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Astron. Astrophys. 321, 305-310 (1997)

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3. Results

In Figs. 2 and 3 we show examples of the processing for three pulsars. With a solid line we show the averaged dispersed and Faraday-modulated pulse profile, with an N point running average applied. The fitted sine plus polynomial are shown as a dotted line. In the Fig. 2 example of PSR 1907 [FORMULA] 10 we have in the 5MHz bandpass full six periods of the Faraday rotation modulation, and their period [FORMULA] is remarkably close for observations at different days, within 1 [FORMULA]. This error constitutes 0.13% of a single measurement of [FORMULA]. Since we directly measure [FORMULA] we can obtain the Rotation Measure RM from Eq. (2) and (3) (e.g. Smirnova 1991) as

[EQUATION]

where tabulated DM values were used (Taylor et al. 1993). In Table 2 we list the DM used, the RM values measured before our work (Hamilton & Lyne 1987 (HL), and Hamilton et al. 1981 (H)) and their errors. We also list our values (and errors): [FORMULA], the absolute values of [FORMULA], and of [FORMULA]. The unweighted average was used when we had more than one observation of a pulsar. The errors in [FORMULA] were obtained from the fitting procedure after the effect of the ionosphere was removed, and depend to a large extent on the signal-to-noise ratio. The errors in RM include the error in T and the published error value of DM (Table 2) (Taylor et al. 1993). To be noted is the DM errors may be the dominant source of error in the value of RM for some cases. For example, for PSR 1907 [FORMULA] 10 if the error of the DM would be 5 times smaller the error in RM would be nearly halved. Another source of error is the time variation of DM, which could have a different value due to different observing epochs (e.g. Phillips & Wolszczan 1991). In our method we measure the actual [FORMULA], regardless of what the DM is at the time.

[FIGURE] Fig. 2. Averaged dispersed pulse profile for PSR 1907 [FORMULA] 10 as observed with our system for two different observing days (solid lines) smoothed out with a 10-point running average. Least-squares fitting of the sum of two functions (a sine and a 2-nd degree polynomial) to the original data curves (dashed lines). The horizontal (time) axis has 512 bins for the full pulse period [FORMULA] and the vertical axis represents linear polarization intensity in arbitrary units.
[FIGURE] Fig. 3. Same as Fig. 2 for a PSR 1915 [FORMULA] 13 and b PSR 1946 [FORMULA] 35.

[TABLE]

Table 2. Pulsars observed at 318 MHz and their known and newly measured parameters: DM, Dispersion Measure and error, Taylor et al 1993; [FORMULA], period of sine modulation and error; [FORMULA], our value for the weighted average of the magnetic field projected on the line of sight and error; [FORMULA], our value of the absolute value of the Rotation Measure and error; RM, HL Rotation Measure and error, Hamilton and Lyne 1987; RM, H Rotation Measure and error, Hamilton et al 1981. Note that our measurements of [FORMULA] and RM have no sign, so their absolute value is listed here.


The ionosphere also contributes to the rotation of the plane of polarization; the high accuracy of our measurements requires that it must be accounted for. An electromagnetic wave traversing two magnetoactive plasmas successively (interstellar medium and ionosphere) will have an [FORMULA] that is the algebraic addition of the two RM 's of the two plasmas [FORMULA]. Hence, if the ionospheric [FORMULA] is known we can obtain the interstellar medium RM. After replacing constants and assuming a constant magnetic field through the ionosphere the [FORMULA] is (a variant of Eq. (1))

[EQUATION]

where [FORMULA] is the projection of the average magnetic field at the ionosphere along the line of sight to the pulsar, for Arecibo a value of [FORMULA] Gauss with a direction [FORMULA] from the horizontal plane and [FORMULA] West of geographic North was used. The ionosphere is thin (200-300 km), over it the Earth's magnetic field varies very little, so that a constant value of [FORMULA] is more than adequate for this correction. [FORMULA] is the ionospheric total electron content along the line of sight to the pulsar, typically during our observations [FORMULA] to [FORMULA] cm-2.

To determine [FORMULA] for each case we measured the ionospheric vertical [FORMULA] value with the help of an ionosonde at the end of each observation run, and calibrated [FORMULA] with on-site incoherent scattering ionospheric radar observations. They show that [FORMULA] (as measured vertically) may vary day to day and hour to hour, by up to [FORMULA] cm-2. Variations of [FORMULA] over the 15-minute observation span may reach 0.2 [FORMULA] cm-2. The period [FORMULA] of the sine modulation corrected for ionospheric effects is

[EQUATION]

where the sign of [FORMULA] follows the same rule as the interstellar medium RM sign. This correction is based on [FORMULA], which is always the case. In Table 2 the listed values are corrected for the ionosphere: [FORMULA], [FORMULA], and [FORMULA], computed from [FORMULA] before the absolute value was taken. The sign of [FORMULA] is not known from our observations. For those pulsars observed by others we used their sign in computing the ionospheric correction, but we included the full ionospheric correction as an error for PSR 2000 [FORMULA] 32, where the sign is unknown. For pulsars observed by us, the ionospheric correction to [FORMULA] ranged from 0.08 to 3 msec, [FORMULA] ranged from 0.8 to 3 rad/m2. The corrections to [FORMULA] go from 0.003 to 0.015 µGauss. The short-term variations of [FORMULA] may give errors in the determination of parameters of the order of [FORMULA] msec, [FORMULA] rad/m2, and [FORMULA] Gauss. The error in a single measurement of [FORMULA] was always better than [FORMULA]. The influence of these corrections and their errors can be reduced through averaging observations over consecutive days, and through a better knowledge of the ionospheric parameters during the observations.

It is of interest in our method that, even if we do not know the sign of the measured [FORMULA] and RM, the ionospheric correction can provide the sign for some of the newly measured values. Observations done on different days will have different ionospheric contributions [FORMULA]. Since the sign of the ionospheric contribution is known the sign of the interstellar medium contribution can be inferred.

For PSR 1737 [FORMULA] 13 the experimental setup parameters were not optimal, hence the errors of our values are large, it should be reobserved at lower frequencies. We see that of all the known pulsars PSR 1907 [FORMULA] 10 has the largest value of [FORMULA] and one of the lowest measurement errors, making it an excellent candidate for long-term monitoring.

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© European Southern Observatory (ESO) 1997

Online publication: June 30, 1998
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