3 Discussion

  

Figure 1: The histograph for the flux comparison. Some pulsars (e.g. these in Table 1) have been missed in the left-half of the distribution (i.e. when Snvss/Spsrcat<1), because scintillation makes them weaker than the NVSS sensitivity

3.1 Scintillation and undetected pulsars

The VLA measurements of the flux densities S_1.4 of most identified pulsars, averaged over about 84 MHz bandwidth and 3$~\times~$23 s in time, are comparable to the flux densities published in Lorimer et al. (1995) and Gould & Lyne (1998). They are generally within a factor of 2 of the published densities (see Fig. 1), but sometimes up to a factor of 3 or more. Most of undetected pulsars ($\sim$400) have flux densities below 2 or 3 mJy. Interstellar scintillation (e.g. Gupta et al. 1994) both helps and hinders the detections (Cordes & Lazio 1991). Some pulsars which have a flux density less than 2 mJy in the pulsar catalog have been detected in the NVSS with a larger flux density. The scintillation effect is more obvious for strong pulsars. For example, PSR B2020+28 should be as strong as 38.0 mJy, but in the NVSS it appears to be a highly polarized source of $3.6\pm0.5$mJy. Among 61 pulsars with known flux densities larger than 5 mJy, about one fourth were missed by the NVSS (as listed in Table 2), some due to scintillation, some due to confusion (Condon, private communication).

  

Table 2: Pulsars stronger than 5 mJy but not detected by the NVSS

3.2 Polarization

When pulsars are observed as continuum radio sources, the polarized intensity, L, and polarization position angle, PA, are calculated from the integrated Q and U values of the final images, i.e., over all the observation time and the bandwidth, so that

$$L_{nvss} = \sqrt{\left(\int_t Q\right)^2 + \left(\int_t U\right)^2},$$ (1)

and

$${PA}_{nvss} = \frac{1}{2}\; \frac{180}{\pi}\; \arctan\left(\frac{\int_t U}{\int_t Q}\right)\cdot$$ (2)

In pulsar observations, however, the total linearly polarized intensity is

$$L_{psr} \equiv \int_t \sqrt{Q^2+U^2},$$ (3)

and the polarization position angle PA is

$${PA}_{psr}=\frac{1}{2}\; \frac{180}{\pi}\; \arctan \left(\frac{U}{Q}\right)$$ (4)

for each pulse longitude. The PA often swings more than $90\hbox{$^\circ$}$ over a pulse. Since a positive value of Q or U in one part of a pulse may cancel a negative value in another part, it is believed that the pulsar emission is depolarized in contiuum observations. Furthermore, the bandwidth depolarization occurs for pulsars with high rotation measures. Therefore the L/S in Table 1 should be taken as the lower limit of pulsar polarization.

  

Figure 2: Histograms of polarization percentage of a few kinds of objects: quasars, BL-Lac objects, all radio sources in one sky area, and pulsars. Note that the abscissa is up to 100% for pulsars, but just 25% for other objects

Even so, pulsars are still the sources with the highest polarization compared to other kinds of objects (see Fig. 2). As seen from Table 1, some pulsars have very high linear polarization, such as PSRs B1742-30 ($L/S \sim 90\%$)and PSR B1929+10 ($L/S \sim 63\%$), even after the smearing and depolarization.

Since the NVSS has very accurate absolute position angle calibrations ($<0.2\hbox{$^\circ$}$), the well measured PA of a few pulsars (with error ) may help to make an absolute PA calibration in pulsar observations. One example is shown in Fig. 3. First, using the VLA measurements of PA at 1400 MHz and the RM values, we calculated the averaged PA over the pulse at the observation frequency accordingly. Second, from the pulsar observations, we got PA for calibration pulsars using Eq. (2) from the pulse profiles (including interpulse if applicable) of Stokes parameters Q and U. Third we compared them to get an offset which represents the instrument PA offset, and used it to calibrate all pulsar observations.

  

Figure 3: Calibration for absolute polarization angle. Pulsar data were observed by von Hoensbroech & Xilouris (1997). In the lower panel, the total intensity, I, and linearly polarized intensity, L, are plotted with a thick continuum line and a dot-dash line, respectively. (The interpulse is almost 100% polarized.) In the top panel, the original PA data are plotted with a thin line (and with an error bar on every second point), and the calibrated PA data are plotted with a thick line

  

Table 3: Pulsar calibrators for absolute polarization angle

In Table 3, we listed 5 pulsars which can be used for calibration purposes. All of them have strong linear polarized intensity that can be easily detected, and their rotation measures RM are either quite small (10 rad m^-2) or accurately measured ( rad m^-2). None of them has any mode-changing (e.g. PSR B1237+25 and PSR B1822+09) or complicated variations in PA across the profile (e.g. PSR B1933+16). All pulsars in Table 3 satisfy $\sigma_{PA} + \sigma_{RM} \cdot \delta(\lambda^2) < 3\hbox{$^\circ$}$, where $\delta(\lambda^2)$ was the difference of the wavelengths squared, and was taken as 1.0.

3.3 Proper motions

  

Table 4: Pulsar proper motions

Pulsar proper motion is a very important quantity to be measured, so that pulsar velociaties can be determined. Pulsar timing can be used to determine the proper motions of millisecond pulsars because of their great timing stability (e.g. Nice & Taylor 1995). However, for most pulsars, the proper motions can only be measured by determining the pulsar position precisely at two or more well-separated epochs using interferometry (e.g. Fomalont et al. 1997).

We compared the pulsar positions given in the pulsar catalog with those from the NVSS whose epoch is simply taken as MJD = 49718, and calculated pulsar proper motions if possible. The results are listed in Table 4. Pulsars with uncertainties of proper motion larger than 200 mas yr^-1 have been deleted. Because of the large uncertainty of the NVSS positions, we obtained only a few significant measurements: proper motion in declination direction of PSR B1133+16, and that in right ascension of PSRs B0823+26 and B2016+28. While the former two are consistent with the previous measurements made by Lyne et al. (1982), the latter one is marginally not. Cross-checking with Table 2 of Taylor et al. (1993), we found that all other measurements in Table 4 are consistent with (though poorer than) those given in the pulsar catalog, except for one new upper limit of PSR B0031-07. VLA A-array observations of these pulsars in Table 1 should provide much more accurate positions, and hence could produce the first measurement of the proper motions of about 20 pulsars.

PSR B0031-07 is a nearby pulsar with distance 0.68 kpc. Its proper motion upper limit indicates that the pulsar has a velocity of $470~\pm~346$ km s^-1, quite normal according to the pulsar velocity distribution (Lyne & Lorimar 1994).