Low Frequency Observations of the Subpulse Drifter PSR J0034-0721 with the Murchison Widefield Array

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by  S. J. McSweeney

Draftversion January25,2017
PreprinttypesetusingLATEXstyleAASTeX6v.1.0
LOW FREQUENCY OBSERVATIONS OF THE SUBPULSE DRIFTER PSR J0034−0721WITH THE
MURCHISON WIDEFIELD ARRAY
S. J. McSweeney1 and N. D. R. Bhat1 and S. E. Tremblay1
International CentreforRadioAstronomyResearch(ICRAR),CurtinUniversity
1TurnerAve.,TechnologyPark,
7 Bentley,6102, W.A.,Australia
1
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2
A. A. Deshpande

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RamanResearchInstitute(RRI)
a
C.V.RamanAvenue,
J
Sadashivanagar,
4
Bengaluru-560080,India
2

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E
S. M. Ord
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CommonwealthScientificandIndustrialResearchOrganisation(CSIRO)
. CornerVimiera&PembrokeRoads
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MarsfieldNSW2122
p
Australia
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s 1ARCCentreofExcellenceforAll-SkyAstronomy(CAASTRO)
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ABSTRACT

1
The phenomenon of subpulse drifting may hold the key to understanding the pulsar emission mech-
v
5 anism. Here, we report on new observations of PSR J0034−0721 (B0031−07), carried out with the
5 Murchison Widefield Array at 185MHz. We observe three distinct drift modes whose “vertical”drift
7 band separations (P ) and relative abundances are consistent with previous studies at similar and
3
6
higher frequencies. The driftbands, however, are observed to change their slopes over the course of
0
. individual drift modes, which can be interpreted as a continuously changing drift rate. The implied
1
acceleration of the intrinsic carousel rotation cannot easily be explained by plasma models based on
0
7 E×Bdrift. Furthermore,wefindthatmethodsofclassifyingthedriftmodesbymeansofP3 measure-
1 ments can sometimes produce erroneous identifications in the presence of a changing drift rate. The
v: “horizontal” separation between driftbands (P2) is found to be larger at later rotation phases within
i the pulse window, which is inconsistent with the established effects of retardation, aberration, and
X
the motion of the visible point. Longer observations spanning at least ∼ 10,000 pulses are required
r
a to determine how the carousel rotation parameters change from one drift sequence to the next.
Keywords: pulsars, pulsars — subpulse drifting, individual pulsars — PSR J0034−0721
1. INTRODUCTION of substructures within individual pulses over time
(Drake & Craft 1968). Also critical is nulling, in which
Despitenearlyhalfacenturyofobservationalandthe-
the radio emission appears to switch off temporar-
oreticalinvestigations,the physicalmechanismsrespon-
ily (Backer 1970; Ritchings 1976), a widespread phe-
sible for the radio emission from pulsars remain unre-
nomenoncloselylinkedtothecoherentemissionprocess.
solved(Michel1991;Beskin et al.1993;Melrose & Yuen
PSR J0034−0721is a bright, long-period(P =0.943s)
2016). Some features of observed pulsar emission 1
pulsar with dispersion measure DM = 10.9pccm−3
are considered vitally important to furthering our un-
that exhibits both subpulse drifting (Backer 1970;
derstanding of these fundamental processes. Chief
Huguenin et al. 1970) and extensive nulling (∼ 45% of
among these is the phenomenon of subpulse drift-
the time, Vivekanand 1995), and thus is an important
ing, which is the systematic shift in pulse phase
object which can potentially reveal vital clues to the
2
underlying emission mechanisms. 3
Subpulses are thought to represent “subbeams”
caused by discrete emission regions that are stable over
many pulsar rotations, which in some cases may be ar- de
o
ranged in a “carousel” pattern centered on the mag- m
netic dipole axisandrotatingarounditatsomerate, D A
1900 )
s
(Ruderman & Sutherland 1975; Rankin 1986). Strong t
2 ni
observationalsupport for this view came with the work u
y
of Deshpande & Rankin (1999, 2000), who were able to er ar
dsteatberlemcianreotuhsaetlctohnesrisetgiunlgarofd2r0iftdeirscPrSetReeBm09is4s3io+n1r0e,ghioanssa. numb mode arbitr
(
One of the earliest and most successful emission mod- se B y
els (Ruderman & Sutherland 1975) invokedE×B drift Pul 1850 nsit
e
toexplainthecarousel’scircularmotion;however,there 1 d
are some outstanding issues with its quantitative pre- ull ux
N Fl
dictions. First,themeasureddriftrateforatleastsome
pulsars are known to be many times smaller than that
predicted by E×B drift (e.g. Mitra & Rankin 2008).
Second, the drift rate of some pulsars is not constant,
1800
but varies over time. The most common manifesta-
0
tion of this is the presence of temporally distinct drift
−20−10 0 10 20 30
modes, characterized by an abrupt change in the drift
rate, usually with a timescale less than a single stel- Rotation phase (◦)
lar rotation (e.g. Redman et al. 2005). Variations in
Figure 1. A subset of the stacked pulses of PSR
drift rate can also occur over longer timescales, with- J0034−0721, from MWA observations at 185MHz. The
out sudden drift modes changes, (e.g. Biggs et al. 1985; driftbands are clearly visible. The horizontal and vertical
separationsbetweenconsecutivedriftbands(indicatedbythe
Bhattacharyya et al. 2009). PSR J0034−0721 exhibits
overlaid white arrows) are P2, measured in degrees, and P3,
bothlongandshorttimescale driftratevariations,with measured in units of P1, respectively. Two of the three
threedistinctdriftmodesdesignatedasModesA,B,and drift modes, A and B, are exemplified here, distinguished
C (Huguenin et al. 1970; Wright & Fowler 1981), and by markedly different P3 values and drift rates. A typical
null sequenceis also present.
with drift rate variations occurring within each mode
(Vivekanand & Joshi 1997).
The methodology of Deshpande & Rankin (2000) in-
volves mapping the intensity sequences from the drift-
ing subpulses onto a coordinate system centered on the Nevertheless, it is vital to resolve the aliasing order so
magnetic axis (the so-called “cartographic transform”), wecanunderstandthe configurationofemissionregions
Ideally, this can be applied to other drifters, such as ofthis pulsarandthe relationshipbetweenits three dif-
PSR J0034−0721,allowing us to determine the geome- ferent drift modes.
try and dynamics of the emission regions. This is not The regularity of both the stellar rotation and of the
alwayspossible,mainlyduetothe difficultyinresolving observed driftbands allows us to define a number of pe-
the presence of aliasing,in which the true carouseldrift riodicities, often used in subpulse drifting analyses (e.g.
rate is different from the measureddrift rate because of Deshpande & Rankin1999;Edwards & Stappers2002).
the sub-Nyquist sampling of the emitting region due to P , P , and P are respectively defined as (1) the pul-
1 2 3
thestar’srotation. Acarouselwithanintegernumberof sar’s rotation period, (2) the temporal separation be-
subbeams admits only a discrete (but possibly infinite) tween two subpulses within a single rotation, and (3)
setofsolutionstoanygivenobserveddriftbandpattern, the time ittakesforasubpulsetoarriveatthe samero-
with higher drift rates corresponding to higher order tation phase as its predecessor. The drifting subpulses
aliasing. Determining the true carousel rate, and hence appear as diagonal driftbands in the pulse stack, which
the order of aliasing present, is difficult because differ- is the (one-dimensional) time series plotted in a two-
ent sets of parameter values (viewing geometry, as well dimensional array,with eachrow correspondingto 360◦
asaliasing)cangiverisetoidentical-lookingdriftbands. of rotation,and time progressingalong the verticalaxis
ThisisespeciallytrueforPSRJ0034−0721,whosemul- (Fig. 1). Visually,P andP arerealizedasthehorizon-
2 3
tiple drift modes complicate the issue, and whose view- talandverticalseparations(respectively)ofconsecutive
inggeometryisnotpreciselyknown(Smits et al. 2007). driftbands. The slope of the driftbands is the observed
3
drift rate, defined as their time-varying behaviour are described in §3. The
theoretical implications of a variable drift rate are dis-
dϕ P cussed in §4, and our conclusions are presented in §5.
D ≡ =± 2, (1)
dp P 2. OBSERVATIONS AND DATA PROCESSING
3
The data were taken with the MWA, a low frequency
where ϕ is the phase, p is the pulse number, and the aperture array located in remote Western Australia.
sign indicates the drift direction. The MWA is now geared for high time resolution sci-
Drift modes are usually characterized by their P ence, with the recently commissioned Voltage Capture
3
value, which is generally found to remain stable over System mode (VCS; Tremblay et al. 2015). The VCS
the course of a drift sequence (defined here as a set of enables the recording of the raw voltages from each of
contiguouspulsesallbelongingtothesamedriftmode). the MWA’s128tiles,whicharedownloadedfromsiteto
Early work on PSR J0034−0721measured P values of thededicateddatastoragefacilityatthePawseySuper-
3
12.5,6.8,and4.5P forModesA,B,andCrespectively computing Centre1.
1
(Huguenin et al. 1970; Wright & Fowler 1981), with in- We recorded 42 minutes (∼18.5TB) of VCS data on
dividualdriftsequenceslastingfromafewtohundredsof 19th January 2016. The data were processed following
pulseperiods(Vivekanand & Joshi1997). Interestingly, a procedure similar to Bhat et al. (2016), whichis sum-
the subpulse phases appear to be correlated across the marized here. Calibration of the data was performed
nulls (Joshi & Vivekanand 2000), indicating organized with the Real Time System (RTS) software (Mitchell,
motionofthesupposedcarouselconfigurationevendur- in prep), using an observation of Pictor A taken im-
ing nulls. mediately prior to the pulsar observation. Using the
Smits et al. (2005, 2007) investigated the behavior calibrationsolution,the rawvoltageswerephasedupto
of these drift modes at nine frequencies ranging from form a pencil beam (∼ 2arcmins in diameter) on PSR
157MHz to 4.85GHz. Their analysis revealed that the J0034−0721.
driftbands of Mode B were largely undetectable at the Theresultingdataset(storedinthePSRFITSformat,
higher frequency. They offered a geometric interpreta- Hotan et al.2004)consistedof24×1.28MHzcoarsefre-
tion, placing the surface plasma events during Mode B quency channels ranging from 169.60 to 200.32MHz,
emission closer to the magnetic pole than the Mode A and a time resolution of 100µs. The data from only
plasma events. The assumed radius-to-frequency map- the central 88 out of 128 (10kHz) fine channels of each
ping implies that at higher frequencies, the Mode B coarse channel were kept because of aliasing effects in-
emission forms too narrow an emission cone to inter- herent in the polyphase filter bank, which attenuates
sect the line of sight. The physical cause of the change the response of the antennas at the edges of the coarse
of magnetic latitude of the surface plasma events, how- channels. Thebestsolutionwasfoundbycalibratingon
ever, was not explored. 115 out of the available 128 antenna tiles, so the data
Indeed, no physical explanation has been offered for from the remaining tiles were rejected from the pulsar
severalkeypropertiesofPSRJ0034−0721’sdriftmodes, analysis.
such as their average duration, the order in which they Finally, the resulting frequency-time data was pro-
appear,their relationshiptothe nullsequences,andthe cessed in DSPSR (Van Straten & Bailes 2011) and
variation (albeit small) in their respective P measure- PSRCHIVE (Hotan et al. 2004) to produce a single-
3
ments. Crucially, the presence or absence of aliasing pulse archive and a timeseries. The time resolution
in PSR J0034−0721has not been determined; however, of the timeseries was 0.921ms, corresponding to 1024
Smits et al.(2007)estimatethenumberofdiscreteemis- phase bins across one pulsar period. The data set is of
sionsinthecarouseltobeabout9,undertheassumption very high quality, with an averageS/N of ∼9 per pulse
that aliasing is not present. (without excising null pulses), approximately a factor
In this paper we present new observations of PSR of 8.5 times higher than that of the same observation
J0034−0721made with the Murchison Widefield Array processed incoherently (i.e. with the signal power de-
(MWA, Tingay et al. 2013), a low frequency precursor tected at each tile summed together), ∼ 20% less than
to the Square Kilometre Array (SKA). We attempt to thetheoreticalexpectation. Thispaperpresentsthefirst
characterize the pulsar’s observed drifting behavior in studyofindividualpulsesforpulsaremissionscienceun-
termsofasmallnumberofparametersthatremaincon- dertaken with the MWA (but see, e.g., Oronsayeet al.
stant over the course of individual drift sequences. The 2015 for previous single-pulse studies with the MWA).
data acquisition and pre-processing are described in §2.
3. SUBPULSE DRIFTING ANALYSIS
Our analysis of the driftbands, and the investigation of
4
Table 1. Statistics of drift mode measurements
Mode Numberof Mean P2 Mean P3 Mean P3 Occurrence Mean
sequences (◦) (PAPS)(P1) (Quad) (P1) fraction (%) duration (P1)
A 9 18.9±1.1 11.9±2.0 12.5±0.8 18.4 54.6
B 31 19.8±0.5 7.0±0.5 7.0±0.2 34.5 29.6
C 2 19.1±2.9 5.9±3.6 4.6±0.3 0.8 11.0
Null 38 - - - 45.5 31.9
Unknowna 6 19.9±3.2 - - 0.8 3.7
Note—The mean P3 values were measured in two ways: (1) the PAPS method of Smits et al. (2005)
involvesFourieranalysisofpulsestackcolumns,andisdescribedin§3.1;(2)the“Quad”methodinvolves
fitting quadratic lines to sets of driftbands, and is described in §3.3. The mean errors are Gaussian-
propagated from thestandard deviations of thesame quantities measured for
individual drift sequences.
a
Sequencesthat were too short to yield a reliable measurement of P3 were uncategorized.
The analysis in this paper is aimed at exploring how responding to the three drift modes are not easily
the behaviour of the driftbands of PSR J0034−0721 resolved in the fluctuation spectra (e.g., Fig. 8 of
variesbothbetweendifferentdriftmodes,andwithinin- Karuppusamy et al. 2011). Any realistic measurement
dividual drift sequences. We analyzed only data within ofP andP (andhencethedriftrate)canthereforeonly
2 3
the on-pulse window, which was chosen to fall between be achievedby first determining the precise locations of
the first and last phase bins whose average flux densi- the transitionsbetweendifferentdriftmodes,andtreat-
ties were 4σ above the off-pulse noise (the noise statis- ing each drift sequence separately. For this pulsar, the
◦
tics were obtained from phase bins more than 90 away drift modes appear to switch on a timescale no longer
from the profile peak). The pulse window was thus de- thanasinglerotationperiod,andsoitbecomespossible
termined to be between −25.3◦ ≤ϕ≤33.0◦, where the to associate each pulse with a distinct mode.
◦
point ϕ = 0 was defined to be the center of the phase One can use the sliding two-dimensional fluctuation
bin which contained the largest average flux density. spectrum (S2DFS; Serylak et al. 2009) to obtain a map
of temporal changes to the drift modes, but the coarse
3.1. Determining the drift mode boundaries
resolution inherent in the technique cannot resolvesud-
Traditional methods of drift mode analysis in- den changes on the time scales of individual pulses. We
clude the Harmonic Resolved Fluctuation Spectrum therefore followed the method of Smits et al. (2005),
(HRFS;Deshpande & Rankin2000)andthemathemat- which measures the average P in a candidate drift se-
3
ically equivalent Two-Dimensional Fluctuation Spec- quence by computing the phase-averaged power spec-
trum (2DFS; Edwards & Stappers 2003). These meth- trum (PAPS), which is the sum of the amplitudes of
ods are designed to measure P2 and P3 by means of the DFT of each phase bin. The beginning and ending
Fourieranalysesofthetimeseries. Thefluctuationspec- boundaries of the drift sequence were then adjusted in-
traofpulsarswith multiple driftmodes willcontainthe crementally until the peak value in the PAPS divided
Fourier components corresponding to the (P2,P3) pairs bythermsoftherestofthePAPSwasmaximized. The
ofeachdrift sequence anda delocalizedcomponent cor- resulting map of drift modes is shown in the top panel
respondingtothedistributionofthedriftmodes,ascan of Fig. 2, and a summary table of drift mode statistics
be seen, for example, in the HRFS of PSR B2303+30 is given in Table 1.
(Redman et al. 2005). The distribution of drift modes in the MWA observa-
Because PSR J0034−0721 exhibits multiple drift tionstronglyresemblesthatofSmits et al.(2005,2007),
modes and long-duration nulls, the components cor- who observed the pulsar for a similar length of time at
similar frequencies (157, 243, 325MHz and above). In
particular,wenotethefollowingsimilarities: ModeAse-
1 https://www.pawsey.org.au/
25
20
)
1
P
( 15
3
P
S
P 10
A
P
5
0
−6
−5
)
1
P
/ −4
◦
(
e
t −3
a
r
t
rif −2
D
−1
0
25 Mode A
Mode B
) Mode C
1
P 20 Null
(
3 Unknown
P
s 15
u
o
e
n
a 10
t
n
a
t
s
n 5
I
0
0 500 1000 1500 2000 2500
Pulse number
Figure 2. Top: Distribution ofP3 valuescalculated viathePAPSmethod ofSmits et al. (2005). Middle: Theslopes of driftbandsfrom thelinearfitdescribed in §3.2.
Thehorizontal length indicates theextent of the given driftband; thevertical length indicates theerror of thedrift rate. Bottom: Thevalues of continuously changing
P3 as predicted by the quadratic fits described in §3.3. The P3 values of Mode B (green) and Mode C (red) appear to be confined to narrow regions (between 6 and
8P1 for B; 3 and 5P1 for C), but those of Mode A (blue) vary dramatically. Color panel: These are the determined modes, by color: mode A, mode B, mode C, nulls
are in black, unclassified in yellow. 5
6
quences are generally longer than modes B and C, and 2100
mode A sequences are often sandwiched between two
mode B sequences with minimal nulling between them.
3.2. Linear fits to driftbands
2080
Thesimplestwaytocharacterizeindividualdriftbands
istotreatthemasindependentlinesegments. Byfitting
alinetoeachdriftband,wehopetoassesswhetherthere
are any systematic changes in the drift rate over the
course of a drift sequence. 2060
r
e
Each pulse was convolved with a narrow Gaussian b
m
(FWHM = 2◦ ≈ 10% of P ) in order to smooth out u
2 n
high frequency noise fluctuations. The phase bin con- e
s
tainingthe mostpowerineachpulsewasidentified,and ul
P 2040
the phase of the interpolated peak (using a cubic spline
to geta sub-binestimation)wastakenasthe phase ofa
subpulse. P has previously been measuredto be ∼20◦
2
at low frequencies (see Fig. 4), so the second highest
peakwasidentifiedwiththe samemethod,butwiththe 2020
◦
constraint that it was not closer than 10 to the first
bin. For the vast majority of pulses, a maximum of two
driftbandswerevisible inanygivenpulse,sowedidnot
attempt to find a third subpulse peak.
2000
Analgorithmwasdesignedto findconnectedseriesof
−20 −10 0 10 20 30
subpulsepeaksthatbelongtothesamedriftband. Start- Rotation phase (◦)
ing at the beginning of the observation, and assuming
thatthesubpulsesfoundinthefirstpulsedoinfact“be- Figure 3. Pulse stack showing 101 pulses of PSR
J0034−0721. The image is saturated at 25%, meaning that
long” to genuine driftbands, we assigned the subpulses
anypixelcontainingavaluemorethan25%ofthemaximum
in the succeeding pulse to the already identified drift-
value in that window is displayed as a black pixel. Overlaid
◦
bands if the subpulse phases arewithin 10 ofthe drift- are red lines showing the linear fits to the drift bands using
band’s projected phase at the pulse in question. The weightedleastsquaresregression,describedin§3.2,andblue
linesshowingthequadraticcurvesfitwithfewerparameters,
projected phases were determined by a weighted least
described in §3.3.
squares fit to each subpulse already associated with a
driftband, where the weighting was proportional to the
subpulses had either been assignedto a driftband or re-
peak amplitude of the subpulse. However,the variation
◦
jected as an outlier (if it didn’t fall within 10 of any
in subpulse position requires that a statistically signifi-
projected driftband), the subpulse positions were fit by
cantnumberofpulsesbealreadyassignedtoadriftband
aweightedleastsquaresregressionasbefore,exceptthat
in order to obtain a reliable extrapolation of the drift-
this was also applied to even short (i.e. containing 4 or
bandlocation. Thus, if a driftband has so far only been
fewer subpulses) driftbands. The results of this algo-
assigned4subpulsesorfewer,weassumeanominaldrift
rate2of−2.5◦/P andonlyperformleastsquaresregres- rithm for a subset of the pulse stack are illustrated by
1
red lines in Fig. 3.
sion to find the phase offset. If a subpulse was found
◦ The errors on the slopes of the driftbands are calcu-
withaphasemorethan10 totherightoftheprojected
lated to be
phases, it was assigned to the beginning of a new drift-
band. The process continues until the onset of a null (wi(ϕi−ϕˆ))2
sequence, and the entire algorithm is repeated for each m =vu 1 Pi , (2)
driftsequence. Theresultingassignmentofsubpulsesto unc uun−2 (wi(pi−p¯))2
t Pi
driftbands was checked by eye for correctness, and the
where the sums are iterated over the subpulses within
same algorithm was successfully applied to the reverse
a given driftband; n is the number of pulses within a
timeseriesto testit forrobustness. Oncealldetermined
driftband; ϕ and ϕˆ are respectively the measured sub-
pulse phase and the phase predicted from the linear fit;
2 For this pulsar, driftrates appear to rangebetween approxi- p is the pulse number; and p¯= n1 ipi.
mately−0.5◦/P1 and−4.5◦/P1,asevidentintheresults. Having obtained a model for eaPch driftband, we can
7
nowassesshowthedriftbandslopesvaryoverthecourse had to be slightly adjusted in order to produce a good
of individual drift sequences (Fig. 2, middle panel). quadratic fit. Finally, the Mode C drift sequence at ap-
Mode A driftbands tend to become steeper (i.e. the proximately pulse number 2050 was too short for the
drift rate decreases), but those of mode B tend to be- PAPS method to yield a reliable P measurement, but
3
come shallower (i.e. the drift rate increases), but not was easily identified as Mode C using the quadratic fit
exclusively. method. Indeed, the difference between the average P
3
valuesforModeCshowninTable1andtheirrespective
3.3. Quadratic fits to driftbands errors is due to the inability of PAPS to deal with such
The linearfits to the driftbands suggestthatthe drift a short sequence.
ratevariesquasi-linearlyoverthecourseofeachdriftse-
3.4. Characterizing P
quence (to afirstorderapproximation,cf. middle panel 2
of Fig. 2). Assuming that this is the case, and also as- The value of P2 in PSR J0034−0721 is consistent
sumingthatP doesnotvaryovertime(consistentwith with being constant in time, irrespective of drift mode
2
what is observed in this data set), we write the follow- (Smits et al.2005,butseeVivekanand & Joshi1997for
ing functionalformforthe nthdriftband withina given evidence of the contrary). However, it has been ob-
drift sequence: servedtodecreaseathigherobservingfrequencies,inac-
cordancewiththeradius-to-frequencymapping(Cordes
ϕ(p)=a p2+a p+a +a n, (3)
1 2 3 4 1978, see our Fig. 4 and references therein). Here, we
wherepisthepulsenumberstartingfromthebeginning report that P2 is also dependent on the rotation phase,
of the drift sequence, and a , a , a , and a are free i.e. where the subpulses fall in the pulse window.
1 2 3 4
parameters to be fit. The drift rate, P2, and P3 can be TheaverageP2valueiscommonlymeasuredbymeans
derived from these parameters thus: ofanautocorrelationfunctionappliedtothepulsestack.
Here,wemeasureP foreachpulseindividually,bysim-
dϕ 2
=2a1p+a2, ply taking the difference of phases of the two subpulse
dp
peaks detected by the peak-finding algorithm described
P =a , (4)
2 4 in §3.2. The resulting P measurements are plotted in
2
P2 a4 Fig. 6 against the average (absolute) phase of the two
P = = .
3
dϕ/dp 2a1p+a2 subpulses. There is a noticeable positive correlationbe-
tween P and (average) phase—i.e. subpulses at later
Notethatthedriftrateislinearinp,andP isconstant, 2
2
phases are generally spaced more widely apart.
as desired.
To confirm this trend, we performed the identical
BecauseEq. (3)islinearina , a , a , a ,theycanbe
1 2 3 4
quadratic fits described above to smaller subsets of
fit to the subpulse position data using least-squares re-
gression. A weighted3 linear fit was performed with the subpulses. Within each drift sequence, the subpulses
were divided into three subsets, based on their absolute
subpulses in each drift sequence, resulting in quadratic
phases. The phase boundaries were not the same for
driftband fits shown in Fig. 3.
each drift sequence; instead, they were chosen to en-
The quadratic fits described by Eq. (3) employ four
sure that the number of subpulses in each subset were
free parameters per drift sequence, while the linear fits
the same (or differed only by one, if the total number
employ two free parameters per driftband. Both types
of subpulses was not divisible by three). P , as mea-
of fit successfully identify the driftbands, but the sub- 2
sured by the fit parameter a (cf. Eq. (3)) for each
pulse position residuals suggest that the linear method 4
subsetisshownplottedagainsttheaveragephaseofthe
fits the subpulses at the extremes of the pulse window
subset in the right-hand panel of Fig. 6. A similar up-
slightly better than the quadratic method (Fig. 5). We
ward trend is evident. We note, in passing, that the
note,however,thatthe quadraticfitmethodcanpoten-
three modes do not appear to be drawn from different
tially be used to correct a misidentification of a drift
distributions of P , which is contrary to the finding of
mode and/or drift mode boundaries, which occurred 2
Vivekanand & Joshi (1997) who reporteda weakly neg-
threetimesinthepresentdataset. Inthefirstinstance,
ativecorrelationbetweenP anddriftratefromanalysis
thequadraticfitfailedtofindaclosefittoasetofdrift- 2
of their observations at 325MHz.
bandswhentheywereerroneouslyassumedtobelongto
the same drift mode. In the second instance, the drift
4. DISCUSSION
sequence boundaries determined via the PAPS method
We have demonstrated the presence of two effects in
PSR J0034−0721 that have previously not been stud-
3 Theweights usedweretheamplitudesofthesubpulsepeaks, ied in detail. Firstly, the drift rate in PSR J0034−0721
asbefore. variesgraduallywithinindividualdriftmodes aswellas
8
50
Thiswork
Karuppusamyetal. (2011)
40 Weltevredeetal. (2007)
Smitsetal. (2007)
Weltevredeetal. (2006)
) 30 Smitsetal. (2005)
g
e Izvekovaetal. (1993)
d
( Hugueninetal. (1970)
P2 20
10
Mode A Mode B Mode C
0
0.1 1 0.1 1 0.1 1
Observing Frequency(GHz)
Figure 4. Comparison of available measurements of P2, with the panels from left to right showing measurements of modes A,
B,andCrespectively. Thefact thatP2 isconsistentwithbeinguniformacross allthreemodesat anygivenfrequencysuggests
that the angular spacing of theemission regions around themagnetic axis does not change between mode switches.
15 )
s
t
Linear model Quadratic model ni
10 u
1
b.
r
) 5 a
◦( (
x
ual 0 flu
sid 0.1 ak
Re −5 pe
e
−10 uls
p
b
−15 0.01u
S
−20 −10 0 10 20 30 −20 −10 0 10 20 30
◦ ◦
Rotation phase ( ) Rotation phase( )
Figure 5. Theresidualsforboththelinearfitstothedriftbands(leftpanel)andthequadraticfits(rightpanel). Thecolorscale
indicatestheamplitudeofthepeakofthesubpulses,whichwereusedasweightsintheregression fits. Thelinearfitsappearto
generate slightly smaller residuals, but requires many more free parameters. Both fits perform worse at the edges of the pulse
window than in thecentral region, suggesting that P2 is a weak function of rotation phase.
50
ModeA (a) (b)
ModeB
40
ModeC
Unknown
30
)
◦
(
2
P 20
10
0
−20 −10 0 10 20 −20 −10 0 10 20
◦ ◦
Mean subpulse phase ( ) Rotation phase( )
Figure 6. Left: The phase differenceof two subpulses (P2 measured for each pulse) against the phaseof the midpoint between
them. The fact that no P2 was measured below 10◦ is a consequence of the algorithm used to measure the subpulse phases.
Right: The valueof the a4 parameter (P2 measured for each drift sequence) against thecentral phase of theswath used in the
fit. Both methods indicate that P2 is positively correlated with rotation phase.
sharply between them (Fig. 2). Secondly, P appears pulsesontherighthandsideofthepulsewindow(when
2
tobe positivelycorrelatedwithrotationphase;i.e. sub- viewed in the pulse stack) are more widely separated
9
than those on the left hand side (Fig. 6). tional variation is very large (≈ 67%) and can only be
Bothofthese effects wereobservedinPSRB0826−34 realistically explained by the same mechanism of fluc-
(Gupta et al. 2004, hereafter GGKS04), another long- tuating surface temperature if higher order aliasing is
period(P =1.85s)drifter,althoughdifferentfromPSR invoked to bring the true drift rate variation down to a
1
J0034−0721 in many respects. PSR B0826−34 has a few percent. For the geometry assumed by Smits et al.
verywideprofile,withupto13distinctdriftbandsbeing (2005),with9subbeamsviewedatα≈β ≈4.5◦,wefind
◦
observed across all 360 . It appears to exhibit nulling, thatthetruedriftratebecomesapproximately(10/k)%
but weak emission (at the 2% level, at 1374MHz) has foraliasingorderk ≥1. Thus,evenaliasingorderk &2
been detected during null periods, enabling the trac- wouldbringthe true driftrateto alevelconsistentwith
ing of the driftbands continuously over several hun- the 8% inferred for PSR B0826−34. However, this can-
dredpulses(Esamdin et al.2005). Bhattacharyya et al. notexplainboth the gradualchangein driftratewithin
(2008), however,reportnoemissionduringnulls (atthe drift sequences and the abrupt change in drift rate be-
1% level) in their observations at 157, 325, 610, and tween them, unless the temperature fluctuated at two
1060MHz. PSR B0826−34 and PSR J0034−0721 are distinct timescales. Even if aliasing is present, one is
suspected to have similar viewing geometries, with α still left with a drift rate that is discontinuous at mode
(the angle between the rotation axis and the magnetic boundaries (cf. Esamdin et al. 2005, who point out the
axis) and β (the angle between then magnetic axis and existence of cusps in the drifting pattern of B0826-34).
the line of sight at closet approach) both being very Thus,inkeepingwiththeobservedtimescaleofdriftrate
small (< 10◦). The parameters α and β are often esti- variation observed in B0826-34 (∼ 100 pulses ≈ 180s),
mated by fitting the polarization angle sweeps to the we surmise that if the surface temperature is indeed re-
magnetic pole model (Radhakrishnan & Cooke 1969). sponsiblefortheintra-sequencedriftratevariation,then
However, for both pulsars, there are several combina- some other, possibly unrelated mechanism must drive
tions ofα andβ thatreproducedthe observedpolariza- the drift mode changes.
tion curve, and current estimates give 1◦.5 ≤ α ≤ 5◦.0 It is of interest to know what the relationship is, if
and 0◦.6≤β ≤2◦.0 for PSR B0826−34(GGKS04) and any, between the drift rates and carousel acceleration
α ≈ β around 0◦.1 to 6◦.0 (Smits et al. 2007). A final parametersofneighboringdriftsequences. Thepresence
difference is that, unlike PSR J0034−0721 whose drift ofaliasingwouldobscuresucharelationship,whichsug-
rate always maintains the same direction and changes gests the possibility that the correct aliasing order and
only graduallythroughoutany givendriftsequence, the number of subbeams may be recognized by their abil-
drift rate of PSR B0826-34 fluctuates about a mean ity to reveal a natural progression of carousel rotation
valueof∼0◦/P ,changingsigninaquasi-periodicman- parameters from one sequence to the next. This, how-
1
ner. ever, requires a much longer data set than presented
here since most drift sequences in PSR J0034−0721are
4.1. Variable drift rate by stellar surface temperature
bordered by nulls (see Fig. 2), and it is as yet unclear
fluctuations
how the subpulse phase, drift rate, and carousel accel-
Given the apparent similarity with PSR B0826−34, erationevolveduringanull(Joshi & Vivekanand2000).
we assess if the explanations that GGKS04 offer for the Basedonthe numberofmode transitionsinthe present
appearanceofthesefeaturesinPSRB0826−34wouldbe data set, we estimate a rate of approximately 40 suit-
applicable to PSR J0034−0721 as well. The variability able mode transitions (i.e. without intervening nulls)
of the drift rate is suggested to arise from fluctuations in 10,000 pulses, a conservative minimum required to
in the stellar surface temperature, which indirectly in- investigate these relationships further.
fluences the E×B drift rate. Moreover, the apparent
4.2. The P dependence on rotation phase
change in drift direction is attributed to an aliasing ef- 2
fect;withhigher-orderaliasing,thedirectionwillappear GGKS04invokeanewideatoexplainthepositivecor-
to change if the true value of P fluctuates over a small relation between the measured P and rotation phases.
3 2
range that straddles an integral multiple of P . In this Theysuggestthatthecarouselpatterniscenterednoton
1
scenario,smallfractionalvariationsinthetruedriftrate the magneticdipoleaxis,butaroundsomeothernearby
can appear to observers as large fractionalvariations in axis (dubbed the “local pole”) that arises perhaps due
measured drift rate. GGKS04 calculate that only up to toamoredominantmultipolarcomponentnearthesur-
8%changeinthetruedriftrateisrequiredtoexplainthe face. In their case, they were able to determine that a
measured variation, and that this upper limit requires local pole which is offset from the dipole axis by ∼ 3◦
only a 0.14% fluctuation in the surface temperature. is able to reproduce the observed P dependence on ro-
2
Even though the observed drift rate in PSR tation phase. We hope that a similar analysis will be
J0034−0721 is ubiquitously unidirectional, the frac- able to find a local pole solution for PSR J0034−0721.
10
This analysis, however, also depends on a known (or first-of-its-kind demonstration of this instrument’s ca-
assumed) number of beams and aliasing order, which pability of producing high quality single-pulse data,
cannot yet be inferred from current observations. in line with its intended science aims (Bowman et al.
Other explanations for this effect are not forthcom- 2013). Our analysis shows that the driftbands of PSR
ing. For example, aberration effects are traditionally J0034−0721 exhibit more complex behavior than what
invoked to explain the asymmetry in pulsar profiles in has been inferred from previous studies. In particular,
whichconalemissionfeaturesareshiftedtolowerphases (1) the measureddrift rate changes continuouslywithin
relative to core emission. Presumably, such effects are individual drift sequences, with a characteristic varia-
present in PSR J0034-0721,but due to the fact that its tion time scale apparently longer than the typical du-
profile contains only a single (conal) component, they ration of individual drift sequences; and (2) P is pos-
2
would not be detectable in the traditional way. How- itively correlated with rotation phase. Both of these
ever, any measurable feature with a dependence on ro- effects were observed and studied in PSR B0826−34by
tation phase (such as P ), should be “stretched” out at Gupta et al. (2004), who explain the variable drift rate
2
lower phases and “compressed” at higher phases, simi- by linking it to surface temperature fluctuations, and
larlytoprofilecomponents(Gupta & Gangadhara2003; the P dependence on rotation phase by determining
2
Dyks et al. 2003). However, exactly the opposite is ob- the positionofa “localpole” aroundwhichthe carousel
served in the P of PSR J0034−0721, so aberration ef- is assumedtorotate. However,theapplicabilityoftheir
2
fects cannot be invoked to explain it. proposed physical explanations to PSR J0034−0721re-
Anotherpossible explanationis the motionofthe vis- quires the knowledgeofthe aliasingorderandthe num-
ible point as discussed by Yuen & Melrose (2014) and berofsubbeamsinthecarousel,whicharecurrentlyun-
Yuen et al. (2016), which takes into account the direc- known for PSR J0034−0721. However,we note that re-
tion of the dipolar magnetic field at the emission site, solvingthe aliasingorderandnumber ofsubbeams may
an effect that has traditionally been neglected in the be helped by assuming that the true drift rate varies
interpretation of P measurements. They showed that continuously over drift mode boundaries, but such an
2
measurementsofP candramaticallyunderestimatethe investigation requires significantly longer observations
2
truesubbeamseparationwhentheanglebetweenthero- than have been presented here.
tation and magnetic axes, α, is sufficiently small, which
is believed to be the case for PSR J0034−0721 (e.g.
Smits et al. 2005, 2007). However, they also showed
ACKNOWLEDGEMENTS
that the discrepancy in P is symmetrical about the
2
fiducial point, with the measured P increasing as one
2
This scientific work makes use of the Murchison
movesaway(ineitherdirection)fromthefiducialpoint.
Radio-astronomyObservatory,operated by CSIRO. We
Again, this is at odds with what is seen from our ob-
acknowledge the Wajarri Yamatji people as the tradi-
servations, where P appears to increase monotonically
2
tional owners of the Observatory site. Support for the
across the pulse window. Even though invoking the ef-
operation of the MWA is provided by the Australian
fect of a moving visible point may explain the varia-
Government (NCRIS), under a contract to Curtin Uni-
tion in P , it will require the assumption that the fidu-
2
versity administered by Astronomy Australia Limited.
cial point lies somewhere to the left of the on-pulse re-
We acknowledge the Pawsey Supercomputing Centre
gion. However, attempts to constrain the fiducial point
whichis supportedby the WesternAustralianandAus-
of PSR J0034−0721have not met with success because
tralian Governments. We would also like to thank the
of the difficulty of locating a zero-crossing point in the
referee, Patrick Weltevrede, for the detailed comments
position-angle sweep of the dominant polarization, due
and suggestions which improved the paper.
toitsflatnessoverthepulsewindow(Smits et al.2007).
Parts of this research were conducted by the Aus-
Thus we are not able to comment on the likelihood of
tralian Research Council Centre of Excellence for All-
this scenario.
skyAstrophysics(CAASTRO),throughprojectnumber
5. CONCLUSION CE110001020. NDRB acknowledgesthe supportfroma
Curtin Research Fellowship (CRF12228).
Wehaveconductedadetailedanalysisofnewobserva-
tionsofPSRJ0034−0721withthe MWAat185MHz, a Facility: MWA
REFERENCES
Backer,D.C.1970,Nature,227,692 Beskin,V.S.,Gurevich,A.V.,&Istomin,Y.N.1993,Physicsof
thePulsarMagnetosphere, arXiv:arXiv:1011.1669v3