The Evolution of Nulling in Pulsars

Abstract

Nulling is a phenomenon where the emission from a pulsar becomes undetectable (or significantly weaker) for a relatively short period of time, followed by a return to a normal emission state. The timescale of nulling ranges from a few pulse periods to many hours or even days. The fraction of time a nulling pulsar spends in a null state varies across the population of canonical pulsars, from 0 to 95 per cent. The long-term behaviour of a pulsar's nulling fraction, however, is currently unknown, as published values have typically been obtained through single observations. Here, we present the first long-term analysis of nulling behaviour in eight pulsars observed in the Parkes Multibeam Pulsar Survey over the course of eight to ten years. We also apply a new Bayesian method for pulse-energy analysis, yielding posterior estimates of the nulling fraction per observation. In several cases, the nulling affects only specific components of the pulse profile, rather than the entirety of the emission. Our analysis reveals that, while most pulsars show no significant trend in their nulling fraction over time, a subset exhibit some evidence for non-zero gradients in nulling fraction. In particular, PSRs J1048$-$3832, J1745$-$3040, and J1825$-$0935 show statistically significant trends over the span of the data. Studying the behaviour of nulling over years and decades is valuable as it can provide insights into the physical emission processes within pulsars. Studying how nulling evolves also provides valuable insights into pulsar evolution and the characterisation of the broader pulsar population.

Figures (21)

• Figure 1: An example histogram capturing the total flux density (intensity) within an on-pulse window during the observation of a nulling pulsar. The x-axis measures intensity, normalized by the mean. The solid black line on the left is a Gaussian component with mean and standard deviation taken from the data captured in an off-pulse window. The shape of this Gaussian should describe observation noise in the absence of any emission (suitable for null pulses in the on-pulse window or any data in an off-pulse window). The solid line on the right is a convolution of the Gaussian function describing off-pulse noise and a lognormal distribution. Convolving permits the function to extend below zero intensity (thereby permitting some non-null pulses to have negative total flux density). The dashed line is the sum of both of the solid lines. For the BPE technique the $\mu$ and $\sigma$ of the lognormal distribution are free parameters as well as the ratio of areas under the two solid lines.
• Figure 2: The difference between actual NF and the calculated NF for simulated nulling-pulsar observations (described in Section \ref{['sec:simulations']}). We compare the BPE and HS NF-calculation methods across three true NF values (0.2, 0.5, and 0.8) and four scenarios per NF: 200 pulse profiles with S/N = 2.0, 200 pulse profiles with S/N = 10.0, 1000 pulse profiles with S/N = 2.0, and 1000 pulse profiles with S/N = 10.0. In each scenario the NF was computed 1,000 times, with the data being generated anew for each iteration.
• Figure 3: Observation of PSR J1048$-$5832 made on MJD 51880. The upper panel shows the intensity of the pulsar signal as a function of pulse phase on the horizontal axis and time, or pulse number, on the vertical axis. The lower panel shows the normalized average of all the single pulses that feature in the upper panel. The central highlighted region marks the on-pulse window, while the outer highlighted regions indicate the off-pulse windows. The pulse profile consists of two components and the trailing-edge component appears to null, even if the overall profile does not. The calculated NF for this observation was $0.03 \pm 0.01$ and $0.06 \pm 0.01$ for the BPE and HS methods respectively.
• Figure 4: Evolution of NF for PSR J1048$-$5832 as a function of time. Top panel: The number of pulsar rotations recorded during each observation. Second panel: An esimation of the S/N of each observation (see Section \ref{['sec:sn_est']}). Third Panel: NFs as calculated by the BPE technique. Error bars show the total $1\sigma$ uncertainty on the NF measurements, incorporating fitting uncertainty, statistical (binomial) sampling uncertainty, and systematic uncertainty associated with the choice of off-pulse window (Section \ref{['sec:all_unc']}). The dashed regression line represents the best-fit linear model for the data points and weighted by their uncertainties. The gray uncertainty band around the regression line represents the 95% confidence interval for the predicted values, accounting for the uncertainty in both the slope and the intercept, illustrating the range of plausible predictions, given the model's uncertainty and data variability. Bottom panel: As the third panel but for the HS technique.
• Figure 5: Observation of PSR J1114$-$6100 made on MJD 52265. The pulse profile resembles a singular Gaussian component. The calculated NF for this observation was $0.14 \pm 0.08$ and $0.21 \pm 0.03$ for the BPE and HS methods respectively. Same format as Figure \ref{['J1048-5832_waterfall']} otherwise.