Gamma-ray novae as probes of relativistic particle acceleration at non-relativistic shocks

0.86 MB·English

by  Brian D. Metzger

Mon.Not.R.Astron.Soc.000,1–??(2014) Printed23April2015 (MNLATEXstylefilev2.2)
Gamma-ray novae as probes of relativistic particle acceleration at
non-relativistic shocks
B. D. Metzger1(cid:63), T. Finzell2, I. Vurm1, R. Hascoe¨t1, A. M. Beloborodov1, L. Chomiuk2
1ColumbiaAstrophysicsLaboratory,NewYork,NY,10027,USA
2DepartmentofPhysicsandAstronomy,MichiganStateUniversity,EastLansing,MI48824,USA
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Received/Accepted
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p
ABSTRACT
A
1 The Fermi LAT discovery that classical novae produce ∼> 100 MeV gamma-rays estab-
2 lishesthatshocksandrelativisticparticleaccelerationarekeyfeaturesoftheseevents.These
shocks are likely to be radiative due to the high densities of the nova ejecta at early times

] coincidentwiththegamma-rayemission.ThermalX-raysradiatedbehindtheshockareab-
E
sorbedbyneutralgasandreprocessedintoopticalemission,similartoTypeIIn(interacting)
H
supernovae. Gamma-rays are produced by collisions between relativistic protons with the
. novaejecta(hadronicscenario)orInverseCompton/bremsstrahlungemissionfromrelativistic
h
electrons(leptonicscenario),whereinbothscenariostheefficiencyforconvertingrelativistic
p
particle energy into LAT gamma-rays is at most a few tens of per cent. The measured ratio
-
o ofgamma-rayandopticalluminosities, L /L ,thussetsalowerlimitonthefractionofthe
γ opt
r shockpowerusedtoacceleraterelativisticparticles,(cid:15) .Themeasuredvalueof L /L for
t nth γ opt
s two classical novae, V1324 Sco and V339 Del, constrains (cid:15) > 10−2 and > 10−3, respec-
a nth ∼ ∼
tively. Leptonic models for the gamma-ray emission are disfavored given the low electron
[
acceleration efficiency, (cid:15) ∼ 10−4 − 10−3, inferred from observations of Galactic cosmic
nth
2 rays and particle-in-cell (PIC) numerical simulations. A fraction f > 100((cid:15) /0.01)−1 and
sh ∼ nth
v > 10((cid:15) /0.01)−1 per cent of the optical luminosity is powered by shocks in nova Sco and
8 ∼ nth
nova Del, respectively. Such high fractions challenge standard models that instead attribute
0
allnovaopticalemissiontothedirectoutwardstransportofthermalenergyreleasednearthe
3
5 whitedwarfsurface.Wepredicthard∼10−100keVX-rayemissioncoincidentwiththeLAT
0 emission, which should be detectable by NuSTAR or ASTRO-H, even at times when softer
1. ∼<10keVemissionisabsorbedbyneutralgasaheadoftheshocks.
0
Keywords: keywords
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:
v
i
X 1 INTRODUCTION central temperature, and accretion rate (e.g., Yaron et al. 2005;
r Hillman et al. 2014). Despite notable successes, models of nova
a As“gueststars”toourancestors,novaehavebeenobservedsince outburstsremainplaguedbyuncertaintiessuchastheefficiencyof
antiquity (Zwicky 1936). Powered by runaway nuclear burning
convectivemixingandtheassumedprescriptionformassloss.This
on the surface of white dwarfs (e.g. Starrfield et al. 1972), nova
makesitchallengingtoaccuratelypredictthequantity,velocity,and
eruptionsareusuallyaccompaniedbytheexpulsionofmatterout-
timehistoryofmatterejectedfromthewhitedwarfsurface.
wardsathighvelocities>103kms−1(Shore2013,andreferences
∼ The Large Area Telescope (LAT) on the Fermi satellite re-
therein).Mostoftheradiatedenergyinanovaoutburstoccursat
cently discovered that classical novae emit > 100 MeV gamma-
optical and ultraviolet wavelengths and is generally attributed to ∼
rays,occurringattimescoincidenttowithinafewdaysoftheop-
theoutwardstransportofthermalenergyproducednearthewhite
ticalpeakandlastingforseveralweeks(Ackermannetal.2014).
dwarf surface (Prialnik 1986; Prialnik & Kovetz 1995; Starrfield
Luminouscontinuumgamma-rayemissionindicatesthepresence
etal.2000).Dynamicalstellarevolutionandhydrodynamiccalcu-
ofstrongshockswhichaccelerateparticlestorelativisticenergies,
lationsareusedtointerpretbasicfeaturesofnovalightcurves,such
producing gamma-rays via leptonic or hadronic processes (e.g.,
as how their rate of evolution depends on the white dwarf mass, Tatischeff & Hernanz 2007). Radio VLBI imaging by Chomiuk
etal.(2014)recentlydetectedcompact,high brightnesstempera-
tureknotsfromV959Mon,confirmingthepresenceofnon-thermal
(cid:63) E-mail:[email protected] shockemissioninagamma-rayproducingnova.
(cid:13)c 2014RAS
2
Evidence for shocks in novae has existed well before Fermi gamma-ray data from novae can be used to probe particle accel-
in the form of hard X-ray emission (e.g., Mukai & Ishida 2001; eration at non-relativistic shocks. The basic concepts of diffusive
Mukai et al. 2008), early peaks in the radio emission which are shockacceleration(DSA)weredevelopedalmostfortyyearsago
inconsistent with thermal emission from freely expanding photo- (e.g.,Axfordetal.1977;Bell1978;Blandford&Ostriker1978).
ionized gas (e.g., Taylor et al. 1987; Krauss et al. 2011; Weston However, only recently have plasma kinetic simulations seen the
etal.2013),andcoronallineemissionduringthenebularphasere- self-consistentdevelopmentoftheDSAcycleincollision-lessnon-
quiring a harder source of ionizing radiation than expected from relativisticshocks(e.g.,Caprioli&Spitkovsky2014a;Kato2014;
thecoolingwhitedwarf(e.g.,Shields&Ferland1978).However, Parketal.2014).Asweshalldiscuss,gamma-raynovaeprovide
sincemostofthesesignaturesareobservedontimescalesofmonths areal-timelaboratoryfortestingthepredictionsofDSAtheoryin
orlateraftertheeruption,shocksappeartohavebeenrelegatedto wayscomplementarytotraditionalmethods,suchasthemodeling
a mere side feature of the main thermonuclear event. The Fermi ofsupernovaremnantemission.
discoveryofluminousshocksincoincidencewiththeopticalpeak Thispapersolidifiestheabovetheoreticalargumentsandputs
unambiguouslyestablishestheirimportancetothequalitativepic- themintopracticeusingdatafromtheclassicalnovaeV1324Sco
ture of nova eruptions. The dearth of X-ray and radio shock sig- andV339Del(hereafter,‘novaSco’and‘novaDel’,respectively).
naturesattimescoincidentwiththegamma-raysisunsurprisingin Thoughwell-studiedatmanywavelengths,wedonotconsiderthe
retrospectduetothehighbound-freeandfree-freeopticaldepths novaV959Monbecauseofthelackofearlyopticalcoveragecon-
created,respectively,bylargecolumnsofneutralandionizedgas current with the gamma-ray detections. The salient properties of
atearlytimes(Hillmanetal.2014;Metzgeretal.2014). nova shocks are reviewed in §2, including their radiative nature
Shocks were unexpected in classical novae because the pre- (§2.1), the high efficiency with which shock power is radiated at
eruptionenvironmentsurroundingthewhitedwarfisoccupiedonly optical/UVfrequencies(§2.2),andtheefficiencyofparticleaccel-
bythelowdensitywindofthemainsequencecompanionstar,re- erationandgamma-rayproduction(§2.3).Acombinedanalysisof
quiring a different source of matter into which the nova outflow the optical and gamma-ray data of V1324 Sco and V3229 Del is
collides. One physical picture, consistent with both optical (e.g., presented in §3, using our theoretical framework to constrain the
Schaeferetal.2014)andradioimaging(e.g.,Chomiuketal.2014), minimumfractionoftheshockpowerplacedintorelativisticparti-
andtheevolutionofopticalspectrallines(e.g.,Ribeiroetal.2013; clesandtheminimumfractionofnovaopticallightcurvesthatare
Shore et al. 2013), is that the thermonuclear runaway is first ac- shockpowered.In§4wediscussourresultsandtheirimplications
companied by a slow ejection of mass with a toroidal geometry, forparticleaccelerationatnon-relativisticshocksandforthepower
the shape of which may be influenced by the binary companion sourcebehindnovaopticallightcurves.
(e.g.,Livioetal.1990;Lloydetal.1997).Thisslowoutflowisthen
followedbyasecondejectionoracontinuouswind(e.g.,Bath&
Shaviv1976)withahighervelocityandmoresphericalgeometry.
Assuming the expanding ejecta cools sufficiently, the subse-
2 SHOCKSINGAMMA-RAYNOVAE
quent collision between the fast and slow components produces
strong“internal”shockswithintheejectawhichareconcentratedin 2.1 Theshocksareprobablyradiative
theequatorialplane.Thefastcomponentcontinuestoexpandfreely
alongthepolardirection,creatingabipolarmorphology(Fig.1). The slow outflow from a nova with velocity v4 = 103v8 km s−1
Interestingly, modeling of the symbiotic gamma-ray novae V407 expandstoaradius
Cyg(Abdoetal.2010)alsoappearedtorequirethepresenceofa
R =v t≈6×1013t v cm (1)
denseequatorialtorus(Martin&Dubus2013),similartothatin- ej 4 wk 8
ferredinclassicalnovae(seealsoSokoloskietal.2008,Orlando byatimet = t week.Thedensityintheslowejectaofassumed
wk
et al. 2009, Drake et al. 2009, Orlando & Drake 2012 for other
thickness∼R andhydrogen-dominatedcompositionisgivenby
ej
evidenceforbipolarejectainsymbioticnovae).
Metzgeretal.(2014)presentasemi-analyticmodelfornova M
n ≈ ej ∼9×1010M t−3v−3cm−3, (2)
shocksandtheirthermalemission,whichtheyfittotheradioand ej 4πR3ejf∆Ωmp −4wk 8
X-raydataofthegamma-raynovaV1324Sco.Akeyfindingwas
thattheshocksresponsiblefortheradiomaximumseenmonthsaf- where f∆Ω ∼ 0.5isthefractionofthetotalsolid-anglesubtended
tertheeruptioncould,atsmallerradiiandearliertimes,alsopower bytheoutflow(Fig.1)and M = 10−4M M istheejectamass,
ej −4 (cid:12)
thenovaopticalemission.Onecangeneralizethebasicargument normalizedtoavaluecharacteristicofthosemeasuredbylatether-
asfollows.Gasaheadofashockwithpowersufficienttocreatethe mal radio emission (Hjellming et al. 1979; Seaquist et al. 1980).
observedgamma-rayemissionisnecessarilydense.Mostoftheki- Weassumearadially-thickoutflowbecausetheresultinglowden-
neticenergydissipatedbyshocksmovingthroughadensemedium sitymakesthisthemostconservativeassumptionwhenarguingfor
isradiatedasthermalX-rays(aso-called“radiative”shock).These radiative shocks. A wide solid angle f∆Ω ∼ 0.5 is also the most
X-raysareabsorbedbyneutralgasaheadorbehindtheshock,re- conservativeassumptionwhenarguingforradiativeshocksandis
processing their energies to lower, optical frequencies, where the neededtoproduceahighefficiencyforconvertingthekineticen-
loweropacityreadilyallowstheirenergytoescape.Theobserved ergyoftheoutflowtoshock,andhencegamma-ray,luminosity.
gamma-ray luminosity is typically only a fraction ∼ 10−4 −10−2 Afasteroutflow(hereafter“wind”)ofmasslossrate M˙ and
ofthatemittedasoptical/UVradiation(§3).However,sinceonlya velocityv ∼2v collideswiththeejectafrombehind.Therelative
1 4
fractionoftheshockpowerisusedtoacceleraterelativisticparti- velocitybetweenthefastandslowoutflowsisunlikelytogreatly
clesandonlyafractionofthatisradiatedintheLATbandpass,one exceed this assumed value ∼ v ∼ 103 km s−1, but if it is much
4
concludesthatasignificantfractionofthenovaopticalemissionis lowerthanassumedthiswouldonlystrengthenoursubsequentar-
shock-powered. gumentthattheshocksareradiative,sincethecoolingtimeisan
The above result also implies that combined optical and increasingfunctionoftheshockvelocity.Thedensityofthewind
(cid:13)c 2014RAS,MNRAS000,1–??
Gamma-raynovaeasprobesofparticleacceleration 3
Herewehaveassumedtheshocksareradiative,forwhichtheve-
locityoftheimmediatepostshockgasslowstothatofthecoldcen-
tralshell,suchthattheshockvelocityequalsthedifferencebetween
thevelocityoftheupstreamgasandthecentralshell.Hereafter,the
velocitiesofbothshocksareparametrizedasv = ηv ,wherewe
sh 4
expectthatη<1fortheFSandη∼1forRS.Alsonotethatforpa-
rametersofinterest,theamountofkineticenergydissipatedbythe
RSisgreaterthanthatbytheFSduetothehighervelocityofthe
RS,potentiallyfavoringtheRSasthesiteofparticleacceleration.
Theshocksheatthegastoatemperature
3
T (cid:39) µm v2 ∼1.4×107v2η2K (4)
sh 16k p sh 8
andcompressesittoadensityn = 4n (FS)or4n (RS),where
sh ej w
wehavetakenµ=0.62.
Gascoolsbehindtheshockonacharacteristictimescale
(cid:40)
3kT /2 1.6×103ηv4M−1t3 s FS,
t = sh ≈ 8 −4 wk (5)
cool n Λ(T ) 7.8×104v4M˙−1t2 s RS,
sh sh 8 −5 wk
where Λ = Λ T1/2 = 2×10−27T1/2 erg cm3 s−1 is the cooling
0
function and we have assumed η = 1 in the RS case. Our cool-
ing function includes just free-free emission, which is conserva-
tive from the standpoint of radiative shocks because line cooling
Figure1.Schematicdiagramoftheproposedgeometry(sideview)ofshock contributes a comparable or greater cooling rate at temperatures
interactioninclassicalnovaoutflows(seetext).Aslowoutflowwithveloc- ∼< 3×107 K(e.g.Schureetal.2009).Herewehaveassumedthat
ityv4∼<103kms−1isejectedfirst,itsgeometryshapedintoanequatorially- electronsandprotonsareefficientlycoupledbehindtheshock,as
concentratedtorus,possiblyduetointeractionwiththebinarycompanion is justified because the timescale for Coulomb energy exchange
ofthewhitedwarf(e.g., Livioetal.1990).Thisoutflowisfollowedwithin t = 14T3/2/n s(NRLPlasmaFormulary;Huba2007)isshort
e−p sh sh
afewdaysbyafasteroutfloworcontinuouswindwithahighervelocity comparedtotheexpansiontimescalet ∼R /v ∼t,
exp ej 4
v1∼2v4.Thefastandslowcomponentscollide,produceaforward-reverse (cid:40)
shockstructure.Kineticenergydissipatedbytheshocksisradiatedasther- te−p ≈ 3×10−5M−−41v68η3tw2k FS, (6)
malX-rays,whichareabsorbedbyneutralgasaheadorbehindtheshock t 1.2×10−3M˙−1v6t RS,
andre-radiatedasthermaloptical/UVemission(Metzgeretal.2014).A −5 8wk
small fraction, (cid:15)nth (cid:28) 1, of the shock power is used to accelerate non- wherewehave(conservatively)assumedapurehydrogencompo-
thermal ions or electrons, which radiate gamma-rays by interacting with sition.
ambientgasorradiation,respectively. Whethertheshocksareradiativedependsontheratioofthe
coolingtimescaletotheexpansiontimescale,
(cid:40)
t 2.7×10−3ηv4M−1t2 FS,
atthecollisionradius(∼radiusoftheslowejecta)isgivenby χ≡ cotol ≈ 0.13v4M˙−1t 8 −4 wk RS, (7)
8 −5 wk
n ≈ M˙ ∼2×109M˙ v−3t−2cm−3, (3) ForthecharacteristicrangeofparametersM−4 ∼0.3−3(Seaquist
w 4πR2m v −5 8 wk &Bode2008),v < 3,η < 1andtimescalescorrespondingtothe
ej p 1 8 ∼
gamma-rayemissiont <fewweeks,oneconcludesthattheFSis
∼
whereM˙ =10−5M˙−5M(cid:12)wk−1isnormalizedtoavalueresultingin likelytoberadiative(χ<1).ItislessclearthattheRSisradiative,
theejectionof∼ 10−5M(cid:12) overaweek.Forinstance,atotalmass since in principle for v8 ∼> 2 and a very low wind mass loss rate
4×10−5M(cid:12) was ejected in the “fast” component of V959 Mon M˙ <1onecanhaveχ>1.
−5∼
(Chomiuk et al. 2014). Our assumption that the fast outflow is a
Theargumentforradiativeshockscanbestrengthenedbycon-
steady wind is also the most conservative one when arguing for
sideringadditionalconstraints.First,theopticaldepthoftheouter
radiative shocks; for a fixed fast ejecta mass, the wind density at
unshockedejectaatopticalfrequencies,
thereverseshockissmallerthaniftheejectionhadoccurredovera
shorterduration. τopt(cid:39)mpnejRejκopt≈0.9M−4v−82tw−2k, (8)
Theinteractiondrivesaforwardshock(FS)throughtheslow mustexceedunity,whereκ ∼ 0.1cm2 g−1 istheopticalopacity
opt
shellandareverseshock(RS)backthroughthewind(Fig.1).As-
setbyDoppler-broadenedironlines(Pinto&Eastman2000).This
suming the shocks are radiative, the post shock material is com-
constraintismotivatedbythelackofclearevidence,e.g.emission
pressed and piles up in a central cold shell sandwiched by (the
lines,forhot,energeticshocksinopticallythinregionsduringthe
ram pressure of) the two shocks. The FS propagates at a veloc-
opticalpeaksofnovaeandduringmostepochsofgamma-rayde-
ity v = v −v (cid:28) v , while the velocity of the reverse shock is
f c 4 4 tection.Overthefirstfewweeksorlongerfollowingoutburst(i.e.,
v = v −v ,wherev isthevelocityofthecoldcentralshell(see
r 1 c c priortothedropofthe“ironcurtain”),novaspectraarecharacter-
Metzgeretal.2014,althoughbewaryofnotational1 differences).
ized by broad P-Cygni line profiles, indicating the presence of a
pseudo-photosphere.
Equation(7)canberewrittenintermsofτ as
opt
1sheInllp(avrctiicnutlhairs,Mpaeptezrg)e.rIenttahli.s(2p0ap1e4r)vdsehfiinnestvesahdasdethneotveeslothceityveolfotchiteycoenfttrhael χ= √9m3p/2k1/2ηv2shκopt ≈(cid:40) 2×10−3ηv28τ−op1t. FS,(9)
shocks. 8 3Λ0(nshmpRejκopt) 0.08M˙−−51M−24τ−op2ttw−3k RS.
(cid:13)c 2014RAS,MNRAS000,1–??
4
Fortheforwardshocktooccurbelowthephotosphere(τ > 1) withoutadiabaticlossesafteratime(Arnett1982)
opt
yetnotberadiative(χ > 1)wouldthusrequireunphysicallyhigh
t ≈0.4M1/2v−1/2d. (11)
ejectavelocities,v > 10,000kms−1.TheRSisalsoradiativeif opt −4 8
4 ∼
τ > 1ontimescalesofacoupleweeksfor M < 3aslongas Thetimescalet alsosetstheminimumtimescalefortheoptical
opt −4 ∼ opt
M˙ >0.2. lightcurvetoriseaftertheonsetoftheexplosion.
−5∼
Asecondrequirementisthatpowerdissipatedbytheshocks Theonsetofgamma-rayemissionfromV1324ScoandV339
L = 9πR2n m v3/32exceedtheobservedgamma-rayluminos- Del was delayed with respect to the peak of the optical radiation
sh ej sh p sh
ity L by an efficiency factor 1/(cid:15) (cid:15) > 100 accounting for the byafewdays(Ackermannetal.2014).Thedominantprocess3by
γ nth γ ∼
fractionoftheshockpowerradiatedasgamma-rays,where(cid:15)nt ac- whichgamma-raysofenergy(cid:15)γ ∼ 0.1−3GeVareattenuatedis
countsfortheefficiencyoftheshockinacceleratingnon-thermal inelastic electron scattering, for which the Klein-Nishina opacity
particlesand(cid:15)γaccountsfortheenergyofthelatterradiatedinthe isκie ∼ 10−3((cid:15)γ/GeV)−1κes ∼ 4×10−3((cid:15)γ/GeV)−1κopt.Theejecta
LATbandpass(see§2.3).Equation(7)canbewrittenintermsof will thus remain opaque to gamma-rays of energy (cid:15)γ until τopt ∼<
Lsh=Lγ/(cid:15)nth(cid:15)γas 250((cid:15)γ/GeV), as occurs after a time tγ which exceeds that of the
nominalopticalrisetime(eq.[11])bytheratio
χ = 25861√π3η4v54m3p/L2kγ1Λ/20Rej(cid:15)nth(cid:15)γ tγ ≈(cid:32) cκie (cid:33)1/2≈1.1(cid:18) (cid:15)γ (cid:19)−1/2v−1/2, (12)
t v κ GeV 8
(cid:32) L (cid:33)−1(cid:18)(cid:15) (cid:15) (cid:19) opt w opt
≈ 0.02η4v68twk 1036erγgs−1 0n.th01γ . (10) i.e.tγ ∼coupledaysfor(cid:15)γ ∼0.1GeV.
Fromtheabovewecandrawtwokeyconclusions:(i)ashock
FormeasuredvaluesL ∼3×1035ergs−1(Ackermannetal.2014) that produces gamma-ray emission which is not absorbed and
γ
theshocksarethusradiative(χ < 1)onatimescaleofweeksfor hence observable (gamma-ray optical depth τ < 1) necessarily
γ
(cid:15) (cid:15) <0.01ifthevelocityoftheshocksis<2,000kms−1. radiatesthebulkofitsdissipatedthermalenergywithoutadiabatic
nth γ ∼
Inconclusion,bothforwardandreverseshocksarelikelytobe lossesatopticalfrequencies(τ <c/v ).Inotherwords,attimes
opt ∼ 4
radiativeattimescorrespondingtotheobservedgamma-rayemis- whenthecolumnofejectaissufficientlylowtoallowgamma-rays
sion,althoughthisstatementisthemostsecureattheearliesttimes. to escape unattenuated, it is also sufficiently low to allow ther-
Onecanneverthelesskeepthefollowingargumentsfullygeneralby mal radiation to escape without significant losses to PdV work.
introducingtheshockradiativeefficiency f =(1+5χ/2)−1,which (ii)gamma-rayabsorption(τ > 1)atearlytimesmayexplainthe
rad γ
equalsunityforχ(cid:28)1butscales∝1/χforχ(cid:29)1(Metzgeretal. delayed onset of the gamma-ray emission. If true, the latter im-
2014). plies that the optical emission near peak can be shock-powered,
even if gamma-ray emission is suppressed at this time. Alterna-
tively,thegamma-raydelaymayresultfromthefinitetimescalere-
2.2 Theshockpowerwillmostlyemergeasopticalradiation quiredtoacceleratethegamma-rayproducingparticlesattheshock
(G.Dubus,privatecommunication).
Absent the immediate presence of a shock, the bulk2 of the nova
ejecta is neutral at early times because the timescale for radia-
tive recombination, trec ∼ 1/nejαrec ∼ 11v38tw3kM−−41Z−2 s, is ex- 2.3 Partitioningtheshockenergy
tremelyshortcomparedtotheevolutiontimescale∼weeks,where
α ∼10−12Z2cm3s−1istheapproximateradiativerecombination Alargefraction frad∼1ofthetotalpowerLshdissipatedbyshocks
rec
goes into thermal X-rays, which are absorbed and re-radiated as
rateforhydrogen-likespeciesofchargeZ (Osterbrock&Ferland
2006). X-rays of temperature T < 107 K (eq. [4]) are thus ab- opticalemission(§2.2).Amuchsmallerfraction(cid:15)nth(cid:28)1goesinto
sh ∼
accelerating non-thermal ions or electrons. The fraction of non-
sorbedbyhighcolumnsofneutralgasaheadorbehindtheshock,
thermalpower(cid:15) radiatedasgamma-rays,L =(cid:15) (cid:15) L ,depends
before being re-radiated as line emission at lower frequencies. If nth γ nth γ sh
alsoonafactor(cid:15) <1accountingfortheradiativeefficiencyofthe
theshockisradiativethenthetimescaleforreprocessingtolower γ
acceleratedparticlesandthefractionofthetotalgamma-rayemis-
temperaturesisalsonecessarilyshortbecausethelinecoolingfunc-
tion Λ(T) increases rapidly with decreasing temperature down to sion emitted in the LAT bandpass. Combining these expressions,
T ∼ 104 K(e.g.Schureetal.2009).However,harderX-rayswith thefractionofthetotalnovaopticalluminositypoweredbyshocks
canbewritten
energies > 10 keV should be free to escape even at these early
∼
timesduethedecreasingbound-freecrosssectionathighphoton f ≡ Lopt,sh ≈ frad Lγ . (13)
frequencies(§4). sh L (cid:15) (cid:15) L
opt γ nth opt
Radiationescapesefficientlyonceitreachestheoptical/near-
Once (cid:15) is specified based on the assumed emission process
UVbandduetothemuchloweropacityatthesefrequenciescom- γ
(hadronicorleptonic),theobservedratioL /L setsalowerlimit
paredtotheUV/X-rayopacityofneutralgas.Reprocessedoptical γ opt
onthevalueof(cid:15) ,i.e.
radiationwillfurthermorenotbedegradedbyPdVlossesprovided nth
that the photon diffusion timescale td ∼ Rejτopt/c is shorter than f <1⇒(cid:15) >(cid:15) = 1 Lγ , (14)
the expansion timescale texp ∼ Rej/v4 ≈ t, where τopt is the opti- sh nth nth,min (cid:15)γ Lopt
cal depth (eq. [8]). Equating these two, optical radiation escapes assumingaradiativeshock(f =1).Alternatively,ifthevalueof
rad
(cid:15) isassumed,thenthemeasuredvalueofL /L determines f .
nth γ opt sh
2 Althoughthebulkoftheejectaisneutralatearlytimes,X-raysfromthe
shocksfullyionizeathinlayerofgasjustaheadoftheshocks(Metzgeretal. 3 Photo-pionproductionisthedominantsourceofopacityforhigheren-
2014).Thus,wedonotexpecttheshocktobemodifiedbythepresenceofa ergygamma-rays(cid:15)γ ∼>3GeV,forwhichtheopacityisκπ ∼ 3×10−4κes
neutralupstreammedium,asmayoccurinsomesupernovaremnants(e.g., (e.g.Anchordoquietal.2002,Montanetetal.1994).Photon-photonpair
Blasietal.2012). creationopacitybecomesimportantatTeVenergies(eq.[25]).
(cid:13)c 2014RAS,MNRAS000,1–??
Gamma-raynovaeasprobesofparticleacceleration 5
Wenowconsiderwhatvaluesof(cid:15) and(cid:15) areexpectedinhadronic onionizationbythefree-freeemission(theireq.[45]).Replacing
nth γ
andleptonicscenarios,respectively. R with∆ inequation(16)resultsin
ej ion
eB v ∆
E = sh sh ion
2.3.1 Hadronicscenario max c
(cid:18) (cid:15) (cid:19)1/2(cid:18) n (cid:19)
Themomentumdistribution f(p)∝ p−4ofnon-thermalprotonsac- ≈ 1.0×109eVη3 B ej M1/2v3/2t−3/2(.18)
celeratedviaDiffusiveShockAcceleration(e.g.,Blandford&Os- 10−6 1010cm−3 −4 8 wk
triker1978)correspondstoanenergydistribution Thus, for typical values of n ∼ 109 −1010 cm−3 (eq. [2], [3])
ej
ddNEpE2p∝(cid:40) cEo1pn/2s,tant, mkTcs2h(cid:28)∼<EEp(cid:28)<Empc2, . (15) a1n0d−4v(8(cid:15)B∼,(cid:63)1∼>, o1n0e−2fi−nd1s)thisatnhoiwghreerqufiierleddsttorehnagvthesEomfax(cid:15)B∼>∼>101100−2eV−.
p p p max
Note,however,thatMetzgeretal.(2014)donottakeintoaccount
thatconcentratesmostofthenon-thermalenergyinrelativisticpar- additionalionizationofhydrogenbytheUVradiationproducedby
ticles.TheHillas(1984)criterionsetsanupperlimitonthemaxi- linecoolingorbythereprocessedX-rays,whichcouldbeimportant
mumprotonenergy atearlytimesofrelevancebecausetheejectaisopaquetoX-rays.
eB v R (cid:18) (cid:15) (cid:19)1/2 Thiscouldincreasetheenergyoftheionizingradiation,andhence
Emax= shcsh ej ≈7×1012eVη2 10B−6 M−1/42v38/2tw−1k/2, (16) the thickness of the ionized layer and Emax, by up to a factor of
∼kT /(2Ryd)∼50η2v2,whereRyd=13.6eVisthecharacteristic
where B is the magnetic field strength near the shock, which is sh 8
sh ionization threshold energy for hydrogen, relaxing constraints on
estimatedbyassumingthatmagneticpressureB2/8πisafraction
sh (cid:15)B,(cid:63).
(cid:15) ofthethermalpressureofthepost-shockgas.
B Thefractionoftheshockpowerplacedintonon-thermalions
Areasonablyhighvalueof(cid:15) isexpectedifionaccelerationis
B (cid:15) can be estimated from observations of other non-relativistic
efficient,becausecosmic-rayinducedinstabilitiesamplifythemag- nth
shocks, such as gamma-ray emission in supernova remnants
neticfieldforsomedistancebehindtheshocktoasignificantfrac-
(e.g. Ackermann et al. 2014). In Tycho, for instance, Morlino &
tionofitsequipartitionvalue.Caprioli&Spitkovsky(2014b)show Caprioli (2012) infer (cid:15) ∼ 0.1 if the gamma-rays are hadronic
nth
thatthemagneticfieldneartheshockisamplifiedfromitsinitial
inorigin.Hybrid(kineticions-fluidelectron)simulationsofnon-
upstreamvalueB0,accordingto(Bsh/B0)2 ≈3(cid:15)nthMA(theireq.2), relativisticshocksalsofind(cid:15) ≈0.1−0.2forcasesinwhichtheup-
whereM =v /v istheAlfve´nicMachnumberoftheupstream4 nth
A sh A (cid:112) streammagneticfieldisquasi-paralleltotheshocknormal(Capri-
flowintheshockframe,v =B / 4πm n ,and(cid:15) isthefraction
A 0 p 4 nth oli&Spitkovsky2014a).However,ifthenovaejectaischaracter-
oftheshockdissipatedkineticenergyplacedintorelativisticions.
izedbyaphaseofapproximatelysteady-stateoutflow,thenradial
Theequipartitionfractionoftheshockregioncanthusbewritten
expansionintwodimensionswillproduceamagneticfielddomi-
as
natedbyitstoroidalcomponent,i.e.perpendiculartotheoutflow
(cid:18)(cid:15) (cid:19)(cid:18) (cid:15) (cid:19)1/2 and hence shock direction (Fig. 1). For such quasi-perpendicular
(cid:15) =3(cid:15) η−1(cid:15)1/2≈10−6η−1 nth B,0 , (17)
B nth B,0 0.1 10−11 magnetic field geometries, Caprioli & Spitkovsky (2014a) infer
muchlowerprotonaccelerationefficiencies(consistentwithzero),
where(cid:15) ≡ B2/(4πn m v2)istheratioofmagneticenergytoki-
B,0 0 4 p 4 apointwereturntoin§4.
neticenergywithintheinitial,unshockedoutflow.
Relativisticprotonsacceleratedattheshocksproducepionsby
Thevalueof(cid:15) withintheunshockednovaejectacanbecon-
B,0 collidingwitheffectivelystationaryprotonsintheejecta.Themean
strainedasfollows.Assumethatthemagneticenergydensityofthe
timebetweeninteractionsisgivenbyt =(κ m n c)−1,where
outflowU isafraction(cid:15) ofthebulkkineticenergyU ∝ρv2/2 p−p p−p p ej
nearthestBellarsurface(rB=,(cid:63)R ),whereρandvaretheoutKflowden- κp−p ∼ 0.025cm−2 g−1 ≈ κopt/4(Kamaeetal.2006)istheopacity
(cid:63) forinelasticprotoncollisionsofenergyE >GeV.Thenumberof
sityandvelocity,respectively.Flux-freezingwithinthe3Dexpand- p ∼
collisionsaprotonexperiencesoveranexpansiontimescalet/t
ingflow(ρ∝r−3)dilutesthefieldstrengthaccordingtoB∝1/r2, p−p
suchthatU /U = (cid:15) attheradiusoftheshock∼ R willbeat thusexceedsunityuntilafteratime
B k B,0 ej
mostafactorofR /R smallerthan(cid:15) .Forcharacteristicvalues
of Rej ∼ 1014 cm(cid:63)andejthe initial radiuBs,(cid:63)R(cid:63) ∼> 109 cm of the out- tp−p≈8.2M−1/42v−83/2weeks. (19)
flowsetbythewhitedwarfsurface,weexpectthat(cid:15) >10−5(cid:15) .
B,0 ∼ B,(cid:63)
Thus,for(cid:15)nth = 0.1andη = 1,evenanextremelysmallvalueof At times t (cid:28) tp−p, protons lose their energy to pion production
(cid:15) >10−18appearssufficienttoaccelerateprotonstoamaximum insteadofadiabaticexpansion;theejectathusactsasanefficient
B,(cid:63) ∼
energyE >1010eV(eq.[16])largeenoughtoexplainthehigh- “calorimeter”forconvertingrelativisticprotonsintogamma-rays.
max ∼
Thefractionof p− pcollisionsproducinggamma-rays(cid:15) is
estLAT-detectedphotonenergiesviaπ creation(Ackermannetal. γ
0 theproductofthefractionofinelasticinteractions,σ /(σ +σ )∼
2014). ie ie e
0.5−0.8(whereσ andσ aretheelasticandinelasticcrosssec-
Wecaution,however,thatthebulkoftheejectaisneutraland e ie
tions,respectively;Kamaeetal.2006),andthefraction(cid:39) 1/3of
hencemaynotbeabletosupportthestrongturbulentmagneticfield
inelasticeventsplacedintothe p+p → π0 → γ+γchannel.We
neededtoaccelerateparticles.InthiscasetheradiusR enteringthe
ej
thustypicallyexpectthat(cid:15) ≈0.2−0.3,dependingonthedetailsof
Hillascriterioninequation(16)shouldbereplacedbythewidthof γ
theacceleratedprotonspectrum,whilealowervaluecouldresultif
theX-rayionizedlayeraheadoftheshock.Metzgeretal.(2014)
estimatethelattertobe∆ion∼9×109ηv (n /1010cm−3)−1cmbased protonsarenotefficientlytrapped,i.e.attimest>tp−p.
8 ej
To summarize, we expect (cid:15) (cid:15) < 0.03 in hadronic scenar-
nth γ ∼
ios if the magnetic field within the ejecta is perpendicular to the
4 Forconcreteness,wefocushereonamplificationofthemagneticfieldof shockplane,butthisvaluemaybeconsiderablylowerifthefield
theslowejectaattheforwardshock,althoughsimilarconsiderationsapply isinsteadparalleltotheshockplane,aswouldbeexpectedgivena
toamplificationofthefieldinthefastoutflowatthereverseshock. phaseofquasi-steadyoutflowfromthewhitedwarfsurface.
(cid:13)c 2014RAS,MNRAS000,1–??
6
2.3.2 Leptonicscenario where we have assumed that that particles with 104 < γ < 105
∼ e ∼
aretheonlyonescontributingintotheLATbandpassandthatthey
In supernova shocks, the ratio of the energy placed into rela-
radiativewith100percentefficiency,i.e.t (cid:28) tort (cid:28) t.
tivistic protons to that in relativistic electrons is estimated to be cool,IC cool,rb
Power-law fits to the gamma-ray spectra of three classical novae
K ∼ 10−4 −10−2 based on observations of individual remnants
ep yieldbest-fitphotonindicesΓ ∼ 2−2.5(Ackermannetal.2014)
(Vo¨lketal.2005;Morlino&Caprioli2012)andsynchrotronemis-
corresponding to p = 2(Γ−1) ∼ 2−3, for which we estimate
sionfromGalacticcosmicrays(Beck&Krause2005;Strongetal.
(cid:15) ∼ 0.2−10−4. To be conservative we hereafter assume p = 2,
2010).Thisvalueisconsistentwithrecentparticle-in-cellsimula- γ
correspondingto(cid:15) =0.2.
tionsofnon-relativisticshocks,whichfindK ∼10−3whenextrap- γ
ep Insummary,adopting(cid:15) ∼10−5−10−3motivatedbysimula-
olatedtoshockvelocitiesv /c<0.01characteristicofthoseinno- nth
sh ∼ tionsandobservations,weestimatethat(cid:15) (cid:15) ∼10−6−10−4inthe
vae(Parketal.2014;Kato2014).Assumingshocksacceleratepro- nth γ
leptonicscenario.
tonswithamaximumefficiency∼ 0.1(§2.3.1),K < 10−2 corre-
ep ∼
spondstoarelativisticnon-thermalelectronfractionof(cid:15) <10−3.
nth∼
ToComptonupscatteropticalseedphotonsofenergy E ∼
opt
eVenergyto∼0.1−10GeVrequireselectronswithenergyE = 3 DATA
e
γemec2andLorentzfactorγe∼104−105.TheratiooftheCompton Thissection describesour analysisofthe gamma-rayand optical
coolingtimescaleoftheelectrontotheexpansiontimescaleisgiven lightcurvesofV1324ScoandV3229Del,eventschosenascur-
by rentlybeingtheonlyclassicalnovaewithbothpublishedgamma-
t 3m c (cid:18) γ (cid:19)−1(cid:32) L (cid:33)−1 ray data and contemporaneous optical coverage. We do not con-
cootl,IC = 4σ Ue γ t ∼0.07τ−op1t 10e4 1038eorpgt s−1 v28twk, sidersymbioticnovaeinthisanalysisbecausetheargumentforthe
T opt e
(20) shocksbeingradiativeislesssecuregiventhatthelatterpropagate
where U ≈ Fτ = L τ /4πcR2 is the radiation energy den- intotheextendedwindofthegiantcompanionstar,insteadofthe
opt opt opt ej
sityneartheshock(forshocksbelowthephotosphere,τ > 1), potentially denser slow ejecta in the case of internal shocks. Our
opt
where we have used the fact that the conserved radiative flux goalistousethemeasuredratioofgamma-rayandopticalfluxes
F ∝ ∂Uopt/∂τ in the diffusion approximation implies that Fτ is toconstraintheparticleaccelerationefficiency(cid:15)nthandthefraction
constantfromthephotosphere(τ∼1)totheshockdepthτ=τopt. oftheclassicalnovaopticallightcurvepoweredbyshocks fsh,fol-
Equation(20)showsthatγ > 104 electronsareinthefastcool- lowingtheargumentsoutlinedin§2.3.
e ∼
ing regime (t (cid:28) t ) for luminosities L > 1037 erg s−1 and
cool exp opt ∼
timescalest∼weeksofrelevance.
3.1 Optical
Relativistic Bremsstrahlung emission represents an alterna-
tive, and possibly dominant, leptonic emission mechanism. The For each nova we use photometric measurements at both opti-
coolingrateofarelativisticelectronofLorentzfactorγ offprotons calandnear-infrared(NIR)wavelengths.Opticalphotometrywas
e
inthenovaejectaisgivenbyq˙ =3×10−22γ3/2n ergs−1(Rybicki taken from the database of the American Association of Variable
rb e ej
&Lightman1979),resultinginacoolingtime Star Observers (Henden 2013). Both nova Sco and Del had BVR
t γ m c2 (cid:18) γ (cid:19)−1/2 bandmeasurements,butonlyDelincludedI band.Tosupplement
cool,rb = e e ≈5.1×10−4 e M−1t2 v3, (21) theNIRfornovaSco,weusedJHKmeasurementsfromtheSmall
t q˙ 104 −4 wk 8
rb andModerateApertureResearchTelescope(F.M.Walter,private
where we have used equation (2). A comparison between equa- communication).Onlyphotometricmeasurementscoincidentwith
tions(20)and(20)showsthatrelativisticbremsstrahlungemission the published Fermi gamma-ray light curve were used; specifi-
canexceedthatfromInverseComptonscatteringfortypicalvalues cally August 16−September 14 2013 and June 15−June 30 2012
ofthenovaluminosity,outflowvelocity,andejectamass.Regard- forV339DelandV1324Sco,respectively.Photometricreddening
lessofwhetherInverseComptonorbremsstrahlungemissiondom- correctionswereappliedtothedatasetsusingan E(B−V) = 0.2
inates, the shock energy placed into electrons with the necessary forV339Del(Munarietal.2013)andE(B−V) = 1.0forV1324
Lorentzfactorstoproducetheobservedgamma-rayemissionwill Sco(Finzelletal.2015).Filterspecificreddeningcorrectionsfor
infactberadiatedwithhighefficiency. the optical/NIR were taken from Schlafly et al. (2011) assuming
Comptonscatteringofelectronswithanacceleratedspectrum R =3.1.
dNe/dEe ∝ Ee−p,whereEe =γemec2,producesagamma-rayspec- V Thetotaloptical/NIRfluxeachnight,Fopt,wasdeterminedby
trum approximating the SED as a blackbody, fitting a temperature and
dNγ ∝(cid:40) E−(p+1)/2, E(cid:28)Ec . (22) normalization,andintegratingoverfrequency.Theearly-timeflux
dE E−(p+2)/2 E(cid:29)E , obtainedforV339Delareconsistentwiththevaluesfoundinthe
c
more detailed analysis of Skopal et al. (2014), who also showed
where E ∼ E γ2 and γ is the minimum electron Lorentz fac-
c opt c c thatthespectralshapewasablackbodyallthewayouttothemid-
tor obeying the fast-cooling condition (t < t ; eq. [20]).
cool,IC ∼ exp IR.WeconfirmedourblackbodyassumptionforV1324Scobyex-
A similar cooling energy can be defined in the case of relativis-
tendingourspectralfituptothenear-UVandcomparingwithflux
tic brehmsstrahlung emission, below which the photon spectrum
valuesfromSwiftUVOT(Pageetal.2012).Afterapplyingredden-
dN /dE ∝ E−(2p−1)/2,i.e.thesameasforInverseComptoninthe
γ ingcorrectionsfromBrownetal.(2010)ourblackbodyfitpredicts
p=2caseofgreatestrelevance(seebelow).
anear-UVfluxof2.1±0.4×10−13ergs−1cm−2,avalueinagree-
Thefractionofthetotalenergyinrelativisticelectronsradi-
mentwiththeobservedflux,2.4±0.16×10−13ergs−1cm−2.Asthe
atedintheLATbandpassisgivenby
near-UVfluxisafactor∼105timeslowerthanintheoptical,this
(cid:15) < (cid:82)110045 ddNEeeEedEe ≈(cid:40) 108−4p−1010−5p(cid:28)0.2, p>(223). efixlec.elRleenstulatgsrfeoermtehnettvoatalildoaptetsictahle/NaIsRsuflmuexdabnladcbkebsotd-fiytstpeemcptrearlapturore-
γ (cid:82)105 dNeE dE 0.2 p=2, asafunctionoftimeareshowninFigure2.
1 dEe e e
(cid:13)c 2014RAS,MNRAS000,1–??
Gamma-raynovaeasprobesofparticleacceleration 7
As only three nights have complete NIR + BVR color data Table1.γ-ray/opticalfluxratioinclassicalnovaeandimplications.
in nova Sco, we also consider separately the flux ratio on other
nights with LAT detections obtained using just the V magnitude (cid:20) (cid:21)
tocalculatetheoptical/NIRflux,assumingabolometriccorrection Nova (cid:104)log LLoγpt (cid:105) log(cid:15)n(ath),min fs(hb)
identicaltothatmeasuredwithbettercolordataonday15.Uncer- V1324Sco -2.2±0.4 -1.5±0.4 0.13((cid:15)nth/0.1)−1
taintyinthetotalfluxisestimatedbycombiningtheuncertaintyin V339Del -3.5±0.2 -2.8±0.2 0.016((cid:15)nth/0.1)−1
thebest-fitconstantoffsetwithanuncertaintyinthetemperaturefit
derivedusingtheerrorinindividualfluxmeasurement.
(a)Minimumfractionofshockpoweredplacedintonon-thermalparticles(eq.[14]),
calculatedassumingradiativeshocksand(conservatively)(cid:15)γ=0.2(§2.3.1,2.3.2).
3.2 Gamma-Ray (b)Fractionofopticalluminositypoweredbyshocks(eq.[13]),
calculatedassumingradiativeshocksand(conservatively)(cid:15)γ=0.2.
TheFermiLATdatafornovaScoandDelaretakenfromAcker-
mannetal.(2014).Spectralfitstothegamma-rayemission(over
itsentireduration)areprovidedbytheseauthorsfortwoprofiles:
PowerLaw(PL,dN /dE ∝ E−Γ)andPowerLawwithExponen-
γ
tialCut-OffatenergyE =Ec(EPL,dNγ/dE ∝E−sexp−E/Ec).The
best-fitvaluesofthefreeparameters,Γ(PL)orsandE (EPL),are
c
providedalongwiththeiruncertainties.
Also provided for each day is the average photon number
fluxabove100MeV, N ∝ (cid:82)100GeV dNγdE.Theenergyflux F ∝
(cid:82)100GeVEdNγdEiscalcuγlated1f0r0oMmeVFdEaccordingto γ
100MeV dE γ
N (cid:82)100GeVEdNγdE
F = γ 100MeV dE , (24)
γ (cid:82)100GeV dNγdE
100MeV dE
whereuncertaintiesinF arederivedfromboththequoteduncer-
γ
taintiesinN andinthebest-fitparametersofthespectralfits.Al-
γ
thoughwecalculatethegamma-rayfluxeachday,ouranalysisas-
sumesaconstantspectralshapeoverthedurationoftheoutburst,
asnecessitatedbythepoorstatisticsofthegamma-raydetections.
3.3 FluxRatio
Our results for the flux ratio L /L = F /F as a function of
γ opt γ opt
timefornovaScoandDelareshowninFigure3.Keyresultsare
summarizedinTable1.TheratioL /L isconsistentwithbeing
γ opt
constant in time in nova Sco, but nova Del shows evidence for a
moderatesecularincrease.
We find an average value L /L ≈ 10−2.2(10−3.5) for nova
γ opt
Sco(Del),respectively.Assumingradiativeshocksandgamma-ray
efficiency(cid:15) < 0.2(§2.3.1,2.3.2),theminimumnon-thermalpar-
γ ∼
ticle acceleration efficiency corresponds to (cid:15) > 0.1 − 0.01 in
nth ∼
nova Sco and (cid:15) > 10−3 in nova Del. This greatly exceeds the
nth ∼
acceleration efficiency expected for electron acceleration at non-
relativisticshocks,disfavoringleptonscenariosforthegamma-ray
emission. Furthermore, assuming a proton acceleration efficiency
of(cid:15) ∼0.01−0.1,weconcludethatafraction f >10−100per
nth sh ∼ Figure2.Totalopticalflux(toppanel)andbest-fitblackbodytemperature
centoftheopticalemissionwasshock-poweredinnovaSco.The (bottompanel)asafunctionoftimesinceoutburstfornovaeV1324Sco
shock-poweredfractionis fsh∼>1−10percentinnovaDel. (blue)andV339Del(red).TimeismeasuredstartingonJune1,2012for
NovaSco(beginningofopticaloutburst),andstartingonAugust16,2013
forNovaDel(epochoffirstgamma-raydetection,withindaysoftheoptical
rise).
4 DISCUSSIONANDCONCLUSIONS
Thehighdensitieswithinthenovaejectaatearlytimescoincident
with the observed gamma-rays imply that the shocks responsible theobservedvaluesofLγ/Lopt,forthehighestgamma-rayefficien-
forthisemissionarelikelytoberadiative(§2.1).Thoughnotob- cies (cid:15)nth ∼ 0.1 expected in hadronic scenarios, we conclude that
served directly, thermal X-rays from the shocks are absorbed by a significant fraction fsh ∼> 10 per cent and ∼> 1 per cent of nova
theejectaandreprocessedtoopticalfrequencies(§2.2).5Basedon optical emission in nova Sco and nova Del, respectively, is pow-
5 NovaDeldidshowX-rayemissionatlatertimes,aftertheepochofpeak hadexpandedorbecamesufficientlyphoto-ionizedtoreducethecolumnof
gamma-rayandopticalemission.Thispresumablyoccurredaftertheejecta neutralabsorbinggas(seebelow).
(cid:13)c 2014RAS,MNRAS000,1–??
8
ilar mechanism of internal shocks within a time-variable outflow
maypoweranopticaltransientfromtheremnantproducedbythe
mergerofbinarywhitedwarfs(Beloborodov2014).
If the majority of nova optical light is powered by radiative
shocks, then the ratio of optical and gamma-ray fluxes should be
relatively constant in time, assuming that the microphysical pa-
rameters of the shocks remain constant (and that the conditions
τ > v /c and t /t < 1 remain satisfied in hadronic and lep-
p−p 4 cool
tonicscenarios,respectively).NovaScoisconsistentwithatem-
porallyconstantratioL /L ,whilenovaDelshowsevidencefor
γ opt
the gamma-ray emission becoming relatively stronger with time
(Fig.3).TheapparentincreaseofL /L innovaDelcouldresult
γ opt
fromthereverseshockthermalemissionbecominglessradiatively
efficientwithtime,i.e.χ∝t(eq.[7]).Alternatively,itmayreflect
theearlytransitioninthiseventtoanebularphase(asoccurredon
Day11;Skopaletal. 2014),resultinginalossoffluxout ofthe
measuredopticalbandandintotheUV.Ifnovashocksareindeed
radiative,thenwepredictthatL /L shouldnotexceed∼0.06at
γ opt
anytime,sincethisrepresentsthelimitofshock-dominatedemis-
sion f =1(eq.[13])forrealisticmaximumefficiencies(cid:15) <0.3,
sh γ ∼
(cid:15) <0.2.
nth∼
Thegamma-raytoopticalfluxratioalsoplacesalowerlimit
on the acceleration efficiency (cid:15) of relativistic non-thermal par-
nth
ticles at non-relativistic shocks. For nova Sco and nova Del we
constrain(cid:15) > 10−2 and10−3,respectively(Table1).Unliketra-
nth ∼
ditional studies modeling particle acceleration in supernova rem-
nants, nova shocks evolve in real-time, in principle allowing for
thestudyoftime-dependenteffects.Modelsusedtoconstrainpar-
ticleaccelerationinsupernovaremnantsalsosometimesrequireas-
sumptionsabouttheescapefractionofrelativisticparticles,e.g.if
gamma-rays are produced by the collision of relativistic protons
with nearby molecular clouds of irregular geometry. By contrast,
nova ejecta serves as a relatively efficient hadronic “calorimeter”
since relativistic protons are probably trapped when gamma-rays
Figure3.Ratioofgamma-rayandopticalluminosities,Lγ/Lopt,fornovae areobserved(eq.[19]).
V1324Sco(toppanel)andV339Del(bottompanel)asafunctionoftime Neitherhadronicnorleptonicscenariosfornovagamma-ray
sinceoutburst.InNovaSco,largesquaresshownightswithfullNIR+VBR
emissioncanberuledoutbymodelingoftheγ−rayspectrumalone
coverage,whilesmalltrianglesshowthefluxratioestimatedusingjustthe
(Ackermannetal.2014).However,thetensionbetweenthevalue
V-band magnitude adopting the same bolometric correction as measured
(cid:15) >10−2wefindisrequiredinnovaScoandthemuchlowerelec-
withthefulldatacolordataonDay15. nth∼
tronaccelerationefficiency(cid:15) < 10−3 inferredfromobservations
nth ∼
ofsupernovaremnants(e.g.Morlino&Caprioli2012)andtheoret-
eredbyshocks.Theselimitsapproachunityformorerealisticef- icalmodeling(Kato2014;Parketal.2014)appearstodisfavorthe
ficiencies (cid:15) < 0.01 expected from the difficulty of accelerating leptonicscenario.Leptonicmodelsalsorequireaflatinjectedspec-
nth ∼
protons given the expected geometry of the magnetic field in the trum p = 2tobeenergeticallyfeasible(eq.[23]).Incontrast,ion
pre-shockedejecta(seebelow). acceleration efficiencies as high as (cid:15) ∼ 0.1 are found for non-
nth
This shock-powered emission mechanism is similar to that relativistic shocks by hybrid PIC simulations, but only in cases
at work in some core collapse supernovae when the ejecta whentheupstreammagneticfieldisparalleltotheshocknormal
from the exploding star interacts with dense circumstellar matter (Caprioli&Spitkovsky2014a);forperpendicularfieldsessentially
(e.g.Chevalier&Fransson1994;Larssonetal.2011),whichinex- no ion acceleration is seen, also inconsistent with our lower lim-
tremecasespowersthemostluminoussupernovaeyetdiscovered itson(cid:15) .Hadronicscenariosinvolvingionaccelerationatquasi-
nth
(Smithetal.2007).Ourfindingthatalargefractionofnovaopti- parallelshocksthusappeartobethemostviablesourceofrelativis-
calemissionispoweredbyshocksrequiresarevisionofstandard ticparticlesresponsiblefornovagamma-rays.
modelsthatinsteadassumenovathermalemissionresultsfromthe However, this conclusion is problematic. Most of the power
direct outwards transport of thermal energy released in the white dissipatedinthesystemoccursatthereverseshock,makingitthe
dwarfenvelopebynuclearburning(e.g.Hillmanetal.2014).The mostnaturallocationforparticleacceleration.Ifthefastoutflowis
ultimateenergysource(thethermonuclearrunaway)isnotinques- ejectedoveratimescalewhichislongcomparedtothedynamical
tion,butshock-poweredemissiontapsintothedifferentialkinetic timenearthesurfaceofthehydrostaticwhitedwarfenvelope(i.e.,a
energy of the outflow instead of its thermal content advected or quasi-steadywind),thenitsmagneticfieldwillbecomedominated
diffusedfromsmallradii.AssuggestedbyMetzgeretal.(2014), byitsazimuthalcomponentatthemuchlargerradiiwherethere-
shock-powered optical emission might also help explain some of verse shock occurs (§2.3.1). Such a field, being perpendicular to
theirregularlightcurveshapes,includingplateausandsecondary theradialshocknormal,isnotconducivetoionacceleration.
maxima,observedinsomenovae(e.g.,Stropeetal.2010).Asim- This mystery could be resolved if particle acceleration oc-
(cid:13)c 2014RAS,MNRAS000,1–??
Gamma-raynovaeasprobesofparticleacceleration 9
curs at localized regions of quasi-parallel shocks, creating spe- anupperlimitof<10−11ergscm−2s−1onthe>50keVemission.
∼ ∼
cial regions of efficient acceleration ((cid:15) ∼ 0.1) with (cid:15) = 0 Gamma-rayemissionwasdetectedbyLATat2−3σsignificance
nth nth
across the larger bulk, thereby resulting in an average value of and a flux of ∼ 10−10 erg cm−2 s−1, but lasting only for 2 days
(cid:15) ∼ 10−3 −10−2 consistent with observations. These localized neartheonsetoftheoutburst(Cheungetal.2014),approximately
nth
regions of conducive field geometry could be caused by global aweekbeforetheNuSTARobservationsandwhen(perhapsnotco-
asymmetriesintheejecta,suchasobliqueshocksoccurringwhere incidentallyinlightofourresultsonshock-poweredopticalemis-
the edge of the slow ejecta torus meets the faster bipolar wind sion)theopticallightcurvewasatitsmaximum.Bythetimeofthe
(Fig.1).Alternatively,inhomogeneityofthenovaejecta(“clumpi- NuSTAR observations, the optical flux had decreased by a factor
ness”)couldalsoresultinlocalizedregionsofobliqueshocksbe- of∼100fromitspeakvalue,suchthatifF /F hadremainedap-
γ opt
tween the clumps. Indeed, low ejecta filling factors are inferred proximatelyconstantintime(asinthenovaeinoursample;Fig.3),
observationally by emission line modeling of the nebular phase thentheNuSTARupperlimitcorrepondsto f <10inthenotation
X ∼
(e.g.,Shoreetal.2013).Radialfieldsmayalsobeproducednear above,i.e.notparticularlyconstraining.Westronglyencouragefu-
theshockastheresultofRayleigh-Taylorinstabilitiesattheinter- tureNuSTARobservationsofgamma-raynovae,ideallycloserto
facebetweenthefastnowoutflowandthedensecentralshell(as theopticalpeakandcoincidentwithLATdetections.
mayoccurinsupernovaremnants;e.g.,Blondin&Ellison2001). Inthispaperwehavefocusedoninternalshocksinclassical
Leptonic versushadronic models fornova gamma-ray emis- novae instead of symbiotic novae, because in the symbiotic case
sion may be further distinguished by their predictions for non- shocksandparticleaccelerationcanresultalsofromtheinteraction
thermal X-ray emission. In nova Sco, Swift XRT observations betweenthenovaejectaandtheeffectivelystationarydensewindof
placed an upper limit of F < 9 × 10−14 erg s−1 cm−2 on the theredgiantcompanion(Abdoetal.2010,Martin&Dubus2013).
X
0.3−10 keV flux on days 22−41 (Page et al. 2012), i.e. three or- Ouranalysisreliesontheassumptionofradiativeshocksinternal
dersofmagnitudelessthanthesimultaneousLAT-detectedfluxof tothenovaejecta,asisjustifiedbythehighermassoutflowrates
F ∼ 2×10−10 erg cm−2 s−1. Such a low value of F /F would M˙ ∼ 10−3M yr−1 and densities that characterize nova ejecta as
γ X γ (cid:12)
atfirstappeartobebarelycompatiblewiththeleptonicscenario, comparedtothelowervalues< 10−5M yr−1 characteristicofred
∼ (cid:12)
even when considering the most conservative case of p = 2 and giantwinds.Nevertheless,muchofthesamephysicsofrelativistic
aslowcoolingspectrumνF ∝ ν1/2 fromkeVto∼GeVenergies particle acceleration could apply to both scenarios. Likewise, the
ν
(eq. [22]). The hadronic scenario fares even worse: secondary e± presence of a dense equatorial structure associated with the nova
pairsfromπ± decaycarryasimilartotalenergytothatreleasedin ejectacouldalsobepresentinsymbioticsystems(aswasinferred
γ−raysfromπ decay.Thesepairs’energies,∼0.1−1GeV,corre- inV407Cyg;Martin&Dubus2013).
0
spondtoLorentzfactorsγ ∼100−1000thatwillupscatter∼eV An additional prediction of the favored hadronic model is a
e
opticaltoenergies∼10−1000keVwithreasonablyhighefficiency GeVneutrinofluxcomparabletothegamma-rayfluxthatmaybe
(eq.[20]).However,amoredetailedcalculationmustaccountfor detectedbyfutureexperiments(Razzaqueetal.2010).Depending
the important role of coulomb losses on the energy of the X-ray on the maximum ion energy, novae may be important sources of
emittingelectrons,whicharelikelysevereduetothehighdensities TeVgamma-rayemission.Sitareketal.(2015)recentlypresented
of nova shocks; this will likely suppress the X-ray emission be- upperlimitsonTeVemissionfromV407CygbytheMAGICtele-
lowthatobtainedbyanaiveextensionoftheICorbremsstrahllung scope(Aliuetal.2012)whichlieafactorof∼ 10belowtheex-
spectrumtolowerenergies. trapolatedFermiLATspectrum;similarTeVupperlimitsonV407
Thisdearthofearly∼keVemissionfromnovashockscould CygwerereportedbyVERITAS(Aliuetal.2012).Theobserved
resultfromthehighcolumnofneutral,X-rayabsorbinggasahead cut-offinthephotonspectrummaybeduetoanintrinsiccut-offin
of the shock at times coincident with the gamma-ray emission theacceleratedionspectrum(eqs.[16,18]),oritmayresultfrom
(Metzgeretal.2014).However,higherenergyX-rays> 10−100 γ−γabsorptionduetoe±pair-creationattenuationbythenovaop-
∼
keV could escape without photoelectric attenuation6, motivating ticallight.TeVphotonscanpaircreateofftargetphotonsofenergy
one to consider the prospects for nova detection with NuSTAR Eopt∼1eV,resultinginanopticaldepth
(Harrison et al. 2013), which has unprecedented X-ray sensitiv- (cid:32)E (cid:33)−1(cid:32) L (cid:33)
ity above 10 keV. If a fraction f of the LAT luminosity is ra- τ ≈n σ R ≈0.3τ opt opt v−1t−1 (25)
X γ−γ γ γ−γ ej opt eV 1038ergs−1 8 wk
diated as X-rays of energy (cid:15) ∼ 30 keV, this results in a num-
X
ber flux of N˙X ∼ fXFγAeff/(cid:15)X ∼ 4 × 10−4(fX/0.01) s−1 for a nearunity,whereσγ−γ ∼ 10−25 cm2 isthephoton-photonabsorp-
typical value F ∼ 10−10 erg cm−2 s−1 (Ackermann et al. 2014) tioncrosssectionnearthresholdandn = L τ /(4πcR2E )is
γ γ opt opt ej opt
and the NuSTAR effective area Aeff ≈ 200 cm2 (Harrison et al. theenergydensityofthetargetopticalphotonsneartheshock(for
2013; their Fig. 2). Given the NuSTAR estimated background of τ > 1).WestronglyencouragefutureadditionalTeVfollow-up
opt
N˙ ∼ 2×10−3 counts s−1 in this energy range across the point ofnovaenearandafteropticalpeak,evenifnotfirstdetectedby
σ
spread function (Harrison et al. 2013; their Fig. 11), we estimate Fermi,asdetectionsorupperlimitscanbeusedtoplacemeaning-
that the integration time required for a 3σ detection is approxi- fulconstraintsonthemaximumacceleratedparticleenergyandthe
mately 9N˙ /N˙2 ∼ 100(f /0.01)−2 ks. Reasonable constraints on locationofthegamma-rayemission.
σ X X
f ∼ 0.01 could thus be achieved for a modest 100 ks exposure. Thesampleofgamma-raynovaeshouldexpandrapidlyinthe
X
ThehardX-rayimageronASTRO-Hshouldalsoproveusefulfor nextfewyearsthankstoanticipatedenhancementsinthesensitivity
novafollow-up. ofFermiLATresultingfromimprovementsinitsabilitytoperform
Orioetal.(2014)reportedNuSTARobservationsofthefast low-level event reconstruction. The method for jointly analyzing
symbioticnovaV745Scowithin10daysoftheoutburst,placing opticalandgamma-raydataemployedinthispaperwillthussoon
be applicable to a greater sample of events. Our results highlight
the importance of obtaining broad (ideally bolometric) frequency
6 Althoughattenuationbyinelasticelectronscatteringcouldbeimportant coverageofnovalightcurves,includingnearinfraredandultravio-
forsufficientlyhighopticaldepths,leadingtohardX-raysuppression. letwavelengths,attimescoincidentwiththegamma-rayemission.
(cid:13)c 2014RAS,MNRAS000,1–??
10
Theutilityofourmodelrestsheavilyontheassumptionofradiative HillasA.M.,1984,ARA&A,22,425
shocks,whichdependssensitivelyonthequantityofmassandve- HillmanY.,PrialnikD.,KovetzA.,SharaM.M.,NeillJ.D.,2014,
locityofthenovaejecta,andhowitispartitionedbetweenthefast MNRAS,437,1962
andslowcomponents.Additionalradiomonitoringofgamma-ray HjellmingR.M.,WadeC.M.,VandenbergN.R.,NewellR.T.,
novaeisthusalsokeytobetterconstrainingtheejectamassfrom 1979,AJ,84,1619
thesesystemsanditsgeometry,therebystrengtheningorrefuting HubaJ.D.,2007,NrlPlasmaFormulary.WexfordCollegePress
theargumentforradiativeshocks. Kamae T., Karlsson N., Mizuno T., Abe T., Koi T., 2006, ApJ,
647,692
KatoT.N.,2014,ArXive-prints
Krauss M. I., Chomiuk L., Rupen M., Roy N., Mioduszewski
ACKNOWLEDGMENTS
A.J.,SokoloskiJ.L.,NelsonT.,MukaiK.,BodeM.F.,Eyres
BDMacknowledgeshelpfulconversationswithDamianoCaprioli, S.P.S.,O’BrienT.J.,2011,ApJL,739,L6
Koji Mukai, Jeno Sokoloski, Andrey Vlasov, and Bob Williams. LarssonJ.,etal.,2011,Nature,474,484
We thank Fred Walter for providing optical data on nova Sco. LivioM.,ShankarA.,BurkertA.,TruranJ.W.,1990,ApJ,356,
BDM gratefully acknowledges support from NASA Fermi grant 250
NNX14AQ68G,NSFgrantAST-1410950,andtheAlfredP.Sloan LloydH.M.,O’BrienT.J.,BodeM.F.,1997,MNRAS,284,137
Foundation. We thank the reviewer, Guillaume Dubus, for help- MartinP.,DubusG.,2013,A&A,551,A37
ful criticism and suggestions that led to an improvement of the MetzgerB.D.,Hascoe¨tR.,VurmI.,BeloborodovA.M.,Chomiuk
manuscript. L.,SokoloskiJ.L.,NelsonT.,2014,MNRAS,442,713
MontanetL.,etal.,1994,Phys.Rev.D.,50,1173
MorlinoG.,CaprioliD.,2012,A&A,538,A81
MukaiK.,IshidaM.,2001,ApJ,551,1024
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