 5. Figure 1.6 plots the orbital and spin periods of all HMXBs that were known at the time of writing. The figure is more commonly known as the Corbet diagram and is adapted from Corbet (1986). Thorough investigation of this parameter space has yielded the classical picture that the 3 types of HMXB (wind-fed SGXBs, disk-fed SGXBs and BeXRBs) occupy different areas. In particular, the BeXRBs show a large variation in the periods seen and seem to show a positive correlation between the two parameters. In the past, this correlation has been assigned a numerical equation that could be used to predict one parameter should the other be known. However, the most recent plots of the available data show a large spread in the correlation and even merging of some extreme systems with the SGXB region. Thus, it is proving less and less reliable to use this relationship as a tool to predict one of the parameters to any
1 10 100 Orbital Period (d) Spin Period (s) 10−2 10−1 100 101 102 103 104
Figure 1.6: The Corbet diagram of HMXB pulsars. The green data points are the wind-fed SGXBs, orange are the disk-fed SGXBs, red are the SFXTs and blue are the BeXRBs. The blue diamonds are the Galactic systems and the blue stars are the Magellanic systems. Private communication from Corbet (2011).
degree of precision, though a ball-park estimate can certainly be made. Even more interesting is the recent emergence of several SFXTs with known orbital and spin periods. The four systems with both periods confirmed are also plotted in Figure 1.6 and appear to occupy both the SGXB and BeXRB regions. This may be telling us something very fundamental about the nature of SFXTs; are they progenitors of the classical HMXBs we see, or do they mark a transitionary state between a BeXRB and a SGXB? There are currently many programmes dedicated to finding and classifying more SFXTs in order to understand where they fit into the standard model of HMXBs.
The classical view on why there may exist a correlation between spin and orbital periods in the BeXRBs involves the spin-down time of the neutron star in the time between its formation and the time the binary starts to accrete. Immediately after the primary supernova, the neutron star is rotating rapidly. The neutron star must spin- down significantly in order to allow inflowing material to overcome the outward force and be accreted. Once the neutron star is rotating slowly enough for material
to be accreted, it will undergo a period of alternating spin-up and spin-down as it moves around its orbit, accreting, or not, at different phases. The amount of time the neutron star spends away from its companion, and hence the amount of time it accretes, is largely dependent on the period and eccentricity of the orbit. As such, a neutron star in a longer orbit will tend to have a longer spin period as it has had more time to spin down. A counter argument to this is that it predicts all systems should be hovering around their equilibrium spin periods. However, this seems not to be the case as there is evidence of a strong bias towards long term spin-up or spin-down trends (e.g. Coe, McBride & Corbet 2010).
1.3
Optical emission from BeXRBs: the Be star
The large mass ratio in HMXBs means that all optical emission seen in such sys- tems comes for the optical counterpart (the accretion disk being much less optically bright in comparison). This is opposite to what is seen in LMXBs where the optical emission from the accretion disk can be studied and the light from the counterpart is swamped. As such, HMXBs offer the best chance to study the donor star in an XRB. In particular, the diversity and variability offered by a Be star counterpart makes the optical properties of the BeXRBs one of the most exciting fields to study. In this section I will introduce some properties of Be stars and discuss what has been learnt from optical observations of BeXRBs.
The Be phenomenon of mass ejection from the equatorial plane of the B star is not well understood (see Porter & Rivinius 2003 for a detailed review). It is thought that the rapid rotation of the photosphere plays a part but that this is not sufficient to explain the disk emission alone as most Be stars rotate just below the critical limit. It has been suggested that non-radial pulsations (the simultaneous expansion and contraction at different radii within the stellar atmosphere) could be the additional trigger needed to push matter at the surface above the escape velocity of the star (see e.g. Emilio et al. 2010 and references therein), though evidence for this is sparse. Regardless of the mechanism(s) that produces the circumstellar emission, its effect is key in our understanding of the optical and X-ray activity we see in BeXRBs.