A marginal temporal variability for the whole orbit of the binary system was reported (see Figure 5.2).
• The eclipsing binary system PSR J1824–2452H in M28 has an orbit period of 10.87 h and
has been observed to show radio eclipses (B´egin 2006). Inspecting the light curves may
reveal a X-ray flux variability with the pulsar’s orbital motion at the∼ 2−4σconfidence
level, depending on the number of phase bins used to construct the light curve (see Fig-
ure 6.11). The minimum in the X-ray light curve at the orbital phase φ ∼ 0.25 can be
plausibly interpreted as a geometric occultation of the shock by the companion star. So far only the MSP W in 47 Tuc has been detected with the orbital variability in the X-ray emission (Bogdanov et al. 2005). The shape of the light curve as well as the orbital phase- resolved spectroscopy are the important tools to constrain the nature of these eclipsing binary system. A repeated coverage of the binary orbit in a longer X-ray observation and a comparison with the present data would provide us not only a better photon statistic but would also allow us to determine the emission geometry with a much higher accuracy than currently possible. Besides, further multiwavelength studies of these interesting eclipsing binary systems are required to place tighter constraints on their emission properties.
9.2 Millisecond Pulsars in Galactic Globular Clusters
Globular clusters have long been known to be breeding grounds for millisecond and binary pul- sars (Camilo & Rasio 2005). The main reason for this is the high stellar density and high rate of stellar interaction in globular clusters relative to most of the rest of the Galaxy. As a result, low-mass X-ray binaries are almost 10 times more abundant in clusters than in the Galactic disk. In addition, exchange interactions between binary and multiple systems in the cluster can result in the formation of exotic binary systems (Nice et al. 1999). To date, searches have revealed 140
pulsars in 26 globular clusters1.
We have conveyed a systematic census of the X-ray population of radio pulsars in Galactic globular clusters by using the imaging data obtained with Chandra X-ray observatory. Among
140 pulsars, only ∼20% have been identified with X-ray counterparts. Therefore, our current
understanding of the high-energy emission nature of the cluster pulsars is seriously prejudiced. By cross-correlating the radio timing positions of the cluster pulsars with the high resolution X-
ray images, thirty-one possible X-ray counterparts have been identified in nine different globular
cluster systems, including the 47 Tuc pulsar population. These include the newly identified X- ray counterparts of PSR J1824–2452G and PSR J1824–2452H in M28 and PSR J1748–2021B in NGC 6440. We have also characterized their spectral properties as well as searched for the possible temporal variability. We have found that the X-ray emission from some cluster pul- sars, i.e. PSR J1740–5340 in NGC 6397, PSR J1824–2452G and J1824–2452H in M28, and PSR J1748–2021B in NGC 6440, are variable. These pulsars are in binary systems. Therefore, the variability can possibly be resulted from the intra-binary shocks.
156 9. Conclusion and Future Prospect
Millisecond pulsars in GCs inhabit an environment with a much higher stellar density than those in the Galactic plane. Therefore, the stellar dynamical interactions in GCs are more fre- quent. GC millisecond pulsars can possibly change their companions a few times throughout their lives. In addition, the magnetic field structure at the neutron star surface might be influenced by the accretion (Cheng 2008), this would result in a much more complicated field structure of the millisecond pulsars in GCs than those in the disk. Therefore, the physical properties of the
millisecond pulsars in the globular clusters are suspected to be different from those in the Galactic
field. As an example, the X-ray emission of millisecond pulsars in the field were found to have a non-thermal component (Becker & Tr¨umper 1997, 1999; Zavlin 2006). However, Grindlay et al. (2002) and Bogdanov et al. (2006) suggested that the X-ray spectra of most millisecond pulsars in 47 Tuc are consistent with blackbody models. In addition, Grindlay et al. (2002) suggested the
X-ray conversion efficiency (i.e. the dependence ofLXon ˙E) for 47 Tuc pulsars to beLX ∝ E˙0.5,
where ˙Eis the spin-down power of the pulsar. Such dependence is obviously shallower than the
linear relationLX ∼10−3E˙ found for the pulsars in the Galactic field and in the globular clusters
(see Becker & Tr¨umper 1997, 1999, 2009).
In order to better constrain the physical properties of the millisecond pulsars in the globular clusters, we have systematically studied the X-ray emission from 31 GC pulsars and re-examined the relation between the X-ray luminosity and the spin-down power of pulsar population in globu-
lar clusters by using the enlarged sample reported in this work. Their X-ray conversion efficiency
was found to span a wide range, which is not consistent with the linearLX−E˙ relation.
As suggested by Becker (2009), the LX = 10−3E˙ relation represents as an upper bound to
the X-ray efficiency instead of a fixed correlation. Since the beaming correction of the X-ray
luminosity is not applied, the X-ray efficiency for those faint pulsars appears to be smaller. An
alternative possible reasons for the flatterLX−E˙ relation for GC pulsars may be due to the lack
of reliable measurement of the spin-down rate ˙P of many GC pulsars. This can be ascribed to
two facts. First, the radio signals from these pulsars are relatively weak and therefore an accurate
timing solution is difficult to obtain. Moreover, the proper motion of the GC pulsars and gravi-
tational effect of a cluster further complicates the estimation of ˙P. Besides the aforementioned
possibilities, the various origins of the X-ray emission for the GC pulsars may lead to this flat-
ness of theLX−E˙ relation. The X-ray emission of some GC pulsars (excluding 47 Tuc pulsars)
may come from the intra-binary shock since they are located in the binary systems, which is not that case for most field pulsars.
We have also constructed the cumulative luminosity functions for the millisecond pulsar pop-
ulation in globular clusters as well as in the Galactic field. No significant difference between these
two cumulative luminosity functions was found in our study. Therefore, we cannot conclude the discrepancy between the globular cluster pulsar population and the Galactic millisecond pulsars
in terms of the current knowledge of their X-ray conversion efficiency and luminosity functions.
Deeper observations of these GC pulsars may help to reduce the errors in determining their X-ray luminosities. Enlarging the X-ray population of the GC pulsars may allow us not only to study