The beam topology and dynamic emission properties of pulsar B0943+10 -- VI. Discovery of a 'Q'-mode precursor and comparison with pulsar B1822-09
aa r X i v : . [ a s t r o - ph . GA ] D ec Mon. Not. R. Astron. Soc. , 1– ?? (2004) Printed 8 November 2018 (MN LaTEX style file v2.2) The beam topology and dynamic emission properties ofpulsar B0943+10 — VI. Discovery of a ‘Q’-mode precursorand comparison with pulsar B1822–09
Isaac Backus , Dipanjan Mitra & Joanna M. Rankin , Physics Department, University of Vermont, Burlington, VT 05405 USA ⋆ National Centre for Radio Astrophysics, Ganeshkhind, Pune 411 007 India † Sterrenkundig Instituut ‘Anton Pannekoek’, University of Amsterdam, NL-1098 SJ
Unreleased
ABSTRACT
This paper reports new observations of pulsars B0943+10 and B1822–09 carriedout with the Arecibo Observatory (AO) and the Giant Metrewave Radio Telescope(GMRT), respectively. Both stars exhibit two stable emission modes. We report thediscovery in B0943+10 of a highly linearly polarized “precursor” component that oc-curs primarily in only one mode. This emission feature closely resembles B1822–09’sprecursor which also occurs brightly in only one mode. B0943+10’s other mode iswell known for its highly regular drifting subpulses that are apparently produced bya rotating “carousel” system of 20 ‘beamlets.’ Similary, B1822–09 exhibits subpulse-modulation behavior only in the mode where its precursor is absent. We survey our18 hours of B0943+10 observations and find that the ‘sideband’-modulation features,from which the carousel-rotation time can be directly determined, occur rarely—lessthan 5% of the time—but always indicating 20 ‘beamlets’. We present an analysis ofB1822–09’s modal modulation characteristics at 325-MHz and compare them in detailwith B0943+10. The pulsar never seems to null, and we find a 43-rotation-period P feature in the star’s ‘Q’ mode that modulates the interpulse as well as the conal fea-tures in the main pulse. We conclude that B1822–09 must have a nearly orthogonalgeometry and that its carousel circulation time is long compared to the modal sub-sequences available in our observations, and the mainpulse/interpulse separation isalmost exactly 180 ◦ . We conclude the precursors for both stars are incompatible withcore-cone emission. We assess the interesting suggestion by Dyks et al that downward-going radiation produces B1822–09’s precursor emission. Key words:
MHD, plasmas, pulsars: radiation mechanism, polarization, mode-changing phenomenon, precursor, interpulse – B0943+10, B1822–09
I. INTRODUCTION
Among the well investigated pulsars that exhibit the phe-nomenon of “mode switching”, B0943+10 provides one ofthe clearest examples of two discrete modes, both exhibit-ing distinct, fully characterizable behaviors (Suleymanova &Izvekova 1984). In this paper, the sixth in a series describ-ing B0943+10 analyses, we (somewhat abashedly) report anewly discovered precursor feature in the profile of this in-triguing star which is bright in the ‘Q’-mode and nearlyundetectable in the ‘B’-mode, suggesting a strong similarity ⋆ [email protected]; [email protected] † [email protected]; to another well studied pulsar with highly discrete modes,B1822–09 (or J1825–0935).During its weak, ‘Q’uiescent mode, B0943+10 is wellknown to exhibit a chaotic subpulse-modulation behavior(Suleymanova et al c (cid:13) Isaac Backus, Dipanjan Mitra, & Joanna Rankin
According to the polar cap emission theory of Ruder-man & Sutherland (1975), the observed subbeam carousel isthought to result from “spark”-induced columns of relativis-tic primary plasma directed into the ‘open’ polar flux tubeand precessing around the magnetic axis under the actionof E × B drift.An important finding for developing a fuller model ofthe polar cap emission region of B0943+10 was the presenceof evenly spaced ‘sidebands’ surrounding the primary mod-ulation feature associated with drifting subbeams. Paper Iargued that these sidebands are the signatures of a mod-ulation on the true (un-aliased) primary drift-modulationfrequency ( f ) corresponding to the circulation time of acarousel of 20 beamlets ( ˆ P = nP , where n is the numberof subbeams and P = f − ), and evidence presented in Pa-per II corroborated this conclusion. However, an importantconsideration in understanding the physical origin of the ob-served fluctuation spectra was left unresolved: how often andunder what circumstances do the sidebands appear?In this paper we continue our analysis of B0943+10and compare its behavior to that of another famous mode-switching pulsar B1822–09. Several basic similarities be-tween the stars prompt further investigation: both have com-parable periods (1.098 s for B0943+10; 0.769 s for B1822–09); and both have estimated surface magnetic fields onthe order of 10 G (ATNF Pulsar Database ). Further-more, both are detectable as X-ray emitters (Zhang, Sanwal& Pavlov, 2005; Alpar, Guseinov, Kiziloglu, & ¨Oegelman1995).More important are the remarkable modal similari-ties between these two pulsars. B1822–09 has fascinatedresearchers because of its several discrete behaviors. LikeB0943+10, it switches between two modes (Fowler et al et al , and the interpulse turns off.Nonetheless, the anti-correlation between B1822–09’s inter-pulse and precursor (hereafter IP and PC; Fowler & Wright1982) presents a difficulty for current emission models: ifB1822–09 is a nearly orthogonal rotator, as has been argued,how does information transfer from one magnetic pole to theother? It has even been argued that the IP and PC origi-nate from the same emission region which reverses emissiondirection in its two modes (Dyks, Zhang & Gil 2005).The organization of the paper is as follows. In § II wedescribe the observations of B0943+10 and B1822–09 usedin this study. In § III we present an analysis of 18 hours ofB0943+10 ‘B’ mode observations and describe the discovery In this paper we choose to continue the terminology estab-lished by Fowler et al for the stars’ two modes. The ‘B’ mode ofB0943+10 exhibits behaviors such as drifting subpulses similar tothe ‘Q’ mode of B1822–09, while the ‘Q’ mode of B0943+10 andthe ‘B’ mode of B1822–09 both display a precursor (see Table 2)The names derive from the relative intensity of the two modesand do not represent their most physically significant properties.In short, the ‘B’ mode in one star does not correspond to the ‘B’mode of the other.
Table 1.
B0943+10 and B1822–09 Observations
MJD Frequency Resolution Length (MHz) ( ◦ longitude) (in pulses) AO B0943+10 a b b GMRT B1822–09 c b The files of the B0943+10 observations used in this analysis were resampled fromtheir original resolution. Higher resolution is available, but was unnecessary forthe analysis presented here. a Only 41 ◦ are available for this observation b These observations lack polarimetry c The original observation contains 2300 pulses. Due to interference, we ignorethe last 223 pulses here. of two new instances of sidebands. Then, in § IV we reportthe discovery of a ‘precursor’ component in B0943+10.In § V we report a study of two GMRT 325-MHz obser-vations of B1822–09, the first ever detailed analysis at me-ter wavelengths. Fluctuation-spectral evidence is reportedsuggesting that the main pulse (hereafter MP) and IP arelinked, contrary to the Dyks et al reversal model. We findthat B1822–09’s modal behaviors, profile forms, and the po-larization properties of its MP and PC are comparable tothose of B0943+10. And like B0943+10, B1822–09 neverseems to null. We further argue that B1822–09 is indeedan orthogonal rotator. In § VI we discuss the implications ofour findings for the emission reversal model of Dyks et al and for a non-radial oscillation model proposed by Clemens& Rosen (2004) to explain the observed supbulse-drift ofB0943+10. Finally, in § VII, we review our findings, and thecase available for assimilating the properties of B1822–09and B0943+10. In particular, the PC emission in the twostars appears to be neither of the conal nor core type, andits geometry could associate it with the so-called “outer gap”where the high-energy emission from pulsars is thought tooriginate.
II. OBSERVATIONS
The B0943+10 observations used in our analyses were madeusing the 305-m Arecibo Telescope in Puerto Rico (here-after AO). The 327-MHz (P band) polarized pulse sequences(hereafter: PS) were acquired using the upgraded instru-ment together with the Wideband Arecibo Pulsar Processor(WAPP ) on a number of different days over a four-year pe-riod as detailed in Table 1. The auto- and cross-correlations (cid:13) , 1– ?? Table 2.
Mode Changes in B0943+10 and B1822–09 Observa-tions
MJD Modes a Switch Length (pulse) (in pulses)
AO B0943+10 b GMRT B1822–09 * Sidebands surrounding the primary modulation feature are observable in thefluctuation spectra of these observations (See § III). a Because the mode changes of B1822–09 occur over several pulses, these valuesrepresent an approximate boundary of the switch. b This represents an approximation because of interference at the mode switchboundary. of the channel voltages were three-level sampled and pro-duced by receivers connected to linearly (circularly duringthe MJD interval 53289 to 54629) polarized feeds. UponFourier transforming, sufficient channels were synthesizedacross a 25-MHz (50-MHz after MJD 54630) bandpass, pro-viding resolutions of about 1 milliperiod of longitude. TheStokes parameters have been corrected for dispersion, inter-stellar Faraday rotation, and various instrumental polariza-tion effects. Some of the PSs have been discussed in previouspapers in this series; however this paper presents the 6 daysof 2+ hour observations since MJD 53491.The two observations of B1822–09 were carried out us-ing the Giant Meterwave Radio Telescope (hereafter GMRT)near Pune, India, using the same techniques as described inMitra, Rankin & Gupta (2007).Table 2 outlines the occurrence of different emissionmodes present in our observations. The spectral analysistechniques utilized in this paper were first presented andexplained in detail in Paper I. We would ask the reader torefer to that paper for a complete description.
III. SIDEBANDS IN B0943+10
An important finding of the first paper in this series wasthe presence of sidebands surrounding the primary subpulsedrift-modulation feature. Both the sidebands and the pri-mary feature arise only during the ‘B’ mode. As argued inPaper I, these sidebands, shown in the longitude-resolvedfluctuation (hereafter LRF) spectra of Figure 1, represent frequency*P1
Figure 1. ‘B’ mode Longitude-resolved fluctuation (hereafterLRF) spectra for the MP of B0943+10 at 430 MHz, averaged overpulses 106-361 of MJD 48914 using a 256-point FFT. The averageprofile is given at the left of the figure and the integral spectrumis at the bottom. The central panel shows the amplitude of thefeatures. This is the first known instance of sidebands surround-ing the primary modulation feature of B0943+10. It was studiedat length in Paper I. At about 0.026 cycle/ P , the sideband spac-ing represents an harmonic relationship with the first-order aliasof the large primary modulation feature, providing evidence thatthe pattern of drifting subpulses in B0943+10 comes from a ro-tating carousel of 20 “sparks” of bright emission. The intensityscale is arbitrary. a “tertiary” modulation of the phase-modulated “drift” fea-ture. Non-uniformity within a regular pattern generates am-plitude modulation. Thus, unless all the subbeams are per-fectly identical in their amplitude and spacing—or are to-tally random—we would expect to detect such a tertiaryperiodicity corresponding to the rotation period (or circu-lation time) of the entire carousel ( ˆ P ). Using the 430-MHzobservation, Paper I determined these sidebands to fall sym-metrically at 0.02680 ± P − above and belowthe primary feature at 0.535 cycle P − . That they are sosymmetric and narrow indicates a regular amplitude modu-lation (of the phase modulation).The brevity of the 430-MHz observation analyzed in Pa-per I prevented the determination of how often these side-bands arise. We are now able to report the results of ananalysis based on a wealth of observations, and we find thatthe sidebands are rarely present in B0943+10. They are infact only known to occur on three separate occasions and ofcourse in the B mode: on MJD 48914 in Paper I at 430-MHz(see Fig. 1); and in the 327-MHz observations on MJD 52709and MJD 53862 (see Figs. 2 and 3). Out of some 58,000 ‘B’mode pulses now available in the AO PSs—comprising 18hours of observations—sidebands can be discerned in fewerthan 3,000. When they do appear, the sidebands are sta-ble for several hundreds of pulses—which indicates that thistertiary modulation can persist over many times the 37- P carousel-circulation time—and yet they vanish for manyhours at a time. They never seem to persist for more thanabout 18 mins. c (cid:13) , 1– ?? Isaac Backus, Dipanjan Mitra, & Joanna Rankin frequency*P1
Figure 2. ‘B’ mode LRF spectra (as in Fig. 1) for the MPof B0943+10 at 327 MHz, averaged over pulses 4085-4340 ofthe MJD 52709 PS using a 256-point FFT. Weak sidebands arepresent, surrounding the main feature; their remarkably evenspacing and their persistence over several hundred pulses allowsus to conclude that they represent a physically significant modu-lation of the primary feature at some 0.46 cycle P − . Note alsothat the primary feature strongly modulates the two subcompo-nents, while the center of the profile is much less modulated... Figure 3. ‘B’ mode LRF spectra (as in Fig. 1) for B0943+10at 327 MHz, averaged over pulses 260-771 of the MJD 53862 PSusing a 512-point FFT. The stability of the sidebands in this ob-servation allowed us to measure their spacing with high precision.We were able to average over 512 pulses without washing out themodulation, allowing the use of a 512-point FFT. Whereas beforethe sidebands were symmetric, in this observation one is clearly‘taller’ than the other.
We can conclusively corroborate several of the findingsof Paper I. The sidebands never appear to be accompaniedby any other pairs, nor is there evidence of any other ter-tiary modulation of the primary feature in PSs where thesidebands are not present. The pair of modulation featuresare always remarkably evenly spaced, the difference in theirspacings from the primary feature always being less than 3%of their actual spacing. The inverse of this spacing remainscommensurate with the carousel circulation time calculatedas 20 P , though the agreement is strongest in the 430-MHzobservation.In the MJD 52709 observation (see Fig. 2), the side-bands occur during a roughly 550-pulse interval, duringwhich ˆ P determined from the alias of the primary mod-ulation feature is 37.008 ± P . In agreement with thefindings of Paper I, these sidebands are of nearly identi-cal height, implying an amplitude modulation. In the MJD53862 observation, sidebands are detectable for some 1000pulses (see Fig. 3). ˆ P , measured from the primary modu-lation feature, is 37.376 ± t = − τ ln[( A (2 / − . / .
16] = ∼
100 min, where A(2/1)is the amplitude ratio of the two components comprisingthe MP, and τ is the characteristic time of some 73 min. (b) t = 1 . × − exp[2 .
077 ˆ P ] = ∼
95 min. These computa-tions are only approximate, but we can conclude that in theMJD 53862 observation, the sidebands show up around anhour further into the ‘B’ mode than they do on MJD 52709(see Fig. 4).
IV. PRECURSOR DISCOVERY IN B0943+10
We now introduce the newly discovered presence of a ‘pre-cursor’ component in B0943+10 which occurs strongly onlyin the ‘Q’ mode. Measuring from the center of the half-power point, the PC lies 52 ◦ before the MP, as can be seenin the upper panel of Figure 5. Because previous analyses ofB0943+10 have focused almost exclusively on its ‘B’-modecharacteristics, most “working” PSs were restricted for con-venience to a 40-60 ◦ window surrounding the MP; and whennot the occasionally present emission in the 40 ◦ -longituderange of the PC was at first dismissed as interference.During the ‘B’ mode, the PC emission levels are com-parable to the noise level, resulting in an integrated profilein which the precursor appears absent (see the lower plotof Fig. 5). During a ‘Q’-mode interval, the PC is ∼
18% of c (cid:13) , 1– ?? C a r ou s e l c i r c u l a t i on t i m e Time after B-mode onset (min)
MJD 53862MJD 48914MJD 52709Model Curve
Figure 4. ˆ P vs. the time after ‘B’-mode onset of the threeknown occurences of sidebands in B0943+10, along with a modelcurve representing the relationship established in Paper IV: t =1 . × − exp[2 .
077 ˆ P ]. There is no discernible relation be-tween the sideband occurrence and the evolution of the ‘B’ mode.The time positions of the MJD-48914 and 53862 observations arecalculated from ˆ P , and should be considered estimations; signfi-cant deviation from the model curve is expected, but not plottedhere. the intensity of the MP (which is itself both weaker andbroader than in the ‘B’ mode). Though weaker, the PC isactually some 1.7 times wider than the MP at half power( ∼ ◦ and ∼ ◦ , respectively). The PC switches off imme-diately at ‘B’ mode onset, producing no integrated emissionabove the noise level. We have no full-longitude observationsof the ‘B’-to-‘Q’ mode transition, so the behavior of the PCat this boundary is unknown.While the PC and the MP are regulated by the samemodes, their properties and behaviors are otherwise distinct.During the ‘Q’ mode, when the PC is most prominent, itsemission is nevertheless sporadic. Individual pulses are com-posed of many short spikes of emission, as shown in Figure 6,and are typically difficult to distinguish from the noise. It ispossible that the PC and the ‘Q’-mode MP null, but the spo-radic pulse shapes and low intensity of the PC make analysisof individual pulses difficult in our observations: nulls sim-ply cannot be distinguished from noise fluctuations. As waspointed out prominently in Paper I, the MP is itself moresporadic in the ‘Q’ mode than in the ‘B’ mode, but it isstill comprised of recognizable subpulses as opposed to thePC. Individual pulses vary greatly, but MPs are composedof a few, comparatively ‘smooth’ subpulses which are muchbroader than those seen in the PC. Conversely, the elementsof PC emission have durations about equal to the samplingtime and appear similar in character to the PC emission inB1822–09 (see Gil et al et al et al (1988), this results from nearly ‘Q’ mode‘B’ mode Figure 5.
Polarization profiles and PPA histograms forB0943+10’s ‘Q’ (1050 pulses of MJD 52832) and ‘B’ (4000 pulsesfrom MJD 53492) modes, respectively. ‘Q’ mode (top) : The PCis highly linearly polarized, with almost no circular polarization,and note the unusual flat polarization position angle (PPA) tra-verse; whereas the MP is almost completely depolarized by nearlyequal levels of OPM power (visible as parallel “tracks” in the PPAdistribution, separated by 90 ◦ ). ‘B’ mode (bottom) : Here theMP retains significant primary polarization-mode power, and itsPPA traverse is well defined. The PPA regularity around –20 ◦ ,which is only seen in very long integrations, may represent weaksecondary polarization-mode (hereafter SPM) PC power in its‘off’ state. The upper and lower panels display the total power(Stokes I ), total linear polarization ( L [= p Q + U ]; dashed red)and circular polarization ( V [LH-RH]; dotted green) (upper), andthe polarization angle ( PPA [= tan − ( U/Q )]) (lower). Individ-ual samples that exceed an appropriate > σ threshold (derivedfrom off-pulse L ) appear as dots with the average PPA (red curve)overplotted. The PPAs are approximately absolute (see text). Theintensity scale is arbitrary.c (cid:13) , 1– ?? Isaac Backus, Dipanjan Mitra, & Joanna Rankin
Figure 6.
A 256-pulse sequence, taken from the MJD 52832 ob-servation. The precursor (top) and main pulse (bottom) in the‘Q’ mode of B0943+10. The individual PC pulses are composedof many small spikes of emission, while the individual pulses ofthe MP are comprised of fewer, broader subpulses. The intensityscale is arbitrary. equal power contributions by the two orthogonal polariza-tion modes (hereafter OPMs). Individual pulses contain sig-nificant linear polarization, but when aggregated, the polar-ization disappears. Accounting for the 90 ◦ separation of thetwo OPMs, the MP has a prominent linear PPA traverse ofabout –3.0 ◦ / ◦ longitude (in both emission modes).The PC, by contast, is highly linearly polarized (85%at the peak); there is clearly one very dominant OPM. Moststriking is that within the errors, the PPA traverse is flat:0 ◦ / ◦ longitude.At ‘B’ mode onset, both components undergo drasticchanges. The main pulse exhibits its well known modulationfeatures discussed throughout this series. Drifting subpulsesappear so rapidly that we are able to determine the timeof the modal switch down to a single pulse (or two). Oneof the OPMs dominates, resulting in an average profile withsignificant linear polarization: about 10% at ‘B’ mode onset,increasing to 40-50% by ‘B’ mode cessation (see Paper V).The PC, by contrast, shuts off almost completely duringthe ‘B’ mode. Because of its weakness, it is impossible todetermine how quickly the PC emission drops off.Despite its weakness during the ‘B’ mode, a trace of thePC can still be detected through its linear polarization. Inintegrations of several thousand pulses, we see nothing of thePC in total power, but enough L remains to define its PPA(see Fig. 5). Over some 20 ◦ of longitude where the PC waspresent during ‘Q’ mode, we now see polarized ‘noise,’ withthe flat traverse characteristic of the PC. Note the contrastwith the other PPAs outside of the PC and the MP that arerandom, as is expected of actual noise. Interestingly, Fig. 5suggests that the ‘B’-mode PC polarization is orthogonal tothat of its ‘Q’-mode counterpart, arguing that it may be theSPM which is seen here.Finally, we emphasize that while the B0943+10 MP iswell understood in conal terms ( e.g. , Rankin 1993; hereafterET VI), this PC feature is aberrant. That the sightline tra-verse is highly tangential is clear from three different per-spectives (see Paper I): the dimensions and frequency evo-lution of its average profiles; the properties of its subbeamcarousel; and that its exceptionally steep RF spectrum isdue to the fact that its emission occurs inside the sightlinecircle at frequencies higher than about 400 MHz. For allthese reasons, the PC appears to fall outside any reasonableexplanation within the hollow-cone/core model. V. METERWAVE STUDY OF PULSAR B1822–09
As we have outlined above, pulsar B1822–09’s mode-associated PC component and IP have attracted great in-terest and have prompted extensive and repeated studyover the years. Virtually all previous single-pulse analysesof B1822–09 have been carried out at frequencies above 1GHz and usually with the Effelsberg telescope ( e.g. , Fowler& Wright 1982). Nonetheless, its tripartite profile and PPA Motivated by the presence of an IP in B1822–09 we have con-ducted a search for such a feature in B0943+10. This search hasproven unsuccessful, but given the weakness of B1822–09’s IP, asimilar interpulse would appear absent for even a slightly differentsight-line traverse, and given the weakness of B0943+10, a diminterpulse could be washed out in the noise.c (cid:13) , 1– ?? -130 40 60 Figure 7.
The full 2077-pulse B1822–09 observation on MJD53780 in 10-pulse averages. The PC and MP components (on theright) are located at their actual relative longitudes; whereas theIP (on the left) is spliced into the plot prior to relative longitude+23 ◦ for convenience (exactly 140 ◦ of longitude is removed at thispoint). The intensity scale at red saturates the MP (and is biasedpositively) in order to better show the IP and PC mode-changes.The anti-correlation between the IP and PC is very clearly shown.When one is ‘on,’ the other is ‘off.’ Note that the MP structurebroadens in the ‘B’ mode when the PC is present; whereas in the‘Q’ mode the 43- P modulation is readily discernible in the IP. traverse have proven difficult to interpret geometrically, andno existing study has provided a fully satisfactory model.Our interest in B1822–09 was prompted by its osten-sible similarity to B0943+10. In order to explore this simi-larity fully, however, we find we need both to conduct somenew analyses of the star’s PSs and to interpret them in thecontext of an understanding of its emission geometry. Inparticular, we have carried out the first in-depth analysis ofB1822–09 at meter wavelengths, but even here we can makeno easy assumptions about fully exploring the pulsar’s ef-fects because our two GMRT 325-MHz observations exhibitdrastically different modal behavior. The MJD 53780 PSdisplays the star’s characteristic mode-switching behavior:the two modes each endure for several minutes (around 200-500 pulses), with the overall profile being comprised fairlyequally of both modes (see Figure 7). The MJD 54864 total-power PS, however, displays an hitherto unknown B1822–09 behavior: a 2106-length PS composed entirely of the ‘Q’mode, never once switching to the ‘B’ mode. Though muchlonger than usual, this ‘Q’-mode PS otherwise appears per-fectly normal.Figure 7 shows the full 2077-pulse observation of MJD53780 in 10-period averages; note that exactly 140 ◦ of longi-tude have been removed at +23 ◦ , so that all three emissionfeatures, the IP, PC and MP appear in this sequence. Themultiple modal transitions are obvious. B1822–09’s ‘Q’ modeis characterized by the presence of its IP, along with a stronglow frequency modulation feature. During the ‘B’ mode, theIP and the regular modulation cease almost completely, and ‘B’ mode‘Q’ mode Figure 8.
Average profiles and polarization histograms of the PCand MP of B1822–09 during its ‘B’ (pulse ‘B’ mode (top) :here the highly linearly polarized PC ‘turns on,’ and its nearly flatPPA traverse is remarkable. Accounting for the 90 ◦ OPM “jump,”the MP PPA is also essentially flat, suggesting a nearly centralsightline traverse. ‘Q’ mode (bottom) : the conal componentsflanking the central MP feature have reduced intensity, so theprofile is narrower. PC emission is still faintly visible, along witha trace of its linear polarization. The quantities plotted are thesame as in Fig. 5.c (cid:13) , 1– ?? Isaac Backus, Dipanjan Mitra, & Joanna Rankin -130 40 60 - Figure 9.
Cross-correlation map of the MJD-53780 PS with itselfat a delay of 2 P calculated over the entire 2077 pulses, includ-ing both modes. The main panel shows the correlation betweendifferent longitudes as marked by the profiles in both the sideand bottom panels. The leading and trailing edges of the MP arepositively correlated with each other and the PC (and negativelycorrelated with the IP), whereas the center of MP correlates withneither. This strongly indicates that the MP has a three-zoneemission structure, although this is not fully clear from its aver-age profile. The ordinate is delayed with respect to the abscissa,and the positive (negative) delay maps are shown below (above)the diagonal; these two maps are virtually identical, indicatingcorrelations that are time-reversable. The three-sigma error inthe correlations is about 6%. a PC some 15 ◦ before the main pulse ‘turns on’. The fig-ure also shows greater breadth and complexity in the MPduring the ‘B’ mode, that partially accounts for its greateraggregate intensity.Partial profiles corresponding to the two emissionmodes are given in Figure 8. The nearly complete linear po-larization of the PC feature in the ‘B’ mode (upper) is wellknown, but striking in contrast to that of the MP. Note alsothat the PPA traverse of the PC is very flat, and that cor-related PPAs at similar angles in the ‘Q’-mode profile (bot-tom) show that some PC power remains. In fact, PPA rota-tion throughout the profile is very shallow: here we see onlyPPAs that are around –40 and +50 ◦ —presumably represent-ing the two OPMs—and the same conclusion follows evenfor the largely depolarized IP [not shown, but see Gould &Lyne (1998) at 1642 MHz]. Finally, the forms of the ‘B’- and‘Q’-mode partial profiles are dramatically different: Manytotal MP profiles show little structure, and care is needed inseparating the emission modes to reveal the different con-tributions to MP power [ e.g. , see Gil et al (1994): Fig. 1].Indeed, on the basis of the modal profiles here, we can onlybe sure that the MP has parts—that is, a bright centralcomponent as well as both a leading and trailing emissionregion. Such evidence we already saw in Fig. 7, where fairlysteady ‘B’-mode central-component power occurs togetherwith leading and/or trailing emission.Finally, Figure 9 shows a longitude-longitude correla- tion map for the entire 2077-pulse length of the MJD-53780PS at a 2- P delay. As we saw in Fig. 7 this observationis comprised of about equal contributions of ‘B’ and ‘Q’-mode intervals, so the map mixes the behaviours of the twomodes. Note, however, the strong correlations between thetwo sides of the MP and the other emission zones. This isseen over all delays of a few pulses, and the nearly identicalmaps for negative and positive delays on either side of thediagonal are compatible with amplitude modulation. ThePC correlations with the sides of the MP reflect the greaterMP activity in these regions during the ‘B’ mode when thePC is present; the negative correlation with the IP, showsthe opposite in the ‘Q’ mode.
1. ‘B’urst mode in B1822–09
Our observations provide only the four brief ‘B’-mode ap-paritions seen in the MJD-53780 observation of Fig. 7. Fluc-tuation spectra of these intervals show no significant peri-odicities. A weak ‘B’-mode modulation feature correspond-ing to about 11 P has been reported at higher frequencies( e.g. , Gil et al et al L / I extends across its entire width, such thatnearly all of its power is in a single OPM. Its PPA traverseis linear and nearly flat with a slope somewhere between 0and 1.3 ◦ / ◦ .The MP form and polarization structure is more typ-ical of core/conal emission. Its edges are completely depo-larized, apparently by the usual OPM activity; whereas hemiddle of the MP (core?) shows a broad region of significantfractional linear that is divided by a 90 ◦ OPM-dominace“jump”. Overall, there is little rotation of the PPA underthe MP: the PPA under the leading part of the profile is es-sentially that of the well defined middle, and the “jump” atabout +7 ◦ longitude is clearly OPM related. With respectto V , there is a weak anti-symmetric signature that is cen-tered at about +9 ◦ longitude, but it is not clear whetherthis is significant.We can now see clearly how it has been that B1822–09’sprofile is difficult to classify and interpret. Little can be madeof its ostensibly “double” average MP profile, and the modalpartial profiles in Fig. 8 are in turn quite complex. We findunassailable evidence for a basic tripartite form—leading,middle and trailing—but even the modal profiles show us no c (cid:13) , 1– ?? frequency*P1 - Figure 10.
Longitude-resolved fluctuation spectra of pulsarB1822–09’s ‘Q’ mode, averaged over pulses 221-750 of the MJD53780 observation, using a 512-point FFT. The MP is at the topof the left-hand panel, the PC in the center, and the IP at thebottom. A strong feature at 0.023 c/ P , corresponding to a P ofabout 43 P , modulates both the MP and the IP, while the weakPC displays no discernible modulation. simple triplicity. That in the top panel of the above figureshows weak early and bright trailing emission around thecentral component, but other ‘B’ episodes in Fig. 7 havea reversed or more balanced character. If then the centralfeature is of the core type, which seems a sensible premiseon multiple grounds, then the MP’s behavior is suggestiveof the T or M profile class and a highly central sightlinetraverse.In this context, B1822–09’s PC component is aberrant,in the sense that it has no clear interpretation within cur-rent understandings of the possibilities of polar cap emission.Its flat PPA traverse and virtually complete linear polariza-tion adds to this strangeness as does the character of itsindividual pulses. Gil et al ’s (1994) Fig. 5 plots a set ofPC and MP single pulses with 50- µ s sampling, and the dif-ference between the respective two regions is startling: onesees no subpulses in the PC as its emission elements typi-cally have widths of only a single sample. The MP emission,by contrast shows emission structures that are several de-grees wide—the subpulses with which we are familiar. This“spiky” emission was also seen by Weltevrede et al (2006b)in B0656+14, where they sometimes referred to its strikinglydifferent character as “rain”. Also, we have seen above (seeFig. 6) that the B0943+10 PC has the same characteristic.
2. ‘Q’uiescent mode
As we saw earlier in Fig. 7, the B1822–09 ‘Q’ mode exhibitsa strong and regular modulation affecting both its IP andMP. Its period there can readily be estimated at about 40 P (see also Weltevrede et al P . The feature modulates both the MP -130 40 60 Figure 11. ‘Q’-mode PS from Fig. 7 folded at the primary mod-ulation period. Pulses 221-750 of the MJD 53780 observation arefolded at 43.75 P corresponding to the bright modulation featurein Fig. 10. Here the unvarying ‘base’ has been removed from thepower in the central panel and the colour-scale compressed bothat small and large intensities. The modulation affects both the IPand MP (see the ‘base’ profile in the bottom panel), producingprimarily an amplitude (stationary) modulation in the IP and aphase modulation in the MP: note the way in which the fluctu-ation power appears at only one phase in the IP; whereas in theMP, fluctuation power appears in both the leading and trailingregions of the profiles at different phases. and IP strongly and corresponds to a P of some 43 P . Anharmonic-resolved fluctuation spectrum (not shown) showsthat the feature represents a mixture of amplitude and phasemodulation. Taking care to measure the primary period ac-curately by appropriately weighting two adjacent frequencycomponents, we find a period of 43.75 ± P .The effects of this modulation periodicity can be furtherexplored by folding the ‘Q’-mode PS at the 43.75- P mod-ulation period, and this display is shown in Figure 11. Herethe unfluctuating ‘base’ power has been removed and thecolour scale somewhat compressed to show the fluctuationsmore clearly. The IP is fully modulated at this periodicity, sowe see its power in only a particular region of the full cycle.The MP, however, shows a “wobble” of fluctuation powerextending from the leading to trailing regions of its overallprofile. Power in the leading profile region occurs nearly si-multaneously with power in the IP, whereas the trailing MPregion is bright at times when the IP power is at a minimum.Similarly, the longitude-longitude correlation map at adelay of 2 P in Figure 12 shows significant correlation be-tween the delayed IP and the leading regions of the MP;however, the map for the reverse (–2 P delay) above thediagonal shows much less correlation. This asymmetry ischaracteristic of a phase modulation that has a “direction”.Similar maps are obtained for other delays of a few periods.Note also that only a trailing region of the IP is modulated,but a long weak region of emission precedes it.Finally, B1822–09’s MP appears to exhibit secularchanges over the several hundred pulses following ‘Q’-mode c (cid:13) , 1– ?? Isaac Backus, Dipanjan Mitra, & Joanna Rankin -130 40 60 - Figure 12.
Cross-correlations of the PS with itself at a delayof 2 P , calculated over pulses 221-750 of the ‘Q’ mode-only MJD53780 observation. Here we see a strong correlation of the IP withitself as well as a significant correlation of the delayed IP with theleading region of the MP profile, but not the reverse. Note alsothat it is a trailing region of the IP that is modulated, but a longleading region precedes it. The 3-sigma error in the correlationsis about 13%. See Fig. 9 for details. Figure 13.
Profile-shape changes in the MP of B1822–09 after‘Q’ mode onset, from the MJD 53780 observation. Each profile isan average of 60 pulses. Directly after the ‘B’-to-‘Q’-mode tran-sition at about pulse 200, the profile has a prominent trailingcomponent. At later times after ‘Q’-mode onset, the leading pro-file region maintains a relatively stable intensity, while the trailingone gradually weakens. A / A Pulse Number (after ’Q’ mode onset)
Figure 14.
Changes in the trailing- ( A
2) to peak- ( A
1) ampli-tude ratio in the B1822–09 MP profile following ‘Q’-mode onset.The amplitudes are measured from 30-pulse averages of the MJD53780 observation. A A ∼ ◦ later, at the peak of the trailing compo-nent. onset. Figure 13 shows a set of 60-pulse averages followingthe first such onset in Fig. 7. Here we see that the power inthe leading profile region remains fairly constant along withthe intensity of the central component; whereas the powerin the trailing profile region first exhibits a distinct compo-nent and thereafter declines progressively over the next 500pulses. That the three long ‘Q’-mode episodes in the MJD53780 PS show a similar behavior is shown in Figure 14where decreases of about 20% relative intensity are seen over200 pulses in all three cases. Clearly, such a behaviour is veryreminiscent of the changes seen in B0943+10 following its‘B’-mode onsets, but on a very much shorter time scale.
3. The emission geometry of B1822–09’s PC & MP
As we have seen above, B1822–09 presents a “main pulse”profile that has been very difficult to interpret. First, it hasnot been clear whether the PC component was or was not apart of this “main pulse” region. Indeed, it has been tempt-ing to regard it as so, because the PC and MP are connectedby a weak bridge of emission that would ostensibly seem toassociate them. Second, in mixed average profiles of boththe ‘B’ and ‘Q’ modes, the MP structure itself is not at allclear; some profiles show hardly more than a single compo-nent with a trailing “bump”, and at best one can discerntwo barely resolved components.We now see clearly, however, that the PC is a completelydifferent sort of “animal” than the MP: it is comprised of avery unusual and distinct kind of emission elements, is highlylinearly polarized, and it is modulated very differently fromthe MP. It is truly and unmistakably a PC and not a partof the “main pulse”. In short, it is almost certainly not of acore/conal origin.Returning now to the MP, which indeed is the totality ofthe “main pulse”, our various single pulse analyses have re-vealed that it is comprised of three very distinct regions, theleading, central and trailing regions. The central region hasa half-power width of some 3 ◦ and shows a very steady emis-sion from pulse to pulse. The leading and trailing regions, bycontrast, are illuminated episodically and only occasionally c (cid:13) , 1– ?? at the same time—and in the ‘Q’ mode their illuminationis periodic with the same 43- P cycle as the IP. The illumi-nation of these leading and trailing regions is responsible inlarge part for the greater intensity of the ‘B’ mode as is veryclear from Fig. 7.For all these reasons, then, there can be very little doubtbut that the MP of B1822–09 should be classified as havinga basically triple profile. In some partial profiles, we see asuggestion of two conal rings in the leading or trailing re-gions, which would suggest a five-component M profile, butsuch behaviour is not seen consistently enough to be certain.Moreover, the softer spectrum of the central component, itsregularity, lack of periodic modulation (and correlation withother profile features), and the hint of antisymmetric V allsuggest that this is a core component.We can then apply the quantitative geometrical meth-ods of ET VI (Rankin 1993) to B1822–09’s MP: Its PPAtraverse is quite shallow, showing little orderly rotation—like that of B1237+25 ( e.g. , Srostlik & Rankin 2005)—so wecan take its central slope to be essentially exceedingly steep,indicating that the sightline passes almost exactly over thepulsar’s magnetic pole. The about 3 ◦ half-power width ofthis putative core further suggests a nearly orthogonal re-lationship between the star’s rotation and magnetic axes asthe angular width of the star’s polar cap can be computedas 2.8 ◦ . Thus the magnetic latitude α and sightline circle ζ are both close to 90 ◦ .With these constraints in mind, we can estimate whatwould be the total half-power angular sizes of the inner andouter conal regions and then compare them with the fullwidth of the B1822–09 profile. These respective conal widthsare about 9.5-10 (=4.33 ◦ P − / ) and 13 ◦ (=5.75 ◦ P − / ). Re-ferring conveniently to Fig. 14, we can see immediately thatthe full outside width of the leading and trailing regionscannot be squared with 13 ◦ , but a width of 9.5-10 ◦ corre-sponding to an inner cone is fully plausible. Therefore, wecan conclude that B1822–09’s MP is fully compatible withthe inner-cone/core T classification.
4. The emission geometry of B1822–09’s IP
Our analyses also shed new light on the IP and its relation-ship to the MP and PC. First, the IP is not a single symmet-rical component, but rather a broad region of emission witha bright trailing component. Figure 15 gives a sensitive 325-MHz profile in which its somewhat double form and nearly20 ◦ width are obvious. In the older publications of Fowler et al and Wright & Fowler, one gets little sense of its ex-tended form, and even in the Gil et al work, the IP appearsas a single asymmetric feature. Clearly, the early observa-tions lacked our sensitivity, and perhaps the IP changes itsform at meter wavelengths, but in either case its broad andasymmetric character must be taken fully into account.The spacing of the IP from the MP is clearly shown inseveral of the previous figures, but the bottom panel of Fig. 7depicts their spacings with respect to the PC as well. In thisand the other diagrams, exactly 140 ◦ of longitude has beenremoved at longitude +23 ◦ , so the relationships between thethree emission features can be measured conveniently. Mostobviously, we see that the interval between the IP and MPpeaks is about 173 ◦ —that is, 33 ◦ as shown on the scale plusthe removed 140 ◦ . This is the measurement that most earlier Figure 15.
A close-up average profile of the IP, averaged over all2106 pulses of the MJD 54864 observation. Dyks etal measure theMP-to-IP separation as ∼ ◦ , but if instead of measuring fromthe peak or the center of the half-power point, we measure fromsome 6 ◦ earlier—at the center of the IP—this separation reducesto almost precisely 180 ◦ . workers have made, but Fig. 15 above shows very clearlythat the IP extends far on the leading side of the peak—soas to suggest a double profile form. If the IP-MP spacingis instead measured from the IP “centroid”—some 6 or 7 ◦ earlier—then the resulting interval is very nearly 180 ◦ !But beyond these basically average-emission propertiesto consider in trying to understand the relationship betweenthe IP and MP, we have seen above that there are also im-portant dynamical connections. First, both the IP and MPshare the 43- P modulation, and such modulation is usuallyconal in character. Second, the IP peak (including its en-tire trailing “component”) shows strong positive correlationwith the leading emission of the MP as well as negative cor-relation with its trailing region (as in the cross-correlationmaps of Figs. 9 and 12 and the folded sequence in Fig. 11).Given that these MP regions are conal in nature, it is tempt-ing to conclude that the IP is comprised of a pair of conalcomponents. In short, the putative conal regions of the IPhave an angular width comparable to that of the MP, andthese respective regions behave similarly dynamically—sothat their dynamic midpoints are again nearly 180 ◦ apart.By contrast, the PC is an entirely different animal: itis not opposite to the IP. It shows a different type of emis-sion. It exhibits no periodic fluctuations. And it shows nostructures that can be regarded as either conal or core-like. VI. IMPLICATIONS FOR CURRENT MODELS
As has been demonstrated throughout this series of papers,the regular modulation features of B0943+10 are adequatelyunderstood in terms of the subbeam carousel model. How-ever, this is not the only extant model for B0943+10’s re-markable subpulse-drift phenomena. There are two papers,Clemens & Rosen (2004) and Rosen & Clemens (2008), thatexplored a non-radial oscillation model and then assessedwhether it can produce the specific observations of PaperI. They reanalyzed the 430-MHz PS of Paper I, confirmedthese earlier results, and reiterated that the sideband featureoccurs only within a small section of the full 18-min obser-vation. They then suggest that the sidebands might be pro-duced by a “stochastic variation in pulse amplitudes,” butclarify that if periodic amplitude modulation occurs withinthe drifting-subpulse sequences, then this would favor the c (cid:13) , 1–, 1–
As has been demonstrated throughout this series of papers,the regular modulation features of B0943+10 are adequatelyunderstood in terms of the subbeam carousel model. How-ever, this is not the only extant model for B0943+10’s re-markable subpulse-drift phenomena. There are two papers,Clemens & Rosen (2004) and Rosen & Clemens (2008), thatexplored a non-radial oscillation model and then assessedwhether it can produce the specific observations of PaperI. They reanalyzed the 430-MHz PS of Paper I, confirmedthese earlier results, and reiterated that the sideband featureoccurs only within a small section of the full 18-min obser-vation. They then suggest that the sidebands might be pro-duced by a “stochastic variation in pulse amplitudes,” butclarify that if periodic amplitude modulation occurs withinthe drifting-subpulse sequences, then this would favor the c (cid:13) , 1–, 1– ?? Isaac Backus, Dipanjan Mitra, & Joanna Rankin carousel as opposed to the non-radial oscillation model. Wehere present two further instances of the tertiary amplitudemodulation, and instances in which the low frequency pe-riodicity is primary are presented in Paper II and PaperIV. That these various instances are compatible with eachother, exhibit orderly and very long secular variations andshow complete frequency independence, would seem to favorthe carousel model for drifting subpulses very strongly.We now turn our attention to the emission-reversalmodel proposed by Dyks et al (2005) to explain the anti-correlation between the intensity of the PC and the IP inB1822–09. They proposed that the PC and the IP are emit-ted from the same source which reverses emission directionduring the different modes. In their model, B1822–09 hasa nearly orthogonal geometry (in agreement with our find-ings). The physical source of the IP and the PC is locatedon the same pole as the MP, and the apparent IP resultsfrom inwardly directed emission from the source of the PC(Dyks et al et al ◦ , not 186 ◦ as found in Dyks et al (2005).This suggests that the MP and IP are both outwardly emit-ted and are produced by similar processes above the two re-spective magnetic poles. The PC is markedly different andnot compatible with core-cone emission, suggesting a phys-ically different origin from the other two components.Another possibility for the emission-reversal model isthat the source of the IP and PC is located on the oppositepole from the MP and that the IP is outwardly emitted,whereas the PC is inwardly emitted. Propagation throughthe closed magnetosphere might explain the unique char-acteristics of the PC emission, and the MP-IP similaritiesare easily explained in this model, but the question of in-formation transfer between the poles arises again: the MPbehavior is regulated by the same modes as the PC and IP.Thus, we conclude that the characteristics of B1822–09are not easily interpreted with the emission reversal modelas outlined above. VII. SUMMARY & CONCLUSIONS
The sideband features in pulsar B0943+10 were first seenin a 430-MHz PS discussed in Paper I. Our analyses abovehave revealed a further two instances of B-mode sidebands inobservations spanning more than 18 hours. Clearly, such ter-tiary modulation features, although remarkably rare, exhibithighly consistent characteristics. We can then conclude withcertainty that these sideband features indicate a physicallysignificant periodicity, which within the subbeam-carouselmodel corresponds to the circulation time ˆ P .One instance above occurs soon after B-mode onset,while the other two follow it by about 90 mins. In addi- tion, evidence of a tertiary modulation in the form of a lowfrequency feature has been seen to occur several times in B-mode PSs at low frequencies (Papers II & III)—and a singleinstance of a corresponding Q-mode feature was identified at327 MHz (Paper IV). All of these apparitions are consistentwith a rotating-carousel subbeam system that has two dis-crete states: either the ‘beamlet’ configuration is sufficientlydisordered so that no primary (“drift”) modulation is ob-served, or it is comprised of just 20 evenly spaced beamlets.We also report the discovery of a bright precursor com-ponent in the Q-mode of B0943+10, falling some 50 ◦ lon-gitude prior to the star’s MP, which dims to nearly un-detectable levels in the B-mode. This PC is almost fullylinearly polarized with a nearly constant PPA traverse. Itsconstituent radiation is “spiky” in character, as opposed tobeing comprised of broad subpulses—in this respect simi-lar to that seen in pulsar B0656+14 ( e.g. , Weltevrede et al e.g. , Mitra et al E pulsars have relatively simpleprofiles that arise from a single cone of emission high in themagnetosphere. In turn, the depolarization effects are lesseffective at larger heights due to field line flaring, and thusthe profiles retain their polarization over a wide range of fre-quencies. This behavior seems compatible with B1822–09’sPC polarization properties: it remains highly polarized frombelow 243 MHz (Gould & Lyne 1998) to 3.1 GHz (Johnston et al c (cid:13) , 1– ?? see the effect of aberration/retardation at the PC location isdifficult. We note also that Petrova (2008a,b) has attemptedto understand B1822–09’s IP, PC and MP emission in termsof scattering effects within the pulsar magnetosphere.The discovery of a PC in B0943+10 which is so sim-ilar to the well-known PC of B1822–09 shows that such acomponent is not unique, and explaining its origins couldhave important ramifactions for our understanding of pul-sar physics. We should expect that there is one underlyingphysical process which regulates the modes and therefore theappearance of such diverse phenomena as subpulse drifting,polarization characterstics, pulse-shape dynamics, and thepresence of a PC. While the similarities between two starsare certainly telling, their dissimilarities are also importantfor any model purporting to explain the PC in either pulsar.We cannot expect that the alignment of the axes, the sight-line traverse, or the mode-dependent changes in brightnessof the pulsar, play a role in the production of the PC andits modal behavior. Acknowledgments:
We are pleased to acknowledge JarekDyks, Janusz Gil, Svetlana Suleymanova and GeoffreyWright for their critical readings of the manuscript. Oneof us (JMR) thanks the Anton Pannekoek Astronomical In-stitute for their generous hospitality and the NWO and AS-TON for their Visitor Grants. Portions of this work werecarried out with support from US National Science Founda-tion Grants AST 99-87654 and 08-07691. Arecibo Observa-tory is operated by Cornell University under contract to theUS NSF. This work used the NASA ADS system.
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