TEMPO2 - beta release

George Hobbs, Russell Edwards

1.0 The plk interface

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.

2.0 The delays plugin

The purpose of the "delays" plugin is to allow the user to access information about the internal algorithms being implemented by tempo2. For instance, the user may wish to know the size of the solar Shapiro delay automatically being added by tempo2, or to check whether an unusual feature observed in the timing residuals corresponds to a sudden change that occurred in the observatory clock standard. This plugin may also be used to predict future events - for example, the time when the Shapiro delay due to Jupiter will be maximised.


Figure 4. Left panel: the UT1 corrections being applied to J1022+1001 observations over a period of 450 days. Right panel: the prediction for the Shapiro delay due to Jupiter for PSR~J1022+1001 until the year 2030.

3.0 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.

4.0 Analysing the timing residuals

The spectral interface is a "tcl/tk" based GUI for analysing post-fit timing residuals. This will continue to be developed and, it is hoped, will include multiresolution CLEAN deconvolution algorithms and periodicity searches.


Figure 5. The spectral graphical interface for analysing pulsar timing residuals. Here a CLEAN power-spectrum is overlaid on a Lomb periodogram. This interface allows the user to simulate time-series or to analyse post-fit timing residuals. Options include: plotting periodograms, interpolation, autocorrelation functions and obtaining statistical information for a range of data points.

On obtaining a new timing model, it is often useful to be able to obtain basic information about the pulsar (e.g. its characteristic age, surface magnetic field strength) and to be able to determine its position of the P-Pdot diagram. The "basic" plugin is available to do this. The plugin also allows the user to zoom in on a region around the current pulsar and to list all the other pulsars within this region that lie within a given declination limit. This allows the user to select similar pulsars that can be observed at the same observatory.


Figure 6. Using the "basic" plugin to plot a pulsar's position on a P-Pdot diagram

5.0 Fitting

The tempo2 fitting routines are based on a singular value decomposition linear algorithm (note: superTempo additions allow non-linear fits to be carried out).

5.1 Fitting to short section of data

It is often useful to be able to fit to short sections of data and to record the post-fit values of one or more parameters in each of these short sections. The "stridefit" plugin provides the ability to do this: 
tempo2 -gr stridefit -f 0458.par 0458.tim -param DM -start 44815 -end 52619 -width 365.25 -dt 365.25
records the dispersion measure in fits that start at epoch MJD 44815 and finish at 52619 with widths of 1 year and steps of 1 year.


Figure 7. Fitting for the dispersion measure of PSR B0458+46 over 15 years in 1 year segments. The stridefit plugin allows the user to fit a straight line to the resulting parameters giving, in this case, a dispersion measure derivative of 0.027(3) cm-3pc yr-1

5.2 Chisq fitting

This interface is used to create and analyse the chi-squared value of the fit or the post-fit rms residual for a one- or two-dimensional grid of parameter values. The results can be displayed as a graph, contour or grey-scale plot.


Figure 8. Producing chi-squared contours using the "chisq"-plugin to improve estimation of the orbital period (PB) and longitude of periastron (OM).

5.3 Obtaining a solution

It is also possible (using the "solution" plugin) to carry-out a brute-force determination of a pulsar timing solution. For instance, a multi-dimensional grid of parameters can be searched in order to obtain the lowest rms residual. This routine has already been used to obtain timing solutions for pulsars with sparsely sampled observations.

6.0 Simulating observations

It is often useful to be able to simulate pulse arrival times. Such arrival times can be used to determine the effects of an unmodelled parameter or to test residual analysis software. The "fake" plugin allows the user to simulate arrival times and to add the effects of timing noise (here modelled as red noise).


Figure 9. Left panel: simulated red-noise arrival times using the "fake" plugin. Right panel: Simulated example of the effects of an unmodelled parallax term.

7.0 Multiple pulsars

Tempo2 has been designed to process multiple pulsars simultaneously. The global fitting algorithms will be discussed as part of "superTempo" elsewhere. However, tempo2 has plugins that allow multiple pulsars to be viewed and analysed simultaneously. For instance, the "splk" plugin is used to plot the timing residuals for multiple pulsars:


Figure 10. Plotting the pre-fit (left) and post-fit (right) residuals for four pulsars using the same date range on the x-axis and the same range for the y-axis. This plot was produced using the splk plugin.

splk can also be used to compare two different timing models for the same pulsar or to compare different clock correction files or planetary ephemeris. To aid such comparison the "compare" plugin can be used that accepts two parameter files for a single set of pulse arrival times and plots the difference in the post-fit residuals.

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