Fluctuation Properties and Polar Emission Mapping of Pulsar B0834+06 at Decameter Wavelengths

0.32 MB·English

by  Ashish Asgekar

Mon.Not.R.Astron.Soc.000,000–000 (0000) Printed2February2008 (MNLATEXstylefilev1.4)
Fluctuation Properties and Polar Emission Mapping of
Pulsar B0834+06 at Decameter Wavelengths
Ashish Asgekar1,2,3 & Avinash A. Deshpande1,4
1Raman Research Institute, Bangalore 560 080 India
2Joint Astronomy Programme, Indian Institute of Science, Bangalore 560 012 India
3Department of Physics & Astronomy, Universityof Manitoba, Winnipeg, Manitoba R3T 2N2 Canada
4NAIC/Arecibo Observatory,HC3 Box 53995, Arecibo, Puerto Rico 00612 USA
5
[email protected], [email protected]
0
0
2

n
a
J ABSTRACT
Recent results regardingsubpulse-drift in pulsar B0943+10have led to the identifica-
8
2 tion of a stable systemof sub-beams circulating aroundthe magnetic axis of the star.
Here, we present single-pulse analysis of pulsar B0834+06at 35 MHz, using observa-

2 tions from the Gauribidanur Radio Telescope. Certain signatures in the fluctuation
v spectra and correlations allow estimation of the circulation time and drift direction
4 of the underlying emission pattern responsible for the observed modulation. We use
1 the ‘cartographic transform’ mapping technique to study the properties of the polar
3
emission pattern. These properties are compared with those for the other knowncase
2
of B0943+10, and the implications are discussed.
1
4 Key words: pulsars: general — pulsars: individual: B0834+06 — radiation mecha-
0 nism: non-thermal
/
h
p
-
o
r 1 INTRODUCTION results from ExB drift. Whether we observe an amplitude
t or phase modulation will, in this picture, depends largely
s
a Therealization thatindividualpulsesfrom pulsars dis- on the viewing geometry for a given pulsar. Although the
: play considerable and often systematic fluctuations (Drake subpulse modulation in B0943+10 shows remarkable and
v
&Craft1968;Suttonetal.1970;Backer1973)followedsoon rare stability, one expects an underlying system of discrete
i
X after the discovery of pulsars. Though amplitude modula- sub-beams and their apparent circulation to exist in other
r tionsofpulsecomponentswerereportedinpulsarswithsin- pulsars too. However, the related details and their possi-
a
gle or multiple components in their average profiles, more bledependenceonpulsarparametersareyettobeexplored
systematic phase modulations or “drifting subpulses”, oc- andunderstood.Furtherprogresswould,therefore,needthe
curring in conal single (Rankin 1986) pulsars, received a identification and detailed studiesof theemission/subbeam
closer attention from observers and theorists. patternstobeextendedtoasizablesampleofpulsars.Some
of the recent investigations on B0834+06 (preliminary re-
Deshpande & Rankin (1999; hereafter DR99), Desh-
sultsreportedinAsgekar&Deshpande2000;Asgekar2002),
pande&Rankin(2001;hereafterPaper-I),Asgekar&Desh-
B0809+74(vanLeeuwenet al.2003),andB0826-34 (Gupta
pande(2001; hereafter Paper-II) and Rankin,Suleymanova
et al. 2004) represent attempts in thisdirection.
& Deshpande (2003; hereafter Paper-III) have reported de-
tailed studiesof driftingsubpulsesofB0943+10 at frequen- Here, we report single-pulse analysis of the pulsar
ciesintherange35–430MHz.Thestudiesledtotheidentifi- B0834+06at34.5MHzbasedonaseriesofobservationsus-
cationofasystemofsub-beamscirculatingaroundthemag- ingtheGauribidanurtelescope. This pulsar displaysa dou-
neticaxisofB0943+10thatwasresponsiblefortheobserved ble profile at frequencies ranging all the way from 35 MHz
steadydriftpattern(seeDR99).The35-MHz&103/40MHz to1 GHz.It displays strong, alternate-pulse intensitymod-
results (paper-II & paper-III) show remarkable similarity ulation without any significant drift at meter wavelengths
with the higher frequency observations. Paper-I introduced (see, e.g. Taylor, Jura & Huguenin 1969; Slee & Mulhall
a ‘cartographic transform’ (and its inverse) which relates 1970; Sutton et al. 1970, Backer 1973). It also exhibits fre-
theobservedpulsesequencetoarotating frame around the quent, short nulls (Ritchings 1976). Thus, B0834+06 offers
magnetic axis in order to map the underlying pattern of usauseful contexttoexaminewhetherthedifferentappar-
emission. The implied configuration and the sub-beam cir- ent (single-pulse) modulations, particularly the amplitude
culation relate well with that envisioned by Ruderman & and phase modulations, share thesame underlyingcause.
Sutherland (1975; hereafter R&S), wherein the circulation Our observations and analysis procedures are outlined
(cid:13)c 0000RAS
2 Asgekar & Deshpande
Figure 1. Longitude-resolved fluctuation spectra of sequences A&B. The strong primary fluctuation feature at 0.46c/P1 appears
barely resolved for the B sequence (right panel). The corresponding A-sequence feature (left panel) is, on the other hand, relatively
broad,indicatingaquasi-periodicmodulation.
inthenextsection.Thesubsequentsectionsdescribethere- tobelessstable,ismoretypical.Thisfeaturerepresentsthe
sults of fluctuation-spectral analysis and our basis for esti- alternate-pulseintensitymodulation observedinthispulsar
matingthetruefrequenciesofthemodulationfeaturesinthe at meterwavelengths. Thefrequent,short nulls(typically 1
spectra as well as theperiod and direction of thesubbeam- or2nullpulsesover∼10−20pulses)mayaffecttheQ-value
systemcirculation. Intheend,wepresentthederivedpolar ofthemodulation,aswasnotedbyLyne&Ashworth(1983)
emission maps and discuss our results along with their im- for pulsar B0809+74. However, due to inadequate sensitiv-
plications. ity, we can not even assess, let alone quantify, the possible
presenceand effect of “nulls” in ourdata. The centroid fre-
2 OBSERVATIONS AND ANALYSIS quencyoffeature-1isslightlydifferentforthetwodatasets,
butsuchsmallvariations(∼1%)appearsimilartothoseob-
Observations of B0834+06 were a part of a recent pro-
served in B0943+10 (Paper-I, Paper-II & Paper-III).
grammeofpulsarobservations(Asgekar&Deshpande1999)
To examine the issue of possible aliasing of the spec-
initiated at the Gauribidanur Radio Observatory (Desh-
tralfeatureshere,wecomputeharmonic-resolvedfluctuation
pande, Shevgaonkar & Sastry 1989) with a new data ac-
spectra (hereafter, “HRF-spectra”, see paper-I: Figure 4)
quisition system for direct voltage-sampling (Deshpande et
for the two pulse sequences A and B. An HRF-spectrum
al. 2004). The pulsar was observed for a typical duration
of a pulse sequence is computed by Fourier transforming
of >1000 s in each session. Several such observations were
∼ the continuous time series, which is reconstructed from the
made during early 1999 and 2002. We discuss three data
(“gated”) pulse sequence by using the available samples
setsonB0834+06 below,denotedas‘A’,‘B’and‘C’,which
on the pulse and filling the unsampled region with zeros.
were observed on February 5 & 6, 1999 and Feb. 5, 2002
Such spectra can be computed for suitable blocks of 128 or
respectively. Most of the analysis on sequence B consisted
256 pulses and then the power spectra are averaged. We
of 256 pulses, whereas that of sequence A & C consisted of
present, in Figure 2, the HRF-spectrum of the B sequence.
128 pulses, unless mentioned otherwise.
The spectrum displays a pair of strong peaksat about 0.47
Inpaper-IIwedetailedourdataacquisitionsystemand
and 0.53c/P1. A similar spectrum for the A sequence (not
reduction procedure used, and our techniques of spectral
shown) contains just thesetwo features, but of about equal
analysis are virtually identical to those used in Paper-I.
intensities. Such pairs of features in HRF-spectra repre-
Readers may refer to these papers for fuller descriptions of
sent the most general form of amplitude modulation (see,
theabove aspects.
e.g.paper-IandAsgekar2002);howeveranadditionalweak
3 FLUCTUATION SPECTRA
phase modulation cannot be ruled out. There is no clue as
Longitude-resolved fluctuation (LRF) spectra (see Backer yet about the order of the aliasing of the primary modula-
1973) for the sequences A & B on B0834+06 are shown in tion,although,as wewill discusslater, theapparent modu-
Figure1.Bothspectrashowastrongfeatureat∼0.47c/P1 lation frequency is more likely to be 0.53 than 0.47c/P1.
(hereafterreferred asfeature-1),whereP1 denotestherota- In addition to theprimary fluctuation features, in Fig-
tion period of the pulsar. The feature appears barely re- ure 2 we also find another pair of features at 0.463 ±
solved in the B-sequence spectrum, indicating a Q-value 0.069c/P1 flanking the feature-1. Here, the side-tone prod-
of ∼ 100, found to be the highest among Qs seen in our uct close to 0.4c/P1 is clearly seen (a frequency of 0.390±
pulsesequences.SequenceA,wheretheperiodicity appears 0.001c/P1), whereas the other (upper side-tone product)
(cid:13)c 0000RAS,MNRAS000,000–000
Fluctuation Properties and Polar Emission Mapping of B0834+06 3
4 ALIASING, THE CIRCULATION TIME,
AND DRIFT DIRECTION
We now fold the pulse A & B sequences separately at
their apparent primary fluctuation periods (P3 tentatively
identified as 1.856P1 & 1.859P1, respectively). The folded
time series are displayed in Figure 4a,b.
The phase of the modulation (not shown) varies very
slowlywithpulselongitudeandisnotwelldefinedatthecen-
treoftheprofile.Theintrinsicphasepatternisalsolikelyto
be smeared by a 5-bin smoothing we performed to improve
the visibility of the otherwise weak pulses. The apparent
◦ ◦
average rate of this phase variation is small (≤ 4 /), con-
sistent with the primary feature being associated with an
amplitudemodulation.
The folded sequences also show that the modulation
patterns under the two components of the average profile
are possibly shifted in phase with respect to each other
(Figures4a,b),butonlyslightly.Theexactdelayisdifficult
to measure due to the very patchy nature of the intensity
patterns. However, in our estimation the magnitude of the
apparent relative delay between the modulations is within
Figure2.HRF-spectrumforsequence Bdata.Apairoffeatures
placedsymmetricallyaround0.5c/P1 areseen.Alsoseenaretwo about0.1ofthemodulationcycle,or 0.2P1,corresponding
to the longitude separation of the peaks of the two well-
sidebandsontheprimaryfluctuation feature,whichindicatethe
presence of aslowermodulation inthe data modulating the pri- definedcomponents in Figure 4b.
maryfluctuation (refertotextfordetails). Therelativedelayinthemodulationunderthetwocom-
ponentscan beexpressed, in general, as
δζ =(X+m),with m=...−2,−1,0,1,2...; (1)
where, X is the apparent phase (or delay) difference be-
tweenthemodulationsunderthetwocomponentsexpressed
as a fraction of the modulation period, and the integer m
accounts for the possible undetected integral cycles of the
falls very close to the ‘alias’ component (at 0.53c/P1) of modulation phase as well as asserts the sense/direction of
the primary fluctuation feature. These features suggest the thedrift(whencombinedwithX).Forthefoldedversionof
presence of a slower, and most likely an amplitude, mod- sequence A shown, X=0.1, and X=-0.1 if the data were to
ulation on the primary fluctuation. The mean period of be folded at P3=2.169P1. For the B sequence, we estimate
this slower modulation is estimated to be 14.5± 1.0P1, X= -0.05 for the presently assumed P3, and X = 0.05 for
where the larger uncertainty reflects uncertainties in the thecorresponding longer P3 (Figure 4).
estimation of frequency of the upper side-tone product lo- Weinterprettherelativedelaybetweenmodulationun-
cated near 0.53c/P1. So, we observe a primary fluctuation der the two components as caused by the ‘passage’ of the
whichismodulatedbyaslowervariation/fluctuation.Over- same emission entity through our sightline as the polar-
all,thisbehaviorisqualitativelysimilartopulsarB0943+10. emission pattern rotates steadily around themagnetic axis.
With this, we also note that there is an excess of power at We can write the geometrical relationship between the ro-
0.073±0.007c/P1 (aperiodof∼13.7±1.4P1)intheLRF- tational longitude δϕand magnetic azimuth angle δθ as,
spectrum computed from sequenceB (see Figure 1b).
δθ = sin−1[sin(α+β)sin(δϕ)/|sin(r )|], (2)
In most parts of sequence C, we find the same fluctu- ϕ
ation spectral feature as seen in sequence A. However, in wherer ,theassociatedmagneticlatitudeatthecomponent
ϕ
a small section of the C sequence, we notice an extreme longitudes,canbecomputedusingthefollowingwellknown
situation where the alternate-pulse modulation feature (i.e. relation
featureI)becomesveryweakandthedominantmodulation
appears to be the slower one. This is clearly evident from sin2(rϕ/2)= sin2(δϕ/2)sin(α+β)sin(α)+sin2(β/2) (3)
thepulsesequence(Figure3a),wherestrongemission isen-
Arotationallongitudeseparationofthecomponentpeaksof
countered about every 15 rotation periods. The fluctuation ◦ ◦
∆ϕ = 6.2 (i.e. ∆ϕ = ±3.1) implies a magnetic longitude
spectrumofthissection ofthedata(Figure3b)alsoreveals ◦ ◦
separation ∆θ ≃ 50 (i.e. δθ ≃ ±25) around the magnetic
a strong feature at 0.06c/P1 that directly relates to the axis of the star⋆. We can now directly estimate the circu-
slow and deep modulation at aperiod of 15.0± 0.8P1. Not lation time of the pattern using eq. (2). Assuming that the
surprisingly,thisperiodisconsistentwiththatsuggestedby
theside-tones seen in theB sequence.
⋆ Here, we have used α = 30◦and β = −3◦in the above esti-
The three data sets presented here display almost a
mation. The value of α as well as the sign of β are uncertain.
completevarietyintherelativedominanceofthetwomodu-
However,themagnitudesofαandβ areconsistentwiththePA-
lationfeatures,andprovidearemarkablyconsistentpicture
sweep rate reported by Stinebringet al.(1984). An independent
of their origin.
detailed assessment based on profile evolution across a wide fre-
(cid:13)c 0000RAS,MNRAS000,000–000
4 Asgekar & Deshpande
Figure3.(Left)A64-pulseslongsectionoftheCsequenceshowningray-scale;and(Right)longitude-resolvedspectrumofthissection
ofthesequence. Notethestrongfeatureat0.07c/P1 andthenearabsenceofmodulationfeatureat0.46c/P1.
Figure4.(Left)SequenceAfoldedatamodulationperiodofP3 =1.856P1.Therelativedelayinthemodulationpeaksunderthetwo
components isevident. Asimilarpattern wouldbeseeneven ifthe other possibleP3 (i.e. ,2.169P1)wereto beusedforfolding;then,
any“drift”(orrelativedelay)wouldappearintheopposite sense.(Right)Sequence BfoldedataP3 of1.859P1.
◦
polar cap periphery is roughly circular (see, for example, Pˆ3 = 360 (X +m)P3 (m=...,−1,0,1,2,...), (5)
paper-I; Mitra & Deshpande 1999), the circulation time is (cid:18) ∆θ (cid:19)
given by
360◦ where ∆θ is themagnetic-longitude separation (in degrees)
Pˆ3 =(cid:18) ∆θ (cid:19)δζP3 (4) of thetwo component peaks.
If the observed amplitude modulation is generated by
or, with eq. (1), thesteadyrotation ofastablepatternaroundthemagnetic
axis, it should produce fluctuations having a period equal
quency range and PA sweep rate (14.5 ◦/◦) gives a somewhat tothecirculationtime.Theestimatesforthetwosequences
differentviewinggeometry, withα=45◦andβ =-2.8◦(Rankin, and different values of m are to be compared with our es-
privatecommunication).Thepresentlyadoptedgeometryimplies timates of the circulation time as suggested by the slower
ashallower PA sweep ( 10◦/◦) that was arrivedat based onthe modulation period (i.e., 14.8P1 or so). It can be shown
‘closure’techniqueresultsdiscussedinthenextsection. that the compatible values of m are +1 and -1. Given the
(cid:13)c 0000RAS,MNRAS000,000–000
Fluctuation Properties and Polar Emission Mapping of B0834+06 5
ric (about the +45◦–slope line) for a delay of two rotation-
periods, that is, the delayed versions of later-longitude se-
quences do not correlate with those at earlier longitudes.
Thisweinterpretassubpulse“motion”fromearliertolater
rotational longitudes, i.e. , positive drift.
Thus, we have identified an internally consistent con-
figuration oftheunderlyingcirculating subbeam systemre-
sponsiblefortheobservedmodulation.Basedonvariousdif-
ferent signatures, we have indeed been able to estimate the
circulationtime,andfindthat14.8±0.8P1isavalueconsis-
tent with our observed sequences. It is worth pointing out
that the actual circulation time is likely to be somewhat
shorter than the above value (by typically 1 P1), given the
typical frequency of nulls. The drift direction is also deter-
mined above, and thesense of thePA sweep is known from
theexisting polarization data.
Thealiasambiguityoftheprimarymodulationfeature,
however,hasyettoberesolved;butthisisreallyonlyofaca-
demic interest, since our further investigations based upon
emission mapping, etc, do not depend on its resolution. As
Figure 5. Longitude-longitude correlation of intensity fluctua- wewillmentionlater,itispossibletosimplylookattheav-
tions at a relative delay of 2 pulse periods, computed for B se-
erage sequence over several circulation times and estimate
quence data (of some 350 pulses). The intensity fluctuations at
theapparent spacing between successive sub-beams.
each longitude bin, shown along the horizontal axis, are cross-
Noneofourderivedestimatessofardependcruciallyon
correlatedseparatelywiththefluctuations seentwopulseperiod
anaccurateknowledgeoftheviewinggeometry,althoughit
laterateverylongitudebinindicatedalongtheverticalaxis.The
central panel gives this correlation map according to the color wasusefulindeterminingthevalueofm,andthegeometry
scaleattheright.Thebottomandtheleftpanelsshowtheaver- will be an explicit ingredient in the cartographic transform
ageprofilesfortheoriginalBsequenceandforthedelayedversion tobeusedforemissionmapping.Wenotethattheavailable
ofit,respectively.Thecolour-scaleusedtodisplaythecorrelation polarization measurements on this pulsar do not effectively
coefficientsinthemapisshownontheright.Theobservedcorre- constrain theviewing geometry, especially thesign of β.
lationmapisasymmetricw.r.t.tothediagonal.Thesenseofthe
asymmetry indicates a subpulse “motion” from earlier to later
longitudes.
5 VIEWING GEOMETRY OF B0834+06
uncertainties in the various relevant parameters, it is not B0834+06, based on its double profile, is a member of
possible as yet to conclusively estimate thesign of m. the “D”-class according to the Rankin classification. The
To help resolve this issue, we have chosen intensity se- emission of this pulsar is believed to arise from the inner
quences corresponding to two longitudes intervals symmet- conalring,andthegeometricalparameterswerederivedac-
ricallyplacedaroundthecentral(zero)longitudeandwitha cordingly (Rankin1993).
separation of 6◦in order to examine their cross-correlation. The ‘inverse’ of the cartographic transform provides a
In every one of the three sequences (i.e., A, B, & C), we powerful “closure” path to verify and refine the input pa-
find that the cross-correlation has a peak when the earlier rameters used to produce the polar map (see paper-I and
longitude data is delayed by two pulse periods w.r.t. that Deshpande2000,foradetaileddiscussionofthispoint).We
at the later longitude, in clear contrast with the other way wished to reconfirm thedrift direction and “tune” our esti-
around.This clearly implies that m=+1,and thatthedrift mateofthecirculationtime.Wealsowantedtofurthercon-
directionisfromearlierlongitudetolater—i.e.,oppositeto strain the assumed viewing geometry using this approach,
thepulsar rotation direction. if possible. To achieve this we carried out a grid search,
Afurtherrelatedconfirmationofthedriftdirection(rel- wherewevariedthevaluesofα,β andPˆ3 overareasonably
ativetothepulsarrotation)comesfromlongitude-longitude wide range and alternated the drift direction as a param-
correlation maps of pulse sequences over delays of integer eter. For each different combination of the parameters in
numberof pulseperiods (such an analysis was first used by the search, we constructed an average-polar map from the
Popov & Sieber 1990). The correlation map computed for observed sequence. The inverse transform was used to gen-
sequence A is displayed in Figure 5, where the estimated erate an artificial sequence from this trial polar emission
(normalized) correlation between fluctuations in the inten- pattern. We then cross-correlated (longitude by longitude)
sity at a range of longitudes (marked along the horizontal theartificial sequencewith thenatural(observed)one.The
axis) and the fluctuations observed two pulse-period later parameter combination for which the procedure yielded a
(atthevariouslongitudesmarkedalongtheverticalaxis) is higher cross-correlation coefficient, averaged over the longi-
shown. tudes,was considered a betterindicator of the truevalues.
◦
Significant auto-correlation (i.e., along the +45–slope For B0834+06, the closure technique involving the in-
line) is apparent at this delay of +2P1, which is related to versetransformturnsouttoberatherinsensitivetochanges
theprimarymodulation periodicityseeninthispulsar.The inthevaluesofαandβ (αbeinglarger for B0834+06 than
cross-correlation map, however, is not diagonally symmet- for B0943+10) and the sign of β was not constrained (see,
(cid:13)c 0000RAS,MNRAS000,000–000
6 Asgekar & Deshpande
Asgekar2002).Thetechniquewas,however,sensitivetothe to those of B0943+10, and show an increased tendency to
circulation timeandthedriftdirection,whichallowed usto fluctuatearound theirmean positions —which may explain
constrain theseparameters. This, in away,also meant that thelower Q value of thisstar’s primary fluctuation feature.
ourresultingpolaremission mapswereratherinsensitiveto We would like to attract the reader’s attention to the
uncertainties in α and β. In what follows, we use the fol- part of the map where five roughly equi-spaced sub-beams
lowing set of refined parameters: Pˆ3 = 14.84P1; α = 30◦; span almost exactly half of the magnetic longitude range.
◦
β =−3.0, with the drift direction same as that of the pul- It is clear from this configuration that the true P3 is about
sar rotation. The resolution of the drift direction is then 1/8th ofthecirculation time, i.e.less than2P1.This, then,
tied to the ambiguity in the sign of β, and a comparison finally appears to resolve the aliasing issue. The LRF fea-
with Ferraro’s theorem (Ruderman 1976) is possible after ture at 0.47 c/P1 is indeed an alias of the true modulation
an unambiguousdetermination of β. frequency of ∼ 0.53 c/P1, making the unaliased P3=1.859
6 POLAR MAPS AND MOVIES P1. This, in turn, implies the typical number of subbeams
tobe8,anumberalsoconsistentwiththeestimatesofmag-
Wecreatedthepolaremission mapsforthethreepulse
netic azimuthal separation of the subbeams (as in section
sequencesdiscussedearlierusingthecartographictransform
4). Nonetheless, the subbeams spacing is not as uniform as
mapping technique of Deshpande & Rankin (DR99, paper-
in B0943+10.
I). Also, series of maps, each from successive short subse-
6.3 Sequence-C (5thFebruary 2002)
quences(ofduration≥ Pˆ3)andwithalargefractionalover-
lap with the neighboring ones, were generated. The result- The short 64-pulse sequence mapped here exhibits a
ing images were viewed in aslow ‘movie’-like fashion. Since deep periodic modulation that reflects the circulation cycle
apolarmapoveronecirculationtimeforB0834+06doesn’t directly.Onlyasingle dominatingemission region isappar-
sample the entire polar cap adequately, each movie frame ent. The streaky and highly elongated shape of the active
wasmadeusing30 pulses(roughlytwicethecirculationtime region is the result of poor sampling and inadequate aver-
Pˆ3).Wefurthersmoothedthispatternover10×10pointsin agingacrossthemaparea.Thisextremesituation israreas
order to reduce the noise contribution, the smaller number well as rewarding, in the sense that it permits us a direct
ofsub-beamsmakingsuchsmoothingpractical. Themovies estimation of thecirculation period.
allowed us to study variation of the polar emission pattern
over the duration of the observation. Here, we present our 7 DISCUSSION
maps and theinsights gained by studyingthemovies.
In the preceding sections we havepresented our analy-
6.1 Sequence-A (5thFebruary 1999)
sis of the fluctuation properties apparent in the decametric
Thepolar map forthissequenceisshown in Figure6a. emissionofpulsarB0834+06,aswellasoureffortstounder-
Only a couple of distinct sub-beams are seen in the av- standtheunderlyingemissionpatternresponsibleforthem.
erage polar map, whereas short averages corresponding to B0834+06 is the only other pulsar (apart from
the frames of the movie show us more distinct sub-beams B0943+10)forwhichwecouldestimatethecirculationtime
that fluctuate around their mean positions and in bright- of the polar emission pattern reliably using its fluctuation
ness. Patterns of strong, distinct sub-beams appear on the properties and viewing geometry. This estimation is based
scalesof∼2Pˆ3,givingrisetoweak(Q-value∼<100)primary solely on our decameter observations. We have made polar
fluctuationfeaturesinthespectra.Onthewholeafewsub- emission mapsfrom our34.5 MHzsequencesusingtheesti-
beams dominate the maps over short intervals, similar to mated Pˆ3 and drift direction, and those were presented in
the case of sequence B below. Such ‘prominences’ last only theearliersection.Incarryingoutouranalysis,wefollowed
about two circulation times, where after those sub-beams ageneral strategy for theestimation of thecirculation time
become weak and some others more prominent. of the polar emission pattern. This approach could be ap-
The bright sub-beams that dominate the emission in plied to other pulsars as well. We initially computed LRF-
a movie frame appear to be broader than the average. As- and HRF-spectrafor thispulsar, and haveshown that
sessing the significance of this impression is difficult given • The primary modulation has a time delay between the
boththesmoothingandthenoisepresent,butattimestwo two components of thestar’s double profile.
adjacent bright sub-beamsappear to touch each other. • We argued that the amplitude fluctuations of the two
The bright, isolated emission patches near the outer components result from the ‘passage’ of the same emission
periphery of the region mapped are due to occasional ex- entities as thepolar emission pattern revolvesprogressively
traordinarilybrightsinglepulsesinoursequence.Wediscuss aroundpulsar’smagneticaxis.This,forthecomponentsep-
these below. aration of50◦inmagneticlongitudeandtheapparentmod-
6.2 Sequence-B (6th February 1999) ulation delay, suggested that the circulation time (Pˆ3) is
∼14.9P1.
This sequence shows the sharpest primary fluctuation • The HRF-spectrum, computed using set-B, exhibits
featurewhichhasaQ-value∼100.Itspolarmap,presented sidebands around the primary modulation (see Fig. 2).
inFigure6b,shows asystem ofdistinct sub-beams.Similar These sidebands imply a slower periodicity modulating the
to the observations of B0943+10, the brightness of individ- primary modulation feature, having a period of ∼ 14.5±
ual sub-beams appear to fluctuate with time. In fact, they 0.8P1.WenoticediscerniblepowerintheLRF-spectrumof
vary by factors of almost 5 between certain short averages. thesamesequence(Fig.1)atafrequencycloseto0.073c/P1
At any given time a few sub-beams dominate the emission (i.e.corresponding toa period of ∼14P1).
andovershadowemissionfromtherestofthepolarcap.The • The rewarding 64-pulse sequence (set-C) allowed a di-
individualsubbeamsherearegenerallylessstablecompared rect estimation of the circulation period, based on the low
(cid:13)c 0000RAS,MNRAS000,000–000
Fluctuation Properties and Polar Emission Mapping of B0834+06 7
Figure 6.(Left)AveragepolaremissionmapforB0834+06sequence-Amadewith250pulses.Thesub-beamsarelessdistinctandnot
equispaced, which contributes to the low Q-value of primary fluctuation. Considerable averaging has been carried out to improve the
map’ssignal-to-noiseratio.Thestringofdotsatthetopshowsthetracksampledbyoursight-line.(Center)Averagepolaremissionmap
forsequence Busing∼350pulses.Thesub-beamsintensitieshereshowasystematicvariationwithazimuth,apropertythatmanifested
itself as the side-tones in the fluctuation spectra of this sequence. (Right) A map made using 64 pulses from sequence C. The streaky
appearance results from inadequate sampling and/or averaging of the mapped region. Note the single prominent emission region and
almostcompletelackofemissionovertherestofthepolarregion.Thecolour-scalesusedtodisplaytheintensitiesinthepolarmapsare
shownontheright-sideofrespectivemaps.Theapparent–ve intensitiesareaconsequence ofnoisedominanceintheoff-pulseregion.
frequency feature in its fluctuation spectrum. This period variation, as noted above, in their relative locations and
estimate (∼15P1) is consistent with the values determined brightness is even more apparent within and across these
from the othertwo sequences. maps. Although it is difficult to quantify these due to lim-
• Webelievethattheseobservationsconclusivelydemon- itedsensitivity,itisclearthatusuallyonlyacoupleofbright
strate thecirculation time to be ∼14.9P1. sub-beamsseemtodominatethepolaremission ofthispul-
• The estimates of the viewing geometry for this pulsar sar.
areuncertain.Wecarried outasearch torefinetheviewing The isolated, bright emission patches close to the pe-
geometry and other parameters of transform using the in- ripheryappearduetoahandfulofstrongpulsesinourdata
verseofthecartographictransform.Thissearchconstrained and these areas receive negligible emission from a majority
the circulation time (now refined to be Pˆ3=14.84P1) and of the pulses. The origin of such intense pulses is unclear,
thedriftdirection ofthepatternrelativetothepulsarrota- however it may correspond to a Q-mode activity similar to
tion, both of which are crucial for our mapping technique. that observed in pulsar B0943+10 (see paper-I).
However, α and β were relatively poorly constrained in the
The significance of our analysis also stems from the
case of this pulsar (B0834+06) and with this approach.
fact that pulsar B0834+06 is different from B0943+10 in
• A system of discrete sub-beams in steady rotation
its physical characteristics, its viewing geometry and hence
around the magnetic axis was found responsible for theob-
in the nature of the apparent modulation it exhibits. The
servedpulse-to-pulsefluctuations.Becauseoftherathercen-
single-pulsefluctuationsheremainlyappearasmodulations
traltraverseoftheobserver’ssightline,thecirculationofthe
of its component amplitudes, unlike the drift patterns (or
sub-beam system manifests as amplitude modulations, not
phase modulation) observed in B0943+10. Nonetheless we
as a subpulse drift.
were able to relate such a general form of modulation to a
well-defined rotating pattern in the polar emission region.
This supports the picture that a set of discrete emitting
The emission sub-beams of B0834+06 are discrete. They
sub-beams circulating within a hollow cone of emission, as
are not uniformly spaced in magnetic azimuth, and are ir-
envisionedinR&S,producesthesingle-pulsefluctuationsin
regular in form. The sub-beams appear to be wide in the
pulsars. The specific characteristics of the apparent fluctu-
radialdirection,with ∆ρ/ρ>25%.Wehadconcludedfrom
∼ ations, e.g. whetherit is an amplitude and/or phase modu-
ouranalysisofB0943+10 thattheregionsofradioemission
lation,wouldthendependmainlyontheobserver’sviewing
correspond to a well-organized system of plasma columns.
geometry.
In B0834+06 we observe less order and more fluctuation in
subbeam locations and brightness. This increased jitter in Wenowwish toquantitativelycompareourcurrentre-
subbeamposition,inadditiontotheirnon-uniformspacings, sultsaswellasthoseobtainedpreviouslyonB0943+10with
couldresultinthelowerQ-valuesobservedinthestar’sfluc- theoretical models. Wetabulate all therelevant parameters
tuation features. It was not possible to account for the null of these two pulsars in Table 1, where the magnetic field
pulses, which could furtheraffect themodulation Q. estimates are derived from their timing behavior.
We also made maps from successive subsections of the R&S express the circulation time of the discrete spark
sequences and viewed them in a ‘movie’-like fashion. The pattern as,
(cid:13)c 0000RAS,MNRAS000,000–000
8 Asgekar & Deshpande
Pˆ3/P1 =K0(B12/P12), (6) observedinsomepulsars(e.g.Backer1973)occurduetothe
where B12 is the average magnetic field (in units of 1012 same underlying reason. The nature of the modulation de-
pends on the geometry; a shallow cut by the locus of the
gauss) in the gap and P1 is the pulsar rotation period in
observer’ssightlineleadingtoaconalsingleprofileandsub-
seconds.Theconstant K0 (=5.6 accordingtoR&S)iscon-
pulsedrift,whereasamorecentralcutwouldleadtogeneral
sidered to be a very shallow function of conditions local to
amplitude modulations of the components of the average
theemission region. From eq. 6 we write,
profile. The subbeam positions and intensities are not as
(Pˆ3)0943+10 (Pˆ3)0943+10 stable as those observed in B0943+10 and we observed less
=K (7)
(cid:18)(Pˆ3)0834+06(cid:19)estimated (cid:18)(Pˆ3)0834+06(cid:19)observed orderinourmapsofB0834+06.Wecomparedourestimates
ofthecirculationtimeforpulsarsB0834+06andB0943+10
suchthattheparameterK accommodatesapossibilitythat
with the predictions of two specific theoretical models. We
K0 in eq. 6 may not be a constant. K=1 would imply that findthatthemodelsfail topredictthecirculation timeina
the proportionality constant K0 (irrespective of its precise consistent manner for the two pulsars. Future similar data
value) in the eq. 6 remains unchanged from one pulsar to
onotherpulsarsshouldhelpclarify possibledependencesof
another. We, however, find the value of K to be 0.29. This
circulation period on magnetic inclination angle and other
suggests that K0 is likely to have significant dependence parameters.
onthepulsarparameters,particularlytheestimatedsurface
magnetic field and the inclination angle α (see Table 1). In
ACKNOWLEDGMENTS
order to meaningfully assess the exact nature of these and
other possible dependences we would need Pˆ3 estimates to Wethankthestaffat theGauribidanurRadioObservatory,
become available for several other pulsars. in particular H.A. Ashwathappa, C. Nanje Gowda, and
Gil & Sendyk (2000; hereafter G&S) have advanced a G. N.Rajasekhar, for their invaluable help during observa-
modified-R&Ssparkmodelforradiopulsars.Theyhaveex- tions. We are thankful to V. Radhakrishnan and Joanna
amined the estimates of subpulse drift and the details of Rankinfor many fruitful discussions and theircritical com-
polaremissionmapsfromDR99andpaper-I.Theyclaimto mentsonthemanuscript.Wealsothankourreferee,Janusz
exactlyreproducesuchabehaviorfromtheirmodel,andthe Gil, for hisuseful comments.This research hasmadeuseof
observationsofB0943+10allowedthemtofixcertainmodel NASA’sADS Abstract Service.
parameters. We computed their predicted circulation time
forB0834+06giventheparametersinTable1.Accordingto
G&SmodelB0834+06’scirculationtimeshouldbe∼103P1 REFERENCES
(for a “filling factor” of 0.1; and ∼78P1 for a filling factor
computedaccordingtotheireq.4),almostanorderofmag- Asgekar,A.2002,Ph.D.thesis,IndianInstituteofScience,Ban-
galore.
nitudehigherthanwehaveestimatedfromourobservations.
Asgekar,A.&Deshpande,A.A.1999,Bull.Astr.Soc.India,302,
On the other hand, interestingly, the circulation time pre-
27
dicted B0834+06 based on the R&S model appears to be
Asgekar, A. & Deshpande, A. A. 2000, ASP Conference Series,
consistent with that observed. However, according to Gil,
Vol. 202; Proc. of IAU Colloquium # 177, (San Francisco:
Melikidze & Geppert (2003; GMG2003) the original R&S ASP),Ed.M.Kramer,N.Wex,andR.Wielebinski,pp.161
derivation is in error (by a factor of 4, in K0). The esti- Asgekar, A. & Deshpande, A. A. 2001, MNRAS, 326, 1249
mates for the circulation times in the two cases, based on (paper-II)
their(i.e.GMG2003’s)recentdetailedformulationofparam- Backer,D.C.1973,ApJ,182,245
eters associated with the ExB drift, show good agreement Deshpande, A. A. 2000, ASP Conference Series, Vol. 202; Proc.
with those observed. of IAU Colloquium # 177, (San Francisco: ASP), Ed. M.
Kramer,N.Wex, andR.Wielebinski,pp.149
Our analyses were carried out using observations ob-
Deshpande,A.A.&Radhakrishnan,V.1994,JApA,15,329
tained at 34.5 MHz alone, and we do not have any polar
Deshpande, A. A., Ramkumar, P. S., Chandrasekaran, S., Vin-
emission maps made using single-pulse sequences at meter-
utha,C.&Prabu,T.2004,inpreparation.
wavelengths for comparison. We believe that such a struc-
Deshpande,A.A.&Rankin,J.M.1999,ApJ,524,1008(DR99)
tureofdiscretesub-beamsisvalidevenathigherfrequencies. Deshpande, A. A. & Rankin, J.M. 2001, MNRAS, 322, 438
It would be possible to better account for the “null” pulses (paper-I)
and their effect on the subbeam motion using the higher Deshpande, A. A., Shevgaonkar, R. K. & Sastry, Ch. V. 1989,
sensitivity of meter-wavelength data. Gil (1987) has re- JIETE,35(6),342
portedthepresenceofstrongorthogonalpolarizationmodes Drake,F.D.,Craft,H.D.,Jr.1968, Nature,220,231
(OPMs) in this pulsar. Hence, this pulsar may provide a Gil,J.A.1987,ApJ,314,629
Gil,J.A.&Sendyk, M.2000,ApJ,541,351
usefulcontext forstudyingpossible causal relationships be-
Gil,J.A.,Melikidze,G.I.&Geppert,U.2003, A&A,407,315
tweenthe“null”pulses,OPMsandamplitudemodulations.
Gupta, Y., Gil, J. A., Kijak, J. & Sendyk, M. 2004, A&A, 426,
229
Lyne,A.G.&Ashworth,M.1983,MNRAS,204,519
8 CONCLUSIONS Mitra,D.&Deshpande,A.A.1999, A&A,346,906
Popov,M.V.&Sieber,W.1990,SovAstron,34,382
OurobservationsofB0834+06at35MHzshowthatthe
Rankin,J.M.1986, ApJ,301,901
regular amplitude modulations observed in this pulsar are
Rankin,J.M.1993, ApJ,405,285
duetoasystem ofdiscretesub-beamsrotatingmoreorless Rankin, J. M., Suleymanova, S. A. & Deshpande A. A. 2003,
steadilyaroundthemagneticaxis.Thisimpliesthatthegen- MNRAS,340,1076
eralamplitudemodulationsandregular“driftingsubpulses” Ritchings,R.T.1976, MNRAS,176,249
(cid:13)c 0000RAS,MNRAS000,000–000
Fluctuation Properties and Polar Emission Mapping of B0834+06 9
Pulsar α β B12 P1 numberof P3 Pˆ3 (R&S) Pˆ3(G&S) Pˆ3 (obs) Pˆ3
s sub-beams (inP1) (inP1) (inP1) (inP1) (s)
B0943+10 11◦.64 −4◦.31 2 1.097 20 1.848 9.3 36.95 36.95 40.57
B0834+06 30◦ −3◦ 3 1.273 8 1.855 13.1 103 14.84 18.9
Table1.ThevariouspulsarparametersforpulsarsB0943+10andB0834+06arelisted.Wealsocomparebetweentheobservedcirculation
timeandthetheoretical estimates (seetext).
Ruderman,M.A.&Sutherland,P.G.1975,ApJ,196,51(R&S)
Ruderman,M.A.1976, ApJ,203,206
Slee,O.B.&Mulhall,P.S.1970,Proc. ASA,1,322
Stinebring,D.R.,Cordes,J.M.,Rankin,J.M.,Weisberg,J.M.
&Boriakoff,V.1984,ApJS,55,247
Sutton, J. M., Staelin, D. H., Price, R. M. & Weimer, R. 1970,
ApJ,159,L89
Taylor,J.H.,Jura,M.&Huguenin,G.R.1969,Nature,223,797
van Leeuwen, A. G. J., Stappers, B. W., Ramachandran, R. &
Rankin,J.M.2003,A&A,399,223
(cid:13)c 0000RAS,MNRAS000,000–000