aa r X i v : . [ a s t r o - ph ] O c t Aso ia ión Argentina de AstronomíaCompa t Obje ts and their Emission, 2008G. E. Romero and P. Benaglia, eds.The physi s of non-thermal radiation in mi roquasarsValentí Bos h-RamonMax-Plan k-Institut fur Kernphysik, Saupfer he kweg 1, 69117Heidelberg, Deuts hland, vbos hmpi-hd.mpg.deAbstra t. Mi roquasars are binary systems that harbor a normal starand a ompa t obje t (bla k-hole or neutron star), and show relativisti out(cid:29)ows (or jets). The matter that forms these jets is of likely stellarorigin, previously expelled from the star and trapped in the potential wellof the ompa t obje t. This matter is a reted by the ompa t obje t,forming a disk due to its angular momentum, and is eventually eje ted inthe form of a bipolar out(cid:29)ow (the jets), whi h generates radio emissionand ould also be a very high-energy emitter. To study and understandthe radiation from mi roquasars, there is a set of elements that an play amajor role and are to be taken into a ount: the photons and the expelledmatter from the star in the ase of high-mass systems; the a reted matterradiation; the jet; the magneti (cid:28)eld arried by the jet or (cid:28)lling the bi-nary system; and the medium surrounding the mi roquasar at large s ales( ∼ p ). In this le ture, we onsider these elements of the mi roquasar s e-nario and brie(cid:29)y des ribe the physi al onditions and pro esses involved inthe produ tion of non-thermal radiation from radio to gamma-rays. Therequired energeti s, parti le a eleration and transport, several radiativeme hanisms, and the impa t of di(cid:27)erent photon absorption pro esses, aredis ussed.1. Introdu tionAmong the di(cid:27)erent lasses of astrophysi al sour es, mi roquasars (see Mirabel& Rodríguez 1999 for a review) are spe ially interesting for the study of di(cid:27)erenttopi s of high energy astrophysi s. The fa t that these obje ts present non-thermal emission in di(cid:27)erent wavelengths, from radio (e.g. Ribó 2005) to infraredwavelengths (e.g. Mirabel et al. 1998), and from X-rays (e.g. Corbel et al.2002) to very high-energy (VHE) gamma-rays (Aharonian et al. 2005, 2006a;Albert et al. 2006; Albert et al. 2007), has several impli ations, being perhapsthe most important the following ones: parti le a eleration takes pla e, whi hmeans that there are large amounts of energy ontained in moving matter andmagneti (cid:28)elds in a low entropi state, ready to be released in the form of heat andradiation; the a eleration e(cid:30) ien ies are high, pointing to quite extreme plasma onditions from the point of view of parti le on(cid:28)nement, (cid:29)ow velo ities, andspe i(cid:28) hara teristi s of radiation, matter, and magneti (cid:28)elds in the emittingregion; the non-thermal energy out ome an be very large, whi h implies thatthe main radiative me hanism is e(cid:30) ient (e.g. lose to the saturation regime,when pra ti ally all the parti le energy is radiated away). In addition, extendedemission in the radio (e.g. Mirabel et al. 1992) and X-ray bands (e.g. Corbel1 V. Bos h-Ramonet al. 2002) has been dete ted, in some ases up to very large s ales, implyingthat there is still e(cid:30) ient non-thermal parti le a eleration at the sites wherethis radiation is generated.Within the lass of mi roquasars, the sub lasses of low- and high-mass sys-tems are distinguished depending on the mass of the stellar ompanion, whi h an be smaller or bigger than the ompa t obje t mass. In general, high-massmi roquasars have OB stars as ompanions, whi h produ e strong stellar windsand are very bright in the opti al/UV band. Therefore, unlike low-mass mi- roquasars, whose radiative pro esses would be determined basi ally by the a - retion/jet system only, high-mass mi roquasars should present a more omplexphenomenology due to the presen e of the wind and the radiation (cid:28)eld fromthe star. In su h an environment the non-thermal radiation would be a(cid:27)e tedin di(cid:27)erent ways, being perhaps the most relevant ones: dynami al intera tionbetween the jet and the stellar wind (e.g. Peru ho & Bos h-Ramon 2008); atten-uation of the radio emission due to free-free absorption in the wind (e.g. Szostek& Zdziarski 2007); inverse Compton (IC) s attering of relativisti ele trons withstellar photons (e.g. Paredes et al. 2000; Kaufman Bernadó et al. 2002); thestellar wind ould provide with targets for proton-proton ollisions (e.g. Romeroet al. 2003; Aharonian et al. 2006b); the gamma-rays of energy above the pair reation threshold would be absorbed via photon-photon intera tions with theradiation (cid:28)eld of the star (Boett her & Dermer 2005); and the reated se ondarypairs would radiate under the magneti and radiation (cid:28)elds present in the starsurroundings (Bos h-Ramon et al. 2008).In this le ture, we try to give a broad overview of the physi al pro essesinvolved in the formation and hara terization of the observed non-thermal emis-sion from mi roquasars. In Se tion 2., a qualitative and semi-quantitative de-s ription of the physi al s enario is given, and the high energy pro esses relevantin mi roquasars are introdu ed; in Se t. 3., the variability and spe tral proper-ties of the emission are dis ussed; (cid:28)nally, in Se t. 4., we on lude summarizingplus some omments and remarks.2. High energy pro esses in mi roquasars2.1. The physi al s enarioIn Fig. 1, we present the pi ture of a mi roquasar in luding the elements of thes enario: the star, the a retion disk1, the ompa t obje t, the jet, the magneti (cid:28)eld, a relativisti population of ele trons and protons in the jet, the stellarwind, the main radiative pro esses, and pair reation. Rather than going todetails about the pro esses of generation of jets, magneti (cid:28)elds, a elerationof parti les, and the like, we will give for granted what we already know fromobservations, i.e. that mi roquasars present all these ingredients. Instead ofthat, what an be done is to onstrain the models that des ribe these physi al The a reted matter has angular momentum, whi h leads to the formation of a disk. Someme hanism (e.g. turbulent vis osity -Shakura & Sunyaev 1973- or an out(cid:29)ow -Bogovalov &Kelner 2005-) an remove energy and angular momentum, allowing the material to drift towardsregions of the a retion disk loser to the ompa t obje t.he physi s of non-thermal radiation in mi roquasars 3entities or pro esses using observations and basi tools from elementary physi s.These tools are presented in the next se tions.2.2. Energeti sNon-thermal radio emission is produ ed in the jets of mi roquasars, but theenergies of the photons produ ed in these jets likely go up to gamma-rays (e.g.Paredes et al. 2000). Therefore, the (cid:28)rst thing to do, in order to understand themi roquasar non-thermal emission, is to look for the origin of the energy poweringthese jets. Natural energy sour es are the potential energy of the a reted matter(see se t. 3.1.2 in Bos h-Ramon et al. 2006 for a semi-quantitative dis ussion),or the rotational energy of the ompa t obje t (e.g. Semenov et al. 2004; seealso Li et al. 2008). Sin e jet a tivity seems to be well orrelated with a retionin mi roquasars (Fender et al. 2004), we will fo us here on the a retion energyrequirements. The observed non-thermal luminosities an rea h large values, ∼ − erg s − , and the jet kineti luminosity is, order of magnitude, similaror above these values, i.e. ∼ > erg s − . For an e(cid:30) ien y of the a retion-eje tion energy transfer of a 10%, the required a retion energy budget will be L acc ∼ erg s − . This value is quite modest, being a few % of the Eddingtonluminosity for a few M ⊙ ompa t obje t. In the phenomenologi al lassi(cid:28) ationof Fender et al. (2004), this L acc -value would orrespond to a mi roquasar in thelow-hard state, when a persistent jet is expe ted to be present, i.e. mi roquasars an persistently power gamma-ray emission.2.3. Parti le a elerationPresently, it is very di(cid:30) ult to distinguish between several me hanisms of par-ti le a eleration in mi roquasar jets (for a dis ussion of this, see Bos h-Ramon2007 and referen es therein). Due to this fa t, for the purpose of this le ture,it is more onvenient to investigate the a eleration of parti les using a simpleapproa h. The (cid:28)rst step is to see whether a ne essary ondition for the a el-eration of a harged parti le with ertain energy is ful(cid:28)lled, whi h is given bythe Hillas riterium (Hillas 1984). This onsists on the fa t that parti les anonly be a elerated if their Larmor radius ( r L = E/qB a ; where B a is the a el-erator magneti (cid:28)eld, and q and E are the harge and energy of the parti le,respe tively) is smaller than the a elerator size ( l a ); otherwise parti les es apethe a elerator. This limits the highest a hievable energy to (if not spe i(cid:28) allystated, the units in this work are gs): E < qB a l a . (1)Making a step further, to determine whether parti les an be a elerated up to a ertain energy, the spe i(cid:28) a eleration and energy loss (or parti le es ape) me h-anisms are to be known: t acc = t cool / esc . In general, the a eleration times ale an be expressed as: t acc = η r L c = η EqBc , (2)where η is a dimensionless phenomenologi al parameter (or fun tion) represent-ing the a eleration e(cid:30) ien y, di(cid:27)erent in ea h a eleration s enario. The par-ti ular ase of η = 1 orresponds to the shortest possible a eleration time in-dependently of the a eleration me hanism. An instan e for η an be given for V. Bos h-Ramon Observere StarB
X−raysgamma−rays
ICsync γ∗ Wind e+ e−pp
Jet/wind interactions radio region
Accretion diskJet e ? Figure 1. Illustrative pi ture of the mi roquasar s enario, in whi hthe main elements and pro esses onsidered in this work are shown(ba kground image adapted from ESA, NASA, and Félix Mirabel -CEA, IAFE/CONICET-).he physi s of non-thermal radiation in mi roquasars 5the ase of non-relativisti di(cid:27)usive sho k a eleration (plane sho k with weakmagneti (cid:28)eld, in the test parti le approximation -Drury 1983-): η = 2 π DD Bohm (cid:18) cV sh (cid:19) , (3)where V sh is the sho k velo ity, and D is the di(cid:27)usion oe(cid:30) ient ( D Bohm in theBohm limit). For V sh = 3 × m s − and D = D Bohm , η ∼ .Without fo using on any parti ular a eleration me hanism, it is worthynoting that the (cid:28)nal produ t of parti le a eleration of a di(cid:27)usive or sto hasti me hanism will be a power-law ( Q ( E ) ∝ E − h ), and h ∼ is ommonly adopted.Di(cid:27)usive non-relativisti strong sho k a eleration results in h = 2 . Anotherpoint to noti e is that, usually, the parti les in the emitter, e.g. the jet, are onsidered to have an isotropi velo ity distribution in the jet referen e frame(RF), due to de(cid:29)e tion in the randomi omponent of the magneti (cid:28)eld, whi hmoves solidary with the jet matter.2.4. Parti le propagationIn a medium of di(cid:27)usion oe(cid:30) ient D , parti les propagate in one parti ulardire tion with the time dependen e l diff ≈ √ Dt . Under the impa t of ooling,the typi al distan e that parti les of energy E TeV = E/ , and under amagneti (cid:28)eld of B G = B/ , an rea h is: l diff ≈ E / B − / t / (cid:18) DD Bohm (cid:19) / cm , (4)where the Bohm rate is the slowest possible di(cid:27)usion rate, D Bohm = r L c/ , and t cool is the ooling times ale in se onds of the dominant loss me hanism. If themedium in whi h parti les are embedded is also moving (e.g. a jet), there is inaddition adve tive transport: l adv ≈ (cid:18) V adv cm s − (cid:19) t cool cm . (5)These formulae allow us to estimate, under di(cid:27)erent ooling pro esses, whetherparti les an propagate signi(cid:28) antly when omparing these distan es with thea elerator size. For instan e, jet adve tion may transport parti les up to largedistan es. If the radiative pro esses were still e(cid:30) ient, su h a situation wouldimply that the emitter size l ≫ l a (for a thorough dis ussion, see Khangulyan etal. 2008).2.5. Cooling pro essesWe onsider here the following non-thermal pro esses: relativisti Bremsstrahlung,syn hrotron and IC (for an exhaustive review, see Blumenthal & Gould 1970),when leptons are the main emitters; and proton-proton intera tions (see Kelneret al. 2006), when protons are the parti les that produ e the emission to study.Here we brie(cid:29)y list the relevant ooling times ales of these pro esses. The adia-bati loss time is also given, sin e relativisti parti les ould lose energy exertingwork on the medium. V. Bos h-RamonRelativisti ele trons radiate Bremsstrahlung under the e(cid:27)e t of the ele tri (cid:28)eld in the surroundings of an atom. The hara teristi ooling times ale is (e.g.Cheng & Romero 2004): t Br ∼ cm − n s , (6)where n is the density of the medium. Syn hrotron radiation originates whenan ele tron moves in an irregular magneti (cid:28)eld, spiraling around the haoti allyoriented magneti lines. The ele tron su(cid:27)ers Lorentz for es and radiate in thedire tion of motion the energy orresponding to the momentum perpendi ularto the magneti (cid:28)eld. The typi al frequen y of the outgoing syn hrotron photonis ν = 6 . × BE . It is thought that a signi(cid:28) ant part of the magneti energy density in jets is in the form of a haoti magneti (cid:28)eld (e.g. Biermann& Strittmater 1987) atta hed to the plasma. This random magneti (cid:28)eld also on(cid:28)nes the relativisti parti les, whi h di(cid:27)use inside the jet instead of es apingfrom it almost at the speed of light. The hara teristi energy loss times ale forsyn hrotron emission is: t sy ≈ × B − E − s . (7)Under the presen e of radiation (cid:28)elds, relativisti ele trons also intera t with theambient photons via IC s attering, in whi h the s attered photon has in reasedits energy by E/m e c ) and takes the dire tion of the s attering ele tron. If theenergy of the target photon ( ǫ ), in the ele tron RF, is < m e c , the intera tiontakes pla e in the lassi al Thomson regime; in the emitter RF, the ele tronenergy must be < m e c /ǫ . The asso iated hara teristi times ale is: t IC T ≈ u rad E TeV s , (8)where u rad is the target photon (cid:28)eld energy density ( gs). In ase the targetphoton, in the ele tron RF, has an energy > m e c , the intera tion enters in theKlein-Nishina regime, with a hara teristi times ale (Khangulyan et al. 2008): t IC KN ≈ ( u rad ) − (cid:18) ǫ
10 eV (cid:19) . E . s . (9)It is worthy noting here that IC s attering has a strong dependen e on the angleof intera tion between the in oming ele tron whi h be omes less important whenentering in the Klein-Nishina regime. This has to be a ounted when omputingthe radiation for a spe i(cid:28) system and orbital phase, sin e the geometry of theintera tion hanges along the orbit (see Khangulyan et al. 2008 for a deeperdis ussion on this; see Blumenthal & Gould 1970 for the angle-averaged rossse tion, and Bogovalov & Aharonian 20002 for the angular dependent one). Wenote however that the parti le distribution is usually assumed isotropi in theemitter RF and t IC will not depend on the angle. This emitter may be moving Eq. (19) in this work la ks a (1 − cos( θ )) inside the integral ( θ is the angle between the ele tronand photon dire tions of motion in the laboratory RF).he physi s of non-thermal radiation in mi roquasars 7in a ertain dire tion with respe t to the observer, e.g. in the jet, in whi h aseDoppler boosting has to be taken into a ount.If relativisti protons are present, they will lose energy intera ting with theambient atoms (e.g. Romero et al. 2003; Aharonian et al. 2006b). At therelevant energies, i.e. > GeV, ionization losses be ome negligible, and proton-proton ollisions are the dominant ooling hannel with times ales: t pp ≈ cm − n t s , (10)where n t is the density of targets ( gs). After olliding, among other possibleintera tion produ ts, about half of the proton energy goes to π / ± , whi h de ayto gamma-rays/ µ ± / ν µ , and µ ± de ay to e ± (see Orellana et al. 2007 for their ra-diative relevan e in mi roquasars), ν e and ν µ . Roughly, 1/6 of the proton energygoes to gamma-rays, a similar amount to ν , and 1/12 to e ± . If dense and veryhot photon (cid:28)elds and ultrarelativisti nu lei were present, photo-meson produ -tion and photo-disintegration ould play some role, and even syn hrotron protonradiation may be e(cid:30) ient under ertain onditions (Vila & Romero 2008). Herewe will not onsider them for simpli ity, but also be ause they are in general littlee(cid:30) ient or start to work at energies that may not be rea hed due to a eleration onstraints (Bos h-Ramon & Khangulyan 2008, in preparation).The ooling times ale for parti les exerting work on the surrounding mediumis: t ad ≈ l V exp s . (11)This an be onsidered to happen in ase the relativisti parti les are on(cid:28)nedwithin a medium that su(cid:27)ers expansion, like a jet in overpressure with its envi-ronment.2.6. Photon attenuation pro essesAbsorption of gamma-rays with energies above the pair reation threshold ( ǫ th =2 m c /ǫ (1 − cos( θ )) ; where ǫ is the target photon energy and θ is the intera tionangle between the dire tions of the VHE and the stellar photons) will o ur ifthere is a photon (cid:28)eld surrounding the VHE emitter. In ase of mi roquasarsharboring massive stars, the opa ity for one photon to be absorbed, related tothe intera tion probability, an be lose to or mu h larger than 1, i.e. photon-photon absorption is either opti ally thin or opti ally thi k. To estimate thesigni(cid:28) an e of this pro ess, we an use the next simple expression: τ γγ ≈ − u rad R orb ǫ ∗ , (12)where typi ally the system size R orb ∼ − m, ǫ ∗ ∼ . × − erg ( T ∗ ≈ × K) is the typi al energy of the stellar photons, and u rad ∼ erg m − . τ γγ is the opa ity for gamma-rays with energies ≈ . × ǫ th in an isotropi targetphoton (cid:28)eld (when the ross se tion is the largest; see Coppi & Blandford 1990,eq. 4.7).A tually, in most high-mass mi roquasars (LS 5039, Khangulyan et al. 2008;Cygnus X-1, Bednarek & Giovanelli 2007; Cygnus X-3, Protheroe & Stanev 1987; V. Bos h-RamonSS 433, Reynoso et al. 2008; and LS I +61 303, Romero et al. 2007) opa itiessigni(cid:28) antly above 1 will o ur. The o urren e of absorption is important notonly be ause it redu es the amount of VHE photons that es ape the system, butalso be ause it depends on θ . This dependen e is present through the intera tionprobability and ǫ th . In mi roquasars, sin e the intera tion angle hanges alongthe orbit, as well as the surfa e density of target photons seen by the observer,opa ity hanges along the orbit (a dis ussion of this an be found in Khangulyanet al. 2008; the angle averaged pair reation rate an be found in Coppi &Blandford 1990, and the angle dependent ross se tion in Gould & S hréder1967)3.Ele tromagneti as ade an take pla e e(cid:30) iently when KN IC losses aredominant and τ γγ ≫ . The former implies that the ambient magneti (cid:28)eldoutside the emitter must be low enough, i.e.: B c < (cid:18) L ∗ erg s − (cid:19) / (cid:18) RR ⋆ (cid:19) − G . (13)At B c , KN IC losses are equal to syn hrotron losses for 1 TeV photons. Ele tro-magneti as ading onsist on a VHE ele tron that reates a VHE photon viaIC, whi h is absorbed in the stellar (cid:28)eld reating a VHE ele tron/positron pair4,whi h to its turn reates another VHE photon via IC, et etera (this is quite onstraining, a tually, sin e B a ould be signi(cid:28) antly larger than B c , as noted inSe t. 2.7.). Ele tromagneti as ading o urring deep in the KN regime redu ese(cid:27)e tively the opa ity of the system. If the magneti (cid:28)eld were similar to orlarger than B c , the absorbed energy would be mainly released via syn hrotronradiation (see Bos h-Ramon et al. 2008).Beside gamma-ray absorption due to pair reation, it is worthy also to notethat radio emission an be attenuated due to free-free absorption in the stellarwind. An estimate for the free-free opa ity (Rybi ki & Lightman 1979) an beobtained from the next formula: τ ν ff ∼ <
40 ˙ M ν
25 GHz R . V
2w 8 . T /
2w 4 , (14)where ˙ M = ˙ M / − M ⊙ yr − is the stellar mass loss rate, ν = ν/ thefrequen y, R . = R/ . the distan e to the star, V w 8 . = V w / × m s − the stellar wind velo ity, and T w 4 = T w / K the wind temperature. Thisestimate ould be a(cid:27)e ted by the real stru ture of the stellar wind, whi h maybe lumpy (e.g. Owo ki & Cohen 2006), redu ed or in reased depending onthe lump mass density and number. This estimate suggests that the observedradio emission is produ ed outside the binary system in high-mass mi roquasars( ∼ > AU ), at spatial s ales that may be only marginally resolvable by the presentradio interferometer instruments, but still far from the jet eje tion region. When omputing the opa ity, the fa tor (1 − cos( θ )) should be also onsidered in the al ulation,as in the ase of angle-dependent IC s attering. Well above the threshold, when as ading is e(cid:30) ient -deep KN IC-, one member of the pairwill take most of the initial photon energy (e.g. Boett her & S hli keiser 1997).he physi s of non-thermal radiation in mi roquasars 9Another sour e of radiation attenuation is syn hrotron self-absorption. Ele -trons of ertain energies, within a sour e of ertain size and magneti (cid:28)eld, ane(cid:30) iently absorb the syn hrotron emission produ ed by them. For an homoge-neous emitter with a population of relativisti ele trons produ ing syn hrotronemission, the syn hrotron self-absorption frequen y is (see hapter 3 in Pa hol- zyk 1970): ν ssa ≈ c ( lc K ) / ( p +4) B ( p +2) / ( p +4) GHz , (15)where K = N ( E ) /E − p ( p here is the one at the relevant ele tron energies) isthe ele tron energy distribution normalization5, c = 6 . × , c ≈ − ( c a tually depends on p , but the given value works for p ≈ − . ), and l is thesize of the emitter. We noti e that, if the emitter has a omplex stru ture or isstrongly inhomogeneous, ν ssa may be signi(cid:28) antly di(cid:27)erent.Finally, ionization of the stellar wind atoms an absorb the lower energypart of the X-ray spe trum, and also indu e relativisti parti les ooling. We donot dis uss these pro esses here though note that they may be relevant in somespe i(cid:28) situations (e.g. Bos h-Ramon et al. 2007; 2008).2.7. Targets for radiation and energy lossesRelativisti parti les intera t with di(cid:27)erent targets: magneti , photon and mat-ter (cid:28)elds, produ ing emission and subsequently losing energy. In mi roquasars,there are di(cid:27)erent sour es for the mentioned targets. Here, we will fo us onthose related to the star (for the ase of high-mass systems), the jet, and theenvironment at large s ales. In the regions lose to the ompa t obje t, wherethe jet is thought to be produ ed, dense target (cid:28)elds from the a retion disk ould be present as well, but given our la k of knowledge on erning the real jetand environment properties in those regions, we do not onsider them here (fora brief dis ussion, see Bos h-Ramon 2007).The star is a very important ingredient in high-mass mi roquasars. On onehand, the stellar photon (cid:28)eld, with typi al luminosities L ∗ ∼ − erg s − and temperatures ∼ × K, renders stellar IC a very e(cid:30) ient pro ess, aswell as photon-photon absorption. On the other hand, the stellar wind providestargets for proton-proton ollisions, ould be a sour e of radio and soft X-rayradiation attenuation, and may play a dominant role on the jet dynami s atspatial s ales ∼ R orb (not treated here; see Peru ho & Bos h-Ramon 2008 for athorough dis ussion). The wind an have a very omplex stru ture as noted inSe t. 2.6., although we estimate its density assuming that this is an homogeneoussupersoni radial (cid:29)ow of velo ity ∼ × m s − : n w = 2 × ˙ M ∗ − M ⊙ s − ! × cm R orb ! cm − . (16) It is worthy noting that the inje tion ele tron spe trum Q ( E ) and the parti le energy distri-bution N ( E ) are di(cid:27)erent fun tions. The (cid:28)rst one gives the energy dependen e of the inje tedparti les, and the se ond one gives the same but for the (cid:28)nal parti les that su(cid:27)ered the di(cid:27)erent ooling and es ape pro esses that take pla e in the emitter. The units may not oin ide.0 V. Bos h-RamonCon erning the stellar photon (cid:28)eld, the photon number density (valid for a bla kbody) an be roughly approximated by: n ph = 2 × (cid:18) L ∗ erg s − (cid:19) × cm R orb ! cm − . (17)For the magneti (cid:28)eld in the surroundings of the star, we an adopt a R -dependen e of B a in the range r = 1 − (Usov et al. 1992), whi h would or-respond to a toroidal(cid:21)radial(cid:21)dipolar dependen e normalized to B ∗ at the stellarsurfa e ( R ∗ ): B a = 100 (cid:18) B ∗
100 G (cid:19) (cid:18) R ∗ R (cid:19) r G . (18)It is worthy noting that B ∗ is typi ally 100(cid:21)1000 G in OB stars, found for instan eusing the Zeeman e(cid:27)e t (Donati et al. 2002). Further eviden es of the presen eof the magneti (cid:28)eld ome from the dete tion of non-thermal radio emissionfrom isolated massive stars (e.g. Benaglia 2005 and referen es there in), and X-ray observations (e.g. Stelzer et al. 2005). Re alling what was said in Se t. 2.6.regarding ele tromagneti as ades, the typi al B ∗ -values would seem to pre ludethe o urren e of e(cid:30) ient as ading in high-mass mi roquasars.The magneti (cid:28)eld in the jet ould be assumed to go like /z (e.g. for atoroidal magneti (cid:28)eld), where z is the jet height, and normalized to the magneti (cid:28)eld value at some height (i.e. B at z ): B jet = 1 (cid:18) B G (cid:19) cm Z ! cm Z ! G . (19)The presen e of magneti (cid:28)eld and relativisti ele trons in the jet leads to syn- hrotron emission. This pro ess generates a target photon (cid:28)eld inside the jetthat ould be suitable, under ertain onditions of jet radius ( R jet ), B jet , andinje ted parti le luminosity ( L rel ), for e(cid:30) ient syn hrotron self-Compton (SSC),i.e. s attering of the syn hrotron photons by the relativisti ele trons that pro-du ed them. A relationship that tells when syn hrotron self-Compton lossesstart to dominate over syn hrotron ones is the following: u B = B π ∼ L sync πR c ∼ < L rel πR c , (20)where the main assumption is that the syn hrotron emission (of luminosity L sync ) omes mostly from one ompa t region of magneti (cid:28)eld B jet . The treatment ofSSC losses, when dominant, is very ompli ated sin e it is non-linear, i.e. theradiation and the parti le distribution are strongly oupled, with feedba k e(cid:27)e ts.Therefore, it is important to know when SSC losses are to be a ounted for (e.g.Bos h-Ramon & Paredes 2004). A tually, in some ases the SSC radiation anbe omputed without the need of taking into a ount its losses sin e other energylosses, like syn hrotron itself, or external IC, are dominant. Finally, the matterdensity of a oni al supersoni jet an be expressed in the next form: n jet = 2 × L jet (Γ jet −
1) 10 erg s − ! cm s − V jet ! cm R jet ! cm − , (21)he physi
s of non-thermal radiation in mi
roquasars 11where V jet is the jet speed and Γ jet the jet Lorentz fa
tor. In general, densitiesare expe
ted to be low, probably not enough to produ
e gamma-ray emission viarelativisti
Bremsstrahlung, or proton-proton intera
tions (regarding the latter,see otherwise the
ase of SS 433, whi
h has very heavy jets -Reynoso et al. 2008-).At the largest s
ales, where the mi
roquasar jet terminates, the treatment ofthe ambient radiation, matter and magneti
(cid:28)elds be
omes more
omplex. For in-stan
e, in massive systems, a powerful stellar wind would redu
e the density andin
rease the pressure of the jet environment via sho
king the ISM, modifying thewhole dynami
s of the jet/medium intera
tion and introdu
ing inhomogeneitiesin the surroundings. Also, high-mass mi
roquasars, being young obje
ts, tend tobe embedded in a dense medium, unlike low-mass mi
roquasars, whi
h
an bequite old and present even in the halo. In the
ase of low-mass systems, the envi-ronment of the mi
roquasar may have very di(cid:27)erent densities, − (cid:21) > m − ,depending on the lo
ation within the Galaxy, and the ISM, whi
h
ould presentby itself strong inhomogeneities at p
s
ales. In addition, a massive and hot star
ould generate a radiation (cid:28)eld above the lo
al one (i.e. the gala
ti
ba
kground).Otherwise, the latter would be the only possible target for IC intera
tions, whi
hwould typi
ally yield quite low e(cid:30)
ien
ies. Like the density, the magneti
(cid:28)eld inthe jet termination regions is an un
ertain parameter, but some equipartition ar-guments and simple jet/medium intera
tion models give values ∼ − − − G,as found e.g. by Bordas et al. 2008. In that work, the authors show that thenon-thermal emission from the jet termination regions
ould be dete
table6.3. On the radiative outputIn this se
tion, we present some examples of the spe
tra and the light
urves thatthe emission from mi
roquasars
ould show. In order to shape the spe
trumand the light
urve, several possible pro
esses to explain observations at di(cid:27)erentwavelengths are
onsidered. First, a semi-qualitative/quantitative insight intothe formation of the parti
le energy distribution is given, as well as a brief de-s
ription of the shape of the spe
trum of the radiation produ
ed from di(cid:27)erentparti
le energy distributions.3.1. The energy distribution of parti
les and the radiation spe
trumIn Se
tion 2.3., we have already mentioned that the inje
ted parti
le spe
trumis usually adopted with index h = 2 . Although the
omplexity of the emitter(radiative losses, non radiative losses, es
ape losses, et
.) may require the useof a very
omplex model setup, the basi
features of the evolved parti
le energydistribution
an be extra
ted from a very simple
ase: a (one-zone) homogeneousemitter with parti
le es
ape in the steady regime (see Eq. 3(cid:21)7 in Khangulyan etal. 2007). The main idea is that the (cid:28)nal parti
le energy distribution, N ( E ) Interestingly, mi
roquasars are not the only gala
ti
sour
es that produ
e non-thermal emissionvia jet-environment intera
tions (see Araudo et al. 2007 and referen
es therein). The emitter is
onsidered steady and homogeneous, without spatial nor time dependen
es in N ( E ) .2 V. Bos
h-Ramonis: ∝ E − p = E − h +1 / ˙ E > minimum injection energy , ∝ / ˙ E otherwise . (22)From ˙ E = − E/t cool ∝ E g , we
an roughly give the N ( E ) shape for di(cid:27)erent pro-
esses, where g = 2 in the
ase of syn
hrotron and Thomson IC, g ∼ in the
aseof KN IC and ionization losses, g ∼ in the
ase of relativisti
Bremsstrahlung, g ∼ in the
ase of proton-proton intera
tions, and g = 1 in the
ase of adi-abati
losses. If an es
ape time is introdu
ed (e.g. due to
onve
tion by theout(cid:29)ow away from the sho
k that a
elerates parti
les), no parti
les older thanthis es
ape time will be present, and they will not
ontribute to the parti
leenergy distribution below the energy at whi
h they es
ape. The parti
les thatdo not have time to
ool will es
ape the sour
e at the same rate whatever theirenergy. It implies that, in general, below the es
ape energy, N ( E ) ∝ E − h (abovethe minimum inje
tion energy) and = 0 (below the minimum inje
tion energy).Analogously, in the time dependent
ase, i.e the age of the a
elerator < the
ooling times
ale at a
ertain energy, the parti
le energy distribution has p = h below this energy (so-
alled break energy). All this is valid for protons and forele
trons. In Fig. 2, the energy distribution of ele
trons evolving under syn-
hrotron
ooling is shown to illustrate the e(cid:27)e
t of energy losses in the inje
tedparti
le spe
trum.For the shape of the spe
tral energy distribution ( νF ( ν ) , where F ( ν ) is thespe
i(cid:28)
(cid:29)ux), it
an be written: νF ( ν ) = ν n ( ν ) = ν Z E max E min( ν ) N ( E ) P ( E, ν ) dE ≈ ν ˙ E rad ( E ( ν )) N ( E ( ν )) dE ( ν ) /dν , (23)in the delta fun
tion approximation for the spe
i(cid:28)
power P ( E, ν ) of one par-ti
le of energy E , approximately valid for the radiative pro
esses presented inSe
t. 2.5.. n ( ν ) is the spe
i(cid:28)
photon number. The
ooling and the radiationrates, ˙ E cool and ˙ E rad , refer to the radiation we
al
ulate and the dominant
ool-ing me
hanism a(cid:27)e
ting parti
les, respe
tively. ˙ E rad and ˙ E cool do not ne
essarilyhave to be the same.To go further, E ( ν ) is required, and a dependen
e of the kind E ( ν ) ∝ ν l willbe adopted, whi
h is roughly
orre
t for the me
hanisms
onsidered here. Forsyn
hrotron and Thomson IC, l = 1 / ; for KN IC, relativisti
Bremsstrahlungand proton proton intera
tions, l ≈ . Therefore, for a
ooled parti
le population, νF ( ν ) ∝ ν ˙ E rad ( E ( ν )) E ( ν ) − h ν l − / ˙ E cool ( E ( ν )) ∝ ν l ( g rad − g cool +2 − h ) , (24)whi
h implies, for instan
e, that νF ( ν ) ∝ onstant for syn
hrotron, ThomsonIC and proton proton radiation under ˙ E rad = ˙ E cool , or ν − for KN IC undersyn
hrotron
ooling. This se
ond
ase is presented in Fig. 3. For an un
ooledparti
le population, νF ( ν ) ∝ ν ˙ E rad ( E ( ν )) E ( ν ) − h ν l − ∝ ν l ( g rad +1 − h ) , (25)and below the minimum inje
tion energy (if parti
les had time to
ool beforees
aping or at the age of the sour
e): νF ( ν ) ∝ ν ˙ E rad ( E ( ν )) ν l − / ˙ E cool ∝ ν l ( g rad − g cool +1) . (26)he physi
s of non-thermal radiation in mi
roquasars 13 l og ( E x N ( E ) [ a r b . un i t s ] ) h=2; synchrotron coolingInjected (uncooled) particle spectrum t age
Figure 2. The sket h of a parti le energy distribution times E isshown. The ele tron population su(cid:27)ers syn hrotron losses and the ooled parti le distribution is ∝ E × E − for h=2. In the ase shownhere, below the break energy the age of the sour e equals or is smallerthan the syn hrotron energy loss times ale, and the spe trum is stillun ooled.4 V. Bos h-Ramon l og ( ν F ν [ a r b un it s ] ) h=2; Thomson/KN IC SED under synchrotron coolinguncooledparticleemissionThomson IC Cooled particleemissionThomson IC Cooled particleemissionKN ICThomson −>KN transitionBreakenergy ν −2 ν ν Figure 3. The sket h of a spe tral energy distribution of IC emissionprodu ed by ele trons ooled by syn hrotron emission. The syn hrotron omponent is not shown.he physi s of non-thermal radiation in mi roquasars 15Below the es ape energy and the minimum inje tion energy, the delta fun -tion approximation does not work, and the proper emissivity fun tion is to bea ounted for (e.g. for syn hrotron/Thomson IC emission: νF ( ν ) ∝ ν / ; forrelativisti Bremsstrahlung: νF ( ν ) ∝ ν ). Complex shapes for the parti le spe -trum, very di(cid:27)erent from a power-law, and the presen e of low energy and highenergy ut-o(cid:27)s or extreme slopes would modify the simple s hema presented here.3.2. Variability and dominant emission me hanisms at di(cid:27)erent wave-lengthsIn this se tion, we des ribe brie(cid:29)y the variability of the sour e depending on theenergy range. For simpli ity, we keep our dis ussion in the ontext of one-zoneor homogeneous models. We note that propagation e(cid:27)e ts, whi h an lead toemitter inhomogeneity, an hange the variability pattern of the radiation, e.g.smoothing it (see Fig. 22 in Khangulyan et al. 2008 for an example of the impa tof parti le adve tion in the light urve and spe trum), or in reasing it via parti lees ape (e.g. Khangulyan et al. 2007).In the simple ontext adopted here, e.g. one-zone model, di(cid:27)erent fa tors an in(cid:29)uen e on the emission behavior, like the parti le inje tion rate, the mag-neti (cid:28)eld, the target photon density, the non-radiative ooling rate, the es apetimes ale, and the geometry hanges of the binary/observer system along theorbit. It is worthy noting that in the saturation regime, the hange of targetdensities does not ne essarily render variability as long as the inje ted lumi-nosity is onstant (e.g. hanging the stellar photon density along the orbit in ane entri system does not imply modulation of the IC emission).RadioRadio emission, of syn hrotron origin in mi roquasars, an be a(cid:27)e ted byall the mentioned fa tors that in(cid:29)uen e on the light urve but the system geom-etry. Nevertheless, it is worth to note that syn hrotron self-absorption makesthe emitter to be ome opaque to its own syn hrotron radiation below a ertainfrequen y. In su h a regime of emission, variations in the observed spe tral breakfrequen y ( ν ssa ; the opti ally thi k-opti ally thin transition) an o ur dependingfrom whi h dire tion the observer sees an (e.g. asimetri ) emitter. We also notethat radio photons are subje t to free free absorption, very likely to o ur in thestellar wind. This will also introdu e orbital dependent variability.X-raysX-rays ould be of syn hrotron origin, produ ed by the high energy partof N ( E ) , or IC origin, produ ed by the low energy part of N ( E ) (i.e. in theThomson regime). In the former ase, the radiation would be a(cid:27)e ted by all thefa tors mentioned above but hanges of geometry, unless the ele tron distributionand/or the magneti (cid:28)eld on(cid:28)guration are themselves anisotropi . Syn hrotronself-absorption is hardly relevant at these energies. IC an be a(cid:27)e ted, togetherwith the other variability sour es, by geometri al e(cid:27)e ts via the next dependen e: νF ( ν ) ∝ (1 − cos( θ )) , sin e ( θ ) will hange strongly along the orbit sin e thestellar photons ome from the star dire tion, whi h is orbital phase dependentfrom the observer point of view. Relativisti Bremsstrahlung an be hardlye(cid:30) ient in this energy range, sin e it is very hard below the energies around theele tron rest mass one ( ∼ MeV) and will fall probably below the syn hrotron6 V. Bos h-Ramonand/or IC (cid:29)uxes. X-ray attenuation due to ionization of wind atoms, with a hanging hydrogen olumn density along the orbit, may be a sour e of variability.Gamma-rays (GeV)The emission in this energy range ould be due to relativisti Bremsstrahlung,proton-proton intera tions, or IC s attering. If hadroni and the leptoni a el-eration were equally e(cid:30) ient, and IC s attering negligible (e.g. under a low-mass ompanion photon (cid:28)eld), relativisti Bremsstrahlung would dominate due to thesmaller energy transferring in the ase of (proton-proton) proton to gamma-rays ompared with (relativisti Bremsstrahlung) ele tron to gamma-rays. Neverthe-less, very high densities would be required (see Se t. 2.5. and 2.7.). If a massiveand hot primary is present, stellar (Thomson) IC will be a mu h more e(cid:30) ientpro ess. SSC radiation ould be still relevant for the ase of a high-mass mi ro-quasar, and ertainly is a good andidate for low-mass mi roquasars8. As notedabove, powerful jets ontaining relativisti protons in low-mass mi roquasarsmay also present signi(cid:28) ant hadroni radiation from other hannels.The variability in this energy range ould be due to all the e(cid:27)e ts mentionedabove. In parti ular, the angular dependen e of (Thomson) IC ( ∼ (1 − cos( θ )) ),implies that less IC emission goes to the observer when the emitter is in frontof the star, re eiving the stellar photons from behind, thought to happen duringthe superior onjun tion of the ompa t obje t. In addition, the IC emissionfrom se ondary pairs or the o urren e of ele tromagneti as ading, repro essingenergy above ∼ GeV down to lower energies, may a(cid:27)e t the GeV variability aswell, sin e the observable out ome of as ading is sensitive to the binary/observergeometry.Gamma-rays (TeV)The radiation pro esses ontributing at these energies are the same as those ontributing in the GeV range. Nevertheless, depending on the parti le energydistribution and ross se tion behavior at high energies, some pro esses may bemore or less signi(cid:28) ant in the GeV and TeV regimes. The nature of the emittingparti les are also relevant. For instan e, a syn hrotron dominated parti le energydistribution is mu h softer than a KN IC one, and ele trons may be softer orharder than protons depending on the ooling onditions, although protons willin general yield a harder radiation spe trum at the highest energies for the same h . The variability at these energies an be produ ed by the same fa tors as inthe GeV range. Regarding the angle-dependen e of IC s attering, at TeV energiesthis pro ess takes pla e in the KN regime. There is still some modulation of theemission, similar to some extent to (1 − cos( θ )) , but the deeper in the KN regimethe IC s attering o urs, the smaller the modulation. At energies ≫ TeV, there isbasi ally no modulation. The hanging angular dependen e at di(cid:27)erent energiesrenders a omplex spe tral time behavior. There is additional modulation due tophoton-photon absorption above the pair reation threshold, due to ∼ (1 − cos( θ )) and ele tromagneti as ading, and the pair reation threshold also depends onthe photon-photon s attering angle (re all: ǫ th = 2 m c / (1 − cos( θ )) ǫ ). There ould be additional IC omponents due to the presen e of strong a retion disk and/or orona photon (cid:28)elds (e.g. Bos h-Ramon et al. 2006).he physi s of non-thermal radiation in mi roquasars 17Fig. 4 gives an idea of the importan e of the angle dependen e of photon-photon absorption and IC s attering for the light urve. Unlike other sour es ofvariability, this modulation o urs for sure if the star is providing the targets forthese intera tion pro esses.4. Final ommentsIn this le ture, we try to show that to understand mi roquasars, (cid:28)rst one anapproa h the problem using simple tools. This an be performed, partially, usingthe available phenomenologi al knowledge on the sour e properties (known ele-ments of the system/emitter and their relationships, observational informationabout the emission behavior). This allows the onstru tion of phenomenologi aljet emission models whi h, at some point, fail to deepen in our understanding ofmi roquasar non-thermal radiation. Therefore, in addition to this phenomeno-logi al modeling, whi h allows us to set up the basi s enario and obtain somegeneral idea of the global radiation behavior, a simple but systemati physi alstudy sour e by sour e is also to be done. With this study, important onstraints an be imposed on the parti le a eleration e(cid:30) ien y, the impa t of parti le on-(cid:28)nement and propagation, and the plausible radiation and attenuation pro esseso urring in mi roquasars.On e the previous step is (cid:28)nished, it will be time to perform hydrodynami- al and magnetohydrodynami al simulations, whi h are powerful heuristi toolsto investigate further the omplexity of the sour e stru ture (e.g. to understandthe evolution of the jet, and its intera tion with the stellar wind and large s aleenvironment, et .). Finally, using high quality data observations, provided bythe next generation instruments, and the theoreti al knowledge a quired withprevious modeling and simulations, one an atta k the problem of whi h me h-anism of parti le a eleration is more suitable to explain the observed radiation,and the radiation me hanism itself, in the ontext of a more onstraint physi als enario.A knowledgments. V.B-R. wants to thank the organizers of the s hoolfor the opportunity of giving this le ture on mi roquasar physi s in su h a ni eenvironment. V.B-R. thanks A. T. Araudo for her bene(cid:28) ial in(cid:29)uen e on thiswork. Finally, V.B-R gratefully a knowledges the help of F. A. Aharonian, S. R.Kelner, D. Khangulyan, J. M. Paredes, M. Ribó and G. E. Romero, in thedevelopment of the ideas presented in this le ture. V.B-R. a knowledges alsosupport from the Alexander von Humboldt Foundation. V.B-R. a knowledgessupport by DGI of MEC under grant AYA2007-68034-C03-01 and FEDER funds.Referen esAharonian, F. A. et al., 2005, S ien e, 309, 746Aharonian, F. A. et al., 2006a, A&A, 460, 743Aharonian, F. A., An hordoqui, L. A., Khangulyan, D., Montaruli, T. 2006b,J.Phys.Conf.Ser., 39, 408 [astro-ph/0508658℄Albert, J. et al. 2006, S ien e, 312, 17718 V. Bos h-Ramon a r b i t r a r y un i t s phase=0 (INFC), phase=0.5 (SUPC) Thomson IC/ γγ absorption angle−dependencepair creation threshold angle−dependence Figure 4. Example of the impa t of the geometry variation along theorbit on both photon-photon absorption and IC s attering. The pair reation threshold (long-dashed line) an go to very large values whentarget photons ome from behind around the inferior onjun tion ofthe ompa t obje t (INFC; phase 0.0). This suppresses photon-photonabsorption below the (in reased) pair reation energy threshold. De-pending on the in lination, i.e. the observer line of sight angle withrespe t to the orbital plane perpendi ular dire tion, the stellar targetphotons an ome, more or less, from behind. The ase represented hereimplies an extreme in lination angle of 90 ◦◦