A growing braking index and spin-down swings for the pulsar PSR B0540-69

The way pulsars spin down is not understood in detail, but a number of possible physical mechanisms produce a spin-down rate that scales as a power of the rotation rate ($\dot\nu\propto-\nu^n$), with the power-law index $n$ called the braking index. PSR B0540-69 is a pulsar that in 2011, after 16 years of spinning down with a constant braking index of 2.1, experienced a giant spin-down change and a reduction of its braking index to nearly zero. Here, we show that following this episode the braking index monotonically increased during a period of at least four years and stabilised at ~1.1. We also present an alternative interpretation of a more modest rotational irregularity that occurred in 2023, which was modelled as an anomalous negative step of the rotation rate. Our analysis shows that the 2023 observations can be equally well described as a transient swing of the spin-down rate (lasting ~65 days), and the Bayesian evidence indicates that this model is strongly preferred.