Flickering of the Vela pulsar during its 2016 glitch Gregory Ashton1;2;3, Paul D. Lasky1;2, Rowina Nathan1;2, and Jim Palfreyman4 1 School of Physics and Astronomy, Monash University, VIC 3800, Australia. Pulse log10 Bp=n β [ms] SAT [s] ∗ 2OzGrav: The ARC Centre of Excellence for Gravitational Wave Discovery, -15433 -0.2 1:2 ± 0:5 −1388:13 ± 0:001 ∗ Clayton VIC 3800, Australia. 3Royal Holloway, University of London, United -1167 -1.5 2:7 ± 0:9 −111:378 ± 0:0009 ∗ Kingdom. 4School of Natural Sciences, University of Tasmania, Australia. 9 -0.5 0:7 ± 0:5 −6:07792 ± 0:0008 The first pulse-to-pulse observations of a neutron star glitch in the 76 117 5:2 ± 0:5 −0:0885894 ± 0:002 Vela pulsar identified a null pulse1 hinting at the sudden disrup- 77 -10.9 – 0 tion of the neutron star’s magnetosphere. The only physical model 4609∗ 0.2 0:5 ± 0:4 405:74 ± 0:002 connecting the glitch and the null pulse relies on a starquake ei- 9526∗ 0.8 1:0 ± 0:4 845:804 ± 0:001 ther triggering, or being triggered by, the glitch itself2. Until now, this was the only null pulse identified from over 50 years of observ- Table 1: The pulse-to-null Bayes factor log10(Bp=n), pulse width β, ing the Vela pulsar1, 3. We identify five other null-like pulses, that and site arrival time (relative to the null pulse) for the outlier pulses we term quasi-nulls, before and after the glitch, separated by hun- observed in Fig. 1a. The pulse width is not measured for the null pulse, dreds of seconds. We verify that such nulls are not found in data pulse 77. Quasi-nulls are marked with an asterisk. away from the glitch. We speculate that the quasi-nulls are associ- ated with foreshocks and aftershocks preceding and following the main quake, analogously with terrestrial quakes. This implies the are clearly needed to decide if these predictions are born out. energy reservoir built up between glitches is not released suddenly, In this work, we perform a systematic study of the individual pulses but over a period of minutes to hours around the time of the glitch. around the time of the 2016 glitch. We set out to answer two questions: 1) What is the statistical significance of the broadening and null pulse In 2016, the Vela radio pulsar increased its rotation frequency by 1 one part in a million1. Such events, known as glitches, provide rare identified in Ref. ? 2) Are there pulse-shape changes during the glitch glimpses into the internal structure of neutron stars. Perhaps most which could help us understand the observed pre-glitch slow-down? In intriguingly, a series of unexpected changes in the pulsations were the following sections, we give an overview of our method, address observed coincident with the Vela glitch. First, a broader-than-usual each of these questions in turn, then provide a discussion and outlook. pulse, pulse 76*. Second, during pulse 77, the emission disappeared, a phenomenon known as a null4. These two anomalous pulses were then Shapelet-based pulse characterisation followed by two pulses with lower-than-usual linear polarization and The initial discovery1 of the magnetospheric alterations during the several pulsations which appeared to arrive slightly later than expected. 2016 Vela pulsar glitch analysed the data using a modification to tra- Individual pulses from radio pulsars typically show a high degree of ditional pulsar timing methods12. A high signal-to-noise ratio (SNR) variability and the Vela pulsar is no exception, but before pulse 77, it template is matched-filtered against individual pulses to identify the has never been known to have nulled3, 5. pulse time of arrivals (TOA), defined at the maximum flux of the tem- Understanding the behaviour of the Vela pulsar during its glitch has plate. (This approach differs from standard usage where interest is in significant scientific value. The glitch itself is likely caused by a sud- the long-term timing of a pulsar, in which case the matched-filter is den coupling of the superfluid interior to the crust of the star6. At the applied to an averaged pulse13). same time, the abrupt changes in the pulses likely arise from changes In this work, we fit a shapelet pulse-model14, 15 to ∼ 33; 000 in- in the magnetosphere. The Vela glitch offers the tantalizing opportu- dividual pulses around the glitch. We provide an overview of the nity to simultaneously understand more about both the interior of the kookaburra package used in the Methods section. To compare to neutron star and the magnetosphere. The broadening and null can be the regular behaviour of the pulsar, we also analyse ∼ 13; 000 pulses explained by a “quake quenching” episode2: a crust quake, which dis- in a data set taken 85 days before the glitch. We pre-process the raw rupts the magnetosphere causing the broadening and null, then triggers data using the PSRCHIVE package16, performing a frequency and po- the superfluid unpinning leading to the observed spin up. larisation “scrunch” and removing the baseline flux. For each pulse, we In addition to the unusual broadening and null, we have previously fit the shapelet flux model with a maximum of six components along found evidence7 that the glitch is not a simple spin-up event. We find with a polynomial model of degree two for the base flux. This en- arXiv:2011.07927v2 [astro-ph.HE] 8 Dec 2020 the rotation frequency of the star “overshoots”, suggesting the exis- ables us to model any remaining base-flux fluctuations not removed in tence of three distinct components to the neutron star8. Modelled fits pre-processing. The shapelet flux model is parameterised by the pulse 9, 10 to the data confirm that a three-component model is able to explain width β, the shapelet coefficients Ci (where i 2 [0; 5]), and the pulse the observed overshoot and infer the physical parameters. We also dis- time of arrival ti. Our analysis yields posterior distributions for these covered the hitherto unseen phenomenon of a slow down in the rotation shapelet and base-flux parameters. We additionally analyse each pulse rate prior to the glitch7 (also consistent with a magnetospheric slip10). using a null model consisting of the base-flux model only. Compar- While the evidence for the overshoot is overwhelming, the slow-down ing the evidence (the fully marginalized likelihood) for the pulse and before the glitch is tentative. Piecing this rich behaviour together into null model yields the Bayes factor Bp=n comparing the pulse and null a unified model holds great promise for delivering new insights into models. In the Methods section, we provide a discussion of the Bayes neutron star physics. Ref11 propose that the cooperative action of crust factor and the sensitivity of the method to finding nulls. breaking and vortex pinning-unpinning may be responsible, yielding predictions for the next glitch time to within a day. Future observations Statistical significance: Identifying quasi-nulls 1 Understanding the significance of the unusual behaviour of the *We follow the notation and numbering of the original analysis in which pulse n refers 2 to the nth set of period-folded data. This naming means that if in the nth data set the pulsar magnetosphere is paramount to drawing physical conclusions . We can nulls (i.e. no pulsation is observed), it is still referred to as pulse n. probe the significance of the null by comparing the Bayes factor Bp=n 1 (a) Data during the glitch; all times are referenced to pulse 77, the null pulse1. (b) Data from MJD 57649, 85 days before the glitch. Figure 1: The pulse-to-null Bayes factor Bp=n against the median inferred site arrival times (SAT) at the Mount Pleasant 26 m observatory. If log10(Bp=n)&1 (as is the case for typical pulses), the represents strong evidence for a pulse rather than a null; if log10(Bp=n). − 1 this represents strong evidence for a null rather than a pulse; intermediate values indicate a weak preference either way. A shaded red region in Figure 7 (a) indicates the ∼ 13 s interval of the inferred glitch-time. A horizontal dashed lines indicates our ln(Bp=n) < 1 quasi-null threshold. of pulse 77 with that of the other pulses in the data set. analysis identifies a null by a failure to calculate the TOA. That is, if a In Fig. 1a, we plot the pulse-to-null Bayes factor for the data sur- matched-filter analysis attempting to identify the TOA fails, the pulse rounding the glitch, Fig. 1a, and the data set 85 days before the glitch, is flagged as a potential null and flagged for follow-up12. The quasi- Fig. 1b. For almost all pulses, log10(Bp=n) > 1, i.e. strong evidence nulls do have some pulse structure (see Fig. 2a) and therefore will not for a pulse rather than a null. Pulse 77 is the most significant null in the be flagged by this failure-to-identify-a-TOA method. By comparison, data set, reaffirming the initial findings1. Pulse 76 is not a significant the shapelet-based method used here effectively quantifies the SNR of outlier in terms of the pulse-to-null Bayes factor. However, it is clearly the pulse; thus giving a scale of how loud the signal is rather than a distinguished in our analysis as an outlier in the measured pulse width simple binary choice between a pulse and a null. This difference has β (see Table 1).