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Overview

TEMPO2: An overview

Tempo2 is a new pulsar timing package. It was developed to be used both for general pulsar timing applications and also for pulsar timing array research in which data-sets from multiple pulsars need to be processed simultaneously. Tempo2 was initially developed by George Hobbs and Russell Edwards as part of the Parkes Pulsar Timing Array project. A summary of the features of tempo2 was published in Hobbs, Edwards & Manchester (2006). Full details of the timing model were published in Edwards, Hobbs & Manchester (2006).

Tempo2 is now being used in pulsar timing research world-wide. It has been used in the analysis of PSR J1600-3053 (Ord et al. 2006), to limit the existence of gravitational waves (Jenet et al. 2006) and in studying pulsar dispersion measures (You et al. 2007).

Tempo2 is based on the original tempo code and can be used (from the command-line) in a similar fashion. However, tempo2 is very versatile and can be extended by the creation of pieces of software called plug-ins. It is expected that many such plug-ins will be written and made available on this wiki.

The plk plug-in

The plk interface provides a graphical interface to tempo2 that allows the user to identify, view and delete observations and to plot the pre- and post-fit residuals. This interface is called using, for example,

tempo2 -gr plk -f mypar.par mypar.tim

This should open a window containing the pulsar's pre-fit residuals and a menu bar. Moving the mouse cursor into the window and pressing 'h' will provide help information. The menu bar allows the user to change the fitted parameters, to redo the fit and to produce new parameter and arrival time files. Clicking on a residuals with the left mouse button identifies the observation, the middle mouse button calls the psrchive software to view the selected profile and the right mouse button deletes an observation.

Figure 1. Example of plotting post-fit residuals using the plk graphical interface. Green points represent 20cm observations, blue are 10cm observations and the red highlighted points are those obtained by the observer indicated by "GH". Note, the ability to add a label "(a)" and to add a vertical line (at 2004.6). The menu bar at the top allows the user to select different parameters to update in the fit (highlighted in red) and to redo the fit, create a new arrival time file and parameter file.

Figure 2. Example of plotting post-fit residuals using the plk graphical interface. In this figure the post-fit residuals are plotted versus the zenith angle of the observation.

Figure 3. The plk plugin can be used to show how the model parameters are updated between the pre-fit and post-fit residuals. For these plots the TOAs were simulated using the "fake" plugin.

Output formats

By default, tempo2 provides a simple output format such as:

 Results for PSR J1022+1001 


 RMS pre-fit residual = 5.551 (us), RMS post-fit residual = 4.204 (us) 
 Fit Chisq = 328 Chisqr/nfree = 328.02/80 = 4.10028      pre/post = 1.32036 
 Number of points in fit = 90 


 PARAMETER       Pre-fit                   Post-fit                 Uncertainty   Difference   Fit 
 --------------------------------------------------------------------------------------------------- 
 RAJ (rad)       2.71821351132165          2.71821366970554          4.5793e-07    1.5838e-07    Y
 RAJ (hms)       10:22:58.1188834           10:22:58.1210613         0.006297      0.0021779    
 DECJ (rad)      0.175100786106638         0.175101202092881         1.1575e-06    4.1599e-07    Y
 DECJ (dms)      +10:01:57.12972           +10:01:57.21552           0.23875       0.085803     
 F0 (Hz)         60.7794489670958          60.7794489674466          1.2099e-10    3.5076e-10    Y
 F1 (s^-2)       -1.69337759279488e-16     -1.70739820420136e-16     4.6312e-19    -1.4021e-18   Y
 PEPOCH (MJD)    50250                     50250                     0             0             N
 POSEPOCH (MJD)  50250                     50250                     0             0             N
 DM (cm^-3 pc)   10.1340857485791          10.1323540071461          0.00032389    -0.0017317    Y
 T0              50246.7162463696          50246.7162473185          8.2856e-07    9.4889e-07    Y
 PB              7.80513016588816          7.80513016328438          2.1745e-09    -2.6038e-09   Y
 A1              16.7654150843515          16.7654147901821          3.3958e-07    -2.9417e-07   Y
 OM              97.67                     97.67                     0             0             N
 ECC             9.73177041814313e-05      9.73614863096607e-05      4.0439e-08    4.3782e-08    Y
 TRACK (MJD)     0                         0                         0             0             N
 ---------------------------------------------------------------------------------------------------

The user can use various "output format"-plugins to modify this style of output. The most general output-formats are called "general" and "general2". The "general" output format provides tools to output the fitted parameters:

 tempo2 -output general -s "{ERRMULT 2}{ALL_l} & {ALL_p} \\ \n" -f 1022.par 1022.tim -tempo1

gives an output such as

 RAJ        &  10:22:58.121(13) \\ 
 DECJ       & +10:01:57.21552(1) \\ 
 F0         & 60.7794489674(3) \\ 
 F1         & -1.707E-16(10) \\ 
 PEPOCH     & 50250 \\ 
 POSEPOCH   & 50250 \\ 
 DM         & 10.1324(7) \\ 
 T0         & 50246.7162473(17) \\ 
 PB         & 7.805130163(5) \\ 
 A1         & 16.7654148(7) \\ 
 OM         & 97.67 \\ 
 ECC        & 9.736E-5(9) \\ 

where all the fitted uncertainties have been multipled by 2 (using ERRMULT 2). Other options are available such as printing positions in radians.

The "general2" output format allows the user to obtain the residuals and arrival times in a generalised format. For instance,

 tempo2 -output general2 -s "bat = {bat} {TAB 30} postfit = {post} \n" -f 1022.par 1022.tim -tempo1

gives

 bat = 53316.913988559192532    postfit = -1.4013812949966899558e-06 
 bat = 53316.942347778044155    postfit = -8.9140037306238170828e-06 
 bat = 53339.763827992275925    postfit = -2.7661638801441797966e-06 
 bat = 53340.766243082893851    postfit = -3.9590484330153836507e-06 
 bat = 53341.767153434344575    postfit = -1.5820342343674639199e-05 
 bat = 53343.759018545078565    postfit = -3.0553744448713572345e-07 
 bat = 53344.769882986722987    postfit = -2.7194151293737169194e-06 
 bat = 53358.794030341607957    postfit = -1.0635224082231780844e-06 
 bat = 53359.788797078278918    postfit = -7.9941970336682482912e-06 
 bat = 53359.839033035550145    postfit = -6.2294153515564813482e-06 
 bat = 53374.722118052548574    postfit = 1.1433216401677192635e-06 
 bat = 53375.672422357200364    postfit = -9.4484079101972596806e-06 
 bat = 53376.709653164930661    postfit = -1.0458710000774904536e-05 
 bat = 53467.530353743119566    postfit = 5.1600086777362405918e-06 
 bat = 53468.496491265916422    postfit = -1.8190372589200010294e-06 
 bat = 53481.467843974453498    postfit = -1.2223221375857372388e-05 
 bat = 53483.3386372527915      postfit = 6.0164368757893214802e-06 
 bat = 53485.340318635574775    postfit = 1.3821827921105905752e-06 
 bat = 53500.446699057582236    postfit = -7.5602620743125784161e-06 

Options include {BAT} to display barycentric arrival times, {SAT} for site-arrival times, {FREQ} for observing frequencies,{PRE} for pre-fit residauls,{POST} for post-fit residuals,{ERR} for TOA error and {BINPHASE} for binary phase. The covariance matrix for the fitted parameters can be obtained using the "matrix" output format:

 tempo2 -output matrix -f 1022.par 1022.tim

gives

 Correlation matrix ... 

        F0              DM              T0              PB              A1              ECC      
 F0      +1.00000000
 DM      +0.04857778     +1.00000000
 T0      -0.46829467     -0.13609983     +1.00000000
 PB      +0.47274520     +0.13568604     -0.99939906     +1.00000000
 A1      -0.14504343     -0.08942360     +0.01717271     -0.01343955     +1.00000000
 ECC     -0.01786535     -0.08594389     +0.09468669     -0.09677360     -0.02684250     +1.00000000  

 gcor    +0.51268893     +0.18087855     +0.99942275     +0.99942647     +0.22477523     +0.14251438 
 dp          +0.3            +0.1            +3.2            +3.2            +0.1            +0.1

where gcor is a measure for the strongest correlation between the fitted variable and a linear combination of all other variables. dp provides an estimate of the number of "insignificant" digits that should be quoted in the timing solution.