3. Data reduction

3.1. Descattering

Pulsars with large dispersion measures exhibited interstellar scattering at 102 MHz (and some pulsars even at 230 MHz) distorting the profile shape and delaying the pulse arrival time, inspite of the use of a or kHz filter bank. This effect was compensated for by application of a scattering correction method proposed by Kuzmin & Izvekova (1993), which is based on the classical solution of the transfer equation of a signal through the interstellar medium:

The intrinsic pulsar profile x(t) is obtained from the observed profile y(t) by Fourier transformation:

where

and



X(f) denotes the Fourier transform of the intrinsic pulsar profile x(t), Y(f) the transform of the observed profile y(t), and G(f) the transform of the interstellar medium transfer function g(t). g(t) was assumed - according to the thin screen model - to be given by

where the scattering time scale , which characterizes the broadening of the profile, was obtained from our observations using procedures as described in Kuzmin & Izvekova (1993). (We may remark, that this procedure removes both, the scattering and the receiver time constant.)

An example of our descattering procedure for the pulsar PSR 0136+57 at 102 MHz is shown in Fig. 1 (click here). is given - together with all the parameters important for the measurement and reduction procedure - in Table 3 (click here).

  
Figure 1: Example of descattering for pulsar PSR 0136+57 at 102 MHz: a) observed profile, b) descattered profile with = 30 ms (abscissa in degrees of pulsar rotation period)

3.2. Reduction of the arrival times to a common frequency, epoch, and location

Our observations were performed at different frequencies, observatories and at nearby but different times. Alignment of the profiles in time requires the reference to a common frequency, location and epoch. This was achieved by referring all observations to the solar system barycenter (common location) by use of the JPL DE200 Earth ephemeris and by adding integral numbers of (barycentrical) periods to observations at different epochs (common epoch), as described in the next section. Applying the cold plasma dispersion relation allowed the reduction to a common frequency, as explained below.

Time alignment is difficult to achieve for observations stretched over long time intervals. We used therefore the fact that both our measurements, in 1984 and 1991, contained observations at nearly exactly 1400 MHz. Profiles measured at this frequency were aligned by overlaying the strongest components of the profiles observed at the two sessions.

3.2.1. Correction of the pulsar period

Referring observations at different times to a common epoch by adding an integral number of periods to the earlier time of arrival requires the knowledge of the exact value of the apparent period P(t). Our first approach was to calculate the period from catalogued values of P and dP/dt (at epoch t₀ and omitting the second period derivative, since it is generally not known for the pulsars in our sample)

and applying a time dependent Doppler correction computed from the Earth ephemeris. The catalogued values of P and represent, however, in general fits to an extended and past time span giving sometimes appreciable residuals at the time of our observations. We decided therefore to correct the computed period values by an amount CorP derived from control measurements made at the same observatory and at the same frequency but at different dates. These control measurements showed often systematic shifts of the profile phase against observation date. The values of CorP are listed in Col. 6 of Table 3 (click here). In august-september 1992 special one-frequency measurements at 102 MHz were performed to confirm that pulsars, for which we applied the correction of the period, really need it.

Additional confirmation may be found by considering the changes of the listed values of in the 1995 catalogue of Taylor et al. (1995) with those of the 1993 catalogue (Taylor et al. 1993) (both are given in Table 3 (click here)). The changes of the period computed from the 1993 and 1995 values of

are highly correlated with our corrections CorP of the period, as demonstrated clearly in Table 3 (click here).

 

PSR 1.4 4.7 10.5

0138+59 1

0809+74 -4

1822-09 0 0 -1.5

2154+40 -3

Table 2: Phase shift (in degrees) of high-frequency profiles relative to the corresponding 0.4 GHz profiles

 

3.2.2. Dispersion delay

Most critical for the alignment at low frequencies is the exact value of the dispersion measure DM, which determines the time delay between observations at different frequencies:

(with in ms for in MHz and DM in cm^-3 pc).

As a first step we used the catalogued values of Taylor et al. (1993), shown in Col. 8 of Table 3 (click here). When deviations were still obvious, we tried, as the next step, to find more appropriate DM values which would align all profiles between 0.1 and 10 GHz as good as possible. These values of DM are shown in Col. 10 of Table 3 (click here) and in the figures. We list in addition, for comparison, the often slightly improved values of the catalogue of 1995 (Taylor et al. 1995).

The positions in time (phase) of the 102 MHz profiles depend heavily on these assumed dispersion measure values, since the corrections influence basically the low-frequency profiles. Independent, precise determinations of the dispersion measure would therefore be highly desirable. We will analyze this subject in a forthcoming paper.

 

PSR P Epoch CorP DM

TML93 TMLC95 TML93 TMLC95 this work

(s) (10^-15 s/s) (year) (ns) (ns) (pc cm^-3) (ms)

1 2 3 4 5 6 7 8 9 10 11

0011+47 1.240 0.561 0.563 1991 0 0.4 30 31.1 31.1

0136+57 0.272 10.6867 10.7003 1984 3.4 2.4 73.7 73.75 73.75 30

1991 11.6 6.4 30

0138+59 1.222 0.3904 0.3904 1984 0 - 34.80 34.80 34.80

0154+61 2.351 188.99 188.841 1991 -16.0 56.9 26 29.8 29.8

0301+19 1.387 1.29613 1.2959 1984 0 0.1 15.69 15.69 15.665

0329+54 0.714 2.04959 2.04959 1984 0 - 26.776 26.776 26.771

1991 0 -

0355+54 0.156 4.3912 4.39747 1984 0 -0.4 57.03 57.14 57.14 5

1991 1.4 1.0 5

0450-18 0.548 5.7564 5.7564 1984 1.7 - 39.93 39.93 39.93

1988 0 -

0450+55 0.340 2.3581 2.3656 1984 0 -0.3 14.3 14.602 14.60

1991 0 1.4

0525+21 3.745 40.045 40.0321 1984 0 3.0 50.877 50.877 50.877

1991 0 0.2

0540+23 0.245 15.42869 15.42378 1991 -3 -2.6 77.58 77.698 77.58

0628-28 1.244 7.107 7.107 1984 0 - 34.36 34.36 34.44

0655+64 0.195 0.00069 0.00069 1984 0 - 8.774 8.774 8.774

0656+14 0.384 55.032 55.0134 1991 0 -3.7 14 14.02 14.0

0740-28 0.166 16.8219 16.81152 1984 0.8 0.8 73.77 73.77 73.77

1991 -1.4 -1.5

0809+74 1.292 0.1676 0.1683 1984 0 0.3 5.751 5.7513 5.751

1988 0 0.4

0818-13 1.238 2.1056 2.1056 1984 0 - 40.99 40.99 40.965 9

0820+02 0.864 0.1039 0.1039 1984 0 - 23.6 23.6 23.6

0823+26 0.530 1.7236 1.7094 1984 0.3 -3.9 19.475 19.4751 19.475

1991 -0.2 -7.1

0834+06 1.273 6.79918 6.7995 1984 0 0.1 12.857 12.8579 12.865

1991 0 0.2

0919+06 0.430 13.7248 13.7202 1991 0 1.8 27.309 27.3091 27.31 2

0950+08 0.253 0.22915 0.22915 1984 0 - 2.970 2.9702 2.970

1133+16 1.187 3.73273 3.73273 1984 0 - 4.847 4.8471 4.847

1991 0 -

1237+25 1.382 0.95954 0.9605 1984 0 0.4 9.275 9.2755 9.29

1991 0 0.6

1508+55 0.739 5.0327 5.0078 1984 -2 -11.4 19.599 19.599 19.62

1530+27 1.124 0.803 0.803 1991 -3 - 14.61 14.61 14.61

1541+09 0.748 0.4303 0.4327 1984 0 1.3 34.99 34.99 34.99

1604-00 0.421 0.30607 0.30610 1984 0 0.0 10.684 10.6846 10.693

1642-03 0.387 1.7810 1.7810 1984 -0.5 - 35.665 35.665 35.73

1991 -1 -

1702-19 0.298 4.14 4.13828 1984 0 0.2 23.1 22.920 22.945

 

 

PSR P Epoch CorP DM

TML93 TMLC95 TML93 TMLC95 this work

(s) (10^-15 s/s) (year) (ns) (ns) (pc cm^-3) (ms)

1 2 3 4 5 6 7 8 9 10 11

1991 25 0.2

1737-30 0.606 465.67 465.3 1991 -1.8 5 153 153 152.1

1742-30 0.367 10.6592 10.66487 1991 -13 -0.8 88.8 88.387 88.387

1749-28 0.562 8.1394 8.1394 1991 -14 - 50.88 50.88 50.88

1804-08 0.163 0.02868 0.02868 1991 -1.6 - 112.8 112.8 112.8

1822-09 0.768 52.432 52.3636 1991 14 10.1 19.9 19.46 19.44

1826-17 0.307 5.5619 5.5619 1991 -14 - 217.8 217.8 216

1839+56 1.652 1.7 1.495 1984 40 28 26.2 26.54 26.72

1845-01 0.659 5.2184 5.2184 1991 -40 - 159.1 159.1 159.1

1929+10 0.226 1.15675 1.15661 1984 0.2 -0.1 3.176 3.176 3.18

1991 0.4 -0.1

1933+16 0.358 6.00354 6.00354 1984 -0.3 - 158.53 158.53 158.47

1952+29 0.426 0.00201 0.00104 1991 0 -0.2 7.91 7.91 7.91

1953+50 0.518 1.366 1.366 1991 3 - 31.8 31.8 32.5

2016+28 0.557 0.14936 0.14936 1984 -0.2 - 14.176 14.176 14.176

1991 -1.0 -

2020+28 0.343 1.8935 1.8935 1984 0 - 24.62 24.62 24.62

1991 0.3 -

2021+51 0.529 3.0518 3.06554 1984 3.0 6.3 22.580 22.580 22.55

1991 7.0 9.3

2045-16 1.911 10.9610 10.9610 1991 0 - 11.51 11.51 11.48

2110+27 1.202 2.6226 2.6226 1984 0 - 24.7 24.7 25.13

2111+46 1.014 0.7195 0.7115 1984 -1.0 -3.4 141.50 141.50 141.36 200

2154+40 1.525 3.417 3.4257 1984 -0.3 3.3 71.0 70.61 71.1 30

2217+47 0.538 2.76421 2.76503 1984 0 0.4 43.54 43.54 43.53

2224+65 0.682 9.671 9.6552 1984 1 -2.8 35.3 36.16 36.1

2306+55 0.475 0.202 0.202 1991 -1 - 47.0 47.0 47.0

2310+42 0.349 0.1155 0.1155 1984 -0.7 - 17.3 17.3 17.275

1991 -0.7 -

2319+60 2.256 7.037 7.037 1984 0 0 93.8 94.78 94.32

1991 0 0

2351+61 0.944 16.226 16.2641 1991 712* 15.1 95 94.34 94.34

* A comparison between the tabulated period values in the catalogues of Taylor et al. (1993) and Taylor et al. (1995) shows indeed a major revision, which explains the need for such a high correction.