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Proceedingsofthe363.WE-HeraeusSeminaron:“NeutronStars and Pulsars”(Postersand contributedtalks) Physikzentrum BadHonnef, Germany,May.14−19,2006, eds.W.Becker,H.H.Huang, MPEReport291,pp.112-115 Radio Emission Physics in the Crab Pulsar J. A. Eilek and T. H. Hankins New Mexico Tech, Socorro NM87801, USA 7 0 0 2 n Abstract. Our high time resolution observations of in- the IP and MP have very different properties. It seems a dividual giant pulses in the Crab pulsar show that both likely that they differ in their emission mechanisms, their J the time and frequency signatures of the interpulse are propagation within the magnetosphere, or both. 9 distinctly different from those of the main pulse. Gi- ant main pulses can occasionally be resolved into short- 1 2. Giant main pulses: strong plasma turbulence lived, relatively narrow-bandnanoshots.We believe these v 2 nanoshots are produced by soliton collapse in strong We initially studied the MP at nanosecond time reso- 5 plasma turbulence. Giant interpulses are very different. lution, because it is usually brighter, and because giant 2 Their dynamic spectrum contains narrow, microsecond- pulses are more common at the rotationphase of the MP 1 long emission bands. We have detected these proportion- (Cordesetal.2004).Wefoundthatmostgiantmainpulses 0 ately spacedbands from4.5 to 10.5GHz. The bands can- 7 (GMPs)consistofonetoseveral“microbursts”,eachlast- 0 not easily be explained by any current theory of pulsar ing a few microseconds at 5 GHz (HKWE). We recently h/ radio emission; we speculate on possible new models. extended our observations to higher frequencies, where 2 p GHz of bandwidth is available at Arecibo. We found the - temporal structure of GMPs is the same at higher fre- o quencies, although the microburst duration is typically r 1. Introduction t shorter than at 5 GHz. Figure 1 shows a typical exam- s a What is the pulsar radio emission mechanism? Does the ple. The dynamic spectrum of the microbursts turns out : v same mechanism always operate? Three types of models to be broadband, filling our entire observing bandwidth. i havebeenproposedtoexplaintheradioemission:coherent An occasional MP, however, contains much shorter, rel- X charge bunches, plasma masers and strong plasma turbu- atively narrow-band, “nanoshots” (HKWE; also Figures r a lence (e.g., Hankins et al. 2003,“HKWE”). Because each 2 and 3). Most of the time the nanoshots overlap, which model makes different predictions for the time signature is consistent with previous modelling of pulsar emission ofthe emission,ourgrouphascarriedout ultra-hightime as amplitude-modulated noise; but in sparse GMPs the resolution observations in order to compare the observed nanoshots can sometimes be individually resolved. time signatures to those predicted by the models. We used simple scaling arguments, and numerical We have focused on the Crab nebula pulsar, because simulations from Weatherall (1998), to compare the its occasional, very strong giant pulses are ideal targets nanoshots to predictions of the three competing theoret- for our observations. The dominant features of this star’s ical models of the radio emission mechanisms. The time meanprofileareamainpulse(MP)andaninterpulse(IP). signature of the nanoshots disagrees with predictions of Although the relative amplitudes and detailed profiles of themaserandchargebunchingmodels;butboththetime these features change with frequency, they can be identi- andfrequency signaturesareconsistentwith Weatherall’s fied from low radio frequencies ( < 300 MHz) up to the numerical models of plasma emission by soliton collapse optical and hard X-ray bands (M∼offet & Hankins 1996). instrongplasmaturbulence.Hismodels predictnanoshot Some models suggest that the MP and IP come from low durations at frequency ν to be νδt O(10); an individ- ∼ altitudes,abovethestar’stwomagneticpoles.Othermod- ual nanoshot is relatively narrow-band, δν/ν O(0.1). ∼ els suggest they come from higher altitudes, possibly rel- In HKWE we suggested, based on the time signature of ativistic caustics (Dyks et al. 2004) which connect to the the nanoshots,that strongplasmaturbulence is the emis- two poles. In either case, the physical conditions in the sion mechanism in GMPs. The time and spectral signa- emission region should be similar, and one would expect tures of the nanoshots in our recent high-frequency work the same radio emission mechanism to be active in the are also consistent with these models. We thus propose IP andthe MP.We weresurprised,therefore,to findthat that microbursts in giant main pulses are collections of J. A. Eilek & T. H.Hankins: Radio Emission Physics in the Crab Pulsar 113 Fig.1. Total intensity and dynamic spectrum of a giant Fig.3.A shortportionofthe sparsemainpulse shownin main pulse, observed at Arecibo and coherently dedis- Figure 2, with total intensity displayed at our maximum persed. As is typical of most GMPs, it contains several time resolution, 0.4 ns. This reveals the temporal signa- broad-band microbursts. The total intensity is plotted ture of individual nanoshots. We believe the nanoshots with 6.4-ns time resolution; the dynamic spectrum has arecreatedbycollapseofsolitonsinstrongplasmaturbu- 25.6-ns time resolution and 19.5-MHz frequency resolu- lence. The dynamic spectralresolutionis 78 MHz and 6.4 tion. ns. nanoshots, produced by strong plasma turbulence in the alsoKunzlet al.1998).Wefindthatlowradiofrequencies emission region. come from densities too low to match the GJ value any- whereinthemagnetosphere.Becausetheemittingplasma feels anunshieldedEfield,andfeeds backonthatfieldas its charge density fluctuates, we expect unsteady plasma flow (and consequently unsteady radio emission). 3. Giant interpulses: emission bands In order to test our hypothesis that strong plasma turbulence governs the emission physics in the Crab pulsar, we went to higher frequencies to get a larger bandwidth andshortertimeresolution.InadditiontotheMP,weob- served giant pulses from the IP, because at high frequencies giant pulses are more common at the rotation phase of the IP.When we usedthe method describedin HWKE to observe giant interpulses (GIPs) with a broad band- Fig.2.Anothergiantmainpulse,processedanddisplayed width, from 6-8 or 8-10 GHz, we were astonished to find the same as in Figure 1, in which the microbursts are that GIPs have very different properties from giant main sparse and short-lived. At higher time resolution some of pulses.GIPsdifferfromGMPsintimesignature,polariza- these bursts can be resolved into even shorter nanoshots, tion, dispersion and spectral properties. In this paper we as in Figure 3. Note the relatively narrow-bandnature of summarize our new results; we will present more details individual nanoshots. We infer that the longer-duration, in a forthcoming paper (Hankins & Eilek 2007). broad-band microbursts, such as those in Figure 1, are “clouds” of these nanoshots. 3.1. Emission bands in the interpulse If our suggestion is correct, it has one important con- The most striking difference between the IP and the MP sequence.Plasmaflowinthe radioemissionregionshould is found in the dynamic spectrum. A giant IP contains be highly dynamic. The plasma flow will be smooth only microsecond-long trains of emission bands, as illustrated if the local charge density is exactly the Goldreich-Julian in Figures 4 and 5. The bands are grouped into regular (GJ)value,sothattherotation-inducedelectricfield,E,is “sets”; 2 or 3 band sets can usually be identified in a fully shielded. Because plasma turbulent emission is cen- givenIP.Individualbandsetslastafewµs.Insomepulses tered on the comoving plasma frequency (νp √γbn, for new band sets turn on partway through the pulse, often ∝ number density n andbulk Lorentzfactor γ ), we cande- coincidentwithasecondaryburstoftotalintensity.Every b termine the local density in the radio emission region(cf. giant interpulse we recorded between 4.5 and 10.5 GHz, 114 J. A. Eilek & T. H.Hankins: Radio Emission Physics in the Crab Pulsar during20observingdaysfrom2004to2006,displaysthese emission bands. However, giant main pulses observed at the same time and processed identically do not show the bands. The bands are, therefore, not due to instrumental or interstellar effects, but are intrinsic to the star. Fig.5. Another giant interpulse, observed on the same day as the IP in Figure 4 and processed and displayed in the same way. Four emission band sets can be identified, including a set which coincides with the second microburst near 2µs, and another which coincides with a third microburst near 4µs. This example also shows the characteristic band drift to higher frequencies. Fig.4. A giantinterpulse fromthe Crabpulsar,observed andprocessedinexactly the samewayasthe mainpulses inFigures1through3.Totalintensitytimeresolution25.6 3.2. Possible causes of the emission bands ns; dynamic spectral resolution 19.5 MHz and 25.6 ns. The dynamic spectrum of the giant interpulses does not Thebandedfrequencystructureinthe dynamicspectrum matchanyofthethreetypesofemissionmodelsdescribed occurs in every IP we have recordedabove5 GHz. In this above. Because each of the models predicts narrow-band example,twobandsetscanbeidentified,startingat1µs, emission at the plasma frequency, none of them can ex- eachcontaining four bright bands;a third band set starts plain the dynamic spectrum of the IP. A new approach is near 2 µs. Note the apparent drift to higher frequencies required here, which may “push the envelope” of pulsar for each band set. radio emission models. While we remain perplexed by the dramatic dynamic At first glance the bands appear to be uniformly spectrumoftheinterpulse,weareexploringpossiblemod- spaced.However,closerinspection ofourdata showsthat els. This exerciseis made particularlydifficult by the fact the bands are proportionally spaced. The spacing between thattheemissionbandsarenotregularlyspaced.Because two adjacent bands, at ν1 and ν2, depends on the mean of this, models that initially seemed attractive must be frequency, as ∆ν/ν = 2(ν2 ν1)/(ν2+ν1) 0.06. Thus, rejected. As an example, if the emission bands were uni- − ≃ two bands near 6 GHz are spaced by 360 MHz; two formlyspacedtheycouldbethespectralrepresentationof ∼ bands near 10 GHz are spaced by 600 MHz. This pro- aregularemissionpulsetrain.Manyauthorshaveinvoked ∼ portional spacing is robust; a set of emission bands can regularly spaced plasma structures (sparks or filaments), drift in frequency (usually upwards, as in Figures 3 and whose passage across the line of sight could create such 4), but their frequency spacing stays constant. All bands a pulse train. Alternatively, strong plasma waves with a inaparticularsetappearalmostsimultaneously,towithin characteristicfrequencywillalsocreatearegularemission 0.1µs; they must all come from a region no larger than pulsetrain.Thedynamicspectrumofeitherofthesemod- ∼ 30 m across. els wouldcontainemissionbands atconstantspacing;the ∼ We suspectthe bands extend overatleasta 5 6GHz proportional spacing we observe disproves both of these − range in a single GIP, but do not occur below 4 GHz. hypotheses. ∼ While wehavenotbeenable to observemore than2GHz We have looked to solar physics for insight. We ini- simultaneously, we have seen no evidence that a given tially remembered split bands in the dynamic spectra of band set cuts off within our observable bandwidth. The TypeIIsolarflares,whicharethoughttobeplasmaemis- characteristics of the bands (proportional spacing, dura- sion from low and high density regions associated with a tion, onset relative to total intensity microbursts) are un- shockpropagatingthroughthesolarcorona.Thisdoesnot changedfrom5to10GHz.Inaddition,therotationphase seemtobehelpfulfortheCrabpulsaremissionbands,be- of the high-frequency IP is slightly shifted relative to the cause the radio-loud plasma would have to contain 10 or low-frequency IP (Moffett & Hankins 1996). This phase 15 different density stratifications, which seems unlikely. offsetsuggeststhat the bands do notcontinue to frequen- However,“zebra bands” seen in Type IV solar flares may cies below 4GHz. be germane. These are parallel, drifting, narrow emission ∼ J. A. Eilek & T. H.Hankins: Radio Emission Physics in the Crab Pulsar 115 bandsseeninthedynamicspectraofTypeIVflares.Band Geometrical models also need an underlying broad- sets containing from a few up to 30 bands have been band radiation source, with at least 5 GHz bandwidth, ∼ reported, with fractional spacing ∆ν/ν .01 .03 (e.g., in order to produce the emission bands we observe. Be- ∼ − Chernovetal.2005).Whilezebrabandshavenotyetbeen cause standard pulsar radio emission mechanisms lead to satisfactorily explained, two classes of models have been relatively narrow-band radiation, at the local plasma fre- proposed,invokingeitherresonantplasmaemissionorge- quency, they seem unlikely to work here. A double layer ometricaleffects.Cansimilarmodelsexplaintheemission might be the radiation source; charges accelerated within bands in the Crab pulsar? thelayershouldradiatebroadband,uptoν L/2πc,ifL ∼ is the thickness of the accelerationregionwithin the dou- Resonantcyclotronemission.Onepossibilityisplasma ble layer. Once again this is a small-scale effect; emission emissionatthecyclotronresonance,ω k v sΩ /γ =0 k k o − − at 10 GHz requires L 1 cm. (where γ is the particle Lorentz factor,Ω =eB/mc, and o ∼ s is the integer harmonic number). Kazbegi et al. (1991) proposedthatthis resonanceoperatesathighaltitudes in 4. Final thoughts the pulsar magnetosphere, and generates X mode waves Ourhightimeresolutionobservationsofgiantpulsesfrom whichcanescapetheplasmadirectly.Alternatively,“dou- the Crab pulsar have raised as many questions as they ble resonant” cyclotron emission at the plasma resonant have answered. The time and frequency signatures of gi- frequencyhasbeenproposedforsolarflares(e.g.,Winglee antmainpulsesareconsistentwithpredictionsofonecur- & Dulk 1986). In solar conditions, this resonance gener- rentmodelofpulsarradioemission,namely,strongplasma ates O mode waves,which must mode convertin order to turbulence. However, the time and frequency signatures escape the plasma. The emission frequency in these mod- of giant interpulses are totally different, and do not seem els is determined by local conditions where the resonance to match the predictions of any current model. This re- is satisfied; the band separation is ∆ν Ω /2πγ. o ≃ sult is especially surprisingbecause magnetosphericmod- Resonant emission models face several challenges be- els generally ascribe the main pulse and the interpulse to foretheycanbe consideredsuccessful.The emissionmust physically similar regions, which simply happen to be on occur at high altitudes, in order to bring the resonant opposite sides ofthe star.One importantclue maybe the (cyclotron) frequency down to the radio band. Close to offset in rotation phase between the high-radio-frequency the light cylinder, where B 3 105G, particle energies ∼ × interpulse, and the interpulse which is seen at low radio γ 103 104 are needed. In addition, such models must ∼ − frequencies andalsoin opticaland X-raybands.Does the be developed with specific calculations which address the high-frequency interpulse originatein anunexpected part fundamentalplasmamodesaswellastheirstability,under of the star’s magnetosphere,where different physicalcon- conditions likely to exist at high altitudes in the pulsar’s ditions produce such different radiation signatures? magnetosphere. It is not clear how the specific, propor- tionalbandspacingcanbeexplained;perhapsalocalgra- Acknowledgements. We appreciate helpful conversations with dient in the magnetic field must be invoked. Joe Borovsky, Alice Harding, Axel Jessner, Jan Kuijpers, Geometrical models. Alternatively, the striking regu- MaximLyutikov,andthemembersoftheSocorropulsargroup. larity of the bands calls to mind a special geometry. If This work was partially supported by the National Science Foundation, through grant AST0139641 and through a coop- some mechanism splits the emission beam coherently, so erative agreement with Cornell to operate the Arecibo Obser- that it interferes with itself, the bands could be interfer- vatory. ence fringes. For instance, a downwards beam which re- flects off a high density region could return and interfere with its upwards counterparton the way back up. Simple References geometrysuggeststhatfringesoccurifthetwopathsdiffer Chernov,G.P.,Yan,Y.H.,Fu,Q.J.&Tah,Ch.M.,2005,A&A, in length by only c/∆ν < 1m. Another geometrical possi- 437, 1047 bility is that cavities fo∼rm in the plasma and trap some Cordes,J.M.,Bhat,N.D.R.,Hankins,T.H.,McLaughlin,M.A. of the emitted radiation, imposing a discrete frequency & Kern, J., 2004, ApJ,612, 375 structure in the plasma (e.g., LaBelle et al. 2003 for solar Dyks,J., Harding, A.K.& Rudak,B., 2004, ApJ,606, 1125 zebra bands). 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