Accounting for Vela's Glitch Behaviour

The use of TEMPO to make predictions for the current pulse frequency is more than sufficiently accurate for most of the stronger and slower (older) pulsars targeted by amateurs (e,g, B0329+54).

However, for Vela, which is a young pulsar, this is not the case.

Vela - the Glitching Pulsar

Vela is the most glitch-prone pulsar, with the Crab Pulsar coming a distant second with about 1/10th the glitch magnitude of Vela. The table below shows 19 glitches over a period of about 45 years (derived from the "ATNF Glitch Database").

Glitch Epoch (MJD Δν/ν (ppm)
40280 2.34
41192 2.05
41312 0.012
42683 1.99
43693 3.06
44888.4 1.14
45192.1 2.05
46259 1.60
47519.8 1.81
48457.4 2.71
49559.0 0.83
49591.82 0.20
50369.3 2.11
51559.3 3.15
53193.1 2.10
53960 2.62
55408.8 1.94
56555.9 3.1
56922 0.00039

The average time between glitches is about 2.5 years and the average glitch amplitude is about 1.8 ppm.  There is a period of recovery of a few months after which the pulsar returns to the normal spin down rate, but not quite the pre-glitch pulse frequency.  Table 2 (from https://arxiv.org/pdf/1604.02661v1.pdf ) below shows that there is a permanent change in spin frequency which can be as high as about 0.6  (1 - Q) of the glitch step.  Consequently any ephemeris parameters derived at a past epoch will over-estimate the slowdown if glitches have occurred after that epoch.

Problems with TEMPO (Windows version)

The ephemeris data in the '0833-45.par' supplied with the Windows version of TEMPO is from epoch 51001 (July 1998).  Looking at the table above it can be seen that after that epoch 6 glitches have occurred, 5 of which are > 2 ppm.  Although the total of the 6 glitches amounts to nearly 13 ppm, the recovery mechanism means that the error will be less than that amount.

The latest ephemeris data for Vela from the ATNF database is from epoch 51559.32 (January 2000) and a small improvement in accuracy can be gained by updating the Windows TEMPO '0833-45.par' file to those values.  The latest ephemeris data the author has is from the Hartebeesthoek Radio Astronomy Observatory (HartRAO) for epoch 57068 (February 2015) and a significant improvement in accuracy is obtained by using those values.  It should be mentioned that obtaining the data from HartRAO was made possible by a sympathetic staff member of HartRAO who no longer works there.

The problem with Vela is that it will continue to glitch and so even the latest HartRAO ephemeris data will become out of date. To illustrate this, if the result from the Windows TEMPO epoch 51001 data is compared to the latest HartRAO epoch 57068 data result, there is a difference of 9.9 ppm in the prediction.  So, over some 17 years there is almost a 10 ppm difference.  However, until another glitch occurs, using TEMPO with the '0833-45.par' file updated to the latest HartRAO values is accurate.  Unfortunately, the next Vela glitch is due in the next year (2017) and so the TEMPO prediction will be inaccurate again - and increasingly inaccurate over time unless a new ephemeris data set can be obtained.

'Linear Fit' Solution

To make available a result for Vela which doesn't drift in accuracy over time, the author loaded all the F0's found for Vela over a number of decades into a spreadsheet.  Then a linear fit equation was derived.  This equation includes all the glitches over time because it is derived from F0's over time.  This provides a prediction curve which is smooth and continuous.  Because of the sawtooth nature of the real pulse frequency curve over time (due to glitches), the smooth linear fit curve will over-estimate the pulse frequency in the time just before a glitch, but under-estimate the pulse frequency just after a glitch.  In the time mid-way between glitches it will be very close to the real pulsar frequency.  The error between the real pulsar frequency and the linear fit prediction is expected to remain less than ±2 ppm.

Final Note

As a general rule when using the Windows version of TEMPO, a check should be made to ensure that latest epoch ephemeris data is loaded in the relevant '*.par' file.  For example, for Vela the ATNF database data epoch is later than the epoch in the '0833-45.par' file supplied with the Windows version of TEMPO.  Conversely, the Windows TEMPO version '0329+54.par' has a later epoch than the ATNF database - resulting in a 0.33 ppm difference in predictions.

It is worth checking...