TEMPO2 Basic Overview
TEMPO2 is a pulsar timing software package. It is described in Hobbs, Edwards, Manchester (2006) and details of the algorithms implemented are in Edwards, Hobbs, Manchester (2006). This tutorial assumes that you have already downloaded and installed the software and have a basic knowledge of the pulsar timing technique.
It is recommended that all TEMPO2 users join our mailing list which provides information on updates to the code.
The timing model
TEMPO2 requires a timing model for each pulsar being studied. An inital model can be obtained from the ATNF pulsar catalogue.
Step 1: Download a timing ephemeris for PSR J1539-5626. You can do this by typing the pulsar name into the "Pulsar names" box and then clicking on "Get Ephemeris" (see below)
Unless the catalogue has been updated the result should be:
The timing model includes the pulsar's name (PSRJ), position (RAJ, DECJ), spin-frequency and its derivative (F0, F1), the epoch of the spin-frequency measurement (PEPOCH) and the pulsar's dispersion measure (DM). The rotation measure (RM) is often included in the ephemeris, but is not needed by TEMPO2 and can be deleted in 1539.par. The EPHVER parameter indicates whether the timing model is in the original tempo format or in the TEMPO2 format and will be discussed later.
Simulating some pulse arrival times
TEMPO2 also requires a file containing the pulse arrival times for the pulsar being studied. It is possible to download raw data files using the Parkes pulsar data archive and then to process the files using psrchive to form arrival times. However, here we will simulate some arrival times at the Parkes radio telescope:
Step 2: Simulate some arrival times for PSR J1539-5626.
The command is divided as follows:
The columns are 1) the filename (note: as this is simulated data, all the files names are the same and default to an arbitrary name), 2) the observation frequency (in MHz), 3) the measured/simulated pulse arrival time (in MJD), 4) the uncertainty on the pulse arrival time measurement (in microseconds) and 5) the telescope identification code (see later for details on the identification code).
Forming and plotting the timing residuals
With a pulsar timing model (e.g., 1539.par) and a set of pulse arrival times (e.g., 1539.simulate), TEMPO2 can be used to calculate and display the pulsar timing residuals.
Step 3: Calculate and display the timing residuals
This can be done using:
The command has:
This produces a graphical interface looking like the following:
The green points (with error bars) represent the timing residuals. The weighted root-mean-square timing residual is displayed near the top (rms = 0.099us). The interface also produced some text output that should look like:
This lists various pieces of information including the number of points in the fit (216), the parameters used in the model and their initial values (pre-fit). We are currently not doing any fitting and so the post-fit values are the same as the pre-fit values. This output also contains useful parameters derived from the timing model parameters such as the rotational period (derived from the rotational frequency) and the total data span (8.2 years).
Changing the model parameters
The simulation above produced arrival times that were exactly predicted by the timing model and then added 100ns of white noise. The timing residuals are therefore white, centred on zero and have an rms of 100ns. We can test the effects of having incorrect model parameters by modifying the values in 1539.par and then re-calculating and re-displaying the residuals.
Change the spin frequency from 4.1085950920 to 4.1085950921 (note: just changing the '0' to a '1' in the last decimal place) and then save the file as bad.par
The result should now look like:
The residuals follow a straight line. The gradient of this line indicates how incorrect our estimate of the spin-frequency is. TEMPO2 can therefore fit a straight-line to these data and use the gradient to obtain an improved estimate of the pulsar's spin frequency. To fit a straight line, click on the white box next to the "F0" label at the top of the plot. The white box should turn red. Then click on the "RE-FIT" button. The text output should now contain:
Notice that the F0 line now has a different pre-fit and post-fit value (columns 2 and 3). Column 4 gives the measured uncertainty in the F0 parameter. The 5th column gives the difference between the post- and pre-fit values and the final column contains a "Y" indicated that a fit for this parameter was carried out. The timing residual plot will not have changed as the pre-fit timing residuals are plotted by default. The panel on the left-hand side selects what will be plotted on the x and y axes. Select that the post-fit residuals should be plotted on the y-axis (post-fit) and the graph should change to look like:
Experiment with changing other parameters in the timing model (such as RAJ, DECJ and F1). Start by making very small changes and then increase the size of the changes that are made.