Single Pulse Studies Of Wide Profile Drifting Pulsars - A Probe Of Pulsar Magnetospheres
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The detailed nature of radio emission processes of pulsars and the exact location and distribution of the pulse emitting regions are still shrouded with mystery. Pulsars with drifting subpulses are considered as an important key for unlocking the mystery of how radio pulsars work. The phenomenon of subpulse drifting (first reported by Drake & Craft (1968)) is manifested as an organized subpulse behavior - subpulses appear at progressively changing longitude in the pulse window following some particular path. The path followed by the subpulses is specific to the individual pulsar concerned and is known as drift band. Drifting is generally characterized by Pm2(horizontal separation between the drift bands, i.e. in pulse longitude) and Pm3(vertical separation between the drift bands, i.e. in pulse numbers). The subpulse drifting phenomenon ﬁnds a natural explanation in the model of Ruderman & Sutherland (1975). According to this model, the subpulse drifting is produced from a system of sub-beams (subpulse associated plasma columns). Sparks (sparking discharges within the vacuum gap) rotating around the magnetic axis under the action of an E x B drift, give rise to a circulating pattern of sub-beams, and the time for one full circulation is referred to as the carousel rotation period, which we designate as P4. As pulsar radiation beams are widely believed to be arranged in concentric cones, it is natural to expect the circulating sparks to be distributed in annular rings on the polar cap. Each of these rings gives rise to one cone in the nested cones of emission. It has been recently shown that, subpulse drift may be fairly common among pulsars (Weltevrede et al. (2006) and (2007)). Hence, the pulsar radio emission mechanism is most likely closely connected with mechanism for drifting. In spite of significant progress both in high quality observations of drifting (e.g. Weltevrede et al. (2006) and (2007)) and attempts for confronting the results from the observations with existing models (e.g. Deshpande & Rankin (1999) and Gupta et al. (2004) etc), the pulsar emission mechanism is still an unsolved puzzle. Backer (1970b) first reported that emission from certain pulsars abruptly switches off for several periods, and suddenly comes back. This phenomenon is known as nulling. Nulling appears to be random, broadband and intrinsic to the concerned pulsar. Nulling is quite common in pulsars (Biggs, 1992). Although different aspects of the phenomenon of nulling are investigated in detail for many pulsars by several authors using high sensitivity observations, nulling is not yet explained by the existing theoretical models for pulsar radio radiation. In this thesis, I have mainly studied phenomenon of subpulse drifting and nulling, with the aim to probe the radio emission processes of pulsars. Most of the pulsars have a narrow duty cycle of emission (5-10 % of pulsar period). This is generally consistent with the expectations of the angular width of the polar cap, for typical viewing geometries. However, there are small but signiﬁcant number of pulsars with unusually wide profiles where the emission is seen for a wide range of longitude (≥ 90 degrees). These are expected to be pulsars which are highly aligned, i.e. the magnetic dipole axis is almost parallel to the spin axis. In such a case, the line of sight (LOS) is very close to both the rotation and the magnetic axes, and consequently, we sample a large region of the polar cap. This has the exciting potential to allow a detailed study of the distribution and behavior of emission regions located in an annular ring around the magnetic axis. The study of pulsars showing systematic subpulse drift patterns provides important clues for the understanding of the unsolved problems of pulsar emission mechanism. Constraints provided by such observations can have far reaching implications for the theoretical models, as exempliﬁed by some of the recent results in this area (e.g. Deshpande & Rankin (1999) and Gupta et al. (2004)). In this context, wide proﬁle drifting pulsars can provide extra insights because of the presence of simultaneous multiple drift bands. During the thesis period, I have mainly concentrated on the study of single pulse properties of two wide proﬁle drifting pulsars, PSR B0818-41 and PSR B0826-34. In depth study of PSR B0818-41 We have studied single pulse properties of a relatively less studied wide profile pulsar, B0818-41 using highly sensitive multi-frequency observations with the GMRT in full polar mode. Detailed investigation of PSR B0818-41 are reported in Chapters 2, 3 and 4 of this thesis. New results from our study are described in the following. We estimate the mean flux of PSR B0818-41 at 5 different frequencies and show that the spectrum flattens at frequencies lower than 325 MHz (at 244 or 157 MHz), providing indication of a low frequency turn-over. Significant linear polarization is observed at 325, 610 and 1060 MHz. Average linear polarization falls off much faster than the total intensity and decreases to zero near the outer edge of the profile. This can be explained by the orthogonal polarization mode jump at the edges of the profile observed at 325 MHz. Polarization angle sweep across the pulse profile evolves remarkably with frequency (between 325, 610 and 1060 MHz), which is not generally observed in other pulsars. Very less circular polarization without any signature of changing handedness is observed at 325 and 610 MHz. But circular polarization changes sign at the middle of the pulse profile at 1060 MHz. We report the discovery of a remarkable subpulse drift pattern in PSR B0818-41, using the high sensitivity GMRT observations. We find simultaneous occurrence of three drift regions with two different drift rates: an inner region with steeper apparent drift rate flanked on each side by a region of slower apparent drift rate. The closely spaced drift bands always maintain a constant phase relationship: the subpulse emission from the inner drift region is in phase with that from the outer drift region on the right hand side, and at the same time the emission in the inner drift region is out of phase with the outer drift region situated on the left hand side. This phase locked relationship (hereafter PLR) is maintained for the entire stretch of the data (for all the epochs of observations at 325 and 610 MHz) and does not appear to get perturbed after intermittent nulling or during changes in the drift rate. We observe frequent changes of drift rates. We see extreme examples of changing drift rates such as transitions from negative to stationary or stationary to negative drift rates, many of which appear to have some connection with nulls. We investigate changes in drift rates for about 10,000 pulses from two different epochs of observations at 325 MHz and observe frequent occurrences of small changes in the drift rate, seven transitions from negative to stationary drift rates, five transitions from stationary to negative drift rates, and two possible signatures of curved drift bands. In addition to the remarkable subpulse drift observed at 325 MHz, we report subpulse drifting at 244 and 610 MHz. At 244 MHz subpulse drifting is observed only in the leading and trailing outer regions, but not in the inner region. Though the drift bands are weaker, subpulse drifting is observed in both inner and outer region at 610 MHz. Pm2, Pm3 and ΔΦs(subpulse width) are determined for the inner and the outer drift regions for different frequencies. Though Pm3 is observed to be the same for the inner and outer drift regions, pm2 and ΔΦsare different for different drift regions. The unique drift pattern of this pulsar can be naturally explained as being created by the intersection of our LOS with two conal rings on the polar cap of a fairly aligned rotator. Based on the frequency evolution of the average profile, observed polarization angle (PA) swing and results from subpulse drifting, we converged on two possible choices of emission geometry: G-1 (inclination angle α= 11 deg and impact angle β= -5.4 deg; which incidentally reproduces the middle part of the PA sweep at 610 MHz) and G-2 (α=175.4 deg and β=- 6.9 deg; geometry derived from RVM fit to 325 MHz PA sweep). Pulsar radiation pattern simulated with both the geometries reproduces the average profile as well as the observed features in the drift pattern quite well. However, G-2 fits the PA sweep much better. We report that the peaks of the emission from the trailing and leading outer regions, as a function of the pulse number, are offset by a constant interval, P5~9P1. We also report a phase locked relation (PLR) between the inner and outer drift regions for PSR B0818-41. A new technique is introduced by us for resolving aliasing, using this constant offset (P5 ~ 9P1) between the peak emission from the leading and trailing outer regions. From the result of this technique, we propose that the subpulse drifting for PSR B0818 -41 is most likely first order aliased, and the corresponding carousel rotation period 4 =10 s. This implies that PSR B0818 -41 has the fastest known carousel. The drift pattern in the inner and outer rings are always phase locked for PSR B0818 -41. This could be a signiﬁcant constraint for the theoretical models of pulsar radio emission, and favors a pan magnetospheric emission mechanism. We observe frequent nulling for PSR B0818-41. We calculate a nulling fraction ~30% at 325 MHz for this pulsar. Lengths of neighboring nulls and bursts are found to be independent. For the inner drift region, our investigations bring out the fact that the nature of the transitions from burst to null are different from the transitions from null to burst. Switching off of pulsar radiation during nulling for PSR B0818 -41 is not abrupt, but is gradual, whereas the transitions from null to burst are found to be rather abrupt for the inner drift region. This effect is not prominent in the outer drift regions. Although, the inner region of the last active pulses before nulls are dimmer, the ﬁrst active pulses after nulls outshines the normal ones. The intensity of the inner region is maximum for the average proﬁle from the ﬁrst active pulse immediately after the nulls and then gradually goes down. This is consistent with the behavior of the individual nulls described above. However, this is not the case for the leading and trailing outer regions. The average profiles from the first active pulse immediately after the nulls follows similar shape as the normal profile but shows an increased intensity (in the form of a bump) in the inner region which is not present in the normal average profile. In addition, the leading and the trailing peaks appear to be of similar intensity, while trailing peak is significantly more intense for the normal profile. The average profiles from the pulses immediately after the nulls are wider than the normal profile. The average profiles of the first active pulses after the nulls are drastically similar between two epochs of observations. This is a very unique result which is not reported for any other pulsar so far and may imply that the phenomenon of nulling is associated with some systematic energy re-distribution in the pulsar magnetosphere. In depth study of PSR B0826-34 PSR B0826-34 is a pulsar with one of the widest known profile. The earlier studies of this pulsar (Durdin et al. (1979), Biggs et al. (1985) and Gupta et al. (2004)) have brought out some unique properties : strong evolution of the average profile with frequency, apparent nulling for 70% of time and a remarkable subpulse drift property- multiple curved drift bands with frequent changes and sign reversals of drift rate. We studied PSR B0826 -34 using the GMRT, simultaneously at 303 and 610 MHz, and individually at 157, 325, 610 and 1060 MHz. Detailed investigation of PSR B0826- 34 are reported in Chapter 5 of this thesis. Some of the interesting new results from our work are, As a natural out-come of the simultaneous dual frequency observations, we obtain an accurate DM value, equal to 52.2(6) pc/cm3, for this pulsar. Unlike most normal pulsars the DM determination for this pulsar is a difﬁcult and trick exercise, mainly because the profile is quite complex, very wide and strongly evolving with frequency. The advantage of our method of DM determination is that the observations at a single epoch are self sufﬁcient for obtaining the DM value at that epoch. Contrary to the earlier study by Esamdin et al. (2005), we find no evidence of weak emission during the typical long null states of this pulsar, simultaneously at 303 and 610 MHz, as well as from non simultaneous observations at 157, 325, 610 and 1060 MHz at separate epochs. We have also obtained absolute flux limits for the non-detection at various frequencies, which should be a useful comparison standard for any more sensitive studies in the future. We present the average profiles at five different frequencies. Main pulse (MP) and inter pulse (IP) emission observed for this pulsar span over wide pulse longitude. There is a remarkable frequency-evolution of pulse profile: IP becomes stronger with increasing frequency. We estimated the mean flux of the MP, IP and the full pulse region of PSR B0826- 34 at different frequencies of observation. Significant correlation in the total intensity of the individual pulses between 303 and 610 MHz is reported from the simultaneous dual frequency observations, which is indicative of the broad-band nature of the emission. The intensity correlations are positive for large lags, indicating that there is some kind of memory in the underlying structure. This memory is the longest for PSR B0826- 34, amongst all known cases. Our study of this pulsar brings out insight into simultaneous behavior of the single pulses from PSR B0826- 34 at 303 and 610 MHz, which has not been examined so far. We see about 6 -7 drift bands in the MP region at 303 and at 610 MHz. At 610 MHz we see about 2 -3 drift bands in the IP region. We observe wide variations in the drift rates, including positive and negative drift rates and curved drift bands, which are simultaneous for both frequencies. We have noticed coherence between simultaneous multiple drift bands - at some given instant of time all the drift bands (6 -7 drift bands) under the MP window show similar kind of drift. Though we find the drift pattern to be very similar in the simultaneous 303 and 610 MHz data, we observe that the drift band separation (Pm2) evolves significantly between these two frequencies, and in a manner opposite to the average profile evolution. In addition, we confirm the dependence of Pm2 on pulse longitude at 303 MHz and find indications for the same at 610 MHz. Significant linear polarization is observed in the MP region which drops abruptly at the edges of the pulse profile. Two orthogonal mode jumps are seen at the edges of the MP for both 325 and 610 MHz. We observe somewhat non orthogonal mode jump at the edges of IP for 610 MHz. Significant circular polarization in the MP along with the sense reversal near the center is observed for both the frequencies. The PA curve shows typical ”S” shaped swing (though there is some hint of a kink in the central part of the PA curve). RVM fit (Radhakrishnan & Cooke, 1969) to the PA curve is obtained with α~ 9.8 deg, β~3.2 deg, at both 325 and 610 MHz. The detailed study of two unique wide profile pulsars, PSR B0818-41 and PSR B0826 -34, was very rewarding and provided fair amount of insight towards the emission properties of pulsars. We broadly conclude that the emission from simultaneous multiple drift bands are coherent. In other words the emission mechanism responsible for generation of the drift bands is heavily correlated in the whole on pulse window. Also the equispaced sparks argues for a more isotropic arrangement of sparks which is favored by the conal model (Rankin, 1983). Drifting from more than one rings are observed only for two pulsars, PSR B0818-41 and PSR B0826-34. For PSR B081841 we observe that the emission from different rings are always locked in phase. This constant phase relation is maintained even during sequences of irregular drifting as well as after nulling. PSR B0826 -34 is another wide profile pulsar for which presence of simultaneous multiple drift regions are observed. For this pulsar the MP and the IP emission are interpreted to be coming from two concentric rings of emission. The drift bands in these regions are locked in phase implying that the emission from the inner and the outer rings are in phase. For PSR B0826- 34 we observe frequent nulling and changes of drift rates which are simultaneous for both the inner and outer rings. Hence for all pulsars for which we know drifting from more than one ring, the drift pattern in the inner and outer rings are always phase locked. No counter example is observed. This requires common drift rate in the inner and outer rings, implying that emission in the two rings are not independent, and the conditions responsible for drifting are similar in both rings. Our finding of PLR between the emission from the inner and the outer rings puts constraints on the theoretical models of pulsar emission mechanism and favors a pan magnetospeheric radiation mechanism. Preliminary study of single pulse properties of six other pulsars Inspired by the success of our study of PSR B0818- 41 and PSR B0826-34 we carried out single pulse study of few other pulsars with diverse profile. Preliminary results from this study are presented in Chapter 6. However, some of the new results form this work are highlighted in the following. We report occasional nulling for PSR B0540+23 which is important in the sense that nulls are not commonly seen in the core components. We observe simultaneous two drift bands for B1819- 22 at 325 and 610 MHz. We observe some kind of mode changing between stronger and weaker modes with changes of drift rates, which are probably associated with occasional nulling observed in this pulsar. For PSR B1839 -04 subpulse drifting is observed under the two peaks of the profile. The emission under the leading and trailing peaks appear to be in phase. Determination of the orbital parameters of binary pulsars Apart from the above work, I got interested in determination of the orbital parameters of the binary pulsars. This work was triggered by the discovery of a binary pulsar PSR J0514- 4002 (the first known pulsar in the globular cluster NGC 1851) at the GMRT in 2004 (Freire et al., 2004). We present a novel method for determination of the orbital parameters of binary pulsars, using data on the pulsar period at multiple observing epochs in contrast to the method described by Freire, Kramer & Lyne (2001) which requires both pulsar period and period derivatives at particular observing epochs. This method uses the circular nature of the velocity space orbit of Keplerian motion and produces preliminary values based on two one dimensional searches. Preliminary orbital parameter values are then refined using a computationally efficient linear least square fit. This method works for random and sparse sampling of the binary orbit. Unlike the method used by Freire, Kramer & Lyne (2001), which works for nearly circular binary orbits, this method works for binary orbit with any eccentricity. We demonstrate the technique on (a) the highly eccentric binary pulsar PSR J0514- 4002 (the first known pulsar in the globular cluster NGC 1851) and (b) 47 Tuc T, a binary pulsar with a nearly circular orbit. Our result agrees with the earlier determination of the orbital parameters of the binary pulsars done with coherent multi-epoch timing (Freire, Kramer & Lyne (2001) and Freire et al. (2007)). In our method the computation involves only one dimensional searches and linear least square fits. This study is reported in Chapter 7. The main conclusions and the possible future works are presented in Chapter 8.
- Physics (PHY) 
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