ELECTRIC DISCHARGES ONTO A BLACK HOLE AND X-RAY TRANSIENT PERIODIC VARIABILITY IN AGN

ELECTRICDISCHARGESONTOABLACKHOLEANDX-RAY

TRANSIENTPERIODICVARIABILITYINAGN

J.A.deDiego,D.Dultzin-Hacyan

InstitutodeAstronom´ıa,UniversidadNacionalAut´onomadeM´exico

and

D.N´un˜ezandR.P´erez

Astrophysical Plasmas: Codes, Models, and Observations (Mexico City, 25-29 October 1999)Editors: Jane Arthur, Nancy Brickhouse, & José FrancoInstitutodeCienciasNucleares,UniversidadNacionalAut´onomadeM´exico

RESUMEN

Presentamosunmecanismoparaproducirvariacionesperi´odicastransitoriasderayos-XenNAG.Ladispersi´ondeComptonenelplasmaquecaeenunagujeronegropuedeinducirunacargael´ectricaenlasingularidad.Losprocesosdecargaydescargapuedenafectarlaluminosidadenrayos-XdelNAG.

ABSTRACT

WepresentamechanismtoproduceX-raytransientperiodicvariationsinAGN.ThismechanismistriggeredoffbyComptonscatteringintheinfallingplasmaintoablackhole,whichcaninduceanelectricchargeinthesingularity.ThecharginganddischargingprocessescanaffecttheX-rayluminosityofAGN.KeyWords:BLACKHOLEPHYSICS—GALAXIES:ACTIVE

—GALAXIES:INDIVIDUAL(IRAS18325-5926)—QUASARS:INDIVIDUAL(3C273)—X-RAYS:GALAX-IES

1.INTRODUCTION

ThehighenergyradiationfieldgeneratedintheinneredgeofanaccretiondiskcanincreasetheseparationbetweenelectronsandprotonsintheinfallingplasmabyComptonscattering,allowingafewelectrons(approx-imately,oneoutof1025)toescapethroughtheinnerfunnelandreachthediskcorona.Theseelectronswillbesupportedinthecoronabyradiationpressurefromthedisk.Asmallnetchargeisinducedintheblackholebytheexcessprotons,anditwilleventuallyincreaseenoughtoreducetheaccretionrate.This,inturn,willreducetheradiationpressureuntiltheelectronscannolongerbesupportedinthecoronaandfalltotheblackhole,thusneutralizingitscharge.Thisprocesscanberepeated,producinglowamplitudequasiperiodicorevenstrictlyperiodicvariationsintheX-rayluminosityoriginatedintheaccretiondisk,whichmaybesuperposedtoothercomponentsoftheX-rayluminosity.

2.COMPTONSCATTERINGONTHEFREEFALLMATTER

Fortheinfallingplasma,embeddedinaradiationfieldwithveryhighenergyphotons,theforceduetoComptonscatteringonelectronsandthegravitationalforceonprotonsaresostrong,thattheycanoccasionallyovercometheelectron-protonCoulombforceintheaccreting󰀂plasma.TheelectricchargeintheinfallingplasmaisshieldedinadistancecalledDebye’swavelength:λD=

X-RAYTRANSIENTPERIODICVARIABILITYINAGN

kineticenergyofthe“struck”electronafteraComptonscatteringprocessisgivenby

Kmax=

hν0

mec2

.

327

(1)

whereν0isthefrequencyoftheincidentphotonandαistheratiobetweentheenergiesoftheincidentphotonandtheelectroninitsrestframe.ForUVandsoftX-rays,ν0∼1016Hz,theelectroncanacquireanenergyoftheorderof10−21J,whichisatleast3ordersofmagnitudelargerthantheelectricenergywiththeprotonfield.Innormalconditions,afteraComptonscatteringoccursinaplasma,anearbyelectronreplacesthescatteredoneandscatteringhasnegligibleeffects.However,neartheblackholehorizon,theinfallingplasmacontainingtheunbalancedprotonproduceanetpositivechargeintheblackhole.

Astrophysical Plasmas: Codes, Models, and Observations (Mexico City, 25-29 October 1999)Editors: Jane Arthur, Nancy Brickhouse, & José Franco3.FORCEBALANCEANDELECTRICDISCHARGE

Oncethedecoupledelectronshavereachedthediskcorona,theradiationpressurewillpreventtheirinfalluntiltheblackholereachesacriticalelectricchargeandtheaccretionratedecreases.Neglectingmagneticeffects,onlygravitational,Coulomb,andradiationpressureforcesactonisolatedparticles,andtheyareproportionaltoR−2,whereRisthedistancefromthecentralsource.Thisallowsasimpletreatmentoftheproblem,independentofR.Theconditionsforaccretionwillbe

fg,e+Qfe−fr,e>0,

fg,p−Qfe−fr,p>0,

wherethefirstsubindexdenotesgravity(g),radiation(r)andelectric(e),andthesecondsubindexdenotesproton(p)andelectron(e).Qdenotesthenumberoffreeelementarycharges.Theftermsaredefinedas

fg,x=GMmx,

fr,x=L

σx

4π󰀞0

.

(2)

whereListheluminosity,andσxistheclassicalcrosssectionoftheparticle(xindicatestheparticle).Theaccretionrateisproportionaltotheinfallingvelocity(v).Thus,thisvelocitymaybeexpressedasa√functionofthedistanceRtothesingularity,andtheaccelerationaontheinfallingparticles:v=

fg,p−Qfe

Substitutinginthisexpressionequation(2)

GMme−κGMmp

󰀁

GMmp−Qe2/(4π󰀞0)

σe

.

4π󰀞0

>0.

Rearrangingtheequation,itcanbewrittenas−X−bX+d>0,

2

whereb=κ

SolvingthequadraticequationforX,thecriticalnumberofelementarychargesQallowedbeforethefreeelectronsbegintofallintotheblackholeisQcrit=(GMmp−X2)4π󰀞0/e2.Thetimerequiredbytheblack

˙,andtheefficiencyholetoreachthecriticalnumberofchargedparticlesQcritdependsontheaccretionrate,M

εoftheprocess

dQ

.mp

󰀂

4π󰀞0

󰀄1/2

.

328DEDIEGOETAL.

Fig.1.IRAS18325–5926X-raylightcurvefromIwa-sawaetal.(1998).Overlapped,themodelfit(seemaintextforexplanation).

Astrophysical Plasmas: Codes, Models, and Observations (Mexico City, 25-29 October 1999)Editors: Jane Arthur, Nancy Brickhouse, & José Franco˙=L/ηc2,whereη≈0.4istheaccretionradiatingefficiency,andintegratingfromzerotoQcrit,SubstitutingM

weobtainthenecessarytime,τ,togetthecriticalblackholecharge

󰀃1/2󰀅σe󰀞0ηmpc

τ=4+κ2+4.(3)Finally,weconsidertheluminosityvariationproducedbythisprocess.Wedefinetheindexofvariabilityas

theratiobetweenthemaximumandtheminimumluminosities,LmaxandLminrespectively.Theluminositymayhaveanunderlying,constantterm(Lc),thatcanbeexpressedasLc=χLE,andweobtain

RL=

Lmax

2χ+κ(

√