Astronomy&Astrophysicsmanuscriptno.salvati˙text (cid:13)c ESO2010 January27,2010 The local Galactic magnetic field in the direction of Geminga (ResearchNote) M.Salvati INAF–OsservatorioAstrofisicodiArcetri LargoEnricoFermi5,I–50125Firenze,Italy e-mail:[email protected] Received/Accepted 0 1 ABSTRACT 0 2 Context.The Milagro hot spot A, close tothe Galactic anticenter direction, has been tentatively attributed to cosmic rays from a n localreservoir(atadistance≈100pc),freelystreamingalongdivergingandsmoothmagneticfieldlines.Thisisatvariancewiththe a geometryofthe≈kpcscaleGalacticmagneticfield,whichisknowntobealignedwiththespiralarms. J Aims.Weinvestigatetheinformationavailableonthegeometryofthemagneticfieldonthescales(≈100pc)ofrelevancehere. Methods.Themagneticfieldimmediatelyupstreamof theheliosphere hasbeeninvestigatedbyprevious authorsby modelingthe 7 interactionofthisfieldwiththesolarwind.Atlargerdistances,weusethedispersionmeasureandtherotationmeasureofnearby 2 pulsars(especiallytowardsthethirdGalacticquadrant).AdditionalinformationaboutthelocalfieldtowardstheNorthPolarSpuris takenfrompreviousstudiesofthediffuseradioemissionandthepolarizationofstarlight. ] E Results.Theasymmetryoftheheliospherewithrespecttotheincominginterstellarmediumimpliesamagneticfieldalmostortho- gonaltothelocalspiralarm,inthegeneraldirectionofhotspotA,butmoretothesouth.Thisisingoodagreementwiththenearby H pulsardataontheoneside,andtheNorthPolarSpurdataontheother. h. Conclusions.The local magnetic field on scales of ≈ 100 parsecs around the Sun seems to be oriented so as to provide a direct p connectionbetweentheSolarsystemandapossiblesiteoftheGemingasupernova;theresidualangulardifferenceandtheshapeand - orientationoftheMilagrohotspotcanbeattributedtothefieldtrailinginthewakeoftheheliosphere. o Keywords.cosmicrays–supernovae:general–supernovae:individual:Geminga–ISM:magneticfield r t s a [ 1. Introduction cosmic rays. Drury and Aharonian (2008, hereafter DA) criti- 1 cized SS on the grounds that the assumed diffusion coefficient v The detection by Milagro of anistropies at small angular sca- wasveryimplausible,and,moreover,afullydiffusiveapproach les in the arrival directions of multi–TeV cosmic ray protons 7 could not accountfor the narrow angular size of the hot spots. (dubbed hot spots A and B, Abdoetal.2008) has stirred a 4 Theysuggestedinsteadthatsomenearby”cosmicrayreservoir” 9 lively debate. Indeed, there was no surprise in the detection wasconnectedto the Solarsystem bya ”magneticfunnel”:the 4 of anisotropies at the measured level, but the expectation was cosmic rays could then stream freely along the (diverging and 1. that such anisotropies would appear on large angular scales, smooth)fieldlines,whileatthesametimetheirpitchangledis- in agreementwith the diffusion mode which accounts success- 0 tribution would narrow down to the observed value. A hybrid fully for the propagation of cosmic rays. A positive excess 0 scenariowasfinallyproposedbySS:therethe”cosmicrayreser- 1 in the general direction of hot spot A (”tail–in” anisotropy) voir”coincideswiththeGemingaSNR;thecosmicrayshaveto : had been already detected by other experiments [Tibet Air diffuse until they reach the ”first useful magnetic line” which v ShowerArray(Amenomorietal.2006)andSuperKamiokande drivesthemtothefunnelandthentotheSolarsystem.Theini- i X I (Guillianetal.2007)], althoughthe narrownessof the feature tialdiffusionaccountsforthespectralfiltering,thefinalstream- (onlyafewdegrees)hadnotbeennoticedbefore. r ingaccountsfortheangulardistribution. a Salvati and Sacco (2008, hereafterSS) pointedoutthat hot There is a major caveat, however. The available informa- spot A is in the general direction of Geminga, and suggested tion about the geometry of the Galactic magnetic field (e.g., thataplausiblesourcecouldbetheGemingasupernovaremnant Hanetal.2006)indicatesthatonscales≈kpctheorderedmag- (SNR) rather than the pulsar. The SNR would be dispersed by netic field is in the direction of the local spiral arm, and the now, and would survive only as an expandingcloud of cosmic chaotic componentof the field is somewhat larger than the or- rays.Thedistance toit couldbe muchsmaller thanthe present dered one. The magnetic funnel scenario, on the contrary, re- distancetothepulsar,ifapositiveradialvelocityisassumedfor quires that (on smaller scales ≈ 100 pc) the field is predomi- the latter. Such a distance could be crossed by diffusion in the nantlyordered,anddirectedtowardtheanticenter.Inthefollow- time elapsed since the explosion (at least with crude assump- ingwediscussevidencethatthiscouldindeedbethecase. tionsaboutthediffusioncoefficient).Alsotheenergeticsturned outright,andtheenergydependenceofthediffusioncoefficient 2. Thelocalandverylocalmagneticfield would account for the hard spectrum (Γ∼1.45) of the excess Informationaboutthe magnitudeanddirectionof themagnetic Sendoffprintrequeststo:M.Salvati field immediately upstream of the heliosphere (i.e., in the very 2 M.Salvati:ThemagneticfieldtowardGeminga(RN) Table1.Nearbypulsarsusedintheanalysis Table2.Magneticfieldobtainedfromvariouspulsarsamples Name ℓ b Dist DM RM sample no.objects ℓ b B χ2 II II II II rid degrees degrees pc cm−3pc radm−2 degrees degrees µG J2144-3933 2.8 -49.5 180 3.35 -2 <300pc 7 16 45 1.9 470 J2124-3358 10.9 -45.4 250 4.60 1.2 IIIquad 4 5 42 3.3 40 J0108-1431 140.9 -76.8 130 2.4 -0.3 <500pc 18 6 28 2.7 1,500 B0656+14 201.1 8.3 290 14.0 23.5 IIIquad 8 9 43 2.5 340 B0950+08 228.9 43.7 260 2.96 -0.66 0.5–2kpc 103 80 -10 2.5 10,000 J0437-4715 253.4 -42.0 160 2.64 1.5 armexcl. 57 100 6 3.1 2,200 B0833-45 263.6 -2.8 290 68.0 31.4 local interstellar medium still unperturbed by the bow shock) the sample to 18 objectsin total, and to 8 in the third Galactic can be gained by modeling the anistropies observed in several quadrant. Finally, we fitted all pulsars with distances between heliopausetracers (see, for instance, Ratkiewicz, Ben-Jaffel, & 500 and 2,000 parsecs (103 objects), which should reproduce Grygorczuk 2008, and references therein). One obtains a very theazimuthalgeometryalreadyestablishedbypreviousauthors. local magnetic field of ∼ 1.8 µG, oriented within the interval On such large scales we include a portion of the Sagittarius 203◦ < ℓ < 231◦, −58◦ < b < −41◦. Note thatthis analysisis – Carina arm, where the field is known to reverse direction insensitivetothesignofthefield,sothatanequallyadmissible (Hanetal.2006);so,inordertokeepthesampleclean,wealso solutionis23◦ < ℓ < 51◦,+41◦ < b < +58◦.Thelattersolution fitted a subsample including only the pulsars lying outside the isplottedinFig.1asacirclelabeled”Bnear”. arm(57objects). In orderto explorethe field on scales of a few hundredsof The results are summarized in Table 2. One sees that the parsecs from the Solar system, we use the dispersion measure < 500 pc sample gives results in broad agreement with the (DM) and the rotation measure (RM) of nearby radio pulsars <300pcsample,whilethe0.5–2kpcsampleindicatesclearlya (Hanetal.2006). We retrieve from the ATNF Pulsar Database rotationofthefieldwhichbecomes(moreorless)alignedwith (Manchesteratal.20051) all the pulsars with measured DM the Galacticplanein the directionofthe localspiralarm.Note and RM, and distances less than 300 parsecs. There are seven especiallythatrestrictingtheanalysistothethirdGalacticquad- such objects,listed in orderofincreasingGalactic longitudein rantdoesnotchangeappreciablythefield,butmakesthereduced Table1.Theirdistancesareobtainedeitherfromtheannualpa- χ2 substantially smaller. The reducedχ2 becomessubstantially rallax, or (for J0108 and J2144)from the DM and an assumed smaller also in the large scale sample, as expected, if one ex- modeloftheelectrondistribution.Giventherelativelysmallvo- cludesthepulsarsinsidetheSagittarius–Carinaarm. lume, we approximate the magnetic field as a constant vector, We regard the substantial agreement between the first four fullydescribedbythreeindependentcomponents,whichwefind setsofvaluesinTable2asahintthatourprocedureismeaning- by minimizing the χ2 between the observed and the predicted ful. Furthermore,the substantial agreementbetween the pulsar RM2 derivedmagnetic field (onscales ≈ 100pc) and the verylocal, heliopause derived magnetic field is a hint that in our Galactic RM =0.81DM (B ·n) neighborhoodthe magneticfield is relativelysmooth.An inde- pred obs µG pendenthint at the field smoothness (a prerequisite for the va- Ontheotherhand,theRMiswellknowntovarywidelyeven lidity of the funnel scenario) comes from the very significant forsmallangulardisplacements,sothattheorderedcomponent decreaseofthereducedχ2 inthethirdquadrantwithrespectto ofthefieldisfoundbyaveragingthedataoverlargeregionsof the all sky value. The two < 300 pc pulsar–derived solutions thesky.Wedonotperformanyaverage,giventhesmallnumber areplottedinFig.1astwocrosseslabeled”Brm”;wehavenot ofentries,howeverwemustbepreparedtofindaχ2 verymuch computeda confidenceregionfromtheχ2 distributionbecause higherthan≈1perdegreeoffreedom.Weusethisestimatoronly ofthecaveatsassociatedwithit,andguesstheuncertaintyfrom to draw some qualitative guesses. The values of DM and RM thedifferencebetweenthetwosolutions. of two particular objects(B0656+14and B0833-45)are by far ThestructureofthemagneticfieldtowardstheGalacticcen- largerthantheothervalues,asonecouldhaveexpectedbecause terislooselyconstrainedbythepulsardata,whichonlysuggest of their location in the Monogem and Vela SNR, respectively. a geometry more complex than a uniform field. A clearer pic- Thisaddsonefurthercaveattoourresults,sinceadense,young turecanbeobtainedbymodelingtheintensityandpolarization SNRcouldbedominatedbyalocalmagneticfieldofitsown. ofthenearbyextendedradioemission(Wolleben2007)andthe If we retain in the fit all the seven pulsars, we obtain B ∼ polarizationofthelightfromnearbystars(Frisch2009). 1.9µG,ℓ ∼16◦,b∼45◦withareducedχ2 ofaround470(!).If The interstellar medium in this general direction has been insteadweretainonlythefourpulsarslyinginthethirdGalactic perturbedbyaseriesofexplosionslikelyduetostarsintheSco– quadrant, since the excess cosmic rays reach the Solar system Cenassociation.Theradiointensityandradiopolarizationmaps from this general direction, we obtain B ∼ 3.3 µG, ℓ ∼ 5◦, show the traces of severalshells, the most prominentof which b ∼ 42◦ with a reduced χ2 of only (!) 40. As a check on our is the North Polar Spur. One of the shells [called ”Shell 1” by findings,wehaverepeatedtheanalysisforallpulsarswith dis- Wolleben(2007)]mayhavereachedtheSun.Inordertoaccount tanceslessthan500parsecs:ontheonehand,we becomesen- forboththeradioandtheopticaldata,themagneticfieldinthe sitive to the field on scales somewhat larger than the ones of perturbedregionisdescribedasauniformfieldoutsidetheshells interest; on the other, we improve the statistics by increasing and,withintheshellthickness,asacompressedfieldlyingalong 1 http://www.atnf.csiro.au/research/pulsar/psrcat/ themeridiancircles.Theradiodatarequiretwodifferentshells, 2 EvenifeachpulsargivesonlytheBcomponent along thelineof while the optical data can be fitted with Shell 1 only, and help sight(B·n),threeormorepulsarswidelyspacedovertheskyaresuffi- toconstrainitsparameterswithinthelargeradio–derivedconfi- cienttoconstrainBindependentofitsdirection. denceregion. M.Salvati:ThemagneticfieldtowardGeminga(RN) 3 havedrawna circle of 10pc radius,representinga fullydevel- opedSNR. 3. Discussionandconclusions The first result we want to stress is the geometry displayed in Fig. 1: the direction of the local magnetic field, the direction of hot spot A, and the direction to a possible location for the Geminga SNR all lie within a few degrees from one another3. Apart from the hot spot, all the other directions in Fig. 1 are notdirectly measured,and are obtainedby modelingthe avail- abledatasets,notalwaysplentiful.If,nonetheless,wetakethese results at face value, one of the main objectionsto a diffusion- plus-funnelscenariocouldberemoved:thefieldontherelevant scalesseemstobealmostorthogonaltothelargescaleone,and topointintherightdirection. Thesecondresultconcernsthesmoothnessofthelocalfield, whichisnecessaryifthecosmicrayshavetostreamfreelyalong the magnetic funnel in order to be focussed within a narrow range of pitch angles. The evidence for such smoothness (ad- mittedlymeager)comesfromtwofindings.Oneisthedramatic dropofthereducedχ2 ifoneselectsformodelingonlythepul- sars lying in the third Galactic quadrant. The other is the near coincidencebetweenthedirectionsoftheverylocal,heliopause Fig.1. Aitoff equal area projection in Galactic coordinates of derivedmagnetic field (”B near”), and the ≈ 100 pc scale one, thesouthernhalfofthethirdGalacticquadrant.Seetextforthe eitherpulsarderived(”Brm”),orradio–opticalderived(forthe meaningofthesymbols.Inallcases,theBfieldisdirectedout unperturbedconfiguration,”B starpol”). Indeed, one notes that ofthepagetowardsthereader. thereisaregularandsmooth”rotation”oftheBfieldvector:it comesfromabouttheanticenterwhenthefieldisdeterminedin thethirdGalacticquadrant;growsinGalacticlongitudebyabout The star symbol labeled ”B starpol” in Fig. 1 is the di- 30◦attheSolarsystem;andgrowsstillbyanother30◦whenthe rection of the uniform field inside which Shell 1 is expanding (unperturbed)fieldisdeterminedinthedirectionoftheGalactic (Frisch2009, no errors given). This would be the direction of center. thefieldoutsidetheheliosphereifShell1hadnotreachedusyet. WesketchtheenvisagedgeometryinFigures2and3.They Otherwise the field would be the onecompressedalongthe lo- are the projection on the Galactic plane and, respectively, the calmeridianlineoftheshell:thetwocrosseslabeled”Bpileup” meridian plane ℓ = 180◦ of the local and very local magnetic representtwopossiblechoicesoftheshellcenter.Notethenear field, and of Shell 1 of Wolleben (2007). The crudeness of the coincidenceof ”B starpol”and”B pileup”,whichis due to the sketchgivestheimpressionofasharpbendatthesolarposition, shell expansion center being at almost 90◦ with respect to ”B whichwouldbeinjustified;butanequallyvalid(andequallyar- starpol”. bitrary)representationcouldinvolvemagneticlineswith acur- Figure1summarizesourfindings.Herethesouthernhalfof vatureradiusaslargeastheFiguresthemselves.Also,theactual thethirdGalacticquadrantisplottedinanAitoffequalareapro- rotationinthreedimensionsamountsto46degreesonly;thisis jection. The various estimates of the B field direction have al- stronglyamplifiedbyprojectioneffects.Finally,thedashedlines ready been discussed. For the sake of comparison, all of them insidetheshellrefertothepre–shellsituation:aftertheshellhas arerepresentedastherespectivepointsat−∞,buttheypertainto overtakenthem,theyaredrapedalongtheshellsurface. differentphysicalregions:Brmshouldbevalidat≈100pcinthe Wedonotregardasamajordiscrepancytheresidualangular thirdquadrant,Bnear andBpileup shouldbevalidonlyveryclose separationbetweentheassumeddirectionoftheGemingaSNR, to the Sun, and Bstarpol should be valid at ≈ 100 pc in the first ”Bnear”,”Brm”,andtheactualpositionofhotspotA.However, quadrant.Inthelatterregionthefieldhasbeenheavilydistorted some plausibility argumentscan be givenwhich could account bytheexpansionoftheradioshells,howeverwhatisplottedhere forthediscrepancy. istheunperturbed,pre–shellfield,sothatwecandrawmeanig- As argued in SS, the SNR responsible for the ”cosmic ray ful conclusionsfrom its smooth connectionwith Bnear and Brm reservoir” (Geminga or other) should be close to the magnetic (seeSection3andFigures2and3). funnel, so that diffusion with reasonable coefficients could ac- The hot spot A and the heliotail direction are represented countforthepropagationofthecosmicraysfromtheSNRtothe by the ellipse labeled ”A” and the small dot inside it. Finally, funnelinthetimeelapsedsincetheexplosion.Atthesametime, the three dots in descendingsequence are: the present position of the Geminga pulsar; the position it would have had at ex- 3 Battaner,Castellano&Masip(2009) havedeveloped amodel for thedipole-likeMilagroanisotropy(note:thisisdifferentfromthepoint- plosion if its motion were parallel to the plane of the sky with like anisotropy discussed here). Their model succeeds in accounting the measured proper motion value; and the position it would forthedipoleundertheassumptionofalocalmagneticfieldbasically have had if the explosion had occurred at the ”minimum” dis- alignedwiththelocalspiralarm,i.e.atalargeanglewiththeonede- tance of 65 pc [i.e., with a positive 160 km s−1 radial velocity rivedhere.Butifoneassumesastreamingmotionofthecosmicrays included, see SS; in both cases, the time elapsed since the ex- alongthemagneticfield,besidetheorthogonalmotionderivedbythem plosion is assumed equal to the spin down age of the pulsar, based on an ad–hoc turbulent stress, the two estimates can be recon- 3.4105yr(Bignami&Caraveo1996)].Aroundthelatterdotwe ciled. 4 M.Salvati:ThemagneticfieldtowardGeminga(RN) line”,otherwiseonewouldmisstheenergyfiltering(neededto explainthespectralhardnessofthecosmicrayexcess). Second,asmallmeanderingofthemagneticfield,sufficient to account for the angular difference between ”B rm” and ”B near”,isnotonlyplausible,butindeedverylikely.Theimportant pointis that such smalldeflectionsoverseveraltensof parsecs arebyfarinsufficienttoaffectthefreestreamingofthecosmic rays. Third,theactualpositionofhotspotAisperhapsdetermined bythe directionofthe verylocalmagneticfield in the wake of the heliosphere. Indeed, the direction of ”B near” depicted in Fig. 1 refers to the field ahead of the heliosphere, before any interactionwith it(Ratkiewicz et al. 2008). After the wind,the field should become more aligned with the heliotail, and it is plausiblethanthealignmentlastsforseveraltimesthedistance to the heliopause, i.e. for about . 1016 cm. Such a distance iscomparablewiththe Larmorradiusofa 10TeV particle;the radiusofcurvatureneededfora20◦ swingoverthisdistanceis of course larger still, so that the free streaming of the cosmic raysshouldnotbedisrupted. Notethattheambientmagneticfieldlineswilltendtowrap aroundtheheliosphereintheplanepassingthroughtheapexand containingthefieldandwinddirections,whiletheywilltendto slipapartonthetwosides;thecosmicrayswillthenbefocused Fig.2.OrthogonalprojectionontheGalacticplaneofthepulsar in the said plane, and de-focusedon the two sides. This corre- derivedfield(therightmostcrossofFig.1,solidlines),theun- spondsroughlyto theellipticalshapeandthe positionangleof perturbedradio–opticalderivedfield(thestarsymbolofFig.1, hotspotA.Qualitatively,thepileupofthelinestowardthehe- dashed lines), and the radio Shell 1 (underthe assumption that liotailcouldalsoaccountforthegradientobservedinhotspotA it has not reached the Sun yet, dotted circle). The heavy line alongthemajoraxis,withthemaximumontheheliotailside. through the center is the heliospheric derived, very local field. Thegeometryofthemagneticfieldwhichwehavediscussed Itsarrowindicatesthefieldorientation.TheaxesarelabeledGC thusfarisperhapstoodetailedincomparisonwiththeavailable (Galacticcenter),AC(anticenter),90◦and270◦(fortheGalactic evidence.Still,itisbyfarinsufficientforaquantitativeestimate longitude). oftheanisotropyamplitude.Inordertoachievethis,oneshould follow with high spatial and temporalresolution the expansion ofthecosmicraycloudinjectedbytheSupernova,includingthe individualfieldirregularitiesthroughoutthecloudvolume.The cloud, which we assume spherical, could well be elongated in onedimension,orhaveacomplicatedtopology.Thebestwecan doatthemomentistoshowthattheobservedanisotropycanbe sustained by a minuscule gradientin the density of the cosmic rays,agradientnotimplausibleforalocationrelativelycloseto arelativelyrecentSupernova. We write the energy flux measured from hot spot A (Abdoetal.2008)asfollows Φ∼510−4×6.710−6 ∼3.310−9ergcm−2s−1sr−1 (1) The magnetic funnelat the injection side is about20 times narrower than at the Sun side (see DA), and the particle pitch angle squared scales inversely by the same factor, so that Φ is constant.Hencetherequireddensityis Φ n∼4π ∼1.410−18ergcm−3 (2) c If the Supernova explosion injects 1050 erg in cosmic rays with the same spectrum as the general cosmic ray population, the 10–TeV reservoir amounts to 1.7 1047 erg. Spreading this reservoir in a sphere of radius100 pc (the length of the funnel Fig.3. The same as Fig. 2, for the meridian plane ℓ = 180◦. suggestedbyDA,andaplausibledistancefortheGemingaex- TheverticalaxisislabeledNGP(NorthGalacticpole)andSGP plosion) one gets n ∼ 1.4 10−15 erg cm−3, i.e. three orders of (SouthGalacticpole). magnitudelargerthanEq.(2). Conversely,we can computethe cloudvolume correspond- ing to the density of Eq. (2), V ∼ 1.21065cm3, and deduce a however,theSNRshouldnotliedirectlyonthe”firstusefulfield diffusion coefficient. Setting the time t since the explosion of M.Salvati:ThemagneticfieldtowardGeminga(RN) 5 Geminga equal to 3.4 105 yr (Bignami & Caraveo 1996), we find D=(cid:16)3V(cid:17)2/3× 1 ∼2.21029cm2s−1 (3) 4π 4t The above value for D is not far from what is usually assumed in cosmic rays modeling (e.g. Hooper,Blasi,&Serpico2009), and is another plausibility argument in favor of our suggestion: hot spot A could be the firstexampleofdirectcosmicrayastronomy. 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