Emission Altitude r/r Pulsar Period P [s] 4.85 GHz

Mon. Not. R. Astron. Soc., { (1997) Radio emission regions in pulsars Jaroslaw Kijak 1;2 and Janusz Gil 1 1 Astronomy Centre, Pedagogical University, Lubuska 2, PL-65-265 Zielona Gora, Poland 2 Max-Planck-Institut fur Radioastronomie, Auf dem Hugel 69, D-53121 Bonn, Germany 11 December 1997 ABSTRACT We study a concept of radius-to-frequency mapping using a geometrical method for the estimation of pulsar emission altitudes. The semi-empirical relationship proposed by Kijak & Gil (1997) is examined over three decades of radio frequencies. It is argued that the emission region in millisecond pulsar occupy the magnetosphere over a distance of up to about 3% of the light-cylinder radius and in normal pulsars about or less than 1% of the light-cylinder radius. Key words: stars: atmospheres - stars: neutron - pulsars: general. 1 INTRODUCTION The systematic increase of component separation and pro- le widths with decreasing frequency suggests that the radiation at dierent frequencies is emitted from dierent altitudes above the polar cap. This idea is known as a radiusto-frequency mapping (RFM). The concept that the main contribution to radio emission at a certain frequency occur at relatively narrow range of altitudes near a particular distance r em (Cordes 1978) can be described as r em /?p : (1) Theoretical estimates for the exponent p range from p = (i.e. no RFM; Barnard & Arons 1986) to p = :66, corresponding to emission at the plasma frequency in a dipolar magnetic eld (Ruderman & Sutherland 1975). Cordes (1992) reviewed the various methods of estimating emission altitudes. To place limits on the location of the emission region, one can use a geometrical method (Gil & Kijak 1993; Kijak & Gil 1997 and Section 2 in this paper), pulsar timing data (Phillips 1992), interstellar scintillation (Smirnowa & Shishov 1989), high quality polarimetry (Blaskiewicz et al. 1991), and VLBI observations (Gwinn et al. 1997). Several authors discussed the concept of the RFM (Craft 197; Cordes 1978; Blaskiewicz, Cordes & Wasserman 1991; Phillips 1992; Gil & Kijak 1993; Xilouris et al. 1996; Hoensbroech & Xilouris 1997; Kijak & Gil 1997; Kramer et al. 1997) and set constraints on the emission radii for a number of pulsars. These estimates show that the pulsar emission region is relatively compact and lies near the surface of the neutron star, apparently closer than about 1% of the light-cylinder radius R LC. Kijak & Gil (1997) estimated the emission altitudes for a number of pulsars at three frequencies using the geometrical method based on the assumption that the low intensity pulsar radiation (corresponding to the prole wing) is emitted tangentially to the bundle of the last open dipolar eld lines. Using a low intensity pulse width data of a number of pulsars at two frequencies (.43 and 1.42 GHz) they argued that the emission altitude depends on pulsar period P, frequency and pulsar age 6 (in units of 1 6 years) in a way which can be described by the semi-empirical formula r KG = (55 5) R?:21:7 GHz?:7:3 6 P :33:5 ; (2) where R = 1 6 cm is the neutron star radius and GHz is the observing frequency in GHz. Thus, the emission region is located close to the neutron star in short period pulsars and further away in longer period pulsars. This RFM r() /?:21 is consistent with previous estimates by Blaskiewicz et al. (1991), Gil, Kijak & Seiradakis (1993), Hoensbroech & Xilouris (1997) and Kramer et al. (1997). However, an apparent period dependence is in strong contradiction with the claim of Rankin (1993) that the emission altitude is independent of pulsar period. A multifrequency study of emission altitudes in pulsars is important for understanding the emission physics in pulsar magnetospheres. Most previous studies were conducted at frequencies below 5 GHz and the validity of RFM at high frequencies was not well understood (e.g. Xilouris et al. 1996; Kramer et al. 1997). The detection of pulsars at high radio frequencies > 3 GHz (Wielebinski et al. 1993; Kramer et al. 1996; Morris et al. 1997) raises the question about the place of origin of the observed radiation. According to the canonical RFM (Eq. 1) it should be generated closer to the neutron star surface than lower frequency radiation. In this paper we discuss the radial locations of the pulsar emission regions using data from two observatories: Effelsberg and Jodrell Bank. In our analysis we use a number of straightforward assumptions: (i) the pulsar radiation is narrow-band with RFM operating in the emission region,

2 J. Kijak and J. Gil (ii) pulsar emission is beamed tangentially to the dipolar magnetic eld lines and (iii) the extreme prole wings originate at or near the last open eld lines. The outline of this paper is as follows: In Section 2 the geometrical method is described and used to analyse data at 4.85 GHz. In Section 3, a multifrequency study of emission altitudes is performed using Eelsberg (at high frequencies) and Jodrell Bank (at low frequencies) data for 16 pulsars. The relationship for the pulsar radio emission altitude (Eq. 2) is examined over three decades of frequencies. We also analyse six millisecond pulsars. Finally, in Section 4 we discuss and summarize our results. 1 1 2 EMISSION ALTITUDES - GEOMETRICAL METHOD OF ESTIMATION This method is based on the original idea of Cordes (1978) followed by Blaskiewicz et al. (1991) and Phillips (1992) and developed further by Gil & Kijak (1993) and Kijak & Gil (1997 hereafter Paper I). The opening angle between the magnetic axis and the tangent to dipolar magnetic eld lines at points where the emission corresponding to the apparent pulse-width originates can be expressed in the form = 1 :24 s r 1=2 6 P?1=2 ; (3) where P is pulsar period, r 6 = r=r is the emission altitude and s is the mapping parameter ( s 1) describes the locus of the eld lines on the polar cap (s = at the pole and s = 1 at the edge of the Goldrech-Julian (1969) circular polar cap). If the pulsar radiation is relativistically beamed along dipolar eld lines, then we can attempt to calculate which eld lines should be tagged as coming from the emission region to the co-rotation limiting region. This should be easiest for the last open magnetic eld lines, which are believed to be associated with the lowest detectable level of radio emission - i.e. at the prole wings. Here, we anal- Table 1. Emission altitudes for pulsars at 4.85 GHz. We calculated r 6 from Eq. 3 and r KG from Eq. 2. For millisecond pulsars we calculated lower limits of r 6 (see text). References are marked for and parameters. PSR W ( ) ( ) r6 rkg Ref. B31+19 17.12:9 5.1: 226 3611 LM B329+54 3.51:1 7.71:2 286 319 R93 B355+54 42.94:4 17.72:8 327 237 R93 B525+21 2.91:3 4.5:7 511 5915 R93 B54+23 37.23:7 13.71: 33 278 G97 B74?28 27.23:3 12.2:9 162 259 R93 B823+26 12.91:1 6.71: 163 288 R93 B834+6 15.83:4 8.42:2 5822 411 LM B919+6 12.12: 8.91:3 224 319 G97 B95+6 55.45:3 11.31:3 213 217 R93 J122+11 27. 18.1 3.4 5.53 X97 B1133+16 13.1:4 7.:7 375 371 LM B1237+25 14.62:1 5.81:4 311 3511 LM B176?16 16.21:7 8.71: 325 338 LM J1713+747 57. 36.3 3.4 3.43 X98 B1855+9 6. 32.1 3.3 3.83 SR86 B1915+13 28.13:6 14.82:8 288 258 R93 B22+28 2.1:7 1.21:4 235 267 LM B245?16 15.85:4 4.91:9 3117 4514 LM B2111+46 8.51:5 6.52:5 2815 329 LM B2319+6 23.51:9 6.51:2 6116 4613 R93 1.1.1 1. Pulsar Period P [s] 4.85 GHz Figure 1. Emission altitude at 4.85 GHz versus pulsar period (data from Table 1). In case of these millisecond pulsars (triangles), lower limits following from 1% pulse widths are marked. yse data at 4.85 GHz from the Eelsberg observatory (Kijak et al. 1997a). We measured pulse prole widths W at the low intensity level (i.e. 1%) of the maximum intensity where s 1 (see Fig. 2 in Paper I for measurement technique) for a high quality prole and calculated opening angles = (W ; ; ), applying the knowledge about the viewing geometry represented by the inclination angle between the rotation and the magnetic axes and the impact angle of the closest approach of the observer to the magnetic axis (see Paper I and references therein for more detailed explanation). Our estimates of emission altitudes from Eq. 3 are listed in Table 1. A plot of emission altitude versus period presented in Fig. 1 indicates a period dependence similar to that revealed at lower frequencies (Paper I), although much lower S/N at this high frequency causes larger errors. A formal weighted t to pulsars older than 1 6 years gives r 6 = (33 2)P :27:5 at 4.85 GHz (Table 2). Following an apparent age dependence (see Eq. 2) we have also excluded from the t a three millisecond pulsars, since their ages are larger than 1 9 years. Because of low signal to noise ratio at 1% level in case of the millisecond pulsars we used pulse widths at 1% (Kijak et al. 1997b) and obtained lower limits for emission altitudes at 4.85 GHz. Table 2. Formal weighted power law ts for emission altitudes r 6/P a at several frequencies. We also calculated the average value a of exponent a. r 6 / P a Ref. (GHz) a.43 :32 :4 Paper I 1.41 :39 :6 Paper I 1.42 :35 :4 Paper I 4.85 :27 :5 this paper a :33 :5

Radio emission regions in pulsars 3 From analysis of four data sets at dierent frequencies (.43 GHz, 1.41 GHz and 1.42 GHz - Paper I and 4.85 GHz - this paper) it is clearly seen that the radio emission altitudes at a given frequency depend on the pulsar period r / P a, where a 6=. We calculated the average value of exponent a (see Table 2) and obtained a = :33:5, inconsistent with Rankin (1993) who claims that a =. An apparent period dependence of emission altitudes is also visible in Figs. 2 and 3, where we arranged pulsars in order of decreasing P. 3 RADIUS-TO-FREQUENCY MAPPING In this Section we attempt to study a concept of the RFM in the sense of Eq. 2 applied to multifrequency data. We have calculated the emission altitude for 16 pulsars throughout the radiation zone using the geometrical method described in Section 2. From an analysis of arrival times from pulsar observations at high frequencies (1.4 GHz - 32 GHz), Kramer et al. (1997) argued that for normal pulsars, radio emission originates in a purely dipolar magnetic eld. This justies a basic assumption of the geometrical method, namely relativistic beaming along a dipolar magnetic eld lines in the emission region. We used Jodrell Bank pulse width data (Gould & Lyne 1997) at low frequencies ( 1:6 GHz) and Eelsberg data at high frequencies ( 1:4 GHz). Results are plotted in Fig. 2 and discussed in Section 4. A radius-to-frequency mapping was derived for each pulsar. The results for the individual objects are listed in Table 3. For a very high frequency data (above 2 GHz) we have used pulse widths at 1% level and calculated lower limits of emission altitude, since the signal-to-noise was not good enough to carry out an analysis at lower intensity level. We obtained the RFM for 16 pulsars covering the frequency range between.3 GHz and 32 GHz. The average value of Table 3. Fits for a radius-to-frequency mapping (RFM) PSR r em() = A?p B329+54 424.28:7 B355+54 432.36:5 B54+23 382.28:4 B74?28 244.22:11 B823+26 435.58:11 B919+6 355.26:11 J122+11 91.1:2 B1133+16 543.32:5 B1642?3 333.24:7 B176?16 393.25:7 J1713+747 71.2:2 B1822?9 1214.5:11 B1845?1 44.1:8 B1855+9 41.21:8 B1915+13 33.16:13 B22+28 342.4:5 B221+51 273.28:6 B231+42 252.11:4 B2319+6 751.17:11 A p the RFM exponent has the mean value p = :26 :9 (see Table 3). This is obviously inconsistent with the RFM model assuming emission at local plasma frequency in which p = :66. We examined the relationship described by the Eq. 2 and the results are presented in Figs. 2 and 3. Solid lines represent ts to data points calculated from the Eq. 3 and error bars reect uncertainties in measurments of the pulse width W () and estimates of viewing angles and, thus in calculating () = (W (); ; ). Dashed lines correspond to the upper and lower limits calculated from Eq. 2. For most cases the emission altitudes ploted against frequency lie between the limits. One should emphasize that Eq. 2 was obtained from pulse width measurements at.43 GHz and 1.42 GHz (Paper I) while calculations from Eq. 3 correspond to completely dierent pulse width measurements at a number of frequencies between.31 GHz to 32 GHz. 3.1 Typical or normal pulsars The calculation related to 16 typical pulsars are presented in Fig. 2. The individual analysis shows that for some pulsars the RFM may have a slightly dierent form than that following from emission altitudes discribed by Eq. 2, although we nd good agreement in general. Only in one pulsar PSR B1822?9 we were not able to t the RFM to constraints following from Eq. 2. However, one should realize that Eqs. 2 and 3 were derived under the assumption of a symmetry with respect to the ducial plane (Paper I) which is almost certainly not satised in the case of PSR B1822-9. In fact, this pulsar demonstrates a wide variety of phenomena observed in one pulsar: mode changing, interpulse emission and weak bridge between the main pulse and interpulse (Gil et al. 1994). One can see from Fig. 2 that the emission altitudes in the PSR B1822-9 seems overestimated by a factor of 1.8 with respect to the region limited by dashed lines. In a simplest viewing situation when 9 and, the pulse width W / r 1=2. In such a case, the above factor of 1.8 could be explained by overestimating the pulse width measurement by a factor of about 1.4. Such an error is possible in this case because of properties mentioned above. Also estimates of the viewing angles and could be another source of error in calculating the opening angles / r 1=2. In summary, the fact that the PSR B1822-9 does not t to the geometrical method is not suprising and even strenghtening the consistency of our results. 3.2 Millisecond pulsars In this subsection we present a RFM analysis for six millisecond pulsars. The results are presented in Fig. 3. Pulse widths were measured at 1% of maximum intensity from published proles (Boriako et al. 1983; Thorsett & Stinebring 199; Foster et al. 1993; Camilo et al. 1996; Sayer et al. 1997) except at 5 GHz (Kijak et al. 1997b) where we used pulse width at 1% (lower limit). Several authors (see Kramer et al. 1998; Xilouris et al. 1998 and referencies therein) argued that the magnetic eld for millisecond pulsars in the emission region is not purely dipolar. In our analysis we found no evidence for deviations from a dipolar form even in millisecond pulsars. The emission altitudes presented in Fig. 3. lie

4 J. Kijak and J. Gil 15 15 15 15 1 5 PSR B2319+6 PSR B1133+16 PSR B1822-9 PSR B329+54 P=2.25s P=1.18s P=.77s P=.71s 1 1 1 5 5 5.1 1 1.1 1 1.1 1 1.1 1 1 15 15 15 15 1 5 PSR B1845-1 PSR B176-16 PSR B823+26 P=.66s P=.65s P=.53s 1 1 5 5 1 5 PSR B221+51 P=.52s.1 1 1.1 1 1.1 1 1.1 1 1 15 15 15 15 1 5 PSR B919+6 PSR B1642-3 PSR B231+42 PSR B22+28 P=.43s P=.38s P=.35s P=.34s 1 1 1 5 5 5.1 1 1.1 1 1.1 1 1.1 1 1 15 15 15 15 1 5 PSR B54+23 PSR B1915+13 PSR B74-28 PSR B355+54 P=.24s P=.19s P=.16s P=.15s 1 1 1 5 5 5.1 1 1.1 1 1.1 1 1.1 1 1 Figure 2. Multifrequency study of emission altitudes for 16 normal pulsars. Data points are calculated from Eq. 3 and error bars reect uncertainties in pulse width measurements and estimates of viewing angles and. Open circles corresponding to lower limits on the emission altitude (see text). Solid lines represent formal weighted t to data points. Dashed lines are upper and lower limits calculated from Eq. 2 and correspond to limiting values of parameters entering into a semi-empirical relationship (Eq. 2) and that is why they look discontinous on the log scale, while the solid line is just a formal t of Eq. 1. Pulsars are ordered according to decreasing period from P = 2:25s (upper left) to P = :15s (lower right). An apparent period depedence of frequency-dependent emission altitude r/r can be noticed.

Radio emission regions in pulsars 5 3 3 3 2 1 PSR B1913+16 PSR J122+11 PSR B1257+12 P=59ms P=16ms P=6.2ms 2 1 2 1.1 1 1 3.1 1 1 3.1 1 1 3 2 1 PSR B1953+29 PSR B1855+9 PSR J1713+747 P=6.1ms P=5.4ms P=4.6ms 2 2 1 1.1 1 1.1 1 1.1 1 1 Figure 3. RFM for millisecond pulsars. Solid lines are formal weighted t to data points. Dashed lines are upper and lower limits calculated from Eq. 2 and open circles are lower limits at 4.85 GHz. Pulsars are ordered with respect to decreasing period. Period dependence of emission altitudes can be noticed even within millisecond pulsars. Notice also that those pulsars would occupy the very bottom of panels in Fig. 2. within our constraints (upper and lower limits are marked by dashed lines) and solid lines represent ts (Table 3) to data points calculated from the Eq. 3. Apparently, radio emission in the millisecond pulsars originates closer to the neutron star than in the case of normal pulsars (compare Figs. 2 and 3). 4 DISCUSSION AND SUMMARY We have calculated the pulsar emission altitudes r 6 at 4.85 GHz using the geometrical method. A period dependence of r 6 has been obtained (see Fig. 1). The average value of exponent a in the relation r 6 / P a was obtained from four data sets a = :33:5 (see Table 2). For a given timing age the emission altitudes seem to follow approximately P :33 period dependence. Old millisecond pulsars lie slightly below the line tted to normal pulsars (see Fig. 3a in Paper I and Fig. 1 in this paper), which is a result of age dependence of emission altitudes (Eq. 2). The emission region is located close to the neutron star in short period pulsars and further away in longer period pulsars but for normal pulsars closer than about 1% of the light-cylinder radius R LC (see also Fig. 3b in Paper I). RFM models of pulsar emission region provide an attractive explanation of why prole widths (usually) increase with decreasing frequency. We have analysed emission altitudes for 16 pulsars throughout radiation zone and derived the exponent p of a RFM (Fig. 1). The average value p = :26 :9 (for 16 pulsars) obtained from the relation r em() = A?p is close to estimates from other papers (Table 4). It is signicant that our result with the exponent p = :26 is consistent with results obtained using dierent estimation methods (see Section 1) and with the exponent following from Eq. 2. The multifrequency study of emission altitudes show that radio emission for pulsars originates within less than 1 km above the surface of the neutron star and high frequency (above 1 GHz) emission comes from 1-2 km above neutron star (see Fig. 2). The total size of radio emission regions in the range between.3 GHz and 32 GHz is about 5 km for normal pulsars. We have also analysed six millisecond pulsars in which a radio emission region is much more compact (see Fig. 3). The total size of their emission regions is 1-2 km, consistent with small light-cylinder radii in millisecond pulsars. An apparent period dependence of emission altitudes is clearly visible in Figs. 2 and 3, where pulsars are ordered according to decreasing P. Xilouris et al. (1996) have calculated emission altitudes using the opening angles (Eq. 3) derived from the pulse widths measured at 1% intensity level for 8 pulsars. Both their results (presented in their Fig. 5) and our results (based on low level width measurements) demonstrate an evidence of RFM (Fig. 2). However, our emission regions are larger by a factor of few to several than their estimates. We believe that the radio emission zone in pulsar is less compact than 1-2 km derived by Xilouris et al. (1996). Our Fig. 2 shows that a total size of emission region in normal pulsars is between few hundred to thousand km (depending slightly

6 J. Kijak and J. Gil on pulsar period). This result is consistent with Gwinn et al. (1997), who estimated in a model independent way a characteristic size of the Vela pulsar's radio emission region. Gwinn et al. (1997) argue that the typical dimension of the emission region is between 25 and 1 km, which agrees very well with our Fig. 4b (one should mention here that Gwinn et al. (1997) have obtained a perpendicular size of the emission region, which however can be regarded as a characteristic dimension of pulsar emission region). Our multifrequency analysis presented in Figs. 2 and 3 gives us more condence in using the semi-empirical formula (Eq. 2) which was obtained only for two frequencies.43 GHz and 1.42 GHz in Paper I. Let us then calculate the emission altitudes from Eq. 2 for a million year old pulsar ( 6 = 1) with dierent periods. These results are presented in Fig. 4a where the value of period and the percentage of the light-cylinder radius R LC = cp=2 corresponding to a 1 MHz emission region is marked for each RFM curve. The radio emission region seems located close than about 1% of the light-cylinder radius in typical pulsars (Fig. 4a). In Fig. 4b we present the emission altitude versus frequency for two well known short period pulsars. The total size of the emission region in Vela pulsars is about 5 km. This is in good agreement with a characteristic size of the emission region obtained for Vela pulsar by Gwinn et al. (1997), using an interstellar scattering method. In summary, we have assumed that the pulsar radiation is beamed along purely dipolar eld lines and that at a given altitude a relatively narrow range of frequencies is emitted. We have derived these emission altitudes from the prole width measurements corresponding to the 1% maximum intensity level, assuming that the low intensity emission originates near the last open eld lines using prole width measurements at several frequencies between 3 MHz and 32 GHz. We conrmed that the emission altitude depends on frequency as well as on P and P_ values, in such a way that it can be described by the semi-empirical formula expressed by the Eq. 2. In particular, we concluded that the total extent of the emission region is smaller than about 5 km in longer period pulsars and correspondingly less in shorter period pulsars. Pulsar radio emission is typically generated at altitudes smaller than few percent of the light-cylinder radii, which agree with independent estimates using a number of dierent methods (Cordes 1992). Our study shows no evidence of dierent emission mechanisms Table 4. An exponent for a RFM obtained by other authors p freq. range Ref. (GHz) :2 :1.43 { 1.42 BCW :66.5 { 4.8 P92 :21 :9 1.41 { 1.5 GKS :12 :8.43 { 1.42 GK :11 :2 1.41 { 1.6 K94 :21 :7.43 { 1.42 Paper I :29 :6 1.41 { 32. K97 :3 :1 1.41 { 1.5 HX :26 :9.31 { 32. this paper 25 2 15 1 5 1% LC 2% LC 3% LC 14% LC 5.s 2.s 1.s.1s a τ =1..1.1 1. 1 1 1 75 5 25 21% LC 47% LC Vela Crab.1.1 1. 1 1 Frequency [GHz] Figure 4. a Emission altitudes from Eq. 2 for a million year old pulsars ( 6 = 1:) with dierent periods. The value of period and the percentage of the light-cylinder radius corresponding to 1 MHz emission region is marked for each radius-to-frequency curve. b The emission altitude versus frequency for well known short period pulsars: Vela and Crab. 7% LC 16% LC between normal and millisecond pulsars. Also the magnetic eld in emission regions of both typical and millisecond pulsars seems to be purely dipolar (but see also Kramer et al. 1998 and X98 for evidence of slight deviations from pure dipole structure). Finally, it should be emphasized that the assumption of the existence of the RFM could be replaced by a wide band emission with and beamwidth varying across the open eld line region. Since the pulsar plasma ow should be relativistic, the beaming will still be determined by the opening angles of dipolar eld lines (Eq. 3). Thus, to t the frequency dependent pulse width W () (Xilouris et al. 1996), the labelling parameter s should satisfy a specic relationship s() = [W (); ; ] 1: 24 P 1=2 6 b 5% LC 9% LC r 1=2 6 () ; (4)

Radio emission regions in pulsars 7 requiring a ne tuning of many unrelated parameters. In a special case of a central cut with the opening angle (W ; ; ) :5W sin and thus s() W () 2: 5 P 1=2 r 1=2 6 () sin : (5) Since the prole widths measurements cover a wide range of values up to 36, the above relationship is hard to satisfy in whole parameter space, especially since s has to be less than 1. For example, if P 1s, sin :7 and r 6 < 1 then s > 1 for W > 4. This is of course inconsistent since there are many pulsars with P 1s and W greater than 4. Taking this into account we nd the RFM hypothesis as the most plausible explanation of systematic increase at the prole width with decreasing frequency. Thus, any reasonable theory of pulsar radiation must generate a coherent radio emission at altitudes consistent with our Eq. 2 describing the RFM in pulsars. Acknowledgments We thank D. Lorimer and M. Kramer for helpful discussion and comments. This work is partially supported by the Polish State Committee for Scientic Research Grant 2 P3D 15 12. Part of this research has made use of the data base of published pulse proles maintained by the European Pulsar Network, availble at: http://www.mpifrbonn.mpg.de/pulsar/data/ Kramer M., Wielebinski R., Jessner A., Gil J., Seiradakis J. H., 1994, A&AS, 17, 515 (K94) Kramer M., Xilouris K. M., Jessner A., Wielebinski R., Timofeev M., 1996, A&A, 36, 867 Kramer M., Xilouris K. M., Jessner A., Lorimer D. R., Wielebinski R., Lyne A. G., 1997, A&A, 322, 846 (K97) Kramer M., Xilouris K.M., Lorimer D. R. et al. 1998, ApJ, in press Lyne A. G., Manchester R. N., 1988, 234, 477 (LM) Manchester R. N., Taylor J. H., 1977, Pulsars, San Francisco, Freeman Morris D., Kramer M., Thum C. et al., 1997, A&A, 322, L17 Phillips J. A., 1992, ApJ, 355, 282 (P92) Rankin J. M., 1993, ApJ, 45, 285 (R93) Radhakrishnan V. Cooke D. J., 1969, Astrophys. Lett. 3, 225 Ruderman M. A., Sutherland P. G., 1975, ApJ, 196, 51 Sayer R. W., Nice D. J., Taylor J. H., 1997, ApJ, 474, 426 Seglestein D. J., Rawley L., Stinebring D. R., Fruchter, A. S., Taylor J. H., 1986, Nat, 322, 714, (SR86) Smirnowa T. V., Shishov V. I., 1989, SvA, L15, 191 Thorsett S. E., Stinebring D. R., 199, 361, 644 Wielebinski R., Jessner A., Kramer M., Gil J., 1993, A&A, 272, L13 Xilouris K. M., Kramer M., Jessner A., Wielebinski R., Timofeev M., 1996, A&A, 39, 481 Xilouris K. M., Kramer M., Jessner A. et al., 1998, ApJ, in press (X98) References Barnard J. J., Arons J., 1986, ApJ, 32, 138 Blaskiewicz M., Cordes J. M., Wasserman I., 1991, ApJ, 37, 643 (BCW) Boriako V., Bucheri R., Fauci F., 1983, Nat, 1983, 34, 417 Camilo F., Nice D. J., Shrauner J. A., Taylor J. H., 1996, 469, 819 Cordes J. M., 1978, ApJ, 222, 16 Cordes J. M., 1992, in Hankins T. H., Rankin J. M., Gil J. eds, Proc. IAU Colloq. 128, The Magnetospheric Structure and Emission Mechanisms of Radio Pulsars, Univ. Zielona Gora Press, Lagow, Poland, p. 253 Craft H. D., 197, PhD Thesis, Cornell University Foster R. S., Wolszczan A., Camilo F., 1993, ApJ, 41, L91 Hoensbroech A.v., Xilouris K. M., 1997, A&A, 324, 981 (HX) Gil J., Kijak J., 1993, A&A, 273, 563 (GK) Gil J., Gronkowski P. Rudnicki W., 1984, A&A, 132, 312 Gil J., Kijak J., Seiradakis J. H., 1993, A&A, 272, 268 (GKS) Gil J., Jessner A., Kijak J., et al. 1994, A&A, 282, 45 Goldreich P., Julian W. H., 1969, ApJ, 157, 869 Gould M., Lyne A. G., 1997, MNRAS, submitted (G97) Gwinn C. R., Ojeda M. J., Britton M. C., et al., 1997, ApJ, 483, L53 Kijak J., Gil J., 1997, MNRAS, 288, 631 (Paper I) Kijak J., Kramer M., Wielebinski R., Jessner A., 1997a, A&AS, 126, 1 Kijak J., Kramer M., Wielebinski R., Jessner A., 1997b, A&A, 318, L63