Millisecond Pulsars in 47 Tucanae

In terms of finding millisecond pulsars, the globular cluster 47 Tucanae has proven to be a gold-mine. The cluster is massive ( $\sim 10^6$ M $_{\odot}$ ), relatively nearby with a distance from the Sun of about 5 kpc, and has a very dense core with a central density of $\sim 10^5$ M $_{\odot}$ pc^-3. These properties are favourable for the formation in the core of neutron-star binary systems by exchange interactions (e.g. Rasio, Pfahl & Rappaport 2000) and the detection of millisecond pulsars formed by subsequent accretion spin-up of the captured neutron stars. Parkes searches at 430 and 640 MHz MHz in the early 1990's (Manchester et al. 1990, 1991, and Robinson et al. 1995) resulted in the detection of 11 millisecond pulsars in 47 Tucanae, already a record number of pulsars for one cluster. These pulsars all had very short periods, in the range 2.1 to 5.8 ms, and three of them were known to be members of binary systems. One, 47 Tuc J, had the very short orbital period of 2.9 h and showed evidence for eclipses of the pulsar signal. Most of these pulsars are very weak and several were only detected occasionally, when interstellar scintillation raised their flux density to a detectable level. Because of this only two of the 11 pulsars, C and D, both isolated (non-binary) pulsars, had coherent timing solutions and hence accurate positions, periods and slow-down rates.

**Figure 7:** Positions relative to the cluster centre of the 15 pulsars in 47 Tucanae with coherent timing solutions. The large circle indicates the size of the cluster core. (Freire et al. 2000).
$\begin{figure} \begin{center} \centerline{\psfig{file=47tuc_posn.ps,width=120mm}} \end{center} \end{figure}$

Matters remained like this for several years, until Camilo et al. (2000b) exploited the high sensitivity of the multibeam system and sophisticated data processing techniques to discover a further nine MSPs in the cluster, all members of binary systems! The complete dominance of binary pulsars in these latest discoveries shows that the low proportion binary systems in the earlier results was purely a selection effect, and that most pulsars in globular clusters (at least 47 Tucanae, but probably all clusters) are binary. Again, all of these pulsars had very short periods, the longest being 7.6 ms. 47 Tuc R has the shortest orbital period known for any radio pulsar, 96 min, and also shows evidence for eclipses. All of the known binary systems in 47 Tucanae have very low-mass companions,

$\stackrel{<}{_{\sim}}0.2$ M $_{\odot}$ .

**Figure 8:** Proper motions of four pulsars in 47 Tucanae (Freire et al. 2000). The filled ellipse represents a weighted average of the pulsar results and its uncertainty. Also shown are two determinations of the cluster proper motion from Hipparcos data by Geffert et al. (1997) and Odenkirchen et al. (1997).
$\begin{figure} \begin{center} \centerline{\psfig{file=47tuc_pm.ps,width=120mm}} \end{center} \end{figure}$

Not only has the multibeam system allowed detection of more pulsars in 47 Tucanae, it has also given us a much higher detection rate on the previously known pulsars. This has allowed timing solutions to be obtained for a further 13 pulsars giving us a much improved knowledge of the pulsar parameters (Freire et al. 2000). This in turn makes possible a number of interesting studies of cluster properties. Fig. 7 shows that the pulsars are concentrated in the central region of the cluster; the core radius is 23 arcsec but the tidal radius is much larger, about 40 arcmin. This indicates that they are in dynamical equilibrium with other cluster stars, with their larger than average mass giving them a smaller than average velocity in the cluster and hence confining them to the central region. Interestingly, a cumulative histogram of number of pulsars versus perpendicular radius from the cluster centre is linear within the uncertainties. This implies that stars with mass similar to that of a neutron star are the dominant stellar species in the core region. Since the maximum mass of main-sequence stars is about 0.8 M $_{\odot}$ , these may be unseen neutron stars or binary systems consisting of two heavy main sequence stars. The existence of such binary systems is suggested by the observation of `blue straggler' stars in the cluster core (Gilliand et al. 1998); these stars are believed to be formed by the coalescence of such binary systems. The positions obtained from timing observations have very small uncertainties, typically

$\stackrel{<}{_{\sim}}1$ mas. Given the improved parameters for cluster pulsars obtained from the recent observations, Freire et al. (2000) were able to go back and reanalyse the data from the early 1990's to obtain two more coherent timing solutions, giving four in all. Comparison of positions from these solutions with those from analyses of recent data allowed determination of the proper motion of the four pulsars. These results are shown in Fig. 8. The observed proper motions are dominated by the motion of the cluster as a whole, not by motions of pulsars relative to the cluster. Their weighted mean already gives a more precise value for the cluster proper motion than that obtained from Hipparchos data and future observations will further improve the reliability of this value.

**Figure:** Observed $\dot P/P$ ratios for pulsars in 47 Tucanae as a function of their radial distance from the cluster core (Freire et al. 2000). The dashed line is the mean observed value of $\dot P/P$ . The curved solid lines give the maximum acceleration based on a King model for the cluster density distribution and the dots represent accelerations of a random sample of pulsars having the mean acceleration and distributed through the cluster with an r^-2 density distribution.
$\begin{figure} \begin{center} \centerline{\psfig{file=47tuc_accel.ps,width=120mm}} \end{center} \end{figure}$

As mentioned in the Introduction, the long-term or secular intrinsic period derivative of all pulsars is believed to be positive. However, observed period derivatives for MSPs near the core of globular clusters are sometimes negative. This is attributed to an acceleration of the pulsar in the cluster gravitational potential dominating over any intrinsic period derivative. Pulsars on the far side of the cluster will be accelerating toward us and hence will appear to be speeding up. Fig. 9 shows the observed $\dot P/P$ ratios along with a model prediction of the probability of a given acceleration being observed. The observed points are consistent with these predictions provided the central velocity dispersion in the cluster is more than 12 km ${\rm s}^{-1}$ (Freire et al. 2000). These results are already impressive. However, with continuing observations using (already installed) filterbanks giving higher time resolution, new and improved results can be expected from the Parkes observations of 47 Tucanae. Already, two more pulsars have been discovered bringing the total known in the cluster to 22. Existing timing solutions will improve and new timing solutions will be obtained, giving improved proper motions and cluster accelerations. There is no doubt that further study of 47 Tucanae will be rewarding.

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Millisecond Pulsars in 47 Tucanae