Correlation of Fermi photons with high-frequency radio giant pulses from the Crab pulsar

0.56 MB·English

by  A. V. Bilous

Draftversion January10,2011
PreprinttypesetusingLATEXstyleemulateapjv.04/20/08
CORRELATION OF FERMI PHOTONS WITH HIGH-FREQUENCY RADIO GIANT PULSES FROM THE
CRAB PULSAR
A. V. Bilous1, V. I. Kondratiev2,3, M. A. McLaughlin4,7, S. M. Ransom5, M. Lyutikov6, M. Mickaliger4,
G. I. Langston7
Draft version January 10, 2011
1
1
ABSTRACT
0
2 To constrain the giant pulse (GP) emission mechanism and test the model of Lyutikov (2007) for
GPemission,wehavecarriedoutacampaignofsimultaneousobservationsoftheCrabpulsaratγ-ray
n
(Fermi) and radio (Green Bank Telescope) wavelengths. Over 10 hours of simultaneous observations
a
we obtained a sample of 2.1 104 giant pulses, observed at a radio frequency of 9GHz, and 77 Fermi
J
×
photons, with energies between 100MeV and 5GeV. The majority of GPs came from the interpulse
7
(IP) phase window. We found no change in the GP generation rate within 10 120s windows at lags
−
of up to 40min of observed γ-ray photons. The 95% upper limit for a γ-ray flux enhancement in
] ±
A pulsedemissionphasewindow aroundallGPsis 4 times the averagepulsedγ-rayflux fromthe Crab.
For the subset of IP GPs, the enhancement upper limit, within the IP emission window, is 12 times
G
the average pulsed γ-ray flux. These results suggest that GPs, at least high-frequency IP GPs, are
. due to changes in coherence of radio emission rather than an overall increase in the magnetospheric
h
p particle density.
- Subject headings: Crab pulsar, Giant Pulses, Fermi
o
r
t
s 1. INTRODUCTION sars (e.g. Herfindal & Rankin 2009), intermittent pul-
a
sars (Kramer et al. 2006), and rotating radio tran-
[ The Crab pulsar was discovered by
Staelin & Reifenstein III in 1968 by its remarkably sients (McLaughlin et al. 2006), GP emission could be
1 due to changes in the coherence of the radio emission,
bright giant pulses (GPs). Giant pulses are short (from
v variationsinthepaircreationrateinthemagnetosphere,
few ns to few µs), sporadic bursts of pulsar radio
4 or changes in the beaming direction. If the GP phe-
emission (Popov & Stappers 2007; Hankins et al. 2003).
3 nomenon is due to changes in the coherence of the radio
The nature of GPs is far from being clear and even
4 emission mechanism, then one would expect little cor-
the precise definition of giant pulse had not yet been
1 relationof the radio GPs with the high-energyemission.
given (Knight et al. 2006). GPs generally occur only
1. in certain narrow ranges of pulse phase that are often However,iftheGPsareduetochangesintheactualrate
0 coincident with pulses seen at X-ray and γ-ray ener- of pair creation in the pulsar magnetosphere, one would
1 gies (Lundgren 1994). Popov et al. (2006) propose that expect an increased flux at high energies at the time of
1 theGPs. Similarly,becausetheradioGPandγ-raycom-
all radio emission from the Crab (except for that in the
: ponentsarealigned,oneexpectsthattheycomefromthe
v precursor) is composed entirely of GPs, consistent with
same place in the pulsar magnetosphere. Therefore, if a
i the alignment of the GP and high-energy components
X GP occurs from a beam direction alteration, one would
seen in other pulsars exhibiting GPs (Cusumano et al.
expect to also see an increase in the high-energy flux.
r 2003; Knight et al. 2006).
a Lundgren et al. (1995) previously attempted to carry
The Crab pulsar shows pulsed emission across the
outsimultaneousradio/γ-rayobservations(50 220keV,
entire electromagnetic spectrum (see Fig. 1, left), re- −
the energy range of CGRO/OSSE) and correlate times
flecting different radiation processes in the pulsar mag-
of arrival of GPs at 800 and 1300MHz with γ-ray
netosphere — from coherent curvature or synchrotron
photons. Their upper limit on the γ-ray flux in-
(radio) to incoherent synchrotron (optical and X-ray)
crease concurrent with radio GPs was 2.5. Later,
and incoherent curvature (γ-ray) radiation. Simi-
≤
Ramanamurthy & Thompson(1998)correlatedthesame
lar to other sporadic variability phenomena seen in
set of GPs with EGRET photons of energy > 50MeV,
pulsar radio emission, represented by nulling pul-
placing an upper limit on concurrent γ-ray flux of 4.6
1Department of Astronomy, University of Virginia, PO Box times the average Crab flux. This suggested that the
400325, Charlottesville,VA22904;[email protected] GP mechanism is largely based on changes in coher-
2Netherlands InstituteforRadioAstronomy(ASTRON),Post- ence and not changes in pair production rates or beam-
bu3sA2,s7tr9o90SApaAceDwCienngteelrooo,fTthheeNLeetbheedrelavnPdsh;yksoicnadlraIntisetvit@uates,trPonr.onf-l ing. Yet, Shearer et al. (2003) performed simultaneous
radio/opticalobservations of the Crab pulsar and found
soyuznayastr. 84/32, Moscow117997,Russia
4DepartmentofPhysics,WestVirginiaUniversity,Morgantown, a weak correlation, i.e. that optical pulses coincident
WV26506 withradioGPswereonaverage3%brighterthanothers.
5National Radio Astronomy Observatory, Charlottesville, VA This observation suggested that the GP emission mech-
22903
6DepartmentofPhysics,PurdueUniversity,WestLafayette,IN anism, whatever its nature, includes small variations in
47907 magnetospheric particle density.
7National Radio Astronomy Observatory, Green Bank, WV Lyutikov(2007)proposedamorespecific,quantitative
24944
2 A. V. Bilous et al.
model of GP emission in which Crab GPs are generated
on closed magnetic field lines near the light cylinder via
anomalous cyclotron resonance on the ordinary mode.
Duringemissionofaphoton,anelectronundergoestran-
sition up in Landau levels. The energy is supplied by
the parallel motion (Ginzburg 1985). The application
of anomalous cyclotron resonance to pulsar radio emis-
sion has been discussed by Lyutikov et al. (1999) and
Machabeli & Usov (1979).
One clear prediction of this model is that radio GPs
(at least those at radio frequencies > 4GHz) should be
accompaniedby γ-rayphotons,asthe highenergybeam
is expected to produce curvature radiation at energies
~γ3Ω 0.1–100GeV, depending on the exactvalue of
∼ ∼
the Lorentz factor γ. These energies fall into the energy
range of the Fermi mission, and so this hypothesis can
alsobetestedthroughhigh-frequencyradioobservations
concurrent with Fermi.
The FermiLargeArea Telescope (LAT), with its large
effective area, broad field of view, and superior angular
resolutionisaperfecttoolfortestingtheLyutikovtheory
and investigating the possible correlation between GPs
andγ-rayphotonsingeneral. Fortheradioobservations,
usingthe100-mGreenBankTelescope(GBT)allowsone
torecordaverylargenumberofGPswithinareasonable Fig.1.—Left. AverageprofileoftheCrabpulsarfromradiotoγ-
observing time, even at frequencies above 4GHz. Thus, rays,fromthepaperofMoffett&Hankins(1996). Right. Average
Crabpulsar radio profile for one out of two sub-sessions with the
a thoroughstudy ofthe correlationbetween high-energy
GBTonSep25,2009.
γ-ray photons and high-frequency GPs is possible.
In this paper, we present the results of simultaneous
GBT/LAT observations of the Crab pulsar. To probe S/N >7 in order not to contaminate our sample by nu-
the level of correlation between GPs and γ-ray photons, merousspurious detections onnoise. Eacheventwas as-
we used two main approaches. First, we searched for signeda width, foundby averagingthe dedispersedtime
a “burst correlation”by examining whether GPs cluster series with different numbers of samples and finding the
nearγ-rayphotonsintime. Second,weanalyzedwhether number that resultedin a peak in S/N. The list of event
the average γ-ray flux of the pulsar increases within the times wasput intoTEMPO2format(Hobbs et al.2006)
pulse phase windows where single GPs are produced. and convertedto the barycentric reference frame for the
In Sections 2 and 3 below we describe the radio obser- correlation analysis with Fermi data. Times of arrival
vations and Fermi data used in this analysis. Section 4 (TOAs) were corrected for delay due to propagation in
discusses the influence of the interstellar medium on the the ionized interstellar medium (ISM).
observedGP sample. We describe the correlationanaly- Estimated timing errors due to an inaccurate DM are
sis between radio GPs and Fermi photons in Section 5, less than our time resolution, assuming that DM varies
and conclude in Section 6. smoothlyandthatbetweenobservingsessionsthechange
in DM is less than the change over two months. For
DM DM = 0.0104pccm−3, timing errors are
2. RADIOOBSERVATIONS abouOtct0.−5µs. Sep
The radio observations were carried out during 12 ob- Fig. 1 (right) shows the average pulse profile (top) of
serving sessions in September–October, 2009 with the theCrabpulsarat8.9GHztogetherwiththesubintegra-
GBT, using the new Green Bank Ultimate Pulsar Pro- tions from one of the two sub-sessions on Sep 25, 2009,
cessor Instrument (GUPPI) at a central frequency of which hadthe highest rate of GP detection of all 12 ses-
8.9GHz, in incoherent dedispersion mode. The total sions. The interpulse (IP) and high-frequency compo-
bandwidthof800MHzwassplitinto256frequencychan- nents (HFCs) are clearly seen, with the weak peak after
nels,andthetotalintensitywasrecordedwithasampling HFC2 being the main pulse (MP). However, on Sep 25
interval2.56 3.84µs. Totalobservingtime was 26hrs the pulsar was the brightest, and during other sessions
or 3 106−pulsar periods. ∼ the averageprofilewasless prominent. During someses-
∼ ×
Therawdatafromeverysessionwerededispersedwith sions we did not accumulate a detectable averageprofile
thecurrentDMoftheCrabpulsar8usingPRESTOpack- at all.
age9,andsearchedforallsingle-pulseeventswithsignal- The system equivalent flux density (SEFD) is mostly
to-noiseratio(S/N)>7. SinceGPsfromtheCrabpulsar determined by the Crab Nebula. Flux densities for the
donothaveanyestablishedlowerlimitonpeakfluxden- Crab Nebula were calculated with the relation S(f) =
sity(Popov et al.2006),wepickedupinitialthresholdof 955 (f/GHz)−0.27Jy (Cordes et al. 2004), accounting
×
for the fact that at 8.9GHz the solid angle of the GBT
8 The DM was 56.8005pccm−3 for September and beamcoversonly25%oftheareaoccupiedbythenebula.
56.8109pccm−3 for October, from the Jodrell Bank Crab pulsar
monthlyephemeris: http://www.jb.man.ac.uk/pulsar/crab.html WeestimateaSEFD=1.3/p∆t/1µsJy,orabout0.7Jy
9 http://www.cv.nrao.edu/$\sim$sransom/presto/ for our most common sampling time, or ∆t, of 3.2µs.
Correlation of Fermi photons with high-frequency radio GPs from the Crab pulsar 3
TABLE 1
SummaryofobservationalparametersandGP/γ-rayoutcome foreach observing
date. Columnsinclude(fromlefttoright): dateofobservation,timeresolution,
system equivalentfluxdensity (SEFD), totalduration of radioobservationsand
the time simultaneouswith Fermi,numberof giantpulses, NGPs,detected during
the whole observingsession andduringthe time simultaneouswith Fermi, number
of γ-rayphotons, Nγ.
Date ∆t SEFD Radiotime NGPs Nγ
Total WithFermi All With
(2009) (µs) (Jy) (min) (min) Fermi
Sep12 2.56 0.81 87.1 28.9 139 8 5
Sep14 3.20 0.73 165.7 62.1 4375 1834 10
Sep16 3.84 0.66 99.3 30.6 98 27 4
Sep19 3.20 0.73 118.5 54.3 6957 1830 5
Sep20 3.20 0.73 110.5 32.2 1846 384 2
Sep21 3.84 0.66 55.1 31.5 27 16 2
Sep22 3.20 0.73 147.7 68.9 1256 603 5
Sep23 3.20 0.73 164.5 82.0 10520 5078 10
Sep24 3.84 0.66 55.3 22.5 38 37 1
Sep25 3.20 0.73 236.5 130.8 14320 10014 13
Sep28 3.20 0.73 72.3 48.1 34 9 5
Oct25 3.20 0.73 157.6 41.3 3164 1261 15
Total 1470.0 633.1 42774 21092 77
Preliminary analysis of all events with S/N > 7 re- (Abdo et al. 2010). Photonarrivaltimes were converted
vealed that GPs appear mostly in the MP and IP phase totheSolarSystembarycenterandassignedphaseswith
windows. Only for 2 observing sessions, namely on Sep the TEMPO2 fermi plugin. The timing accuracy of the
25and28,werethereseveralGPsdetectedinthe HFCs, Fermi LAT is better than 1µs (Abdo et al. 2010). LAT
allwithS/Ncloseto9. Thisistosomeextentsurprising, dead time per event is less than 100µs10, which is less
sinceJessner et al.(2005)observedtheCrabpulsarwith than3%ofpulsarrotationalphase. Overthecourseofall
similar parameters and timespan, and found about 120 radio observations we accumulated 10.5hours of Fermi
GPs in HFCs versus 350 GPs in the MP and IP. How- data within GTIs, resulting in 77 photons with energies
ever,theirthresholdpeakfluxdensityof25Jywasmuch above 100MeV (see Table 1).
higher than our threshold of about 6Jy, suggesting that Fig.2givesaquickvisualsummaryofoursimultaneous
the GPs from HFCs are rarer but brighter. observations,showingFermi photonsandradioGPsver-
Some of our sessions were heavily contaminated with sus observing time for each session. The distribution of
broadradiofrequencyinterference(RFI)pulseswithtyp- number and energy/peakintensity of photons/GPswith
icalS/N<10. Therefore,weanalyzedonlyeventswitha respect to pulsar rotational phase is shown in Fig 3. As
peakfluxdensityexceeding8.1Jy(S/N=10fortheses- reported earlier, γ-ray and radio emission windows are
sion with smallest sampling time) and which arrived in aligned.
the MP orIP phase windows. Additionally, we excluded
all events with width larger than 30 sample intervals, as 4. PROPAGATIONEFFECTSFORGIANTPULSES
being presumably caused by RFI. These cuts resulted in Athighfrequencies,GPsarestronglyaffectedbyinter-
the selection of more than 40000 GPs. Comparing the stellar scintillations (Cordes et al. 2004), which change
number of single pulses above 8.1Jy and narrower than their apparent rate and peak intensities. Careful treat-
30 samples in and out of the pulsed emission phase win- ment of ISM effects is crucial for a proper correlation
dows,wecanestimatetheproportionoffalse GPs inour analysis. Unfortunately,wedidnotmakedirectmeasure-
final data set to be less than 0.001%. mentsoftypicalISMdiagnosticparameters,suchasscin-
The summary of observations is given in Table 1. For tillation bandwidth and pulse broadening time. Instead,
each observing date the listed columns are: time resolu- we use the scintillation timescales scaled from other fre-
tion,SEFD, totaldurationofradioobservationsandthe quencies. These values give only a rough estimate of
time simultaneous with Fermi, number of giant pulses, scintillation timescales at 8.96GHz, since for the Crab
detected during the whole observing session and during pulsar the main contributionto scintillations is made by
the time simultaneouswithFermi, andthe number ofγ- the turbulent and quickly changing Crab Nebula. Scin-
ray photons selected for further analysis (see Section 3). tillation parameters for the Crab have been shownto be
3. FERMI DATA stronglyvariablewithtime (seeCordes et al.(2004)and
references therein).
Weextracted“Diffuse”classeventswithenergiesfrom The refractive interstellar scintillation (RISS)
100MeV to 300GeV from the Fermi database, concur- timescale, τ , can be scaled using the ν−2.2 de-
RISS
rent with each radio observation. Photons with zenith
pendence derived from a five frequency data set
angles greater than 105◦ were excluded to eliminate the
(Rickett & Lyne 1990). At 8.96 GHz, τ is about
RISS
γ-rays generated in the Earth’s atmosphere.
80 minutes, thus roughly matching the observed day-to-
We selected only photons in Good Time Inter-
vals (GTIs) within an angle θ < Max(6.68 10 ThedeadtimewastakenfromFermi TechnicalHandbook,
1.76log(E/1000MeV),1.3)◦ of the radio pulsar positio−n http://fermi.gsfc.nasa.gov/ssc/proposals/manual/
4 A. V. Bilous et al.
Fig.2.— Time series of radioGPs and Fermi photons during12 observing sessions. X-axis – time from the beginning of each session,
in minutes. Y-axis (left) – peak flux density of radio GPs. Y-axis (right) – energy of γ-ray photons. Both scales are the same for each
observingsession. TheyellowshadedregionsmarkthetimewhenweactuallywererecordingradiodataandthebluearetheFermi Good
Time Intervals. The observing date is given in the upper right-hand corner of each subplot. For the observing session on Oct 25 two
photons camewithinshorttimeinterval,sotheirmarkersoverlapandonecanseeonly14photons, insteadof15.
Fig.3.— Left: histograms of GPs for all radio observing time (bottom) and Fermi photons during the simultaneous time (top). For
illustrativepurposes,scaledradioandγ-rayprofiles(grey)areshownwitharbitraryoffsetalongy-axis. Thescaledradioprofileisfromthe
second scanof GBT sessiononSep25, 2009 (as showninFig.1), and the γ-rayprofileisthe Fermi profileaccumulated duringSep-Oct,
2009. Right: distributionof peak flux density of GPs and energy of γ-rayphotons over pulsarrotational phase. Also, there is shownthe
scaledradioprofileasforhistogramontheleft.
Correlation of Fermi photons with high-frequency radio GPs from the Crab pulsar 5
Fig. 4.— Left: cumulative peak flux distribution of GPs (MP and IP together) for different observing sessions and 2 subsessions of
Sep25withapparentlydifferentGPrates. Poissonerrorsarealsoshown. Right: χ2valuesversustheRISSdampingcoefficient,k,foreach
observingsession.
day variation of the GP rate (see Fig. 2). Also, for the
TABLE 2
longest,4-hsession,note the change ofGP rate between RISScorrection coefficients k foreachobserving session.
two 2-h scans in Fig. 2 (observing settings were the
same for both scans). Session RISScorrectioncoefficient k χ2min
Following Cordes et al. (2004), for calculating the Sep12 6.4 3.1
Sep14 2.2 21.7
diffractive interstellar scintillation timescale, τ , we
DISS Sep16 7.2 4.7
adopted the thin screen model with a Kolmogorovspec-
Sep19 1.4 3.8
trum of irregularities and reference pulse broadening
Sep20 2.7 3.9
time τ = 0.5ms at 0.3GHz. At 8.9GHz, with band-
d Sep21 8.5 3.3
width of 800MHz, this gives us a scintillation strength Sep22 3.4 6.6
u = 8.9, well into the strong scintillaton regime, and Sep23 1.3 4.8
τ =τ /u2 9min. Sep24 7.7 2.5
DISS RISS
≃
The variation of the GP rate within each observing Sep25/1 5.0 2.0
subsession was estimated by autocorrelating the rate of Sep25/2 1.0 0.0
GP emission in 10-second bins. The autocorrelation Sep28 8.5 1.7
analysisshowstwoshorterGPratevariabilitytimescales Oct25 2.5 5.2
of 20 minutes and 2 4 minutes. Both of them agree
∼ −
fairlywellwiththe DISS estimations,consideringallthe stead, we compared the intensity distributions of GPs
uncertaintyinthescintillationparameters. Ontheother between sessions. If the change in rate and mean inten-
hand,thereisnoevidenceagainstthe hypothesisthatat sity of GPs on timescales of a few hours is due to RISS,
least one of these timescales is due to intrinsic GP rate thenthepeakintensity distributionsforeachdayshould
variability. have the same shape, but with different values of peak
The following analysis assumes that observed day-to- flux density. The distributions in Fig. 4 (left) show that
day variation (or, in case of Sep 25, variation between 2 this assumption is basically correct.
subsessions) of the GP rate and mean intensity is caused As the reference session, we picked the one with the
by RISS. If intrinsic GP rate and mean intensity are highest rate of GPs, the second subsession of Sep 25
constant on timescales larger than 90min, then it is rel- (from now on called “0925/2” or “reference session”).
atively easy to make a GP sample corrected for refrac- For each day and for the two subsessions on Sep 25 sep-
tive scintillation. We accomplish this by estimating the arately, we determined the RISS damping coefficient, k,
amount of RISS intensity damping on each observation by minimizing χ2:
session with respect to the session with the highest GP
rate. Then, we multiplied the intensities of all pulses in 1 [N (I ) N(I /k)]2
each separate session by those amounts, and threw out χ2k = N 1X ref σi2− i , (1)
allGPsbelowathreshold,commonforthecorrectedGPs bins− Ii N(Ii/k)
over all sessions.
where N(I ) is the number of GPs with peak intensity
i
A simple way to calculate the intensity variation due
higher than I , per hour of observation. N is the
i bins
to RISS would be by comparing mean profiles of pulsed
numberofbins inthe distributions being compared,and
emission accumulated during each session. However, at
these frequencies, our observations were not sensitive σN(Ii/k) = pN(Ii/k)/Thrs is the Poisson error in each
bin if T is the duration of the session in hours and
enough to accumulate the normal Crab pulse profile ex- hrs
assuming that the energy of each GP does not depend
cept on one or two sessions where scintillations caused
on the energy of the preceding one.
a boosting of the average flux density of the pulsar. In-
Theχ2 curvesareplottedinFig.4(right). Allbutone
k
6 A. V. Bilous et al.
Fig.5.— The distribution of time lags between GPs and γ-ray photons for 2-min bins, for all GPs > 8.1Jy (21000 GPs; left) and the
RISS-corrected GPs (180 GPs; right). Real Fermi photons (blue line) are contrasted to the mean and 95% percentile on the pool of
simulated data sets (grey and black). The fact that the distribution for the real data lies within 95% of the simulated ones indicates no
apparentchangeinGPgenerationrateon2-mintimescalewithanypossibletimelagupto 40minuteswithrespecttotheγ-rayphotons.
The maximum lag value, 40min, corresponds to the size of the largest GTI window. All±other bin widths (down to 10s) give the same
result.
haveasharpminimumofχ2 .10,indicatingreasonable (see 5.2). When we simulated zero flux from the Crab
k
fits, at ks between 1 and 10. The only outlier is the pulsar, we simply removed the pulsar from the list of
session of Sep 14th, with χ2 = 21.7, which has an simulated sources.
min
abnormal excess of intrinsically strong GPs (see Fig. 2). We modeled the Crab Nebula as a point source (for
These GPs do not exhibit any other peculiar properties, theenergyrangesinquestionitsangulardiameterisless
other than relatively high peak flux density. than the Fermi region of interest), with the spectrum
Both RISS coefficients and the corresponding χ2 as determined in Abdo et al. (2010) and integral flux
min
for each day are listed in Table 2. We corrected the above 100 MeV of 9.8 10−7cm−2s−1. For the Galactic
session GPs by multiplying their flux densities by k andextragalacticback×groundsweusedthe“GalacticDif-
and set the intensity threshold for corrected pulses as fuse v02”and “IsotropicDiffuse v02” models. The simu-
8.1Jy max(k)=69Jy (8.1Jy was our initial threshold, latedphoton files were processedin the same wayas the
×
see Section 2). real data.
Thus, we effectively selected only those pulses which
5.1. Is GP rate correlated with single γ-ray photons?
would have had peak flux density larger than 8.1Jy
if they were observed during the session with highest To test if γ-ray photons are correlated with the GP
RISS damping. Our uniformsample ofsuchintrinsically generation rate, we calculated the distribution of time
brightest pulses numbered 180 GPs with TOAs within lags between each photon and all GPs in that photon’s
the Fermi observing time. GTI. The same procedure was applied to the simulated
γ-raydata sets, such that if there were any clustering of
5. CORRELATIONANALYSIS
GPs around γ-ray photons (or with some time lag with
The correlationanalysisfocused on two distinct tasks. respect to the γ-ray photons), it would be seen as a dis-
The first one aimed to probe if the GP generation rate crepancy between the real and simulated distributions
correlates with observed γ-ray photons. For the second, of the high-energy data. Changing the bin size of the
we investigated the hypothesis of Lyutikov (2007) that distribution makes it sensitive to different timescales of
the γ-ray photon flux increases during GPs. For both possible clustering of GPs. In this study, we tried a set
cases, we used simulated high-energy data sets with no of bin widths, starting from 10 seconds and increasing
assumedintrinsiccorrelationbetweentheGPsandγ-ray the width by 10 seconds up to 2 minutes. Two minutes
photonstotestthe statisticallevelofcorrelationpresent corresponds to the smallest timescale of GP clumping
in the real data. (likely caused by interstellar scintillation), as shown in
The simulations used the gtobssim software from the Fig. 2. On timescales less than 10s, the Poisson noise
Fermi tools package. We used the latest version of in- due to a discrete number of time lag measurements be-
strument response function, Pass6 v3 together with the comestoohigh. Weperformed1000simulationrunsand
same spacecraft/pulsar ephemeris as in real data analy- contrasted the real-data distribution with the mean and
sis. 95% percentile of all of the simulated data sets.
We simulatedthepulsarusingthe PulsarSpectrumli- Fig.5showsthedistributionoftimelagsbetweenGPs
brary, with the light curve, spectrum and integral flux andphotonsforallGPsandforaRISS-correctedsample
above 100MeV taken from Abdo et al. (2010). The in- of GPs for one particular bin width, namely, 2min. In
tegralflux was set to F =2.09 10−6cm−2s−1 for the both cases the real data set lies all within the 95% per-
av
×
burst correlationanalysisand varied from0 up to about centileofthe simulations,indicatingno apparentchange
a hundred F for the single-pulse correlation analysis inGPgenerationrateon2-mintimescaleswithanypossi-
av
Correlation of Fermi photons with high-frequency radio GPs from the Crab pulsar 7
bletime lagwithin 40minutes (maximumGTI length) of p due to limited numbers of simulations performed.
±
ofthe arrivalofthe γ-rayphotons. All otherbin widths, However, there is another major source of uncer-
down to 10s, gave the same result. tainty connected to the fact that we record discrete
number of photons around the GPs. Since photon
5.2. Does γ-ray flux change around single GPs? detection is very well described as a Poisson process
(Ramanamurthy & Thompson 1998), the error on de-
Another question of interest is whether the averageγ-
tecting N photons in a certain window around GPs will
rayfluxfromtheCrabpulsarincreasesduringindividual
giant pulses, as predicted by Lyutikov (2007). To inves- be√N. Inourcase,forallwindowswehadN =1,soto
tigate that, we looked for the number of γ-ray photons estimate the true value of the likelihood we should take
in on-pulse emission windows around each GP. We per- into consideration also the likelihood curves for N = 0
formedaseparatesearchforallGPs,lookingforphotons and N =2. These estimates for both windows are plot-
inalargewindowconsistingofthemainpulse,interpulse ted in Fig. 6, left. The shaded region around each curve
andbridgebetweenthem,andalsoforIPGPsonly,limit- corresponds to σp, calculated by the above formula.
±
ingthecorrelationwindowtotheinterpulsephaserange. For both correlation windows N = 1 likelihood curves
If a photon was detected in a window around a GP, have maximum around F0/Fav = 1, which means that,
it was called a “match”. For 10.5 hours of simultaneous mostprobably,pulsedγ-rayflux does notchangeduring
observations,we detected only one suchmatch: aphoton GPs(nocorrelation),orchangesnomorethanfewtimes
withE =403.7MeVwasdetectedwithin1.3msofIPGP (weak correlation).
with peak flux density of 8.9Jy. Nonetheless, knowing Withourlimiteddatasetwecannotsayanythingmore
the observed number of matches N = 1, the probability about the exact value of γ-ray flux during GPs, but we
thatthe γ-rayflux duringGPsis equalto somevalueF can place upper limits on it. On the grid of simulated
0
can be estimated with the simple Bayesianformula: fluxes Fi, one can convert the continuous formula for
posterior probability density (eq. 2) into a discrete one
p(F0) p(N F =F0) for the probability that pulsed flux around GPs is less
p(F =F N)= · | (2)
0| Fmaxp(F ) p(N F =F )dF than F0:
R0 0 · | x x
0.5 (p +p )(F F )
wF0h)eries pth(Fe0l)ikiesltihhoeopdr,ioir.ed.istthreibpurtoiobnabfoilritFy0taongdetp(tNhe|Fob=- P(F ≤F0|N)= ·0P.5F·iP+1(≤pFi0+pii+1)i(+F1i+1−i+1F−i) i ,
servednumberofmatchesN ifthepulsarγ-rayfluxdur- (4)
ing GPs is equal to F0. where pi ≡p(N|F =Fi).
Sincelittleisknownaboutp(F0),thepriordistribution To estimate errors in P(F ≤ F0|N), we assumed that
for F0, we chose the prior to be uniform in a flux range our uncertaintyin pi due to a limited number of trials is
from 0 (the Crab pulsar turns off γ-ray emission during much larger than the error from calculating the integral
GPs) to as a sum. As one can see in Fig. 6, left, this simplifica-
tionisreasonable. Assumingallσ areindependent,the
observing timespan pi
uncertainty in P(F F N) is determined by standard
F F , (3) 0
max av ≤ |
≡ N length of window error propagation.
GP
×
In Fig. 6 we show the resulting probabilities that the
whereF istheaveragepulsedγ-rayfluxfromtheCrab
av γ-rayflux fromthe CrabpulsarduringGPsdoesnotex-
pulsar. F correspondstothehypothesisthatall γ-ray
max ceed a given number of times the mean flux reported by
photonsfromtheCrabpulsarcomeduringGPs. Forour
Abdo et al. (2010). Errors due to the limited number of
choiceofwindows,F rangedfrom60F (foron-pulse
max av simulation runs are plotted as errorbars, whereas those
phase window) to 150 F (for IP window).
av due to a discrete number of GP/photon matches are
Thelikelihoodp(N F =F )wascalculatedbyrunning
| 0 givenby separate posterior probability curves for N =0
simulations with different pulsed flux F and computing
0 and N =2.
the fraction of runs with a number of matches N. The
Obviously, the smaller the correlation window for a
grid of trial flux values, in units of F , was as follows:
av fixed observation timespan and the smaller the number
from 0 to 1 with the step of 0.25, from 1 to 20 with the
of GPs in the sample, the larger F , and the broader
step of 1 or 0.5, and then from 20 to 30 with the step of max
is the resulting posterior probability density. That is
5. Forbothchoicesofcorrelationwindowtheprobability
why for our data setwe could obtainthe posteriorprob-
densitywentdownto0before30F . Hereweimplicitly
av ability densities only for correlation windows which in-
assumedthatahigherfluxoutsideselectedwindowsdoes
cluded the IP, because most of GPs come within this
not influence the correlation within windows.
phase range. For the main pulse GPs, p(F = F N) is
SincethenumberofsimulationrunsforeachtrialF0 is very broad, having almost the same probability d0|ensity
finite, it leads to an uncertainty in estimating the likeli-
up to 100F . For the same reasons, the analysis on
hood. We estimatedthe statisticalerrorsfromthe simu- ∼ av
the sample of GPs corrected for refractive scintillation
lationusingthefollowingmethod. Supposethatforsome
did not give any meaningful results.
value of F we have run n simulations with y successes
0
(i.e. cases where the number of matches in the simula- 6. CONCLUSIONS
tionequalstheoneobtainedforrealdata,N). Theny/n
No obvious correlation was found between Fermi pho-
defines the estimate of probability of success p, which is
tons of energies > 100 MeV and radio giant pulses at
alsothe likelihooddensity p(N F =F ). More precisely,
0 the frequency of 8.9GHz. No change in the Crab GP
|
pyhasaBetadistribution,withmean(y+1)/(n+1)and
generationrate wasfound ontimescalesfrom10 to 120s
|
variance σ2 = (y+1)(n−y+1). We adopted σ as an error around γ-ray photons and with any possible lag within
p (n+3)(n+2)2 p
8 A. V. Bilous et al.
Fig.6.— Left: Likelihood, the probability of observing N photons in a certain window around a GP if the γ-ray flux from the pulsar
inthis window wereF0. Foreach window size, weobservedonlyone suchmatchbetween GP andγ-rayphoton, soN =1. Since photon
arrival times are a Poisson process, the error on N is √N =1, thus likelihood curves for N =0 and N =2 are also shown. The shaded
regionaroundeachcurvecorrespondstouncertainty duetothelimitednumberofsimulationruns(seetextforexplanation). BothN =1
likelihoodcurvespeaknearF0/Fav=1,sonoorweakcorrelationbetween GPsandγ-rayphotons isthemostprobable. Right: Posterior
probability that γ-ray flux in a window around GP is less than F0, given the observed number of matches N. Errors due to the limited
number of simulation runs are plotted as errorbars, whereas those due to a discrete number of matches are given by separate posterior
probabilitycurvesforN =0andN =2. Fav,theaveragepulsedγ-rayfluxfromCrabpulsar,isfromAbdoetal.(2010).
40min with respect to γ-ray photons. tions.
±
With95%probability,thehighenergyfluxoftheCrab Overall,ourresultssuggestthatenhancedpaircreation
pulsar during GPs is less than 4 times the average γ- is not a dominant factor for GP occurrence, at least for
raypulsedfluxfortheon-pulse(MP+IP+bridgebetween high frequency IP GPs. However, our flux increase esti-
them) phase window. For IP GPs only, the 95% upper mations are not on the level of a few percent, as in the
limit on γ-ray flux in the IP phase window is 12 times work of Shearer et al. (2003) at optical wavelengths. To
the average pulsed flux. If we consider the uncertainty reachthatsensitivityweneedmoredata,whichwillhelp
duetodiscretenumbersofmatchesbetweenphotonsand push down the upper limit on flux during GPs and will
GPs, the 95% upper limits are 3 5.5 times the average make possible the analysis on subsamples of GPs, such
−
pulsedfluxforthepulsedemissionwindow,and8 16for as the brightest ones. Also, including radio frequencies
−
the IP window. below4GHz is potentially interestingnot onlyfor inves-
A few explanations may be offered for the non- tigatingthecorrelationforMPGPsseparately(MPGPs
detection of GP-γ-photon correlations. The most natu- are much more common at lower frequencies), but also
ralis that productionof GPs depends onnon-stationary forre-doingthe analysisfor low-frequencyIP GPs,since
changingcoherenceconditions,whichvarybyalargede- they might be generated by different physical processes
gree even for similar magnetospheric particle densities. thanthehigh-frequencyIPGPs(Moffett1997). Allthese
Another possibility is that beaming in radio and at high questions are being investigated with our ongoing radio
energies are somewhat different, so that simultaneous observationcampaignusingthe42-fttelescopeattheJo-
GPs and γ-ray photons are emitted in different direc- drellBankObservatory(UK)andthe140-fttelescopeat
Correlation of Fermi photons with high-frequency radio GPs from the Crab pulsar 9
the Green Bank Observatory (WV). M. A. McLaughlinis anAdjunct Astronomer atthe Na-
tionalRadioAstronomyObservatoryandissupportedby
a Cottrell Fellowship, a SloanFellowship, and a WVEP-
SCOR Research Challenge Grant. A. V. Bilous thanks
The NationalRadio AstronomyObservatoryis a facil- T. T. Pennucci (UVa) for the useful comments on the
ity of the National Science Foundation operated under paper draft.
cooperative agreement by Associated Universities, Inc.
ThisworkwassupportedbyFermi grantNNX10AD14G.
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