Chapter 3: The parameter files
3.1 The basic timing model parameters
The parameter files (that contain the pulsar timing model and various instructions for the tempo2 fitting routines) have the same form as in the earlier tempo implementation. Each of the pulsar parameters has a label, a value and may have an uncertainty on the value and a flag indicating whether tempo2 should fit for this parameter or whether the parameter should be held constant (0 = default = hold constant; 1 = fit). The parameters labels are described in Table 3.1 at the bottom of this page. An example of a parameter file for PSR J0437-4715 taken from the ATNF pulsar catalogue (by selecting the ephemeris option):
PSRJ J0437-4715 RAJ 04:37:15.7865145 1 7.000e-07 DECJ -47:15:08.461584 1 8.000e-06 DM 2.6469 1.000e-04 PEPOCH 51194.000 F0 173.6879489990983 1 3.000e-13 F1 -1.728314E-15 1 1.600e-20 PMRA 121.438 6.000e-03 PMDEC -71.438 7.000e-03 BINARY DD PB 5.741046 1 3.000e-06 ECC 1.9186E-5 1 5.000e-09 A1 3.36669157 1 1.400e-07 T0 51194.6239 1 8.000e-04 OM 1.20 1 5.000e-02 OMDOT 0.016 1.000e-02 START 50640.928 FINISH 52088.897 CLK UTC(NIST) EPHEM DE200 PBDOT 3.64E-12 2.000e-13 TZRMJD 51204.64376750220085 TZRFRQ 1413.400 TZRSITE 7 RM +1.5 5.000e-01 PX 7.19 1.400e-01 SINI 0.6788 1.200e-03 M2 0.236 1.700e-02
This indicates to tempo2 that all parameters should be held fixed except for the astrometric parameters (RAJ, DECJ), pulse parameters (F0, F1) and the Keplerian orbital parameters (PB, ECC, A1, T0 and OM). Uncertainties are given on many of the parameters.
In more detail, a pulsar which has a spin period of P0=1.23456 s and no fitting is required then use:
To request that tempo2 fits for this parameter:
P0 1.23456 1
or to include an uncertainty on the measurement (which is ignored by the main tempo2 software)
P0 1.23456 1 0.00003
Other commands may be given in parameter files that control the algorithms used by tempo2. Tempo2 only required the following parameters: PSRJ, DM, F0, PEPOCH, RAJ and DECJ. It is also possible to provide the pulsar parameters in the old-style tempo format where the arrival times and the parameters are given in the same file. Details of this mode (which we do not recommend) are given here.
3.2 Phase jumps
It is often necessary to fit for a constant offset between two sets of arrival times. For instance, the templates used to determine arrival times at different observatories may be perfectly aligned. The command "JUMP" in the parameter file can be used to define such jumps:
JUMP -i PKS_DFB 0.234 1 JUMP FREQ 1400 1500 0 1 JUMP TEL PKS 0.342
which would initialise a jump for all observations with the "-i" flag set to "PKS_DFB" with the value of 0.234 and then fit for the jump. A jump would be included (and fitted) for all observations with frequencies between 1400 and 1500 MHz and a set (i.e. not fitted) jump would be included on all data observed using the "PKS" telescope.
3.3 Removing timing noise
Even with accurate spin and positional parameters, the timing residuals for some (particularly the young) pulsars contain remnant structures. Some of these structures are understood; cusps, for instance, signify sudden changes in the pulsar's spin rate during a glitch, sinusoidal oscillations can represent unmodelled companions (such as planets) or the pulsar precessing. However, many of the structures seen in the residuals are still not understood and are known as "timing noise". To obtain the most accurate pulsar's positional and proper motion parameters (and dispersion measure) it is essential to remove this timing noise. Traditionally this has been carried out by fitting higher order pulsar rotational derivative terms. However, Hobbs et al. (2004) described an improved method that used the fitting of harmonically related sinusoids.
Such sinusoidal terms can be included in tempo2 parameter files.
WAVE_OM 0 1 WAVE1 0 0 WAVE2 0 0 WAVE3 0 0
would allow tempo2 to select the fundamental frequency for the sinuosoids based on the data-span (see the algorithm described in Hobbs et al. 2004) and subsequently fit for 3 sine and cosine waves.
3.4 Coping with badly wrong ephemerides
Under normal circumstances, tempo2 should be able to predict exactly the number of turns between any two observations, so that the residual phase error is considerably less than one turn. In early stages of timing a pulsar, during the process of "phase connecting" the data, this may not be true, and phases may "wrap". tempo2 provides several tools to help in this situation.
Most simply, one may add the PHASE command to an observation file. Adding PHASE n tells tempo2 that at that point, n extra phase turns occurred compared to what tempo2 would otherwise assume. Thus PHASE 1 has the effect of adding one full turn to all following arrival times. Naturally as the ephemeris changes the number of turns tempo2 would assume will change, and these will frequently need to be added or removed (hopefully removed).
A more automated approach is to use one of the modes of the TRACK command. TRACK 0 is the default mode of tempo2. TRACK 1 tells tempo2 to assume that the phase error of each residual is within one-half turn of the previous residual, rather than within one-half turn of zero. This only makes sense if the residuals are provided to tempo2 in time order, though tempo2 only warns about this condition. TRACK -1 uses several data points to guess the correct number of turns. TRACK -2 allows a number of turns to be specified for each TOA using the "-pn" flag; it behaves similarly to the PHASE command.
Table 3.1: Pulsar parameters than can be entered in a parameter file
Note that PBBOT, XPBDOT, and A1DOT have special handling: the units are natively s/s or lt-s/s, but if the value is larger than 1e-7, it is scaled down by 1e-12; you may therefore see values like 100 to mean 1e-10.
When PBDOT or other derivatives or orbital quantities are specified, PB, A1 and so on are the binary parameters at the time T0 (not PEPOCH).