The braking index of PSR J1734-3333 and the magnetar population

PSR J1734-3333 is a radio pulsar rotating with a period P=1.17 s and slowing down with a period derivative Pdot=2.28 x 10^{-12}, the third largest among rotation-powered pulsars. These properties are midway between those of normal rotation-powered pulsars and magnetars, two populations of neutron stars that are notably different in their emission properties. Here we report on the measurement of the second period derivative of the rotation of PSR J1734-3333 and calculate a braking index n=0.9 +- 0.2. This value is well below 3, the value expected for an electromagnetic braking due to a constant magnetic dipole, and indicates that this pulsar may soon have the rotational properties of a magnetar. While there are several mechanisms which could lead to such a low braking index, we discuss this observation, together with the properties exhibited by some other high-Pdot rotation-powered pulsars, and interpret it as evidence of a possible evolutionary route for magnetars through a radio-pulsar phase, supporting a unified description of the two classes of object.

💡 Research Summary

The authors present a detailed timing study of the high‑Ṗ radio pulsar PSR J1734‑3333, whose spin period (P = 1.17 s) and period derivative (Ṗ = 2.28 × 10⁻¹² s s⁻¹) place it between ordinary rotation‑powered pulsars and magnetars in the P‑Ṗ diagram. Using 13.5 years of observations from the Parkes 64‑m and Jodrell Bank 76‑m telescopes, they obtain a precise measurement of the second derivative of the spin frequency (ν̈ = 2.8 ± 0.6 × 10⁻²⁴ Hz s⁻²). This yields a braking index n = ν̈ ν/ṽ² = 0.9 ± 0.2, far below the canonical value n = 3 expected for pure magnetic‑dipole braking with a constant dipole field.

The paper reviews why such a low n cannot be explained by simple dipole radiation. Possible contributors include (i) a secular change in the neutron‑star moment of inertia, (ii) evolution of the magnetic inclination angle, (iii) an additional torque from a relativistic particle wind (a “wind braking” scenario), and (iv) growth of the surface dipole magnetic field due to the emergence of a buried internal field (ohmic diffusion). The authors argue that (i) and (ii) are unlikely: the moment‑of‑inertia decrease would be transient, and observed inclination‑angle evolution in pulsars occurs on Myr timescales, not the ~10⁴ yr required here. The wind‑braking hypothesis would predict an observable pulsar wind nebula, yet deep X‑ray observations have found none around PSR J1734‑3333.

Consequently, they favor the magnetic‑field‑growth scenario. In this picture, a strong internal field, possibly buried by fallback accretion after the supernova, diffuses outward on timescales of 10²–10⁶ yr. As the surface field strengthens, the spin‑down torque increases, driving the pulsar’s trajectory upward and to the right in the P‑Ṗ diagram. Maintaining n ≈ 0.9 implies that, in roughly 30 kyr, the star will reach a period of ~8 s and a period derivative of ~10⁻¹¹ s s⁻¹, placing it squarely among the magnetar population.

The authors place this result in the broader context of other high‑Ṗ objects, such as the radio‑magnetars and the X‑ray pulsar PSR J1846‑0258, which have shown magnetar‑like outbursts despite being rotation‑powered. All these sources share very high inferred dipole fields (≥10¹³ G), supporting the idea that magnetic field strength is the primary driver of their diverse phenomenology.

In conclusion, the measured braking index of PSR J1734‑3333 provides strong empirical evidence for an evolutionary link between rotation‑powered pulsars and magnetars. The data suggest that at least some magnetars may pass through a long‑lived radio‑pulsar phase during which their surface magnetic fields grow, eventually leading to the extreme spin‑down and high‑energy activity characteristic of magnetars. Future high‑sensitivity timing, X‑ray, and possibly infrared observations will be essential to track the magnetic field evolution and to search for any emerging wind nebula or magnetar‑like bursts, thereby testing the proposed evolutionary pathway.