## 4. Data analysisExcept for the observations at 2.25 GHz and 8.5 GHz, our measurements were not made simultaneously at different frequencies. For this reason, we have to apply timing models to the data in order to keep track of the pulse phase between the observations. A time delay given by Eq. (11) will then appear as a deviation of the observed arrival time from the expected one, determined by the timing model. ## 4.1. Timing modelsRegular timing observations of long period pulsars are made by the Jodrell Bank pulsar group, using the 76m-Lovell telescope (Martin & Lyne in prep.). We consider the timing models obtained from these observations as the best available and use the Jodrell Bank models for the reduction of our data. However, the timing data of many pulsars exhibit deviations from the simple spin-down model including only parameters for the period and period derivative, i.e. where is the rotational phase at time T
(measured in the pulsar frame), the phase at
, the pulsar spin
frequency and its first derivative. These
rotational variations known as From an analysis of many pulsars, it has been shown that the
amplitude of the timing noise is strongly correlated with the period
derivative, , (e.g. CD85, Arzoumanian et
al. 1994). Depending on the time interval analyzed, timing
residuals may appear as regular variations with fairly large
amplitudes (for an impressive collection see CD85). In general one can
try to account for such large variations if the second derivative of
the spin frequency, , is included in the spin
down model (Eq. 13). Although the resulting value, noticeable by
a non-zero , might not have any physical meaning
(i.e. it might not be related to a ## 4.2. TOA measurementsThe topocentric TOA of a pulse profile was determined by
cross-correlating the profile with a high signal-to-noise ratio (S/N)
Craft (1970) showed that the midpoint of pulse profiles is such a fiducial point. Phillips & Wolszczan (1992, hereafter PW92) and P92, respectively, investigated dispersion measures and emission altitudes of data observed between 26 MHz and 4.80 GHz. As a selection criterion, PW92 restricted their sample of pulsars to those with simple or double component profiles, so that a determination of the profile midpoint was possible with high accuracy. Our sample, however, is determined by other aspects, i.e. the ability to detect the sources at the highest possible frequencies. Therefore, our sources do generally not exhibit such regular pulse shapes as would be desirable for a straightforward choice of the fiducial point. Consequently, we used a special technique reported by Kramer et al. (1994) in order to determine the profile midpoint. We first separated the profile into individual components by fitting Gaussians curves to the pulse shape. Averaging the results of several such fits applied to different data, we obtained the mean properties of individual components. These mean components were finally combined again to form a typical average waveform. Since this average waveform represents the sum of several pure Gaussians curves, it is completely free of noise and, therefore, the ideal template for timing. This approach has three major advantages. Besides the fact that the obtained profile template has an infinitely large signal-to-noise ratio, S/N, the determination of the profile midpoint, even in cases of rather complicated pulse shapes, is fairly accurate since the template is a composition of well defined functions. For the same reason, the template is also independent of any profile resolution since it can be scaled to match any possible gridding of the real data. This ensures, that regardless of the actual resolution chosen during the observations, the same template with the same determined fiducial point can always be used for the analysis. For observations made at 1.41 GHz, 4.75 GHz and 10.55 GHz, respectively, we constructed the template out of fit results presented by Kramer (1994), since they reflect the results of a large number of independent measurements. For observations at 2.25 GHz and 8.5 GHz, fewer independent measurements were typically available, so that resulting TOAs have larger uncertainties. The 32-GHz profiles were of much lower S/N and of generally simple waveform (cf. Kramer et al. 1996), so that in most of the cases, we thus chose the profile peak as the fiducial point. ## 4.3. Profile alignmentIn order to align pulse profiles, corresponding topocentric TOAs were converted into arrival times at the solar system barycentre using Jodrell Bank timing ephemeredes (Martin & Lyne in prep.), the pulsar timing software TEMPO (Taylor & Weisberg 1989) and the DE200 ephemeris of the Jet Propulsion Laboratories (Standish et al. 1992). The resulting barycentric arrival times were finally corrected for dispersion delays by transforming them into arrival times at a formal infinite radio frequency using Eq. (4) and -values determined from the Jodrell observations. The resulting TOA residuals, i.e. the phase differences of the observed arrival times to those expected from the timing model, were used to shift the corresponding pulse profiles with respect to each other. From each timing residual we additionally subtracted the phase offset for the profile measured at the lowest frequency, so that the TOA of this profile is identified with phase zero. In contrast to most analyses of timing data (e.g. Manchester
& Taylor 1977), we adjusted only the global phase offset
(cf. Eq. 13) to minimize the TOA
residuals. Most importantly, we did not adjust the dispersion measure,
! This is in contrast to all previous, low
frequency studies (e.g. PW92), since at low frequencies the
dispersion measure is actually Our approach to keep the -value fixed, is
justified by the following estimation. PW92 found long term variations
of the dispersion measure as large as
cm Supposing that pulsar ephemeris describes © European Southern Observatory (ESO) 1997 Online publication: June 5, 1998 |