Gamma-ray observations of MAXI J1820+070 during the 2018 outburst

†

M. Delfino,

‡ J. Delgado,

‡ C. Delgado Mendez,

D. Depaoli,

F. Di Pierro,

L. Di Venere,

D. Dominis Prester,

A. Donini,

D. Dorner,

M. Doro,

D. Elsaesser,

G. Emery,

V. Fallah Ramazani,

§ L. Fari na, ˜

A. Fattorini,

L. Font,

C. Fruck,

S. Fukami,

Y. Fukazawa,

R. J.

Garc ´ıa L ´opez,

M. Garczarczyk,

S. Gasparyan,

M. Gaug,

J. G. Giesbrecht Pai v a,

N. Giglietto,

F. Giordano,

P. Gliwny,

N. Godinovi ´c,

R. Grau,

D. Green,

J. G. Green,

D. Hadasch,

A. Hahn,

T. Hassan,

L. Heckmann,

ࢱ J. Herrera,

J. Hoang ,

D. Hrupec,

M. H ¨utten,

R. Imazawa,

T. Inada,

R. Iotov,

K. Ishio,

I. Jim ´enez Mart ´ınez,

J. Jormanainen,

D. Kerszberg,

Y. Kobayashi,

H. Kubo,

J. Kushida,

A. Lamastra,

D. Lelas,

F. Leone,

E. Lindfors,

L. Linhoff,

S. Lombardi,

F. Longo,

R. L ´opez-Coto,

M. L ´opez-Moya,

A. L ´opez-Oramas,

S. Loporchio,

A. Lorini,

E. Lyard,

B. Machado de Oliveira Fraga,

P. Majumdar,

# M. Makariev,

G. Mane v a,

N. Mang,

M. Manganaro,

S. Mangano,

K. Mannheim,

M. Mariotti,

M. Mart ´ınez,

A. Mas Aguilar,

D. Mazin,

S. Menchiari,

S. Mender,

S. Mi ´canovi ´c,

D. Miceli,

T. Miener,

J. M. Miranda,

R. Mirzoyan,

E. Molina ,

H. A. Mondal,

A. Moralejo,

D. Morcuende,

V. Moreno,

T. Nakamori,

C. Nanci,

L. Nava,

V. Neustroe v,

M. Nie v as Rosillo,

C. Nigro,

K. Nilsson,

K. Nishijima,

T. Njoh Ekoume,

K. Noda,

S. Nozaki,

Y. Ohtani,

T. Oka,

A. Okumura,

J. Otero-Santos,

S. Paiano,

M. Palatiello,

D. Paneque,

R. Paoletti,

J. M. Paredes,

L. Pavleti ´c,

M. Persic,

** M. Pihet,

G. Pirola,

F. Podobnik,

P. G. Prada Moroni,

E. Prandini,

G. Principe,

C. Priyadarshi,

I. Puljak,

W. Rhode,

M. Rib ´o,

J. Rico,

C. Righi,

A. Rugliancich,

N. Sahakyan,

T. Saito,

S. Sakurai,

K. Satalecka,

F. G. Saturni,

B. Schleicher,

K. Schmidt,

F. Schmuckermaier,

J. L. Schubert,

T. Schweizer,

J. Sitarek,

V. Sliusar,

D. Sobczynska,

A. Spolon,

A. Stamerra,

J. Stri ˇskovi ´c,

D. Strom,

M. Strzys,

Y. Suda,

T. Suri ´c,

H. Tajima,

M. Takahashi,

R. Takeishi,

F . T av ecchio,

P. Temniko v,

K. Terauchi,

T. Terzi ´c,

M. Teshima,

L. Tosti,

S. Truzzi,

A. Tutone,

S. Ubach,

J. van Scherpenberg,

M. Vazquez Acosta,

S. Ventura,

V. Verguilov,

I. Viale,

C. F. Vigorito,

V. Vitale,

I. Vovk,

R. Walter,

M. Will,

C. Wunderlich,

T. Yamamoto,

D. Zari ´c,

(The MAGIC Collaboration), H. Abdalla,

F. Aharonian,

F. Ait Benkhali,

E. O. Ang ¨uner,

H. Ashkar,

M. Backes,

V. Baghmanyan,

V. Barbosa Martins,

R. Batzofin,

Y. Becherini,

D. Berge,

K. Bernl ¨ohr,

M. B ¨ottcher,

C. Boisson,

J. Bolmont,

M. de Bony de Lavergne,

F. Bradascio,

M. Breuhaus,

R. Brose,

F. Brun,

T. Bulik,

T. Bylund,

F. Cangemi,

 E-mail:contact.magic@mpp.mpg.de(JH,EM);contact.hess@hess-experiment.eu(SLS,DM);nahee.park@queensu.ca(NP)

∗ Alsoat:InternationalCenterforRelativisticAstrophysics(ICRA),Rome,Italy.

†Nowat:UniversityofInnsbruck,InstituteforAstroandParticlePhysics.

‡Alsoat:Portd’Informaci´oCient´ıfica(PIC),E-08193Bellaterra(Barcelona),Spain.

§ Nowat:Ruhr-Universit¨atBochum,Fakult¨atf¨urPhysikundAstronomie,AstronomischesInstitut(AIRUB),44801Bochum,Germany.

ࢱAlsoat:UniversityofInnsbruck,InstituteforAstro– andParticlePhysics.

¶^Alsoat:DipartimentodiFisica,Universit`adiTrieste,I-34127Trieste,Italy.

#Alsoat:UniversityofLodz,FacultyofPhysicsandAppliedInformatics,DepartmentofAstrophysics,90-236Lodz,Poland.

∗∗ Alsoat:INAFTriesteandDept.ofPhysicsandAstronomy,UniversityofBologna,Bologna,Italy.

© 2022TheAuthor(s)

S. Caroff,

S. Casanova,

M. Cerruti,

T. Chand,

S. Chandra,

A. Chen,

O. U. Chibueze,

G. Cotter,

P. Cristofari,

J. Damascene Mbarubuc ye ye,

J. Devin,

A. Djannati-Ata ¨ı,

A. Dmytriiev,

K. Egberts,

J.-P. Ernenwein,

A. Fiasson,

G. Fichet de Clairfontaine,

G. Fontaine,

M. F ¨ußling,

S. Funk,

S. Gabici,

S. Ghafourizadeh,

G. Giavitto,

D. Glawion,

J. F. Glicenstein,

P. Goswami,

G. Grolleron,

J. A. Hinton,

M. H ¨orbe,

C. Hoischen,

T. L. Holch,

M. Holler,

D. Horns,

Zhiqiu Huang,

M. Jamrozy,

F. Jankowsky,

V. Joshi,

I. Jung-Richardt,

E. Kasai,

K. Katarzy ´nski,

U. Katz,

B. Kh ´elifi,

W. Klu ´zniak,

Nu. Komin,

K. Kosack,

D. Kostunin,

R. G. Lang,

S. Le Stum ,

A. Lemi `ere,

M. Lemoine-Goumard,

J.-P. Lenain,

F. Leuschner,

T. Lohse,

A. Luashvili,

I. Lypova,

J. Mackey,

J. Majumdar,

D. Malyshev ,

D. Malyshev,

V. Marandon,

P. Marchegiani,

G. Mart ´ı-Devesa,

R. Marx,

G. Maurin,

M. Meyer,

A. Mitchell,

R. Moderski,

L. Mohrmann,

A. Montanari,

E. Moulin,

J. Muller,

T. Murach,

K. Nakashima,

M. de Naurois,

A. Nayerhoda,

J. Niemiec,

A. Priyana Noel,

P. O’Brien,

S. Ohm,

L. Olivera-Nieto,

E. de Ona Wilhelmi,

M. Ostrowski,

S. P ann y,

M. P anter,

R. D. Parsons,

V. Poireau,

D. A. Prokhorov,

H. Prokoph,

G. P ¨uhlhofer,

M. Punch,

A. Quirrenbach,

P. Reichherzer,

A. Reimer,

O. Reimer,

M. Renaud,

F. Rieger,

G. Rowell,

B. Rudak,

H. Rueda Ricarte,

E. Ruiz-Velasco,

V. Sahakian,

H. Salzmann,

A. Santangelo,

M. Sasaki,

J. Sch ¨afer,

F. Sch ¨ussler,

H. M. Schutte,

U. Schw ank e,

J. N. S. Shapopi,

H. Sol,

A. Specovius,

S. Spencer,

Ł. Stawarz,

R. Steenkamp,

S. Steinmassl,

C. Steppa,

I. Sushch,

H. Suzuki,

T. Takahashi,

T. Tanaka,

C. Thorpe-Morgan,

M. Tluczykont,

L. Tomankova,

N. Tsuji,

Y. Uchiyama,

C. van Eldik,

B. van Soelen,

M. Vecchi,

J. Veh,

C. Venter,

J. Vink,

S. J. Wagner,

R. White,

A. Wierzcholska,

Yu Wun Wong,

A. Yusafzai,

M. Zacharias,

R. Zanin,

D. Zargaryan,

A. A. Zdziarski,

A. Zech,

S. J. Zhu,

S. Zouari,

N. Zywucka, ˙

(The H.E.S.S. Collaboration), A. Acharyya,

C. B. Adams,

P. Batista,

W. Benbow,

M. Capasso,

J. L. Christiansen,

A. J. Chromey,

M. Errando,

A. Falcone,

Q. Feng,

J. P. Finley,

G. M. Foote,

L. Fortson,

A. Furniss,

A. Gent,

W. F. Hanlon,

O. Hervet,

J. Holder,

B. Hona,

T. B. Humensky,

W. Jin,

P. Kaaret,

M. Kertzman,

M. Kherlakian,

T. K. Kleiner,

S. Kumar,

M. J. Lang,

M. Lundy,

G. Maier,

C. E. McGrath,

J. Millis,

P. Moriarty,

R. Mukherjee,

S. O’Brien,

R. A. Ong,

N. Park ,

S. R. Patel,

K. Pfrang,

M. Pohl,

E. Pueschel,

J. Quinn,

K. Ragan,

P. T. Reynolds,

D. Ribeiro,

E. Roache,

J. L. Ryan,

I. Sadeh,

L. Saha,

M. Santander,

G. H. Sembroski,

R. Shang,

M. Splettstoesser,

D. Tak,

J. V. Tucci,

A. Weinstein,

D. A. Williams,

T. J. Williamson,

(The VERITAS Collaboration), V. Bosch-Ramon,

C. Celma,

M. Linares,

D. M. Russell

and G. Sala

Affiliationsarelistedattheendofthepaper

Accepted2022September17.Received2022September2;inoriginalform2022May24

ABSTRACT

MAXIJ1820+070isalow-massX-raybinarywithablackhole(BH)asacompactobject.Thisbinaryunderwentanexceptionally brightX-rayoutburstfrom2018MarchtoOctober,showingevidenceofanon-thermalparticlepopulationthroughitsradio emission duringthiswholeperiod.The combinedresults of59.5 h of observationsof the MAXIJ1820+070 outburstwith the H.E.S.S.,MAGIC andVERITASexperiments atenergiesabove200 GeV are presented,together withFermi-LAT data between0.1and500GeV,andmultiwavelengthobservationsfromradiotoX-rays.Gamma-rayemissionisnotdetectedfrom MAXIJ1820+070,buttheobtainedupperlimitsandthemultiwavelengthdataallowustoputmeaningfulconstraintsonthe sourcepropertiesunderreasonableassumptionsregardingthenon-thermalparticlepopulationandthejetsynchrotronspectrum.

Inparticular,itispossibletoshowthat,ifahigh-energy(HE)gamma-rayemittingregionispresentduringthehardstateofthe source,itspredictedfluxshouldbeatmostafactorof20belowtheobtainedFermi-LATupperlimits,andclosertothemfor

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accretionontothecompactobjectnormallytakesplacethroughan accretiondiscgeneratedbytheRochelobeoverflowmechanism(e.g.

Remillard&McClintock2006).Typically,low-massX-raybinaries withaBH(BH-LMXBs)alsofeaturetransientjetslaunchedfrom theBH,whicharepoweredbytheaccretionprocess,themagnetic field,theBHrotation,oracombinationofthem(seeRomeroetal.

2017,andreferencestherein).Thesejetscanefficientlyaccelerate chargedparticles,potentiallyuptoGeVorTeVenergies,andemit non-thermalradiationfromradioto gammaraysasaresultofthe radiativecooling of the accelerated particles(seee.g. Mirabel&

Rodr´ıguez1999;Fender&Munoz-Darias˜ 2016,forareviewonjets inX-raybinaries).

Most of the time, BH-LMXBs are in a quiescent state until theyundergoperiodicoutburstslikelytriggeredbyvariationsinthe propertiesoftheaccretiondiscthatresultinachangeofthemass accretionrateontotheBH(e.g.Fender&Belloni2012).Duringone oftheseoutbursts,whichmaylastforseveralmonths,theluminosity ofaBH-LMXBincreasesby severalordersofmagnitude.ABH- LMXBcan bedetectedin a soft state(SS) ora hardstate (HS) basedon thehardness of itsX-rayspectrum during one ofthese outbursts.Atthebeginningoftheoutburst,aBH-LMXBistypically intheHS,inwhichtheX-raysexhibitahard-spectrumcomponent.

ThisemissionlikelyoriginatesinahotcoronaaroundtheBH,where inverseCompton(IC)scatteringoflow-energyphotonscomingfrom theaccretiondisctakesplace.TheHSalsofeaturesjetsynchrotron emission,whichismostlyseenatradioand infraredwavelengths, althoughitmayalsoberesponsibleforasignificantcontributionto theX-rayoutputofthesystem(e.g.Fender&Munoz-Darias˜ 2016).

Astheoutburstcontinues,thesource willtransitionto theSS. In thisstate,mostoftheX-raysareofthermalorigin,emittedbythe hotinnerregionsoftheaccretiondisc.Also,radioemissionfades away,indicatingalackofjetactivity(althoughweakjetsmaystillbe presentandremainundetected).Inatypicaloutburst,aBH-LMXB normallycompletestheHS–SS–HScycle,goingthroughshort-lived intermediate statesduring the HS–SSand SS–HS transitions. As happenedwith the triggering of the outburst, the changes in the spectralstatesofBH-LMXBsareprobablyproducedbyvariationsin theaccretiondiscproperties.Duringthestatetransitions,especially theHS–SSone,discreteblobsofplasmamovingawayfromtheBH cansometimesberesolvedinradio,ratherthanthecontinuousjets typicaloftheHS(seeFender&Belloni2012,andreferencestherein foramoredetaileddescriptionofthestatesofBH-LMXBs).

With one possible exception, no high-energy (HE, above 100MeV)orvery-high-energy(VHE,above100GeV)gamma-ray emissionisdetectedfromBH-LMXBs(Ahnenetal.2017a;H.E.S.S.

Collaborationetal.2018b).Thepossibleexceptiontothisisthe∼4σ excessatHEofV404Cygniduringanoutburstin2015(Lohetal.

2016;Pianoetal.2017;althoughwenotethelackofasignificant

amongothers. We notethat LMXBs hostinga neutronstar have beendetectedatHE(seee.g.Harvey,Rulten&Chadwick2022).In thesesystems,thegamma-rayemissionlikelyoriginatesinprocesses involvingtheneutronstar,whicharethereforenotapplicableinaBH scenario(e.g.Straderetal.2016,andreferencestherein).

For high-mass X-ray binaries, there is already evidence for gamma-rayemission.HE gamma raysare detectedfrom systems likeCygnusX-1andCygnusX-3,likelyoriginatingfromthejetsin bothcases(seeFermiLATCollaborationetal.2009;Tavanietal.

2009;Zaninetal.2016;Zdziarskietal.2018).HEemissionisalso detectedfromregionsofSS433farfromthecentralbinary,where the jets terminateinteractingwith the supernovaremnant around the source(Fang,Charles& Blandford2020;Lietal.2020).On the otherhand,the VHEdetectionofhigh-mass X-raybinariesis still elusive(Aleksi´c etal. 2010,2015;Archambault etal. 2013; Archeretal.2016;Ahnenetal.2017b),withtheexceptionofSS433 (andexcludinggamma-raybinariesfromthissourceclass).Forthis source,theHAWCCollaborationdetectedphotonswithenergiesof

∼20 TeVoriginatingin regions veryfarfromthe binary system, although notspatiallycoincident withthe HE-emitting sites.The post-trialdetectionsignificancerangedfrom4.0to4.6σ depending on the analysed region, and reached 5.4σ for a joint fit of the interactionregions(Abeysekaraetal.2018).

MAXIJ1820+070(RA = 18^h20^m21^s.9,Dec. = +07 ◦11  07  ; Galacticcoordinatesl=35.^◦8536,b=+10^◦.1592)isaBH-LMXB discoveredintheopticalbandon2018March6(MJD58184.1)by theAll-SkyAutomatedSurveyforSupernovae(ASAS-SN;Tucker etal.2018),andonMarch11(MJD58188.5)wasalsodetectedin X-raysbytheMonitorofAll-skyX-rayImage(MAXI;Kawamuro etal. 2018).Soonafteritsdiscovery,MAXIJ1820+070 showed anexceptionally highX-rayflux peakingat∼4 timesthatof the CrabNebula(e.g.DelSanto&Segreto2018;Shidatsuetal.2019).

Adistancetothesourceofd=2.96± 0.33kpcwasdetermined fromradioparallax(Atrietal.2020),whichisconsistentwiththe distanceof3.28 + 0 . 60

−0 . 52 kpcobtainedfromGaiaDR3data(Bailer-Jones etal.2021).JetactivitywasdetectedfromMAXIJ1820+070inthe formofradioandinfraredemission,whichclassifiesthesourceasa microquasar(e.g.Brightetal.2020;Rodietal.2021).TheLorentz factorofthejetduringtheHSwasestimatedtobe=1.7–4.1from radio-to-opticaldata,theupperandlowerlimitsofthisrangebeing determinedfromconstraintsonthejetpowerandthepairproduction rate,respectively(Zdziarski,Tetarenko&Sikora2022).Fordiscrete ejectionstakingplaceintheHS–SStransition,aLorentzfactorof

=2.2 + 2 . 8

−0 . 5 wasobtained(usingadistancetothesourceof2.96kpc;

Atrietal.2020).Thejetinclinationwasmeasuredtobeθ=64 ◦± 5 ◦fromradioobservations(Woodetal.2021),anditshalf-opening angleintheHSwasfoundtobe1^◦.3± 0.^◦7(Zdziarskietal.2022).

Usingopticalpolarizationobservations,thejetmisalignmentwith

Table 1. Starting and ending times used for each X-ray state of MAXIJ1820+070,based ontheresults ofShidatsu etal.(2019).Hard StateIandIIrefer,respectively,totheinitialandfinalstatesofthesource,as depictedinFig.1.

Sourcestate Start End Start End

(MJD) (MJD) (Gregorian) (Gregorian)

HardStateI 58189.0 58303.5 12Mar.2018 4Jul.2018 HS→SS 58303.5 58310.7 4Jul.2018 11Jul.2018 SoftState 58310.7 58380.0 11Jul.2018 19Sep.2018 SS→HS 58380.0 58393.0 19Sep.2018 2Oct.2018 HardStateII 58393.0 58420.0 2Oct.2018 29Oct.2018

respectto the perpendiculartothe orbitalplane wasmeasuredto beatleast40 ◦[witha68percentconfidencelevel(CL);Poutanen etal.2022].Anorbitalperiodof16.4518± 0.0002hwasdetermined fromopticalspectroscopicobservations(Torresetal.2019).TheBH and stellarmasses wereconstrained throughfurtherspectroscopy measurementsto a95percentconfidence intervalof5.7–8.3 and 0.28−0.77M _, respectively, fororbital inclinations between66 ◦

and81 ◦(Torresetal.2020).Theparametersaboveyieldanorbital semimajoraxisof∼4.5× 10¹¹ cm.Anestimateofthedonorstar parametersisdiscussedinMikołajewskaetal.(2022).

MAXI J1820+070 remainedin the HS fromthe beginningof the outburst in March until early July 2018, when it began its transitiontothe SS.Thissourcestatelasted untillate September, whenMAXIJ1820+070startedtransitioningbacktotheHSshortly beforebecomingquiescentandputtinganendtotheoutburst,which lastedatotalof∼7months.Duringitsoutburst,MAXIJ1820+070 wasobservedwithawidevarietyofinstrumentsatradio(e.g.Atri etal.2020;Brightetal.2020),near-infrared(e.g.S´anchez-Sierras&

Munoz-Darias˜ 2020),optical(e.g.Shidatsuetal.2019;Torresetal.

2019;Veledinaetal. 2019),and X-ray(e.g.Buisson etal.2019; Roques&Jourdain2019;Shidatsuetal.2019;Chakrabortyetal.

2020;Fabianetal.2020;Zdziarskietal. 2021a)frequencies. We makeuseoftheresultsofShidatsuetal.(2019)todefinetheexact datesofthe beginningandend ofeachsourcestate,basedon the MAXIGasSlitCamera(MAXI/GSC)hardnessratio(i.e.theflux ratioofHEtolow-energyX-rays)betweenthe6–20-and2–6-keV photonfluxes.ThesedatesareshowninTable1.Theevolutionofthe X-raystateofMAXIJ1820+070canbeseeninthebottompanelof Fig.1,whichshowsitshardnessratiofromMAXI/GSCdata.

In this work,wepresent theresults ofcombined observations, by the H.E.S.S.,MAGIC and VERITAS collaborations,of VHE gammarays fromMAXIJ1820+070,the brightestBH-LMXBin X-rayseverobserved.Inordertogiveamorecompletepictureof thesource, Fermi-LATdata inHEgammarays arealsoincluded, aswellasmultiwavelengthobservationsfromradiotoX-rays.This workisstructuredasfollows:Section2describestheHEandVHE observationsanddataanalysisforeachtelescope.Section3presents theresultsofthiswork,forwhichadiscussionisgiveninSection4. Finally,weconcludewithasummaryinSection5.

2 O B S E RVAT I O N S A N D DATA A N A LY S I S

2.1 H.E.S.S.,MAGIC,andVERITASdata

MAXIJ1820+070wasobservedduringits2018outburstwiththe H.E.S.S.,MAGIC,andVERITASImagingAtmosphericCherenkov Telescope(IACT)arrays.H.E.S.S.isanarrayoffiveIACTslocated intheKhomasHighland,Namibia(23 ◦S,16 ◦E,1800-mabovesea level).Itcomprisesfourtelescopeswitha12-mdiameterdishand

afieldofview(FoV)of5 ◦(foradescription,seeAharonianetal.

2006a),andonetelescopewitha28-mdiameterdishanda3^◦.2FoV (Bolmont et al. 2014). H.E.S.S. investigates gamma rays in the energyrangefrom∼20GeV(H.E.S.S.Collaborationetal.2018a) to∼100TeV(Abdallaetal.2021).MAGIC(Aleksi´cetal.2016a) isastereoscopicsystemoftwoIACTslocatedattheRoquedelos MuchachosObservatoryinLaPalma,Spain(29 ◦N,18 ◦W,2200m abovesealevel).Thetelescopeshavea3^◦.5FoV,andareequipped withaprimarydishwithadiameterof17 m.MAGICcandetect gammaraysfrom∼15GeV(MAGICCollaborationetal.2020b) to ∼100TeV(MAGIC Collaborationetal. 2020a).VERITAS is an array of four IACTs located at the Fred Lawrence Whipple ObservatoryinsouthernArizona,USA(32 ◦N,111 ◦W,1270mabove sealevel;Weekesetal.2002).EachtelescopecoversaFoVof3^◦.5, collectinglightfroma12-mdiameterreflector.VERITASissensitive to gamma-ray photonsranging from∼85 GeVto 30 TeV.The performanceofVERITASisdescribedinParketal.(2015).

TheMAGICandH.E.S.S.observationswereperformedfrom2018 MarchtoOctober,coveringtheinitialHSofthesource,thebeginning oftheSS,andthestatetransitions.TheVERITASdatawerecollected fromMarchtoJune,whenthesourcewasintheHS.Afterdataquality cuts,26.3,22.5,and10.7hofeffectiveobservationtime(defined as the exposure time corrected fordead-timelosses) remainsfor H.E.S.S.,MAGIC,andVERITAS,respectively,foracombinedtotal of59.5h.ThedatasamplewasdividedaccordingtotheX-raystate (ortransition)ofthesourceasdefinedinSection1.Asummaryof theobservations,includingtheirzenithangle,isshowninTable2. TheobservationdatesofeachtelescopeareshowninTableA1,and theyarealsorepresentedinFig.1superimposedonthehardX-ray lightcurve(LC)ofthesource.

Thelow-leveldataanalysesofH.E.S.S.,MAGIC,andVERITAS were performed usingstandard collaborationprocedures, eachof them including an independent cross-check (i.e. an independent analysis,performedwithadifferentsoftwarepipeline,thatyielded compatibleresultswiththemainanalysis).Theselow-levelanalyses comprise,amongothers,calibration,andimagecleaningprocedures, methods to separate atmospheric showers triggered by gamma rays fromthosetriggeredby hadrons,andgamma-rayenergyand directionreconstruction(seedeNaurois&Rolland2009;Holleretal.

2015fortheH.E.S.S.mainanalysis;Parsons&Hinton2014forthe H.E.S.S.cross-check;Aleksi´cetal.2016bforMAGIC;Danieletal.

2008fortheVERITASmainanalysis;andMaier&Holder2017for theVERITAScross-check).TheVHEemissionwasassumedpoint like(sinceitisexpectedtocomefromregionsclosetothebinary system,withangularsizessmallerthantheinstruments’resolutions), andthesignalregionwasdefinedbyaradiusof0^◦.12,0^◦.14or0^◦.10 around the sourcepositionforH.E.S.S.,MAGIC,and VERITAS, respectively.Inordertomaximizethesourceeffectiveobservation time, andthus theprobabilityofdetection,ajointanalysisofthe data fromthethreeexperimentswasalsodone(seeAppendixB).

Nosignificantsignalwasdetectedfromtheindividualorcombined datasets,regardlessoftheenergyrangeconsidered.Thegamma-ray upperlimits(ULs)indifferentenergybinswerecomputedfollowing amaximum-likelihoodratiotestasdescribedinAppendixB,both fortheindividualandcombineddatasets.Wealsoreferthereader toMAGICCollaborationetal.(2018)forasimilarmethod.ACLof 0.95wasused,andaglobalfluxsystematicuncertaintyof30percent wastakenforeachexperiment,whichaccountsforthesystematic errorin boththefluxnormalizationandtheenergyscale(seee.g.

Aleksi´cetal.2012).Thechoiceofacommonvalueofthesystematic uncertainty forthe threeexperiments ismotivated by the similar values ofthesystematicerrors amongthem(seeAharonianetal.

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Figure1. Toppanel:X-rayfluxinthe15–50-keVbandasseenbySwift/BAT,withtheVHEobservationdatessuperimposedasverticallineswithdifferent stylesforeachcollaboration.Onlythedayswithdataafterqualitycutsareshown.Bottompanel:EvolutionoftheMAXIJ1820+070hardnessratioofthe4–10- to2–4-keVfluxesasseenbyMAXI/GSC.Thesourcestatesaresuperimposedaslightred(HS),lightblue(SS)andlightyellow(HS–SS/SS–HS)background colours.

Table2. SummaryoftheobservationsofMAXIJ1820+070bytheH.E.S.S., MAGIC,andVERITAScollaborations,afterdataqualitycuts.Theeffective observationtime,thezenithanglerange,anditsmedianareshownforeach sourcestateandexperiment.

Sourcestate Experiment Time(h) Zenithangle(median)(^◦)

HardState H.E.S.S. 17.9 30–61(33)

MAGIC 14.2 21–58(34)

VERITAS 10.7 20–39(28)

HS→SS H.E.S.S. 4.0 30–38(32)

MAGIC 4.9 21–48(27)

SoftState H.E.S.S. 2.6 30–34(31)

SS→HS H.E.S.S. 1.8 37–53(43)

MAGIC 3.4 28–56(41)

TOTAL H.E.S.S. 26.3 30–61(33)

MAGIC 22.5 21–58(32)

VERITAS 10.7 20–39(28)

2006a;Aleksi´cetal.2016b;Adamsetal.2022,fortheestimationof systematicerrorsinH.E.S.S.,MAGIC,andVERITAS,respectively).

The VHEgamma-ray spectrum was assumed to followa power lawwithspectralindexα=2.5,i.e.dN/dε∝ε −α,whereNisthe numberofgamma-rayphotonsandεistheirenergy.Thisspectral shapeischosen asitresembleswhathasbeenobserved forother binarysystemsdetectedatVHE(e.g.Albertetal.2006;Aharonian etal.2006b;Adamsetal.2021),sincesimilarparticleacceleration mechanismsand non-thermalemissionprocessesofVHEgamma raysareexpectedtooccurinMAXIJ1820+070.

2.2 Fermi-LATdata

TheLargeArea Telescope(LAT)(Atwoodetal. 2009)is apair- conversiondetectorontheFermiGamma-RaySpaceTelescope. It consistsof a tracker and a calorimeter, eachof them made of a

4× 4arrayofmodules,ananticoincidencedetectorthatcoversthe trackerarray, andadataacquisition systemwithaprogrammable trigger.TheFermi-LATislocatedatalow-Earthorbitwith90-min period andnormallyoperatesin surveymode,witha2.4srFoV.

Suchanobservationalstrategy allowstheinstrumenttocover the wholeskyin∼3h.Thedataselectedfortheanalysispresentedin thispapercovertheperiodMJD58189–58420.The0.1−500GeV datawereanalysedwiththelatestavailablefermitoolsv.2.0.8 withP8R3V3responsefunctions(SOURCEphotonclass;maximum zenithangleof90 ◦).

Astandard binnedlikelihood analysis (Mattox et al. 1996) of the data taken froma 14 ◦-radiusregion of interest(ROI)around the MAXI J1820+070 position wasperformed.¹ The analysis is based on the fitting of a spatial and spectral model of the sky regionaroundthesourceofinteresttothe data.Themodelofthe regionincludedallsourcesfromthe4FGLDR3catalogue(Abdollahi etal.2020)aswellascomponentsforisotropicandgalacticdiffuse emissions given by the standard spatial and spectral templates isoP8R3 SOURCEV3v1.txtandgll iemv07.fits.

Thespectraltemplate foreach4FGLsource inthe region was selected accordingto thecataloguemodel.Thenormalizationsof the spectraof thesesources,aswell asthe normalizationsof the Galactic diffuse and isotropic backgrounds, were assumed to be free parameters during the fit. MAXI J1820+070 was modelled as a point-likesource witha power-lawspectrum.Following the recommendation of the Fermi-LAT collaboration, our analysis is performedwiththeenergydispersionhandlingenabled.Tominimize thepotentialeffectsfromthesourcespresentbeyondtheconsidered ROI,weadditionallyincludedintothemodelallthe4FGLsources upto10 ◦beyondtheROI,withallthespectralparametersfixedtothe cataloguevalues.TheparametersusedfortheFermi-LATanalysis aresummarizedinTable3.

1Seee.g.https://fermi.gsfc.nasa.gov/ssc/data/analysis/scitools/binnededispt utorial.html.

Table3. DetailsofFermi-LATdataanalysis.Fromtoptobottompanels, theparametersoftheanalysisaretypeofresponsefunctions;eventclassand type;maximumzenithangle;spatialandenergybinswidthsforthelikelihood analysis;numberofenergydispersionbins;energyrangeusedfortheanalysis;

radiusoftheregionofinterestuptowhichthesourceswereincludedwithfree normalization[ROI(free)];radiirangeinwhichthesourceswereincluded withallparametersfixedto4FGL-DR3values[ROI(fixed)];usedcatalogue;

Galacticdiffuseandisotropicdiffusebackgroundtemplates;andtimerange (inFermiseconds)usedfortheanalysis.

Parameter Value

Responsefunctions P8R3V3

evclass 128

evtype 3

zmax 90^◦

Spatialbinwidth 0^◦.05

Energybinsperdecade 5

edispbins −3

Energyrange 0.1–500GeV

ROI(free) 14^◦

ROI(fixed) 14^◦–24^◦

Catalogue 4FGL-DR3

Background(galactic) glliemv07.fits

Background(isotropic) isoP8R3SOURCEV3v1.txt Likelihoodanalysisoptimizer NEWMINUIT

Timeranges 542505605–562464005(TOTAL)

542505605–552398405(HSI) 552398405–553020485(HS–SS)

553020485–559008005(SS) 559008005–560131205(SS–HS)

560131205–562464005(HSII)

In order to check the quality of the considered model of the region atthe initial stepof the analysis, webuilt a test-statistics (TS)mapshowingtheTSvalueofapoint-likesourcenotpresentin themodellocatedinagivenpixelofthemap.TheTSmapobtained isshownin theleft-handpanelofFig.2.Themapillustratesthat theselectedmodeldescribestheregionwellintheenergyandtime- rangesconsidered.Wenotethe presenceofaTS∼10residualat RA=275.88 ◦,Dec.=5.84 ◦(withapositionaluncertaintyof0.15 ◦), markedasn1onthemap.Thisresidualispositionallycoincidentwith PSRJ1823+0550(PSRB1821+05).Wemodelledthissourceasa point-likesourcewithapower-lawspectrum,dN/dε=Kε −α,with Kbeingthefluxnormalization. Thebest-fittingparametersin the selectedtimerangeandinthe0.1−500-GeVenergybandareK= (1.3± 0.4)× 10 ⁻¹² phcm −2 s −1 MeV −1 at1GeV,andα=2.3± 0.2.

Weincludedthissourcetotheconsideredmodeloftheregionwith afree normalizationand theindexfixed tothe best-fitting value.

Afterallthesesteps,MAXIJ1820+070wasnotdetectedwiththe binned-likelihoodanalysisforthetimeperiodconsidered(assuming a power-law spectrum model with a free spectral index), and is thereforenotpresentattheTSmapofFig.2.

In what follows, the Fermi-LAT flux upper limits for MAXIJ1820+070 werecalculatedata0.95CL withthe helpof theIntegralUpperLimitmoduleprovidedasapartofstandard Fermi-LATdataanalysissoftwareforapower-lawindexfixedtoα= 2.5,asfortheVHEdataanalysis(andalsosimilartowhatisobserved forhigh-massmicroquasarsintheFermi-LATenergyrange,seee.g.

Zaninetal.2016;Zdziarskietal.2018).

In order to search for a possible short time-scale variability observedinseveralmicroquasarsdetecteduptoGeVenergies,we computedtheLCofthesourcewithvariable(adaptive)timebinning (e.g.Lottetal.2012).Namely,weselectedatimebindurationsuch

thateachbinreceives16photonsinthe0.1−500GeVenergyrange andinaradiusof1 ◦aroundtheMAXIJ1820+070position.This resultedin55timebinsinthetotaltimerangeconsideredwithan average duration of4.2d (minimum:1d,maximum: 27d).Such timebinselectionallowsustoidentifytheshortestpossibleperiods duringwhichthesourcepotentiallycouldbedetectedwithuptoa

∼4σsignificance.Asimilarapproachwasfoundtobeeffectivefor asearchofshortflaresduringtheperiodsofstrongGeVvariability of PSR B1259-63 in the analysis of Chernyakova et al. (2020), Chernyakova etal.(2021).Theperformedanalysis didnot result inthedetectionofMAXIJ1820+070inanyofthetimebins,and theresultingULsareshownintheright-handpanelofFig.2.

2.3 Additionalmultiwavelengthdata

Datafromseveralradiotelescopesatdifferentfrequenciesaretaken fromBrightetal.(2020).OpticaldataaretakenfromCelma(2019), in which observations performed with the Joan Or´o Telescope (TJO;Colom´eetal.2010)andSwiftUltraviolet/OpticalTelescope (Swift/UVOT;Romingetal.2005)arereported.Theopticalfluxes areobtainedfromimagestakenwiththefiveJohnson–Cousinsfilters (withcentralwavelengthsaround366,435,548,635,and880nm, respectivelyfromtheUtoIfilters),andtheyarealreadycorrected forinterstellarextinctionwithvaluesrangingfrom0.2to0.6mag (seeFitzpatrick1999;Celma2019,andreferencestherein).Public LCsfromMAXI/GSC(Matsuokaetal.2009)andSwiftBurstAlert Telescope(Swift/BATKrimmetal.2013)arealsoincluded.

Forthespectralenergydistributions(SEDs)ofMAXIJ1820+070, International Gamma-RayAstrophysics Laboratory(INTEGRAL;

Winkler et al. 2003) data are added to that of the previously mentioned instruments, based on results by Roques & Jourdain (2019) from MJD 58206 to 58246, during the first half of the HS. Data from the Neutron star Interior Composition Explorer (NICER,Gendreau,Arzoumanian&Okajima2012)arealsoused.

NICER is designedto study neutron stars via soft X-ray timing spectroscopyandhasbeenoperatingfromtheInternationalSpace Stationsince2017.Itobservedfor109,21.8,and4.56hduringthe HS,theHS–SStransition,andSS–HStransition,respectively.Pre- processed eventfiles were retrievedthrough the HEASARCdata base. Reprocessingandfilteringweredoneusingstandardcriteria withthenicerl2taskfromtheNICERDASsoftwareavailablein theHEAsoftdistribution² (v6.26).Spectrawereextractedusingthe extractorfunctionfromtheftoolspackage.Errorbarsaccountonly forthestatisticaluncertaintyondetectorcounts,namely±1standard deviation of a Poisson distribution. Energyand gain calibrations wereperformedusingtheHEASARCCalibrationDatabaseversion XTI(20200722).Toavoidtelemetrysaturation,thefractionofactive moduleshadtobeadjusted.Thiswastakenintoaccountconsidering thateachmodulecontributesequallytotheeffectivearea.Thefluxes werecorrectedforinterstellarextinctionusingahydrogencolumn densityofN _H =1.4× 10²¹ cm −2 (Dziełak,DeMarco&Zdziarski 2021).

3 R E S U LT S

TheobservationsofMAXIJ1820+070reportedinthisworkdonot show anysignificantemissionineitherHEorVHEgammarays, regardlessofthesourcestate.ThecomputedintegralfluxULsfor Fermi-LATdataandthecombineddatasetofH.E.S.S.,MAGIC,and

2https://heasarc.gsfc.nasa.gov/docs/software/lheasoft/

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Figure2. Left-handpanel:Test-statisticsmapinGalacticcoordinatesofa5^◦× 5^◦regionaroundMAXIJ1820+070(cyancircleatthecentre)inthe0.1−500- GeVenergyrange,witha0.^◦1pixelsize.Greensymbolsshowthe4FGLFermi-LATsourcespresentintheregion.Thecyancirclemarkedasn1showsaTS∼10 point-likeresidualpositionallycoincidentwithPSRJ1823+0550.Right-handpanel:Fermi-LATLCofMAXIJ1820+070inthe0.1−500-GeVenergyband withanadaptivetimebinning.Thebinwidthscorrespondto16photonsarrivedina1^◦-radiusaroundMAXIJ1820+070.Sourcestatesarerepresentedwith lightred(HS),lightblue(SS),andlightyellow(HS–SS/SS–HS)backgroundcolours.

Table4. Integralfluxupperlimitswitha0.95C.L.duringdifferentsource states,between0.1and500GeVfromFermi-LATdata,andabove200GeV fromthecombinedH.E.S.S.,MAGIC,andVERITASdata.FortheSS→ HStransition,theULabove300GeVisshowninstead.

Fermi-LATUL IACTUL

Sourcestate (0.1−500GeV) (>200/300GeV) (phcm⁻²s⁻¹) (phcm⁻²s⁻¹)

HardStateI 3.1× 10⁻⁸ 9.5× 10⁻¹³

HS→SS 1.6× 10⁻⁷ 9.5× 10⁻¹³

SoftState 2.5× 10⁻⁸ 1.6× 10⁻¹²

SS→HS 5.2× 10⁻⁸ 2.2× 10⁻¹²

HardStateII 6.0× 10⁻⁸ −

TOTAL 1.8× 10⁻⁸ 7.2× 10⁻¹³

VERITASare shownin Table4foreachX-raystate.Theformer arecalculatedforphotonenergiesε> 100MeV, whilethelatter arecomputedatε >200 GeVforthe HS,the HS–SStransition, theSSandthewholesample,andatε>300GeVfortheSS–HS transition.Theincreaseinenergythresholdofthelastdatasetisdue toahigheraveragezenithangleoftheobservations,whichdoesnot allowelectromagneticshowerstriggeredby lowerenergy gamma raystobedetected.WenotethattheVHEULfortheSS,shownhere forcompleteness,may not berepresentativeof the whole source state,sinceitonlycoverstheveryfirstdaysoftheSS(seethetop panelofFig.1).

Fig. 3presents the ULs on the VHEdifferential fluxobtained for five different energy bins and each source state for which observationswere performed (excluding the poorly covered SS).

BothindividualandcombinedULsareshownineachcase.Forthe SS–HStransition,thelowestenergybinisnotcomputedduetothe increasedenergythresholdofthecorrespondingobservations.The differencesbetweenindividualULsinthesameenergybinoriginate fromthedifferentinstrumentsensitivitiesandobservationtimes,as well as fromstatistical fluctuations(see Appendix B).Except in thecaseofsignificantdifferencesbetweentheindividualULs,the combinedULsaretighterthananyoftheindividualones.

Fig. 4 shows the LCs of MAXI J1820+070 at different fre- quencies, with the gamma-ray LC corresponding to the ULs in Table4. The radiofluxes in the top panel includeboth the core

emissionfromthe jet regionsclosetothe binary system,and the radiationemittedbydiscreteejectionslaunchedduringtheHS–SS transition.CoreemissionisdominantduringthesourceHS,while the ejectionsdominate throughout the SS, during which no core emissionis detected(seeBrightetal. 2020,forthe details).The opticalfluxesinthesecondpanelare obtainedfromatotalsetof 16457imagesdistributed over 113differentnightsbetween2018 March andNovember(Celma2019).TheX-ray LCs inthe third panelareobtainedfromthedailyfluxesofMAXIJ1820+070from MAXI/GSC(for2≤ ε≤ 20keV)and Swift-BAT(for15 ≤ ε≤ 50keV).Thegapsrepresenttheperiodswhenthesourcewasnot observedwiththeseinstruments.

TheSEDsofMAXIJ1820+070,averagedforthosesourcestates well representedby theVHEdata,are shownin Fig.5.Wenote thatthejumpbetweenNICERandINTEGRALdatainthetoppanel isjustaneffectofthedifferenttimecoverageoftheobservations.

While NICER data are averaged over the whole duration of the HS,INTEGRAL data only cover roughlythe first halfof it (see Section2.3),whentheaverageX-rayfluxwashigher.

4 D I S C U S S I O N

Inthissection, weprovideashortdescriptionofmultiwavelength measurementsofMAXIJ1820+070fromradiotoX-rays.Basedon someassumptionsregardingtheextrapolationofthejetsynchrotron spectrum and the distribution (energydependence and maximum energy)ofthenon-thermalparticles,weestimatetheexpectedjet emissioninHEandVHEgammaraysanalytically.Thisexpected emission is then compared to the measured ULs, and used to constrainthepropertiesofapotentialgamma-rayemissionregionin MAXIJ1820+070.

4.1 Multiwavelengthoverviewofthesource

RadioemissionfromMAXIJ1820+070providesevidenceforjet activityduringthewhole2018outburst.Thisemissionisdominated byasteadyjetintheHS,adiscreteblobintheHS–SStransition(the emissionofwhichisalsodominantthroughouttheSSastheblob movesawayfromthebinarysystem),andajetrebrighteningduring the SS–HStransition(Brightetal.2020).Withoutaccountingfor blobemissionduringtheSS,theradioandhardX-rayfluxeshave

Figure3. DifferentialfluxupperlimitsofMAXIJ1820+070fordifferentenergybinsandsourcestates(indicatedinthelegend).Colouredmarkersrepresent theresultsfortheindividualexperiments,whileblacklinesshowthecombinedupperlimits.

similar behaviours: they decrease slowlythroughthe HS,have a steepdecreaseintheHS–SStransition,arepracticallyundetectable during the SS, and increase again in the SS–HS transition. This isexpectedfromthestandardpictureofBH-LMXBs,wheresteady radiojetsintheHScoexistwithahardX-rayemittingcorona,bothof themdisappearingintheSS.DuringtheHS,synchrotronemission fromthe jetislikely thedominantcontribution tothe SEDup to infraredfrequencies,beyondwhichthespectrumbecomesdominated bydiscandcoronalemission(Rodietal.2021;Tetarenkoetal.2021; Zdziarskietal.2021b).WenonethelessnotethatthejetsinLMXBs may stillcontribute significantlyup to hard X-raysthroughtheir synchrotronemission(e.g.Markoff,Nowak&Wilms2005).

Regarding the contribution from the star to the overall SED, MAXI J1820+070 had a magnitude of 17.4 in the G filter – with a central wavelength around 460 nm – before the outburst (Wengeretal.2000;GaiaCollaboration2018),whichisatleastthree magnitudesabovetheBmagnitudeduringtheflare(fromthefilters showninthesecondpanelofFig.4,theBfilteristheclosestoneto theGfilter).ThismeansthattheopticalfluxofMAXIJ1820+070 duringtheflarewasatleastabout15timeslargerthanbeforethe outburst. Nonetheless,this increase in flux cannotbeexclusively associatedtothebrighteningoftheaccretiondisc,sincethestellar luminositycanalsoincreaseduringtheoutburstowingtotheheating ofthestellarsurfaceproducedbytheX-rayemissionclosetotheBH (e.g.deJong,vanParadijs&Augusteijn1996).Assumingastellar radiusof∼10¹¹ cmequaltothatoftheRochelobe,thesolidangle

ofthestarasseenbytheBHis∼0.01sr.Thismeansthattheoptical luminosityofthe X-raysreprocessed inthe stellarsurfaceshould beabouttwoordersofmagnitudebelowtheX-rayluminosity.This opticalluminosityiscomparabletowhatisobservedfromthewhole system(seeFig.5),sowecanconcludethatthestellarcontribution totheopticalfluxofMAXIJ1820+070maybesignificant.

4.2 Analyticalestimates

Fortheestimatesperformedinthissection,theparticlesresponsible for the non-thermal emission are assumed to be only electrons (and positrons), although we note that hadrons might contribute to the overall emission of the system (see e.g. Bosch-Ramon &

Khangulyan2009,fortypicalelectronandprotoncoolingtimescales inmicroquasarenvironments).Theseelectronsarelikelyaccelerated uptorelativisticenergiesclosetotheBH,anddifferentacceleration mechanismsmayplayarole(seee.g.Bosch-Ramon&Rieger2012, foradescriptionofdifferentprocessesthatcancontributetoparticle acceleration).Thenon-thermalemissionoftheelectronsisassumed to come from their synchrotron and IC cooling.The derived jet inclination and speedin MAXIJ1820+070 makethe counter-jet emissionsignificantlymoredeboostedthanthatfromthe jet.The discussion can thereforebefocused on the jet emission, and the counter-jetcontributioncanbeneglected.Inthefollowing,primed quantitiesrefertothereferenceframemovingwiththejetflow,while

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Figure4. Fromthetoptobottompanels:radio,optical,X-ray,andgamma- rayLCs ofMAXIJ1820+070 duringits 2018outburst (MJD58189.0–

58420.0).TheshadedareascorrespondtotheHS(lightred),theHS–SSand SS–HStransitions(lightyellow),andtheSS(lightblue).Theunitsofthe thirdpanelare(phcm⁻² s⁻¹)forMAXI/GSC,and(countcm⁻² s⁻¹)for Swift/BAT.Thelatterfluxesaremultipliedby10forabettervisualization.

Thebottom panelshows theFermi-LATULs above 100MeV, and the H.E.S.S./MAGIC/VERITAScombinedULs (multipliedby 10⁴)for each sourcestateandtransitionforwhichdataareavailable,aswellasforthe wholeoutburst.TheVHEULsarecomputedabove 200GeVexceptfor theSS–HStransition(MJD58380.0–58393.0)forwhich300GeVULsare shown.

unprimedonesrefertoquantitiesinthelaboratoryframeorasseen bytheobserver.

4.2.1 AsteadyjetintheHS

Some jet properties during the initial HS of the source were constrainedbyZdziarskietal.(2022)basedontheradiotooptical emission. In particular, the synchrotron break frequency (above whichthe emissionbecomesopticallythin) ismeasuredtobeν₀

≈ 2× 10⁴GHz.TheyalsofindthatforajetLorentzfactorof≈ 3,theonsetofthejetsynchrotronemissioncomesfromadistanceto theBHofr≈ 3.8× 10¹⁰cm,wherethemagneticfieldisB  ≈ 10⁴G ifequipartitionbetweenthemagneticandparticleenergydensitiesis assumed(theequipartitionconditionapproximatelycorrespondsto theminimumenergyrequirementforsynchrotronradiation,which happensforamagneticenergyof∼0.75timestheparticleone;e.g.

Longair1981).

Toestimatethegamma-rayemissionofthesource,weassumethat gammaraysareproducedbyICscatteringofphotonscomingfrom theaccretiondiscorthecoronabyjetelectrons.Thismeansthatthe targetphotonsreachthejetmainlyfrombehind,whichisverylikely thecaseforX-raysinMAXIJ1820+070,andisalsoapproximately the case foropticalphotons. Given the conditions in the source, theestimatescanbedoneinthecontextoftheThompsonregime,

Figure5. Fromtoptobottompanels:SEDsofMAXIJ1820+070averaged overtheHS,theHS–SStransition,andtheSS–HStransition.Fermi-LAT pointsincludethecontributionfromthetwoHSsofthesource.TheeMERLIN datashownarethoseat5.07GHz.MeerKATdataareusedinthebottompanel insteadofeMERLINs.

whichisapproximatelyvalidattheadoptedenergies(γ ε࣠m _e c² , seebelow),andsimplifies thecalculations(e.g.Longair1981).In thisregime,ICismoreefficientandtheenergygainofthescattered photonsisproportionaltothesquareoftheelectronLorentzfactor γ.

ForHEgammarays,acharacteristicenergyofε=100MeVis taken,whichwouldbetheresultof theIC scatteringtowardsthe observeroftargetX-rayphotonswithtypicalenergiesof∼1keVby E  HE ∼ 250MeVelectrons(γ^ ∼ 500).Thesearereferencevalues forwhichdataatthetargetphotonenergy areavailable,although targetphotonswithenergiessimilartothechosenoneswouldalso contributetotheICemissionaroundε=100MeV.Theelectronswith energyE  HEemitsynchrotronphotonswithanobservedfrequencyof νsyn≈ 1.5× 10⁶GHz.Theobservedfluxdensityatthisfrequency (extrapolatedfromtheinfrareddatainZdziarskietal.2022)isF_ν^syn ∼ 30mJy.TheobservedICfluxoftheelectronswithenergyE  HE can thenbeestimatedas

ε² dN dε

_IC =ν_IC F_ν^IC ≈ νsyn F_ν^syn E˙  IC

E˙  syn

, (1)