Pulse periods and slowdown rates

2.2 Pulse periods and slowdown rates

The pulsar catalogue [251 , 13 ] contains up-to-date parameters for 1775 pulsars. Most of these are “normal” with pulse periods $P ∼ 0.5 s$ which increase secularly at rates $P˙∼ 10−15 s∕s$ . A growing fraction are “millisecond pulsars”, with $1.4 ms ≲ P ≲ 30 ms$ and $P˙ ≲ 10− 19 s∕s$ . As shown in the “ $˙ P –P$ diagram” in Figure 3

, normal and millisecond pulsars are distinct populations.

Figure 3: The $P –P˙$ diagram showing the current sample of radio pulsars. Binary pulsars are highlighted by open circles. Lines of constant magnetic field (dashed), characteristic age (dash-dotted) and spin-down energy loss rate (dotted) are also shown.

The differences in $P$ and $˙ P$ imply fundamentally different magnetic field strengths and ages. Treating the pulsar as a rotating magnetic dipole, one may show [229 ] that the surface magnetic field strength $B ∝ (P ˙P)1∕2$ and the characteristic age $τc = P ∕(2P˙)$ . Lines of constant $B$ and $τc$ are drawn on Figure 3 , from which we infer typical values of 10¹² G and 10⁷ yr for the normal pulsars and 10⁸ G and 10⁹ yr for the millisecond pulsars. For the rate of loss of kinetic energy, sometimes called the spin-down luminosity, we have $˙ ˙ 3 E ∝ P ∕P$ . The lines of constant $˙ E$ shown on Figure 3 indicate that the most energetic objects are the very young normal pulsars and the most rapidly spinning millisecond pulsars.

The most rapidly rotating neutron star currently known, J1748–2446ad, with a spin rate of 716 Hz, resides in the globular cluster Terzan 5 [144 ]. As discussed by Lattimer & Prakash [209 ], the limiting (non-rotating) radius of a $1.4M ⊙$ neutron star with this period is 14.3 km. If a precise measurement for the pulsar mass can be made through future timing measurements (Section 4), then this pulsar could be a very useful probe of the equation of state of super dense matter.

While the hunt for more rapidly rotating pulsars and even “sub-millisecond pulsars” continues, and most neutron star equations of state allow higher spin rates than 716 Hz, it has been suggested [40 ] that the dearth of pulsars with P < 1.5 ms is caused by gravitational wave emission from Rossby-mode instabilities [7 ]. The most rapidly rotating pulsars [144 ] are predominantly members of eclipsing binary systems which could hamper their detection in radio surveys. Independent constraints on the limiting spin frequencies of neutron stars come from studies of millisecond X-ray binaries [68 ] which are not thought to be selection-effect limited [69 ]. This analysis does not predict a significant population of neutron stars with spin rates in excess of 730 Hz.