Generating and refreshing pulsar ephemerides

The validity of pulsar ephemerides : the road to D4.fits

Created 7 November 2006, Lucas G., Updated 10 November 2006.

Our goal is :

To collect pulsar ephemerides from radio observatories and load them into D4.fits using gtpulsardb
To verify whether ephemerides are precise enough, still valid, etc.

Getting the ephemerides

Radio telescopes will soon provide us with pulsar ephemerides, here is an example, which is the result of observations of PSR J0437-4715 by the Nançay Telescope (TEMPO output). A full-set of ephemerides for each pulsar was extracted from the ATNF Pulsar Catalogue (www.atnf.csiro.au/research/pulsar/psrcat/), using the file psrcat.db included in George Hobbs’ psrcat package (http://www.atnf.csiro.au/research/pulsar/psrcat/psrcat.tar.gz). Although these ephemerides are pretty incomplete and old (see Figure 5) it is a good exercise to take every ephemeris and try to evaluate when it will need to be refreshed. Using the psrcat package, we have created the D4.fits output with gtpulsardb :

Fig 1 - It works !

We defined a list of best gamma ray candidates using the following condition :

We obtain a list of 215 pulsars, divided into two parts : 152 "MUST-DO" pulsars with dE/dt > 3.10^(34) erg/s, and 63 "WORTHWILE" pulsars with 10^(34) erg/s < dE/dt < 3.10^(34) erg/s (see https://confluence.slac.stanford.edu/display/GLAMCOG/Pulsar+Timing).

Verifications

A very important issue is to make our code warn the user when ephemerides are approaching their limit of validity. Two tests are applied :

R.W. Romani predicts how often a given pulsar needs to be observed with VperY, which is the number of radio observations required every year (see https://confluence.slac.stanford.edu/download/attachments/2162/TimingTriage.pdf?version=1) :

where :

(Arzoumanian, Nice & Thorsett '94)

and :

where :

These quantities allow us to define a "spoiling time", which controls the validity of ephemerides. This plot shows this spoiling time (in days) as a function of the frequency of pulsars, for our list of 215 objects :

Fig 2

VperY is useful to evaluate needed telescope time when requests need to be made, but it is based on the timing noise trend of a hundred pulsars observed by the Green Bank Telescope. It is necessary to adopt a second method, which focuses on individual pulsars.

For a set of measured timing parameters on a given pulsar, we can calculate the growing uncertainty δN in the number of turns N (assuming no glitches, in first approx.) :

Hence :

In this expression, δf 0 and 1 denote the uncertainty in frequency and frequency derivative. Again, the ephemeris is no longer valid when :

If we plot the "spoiling time" derived from this second method for our list of best gamma ray candidates, we can see :

Fig 3

With these two methods, it is possible to determine whether ephemerides are good enough to make accurate timing measurements, whether we will have to update them soon, or if they are out of date. The following plot shows the spoiling time found with the first method, against the one derived from the second method :

Fig 4

One can see that there's an overall agreement, though ephemerides seem to get out of date faster with the second method. Eventually, these calculated spoiling times allow us to predict the date when an ephemeris can't be used anymore, by :

Where T0 is a reference TOA, between the first TOA and the last TOA used to calculate the ephemeris. To illustrate this discussion, let us consider the example of the ephemeris of PSR J0437-4715, given on the top of this page. We have :

We can evaluate the spoiling date with both methods :

In this example, our two tests predicts very long spoiling times, especially the second one which is based on the uncertainties, due to the precision in the observed parameters. Inversely, noisy pulsars will have less precise ephemerides and therefore they will need to be observed more frequently. The following plot shows the spoiling dates for our 215 pulsars, using the two methods. Red crosses represent T0 for a given pulsar, green crosses represent its spoiling date calculated with the first method (Arzoumanian et al.) and blue stars represent the spoiling date calculated with the second method (Number of turns).

Fig 5

Due to the incompleteness of the psrcat ephemerides database, many reference TOAs (T0) are unknown. In this case they are given the value of 0. If we zoom on the dashed rectangle (which contains the known reference TOAs), we can see :

Fig 6

Almost all ephemerides are out of date in the psrcat database. Some ephemerides are still good though, especially those of the more stable millisecond pulsars. However, it should be noted that many of our pulsars have been observed during the last 2 years, so that we may already have up-to-date data for these objects.

Another important issue is to control the order of precision of the ephemerides. For the moment, our code tests whether RA, DEC, f0 and f1 are known with an acceptable number of decimals.

Conclusions

These procedures have been implemented, and they seem to work.
High-precision ephemerides are needed…
What order of precision can be reached in RA, DEC, f0 and f1 ?
What other quantity needs to be very precise ?