Probes of Diffusive Shock Acceleration using Gamma-Ray Burst Prompt Emission

0.12 MB·English

by  Matthew G. Baring

ToappearinProc.ofthe6thHuntsvilleGamma-RayBurstSymposium(2009),
eds.C.A.Meegan,N.Gehrels,&C.Kouveliotou(AIPConf.Proc.,NewYork).
Probes of Diffusive Shock Acceleration using
Gamma-Ray Burst Prompt Emission
Matthew G. Baring
DepartmentofPhysicsandAstronomy,MS-108,RiceUniversity,P.O.Box1892,
9
Houston,TX77251-1892,USA Email:[email protected]
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2 Abstract. Theprincipalparadigmforgamma-raybursts(GRBs)suggeststhattheprompttransientgamma-raysignalarises
from multiple shocks internal to the relativistic expansion. This paper explores how GRB prompt emission spectra can
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constrainelectron(orion)accelerationpropertiesattherelativisticshocksthatpertaintoGRBmodels.Thearrayofpossible
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high-energypower-lawindicesinacceleratedpopulationsishighlighted,focusingonhowspectraabove1MeVcanprobethe
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fieldobliquityinGRBinternalshocks,andthecharacterofhydromagneticturbulenceintheirenvirons.Whenencompassing
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theMeV-bandspectralbreak,fitstoBATSE/EGRETburstdataindicatethatthepreponderanceofelectronsresponsibleforthe
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promptemissionresideinanintrinsicallynon-thermalpopulation.Thisdiffersmarkedlyfromtypicalpopulationsgenerated

inaccelerationsimulations;potentialresolutionsofthisconflictsuchastheactionofself-absorptionarementioned.Spectral
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E modelingalsosuggeststhatthesynchrotronmechanismisfavoredoversynchrotronself-Comptonscenariosduetothelatter’s
typicallybroadcurvaturenearthepeak.Suchdiagnosticswillbeenhancedbythebroadbandspectralcoverageofburstsbythe
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FermiGamma-RaySpaceTelescope;theGBMwillprovidekeyinformationonthelowerenergyportionsofthenon-thermal
. particlepopulation,whiletheLATwillconstrainthepower-lawregimeofparticleacceleration.
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p Keywords: Gamma-raybursts,non-thermalemission;diffusiveshockacceleration;hydromagneticturbulence
- PACS: 98.70.Rz;95.85.Pw;98.70.Sa;52.35.Ra;52.25.Xz;52.27.Ny;52.35.Tc;52.65.Pp
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r
t
s INTRODUCTION
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The gamma-rayburstparadigmhas evolveddramaticallyoverthe last decadesince the first redshiftdeterminations

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providedunambiguousevidenceforacosmologicaldistancescale.Yetmuchisstilltobelearnedaboutassociations,
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progenitors,andtheenvironmentofboththepromptandafterglowemissionregions,andthephysicalprocessesactive
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therein.For promptburstemission, the measurementof the high energyspectralindexprovidesa key constrainton
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5 theinterpretationoftheelectronaccelerationprocess.Presumingthepopularburstparadigmofradiativedissipation
2 at internalshocksthataccelerateparticles[1–3], it is ofgreatinterestto understandwhatphysicalconditionsin the
. shockedenvironscanelicittheobservedindicesandthespectralstructurearoundtheMeV-bandpeak.Toassessthis,
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0 oneturnstomodelsofdiffusiveshockaccelerationinrelativisticsystems.Thesecomeindifferentvarieties,including
9 semi-analyticsolutionsofthediffusion-convectionequation[4,5],MonteCarlosimulations[6–9],andparticle-in-cell
0 (PIC) full plasma simulations [10–13]. Each has its merits and limitations. Tractability of the analytic approaches
: generallyrestrictssolutiontopower-lawregimesfortheparticlemomentumdistributions.PICcodesarerichintheir
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i informationon turbulenceand shock-layerelectrodynamics.To interfacewith GRB data, a broaddynamicrangein
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momentaisdesirable,andthisisthenaturalnicheofMonteCarlosimulationtechniques,thefocusofthispaper.
r AkeypropertyofaccelerationattherelativisticshocksthatarepresumedtoseedpromptGRBradiativedissipation
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is that the distribution functions f(p) are inherently anisotropic. This renders the power-law indices and other
distribution characteristics sensitive to directional influences such as the magnetic field orientation, and the nature
of MHD turbulence that often propagatesalong the field lines. Accordingly,familiar results from relativistic shock
acceleration theory such as the so-called canonical s =2.23 power-lawindex [5], while providinguseful insights,
are of fairly limited applicability. This is fortunate since the GRB database so far has exhibited a substantial range
ofspectralcharacteristics,soanyuniversalsignatureintheaccelerationpredictionswouldbeunnecessarilylimiting.
ThispaperexploressomeofthefeaturesofdiffusiveshockaccelerationusingresultsfromaMonteCarlosimulation,
andaddressesprobesofthetheoreticalparameterspaceimposedbyextantGRBobservationsaroundandabovethe
MeVspectralbreak.Palpablediagnostics[14]havealreadybeenenabledbydataprovidedbytheBATSEandEGRET
instrumentsontheComptonGamma-RayObservatory(CGRO)forahandfulofbrightbursts.Theburstcommunity
expects significant advances in the understanding of such constraints in the next few years, afforded by the broad
spectralcoverageandsensitivityoftheGBMandLATexperimentsonNASA’sFermiGamma-RaySpaceTelescope.
DIFFUSIVEACCELERATION ATRELATIVISTIC SHOCKS
MostinternalGRBshocksthatareputativelyresponsibleforthepromptemissionaremildly-relativisticbecausethey
areformedbythecollisionoftwoultra-relativisticshells.Hence,thisregimeformsthefocusofthisexposition.The
discussionwilladdressthetheoreticalmethodologyemployed,andtheresultingcharacteristicsofthediffusiveaccel-
erationprocess,beforemovingontoconstraintsontheoreticalparametersimposedbythepromptGRBobservations.
ThesimulationusedheretocalculatediffusiveaccelerationinrelativisticplanarshocksisakinematicMonteCarlo
technique that has been employed extensively in supernova remnant and heliospheric contexts, and is described in
detailinnumerouspapers[6,7,15–18].ItisconceptuallysimilartoBell’s[19]testparticleapproachtodiffusiveshock
acceleration.Particlesareinjectedupstreamandgyrateinalaminarelectromagneticfield,withtheirtrajectoriesbeing
governedbyarelativisticLorentzforceequationintheframeoftheshock.Ingeneral,thefluidframemagneticfieldis
inclinedatanangle Q Bf1 totheshocknormal.Becausetheshockismovingwithavelocityu(x)relativetotheplasma
restframe,thereis,ingeneral,au×Belectricfieldinadditiontothebulkmagneticfield.Particleinteractionswith
Alfvénwaveandotherhydromagneticturbulenceismodeledbyusingaphenomenologicalscatteringofthecharges
intherestframeoftheplasma.Thescatteringprecipitatesspatialdiffusionofparticlesalongmagneticfieldlines,and
to a varyingextent,acrossthem as well. Thescatteringsare also assumedto be quasi-elastic,an idealizationthat is
usually valid because in most astrophysicalsystems the flow speed far exceedsthe Alfvénspeed, and contributions
fromstochasticsecond-orderFermiaccelerationaresmall.Thediffusionpermitsaminorityofparticlestotransitthe
shockplanenumeroustimes,gainingenergywitheachcrossingviatheshockdriftandfirst-orderFermiprocesses.
A continuumof scattering angles,between large-angle(LAS) or small-anglecases, can be modeledby the simu-
lation. In the local fluid frame, the time, d t , between scatterings is coupled [6] to the mean free path, l , and the
f
maximumscattering (i.e. momentumdeflection) angle, q scatt via d tf ≈lq s2catt/(6v) for particles of speed v≈c.
Usually l isassumedtobeproportionaltoapoweroftheparticlemomentum p (see[6,20]formicrophysicaljus-
tificationsforthischoice),andforsimplicityitispresumedtoscaleastheparticlegyroradius, r ,i.e. l =h r (cid:181) p.
g g
Theparameter h inthemodelisameasureofthelevelofturbulencepresentinthesystem,couplingdirectlytothe
amount of cross-field diffusion, such that h =1 correspondsto the isotropic Bohm diffusion limit, where the field
fluctuationssatisfy d B/B∼1.Inkinetictheory, h couplestheparallel(k =l v/3)andperpendicular(k )spatial
k ⊥
diffusioncoefficientsviatherelation k /k =1/(1+h 2) [16,21].Inparallelshocks,wheretheBfieldisdirected
⊥ k
alongthe shocknormal(Q Bf1=0), h hasonlylimitedimpactonthe resultingenergyspectrum,principallydeter-
miningthe diffusivespatialscale normalto the shock.However,in obliquerelativistic shockswhere Q Bf1>0, the
diffusivetransportofparticlesacrossthefield(andhenceacrosstheshock)becomescriticaltoretentionoftheminthe
accelerationprocess.Accordingly,forsuchsystems,theinterplaybetweenthefieldangleandthevalueof h controls
thespectralindexoftheparticledistribution[7,22],afeaturethatiscentraltotheinterpretationofGRBspectrabelow.
Acceleration Properties atRelativisticShocks
Representativeparticledifferentialdistributions dN/dp thatresultfromthesimulationofdiffusiveaccelerationat
mildly-relativistic(internalGRB)shocksaredepictedintheleftpanelofFigure1(see[7,9]for G ≫1 simulation
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results);thesedistributionsareequallyapplicabletoelectronsorions,andsothemassscaleisnotspecified.Astriking
feature is that the slope and shape of the non-thermal particle distribution depends on the nature of the scattering.
Theoftencitedasymptotic,ultrarelativisticindexof s =2.23 for dN/dp(cid:181) p−s isrealizedonlyforparallelshocks
with Q Bf1 =0◦ in the mathematical limit of small (pitch) angle diffusion (PAD), where the particle momentum is
stochasticallydeflectedonarbitrarilysmallangular(andthereforetemporal)scales.Inpractice,PADresultswhenthe
maximum scattering angle q scatt is inferiorto the Lorentz cone angle 1/G 1 in the upstream region.In such cases,
particles diffuse in the region upstream of the shock only until their velocity’s angle to the shock normal exceeds
around 1/G ,afterwhichtheyarerapidlysweptdownstreamoftheshock.TheFigureindicatesclearlythatwhenthe
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field obliquity increases, so also doesthe index s , with values greater than s ∼3 arising for Q Bf1 &50◦ for this
mildly-relativisticscenario.Thisisaconsequenceofmoreprolificconvectiondownstreamawayfromtheshock.
Figure1alsoshowsresultsforlargeanglescatteringscenarios(LAS,with 4/G 1.q scatt.p ),wherethedistribu-
tionishighlystructuredandmuchflatteronaveragethan p−2.Thestructurebecomesmorepronouncedforlarge G
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[7,9,22],andiskinematicinorigin,wherelargeangledeflectionsleadtofractionalenergygainsbetweenunityand
G 2 insuccessiveshockcrossings.Eachstructuredbumporspectralsegmentcorrespondstoanincrementoftwointhe
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numberofshocktransits.For p≫mc, theyasymptoticallyrelaxto a power-law,in thiscase with index s ≈1.62.
FIGURE1. Leftpanel:ParticledistributionfunctionsdN/dpfrommildly-relativisticshocks(G 1b 1=3,i.e.b 1=u1/c=0.949)
of upstream-to-downstream velocity compression ratio r=u1x/u2x ≈3.24. Simulation results can be divided into two groups:
parallel shock runs (Q Bf1 =0◦, upper three histograms), and oblique, superluminal shock cases (Q Bf1 =20◦,40◦,60◦, lower
three histograms). Scattering off hydromagnetic turbulence was modeled by randomly deflecting particle momenta by an angle
withinacone,ofhalf-angle q scatt,whoseaxiscoincideswiththeparticlemomentumpriortoscattering;theratioofthediffusive
mean freepath l tothegyroradius rg was fixedat h =l /rg=5. Theheavyweight lines(twouppermost histograms) arefor
the large angle scattering cases (LAS: 1/G 1 ≪q scatt ≤p ). All other cases constitute pitch angle diffusion (PAD) runs, when
q scatt.1/G 1 andthedistributionsbecomeindependentofthechoiceof q scatt.Alldistributionsasymptoticallyapproachpower-
lawsdN/dp(cid:181) p−s athighenergies.Forthetwocasesbracketingtheresultsdepicted,thepower-lawsareindicatedbylightweight
lines,withindicesof s =1.61 (Q Bf1=0◦, q scatt≤p )and s =3.31 (Q Bf1=60◦, q scatt≤10◦),respectively.
Rightpanel:Power-lawindices s forsimulationrunsinthelimitofsmallanglescattering(pitchanglediffusion),foranalmost
non-relativisticshockofupstreamflowspeed b 1x≡u1x/c=0.5,andanMHDvelocitycompressionratio r=4.Theindicesare
displayedasfunctionsoftheeffectivedeHoffman-Tellerframeupstreamflowspeed b 1HT=b 1x/cosQ Bf1,withselectvaluesof
thefluidframefieldobliquityQ Bf1 markedatthetopofthepanel.Obliquitiesforwhichb 1HT>1constitutesuperluminalshocks.
Thedisplayedsimulationindexresultswereobtainedfordifferentdiffusivemeanfreepaths l paralleltothemeanfielddirection,
namely l /rg=1 (blue squares), l /rg=10 (black triangles), l /rg=102 (green pentagons), l /rg=103 (red triangles) and
l /rg=104 (magentahexagons),aslabelled.ThelightweightblackcurveatthebottomlabelledKH89definesthesemi-analytic
resultfromKirk&Heavens’[4]solutiontothediffusion-convectionequation,correspondingto l /rg→¥ .
Both panels: The short heavyweight magenta lines labelled GRB 930131 indicate the approximate spectral index s that is
appropriateforthisEGRETburst,ifacooledsynchrotronemissionscenarioisoperable(seetextforadiscussion).
IntermediatecasesarealsodepictedinFigure1,with q scatt∼4/G 1.Thespectrumissmooth,likeforthePADcase,
buttheindexislowerthan2.23.Fromtheplasmaphysicsperspective,magneticturbulencecouldeasilybesufficient
toeffectscatteringsonthisintermediateangularscale,acontentionthatbecomesevenmoregermaneforultrarelativis-
tic shocks[9].Astrophysically,suchflatdistributionsmayprovedesirableinmodelsofGRB orblazarjetemission,
particularly if efficient radiative cooling is invoked.Note that acceleration distributions are qualitatively similar for
ultra-relativisticshocks, i.e. those perhapsmoreappropriateforGRB afterglowstudies, with a trend [5–7, 9, 22] of
declining s forhigher G ,theconsequenceofanincreasedkinematicenergyboostingincollisionswithturbulence.
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It is clear thatthere is a considerablerangeof indices s possible for non-thermalparticlesacceleratedin mildly
relativistic shocks, a non-universality that can attractively mesh with GRB observations.. The two key parameters
that dictate the array of possible spectral indices s are the shock field obliquity Q Bf1, and the ratio h =l /rgof
thediffusivemeanfreepathtotheparticle’sgyroradius r .Aparametersurveyfordiffusiveaccelerationatatypical
g
mildly-relativistic shock is exhibited in the right panel of Fig. 1, where only the pitch angle diffusion limit was
employed.Thepower-lawindex s isplottedasafunctionofthedeHoffman-Teller(HT[23])framedimensionless
speed b 1HT=b 1x/cosQ Bf1,wherethesubscript x denotescomponentsalongtheshocknormal.Thisistheupstream
flow speed in the shock rest frame where the flow is everywhere parallel to the magnetic field; it correspondsto a
physical speed when b 1HT <1 (i.e. the upstream field obliquity satisfies cosQ Bf1 <b 1x, and the shock is said to
besubluminal.Whenmathematically b 1HT>1,theshockistermedsuperluminal,andthedeHoffman-Tellerframe
technicallydoesnotexist—noLorentzboostcanrendertheflowparalleltoB.Clearly,thex-axismapsvariationsin
Q Bf1,withmorehighlyobliqueshockscorrespondingtotherightoftheplot.
Afeatureofthisplotisthatthedependenceof s onfieldobliquityisnon-monotonic.When l /r ≫1,thevalueof
g
s atfirstdeclinesas Q Bf1 increasesabovezero.Thisleadstoveryflatspectra.As b 1HT approachesandeventually
exceedsunity,thistrendreverses,and s thenrapidlyincreaseswithincreasingshockobliquity.Thisisthecharacter
of near-luminal and superluminal shocks evinced in the left panel of Fig. 1, precipitated by inexorable convection
ofparticlesawaydownstreamoftheshock,steepeningthedistributiondramatically.Theonlywaytoamelioratethis
rapiddeclineintheaccelerationefficiencyistoreduce l /r tovaluesbelowaround 10.Physically,thisistantamount
g
toincreasingthehydromagneticturbulencetohighlevelsthatforcetheparticlediffusiontoapproachisotropy.Then,
transportofchargesacrossthemeanfieldbecomessignificantongyrationaltimescales,andtheycanberetainednear
theshockforsufficienttimestoaccelerateandgeneratesuitablyflatdistributionfunctions.Suchlowvaluesof l /r
g
render the field direction immaterial, and the shock behaves much like a parallel, subluminal shock in terms of its
diffusivecharacter.Then, s isonlyweaklydependenton Q Bf1,thesecondkeypropertyillustratedintherightpanel.
The origin of the extremely flat distributions with s ∼1 is in the coherent effect of shock drift acceleration at
the shock discontinuity.This phenomenonhas been widely understood in non-relativistic shocks, and is due to the
energy gain of charges when they repeatedly encounter u×B electric fields (in frames other than the HT frame)
in gyrations straddling the shock discontinuity. The energy gain rate then scales as the gyrofrequency c/r , i.e.
g
is proportionalto the particle’s energy/momentum,so that the equilibrium distribution realized in pure shock drift
accelerationis dN/dp(cid:181) p−1 [18].Reducing l /r andtherebyintroducingextremelymodestamountsofcross-field
g
diffusion disrupts this coherence, removes particles from the shock layer, and steepens the spectrum. It is noted in
passingthatthechoiceofthesomewhatlarge(for b =0.5)compressionratio r=4 wastoafforddirectcomparison
1x
with thesemi-analyticconvection-diffusionequationresultsofKirk &Heavens[4],whichphysicallycorrespondto
l /r ≫1 caseswithminimalcrossfielddiffusion.Thedifferencesbetweenoursimulationindicesinthislimitand
g
thoseof[4]arisebecausetheadiabaticapproximationemployedin[4]todescribeshockcrossingsdoesnottakeinto
accountthegyrationaltrajectoriesofchargesintheshocklayer.Thesesubtletiesarediscussedfurtherin[18].
CONSTRAINTS ONACCELERATIONTHEORY FROMGRBOBSERVATIONS
Gleaningmeaningfulinsightsintotheconnectionbetweenaccelerationtheoryandpromptburstsignalshingesupon
twoaspects:thehighenergyspectralindex a (=−b forBandmodel[24]index b ),whenthedifferentialspectrum
h
is dn/deg (cid:181) eg−a h,andgeneratingburstspectralshapeatandbelowthe n -Fn peak.Thesewillbeconsideredinturn.
The a High-Energy Spectral Index
h
Thehigh-energyphotonspectralindices a fortheCGROEGRETandComptelburstsaretabulatedin[25].One
h
oftheseEGRETdetections,GRB930131,hadanindex a ≈2,whichcorrespondstotheindicationinbothpanelsof
h
Fig.1ifasynchrotronorinverseComptoncoolingmodelisadopted.ThisisontheflatendoftheEGRET a index
h
distribution[26], for whicha handfulof sourcesevincedphotondifferentialspectrumindicesscattered in the range
2.a .3.7 (thoughnotethatEGRETsparkchamberdetectionswereconcentratedintheindexrange a .2.8 [25]).
h h
TheCGRO BATSE a indexdistribution[27]issimilarlybroad,butwith 1.5.a .3.5 andfargreaterstatistics.
h h
The recentFermi detection of GRB 08016Cin both the GBM and LAT instrumentsoffereda high energyindex of
a ∼2.2 initsmostluminousepoch,andasteeperspectrumatothertimes[28].Accordingly,observationally,shock
h
accelerationmodelsmustaccommodatearadiationspectralindexintherange 2.a .4 inordertobeviable.
h
Thephasespaceforachievabilityofthisdependsontheradiationmechanism,andalsouponwhetherornotcooling
isinvoked.ThemostpopularmodelscenariofortheproductionofthepromptGRBsignalisquasi-isotropicelectron
synchrotronemission[2,3].Inthiscase,aswithinverseComptonscattering,thephotondifferentialspectralindexis
given by a h =(s +1)/2 abovethe n -Fn peak, if coolingis not efficient, and a h =(s +2)/2 if the particles are
continuously cooled in a large volume before being re-injected into an acceleration process, for which the particle
distributionindexissteepenedbyunity.FromtheFigure,itisevidentthatthisisreadilyachievableforGRB930131
forquasi-parallelshockswithperhapssomecomponentofmodestanglescattering,orformoderatelyobliqueshocks
as long as l /r .3−10. The EGRET GRB index range 2.a .3.7 then correspondsto diffusive acceleration
g h
with 2.s .5.4 in the presenceof cooling,and 3.s .6.4 otherwise.In either case, subluminalshocks, either
quasi-parallel(Q Bf1.20◦) or moderatelyoblique(20◦.Q Bf1.60◦) are requiredto explain flatter GRB spectra
as in GRB 910503, GRB 930131, GRB 950425 or GRB 080916C. For bursts with somewhat larger a indices,
h
superluminal shocks can be viable, but only if the scattering is strong, i.e. l /r .3−10. Otherwise, convection
g
awayfromtheshockdominatestheacceleration,andtheelectrondistributionbecomestoosteep.Forthelesspopular
uncooled hadronic models, the photon and particle indices trace each other, i.e. a =s , and a similar conclusion
h
thattheenvironmentisrestrictedtosubluminalormodestlysuperluminalobliqueshocksisderived.Notethatwhile
Lorentz transformations of circumburst fields of arbitrary orientation render ultra-relativistic external GRB shocks
quasi-perpendicular(Q Bf1≈90◦),moderatefieldobliquitiesareoftenattainedinmildly-relativisticinternalshocks.
Discriminating between the s constraints in the presence or absence of synchrotron cooling mandates a brief
discussion of the balance between acceleration and cooling. Diffusive shock acceleration is usually dominated by
gyroresonantinteractionsbetweenchargesandhydromagneticturbulence[29].Ifthisisthecase,thenforachargeof
Lorentzfactor g ,theaccelerationrateessentiallyscalesas g timestheparticle’sgyrofrequency,implying dg /dt(cid:181) g 0.
In contrast, synchrotronand inverseComptoncoolingrates yield dg /dt (cid:181) −g 2. Accordingly,simultaneousand co-
spatial accelerationand synchrotroncoolingyield a power-lawdistribution with the “raw” accelerationindex s up
to a maximumenergywhere cooling beginsto dominate, and generatesan exponentialturnover.This is the widely
consideredscenarioforX-ray/TeVsupernovaremnantstudies.ForexternalGRBshocksspawningafterglowsignals,
there is plenty of time for accelerated charges to diffuse away from the shock and subsequently cool, so that the
cumulativeeffectisemissionfromacooling-steepenedinjectedpower-law.Thesituationisverydifferentforinternal
shocks.Theaccelerationmustpersistuptothemaximumenergyseenintheobservations,forexample1GeVinGRB
930131and13GeVinGRB080916C,andonatimescale D t commensuratewiththevariabilityattheseenergies,i.e.,
D t.1secormuchless.Coolingbreaks,byanindexof D a =1/2,arenotobservedabove1MeVinburstemission,so
h
ifthespectraspanning1MeV–10GeVcorrespondtoacooling-dominatedcontribution,theaccelerationmustoperate
inshort,impulsiveperiods,followedbylongcoolingepochsthatpermittheelectronstodeclineinmomentumbya
factorof 102 orso.Accordingly,thecoolingepochsshouldpossessdurationsofaround4ordersofmagnitudelonger
than the impulsive acceleration epochs. It is not clear that the superposition of a host of these presumably pseudo-
FRED-likeprofilescanmimictypicalbursttimehistorieswhilemaintainingthetime-averagedspectralbehavior.
Constraints from the n -Fn Peak
An additional requirement for the success of an acceleration model is that when convolved with a radiation
process such as synchrotronradiation, it can generate the shape of the GRB spectrum around and below the n -Fn
peak. This was the focusof the investigationby Baring & Braby [14]. Early work on broad-bandspectralfitting of
burstswasprovidedbyTavani[30],whoobtainedimpressivefits totime-integratedspectraof severalbrightCGRO
BATSE bursts using a phenomenologicalelectrondistribution and the synchrotronemission mechanism.While this
succeededinthislimitedsample,providingadriverforthepopularityofthesynchrotronGRBemissionmodel,there
are difficulties with fitting low energy (i.e. .100keV) spectra in about 1/3 of bursts [31]. Employing perspectives
based on acceleration theory, this investigative effort was extended and refined by [14], who pursued a program of
spectralfittingofGRBemissionusingalinearcombinationofthermalandnon-thermalelectronpopulations.These
fitsdemandedthatthepreponderanceofelectronsthatareresponsibleforthepromptemissionresideinanintrinsically
non-thermal population. Such a constraint, dictated by the narrowness of the n -Fn peak, is commensurate with
electrondistributionsfrequentlypresumedin GRB spectralmodels, i.e. truncatedpower-laws.Yet, this requirement
stronglycontrastsparticledistributionsobtainedfromaccelerationsimulations,exemplifiedbythosedepictedinFig.1,
andfurtherillustratedinnumerouspapers[6,7,9,16,17].Moreover,particle-in-cell(PIC)plasmasimulations[10–
12]generallyexhibitlargelyMaxwelliandistributions,andintheisolatedrecentsuggestion[13]ofanon-thermaltail
generatedbydiffusivetransport,thethermalpopulationstronglydominatesthehigh-energytail.
Theconsequenceisobviouslyapotentialconflictforaccelerationmodels,sincethenon-thermalelectronsarealmost
always drawn directly from a thermalgas. This does not necessarily mean that acceleration at relativistic shocks is
notprecipitatingthepromptemission.Itispossiblethatsomehow,relativisticshockscansuppressthermalizationof
electrons,thoughsuchaconjecturepresentlyhasnosimulationalevidencetosupportit.Or,radiativeefficienciesmight
becomesignificantonlyathighlysuperthermalenergies:aconvenientresolutiontothisdilemmaisthatstrongradiative
self-absorptioncouldbeacting,inwhichcase n -Fn peaks(andthereforeBATSEandFermiGBMspectralprobes)are
notactuallysamplingthermalelectrons.Itisalsopossiblethatothermechanismssuchaspitch-anglesynchrotron,or
jitterradiationmayprovemoredesirable.Acautionarynoteisthatthiscomplicationfortheinterpretationispredicated
upon spectra integratedover the burst duration,which can differsignificantly from those obtainedin temporalsub-
intervals(e.g.see[28]).Notwithstanding,cumulativespectraprovideaglobalindicationofanarrownessoftheMeV
spectralbreak,andthismustbeacharacteristicofatleastthemostluminousportionsofthebursttimehistory.Wenote
alsothat[14]concludedthatthesynchrotronself-ComptonprocesswasunlikelytobeabletogeneratetheMeVband
emission in prominentEGRET bursts because of its intrinsic spectralbreadth,even with extremelynarrow electron
distributionfunctions.Onlyaself-absorptioninthesynchrotronseedspectrumcanaiditsviability.
CONCLUSION
Thispaperexplorestheconnectionbetweendiffusiveshockaccelerationtheoryandpromptemissioninbursts.Sim-
ulation results presented clearly highlight the non-universalityof the index of energetic, non-thermalelectrons and
ions,spawnedbythevarietyofshockobliquitiesandthecharacterofhydromagneticturbulenceintheirenvirons.This
non-universalityposesnoproblemformodelingGRBhigh-energypower-lawindices,thoughobservationsgenerally
constrainthe parameterspace tosubluminalorhighly-turbulentsuperluminalshocksnearthe Bohmdiffusionlimit.
Also, demanding a connection between the thermal electron population and the GRB n -Fn peak gives rise to an
inconsistency in that acceleration simulations predicta dominanceof the thermalpopulation,whereas the radiation
modelsdemandthatthecontributingparticlesareintrinsicallynon-thermal.Escapeclausesincludeinvokingradiative
selfabsorption,orperhapsrelinquishingpreferredemissionmechanisms,i.e.,synchrotronorinverseComptonradia-
tion.Theprospectofanumberofplatinumstandard,broad-bandGRBdetectionsbyFermithatpermittime-dependent
spectroscopyshouldhoneourunderstandingoftheconnectionbetweenshockaccelerationandpromptemission.
Acknowledgments:thisresearchwassupportedinpartbyNASAgrantNNG05GD42GandNSFgrant0758158.
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