Strong and weak pulsar radio emission due to thunderstorms and raindrops of particles in the magnetosphere
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The document reports the detection of sporadic dwarf pulses from the pulsar PSR B2111+46 using the Five-Hundred-Meter Aperture Spherical radio Telescope (FAST). Detailed analysis of these dwarf pulses, which occur in the pulsar's nulling state, provides insights into pulsar nulling and magnetosphere processes. The dwarf pulses have much lower energies than normal pulses and consist of only one or a few narrow emission components. Polarization measurements indicate the dwarf pulses follow the average polarization angle curve of normal pulses, suggesting no change in the magnetic field structure between emission states.
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Strong and weak pulsar radio emission due to thunderstorms and raindrops of particles in the magnetosphere
- 1. Nature Astronomy natureastronomy https://doi.org/10.1038/s41550-023-02056-z Article Strongandweakpulsarradioemissiondueto thunderstormsandraindropsofparticlesin themagnetosphere X. Chen1,2 , Y. Yan1,2 , J. L. Han 1,2,3 , C. Wang1,2,3 , P. F. Wang1,2,3 , W. C. Jing 1,2 , K. J. Lee 4,5 , B. Zhang 6,7 , R. X. Xu4,5 , T. Wang 1,2 , Z. L. Yang 1,2 , W. Q. Su1,2 , N. N. Cai1,2 , W. Y. Wang2,4,5 , G. J. Qiao2,4 , J. Xu1,3 & D. J. Zhou 1,2 Pulsarsradiateradiosignalswhentheyrotate.However,someold pulsars oftenstopradiatingforsomeperiods.Theunderlyingmechanismremains unknown,asthemagnetosphereduringnullingphasesishardtoprobedue totheabsenceofemissionmeasurements.Herewereportthedetection andaccuratepolarizationmeasurementsofsporadic,weak,narrowdwarf pulsesdetectedintheordinarynullingstateofpulsarB2111+46viathe Five-Hundred-MeterApertureSphericalradioTelescope.Furtheranalysis showsthattheirpolarizationanglesfollowtheaveragepolarization anglecurveofnormalpulses,suggestingnochangeofthemagnetic-field structureintheemissionregioninthetwoemissionstates.Whereasradio emissionofnormalindividualpulsesisradiatedbya‘thunderstorm’of particlesproducedbycopiousdischargesinregularlyformedgaps,dwarf pulsesareproducedbyoneorafew‘raindrops’ofparticlesgeneratedbypair productioninafragilegapofthisnear-deathpulsar. Howandwhypulsarsradiatehasremainedelusivesincetheirdiscovery over 50 years ago. In general, a pulsar radiates pulses continuously in every rotation period. The averaged pulse profiles often occupy a small fraction of the rotation longitude, which defines the emission window1 .Analysisofthepulsepolarizationpropertiessuggestedthat radio emission is generated by highly relativistic particles streaming in the open magnetic-field lines footed on the polar cap2,3 , and the polarization angles reflect the magnetic-field geometry of the emis- sion region sweeping across the line of sight4 . Although the averaged pulse profile of a pulsar is generally stable, individual pulses in each periodshowdiversevariations.Somerelativelyoldpulsarsoftencease radiating for some periods, which is called ‘nulling’5,6 . The magnetosphere of an active pulsar is believed to be filled with a continuously replenished electron–positron plasma7 . Recent particle-in-cellsimulations8–11 haveshownthatgaps,electricdischarge andpairproductioncanoccurinseveralpreferableregionsinthepul- sarmagnetosphere.Radioemissionofapulsarcanquenchduetotwo possibilities.Thefirstisthestandardpictureofpaircascadedepletion due to the inadequate electric potential in the gap. The second is that agapisfloodedbyapairplasmaproducedandinjectedfromelsewhere inthemagnetosphere.Themagnetosphereshouldbeinaverydifferent physical state when the emission ceases. A clear hint comes from the much smaller spin-down rates of a few pulsars12–14 during their long-term nulling state, compared with those in the emission-on state, indicating an interplay between the pulsar braking and outer-flowing particles in the magnetosphere. However, it is almost impossible to probe the magnetosphere state when emission completelyceases. Received: 15 September 2022 Accepted: 14 June 2023 Published online: xx xx xxxx Check for updates 1 National Astronomical Observatories, Chinese Academy of Sciences, Beijing, China. 2 School of Astronomy and Space Sciences, University of Chinese Academy of Sciences, Beijing, China. 3 CAS Key laboratory of FAST, National Astronomical Observatories, Chinese Academy of Sciences, Beijing, China. 4 Department of Astronomy, Peking University, Beijing, China. 5 Kavli Institute for Astronomy and Astrophysics, Peking University, Beijing, China. 6 Nevada Center for Astrophysics, University of Nevada, Las Vegas, NV, USA. 7 Department of Physics and Astronomy, University of Nevada, Las Vegas, NV, USA. e-mail: hjl@bao.ac.cn
- 2. Nature Astronomy Article https://doi.org/10.1038/s41550-023-02056-z interference (RFI) is removed and the data are calibrated, the polari- zation profiles for each individual period and the mean profiles for each session are obtained (Fig. 1 and Extended Data Figs. 1–4). Owing to the high sensitivity of FAST, we detected a large number of dwarf pulses(Fig.1andExtendedDataFigs.1–5)emergingoccasionallyfrom ordinarynullingperiods,andtheirpolarizationpropertiesarealsowell measured. Such dwarf pulses are rare, and only a few have previously beendetectedfromPSR J1107−590722 ,andnofurtherinformationwas previously available for further physical studies. The dwarf pulses of PSR B2111+46 are generally undetectable in low-sensitivity and/or low time-resolution observations, and hence these periods with dwarf pulses are usually thought to be in the nulling state. Therefore, these distinctive dwarf pulses are nice probes for physical processes and the emission region in most asymptotic quenched states of the magnetosphere. DwarfpulsesofPSR B2111+46distinguishthemselvesfromnormal pulsesbytheirdistinctlysmallenergies(Fig.2).Formanypulsars,the energydistributionofindividualpulsesfollowsalog-normaldistribu- tion23 . The emission of PSR B2111+46 in the normal state also follows suchadistribution.However,thedwarfpulseswedetectareveryweak andnarrow.Therefore,theyarefarawayfromthenormalpulseenergy distribution(Fig.3).Insharpcontrasttothegiantpulsesobservedfrom someyoungpulsars,mostdwarfpulseshavelowerpeakfluxdensities thanregularpulses,whilegiantpulseshavefluxdensitiestypicallymore thanoneorderofmagnitudehigherthannormalpulses23,24 . In addition to small energies, the dwarf pulses detected from PSR B2111+46 have very narrow pulse widths (see the distribution of WinFig.3).Withasamplingtimeof49.152 μsforeachdatabinduring observationsofPSR B2111+46,FASTcanmeasuretheradioemissionof We detected a number of sporadic dwarf pulses (Fig. 1), that is, thenarrow,weakpulses,inthemostlyasymptoticemission-quenched stateofPSR B2111+46usingtheFive-Hundred-MeterApertureSpherical radioTelescope(FAST).Detailedanalysesofthesedwarfpulses,suchas theenergydistribution(Fig.2),emergingphaseinrotationlongitudes andthepolarizationproperties,shedlightonthelong-standingenigma of pulsar nulling and mode switching, offering understanding of the physicalprocessesinpulsarmagnetospheres. PSR B2111+46isastrongpulsarwithaperiod15 of1.0146848 sand a dispersion measure of 141.40 rad m−2 , discovered at Jodrell Bank Observatory16 .Itsradioemissionshowstwoknownstates.Inthenormal emissionstate,themeanpulseprofileshowsthreedominantcompo- nents17 : a central core component coming from the emission beam centre and two shoulders from the conal emission. Two additional hidden components were revealed by model fitting18,19 . These promi- nent strong components in total occupy a longitude range of about a quarteroftherotationperiodaccordingtothemeanprofileofprevious observations. Analyses of the polarization profiles suggest that the magneticaxisisclosetotherotationaxis,andthelineofsightcutsthe emissionbeamalongalargearc.Thepulsedemissionisgeneratedfrom aregionatseveralhundredstomorethanathousandkilometresabove the neutron star surface17–19 . The nulling state of PSR B2111+46 is very impressive(ExtendedDataFigs.1–4),whichoccursforabout10–20% of the total periods6,20 depending on the observational frequencies. Intheperiodsofnulling,thepulsarsuddenlybecomesundetectable. PSR B2111+46wasserendipitouslyobservedbyFASTinthreeses- sionsinAugustandSeptember2020(Table1)duringtheFASTGalactic Plane Pulsar Snapshot survey21 , and the verification observations for the dwarf pulses were made in March 2022. After radio frequency 255 a b c d 252 249 246 243 Period number and intensity 240 237 234 231 100 8 March 2022 Period 233 8 March 2022 Period 237 8 March 2022 Period 248 50 0 –90 0 90 PA (°) I/σ bin 50 0 –90 0 90 PA (°) I/σ bin 50 100 0 –90 150 0 90 PA (°) I/σ bin 228 225 –50 0 Longitude (°) 50 –20 –40 0 Longitude (°) 20 40 I L V I L V –20 –40 0 Longitude (°) 20 40 11 12 13 14 Longitude (°) 15 I L V Fig.1|FASTdetectionofadwarfpulseinaseriespulsesofPSR B2111+46. a,AsegmentofpulsetrainsofPSR B2111+46observedinthesessionon8March 2022byFAST,showingsomeemissionandnullingperiods.b–d,Polarization profilesofthreeindividualpulses:period248(b),period237(c)andperiod233 (d).InthelowersubpanelsthetotalintensityI,linearpolarizationLandcircular polarizationV(withpositivevaluesfortheleft-handsense)areplottedinthe originaltimeresolution(49.152 μs)oftheFASTobservations,andthePAsare plottedintheuppersubpanels.Thedwarfpulseintheperiod237hasonlyone resolvedemissioncell,almostfullylinearlypolarizedwithawidthofabout0.1°. Manynotchesoftheothertwopulseprofilesaresensitivesignificantdetection ofrealintensityfluctuationscausedbyemissioncellswithdifferentstrengths. TheerrorbarforPAis±1σ.Theintensityisscaledwiththeoff-pulsefluctuations expressedbyσbin.
- 3. Nature Astronomy Article https://doi.org/10.1038/s41550-023-02056-z morethan8,870samplesinsidetheemissionbeam(seethelongitude rangedefinedbytheprofileinFig.4)ofPSR B2111+46amongthetotal 20,643datapointseveryperiod.Thenormalindividualpulsesmostly havepulsewidthsintherangeof60° < W < 100°withdiverseintensity fluctuationsalonglongitudes,asthoughinthe‘thunderstormmode’, composited by a large number of emission ‘cells’ (see Fig. 1 and also twomoreexamplesinExtendedDataFig.5),whereasthedwarfpulses consist of only one (see period 237 in Fig. 1) or a few resolved peaks (ExtendedDataFig.5)asthoughonlyoneorafewraindropsintheclear sky,witheachelementarypulseabout0.1°(about0.3 ms).Suchatime- scaleismuchshorterthantheclassicsubpulsesbutmuchlongerthan micropulsesthathaveatimescaleofnanosecondsormicroseconds25,26 . Thedwarfpulsescanappearacrossawiderangeofphasesforboththe core and conal components and in between, with a preference in the trailingcomponent(ExtendedDataFig.6). Polarization measurements provide a physical link between the detectedemissionandthemagnetic-fieldlinesintheemissionregion4 . PSR B2111+46 has an S-shape polarization angle (PA) curve for the mean linear polarization profile, which has been used to estimate the emissionheightandsweepbackofmagnetic-fieldlinesforthecentral emission components17 . From our sensitive observations, we found a muchextendedleadingwingandtheorthogonalmodeforweakconal emissionwingsinbothleadingandtrailinglongitudes(Fig.4).Insome periods, radio emission was detected for only one or two of the three main components (Extended Data Figs. 1–4), which corresponds to partial nulling20 . The most intriguing fact is that the PAs of the dwarf a b 140 24 August 2020 26 August 2020 60 40 20 0 0 20 0 25 50 75 100 125 150 E/σE E/σE 0 50 100 150 200 E/σE 0 25 75 50 100 125 150 E/σE 0 25 50 75 100 125 150 E/σE 40 120 100 80 Number Number 60 Number 1,200 1,000 800 600 400 200 0 40 20 0 140 160 120 100 80 Number 60 40 20 0 140 120 100 80 Number 60 40 20 0 c d 60 40 20 0 0 20 E/σE 40 Number 17 September 2020 8 March 2022 80 60 40 20 0 0 20 E/σE 40 Number 1,500 1,000 500 0 0 25 E/σE 75 50 Number Fig.2|Dwarfpulsesdetectedinthenullingperiodswithverylowenergy. a–d,Theenergydistributionof822(a),886(b),885(c)and7,097(d)individual pulsesofPSR B2111+46observedinfourFASTobservationsessions.Thepulse energyE(that,isthefluence)foreveryperiodisthesumoftheenergyofan individualpulseoverthefullpulse-onwindowdefinedbythemeanprofile.To expressthedataqualityoftheobservations,thedistributionisscaledbythe standarddeviationsσE ofthestochasticenergyinthesamesizebutpulse-off window,ratherthantheaveragedenergy〈E〉asinliterature,whichistoohigh forFAST-detecteddwarfpulses.Theemissionstateandthenullstateshowtwo mainpeaksinthehistogram.Theorangepartoverlappingonthenullingstate indicatesdwarfpulses.Thegreencurveisthebestlog-normalfittingforthe normalemissionenergydistribution. Table 1 | Details of FAST observations of PSRB2111+46 Observation date Target name Beam name Offset (′) Observation time (min) Number of periods Number of dwarf periods Number of nulling periods Number of periods removed 24 August 2020 J2113+4642 P1M01 2.2 15 886 11 182 64 26 August 2020 J2113+4645 P1M01 2.4 15 886 7 180 0 17 September 2020 J2114+4655 P1M12 2.4 15 885 8 177 0 8 March 2022 B2111+46 P1M01 0.0 120 7,098 149 1,563 1 The table includes observation date, observation target name, FAST beam name for the pulsar detection, the offset of the pulsar location from the beam centre, observation time, number of pulsar periods, number of periods with dwarf pulses detected, number of nulling periods recognized and number of periods removed due to RFI.
- 4. Nature Astronomy Article https://doi.org/10.1038/s41550-023-02056-z pulses, together with the partially nulling pulses, all nearly follow thePAcurveofthemeanprofileorattherespectiveorthogonalmode (Fig.4).Thedetectionofdwarfpulsesintheordinarynullingstatefrom PSR B2111+46thatstillkeepthesamepolarizationpropertiesasnormal pulsessuggeststhatthemagnetic-fieldconfigurationdoesnotchange atthetransitionphasetothecompletelynullingphase. Howandwherearethesedwarfpulsesgeneratedinsuchordinary nulling periods? Why does the radio emission of PSR B2111+46 often cease?Thenullingstatereflectsadeficitofouter-flowingparticlesfor radiation,orthefailureofthecoherenceconditionforparticles,orthe quenched gaps by flooding pairs formed in other parts in the pulsar magnetosphere.PSR B2111+46hasacharacteristicageof2.25 × 107 yr andasurfacemagneticfieldof8.62 × 1011 Gandislocatedinthedeath valley in the pulsar period and period derivative diagram (i.e. the P– ̇ P diagram in Extended Data Fig. 7). The pair creation of such a pulsar can operate effectively only above the magnetic polar cap9,10 throughtheγ−Bprocesswherethefieldisstrongenough.Forsuchan old pulsar with a weak magnetic field, the gap voltage is often barely enough to ignite electron–positron discharges, so a pulsar may fail toradiatefromtimetotime. Ifdwarfpulsesaregeneratedbyoneorafewraindropsofstream- ingparticlesfromtheotherwisenullingstate,thismeansthatonlyone orafewlightningsigniteabovethepolarcapsothatabarelyformedgap is very quickly discharged. Our observations shown in Fig. 5 indicate that the spectra (i.e. the flux density S changes agaist frequency ν in the form of S ≈ να ) of some distinguishable emission components are variable,withapossiblespectralindexαfrom−5totheunexpected+5, and that the dwarf pulses are more likely to have a reversed spectrum (ExtendedDataFig.8).Normalindividualpulseswithmanydistinguish- able peaks, revealed by the FAST observations in Fig. 1 and Extended Data Fig. 5, indicate that the lightning, pair-creation cascades and relatedphysicalprocessesoccurinaverywideareaofthepolarcap,as though the emission is produced by a thunderstorm of particles. The phase-resolvedspectraaremorelikelytobeflatterorevenreversedin thetwo-sideconalphaseranges(ExtendedDataFig.9). The plasma properties in the magnetosphere can be examined bythepropagationeffects27–29 ,suchasadiabaticwalkingandpolariza- tion limiting radius. The plasma density changes in the nulling state could cause the PA curve to shift to an earlier or later rotation phase withtheextentdependingonthebackgroundplasmapropertiesand magnetic-field strength. The longitude shift of the PA curves of the dwarfpulsesfromthatofthenormalpulsesisfoundtobe−0.77° ± 0.25° (ExtendedDataFig.10)fromourFASTmeasurementsforPSR B2111+46, which is marginally significant and implies not only no change to the magnetic-field configuration in the emission region but also only a slight change or no change (22 ± 7%) of the density of the magneto- spheric background plasma in the nulling state, compared with that forthenormalemissionstate. In addition to PSR B2111+46, dwarf pulses have also been detected from some nearly-nulling periods of several other pulsars by FAST observations, such as PSR J0540+3207, PSR J1851−0053 and PSR J1946+1805.Asmallnumberofnarrowpulsespreviouslydetected a 100 4 4 5 2 0 0 10 20 Partial nulling Normal pulses Dwarf pulses Partial nulling Normal pulses Dwarf pulses 24 August 2020: 640 + 26 August 2020: 706 + 17 September 2020: 708 = 2,054 8 March 2022: 5,534 24 August 2020: 640 + 26 August 2020: 706 + 17 September 2020: 708 = 2,054 8 March 2022: 5,534 80 60 E (Jy ms) 2.0 1.5 1.0 0.5 0 S peak (Jy) 2.0 1.5 1.0 0.5 0 S peak (Jy) 40 20 0 0 20 40 60 W (°) 80 100 0 20 40 60 W (°) 80 100 120 140 0 20 40 60 W (°) 80 100 0 20 40 60 W (°) 80 100 120 140 100 80 60 E (Jy ms) 40 20 0 b c d 4 2 0 0 10 20 4 1 5 6 7 3 2 4 5 3 4 5 6 2 1 4 3 3 5 8 4 Partial nulling Normal pulses Dwarf pulses 0.3 0.2 0.1 0 0 10 20 Partial nulling Normal pulses Dwarf pulses 0.3 0.2 0.1 0 0 10 20 5 6 7 7 5 7 6 3 4 2 5 6 8 9 3 4 4 3 5 7 9 5 3 1 4 2 6 8 7 Fig.3|DwarfpulsesofPSR B2111+46asadistinctpopulationfromthepartial nullingandnormalpulses.Pulsewidthismeasuredatthemostouterprofile atthe3σdetectionlevel.a,b,Pulsefluenceintegratedovereachpulse,E,against pulsewidth,W.Thedensitydistributionofthedataisshownincolourandalso incontoursatlevelsof1/2−n ofthemaximumdensity(n = 1–8).Moresensitive observationson8March2022shownin(b)givealargerwidthrangefornormal pulses.Theinsetsshowthedataislandofdwarfpulsesforclarity.Normalpulses areconcentratedaroundthemainpeak,withafluenceintherangeof10 Jy ms toabout50 Jy msandapulsewidthof60° < W < 100°.Thedwarfpulsesare concentratedonanotherpeak,withafluenceoflessthan1 Jy msandapulse widthoflessthan15°(thatis,40 ms).Inbetweenarepartiallynullingpulses (see‘NullingandPartialNulling’inMethods).c,d,Thesameasinaandbbutfor thepeakfluxdensitySpeak againstthepulsewidthW.a,c,Forindividualpulses obtainedinthethreesessionsin2020.b,d,Forpulsesdetectedinthelonger verificationobservationsessionon8March2022.
- 5. Nature Astronomy Article https://doi.org/10.1038/s41550-023-02056-z from PSR B1237+2530 are similar to the dwarf pulses presented here. Dwarf pulses are probably a common phenomena for old nulling pul- sars,adistinct,veryweak,emissionmode31 standingoutmoreclearly inobservationswithahighersensitivity.Detailedhigh-time-resolution polarizationobservationsofdwarfpulses,asinthispaper,canpromote furtherourunderstandingoftheradiationmechanismofradiopulsars. Methods FAST observations of PSR B2111+46 PSR B2111+46wasserendipitouslydetectedin1ofthe19beamsofthe L-band 19-beam receiver on 24 August, 26 August and 17 September 2020 while FAST was tracking other objects for verification of pulsar candidates from the FAST Galactic Plane Pulsar Snapshot survey21 . Each tracking observation lasted for 15 min (see Table 1 for details), thatis,885/886periodsofPSR B2111+46.On8March2022,thecentral beam of the L-band 19-beam receiver of FAST was focused on PSR B2111+46 for 2 h, without beam offset, to verify the detection of dwarfpulses. Inallobservations,thesignalsfromtheXandYpolarizationchan- nelsintheradiofrequencyrangeof1.0 GHzto1.5 GHzwereamplified and then transferred to the digital room via optical fibres. Radio fre- quencysignalswererecoveredandsampled,andthenchannelizedto 2,048 channels in the digital backend and composited to 4 polariza- tions for each channel, XX, YY and X*Y and XY* (see details in ref. 21). These polarization data were collected every 49.152 μs (the sample rateforthe4polarizationchannels)andrecordedintoasetoffitsfiles. For each session, we have 2 min observations before the session with calibration signals of an amplitude of 1 K switching on–off every 1 s. This part of the data were processed to form a calibration reference file,whichwasusedtocalibratethepolarizationchannels. Dataprocessing The raw data of FAST observations of PSR B2111+46 were all saved in a search mode, with the 4 polarization channels recorded every 49.152 μs. On the basis of the pulsar ephemeris obtained from the Australia Telescope National Facility (ATNF) pulsar catalogue32 , 180 a b c d 120 Dwarf Average PA (°) 60 0 –60 1.0 0.8 0.6 Normalized intensity 0.4 0.2 0 –0.2 –50 –25 0 Longitude (°) 25 50 I L 24 August 2020 N = 2 20 60 120 V 180 120 Dwarf Average PA (°) 60 0 –60 1.0 0.8 0.6 Normalized intensity 0.4 0.2 0 –0.2 –50 –25 0 Longitude (°) 25 50 I L 26 August 2020 N = 2 20 60 120 V 180 120 Dwarf Average PA (°) 60 0 –60 1.0 0.8 0.6 Normalized intensity 0.4 0.2 0 –0.2 –50 –25 0 Longitude (°) 25 50 I L 17 September 2020 N = 2 20 60 120 V 180 120 Dwarf Average PA (°) 60 0 –60 0.02 0.01 Normalized intensity 0 –0.01 –0.02 –100 –75 –50 –25 0 Longitude (°) 25 50 75 I L 8 March 2022 N = 2 20 100 360 V Fig.4|PAdistributionofdwarfpulsescomparedwiththedataofnormal pulses.a–d,ThePAdataofeachbinofdwarfpulses(orange)areplotted againstthoseofnormalpulses(green,darknessscaledtothedatanumberN) andthemeanpolarizationprofilesforthefourFASTobservationsessions: 24August2020(a),26August2020(b),17September2020(c)and8March2022(d). Theorthogonalmodesaremostlypredominantinthewingsoftheconal components.Themagnifiedpolarizationprofilesfor8March2022showthe newlydetectedmuchextendedleadingweakprofilewing.Theerrorbarfor PAis±1σ.Theintensityisscaledwiththepeakvalue.
- 6. Nature Astronomy Article https://doi.org/10.1038/s41550-023-02056-z we processed the pulsar data using the package DSPSR33 . The data were de-dispersed according to the dispersion measure (DM) value DM = 141.26 pc cm−3 initially15 , and were then folded according to the period P = 1.0146848 s. A better DM value DM = 141.378 pc cm−3 was found using our high-time-resolution data for the sharp peaks of individual pulses. The polarization leakages were calibrated34 , and the band distortion was corrected according to the calibration reference file obtained from the 2 min calibration on–off data. Some frequency channels with strong RFI were weighted to zero using the softwarePSRZAP35 .Thepolarizationdatafromallchannelswerethen rotation-measure-correctedaccordingtotheknownrotationmeasure (RM)valueofRM = −218.7 rad m−2 (ref.36)usingthepulsarprocessing program PAM in the package PSRCHIVE35 . After the data from all fre- quencychannelswereintegrated,thefourStokesparameters(I,Q,U,V) were then saved for 512 bins each period for the normal detection of nullingpulses.Wealsodeterminedtheprofileswith1,024,2,048,4,096 and 20,643 bins, and found that those with 512 bins were the best for detectingdwarfpulses. Pulseprofilesandpolarization For each session, the mean profile of PSR B2111+46 was obtained (ExtendedDataFigs.1–4)afterindividualpulsesfromallperiodswere a b c d 1,500 0 5 1,350 1,200 Frequency (MHz) PA (°) Spectral index PA (°) Spectral index PA (°) Spectral index PA (°) Spectral index I/σ bin I/σoff 0 4 I/σoff 0 6 12 I/σoff 0 4 I/σoff 1,050 5 0 –5 60 0 –60 8 March 2022 Period 2,453 50 0 1,500 1,350 1,200 Frequency (MHz) I/σ bin 1,050 3 0 –3 60 0 –60 50 100 0 –40 –20 0 Longitude (°) 20 40 60 –40 –30 Longitude (°) –20 –10 0 V L I 1,500 1,350 1,200 Frequency (MHz) I/σ bin 1,050 3 0 –3 60 0 –60 40 20 0 1,500 1,350 1,200 Frequency (MHz) I/σ bin 1,050 3 0 –3 60 0 –60 40 20 0 8 March 2022 Period 3,766 8 March 2022 Period 237 8 March 2022 Period 369 V L I V L I V L I 12.0 12.5 13.0 Longitude (°) 13.5 14.0 14.5 23 24 Longitude (°) 25 26 27 Fig.5|Phase-resolvedspectralindexfortwoindividualpulsesandtwodwarf pulsesobservedon8March2022byFAST. a–d,Waterfallplotfortheindividual pulseintensityonthephase–frequencyplane(uppersubpanels;thefrequency channelscontainingRFIshavebeenremoved)fortwonormalpulsesinperiod 2453(a)andperiod3766(b)andtwodwarfpulsesinperiod237(c)and369(d), clearlyshowingthevariationofthephase-resolvedspectralindexforindividual pulses(seconduppersubpanels).ThepolarizationprofilesofthepulseandthePA values(green)togetherwiththemeanPAcurve(grey)areplottedinthebottom subpanelsandthesecondbottomsubpanels,respectively.Theobservationdate andtheperiodnumberoftheindividualpulsearemarkedinthebottompanel. ThePAcurvesarefittedwiththerotatingvectormodel2 .TheerrorbarforPAis ±1σ.Theintensityisscaledwiththeoff-pulsefluctuationsexpressedbyσbin.
- 7. Nature Astronomy Article https://doi.org/10.1038/s41550-023-02056-z averaged.Nocleardifferencewasfoundbetweenthethreepolarization profiles(seeFig.4forthe2020sessions)andtheywereconsistentwith theresultsat610 MHzand1,408 MHz(refs.37,38)and1,500 MHz(ref.39) after the opposite definition of circular polarization is considered. However, much more extended profile wings were detected in the targeted verification observations on 8 March 2022 that have a much better sensitivity owing to the targeted good pointing. These results indicate the excellent performance of polarization measurements fortheL-band19-beamreceiver,evenwhentheobjectiswelloffofthe beamcentre.Intheresults,anumberofperiodsoccasionallyhaveRFI (see Table 1) and these were cleaned and marked with a dashed line in thepulsestacksofindividualpulses,suchasperiods683,684,694and 695inthe24August2020session(seeExtendedDataFig.1). The mean pulse profiles show triple components for both cone and core emission, with a strong linear polarization for almost all longitudes except for these in the two edges. The Gaussian fittings to the mean profile always give five components18 . The observations on 8 March 2022 show two highly polarized prefix mean profile com- ponents (Fig. 4), so that the mean profile has a wide longitude range of more than 155°. The reversed sense of circular polarization at the centre of the mean profiles indicates the core nature of the central component37,40 . The PA curves follow an S shape17,39 , which can be well interpreted by the rotating vector model2 . The orthogonal modes of the PA distributions are revealed by our FAST observations from the conalandtwonewlydetectedprefixwingemissioncomponentsshown in Fig. 4. The smoothly changing PA curve extends in the two sides of mean profiles and smoothly varies for more than 220°. Our fitting to the PA curve suggests that PSR B2111+46 is an aligned rotator, that is, with a small inclination angle of only 6.3° between the magnetic axis fromtherotationaxis,andthelineofsightimpactstheradioemission beam only 0.7° below the magnetic axis. The line of sight impacts the emission beam in about 40% of a period, and FAST obtains more than 8,750 independent samples of the emission beam among the 20,643 datapointseveryperiod. The polarization profiles of individual pulses at high-temporal resolution (Extended Data Fig. 5) can reveal many details about emis- sion.OwingtotheextremesensitivityofFASTobservations,individual pulses frequently contain numerous peaks, indicating real variations in emission. These fine subpulses are considered to be elementary emission cells and have a much smaller width than conventional sub- pulses. An example of a highly isolated elementary pulse can be seen in period 237 in Fig. 1, which is a dwarf pulse and exhibits nearly 100% polarization.ThePAsofsuchdwarfpulsesmostlyfollowthePAcurveof meanprofile,asseeninFig.4.ThePAvaluesofmostelementarypulses of normal individual pulses also conform to the PA curve of the mean profile, with deviations occasionally observed at various longitudes, probably owing to the overlaps of orthogonal modes. More intrigu- ing is the sense change of circular polarization for some elementary pulses not near the centre of the core component but in some other longitudes, even of the conal components (for example, periods 700 and 679 in Extended Data Fig. 1, period 354 in Extended Data Fig. 2, period 137 in Extended Data Fig. 3 and period 1,551 in Extended Data Fig.5).Thischallengesthesimplegeometricalexplanationforcircular polarization41–43 . Nullingandpartialnulling Thenullingphenomenonisoftenobservedforpulsarsnearthedeath- lineintheP– ̇ P diagram44,45 .PSR B2111+46islocatedinthedeathvalley (Extended Data Fig. 7). Nulling of PSR B2111+46 has previously been observed, and the nulling fraction is 12.5% at 408 MHz (ref. 6) and increasesto21%at610 MHz(ref.20).ThestatisticsfromTable1forour FASTobservationsgiveanullingfactorofabout20%at1,250 MHz. The nulling fraction varies from component to component20 . Partial nulling of PSR B2111+46 has previously been suggested20 , and our high-quality FAST data clearly manifest the phenomenology (seeexamplesinExtendedDataFigs.1–4).Thepartialnullingphenom- enon means that only one or two mean profile emission components existwithouttheothercomponents.Onthebasisofourverysensitive FAST observations, we find that many individual pulses have normal emission for only one or two components, and clearly lack emission for the other mean profile components, for example, period 679 in Extended Data Fig. 1, periods 365 and 371 in Extended Data Fig. 2 and periods 137 and 140 in Extended Data Fig. 3. These partially nulling pulses, if they appear, have a peak flux density comparable to the normalpulses.ThePAvaluesofeachbinfollowthemeanPAcurvewell. There is no question that partial nulling pulses have a smaller pulse widththannormalpulses,typically10° < W < 60°. Dwarfpulsesandpulseenergydistribution The most fascinating features observed are the ‘dwarf’ pulses, which areweakandnarrowinnature(ExtendedDataFigs.1–4).Thesedwarf pulses appear across a wide range of phases for both the core and conal components and in between, with a preference in the trailing component (as seen in Extended Data Fig. 6). To describe the narrow width of these weak pulses, the pulse width in this study is measured at a level of 3σbin, which is slightly different each period due to differ- entRFIcleaning;therefore,amuchlargerthantraditionalpulsewidth measured at a level of 50% or 10% of the peak, which is suitable for single Gaussian components rather than the complicated combina- tions of many strong and weak pulses for PSR B2111+46. The start and end phases of the on-pulse region are defined as the left-most and right-most sides with three successive data points higher than 3σbin. By counting the consecutive points over 3σbin, we obtain the width of a pulse. It is possible that some narrow pulses have only one or two bins, which are selected as real detection of a pulse only if the peak flux density is larger than 8σbin. Most dwarf pulses can be resolved in high-samplingFASTobservations,asshowninExtendedDataFig.5,and therefore they are composited by a few elementary pulses, probably generated by several ‘raindrops’ of particles streaming in the pulsar magnetosphere,insteadofthe‘thunderstorm’ofparticlesfornormal individualpulsesoverawidelongitude. Incontrasttogiantpulsesdetectedfromsomepulsars23,46 ,which are strong pulses with a few tens or even hundreds times of the peak fluxdensityofnormalpulses,thedwarfpulseshaveapeakfluxdensity that is, in general, much less than that for normal pulses. We checked andfoundthatPSR B2111+46hasnogiantpulses,thatis,anarrowpulse withapeakfluxdensityafewtimeshigherthantheaverage.According toExtendedDataFig.6,mostdwarfpulseshaveapeakfluxdensityless than50 mJy,morethan5timesweakerthantheaveragepeak,exceptfor afewverynarrowpulses(forexample,period237inFig.5)whichhave a high peak. We tried to define the dwarf pulse as a peak flux density lessthan,forexample,20%ofthepeakintheaverageprofile,butfound thatthepeakisbin-numberdependent. When the fluence of an individual pulse is counted by the area underneatheachpulseprofile,thenormalpulseshaveanenergyfollow- ing the log-normal distribution, similar to other pulsars23 . The partial nulling pulses have less energy, mainly because of their lack of some emission components. The dwarf pulses have the smallest energy, as showninFig.2,sotheyarehiddenintheenergydistributionpeaksfor nulling,butdistinctlystandawayfromthelog-normaldistributionof normalpulses.Ifobservationsweremadewithabettersensitivity,that is,withamuchsmallerσE inFig.2,thesedwarfpulseswouldstandout clearly from the histogram peak for nulling periods. Although some dwarf pulses have previously been detected from PSR J1107−590722 , theFASTdatahereforPSR B2111+46showthedwarfpulsesasadistinct population.Theirdistinctivedistributioninthetwo-dimensionalplot of pulse width and pulse energy in Fig. 3 suggest that they belong to a newclassofpulsesfortheweakemissionmode31 . Combining the energy and width information, dwarf pulses have a pulse width narrower than 15° and a fluence E < 2 Jy ms (Fig. 3),
- 8. Nature Astronomy Article https://doi.org/10.1038/s41550-023-02056-z and reside at the lowest ends of the distribution in a separate island from the main pulses. This differs from the general mode-changing pulses23 thathaveasimilarpulse-widthdistributionasthemainpulses or the sparse pulses in the rotating radio transient PSR J0941−3947 and PSR B0826−3448 , which have similar peak flux densities to the normalpulses. Possiblephysicalprocessesfordifferentemissionmodes PSR B2111+46 shows four emission modes: the normal pulse mode consisting of many small, distinct elementary emission cells and somewide,undistinguishedemissioncomponents;thepartialnulling modethatlacksemissioninsomecomponents;thedwarfpulsemode characterized by only one or a few emission cells; and the completely nulling mode. The four modes of radio emission should respond to differentphysicalstatesinthemagnetosphere. Intheconventionalpicture,a‘gap’withchargedensitybelowthe Goldreich–Julian density49 is believed to be produced near the polar capregion,eitherintheformofavacuumgap3 orspace-charge-limited floe50 , or formed in the outer magnetosphere beyond the null-charge surface51 or in the annular region52 extending from the surface to outer magnetosphere in the form of a slot gap53 . Pulsar radio emis- sioniscoherentlyproducedbyabunchofparticles,asindicatedbyits extremely high brightness temperature, and the coherency must be realizedbyorderingparticlesinphasebythelongitudinalelectrostatic wavesorbythe‘antennamechanism’.Aclumpofrelativisticparticles streaming along a bunch of magnetic-field lines can produce visible radioemissionatagivenfrequencybandfromfiniteheightregions.The lowerfrequencyemissionisgenerallygeneratedfromahigher-altitude regioninthepulsarmagnetosphere. The most probable region of gap formation for this old pulsar with such a weak magnetic field, however, should be above the polar cap, as shown by recent simulations9,10 , which converges to the con- ventional concepts for the inner gap and the cascades of pairs via γ–Bprecess3,7 .Theelectron–positrondischargenearthepulsarpolar cap is non-stationary8,10 , which leads to large amplitude fluctuations of the electric field and collective plasma motions. Any break of the non-stationary nature will lead to incoherency for the radiation, and then the emission would be very weak even though the particles are stillflowingoutalongthefieldlines. Thenullingstateofpulsaremissiondemonstrateseitheradeficit of outer-flowing particles for radiation, or a lost of coherence forparticlesorthefailureofgapformation.Anotherpossibilityisthat thepolargapisfloodedwiththepairplasmacreatedfromothergaps, sothatthegapandradioemissionarescreened11 .Currentobservations seem to support the former possibility, especially when the pulsar is oldandneartheradiodeathline44,45 . For the emission state of PSR B2111+46, the accurate measure- ments of the polarization properties and the fine fluctuations for the well-resolved normal pulses in Extended Data Fig. 5 and the dwarf pulsesinFigs.1and5clearlyshowthatnormalpulsaremissioniscom- posited by the radiation from the thunderstorm of particles over a widely distributed area above the polar cap, with a very large multi- plicityofcascadesandalsoahigherplasmadensity.Thedwarfpulses of PSR B2111+46 are produced by one or a few raindrops of particles producedbythepairdischarges,withamuchlowermultiplicity. In principle, the gap voltage for the normal pulse emission state is higher than that for dwarf pulses, so that the pair-production multiplicity is large and that the energy distributions of the created particlesmayalsobedifferent.Tofindhintsoftheseprobablechanges, wethenexaminethespectraofphase-resolvedemissionofindividual pulses. As shown in Fig. 5, the spectra (S ≈ να ) of some distinguishable emission components are variable, with a possible index α from −5 to the unexpected +5. In the phase range for the positive spectral index, the PA values firmly follow the average PA curve. For a given dwarf pulse, the spectra do not vary along the pulse phase in such a narrow phase range. The distributions of mean spectral indexes for three kinds of individual pulses, normal pulse, partial nulling pulses and dwarf pulses, are shown in Extended Data Fig. 8. Dwarf pulses most likely have a reversed spectrum with a positive index, which means the primary particles in the gap may be responsible for dwarf pulses. Recent numerical simulations9,10 have shown that the core and conal components of pulsar radio emission may be preferably produced in someanglesbetweenthepair-productionfrontsandthebackground magneticfields.This,inprinciple,shouldinduceahigherprobability for elementary emission in the beam centre and beam edge, which is consistent with the mean profile of PSR B2111+46. The emission of the much extended phase range should be caused by the curvature of magnetic fields in the edge of the emission beam. We examine the phase-resolvedspectraforallnormalpulses,andfoundthatingeneral thespectrabetweenthephaserangeof±(20°−25°)areflatterthanthose atotherphasesandevenmorelikelyreversed(ExtendedDataFig.9). Plasmamultiplicityandpropagationeffectsinthepulsar magnetosphere Whenpulsaremissionisceased,eitherduetothefailureofgapforma- tion or the loss of coherence of emission particles, the pulsar magne- tosphere should always have a pair plasma filled but with a different multiplicity. The propagation effects of radio emission in the pulsar magnetosphere should be affected, which can be probed by the changesofthepolarizationproperties28,29 .Forexample,thePAfollows thedirectionofthelocalmagneticfieldduetoadiabaticwalking27 until the polarization limiting radius, after which the natural wave mode evolution becomes non-adiabatic and the PA angle is frozen. In this case, the PA curve should be shifted to an earlier rotation phase (see equation5.88inref.28) ϕshift ≈ −10.5∘ (η/100) 1/3 (γ/100) −1 , (1) hereη = N/NGJ istheplasmamultiplicityinthepulsarmagnetosphere, N is the charged particle density and NGJ is the density enviseaged by Goldreich and Julian49 , and γ is the Lorentz factor of the background plasmastream.Inprinciple,thephaseshiftϕshift canbedirectlydeter- mined by the phase difference between the steepest position of PA curve and the centre of the emission profile determined by the whole openfieldlineemissionregion.However,itisdifficulttodeterminethe central phase of the profile as the edges of emission region cannot be determinedclearly,andthereforewecannotobtaintheplasmamulti plicity. Nevertheless, we can compare the PA curves of dwarf pulses to the mean PA curve of normal pulses, and obtain the difference of phaseshiftsasbeingΔϕshift = ϕshift,dwarf-pulse − ϕshift,normal-pulse.Becauseradio emissionatthetwostatescomesfromalmostthesameregionwiththe samefieldgeometry,thechangeofplasmadensitycanbelimitedby Δη/η ≈ −0.3(Δϕshift/1∘ )(η/100) −1/3 (γ/100), (2) foragivenLorentzfactorγ. Theaccuratepolarizationmeasurementsofdwarfpulsesbysensi tive FAST observations provide a chance to probe the decrease of plasma density in such an emission-almost-quenched pulsar magne- tosphere. The PA values of dwarf pulses almost follow the mean PA curve. The phase shift of PA for each dwarf pulse is obtained from the differencebetweenthephaseofthedwarfpulseandthephaseforthe same PA value in the mean PA curve. Taking all phase-shift values for all dwarf pulses, we fit the distribution with a Gaussian function and obtainthemeanshiftasΔϕshift ≈ −0.77° ± 0.25° (ExtendedDataFig.10), which is marginally significant and implies a small increase of back- groundplasmadensityinthepulsarmagnetospherebyanamountof Δη/η ≈ (22% ± 7%)(η/100)−1/3 (γ/100).Maybethenullingofthispulsaris causedbythefloodingofpairplasmatotheinnergap11 ,sothatthepair productionandthefollowingradioemissionprocesscease.However,
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- 15. Nature Astronomy Article https://doi.org/10.1038/s41550-023-02056-z ExtendedDataFig.5|Examplesofpolarizationprofilesfortwodwarfpulses andtwostrongindividualpulsesinhightimeresolution.Allofthemare observedon2022-03-08byFASTwithtimeresolutionof49.152μs.Polarization profilesfortwostrongindividualpulsesareshownfortheirelongatedcentral partinthenextpanel.Eachripintheprofilesisreal,well-significantabovethe noisefluctuations.Theseunrepresenteddetailsindicatethattheobserved individualpulsesareanincoherentcollectionofmanyelementarypulses generatedseparatelyinthemagnetosphere.TheerrorbarforPAis ± 1σ.The intensityisscaledwiththeoff-pulsefluctuationsexpressedbyσbin.
- 17. Nature Astronomy Article https://doi.org/10.1038/s41550-023-02056-z ExtendedDataFig.7|Pulsarperiodandperiodderivative(P − ̇ P)diagram andthelocationofPSRB2111+46inthedeathvalley.Thedeathlinesaregiven forthecurvatureradiationinadipolefield(upperone)andanextremelycurved field(lowerone)inthevacuumgapmodel(soldlines)andthespace- charged-limitedflowmodel(dashedlines)givenin44 .Allpulsardataaretaken fromtheATNFpulsarCatalogue32 (version1.70).Thebackgroundgraydashed anddottedlinesstandforconstantsurfacemagneticfieldstrengthsand characteristicages,respectively.