2.2 Pulse periods and slowdown rates

The pulsar catalogue [25113] 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 3View Image, normal and millisecond pulsars are distinct populations.
View Image

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 [229Jump To The Next Citation Point] 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 3View Image, 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 3View Image 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 [144Jump To The Next Citation Point]. As discussed by Lattimer & Prakash [209Jump To The Next Citation Point], 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 [40Jump To The Next Citation Point] 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 [144Jump To The Next Citation Point] 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 [68Jump To The Next Citation Point] which are not thought to be selection-effect limited [69Jump To The Next Citation Point]. This analysis does not predict a significant population of neutron stars with spin rates in excess of 730 Hz.

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