Photons to axion-like particles conversion in Active Galactic Nuclei

(1)

2015

Publication Year

2020-03-10T10:48:05Z

Acceptance in OA@INAF

Photons to axion-like particles conversion in Active Galactic Nuclei

Title

TAVECCHIO, Fabrizio; RONCADELLI, MARCO; GALANTI, GIORGIO

Authors

10.1016/j.physletb.2015.04.017

DOI

http://hdl.handle.net/20.500.12386/23191

Handle

PHYSICS LETTERS. SECTION B

Journal

744

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Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Photons

to

axion-like

particles

conversion

in

Active

Galactic

Nuclei

Fabrizio Tavecchio

a

,

Marco Roncadelli

b

,

Giorgio Galanti

c

,

∗

a_INAF_–_Osservatorio_Astronomico_di_Brera,_Via_E._Bianchi_46,_I-23807_Merate,_Italy

b_INFN,_Sezione_di_Pavia,_Via_A._Bassi_6,_I-27100_Pavia,_Italy

c_Dipartimento_di_Fisica,_Università_{dell’Insubria,}_Via_Valleggio_11,_I-22100_Como,_Italy

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received19January2015

Receivedinrevisedform8April2015 Accepted9April2015

Availableonline14April2015 Editor: A.Ringwald

Keywords:

Axion

Photonpropagation

Theideathatphotonscanconverttoaxion-likeparticles(ALPs)

γ

→a inoraroundanAGNandreconvert backtophotonsa→

γ

intheMilkyWaymagneticﬁeldhasbeenputforwardin2008andhasrecently attractedgrowinginterest.Yet,sofarnobodyhasestimatedtheconversionprobability

γ

→a ascarefully asallowedbypresent-dayknowledge.Ouraimistofillthisgap.WefirstremarkthatAGNwhichcan bedetectedabove100 GeVareblazars,namelyAGNwithjets,withone ofthempointingtowardsus. Moreover,blazarsfallintotwowelldefined classes:BLLacobjects(BLLacs)and FlatSpectrumRadio Quasars(FSRQs),withdrasticallydifferentproperties.InthisLetterwereportapreliminaryevaluationof the

γ

→a conversionprobabilityinsidethesetwoclassesofblazars.Ourﬁndingsaresurprising.Indeed, whileinthecaseofBLLacstheconversionprobabilityturnsouttobetotallyunpredictable duetothe strongdependenceonthevaluesofthesomewhatuncertainpositionoftheemissionregionalongthe jetandstrengthofthemagneticﬁeldtherein,forFSRQsweareabletomakeaclear-cut prediction.Our resultsareofparamountimportanceinviewoftheplannedvery-high-energyphotondetectorslikethe CTA,HAWK,GAMMA-400andHISCORE.

1. Introduction

Many extensions of the Standard Model of particle physics – and chieﬂy among them superstring theories – generically pre-dicttheexistence ofaxion-like particles (ALPs)(fora review,see [1,2]), which arespin-zero, neutraland extremelylight bosons – tobe denoted by

a –

closelyresembling theaxion (for areview, see[3])apartfromtwofacts thatmakesthemasmuchas model-independentaspossible.

•

Possible couplings tofermions and gluonsare discarded and onlytheirtwo-photoncoupling

a

γ γ

istakenintoaccount.

•

The ALP mass m is totally unrelated to their a

γ γ

coupling constant 1

/

M. The most robust lower bound on M is set by the CASTexperimentCERN whichyields M

>

1

.

14

·

1010 GeV for

m

<

0

.

02 eV [4].Somewhat weakerboundsare M

>

1

.

5

·

1010_{GeV for}

_m

_<

_{1 keV from}_the_analysis_of_evolution_of

glob-ularclusters[5]and

M

>

1

.

9

·

1011_{GeV for}

_m

_<

₄

_.

₄

_·

₁₀−10_eV

*

Correspondingauthor.

E-mailaddresses:fabrizio.tavecchio@brera.inaf.it(F. Tavecchio),

marco.roncadelli@pv.infn.it(M. Roncadelli),gam.galanti@gmail.com(G. Galanti).

fromthelack ofALPdetectionsupposedly emitted by super-nova1987A[6].

Asaconsequence,ALPsaredescribedbytheLagrangian

L

0 ALP

=

1 2

∂

μ_a

_∂

μa

−

1 2m 2_a2

₊

1 ME

·

B a

,

(1)

where E and B denotethe electric andmagnetic components of theﬁeldstrength F μν . ObservethatbecauseE isperpendicularto the

γ

momentum, the structure of the last term in Eq. (1) im-pliesthatonlythecomponentBT transversetothe

γ

momentum couples to a. Throughout this Letter, E is the electric ﬁeld of a propagating photonwhileB isan external magnetic ﬁeld. Accord-ingly, the massmatrix of the a

γ

system is off-diagonal, thereby implyingthat thepropagationeigenstates differfromthe interac-tion eigenstates.Therefore

γ

↔

a oscillations take placemuch in the same waythat occursfor massive neutrinos ofdifferent ﬂa-vor,apartfromtheneedofB in ordertocompensateforthespin mismatch[7,8].However,inthesituations tobeaddressedbelow also theone-loop QED vacuumpolarization in the presenceof B hastobetakenintoaccountandisdescribed bytheeffective La-grangian[9–11]

LHEW

=

2

α

2 45m4e

E2

−

B2

2

+

7

E

·

B

2

,

(2) http://dx.doi.org/10.1016/j.physletb.2015.04.017

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376 F. Tavecchio et al. / Physics Letters B 744 (2015) 375–379

where

α

istheﬁne-structureconstantand

m

e istheelectronmass. So,throughoutthisLettertheconsideredALPLagrangianis

LALP

=

L

0

ALP

+

LHEW

.

Inordertoavoidanymisunderstanding,thesymbol E denotes

henceforththe

energy rather

thantheelectricﬁeld.

Letusnowturnourattentiontovery-high-energy(VHE) astro-physics, namely to observed photons with energies in the range 100 GeV

<

E

<

100 TeV andtotheirextragalacticsources,the ma-jorityofwhichare ActiveGalacticNuclei(AGN). Generally speak-ing,AGNarepowered bya supermassiveblackhole(SMBH) with

MSMBH

∼

108–109Mlyingatthecentreofabrightgalaxyand ac-cretingmatterfromthesurrounding,which–beforedisappearing into the SMBH –heats up emitting an enormous amount of ra-diation.Nearly10% ofAGNsupports twoopposite relativisticjets (withabulkLorentzfactor

γ

10–20)propagatingfromthe cen-tralregionsouttodistancesthat,inthemostpowerfulsources,can reach1 Mpc.Ultra-relativisticparticles(leptonsand/orhadrons)in the plasma carriedby these jetsemit non-thermal radiation ex-tending from the radio up to the VHE band. Aberration caused bytherelativisticmotionmakestheemissionstronglyanisotropic, mainly boosted in the direction of the motion. Blazars are AGN withonejetpointing–merelybychance–almostexactlytowards the Earth. Blazars fall into two broad classes: BL Lac objects (BL Lacs)–whichrepresentthegreatmajorityofextragalacticsources detected intheVHEband – andflatspectrum radioquasars (FS-RQs)[12].As arule, theblazarspectral energydistribution(SED) showstwobroadhumps,thefirstonepeakingatlowfrequency– fromIR to softX-rays, depending on the specific source –while thesecondoneinthe

γ

-rayband.InBLLacsthelattercomponent extendsto VHE, oftenreaching multi-TeV energies. In thewidely assumedleptonic models,theVHE

γ

-rayemissionistheresultof theinverseCompton (IC)scatteringofsoftphotonsby relativistic electronsinthejet.Moreover,itiswidelyacceptedthatthe dom-inant soft photon population derives – through the synchrotron mechanism–bythesameelectronsthatscatterthemintotheVHE band. Thisis thescheme whichlies atthe basis ofthe so-called synchrotronselfCompton(SSC)model[13,14].

Yet,theVHEbandisplaguedbytheexistenceofthe

extragalac-tic background light (EBL) which is the light emitted by galaxies duringthewholecosmichistoryandextendsfromthefar-infrared to the near-ultraviolet (for a review, see [15]). What happens is thatwhenaVHE

γ

emittedbyadistantblazarscattersoffanEBL

γ

it has a good chance to disappear into an e+e− pair [16,17]. Indeed,accordingtoconventionalphysicsthiseffectbecomes dra-maticevenfor E above afew TeV(see Fig. 1of[18]),a factthat drasticallyreducesthe

γ

-rayhorizonatincreasing E.

A breakthroughcame in2007 when it was ﬁrst realized [19] (see also[20]) that

γ

→

a

→

γ

oscillationstakingplace in inter-galacticspacecangreatlydecreasetheEBLdimmingforsuﬃciently far-away blazars and high enough E provided that a large-scale magnetic ﬁeld in the 0.1–1 nG range exists with a domain-like structure, which is consistent with all presently available upper bounds(fora review,see[21]). Whythishappenscan be under-stood in an intuitive fashion (discardingcosmological effects for simplicity).Photon–ALPoscillationsgiveaphotonasplit personal-ity:asitpropagatesfromtheblazartous,itbehavessometimesas a

true photon

andsometimesasan ALP.When itpropagatesasa photonitundergoesEBLabsorption,butwhenitpropagatesasan ALPitdoes

not.

Therefore,theeffectivephoton meanfree pathin extragalacticspace

λ

γ,eff(E

)

is

larger than

λ

γ

(

E

)

aspredictedby

conventional physics. Correspondingly, the photon survival prob-abilitybecomes Pγ→γ

(

E

)

=

exp

−

Ds

/λ

γ,eff(E

)

,where Ds isthe blazardistance.So,becauseoftheexponentialdependenceonthe meanfreepatheven asmallincreaseof

λ

γ,eff(E

)

withrespectto

λ

γ

(

E

)

producesa largeenhancementof Pγ→γ

(

E

)

,therebygiving

risetoadrasticreductionoftheEBLdimming.

Before proceeding further, a remarkis in order.From time to timeatensionbetweenthepredictedEBLlevelcausingphoton ab-sorptionandobservationsintheVHErangehasbeenclaimed[22, 23], buta subsequentbetter determination oftheEBL properties hasshownthatnoproblemexists.Actually,afteralongperiodof uncertaintyontheEBLpreciseproperties,nowadaysaconvergence seems tobe reached[15],well representede.g. bythe modelsof Franceschini,RodighieroandVaccari(FRV)[24]andofDomínguez

et al. [25]. Nevertheless, it has been claimed that VHE observa-tions requirean EBL level evenlower than that predictedby the minimal EBL model normalized to the galaxy counts only [26]. This is the so-called pair-production anomaly, which is based on the Kolmogorov test and so does not rely upon the estimated errors. It has thoroughly been quantiﬁed by a global statistical analysisofalargesampleofobservedblazars,showingthat mea-surements in theregime oflarge optical depthdeviate by 4.2

σ

from measurements in theoptically thinregime [27].Systematic effectshavebeenshowntobeinsuﬃcienttoaccountforsuchthe pair-productionanomaly,which lookstherefore real.Actually,the discovery of newblazars atlarge redshift likethe observationof PKS1424

+

240 havestrengthenedthecaseforthepair-production anomaly [28].Quiterecently,theexistence ofthepair-production anomalyhasbeenquestionedbyusinganewEBLmodelanda

χ

2

test, inwhicherrorsplay insteadanimportantrole [29].Because the Kolmogorov test looks more robust in that it avoids taking errors into account, we tend to believe that the pair-production anomaly is indeed atthe levelof 4.2

σ

. It looks tantalizingthat forasuitablechoiceofthefreeparametersithasbeenshownthat the mechanismdiscussed above provides a solution to the pair-productionanomaly[27,30].Anevenmoreamazingfactisthatfor the

same choice

ofthefree parameteralsotheobserved redshift-dependenceoftheblazarspectraisnaturallyexplained[31].

Comingbacktoourmainlineofdevelopment,asafollow-upof the previousproposalsthat

γ

→

a conversions occurinAGN[32, 33], a complementary scenario was put forward in 2008 [34]. Schematically,VHEphotonsaresimply

assumed to

substantiallyor evenmaximally convertto ALPsinsideablazar,sothat the emit-ted ﬂuxcan consist inup to 1

/

3 of ALPsandin2

/

3 ofphotons. ALPstravelunaffected bytheEBLandwhentheyreachtheMilky Way(MW)canconvertbacktophotonsintheMWmagneticfield. Clearly, the amount of back-conversion strongly depends on the galacticcoordinatesoftheblazar,sincethemorphologyoftheMW magneticfieldisquitecomplicatedandbynomeansisotropic. Ev-idently also in thiscase the EBLdimming isdrastically reduced. Basically the same idea hasbeen taken up subsequently [35,36]. Unfortunately, eitherthe blazarhasnot been modeled atall [32, 34] oran incorrectdomain-like structuremodel forthejet mag-neticfieldisassumed[35,36].

Prompted by the appearance of very recent papers address-ing the considered scenario in connection with the upcoming CherenkovTelescopeArray (CTA)[37–40],we havedecided to re-porta preliminaryevaluationofthe

γ

→

a conversion probability

Pγ→a

(

E

)

insidethetwo classesofblazarsascarefullyaspossible consistentlywiththepresentlyavailableknowledge.So,theaimof thisLetterisbasically tospeedupthepresentationofourresults. Amorethoroughanalysisalongwithallrelevantcalculationswill bethesubjectofafuturemuchmoredetailedpaper.

2. BLlacs

They are the simplest blazars, and so we better start from them. Denoting by y the coordinate along the jet axis, in order to achieve our goal two quantities are needed where the

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pho-ton/ALPbeampropagates:thetransversemagneticﬁeldBT

(

y

)

and theelectron density

n

e

(

y

)

proﬁles. Becausethe electrons are ac-celerated in shocks generated in the ﬂow, the VHE photons are producedinawell-localizedregion

RVHE

prettyfarfromthe cen-tralengine. So, fourcrucial parameters are: thedistance dVHE of

RVHE

fromthecentre,thesizeof

RVHE

,andthevaluesof BT,VHE

and

n

e,VHE insideit.TheSSCdiagnosticsappliedtotheSEDofBL

Lacs[41] provides themainphysical quantitiesconcerning

RVHE

. Theyare BT,VHE

=

0

.

1–1 G and

n

e,VHE

5

·

104 cm−3,leading to

a plasma frequencyof 8

.

25

·

10−9 eV. The quantity dVHE is

diﬃ-culttodeterminedirectly,becausethecurrentinstrumentalspatial resolution is still too poor. A common indirect way consists in inferring

d

VHE fromthesize RVHEof

RVHE

,assumedtobea

mea-sureofthejet cross-section,derived inturnfromspectralmodels and the observed variability timescale. Typical values lie in the range1015_–1016_cm._Whenever_the_jet_aperture_angle

_θjet

_is

mea-surable – which is certainly the case for BL Lacs at a relatively largedistance–itisgenerallyfound

θjet

0

.

1 rad, sothatunder the assumption of a simple conical geometry for the jet it fol-lowsthat

d

VHE

=

RVHE/θjet

1016–1017cm.Beyond

RVHE

photons

traveloutwardsunimpededuntiltheyleave thejetwithatypical lengthof1 kpc andpropagateintothehostgalaxy.Giventhefact that dVHE is a fairly large quantity,the component ofB relevant

forusis thetoroidal partwhichistransverse tothe jetaxis and goeslike

y

−1_[42]_._The_same_conclusion_follows_from_the

conserva-tionofthemagneticluminosityifthejetconservesitsspeed[43]. Moreover, recent work has succeeded to observationally charac-terize the B structure over distances in the range 0.1–100 pc in severaljetsof BLLacs through polarimetric studies,showing un-ambiguouslythat inBLLacsB isindeedsubstantially

ordered and

predominantly

traverse to

thejet [44].We stress that in particu-lartheseresults are inconsistent witha domain-likestructure of B inthe jetasassumede.g. in [35,36].Turning nextto the elec-trondensity,undertheusualassumptionthatthejethasaconical shapeweexpectthatitgoeslike y−2.Whence

BT

(

y)

=

BT,VHEdVHE

y

,

ne

(y)

=

nVHEd2_VHE

y2

,

(3)

fory

>

dVHE.ObservethatEqs.(3)hold trueinaframeco-moving

withthejet,sothatthetransformationtoaﬁxedframeiseffected by E

→

γ

E. Weremarkthatthisrelationisstrictly trueifthejet isobservedatanangle

θ

v

=

1

/

γ

withrespecttothejetaxis.More generally,the transformationreads E

→

E

δ

,where

δ

is the

rela-tivistic Doppler factor (for details,see[12]).Herewehave

γ

=

15. 3. FSRQs

Thesearethemostpowerfulblazarsandareinasenseamore complicated version of BL Lacs. The additional components are: (1) thebroad line region (BLR) consistingin a spherical shell of manyclouds photo-ionizedby the radiation fromthe matter ac-cretingontotheSMBH, locatedatabout

d

BLR

1018 cm fromthe

centreandrapidlyrotatingaboutit;(2) a dustytorusreprocessing partoftheaboveradiationintheinfraredband;(3) theradiolobes consistinginahotnon-thermalplasmainﬂatedwherethejets col-lidewiththeextragalacticgas.BecauseboththeBLRandthedusty toruslie

beyond

RVHE

andarequiterichofultravioletandinfrared photons,respectively,theygiverisetoahugeabsorptionof

γ

rays withEγ

>

10–20 GeV throughthesame

γ γ

→

e+e−process con-sideredabove. Onthe other hand, thelobes – beingmagnetized – represents a further conversion region. The jets in FSRQs are longerandlesspronetoinstabilitiesthan thoseoftheweakerBL Lacs. Presently, concerning the VHE

γ

-ray emission region

RVHE

we take dVHE larger by a factor of 3 ascompared to the BL Lac

Fig. 1. PlotofPγ→a(E)foraBLLactakingM=5·1010GeV.Thedifferentcurves

correspondto B=0.1 G (solidblue),0.2 G (dashedcyan), 0.5 G (longdashed, green)and1 G (dot-dashed,red).Thethreepanelscorrespondtothreevaluesof thedistanceoftheemittingregion,namelydVHE=1016cm (bottom),3·1016cm

(middle),1017_{cm (upper).}_(For_{interpretation}_of_the_references_to_color_in_this

ﬁg-urelegend,thereaderisreferredtothewebversionofthisarticle.)

Fig. 2. PlotofPγ→a(E)foraBLLactakingM=5·1011GeV.Thedifferentcurves

correspondto B=0.1 G (solidblue),0.2 G (dashedcyan),0.5 G (long dashed, green)and1 G (dot-dashed,red).Thethreepanelscorrespondtothreevaluesof thedistanceoftheemittingregion,namelydVHE=1016cm (bottom),3·1016cm

(middle),1017_{cm (upper).}_(For_{interpretation}_of_the_references_to_color_in_this

ﬁg-urelegend,thereaderisreferredtothewebversionofthisarticle.)

case, based on the larger variability time scales [45]. The mod-eling of the SED with state-of-the-art emission models provides

BT,VHE

=

1–10 G and

n

VHE

104cm−3[45].Thegeometryandthe

intensityofB inthejetbeyond

RVHE

arefarlessclearthaninthe caseofBLLacs.Infact,thereareindicationsthat B hasaglobally ordered structure,butits inclination angle

ϕ

withrespect to the

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378 F. Tavecchio et al. / Physics Letters B 744 (2015) 375–379

Fig. 3. Plotof Pγ→a(E)foraFSRQtakingM=5·1010 GeV.Thedifferentcurves

correspondtoB=1 G (solidblue),2 G (dashedcyan),5 G (longdashed,green) and10 G (dotred).Thethreepanelscorrespondtothreevaluesofthedistance oftheemittingregion,namelydVHE=3·1016 cm (bottom),1017cm (middle),3·

1017_{cm (upper).}_(For_{interpretation}_of_the_references_to_color_in_this_ﬁgure_legend,

thereaderisreferredtothewebversionofthisarticle.)

Fig. 4. Plotof Pγ→a(E)foraFSRQtakingM=5·1011 GeV.Thedifferentcurves

correspondtoB=1 G (solidblue),2 G (dashedcyan),5 G (longdashed,green) and10 G (dotred).Thethreepanelscorrespondtothreevaluesofthedistance oftheemittingregion,namelydVHE=3·1016 cm (bottom),1017cm (middle),3·

1017_{cm (upper).}_(For_{interpretation}_of_the_references_to_color_in_this_ﬁgure_legend,

thereaderisreferredtothewebversionofthisarticle.)

jetaxisdoesnothaveauniquevalueforallsources,actually cov-eringthe whole interval 0–90◦. Fordeﬁniteness, we assume the sameproﬁlesof

B

T

(

y

)

and

n

e

(

y

)

asinEq.(3),taking

ϕ

=

45◦and

γ

=

10.Radiopolarimetricobservationsyieldagoodamountof in-formationaboutthestructure andtheintensityofB in theradio lobes.Speciﬁcally, one gets a turbulent B whichcan be modeled

asadomain-like structurewithhomogenousstrength B

=

10 μG, coherencelength10 kpc andrandomorientationineachdomain. 4. Results

Because of lack of space, we cannot report the explicit cal-culation of the

γ

→

a conversion probability Pγ→a

(

E

)

which is anywayastraightforwardapplicationofthetechniquediscussedin greatdetailin[20].Weassumeasbenchmarkvalues

m

≤

10−9 eV aswell as M

=

5

·

1010 _{GeV and} _M

₌

₅

_·

₁₀11_GeV. _Basically,_our

resultscanbesummarizedasfollows.

Owingtotheleadingrole playedbytheQEDterm,inthecase ofBLLacsPγ→a

(

E

)

showsarathercomplexbehavior andastrong dependenceon BT,VHE and

d

VHE,asshowninFigs. 1 and 2.As a

consequence,

Pγ

→a

(

E

)

turnsouttobe

intrinsically unpredictable.

In addition,as

M decreases

onlyforthelargestconsideredvaluesof the magneticﬁeld takestheconversion probability sizablevalues andnooscillatorybehavior showsup.

On thecontrary, forFSRQsdueto the eﬃcient

γ

↔

a

oscilla-tionsintheradiolobes–whichactuallyleadstotheequipartition among the three degrees of freedom – the peculiar features ex-hibited by BL Lacs get smoothed out and below 20 GeV we get

Pγ→a

(

E

)

=

1

/

3 regardless of the value of M. Above 20 GeV in-steadtheabove-mentionedabsorptionleadstoadrasticreduction oftheemittedALPﬂux.Altogether,inthecaseofFSRQswemake aclear-cutpredictionwhichisexhibitedinFigs. 3 and 4,whichis againalmostindependentofthevalueof

M.

Ourresultsareofgreatimportancefortheplanned very-high-energydetectors liketheCTA, HAWK,GAMMA-400 andHISCORE, andforthosebasedonthetechniquesdiscussedin[46–48]. More-over, westress thatall analysesofthescenarioof

γ

→

a

conver-sion in a blazar and a

→

γ

reconversion in the MW should be properlyrevisedaccordingtothepresentconclusions.

Acknowledgements

We thank Alessandro DeAngelis, Luigina Ferettiand Marcello Girolettiforusefuldiscussions.F.T.acknowledgescontributionfrom a grant PRIN-INAF-2011.The work of M.R. is supported by INFN TAsPandCTAgrants.

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