aa r X i v : . [ a s t r o - ph . H E ] J u l First La Plata International S hoolCompa t Obje ts and their Emission, 2008I. Andru how and G. E. Romero, eds.Bla k Holes in the GalaxyJosep M. ParedesDepartament d'Astronomia i Meteorologia and Institut de Cièn ies delCosmos (ICC), Universitat de Bar elona (UB/IEEC), Martí i Franquès1, 08028 Bar elona, SpainE-mail: jmparedesub.eduAbstra t. The most ompelling eviden es for the existen e of stellar-mass bla k holes have been obtained through observations of X-ray binarysystems. The appli ation of lassi al methods and the development of newte hniques have allowed us to in rease the number of stellar-mass bla kholes known. I summarize here the observational signatures of the bla kholes, su h as the mass determination, the event horizon and the spin. Ialso present some observational results on the Gala ti entre bla k hole.1. Introdu tionThe ontribution presented here is part of a ourse on Compa t Obje ts andtheir Emission given in the First La Plata International S hool on Astronomyand Geophysi s. The ontribution is fo used on the observational eviden es ofstellar mass bla k holes in our Galaxy and the super-massive bla k hole in its entre. The four Le tures that were given about the bla k holes in the Galaxyhave been distributed here in (cid:28)ve Se tions.In Se tion 2 a brief a ount about how a neutron star or a bla k hole areformed is presented, a brief bla k hole history is also introdu ed and some on- epts su h as the S hwarz hild radius, the event horizon and Kerr bla k holeare given. As the X-ray binaries play a fundamental role for the study of stellarmass bla k holes, Se tion 3 is devoted to introdu e the X-ray binaries and explainsome of their most important hara teristi s. In Se tion 4, the (cid:28)rst bla k hole andidates are introdu ed, how were they dis overed and how many of them are urrently known. Se tion 5 is devoted spe i(cid:28) ally to introdu e the observationalsignatures of the bla k holes. In parti ular, some methods to estimate the mass,to (cid:28)nd possible eviden es for the event horizon and to measure the bla k holespin are explained. Finally, Se tion 6 is devoted to the super-massive bla k holein the entre of our Galaxy.2. Physi al ba kground2.1. Dead starsDuring their life stars evolve through di(cid:27)erent states that are linked to the nu learburning. When the ore of the star runs out of nu lear fuel, it ollapses untilsome other form of pressure support enables a new equilibrium on(cid:28)gurationto be attained. The possible equilibrium on(cid:28)gurations whi h an exist when1 J. M. Paredesthe star ollapses are: White Dwarfs (WD), Neutron Stars (NS), Bla k Holes(BH). A ording the initial star mass ( M init ), there will be di(cid:27)erent types of ollapse and di(cid:27)erent supernova explosions. When M init < 8 M ⊙ , there is no SNexplosion, only ontra tion, and a WD is formed. If the WD a retes mass it willexplode as a type Ia SN. When M init > 8 M ⊙ , thermonu lear SN explosions ofdi(cid:27)erent types are produ ed (types Ib, I and no H lines; Types II and H lines).As a result, a NS or a BH is formed.In WD and NS, the pressure whi h holds up the star is the quantum me- hani al pressure asso iated with the fa t that ele trons, protons and neutronsare fermions (only one parti le is allowed to o upy any one quantum me hani alstate). WD are held up by ele tron degenera y pressure, and their mass is belowthe Chandrasekhar limiting mass M Ch = 1.46 M ⊙ . With in reasing density, thedegenerate ele tron gas be omes relativisti and, when the total energy of theele tron ex eeds the mass di(cid:27)eren e between the neutron and the proton, theinverse β -de ay pro ess an onvert protons into neutrons. It is the degenera ypressure of this neutron gas whi h prevents ollapse under gravity and results inthe formation of a NS.The same physi s for the WD is responsible for providing pressure supportfor the NS, the only di(cid:27)eren e being that the neutrons are about 2000 times moremassive than the ele trons, and onsequently degenera y sets in at a orrespond-ingly higher density. NS, in whi h neutron degenera y pressure is responsible forthe pressure support, an have a mass given by the Tolman-Oppenheimer-Volko(cid:27)mass limit. This mass is not analyti ally well (cid:28)xed be ause of its dependen eon the equations of state for nu lear matter. In any ase, most equations ofstate do not allow the neutron degenera y pressure to support more than 3 M ⊙ ,indi ating that dead stars more massive than 3 M ⊙ must be BHs. Figure 1 showsan s heme of the relation between the original mass and the (cid:28)nal mass of a deadstar.2.2. Brief Bla k Hole HistoryJohn Mi hell (cid:28)rst des ribed the on ept of a bla k hole in a paper that appearedin Philosophi al Transa tions of the Royal So iety of London in 1783. Mi helldis ussed the possibility of a star with a gravitational for e so strong that noteven light ould es ape from it, thus preventing astronomers from observingsu h phenomena. Pierre-Simon Lapla e mentioned the possibility of su h starsin the (cid:28)rst few editions of his book Exposition du système du Monde (1796),although he failed to in lude it in later editions be ause the idea of a star witha gravitational for e that ould overpower light did not omply with the wavetheory of light, whi h was generally a epted at that time. This theory seemedto suggest that light ould not be a(cid:27)e ted by gravity, a on ept that is key tothe theories of Mi hell and Lapla e. In the early 1800's experiments on opti alinterferen e led to the predominan e of the wave theory of light and the endof the orpus ular theory. Sin e light waves were thought to be una(cid:27)e ted bygravitation, interest in the hypotheti al "dark stars" eased.In 1905 Albert Einstein published his Spe ial Theory of Relativity and in1915 his General Theory of Relativity (GR). The GR was a new theory of grav-itation and one of its fundamental predi tions was the e(cid:27)e t of gravity on light.Matter auses spa e-time to urve and therefore the paths followed by light raysla k Holes in the Galaxy 3Figure 1. Relation between the original mass and the (cid:28)nal mass of astar (from Comins-Kaufmann 1991). J. M. Paredesor matter are determined by the urvature of the spa e-time. This allowed for amodern s ienti(cid:28) proof of Mi hell's hypothesis.A short time after Einstein published his GR, the German physi ist KarlS hwarz hild wrote a paper des ribing a stru ture alled a singularity. He arguedthat matter ould theoreti ally be drawn into a point with virtually no volumeand a in(cid:28)nite density. He alled this obje t a point mass, later dubbed a sin-gularity. In addition, S hwarz hild determined that there is a de(cid:28)nite boundaryaround a singularity alled the event horizon.In 1928, through his resear h on WD, Subrahmanyan Chandrasekhar hy-pothesized that a dying star of a ertain mass might form a point with enoughgravitational pull to trap light.In 1939, Ameri an physi ist Robert Oppenheimer developed a possible ex-planation for the nature of these points of in(cid:28)nite density. Oppenheimer theo-rized that the gravitational pull of a star with in(cid:28)nite density would ause lightrays to deviate from their path and bend towards the star. Eventually, the grav-ity of the star would be ome so great that the light would be ome trapped by itand would be unable to es ape, preventing one from observing it. At this pointthe star is a BH. The Ameri an s ientist John Wheeler oined the term "bla khole" in 1969, although from a non astrophysi al point of view, the expression"bla k hole" was oined before in Cal utta to des ribe a small dungeon wheretroops of the Nawab of Bengal held British prisoners of war after the apture ofFort William on June 20, 1756.2.3. S hwarz hild radius, Event horizon, Kerr BHPerforming a lassi al al ulation, the es ape velo ity from the surfa e of a starof mass M and radius r is mv = GM mr → v e = q GM/r (1)and setting v e = c , the radius of su h star would be r = 2 GM/c . As wewill see later, this is just the expression for the S hwarz hild radius of a BH ofmass M , and the spheri al surfa e of radius r plays the role of the surfa e of theBH. The es ape velo ity from the Earth is 11 km s − , from the Sun is 617 kms − , from a NS (2 M ⊙ and radius 10 km) is 230 000 km s − and from a BH shouldbe greater than c .Some months after the Einstein's de(cid:28)nitive formulation of the GR in 1915,S hwarzs hild dis overed the solution for the metri of spa e-time about a pointmass M : d s = (cid:16) − GMrc (cid:17) d t − c " d r (cid:16) − GMrc (cid:17) + r (d θ + sin θ d φ ) (2)This metri , known as the S hwarzs hild metri , has the same meaning asthe interval d s in spe ial relativity, whi h is known as the Minkowski metri : d s = d t − c h d r + r (d θ + sin θ d φ ) i (3)la k Holes in the Galaxy 5In the limit of large distan es from the point mass, r → ∞ , the two met-ri s be ome the same. They are, however, very di(cid:27)erent for small values of r , re(cid:29)e ting the in(cid:29)uen e of the mass M upon the geometry of spa e-time.In the ase of the S hwarzs hild metri , the time interval between events a - ording to an observer who is stationary in S and lo ated at the point r isd t ′ = d t (1 − GM/rc ) / .This notation makes it lear how the time interval d t ′ depends upon thegravitational potential in whi h the observer is lo ated. d t ′ only redu es tod t in the limit of very large distan es from the origin, r → ∞ , at whi h thegravitational potential goes to zero.Redshift of ele tromagneti waves. If the time interval ∆ t ′ orresponds tothe period of the waves emitted at the point r , the observed period of the waveat in(cid:28)nity ∆ t is given by ∆ t ′ = − GMrc ! ∆ t (4)Therefore, the emitted and observed frequen ies, ν e and ν ∞ , respe tively,are related by ν ∞ = ν e − GMrc ! (5)This expression is the general relativisti result orresponding to Mi hell'sinsight. If the radiation is emitted from radial oordinate r = 2 GM/c , thefrequen y of any wave is redshifted to zero frequen y, and no information anrea h in(cid:28)nity from radii r ≤ r Sch = 2
GM/c . Here r Sch is the S hwarzs hildradius. Sin e, a ording to GR, no radiation an es ape from within this radius,the surfa e r = r Sch is bla k.The S hwarzs hild radius de(cid:28)nes the event horizon. Not even light anes ape, on e it has rossed the event horizon. It an be written as r Sch = 3 (cid:16) MM ⊙ (cid:17) km. Another important aspe t of the S hwarzs hild metri is the dynami s of testmasses in the gravitational (cid:28)eld of the point mass. In a Newtonian treatment,from the onservation of energy we obtain mv − GM mr = 12 mv ∞ → ˙ r + ( r ˙ θ ) − GMr = v ∞ (6)and from the onservation of angular momentum, m ˙ θr = constant . Intro-du ing the spe i(cid:28) angular momentum of the parti le (angular momentum perunit mass) h = ˙ θr , we an write ˙ r + h r − GMr = ˙ r ∞ (7)As long as h = 0 , the parti le annot rea h r = 0 be ause the energy termasso iated with the entrifugal for e, h /r , be omes greater than the gravita-tional potential energy GM/r for small enough values of r . J. M. ParedesIn a General Relativisti treatment the dynami s of the test mass is givenby ˙ r + h r − GMr − GM h r c = ( A − c (8)There are two main di(cid:27)eren es when omparing this relativisti equationwith the Newtonian equation. There is an extra term and onstants and variableshave di(cid:27)erent meaning in GR ( r angular diameter distan e, ˙ r means d r /d s ,where s is proper time, h and ( A − are onstants equivalent to h and ˙ r ∞ ).The most important di(cid:27)eren e is the additional term GMh r c , whi h has thee(cid:27)e t of enhan ing the attra tive for e of gravity, even when the parti le hasa (cid:28)nite spe i(cid:28) angular momentum h (the greater the value of h , the greaterthe enhan ement). This result an be understood by re alling that the kineti energy asso iated with the rotational motion around the point mass ontributesto the inertial mass of a test parti le and thus enhan es the gravitational for eupon it. From the analysis of the relativisti equation, some interesting results an be found:1) For su(cid:30) iently small values of r , the general relativisti term GMh r c be omesgreater than the entrifugal potential term, implying that this purely generalrelativisti term in reases the strength of gravity lose enough to r = 0 . It anbe shown easily that if the spe i(cid:28) angular momentum of the parti le h ≤ r Sch c it will inevitably fall in to r = 0 .2) There is a last stable ir ular orbit, of radius r = 3 r Sch , around the point mass.There are no stable ir ular orbits with smaller radii than this value be ause theparti les would spiral rapidly into r = 0 . This is why the BH is alled hole,matter inevitably ollapses in to r = 0 if it omes too lose to the point mass.3) From the metri given in Eq. 2, it appears that there is a singularity at r Sch . It an be shown that this is not a physi al singularity. However, at r = 0 , there is areal physi al singularity, and a ording to the GR, the infalling matter ollapsesto a singular point.However, these S hwarzs hild singularities are unobservablebe ause no information an arrive to the external observer from within r Sch .For all pra ti al purposes, the BH may be onsidered to have a bla k spheri alsurfa e at r Sch . From the lassi al point of view, physi s breaks down at r = 0 .Kerr bla k holes. In 1962, Kerr dis overed the general solution for a BHwith angular momentum J . It has been shown that isolated BHs an be om-pletely hara terized by only three properties: mass M , harge Q and angularmomentum J . The rotating BHs (Kerr BHs) are relevant to many aspe ts ofhigh energy astrophysi s. The Kerr metri in Boyer-Landquist oordinates isgiven by: d s = − GM rρc ! d t − c " GM r a sin θρc d t d φ + ρ ∆ d r + ρ d θ ++ r + a + 2 GM r a sin θρc ! sin θ d φ (9)where a = J/M c is the angular momentum of the BH per unit mass, ∆ = r − (2 GM r/c ) + a and ρ = r + a cos θ . If the BH is non-rotating, J = a = 0 la k Holes in the Galaxy 7and the Kerr metri redu es to the standard S hwarzs hild metri . Just as inthe ase of S hwars hild metri , the metri oe(cid:30) ient of d r be omes singular ata ertain radial distan e, when ∆ = 0 . This radius orrespond to the surfa e ofin(cid:28)nite redshift or the horizon of the rotating BH, and is given by the solutionof ∆ = 0 . Taking the larger of the two roots, the horizon o urs at radius r + = GMc + " GMc ! − JM c ! (10)This spheri al surfa e has exa tly the same properties as the S hwars hildradius in the ase of non-rotating BHs. Parti les and photons an fall in throughthis radius, but they annot emerge outwards a ording to the lassi al theoryof GR. If the system has too mu h angular momentum J, no BH will be formed.The maximum angular momentum orresponds to J = GM /c . For a maximallyrotating BH, the horizon radius is r + = GM/c , just half the result for the ase ofS hwars hild BH, r Sch = 2
GM/c . For maximally rotating BHs the last stable ir ular orbit is lo ated at (Shapiro & Teukolsky 1983) r = r + = GM/c for orotating test parti les and at r = 9 r + = 9 GM/c for ounter-rotating parti les.(Re all: for non-rotating BHs, the last stable orbit is at r = 3 r Sch = 6
GM/c ).Correspondingly, the maximum binding energies of these orbits an be found,that is, the amount of energy that has to be lost in order for the material toattain a bound stable ir ular orbit with radius r. In the orotating ase, 42.3%of the rest mass energy of the material an be released as it spirals into the BHthrough a sequen e of almost ir ular equatorial orbits. In the ounter-rotating ase it is 3.8%. This is the pro ess by whi h energy is liberated through thea retion of matter onto BHs, and is likely to be the sour e of energy in someof the most extreme astrophysi al obje ts. The energy available is mu h greaterthan that attainable from nu lear fusion pro esses, whi h at most an releaseabout 1% of the rest mass energy of matter. A more omplete treatment of thetopi s developed in this subse tion an be found in Longair (1994a, 1994b).3. X-ray binariesAn X-ray binary is a binary system ontaining a ompa t obje t, either a neutronstar or a stellar mass bla k hole, that emits X-rays as a result of a pro essof a retion of matter from the ompanion star. Several s enarios have beenproposed to explain this X-ray emission, depending on the nature of the ompa tobje t, its magneti (cid:28)eld in the ase of a neutron star, and the geometry ofthe a retion (cid:29)ow. The a reted matter is a elerated to relativisti speeds,transforming its potential energy provided by the intense gravitational (cid:28)eld ofthe ompa t obje t into kineti energy. Assuming that this kineti energy is(cid:28)nally radiated, the a retion luminosity an be omputed, (cid:28)nding that thisme hanism provides a very e(cid:30) ient sour e of energy, even mu h higher e(cid:30) ien ythan that for nu lear rea tions.On its way to the ompa t obje t, the a reted matter arries angular mo-mentum and usually forms an a retion disk around it. The matter in the dis looses angular momentum due to vis ous dissipation, whi h produ es a heatingof the dis , and falls towards the ompa t obje t in a spiral traje tory. The bla k J. M. Paredesbody temperature of the last stable orbit in the ase of a BH a reting at theEddington limit is given by: T ∼ × M − / (11)where T is expressed in Kelvin and M in M ⊙ (Rees 1984). For a ompa t obje tof a few solar masses, T ∼ K. At this temperature the energy is mainlyradiated in the X-ray domain.In High Mass X-ray Binaries (HMXBs) the donor star is an O or B early typestar of mass in the range ∼ (cid:21) M ⊙ and typi al orbital periods of several days.HMXBs are onventionally divided into two subgroups: systems ontaining a Bstar with emission lines (Be stars), and systems ontaining a supergiant (SG) Oor B star. In the (cid:28)rst ase, the Be stars do not (cid:28)ll their Ro he lobe, and a retiononto the ompa t obje t is produ ed via mass transfer through a de retion dis .Most of these systems are transient X-ray sour es during periastron passage.In the se ond ase, OB SG stars, the mass transfer is due to a strong stellarwind and/or to Ro he lobe over(cid:29)ow. The X-ray emission is persistent, and largevariability is ommon. The most re ent atalogue of HMXBs was ompiled byLiu et al. (2006), and ontains 242 sour es.In Low Mass X-ray Binaries (LMXBs) the donor has a spe tral type laterthan B, and a mass ≤ M ⊙ . Although it is typi ally a non-degenerated star,there are some examples where the donor is a WD. The orbital periods arein the range 0.2(cid:21)400 hours, with typi al values < hours. The orbits areusually ir ular, and mass transfer is due to Ro he lobe over(cid:29)ow. Most LMXBsare transients, probably as a result of an instability in the a retion dis or amass eje tion episode from the ompanion. The typi al ratio between X-ray toopti al luminosity is in the range L X /L opt ≃ (cid:21) , and the opti al emissionis dominated by X-ray heating of the a retion dis and the ompanion star.Some LMXBs are lassi(cid:28)ed as `Z' and `Atoll' sour es, a ording to the patterntra ed out in the X-ray olor- olor diagram. `Z' sour es are thought to be weakmagneti (cid:28)eld neutron stars of the order of G with a retion rates around0.5(cid:21)1.0 ˙ M Edd . `Atoll' sour es are believed to have even weaker magneti (cid:28)elds of ≤ G and lower a retion rates of 0.01(cid:21)0.1 ˙ M Edd . The most re ent atalogueof LMXBs was ompiled by Liu et al. (2007), and ontains 188 sour es.Re ently, Grimm et al. (2002) estimated that the total number of X-ray bi-naries in the Galaxy brighter than 2 × erg s − is about 705, being distributedas ∼
325 LMXBs and ∼
380 HMXBs.3.1. Radio emitting X-ray binaries (REXBs)The (cid:28)rst X-ray binary known to display radio emission was S o X-1 in the late1960s. Sin e then, many X-ray binaries have been dete ted at radio wavelengthswith (cid:29)ux densities ≥ . (cid:21) mJy. The (cid:29)ux densities dete ted are produ ed insmall angular s ales, whi h rules out a thermal emission me hanism. The moste(cid:30) ient known me hanism for produ tion of intense radio emission from astro-nomi al sour es is the syn hrotron emission me hanism, in whi h highly rela-tivisti ele trons intera ting with magneti (cid:28)elds produ e intense radio emissionthat tends to be linearly polarized. The observed radio emission an be explainedby assuming a spatial distribution of non-thermal relativisti ele trons, usuallywith a power-law energy distribution, intera ting with magneti (cid:28)elds.la k Holes in the Galaxy 9Sin e some REXBs, like SS 433, were found to display elongated or jet-likefeatures, as in A tive Gala ti Nu lei (AGN) and quasars, it was proposed that(cid:29)ows of relativisti ele trons were eje ted perpendi ular to the a retion dis ,and were responsible for syn hrotron radio emission in the presen e of a mag-neti (cid:28)eld. Models of adiabati ally expanding syn hrotron radiation-emitting oni al jets may explain some of the hara teristi s of radio emission from X-raybinaries (Hjellming & Johnston 1988). Several models have been proposed forthe formation and ollimation of the jets, in luding the presen e of an a retiondis lose to the ompa t obje t, a magneti (cid:28)eld in the a retion dis , or ahigh spin for the ompa t obje t. However, there is no lear agreement on whatme hanism is exa tly at work.There are eight radio emitting HMXBs and 35 radio emitting LMXBs. Sin ethe strong magneti (cid:28)eld of the X-ray pulsars disrupts the a retion dis atseveral thousand kilometers from the neutron star, there is no inner a retiondis to laun h a jet and no syn hrotron radio emission has ever been dete tedin any of these sour es. Although the division of X-ray binaries in HMXBs andLMXBs is useful for the study of binary evolution, it is probably not importantfor the study of the radio emission in these systems, where the only importantaspe t seems to be the presen e of an inner a retion dis apable of produ ingradio jets. However, the eight radio emitting HMXBs in lude six persistent andtwo transient sour es, while among the 35 radio emitting LMXBs we (cid:28)nd 11persistent and 24 transient sour es. The di(cid:27)eren e between the persistent andtransient behavior learly depends on the mass of the donor.Ex luding X-ray pulsars, to of the atalogued gala ti X-ray binarieshave been dete ted at radio wavelengths regardless of the nature of the donor.The orresponding ratio of dete ted/observed sour es is probably mu h higher.However, it is di(cid:30) ult to give reliable numbers, sin e observational onstrainsarise when onsidering transient sour es observed in the past (large X-ray errorboxes, single dish and/or poor sensitivity radio observations, et .), and likelymany non-dete tions have not been published.3.2. Mi roquasarsA mi roquasar is a radio emitting X-ray binary displaying relativisti radio jets.The name was given not only be ause of the observed morphologi al similaritiesbetween these sour es and the distant quasars but also be ause of physi al sim-ilarities, sin e when the ompa t obje t is a bla k hole, some parameters s alewith the mass of the entral obje t (Mirabel & Rodríguez 1999). A s hemati illustration omparing some parameters in quasars and mi roquasars is shown inFigure 2.From Eq. 11, a typi al temperature of the a retion dis of a mi roquasar ontaining a stellar mass bla k hole is T ∼ K, while that of a quasar ontain-ing a super-massive bla k hole ( (cid:21) M ⊙ ) is T ∼ K. This explains whyin mi roquasars the a retion luminosity is radiated in X-rays, while in quasarsit is radiated in the opti al/UV domain. The hara teristi jet sizes appear tobe proportional to the mass of the bla k hole. Radio jets in mi roquasars havetypi al sizes of a few light years, while in quasars may rea h distan es of up toseveral million light years. The times ales are also dire tly s aled with the massof the bla k hole following τ ≃ R Sch /c = 2 GM X /c ∝ M X . Therefore, phenom-0 J. M. ParedesFigure 2. Comparative illustration of the analogy between quasarsand mi roquasars. Note the extreme di(cid:27)eren es in the order of mag-nitude of the physi al parameters involved. Figure reprodu ed fromMirabel & Rodríguez (1998).ena that take pla e in times ales of years in quasars an be studied in minutesin mi roquasars. Thus, mi roquasars mimi , on smaller s ales, many of the phe-nomena seen in AGNs and quasars, but allow a better and faster progress in theunderstanding of the a retion/eje tion pro esses that take pla e near ompa tobje ts.The urrent number of on(cid:28)rmed mi roquasars is ∼
16 among the 43 ata-logued REXBs (Paredes 2005). Some authors (Fender 2001) have proposed thatall REXBs are mi roquasars, and would be dete ted as su h provided that thereis enough sensitivity and/or resolution in the radio observations.A retion dis and jet eje tion The theoreti al models attempting to under-stand the jet formation and its onne tion with the a retion dis had a seminal ontribution in the works by Blandford & Payne (1982). These authors exploredthe possibility of extra ting energy and angular momentum from the a retionla k Holes in the Galaxy 11dis by means of a magneti (cid:28)eld whose lines extend towards large distan esfrom the dis surfa e. Their main result was the on(cid:28)rmation of the theoreti alpossibility to generate a (cid:29)ow of matter outwards from the dis itself, providedthat the angle between the dis and the (cid:28)eld lines was smaller than 60 ◦ . Lateron, the (cid:29)ow of matter is ollimated at large distan es from the dis by the a tionof a toroidal omponent of the magneti (cid:28)eld. In this way, two opposite jets ould be formed (cid:29)owing away perpendi ularly to the a retion dis plane.To on(cid:28)rm observationally the link between a retion dis and the genesis ofthe jets is by no means an easy task. The ollimated eje tions in GRS 1915+105provide one of the best studied ases supporting the proposed dis /jet onne tion.In Figure 3, from Mirabel et al. (1998), simultaneous observations are presentedat radio, infrared and X-ray wavelengths. The data show the development of aradio outburst, with a peak (cid:29)ux density of about 50 mJy, as a result of a bipolareje tion of plasma louds. However, pre eding the radio outburst there was a lear pre ursor outburst in the infrared. The simplest interpretation is that both(cid:29)aring episodes, radio and infrared, were due to syn hrotron radiation generatedby the same relativisti ele trons of the eje ted plasma. The adiabati expansionof plasma louds in the jets auses an energy loss in the ele tron population and,as a result, the spe tral maximum of their syn hrotron radiation is progressivelyshifted from the infrared to the radio domain.It is also important to note the behaviour of the X-ray emission in Fig-ure 3. The emergen e of jet plasma louds, that produ e the infrared and radio(cid:29)ares, seems to be a ompanied by a sharp de ay and hardening of the X-rayemission (8.08(cid:21)8.23 h UT in the (cid:28)gure). The X-ray fading is interpreted as thedisappearan e, or emptying, of the inner regions of the a retion dis (Belloniet al. 1997). Part of the matter ontent in the dis is then eje ted into thejets, perpendi ularly to the dis , while the rest is (cid:28)nally aptured by the entralbla k hole. Additionally, Mirabel et al. (1998) suggest that the initial time ofthe eje tion oin ides with the isolated X-ray spike just when the hardness ratiosuddenly de lines (8.23 h UT). The re overy of the X-ray emission level at thispoint is interpreted as the progressive re(cid:28)lling of the inner a retion dis with anew supply of matter until rea hing the last stable orbit around the bla k hole.This behaviour in the light urves of GRS 1915+105 has been repeatedlyobserved by di(cid:27)erent authors (e.g. Fender et al. 1997; Eikenberry et al. 1998),providing thus a solid proof of the so- alled dis /jet symbiosis in a retiondis s. All the observed events were shorter than 1/2 h, and their equivalent inquasars, or AGNs, would require a mu h longer minimum time span of some fewyears. Despite the omplexity in the GRS 1915+105 light urves, the episodesof X-ray emission de ay with asso iated hardening are reminis ent of the wellknown low/hard state typi al of persistent bla k hole andidates (Cygnus X-1,1E 1740.7 − −
258 and GX 339 − ∼ M ⊙ . Su h observations strongly support the idea of ontinuity between gala ti mi roquasars and AGNs in the Universe.4. The (cid:28)rst BH andidatesOne of the (cid:28)rst opti al ounterparts to be identi(cid:28)ed was the 9th magnitudesupergiant star HD 226868, asso iated with the HMXB Cyg X-1. It showedradial velo ity variations whi h made it a prime andidate for a stellar mass BH(Webster & Murdin 1972, Bolton 1972). The supergiant star was shown to movewith a velo ity amplitude of 64 km s − (later re(cid:28)ned to 75 km s − ) in a 5.6 dayorbit due to the gravitational in(cid:29)uen e of an unseen ompanion (see Fig. 4). Themass fun tion of the ompa t obje t was f ( M ) = 0.25 M ⊙ . The mass of thebright ompanion M is large and has a wide range of un ertainty. If the opti alstar were a normal O9.7Iab its mass would be 33 M ⊙ whi h, for an edge-onorbit ( i = 90 ◦ ) would imply a ompa t obje t of ∼ ⊙ . However, the opti alstar is likely to be undermassive for its spe tral type as a result of mass transferand binary evolution, as has been shown to be the ase in several NS binaries(e.g. Rappaport & Joss 1983).It ould be undermassive by as mu h as a fa tor of 3 given the un ertaintyin distan e, log g and T eff . A plausible lower limit of 10 M ⊙ , ombined withan upper limit to the in lination of 60 ◦ , based on the absen e of X-ray e lipses,leads to a ompa t obje t of > ⊙ (Bolton 1975).In 1975, the X-ray satellite Ariel V dete ted A0620-00. This sour e is a X-ray transient (XRT), a sub lass of LMXBs whi h undergo dramati episodes of4 J. M. ParedesFigure 5. Radial velo ity urve of the K0 ompanion in the tran-sient LMXB V404 Cyg during quies en e. This graph ontains velo itypoints obtained between 1991 and 2005 (Casares et al. 1992, 2007).enhan ed mass-transfer or "outbursts" triggered by vis ous-thermal instabilitiesin the dis . During outburst, the ompanion remains undete ted be ause it istotally overwhelmed by the intense opti al light from the X-ray heated dis . Aftera few months of a tivity the X-rays swit h o(cid:27), the repro essed (cid:29)ux drops severalmagnitudes into quies en e and the ompanion star be omes the dominant sour eof opti al light. This o(cid:27)ers the opportunity to perform radial velo ity studies ofthe ool ompanion and unveil the nature of the ompa t star.The (cid:28)rst dete tion of the ompanion in A0620-00 revealed a mid-K starmoving in a 7.8 hr period with velo ity amplitude of 457 km s − . The impliedmass fun tion was 3.2 ± ⊙ , the largest ever measured (M Clinto k &Remillard 1986). A lower limit to the mass of the ompa t star of 3.2 M ⊙ wasestablished by assuming a very onservative low-mass ompanion of 0.25 M ⊙ and i < ◦ , based on the la k of X-ray e lipses. This ex eeds the maximum massallowed for a stable NS and hen e it also be ame a very ompelling ase for aBH. In the 1980s there was a hot debate about the real existen e of BHs. Therewere three (cid:28)rm andidates, two HMXBs (Cyg X-1 and LMC X-3) and a transientLMXB (A0620-00), all with lower limits to M very lose to the maximum massfor NS stability. Alternative s enarios were proposed to avoid the need for BHssu h as multiple star systems (Bah all et al. 1974) or non-standard modelsinvoking exoti equations of state (EoS) for ondensed matter. It was proposedthat the "Holy Grail in the sear h for BHs is a system with a mass fun tion thatis plainly 5 M ⊙ or greater" (M Clinto k 1986).In 1989, Ginga dis overed a new XRT in outburst named GS2023+338 (=V404 Cyg). Its X-ray properties drew onsiderable attention be ause of thela k Holes in the Galaxy 15exhibition of a possible luminosity saturation at L X = erg s − and dramati variability (Zy ki et al. 1999). Spe tros opi analysis during quies en e revealeda K0 star moving with a velo ity amplitude of 211 km s − in a 6.5 day orbit(see Fig. 5). The obtained mass fun tion, f ( M ) = 6.08 ± ⊙ , implies the ompa t obje t must be more massive than 6 M ⊙ (Casares et al. 1992).4.1. BH binaries in the Milky WayThe mass fun tion of V404 Cyg was the highest yet measured and, very learly,pla ed an a reting ompa t obje t omfortably above the upper limit of maxi-mally rotating NSs for any "standard" EoS assumed. This work on V404 Cygnirevolutionized the (cid:28)eld of BH sear hes and this sour e is widely onsidered asthe best eviden e for a BH, where no additional assumptions on i nor M haveto be invoked.This remarkable result obtained by Casares and ollaborators establishedV404 Cyg as the "Holy Grail" BH for almost a de ade.Sin e then, many other BHs have been unveiled through dynami al studiesof XRTs in quies en e, some of them having mass fun tions also in ex ess of5 M ⊙ . This has been possible thanks to the improvement of the instrumentationand the new generation of 10-m lass teles opes. The list of the on(cid:28)rmed stellarBHs has in reased re ently with the addition of two stellar BHs. One of them,M33 X-7, is a 15.65 ± ⊙ BH in an e lipsing binary in the nearby spiralgalaxy M33 (Orosz et al. 2007). The other is IC 10 X-1, lo ated in the Lo alGroup starburst galaxy IC 10, and with a mass of 32.7 ± ⊙ , being indeedthe most massive known stellar mass BH (Silverman & Filippenko 2008). InTable 1 is presented a ompilation of the all on(cid:28)rmed stellar BHs made byCasares (2007), with the addition of these two new BHs.5. Observational signatures of the BHs5.1. Mass determinationA omplete determination of the omponent masses in a binary system requiresthe radial velo ity urves of both stars and a knowledge of the in lination angle.The determination of masses in LMXBs is usually redu ed to a single line spe -tros opi binary problem where all the information has to be extra ted from theopti al star. A omplete solution to the system parameters an be obtained fromthree observational experiments involving high resolution opti al spe tros opyand infrared photometry (the mass fun tion, rotational broadening and ellip-soidal modulation).The mass fun tion. This is a fundamental equation for the determination ofbinary system parameters whi h an be derived dire tly from Kepler's 2nd and3rd laws. It relates the masses of the two stars ( M , M ) and the in linationangle ( i ) through two observable quantities whi h are readily measured from theradial velo ity urve of the opti al star: the orbital period P orb and the radialvelo ity semi-amplitude K . f ( M ) = K P orb πG = M sin i ( M + M ) = M sin i (1 + q ) (12)6 J. M. ParedesTable 1. Con(cid:28)rmed bla k holes and mass determinations. Table fromCasares (2007) updated with M33 X-7 and IC 10 X-1.System P orb f ( M ) Donor Classi(cid:28) ation M x [days℄ [M ⊙ ℄ Spe t. Type [M ⊙ ℄GRS 1915+105 33.5 9.5 ± ± ± ± ± ± a ± ± > ± ± ± ± ± > ± ± ± ± ± b ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± a Orosz et al. (2007). b Silverman & Filippenko (2008).la k Holes in the Galaxy 17
BW CirGX 339-4J1859+226J1650-500 CYG X-1LMC X-1LMC X-3J1118+480J0422+320GRS1009-45A0620-00GS2000+25GS1124-684H1705-254U1543-47J1550-564J1655-40J1819-254V404 CYGGRS1915+105
Figure 6. Mass distribution of ompa t obje ts in X-ray binaries.Arrows indi ate lower limits to BH masses. Figure reprodu ed fromCasares (2007).where q = M /M is the mass ratio. f ( M ) represents an absolute lowerlimit to M , i.e. at the extreme ase when the mass of the ompanion star isnegle ted (i.e. q → ) and the binary is seen edge on ( i = 90 ◦ ) . However, f ( M ) ∝ K implies thar the mass fun tion is extremely sensitive to un ertaintiesin the radial velo ity amplitude. Any non-uniform brightness distribution a rossthe surfa e of the ompanion star will modify the radial velo ity urve and a(cid:27)e tour system parameter determination.A sour e of systemati error in the determination of K is produ ed by theX-ray irradiation, whi h tends to suppress the absorption lines near the L1 point.The onsequen e of the X-ray irradiation is the displa ement of the entre of lightaway from the ompanion's entre of mass and the radial velo ity urve will besigni(cid:28) antly e entri . A sine-wave (cid:28)t to it will give an observed K obs whi h willbe larger than the true K . Irradiation is onsidered to be negligible in quies entX-ray transients (where L x ≤ erg s − ) but it an be important in X-raya tive states. An example of the importan e of this e(cid:27)e t was given by GROJ1655 −
40 (=N S o 94). During the de ay of the 1994 outburst ( L x = 1 . × erg s − ) the radial velo ity urve was (cid:28)tted with a simple sine-wave, obtaining K = 228 . ± . km s − . This, ombined with P = 2 . d gave f ( M ) = 3 . ± ⊙ and hen e was a strong ase for a BH (Orosz & Bailyn 1997). Thesame data was subsequently (cid:28)tted by other authors using an irradiation model,obtaining K =
192 (cid:21) 214 km s − whi h redu es the mass fun tion to f ( M ) = ⊙ (Phillips et al. 1999). This latter result was (cid:28)nally on(cid:28)rmedby observations in true quies en e whi h give K = 215 . ± . km s − and f ( M ) = 2 . ± ⊙ (Shahbaz et al. 1999). The new mass fun tion is 16%8 J. M. Paredeslower than the (cid:28)rst reported value, enough to dis laim GRO J1655-40 as a se ureBH andidate.Rotational broadening. The ompanion stars transfer matter onto their om-pa t obje ts and hen e they must be (cid:28)lling their Ro he lobes. In addition, theshort orbital periods ( ∼ hr) and old ages (> 10 yr) of these lose binaries sug-gest that the ompanion stars must be syn hronised, i.e. ω s = ω orb where ω s and ω orb are the stellar and orbital angular velo ities respe tively. The proje tedlinear velo ities would then be V rot sin iR = K + K a = K (1 + q ) a (13)where q = M /M = K /K , R is the equivalent radius of the ompanion'sRo he lobe and a is the binary separation. Combining with R a ≃ . (cid:16) q q (cid:17) / one obtains V rot sin i = 0 . K q / (1 + q ) / . Therefore, the mass ratio q anbe measured dire tly from the radial velo ity urve and the observed rotationalbroadening ( V rot sin i ) of the se ondary's absorption lines (Gies & Bolton 1986).The rotational velo ity is determined by omparing our target with broadenedversions of spe tral type templates (e.g. through a χ minimization te hnique)(Marsh et al. 1994). An example of rotational broadening analysis, applied toV404 Cygni, an be found in Casares & Charles (1994).Ellipsoidal modulation. The light urves of ompanion stars in onta t binariesdisplay the hara teristi double-humped variation on the orbital period, withamplitudes ≤ . This modulation is a onsequen e of the tidal distortion ofthe se ondary star and the non-uniform distribution of the surfa e brightness,due to a ombination of limb and gravity darkening. The dependen e of T eff onthe lo al surfa e gravity g implies that the inner hemisphere of the se ondary(fa ing the ompa t obje t) will be ooler and, therefore, the phase 0.5 minimumbe omes deeper than the minimum at phase 0. Model al ulations show that theshape and amplitude of the ellipsoidal modulation are fun tions of q and i . Inparti ular, the amplitude is a strong (in reasing) fun tion of i , and is insensitiveto q if q ≤ . . This is normally the ase in SXTs and therefore model (cid:28)ts to theellipsoidal modulation an be used to determine i dire tly.Fluores en e emission from the irradiated donor There are 20 XRBs that la kradial velo ity data. Most of them even la k an opti al ounterpart, and onlythree have known orbital periods. Nevertheless, they are onsidered bla k-hole andidates be ause they losely resemble bla k hole binaries in their X-ray spe -tral and temporal behavior (Remillard & M Clinto k 2006). Unfortunately, theyhave never been seen in quies en e, or they simply be ome too faint for an opti aldete tion of the ompanion star. Fortunately, a new te hnique to extra t dynam-i al information during their X-ray a tive states has been applied re ently. Itutilises narrow high-ex itation emission lines powered by irradiation on the om-panion star, in parti ular the strong CIII and (cid:29)uores en e NIII lines from theBowen blend at λλ − whi h de(cid:28)nes a stri t lowerlimit to the velo ity amplitude of the ompanion star be ause these lines arisefrom the irradiated hemisphere and not the entre of mass of the donor. A solidlower bound to the mass fun tion is 5.8 M ⊙ whi h provides ompelling eviden efor a BH in GX 339 − ˙ M , a ording to binary masstransfer models (Menou et al. 1999). By omparing quies ent BHs and NSs withsimilar orbital periods, the un ertainty in the mass a retion rate is eliminated(Gar ia et al. 2001). The explanation for this result is that a retion in thesequies ent systems o urs via a radiatively ine(cid:30) ient mode (adve tion-dominateda retion), as on(cid:28)rmed through spe tral studies (e.g, Narayan et al. 2002).Therefore, the dis luminosity L disc ≪ ˙ M c and most of the binding energy thatis released as gas falls into the potential well is retained in the gas as thermalenergy. In the ase of an a reting NS, this energy is eventually radiated from thestellar surfa e, and so an external observer still sees the full a retion luminosity ∼ . M c . In the ase of a BH, however, the superheated gas falls through theevent horizon, arrying all its thermal energy with it. The observer thereforesees only the dis luminosity L disc , whi h is extremely small.BHs la k a soft thermal omponent (quies en e) BHs la k a soft thermal om-ponent of emission that is very prevalent in the spe tra of NSs and an be as ribedto surfa e emission (M Clinto k et al. 2004).Type I thermonu lear bursts and la k of pulses This has been quanti(cid:28)ed usingobservations of dynami al BHs over 9 years of RXTE data. The probability thatthe non-dete tion of bursts were onsistent with a solid surfa e is found to be ∼ × − (Remillard et al. 2006)0 J. M. ParedesFigure 7. BH (red ir les) and NS (blue stars) X-ray transients inquies en e. Figure reprodu ed from M Clinto k et al. (2007)la k Holes in the Galaxy 21High-frequen y timing noise The study of the Fourier power spe tra at highfrequen ies o(cid:27)ers a way to distinguish a NS from a BH (Sunyaev & Revnivtsev2000). After the analysis of the power density spe tra (PDS) of a sample of9 NS and 9 BH binaries in the low/hard spe tral state, it is on luded thatin the a reting NS with a weak magneti (cid:28)eld, signi(cid:28) ant power is ontainedat frequen ies lose to one kHz. In the ase of the a reting BH, the PDSshow strong de line at frequen ies higher than 10 (cid:21) 50 Hz. These empiri alphenomenology ould be used to help to distinguish the a reting NS from BHin X-ray transients. The XRT with noise in their X-ray (cid:29)ux at frequen ies higherthan 500 Hz should be onsidered NS. Sunyaev & Revnivtsev propose to explainthe observed di(cid:27)eren e as a result of the existen e of a radiation dominatedspreading layer on the NS surfa e.A distin tive spe tral omponent from a boundary layer The lassi olour- olour diagram of XRBs at high a retion rates shows a lear separation in theevolution of NS and BH binaries. This has been as ribed to the presen e of aboundary layer in NS whi h gives rise to an additional thermal omponent inthe spe trum and drags NS outside the BH region (Done & Gierlinski 2003).All approa hes to this subje t an provide only indire t eviden e for theevent horizon be ause it is quite impossible to dete t dire tly any radiation fromthis immaterial surfa e of in(cid:28)nite redshift. Nevertheless, barring appeals to veryexoti physi s, the body of eviden e just onsidered makes a strong ase thatdynami al BH andidates possess an event horizon.5.3. Measuring Bla k Hole SpinAn astrophysi al BH is des ribed by two parameters, its mass M and its di-mensionless spin parameter a ∗ . Be ause the masses of 21 BHs have already beenmeasured or onstrained, the next obvious goal is to measure spin. Several meth-ods have been used to measure the BH spin. The (cid:28)rst method, based on X-raypolarimetry, appears very promising but thus far has not been in orporated intoany ontemporary X-ray mission. The se ond method, based on X-ray ontin-uum (cid:28)tting, is already produ ing useful results. The third method, based on theFe K line pro(cid:28)le, has also yielded results, although the method is hampered bysigni(cid:28) ant un ertainties. The fourth method, based on high-frequen y QPOs,o(cid:27)er the most reliable measurement of spin on e a model is established. Herefollows some details of these methods.X-ray polarimetry. The polarization features of BH dis radiation an be af-fe ted strongly by GR e(cid:27)e ts. Conventional dis models predi t that higher en-ergy photons ome from smaller dis radii. Then as the photon energy in reasesfrom 1 keV to 30 keV, the plane of linear polarization swings smoothly throughan angle of about 40 ◦ for a 9M ⊙ S hwarzs hild BH and 70 ◦ for an extreme KerrBH (Connors et al. 1980). The e(cid:27)e t is due to the strong gravitational bendingof light rays. In the Newtonian approximation, the polarization angle does notvary with energy. A gradual hange of the plane of polarization with energy isa purely relativisti e(cid:27)e t, and the magnitude of the hange an give a dire tmeasure of a ∗ . Polarimetry data do not even require M , although knowledge of i is useful in order to avoid having to in lude that parameter in the (cid:28)t.2 J. M. ParedesX-ray ontinuum (cid:28)tting. This te hnique, determines the radius R in of the inneredge of the a retion dis and assumes that this radius orresponds to R ISCO (innermost stable ir ular orbit). Be ause R ISCO /R g is a monotoni fun tion of a ∗ , a measurement of R in and M dire tly gives a ∗ . R in an be estimated providedthat: (a) i and D are su(cid:30) iently well known, (b) the X-ray (cid:29)ux and spe traltemperature are measured from well- alibrated X-ray data in the thermal stateand, ( ) the dis radiates as a bla kbody. The ontinuum (cid:28)tting is the best urrent method for measuring spin, although its appli ation requires a urateestimates of BH mass ( M ), dis in lination ( i ), and distan e.The Fe K line pro(cid:28)le. The (cid:28)rst broad Fe K α line observed for either a BHB oran AGN was reported in the spe trum of Cyg X − r ISCO = 1 r g , as ompared to S hwarzs hild BHs, r ISCO = 6 r g . As a onse-quen e the line emission omes from regions that are deeper in the gravitationalpotential if the BH rotates. Therefore, the line pro(cid:28)les from the vi inity of KerrBHs are more in(cid:29)uen ed by gravitational redshift (see Figure 9). The line hasbeen modeled in the spe tra of several BHBs. In Figure 10, relativisti X-raylines from the inner a retion dis s around four BHs are shown (Miller 2007).GRS 1915+105 is learly not as skewed as the others, and does not stronglyrequire BH spin. In this sour e there has been some ontroversy about the valueof the spin, being onsidered a rapidly rotating Kerr BH in one ase, a ∗ > . (M Clinto k et al. 2006) and an intermediate spin, a ∗ ∼ . in the other ase(Middleton et al. 2006).la k Holes in the Galaxy 23Figure 8. Example of a relativisti emission line pro(cid:28)le that is emittedfrom a thin a retion dis around a Kerr BH with a/M = 0 . . Theline pro(cid:28)le is subje t to the Doppler e(cid:27)e t due to rotation of the dis ( auses two horns); spe ial relativisti beaming (intensi(cid:28)es the blue linewing), and gravitational redshift (smears out the whole line pro(cid:28)le andprodu es an extended red line wing). Figure reprodu ed from Mueller(2007)In V4641 Sgr, the inner dis radius dedu ed from the line pro(cid:28)le is onsistentwith the R g radius of the ISCO of a S hwarzs hild BH, suggesting that rapidspin is not required (Miller et al. 2002).In GX 339 −
4, the inner dis likely extends inward to (2 (cid:21) 3) R g , implying a ∗ ≥ . − . (Miller et al. 2004). XTE J1650 −
500 is the most extreme asewith the inner edge lo ated at ≈ R g , whi h suggests nearly maximal spin (Milleret al. 2002; Miniutti et al. 2004). Large values of a ∗ have also been reported forXTE J1655 −
40 and XTE J1550 −
564 (Miller 2007). Broadened Fe K lines datado not even require M to obtain the spin parameters, although knowledge of i is useful in order to avoid having to in lude that parameter in the (cid:28)t.High-frequen y QPOs High-frequen y quasi periodi os illations (HFQPO) arelikely to o(cid:27)er the most reliable measurement of spin on e the orre t model isknown. Typi al frequen ies of these fast QPOs, e.g., 150 (cid:21) 450 Hz, orrespondrespe tively to the frequen y at the ISCO for S hwarzs hild BHs with masses of15 (cid:21) 5 M ⊙ , whi h in turn losely mat hes the range of observed masses. TheseQPO frequen ies (single or pairs) do not vary signi(cid:28) antly despite sizable hangesin the X-ray luminosity. This suggests that the frequen ies are primarily depen-dent on the mass and spin of the BH. Those BHs that show HFQPOs and havewell- onstrained masses are the best prospe ts for onstraining the value of theBH spin ( a ∗ ). Theoreti al work aimed at explaining HFQPOs is motivated bythree sour es: GRO J1655 −
40, XTE J1550 −
564 and GRS 1915+105. These4 J. M. ParedesFigure 9. Comparison of observed relativisti emission line pro(cid:28)lesaround a Kerr ( a/M = 0 . , blue) and a S hwarzs hild BH ( a/M = 0 ,green). Figure reprodu ed from Mueller (2007) GRS 1915+105XTE J1550−564 GRO J1655−40Cygnus X−1
Figure 10. Relativisti X-ray lines from the inner a retion dis saround four BHs. Figure reprodu ed from Miller (2007)la k Holes in the Galaxy 25sour es are presently the only ones that both exhibit harmoni (3:2) HFQPOsand have measured BH masses. If these HFQPOs are indeed GR os illations,then it would be possible that the three BHs have similar values of the spinparameter a ∗ . It is relevant to try to on(cid:28)rm this result by taking frequen y andmass measurements for more sour es. Assuming we have a well-tested model,QPO observations only require knowledge of M to provide a spin estimate.6. A super-massive Bla k Hole in the Milky Way6.1. Galaxies and BHsBH with masses of to few M ⊙ are believed to be the engines that powernu lear a tivity in galaxies. AGN range from faint, ompa t radio sour es likethat in M31 to quasars like 3C 273 that are brighter than the whole galaxy inwhi h they live. Some nu lei (cid:28)re jets of energeti parti les millions of lightyearsinto spa e. It is believed that this enormous (cid:29)ow of energy omes from the starsand gas that are falling into the entral BH.In the past years, the sear h for super-massive BHs has been done by mea-suring rotation and random velo ities of stars and gas near gala ti entres. Ifthe velo ities are large enough, then they imply more mass than we see in stars,being a BH the most probable explanation. More than 50 have been found, withmasses in the range expe ted for nu lear engines, and onsistent with predi tionsbased on the energy output of quasars.The powerful gravitational for e exerted by a super-massive BH in a gala ti nu leus on nearby gas and stars, auses them to move at high speeds. This isdi(cid:30) ult to see in quasars, be ause they are far away and be ause the dazzlinglight of the a tive nu leus swamps the light from the host galaxy. However, inradio galaxies with fainter nu leus, the stars and gas are more visible. The giantellipti al galaxy Messier 87, one of the two brightest obje ts in the Virgo lusterof galaxies, is a radio galaxy with a bright jet emerging from its nu leus. It haslong been thought to ontain a BH. Observations of Messier 87 with the HSTrevealed a dis of gas 500 lightyears in diameter, whose orbital speeds imply a entral mass of × M ⊙ . The ratio of this mass to the entral light outputis more than 100 times the solar value. No normal population of stars has su ha high mass-to-light ratio. This is onsistent with the presen e of a BH, but itdoes not rule out some other on entration of underluminous matter.Fortunatelly, the masers o(cid:27)er the possibility to have more onvin ing argu-ments. The Seyfert galaxy NGC 4258 is one of the few nearby AGN known topossess nu lear water masers (the mi rowave equivalent of lasers). The enormoussurfa e brightnesses ( ≥ K), small sizes ( ≤ m), and narrow linewidths(a few km s − ) of these masers make them ideal probes of the stru ture anddynami s of the mole ular gas in whi h they reside.VLBI observations (angular resolution 100 times better than that of HST) ofthe NGC 4258 maser have provided the (cid:28)rst dire t images of an AGN a retiondis , revealing a thin, subparse -s ale, di(cid:27)erentially rotating warped dis in thenu leus of this relatively weak Seyfert 2 AGN. The measurements imply that × M ⊙ lie within half a lightyear of the entre (Herrnstein et al. 1999). Thismaterial an hardly be a luster of dead stars. In the ase there were failedstars (brown dwarfs) that never get hot enough to ignite the nu lear rea tions6 J. M. Paredesthat power stars be ause their low mass ( < . M ⊙ ), there would have to bemany of them to explain the dark mass in NGC 4258. This would imply theywould have to live very lose together and most of them would ollide withother brown dwarfs and the dark luster would light up. In the ase therewere dead stars (WDs stars, NSs, or stellar mass BHs), these are more massivethan brown dwarfs, so there would be fewer of them. It is well known thatduring the gravitational evolution of lusters of stars, individual stars get eje tedfrom the luster, the remaining luster ontra ts, and the evolution speeds up.Cal ulations show that a luster of dead stars in NGC 4258 would evaporate ompletely in about 100 million years. This time is mu h less than the age ofthe galaxy. Therefore the most astrophysi ally plausible alternatives to a BH an be ex luded. It seems unavoidable the on lusion that NGC 4258 ontainsa super-massive BH.6.2. The BH in the Gala ti entreThe entre of our Galaxy is only 25000 lightyears away. Although its visible lightis ompletely absorbed by intervening dust, its IR light penetrates the dust. Thesuper-massive BH in the entre of the Milky Way was dis overed as a brightnon-thermal radio sour e in the 1970s and termed Sagittarius A ∗ (Sgr A ∗ ). Theradio emission of SgrA ∗ only varies slowly on time s ales of several days to afew hundred days and generally with an amplitude < . Potential X-rayradiation by Sgr A ∗ was dete ted with the X-ray observatory ROSAT in the1990s. A reliable identi(cid:28) ation of X-rays from Sgr A ∗ was (cid:28)nally possible withthe new X-ray satellites Chandra and XMM. A general review of Sgr A ∗ an befound in Melia & Fal ke (2001).Motions of individual stars Two groups, Genzel (Muni h) and Ghez (UCLA),have measured the motions of individual stars near the GC as proje ted on theplane of the sky. They used the spe kle image te hnique.The rapid motions show that there is a mass of × M ⊙ entered on SgrA ∗ . The mass en losed inside a parti ular distan e from Sgr A ∗ stops droppingtoward the entre at a distan e of about 1 p (see Figure 11). This means thatthe mass in stars inside 3 lightyears has be ome negligible ompared to the darkmass at the entre (S hödel et al. 2003). As in NGC 4258, the implied density ofmatter is too high to allow a luster of dark stars or stellar remnants. NGC 4258and the Milky Way give us important proof that BH exist.The velo ity dispersion in reases to 400 km s − at a distan e of 0.03 lightyearsfrom Sgr A ∗ . Here stars have su h small orbits that they revolve around theGala ti entre in a few de ades. Motions in the plane of the sky have been mea-sured for these stars for several years (Eisenhauer et al. 2005; Ghez et al. 2005).From a global (cid:28)t to the positions and radial velo ities of the six best stars (seeFigure 12) within 0.5"(=0.02 p ) of Sgr A ∗ improved three dimensional stellarorbits were derived and their orbital parameters updated. The updated estimatefor the distan e to the Gala ti entre from the S2 orbit (cid:28)t is . ± . kp ,resulting in a entral mass value of (3 . ± . × M ⊙ (Eisenhauer et al.2005).Size of Sgr A ∗ VLBI observations of Sgr A ∗ have revealed an east(cid:21)west elon-gated stru ture whose apparent angular size at longer wavelengths is dominatedla k Holes in the Galaxy 27Figure 11. Central mass distribution in our Galaxy implied by theobserved velo ities measured on the parse and subparse s ale. Thesolid urve represents the stars plus a point mass of . × M ⊙ . Thedashed urve gives the ontribution from the star luster on the parse -s ale. Figure reprodu ed from S hödel et al. (2003).8 J. M. ParedesFigure 12. Proje tion on the sky of the six S stars in luded in the(cid:28)tting. Figure reprodu ed from Eisenhauer et al. (2005).la k Holes in the Galaxy 29by the interstellar s attering angle, θ obs = θ cm obs λ , where θ obs is the observed size,in mas, at wavelength λ in m. Thus, VLBI observations at shorter millimetrewavelengths, where the intrinsi stru ture of Sgr A ∗ ould be ome omparableto the pure s attering size, are expe ted to show deviations of the observed sizefrom the s attering law. This has been demonstrated by the dete tion of theintrinsi size at 7 mm (Bower et al. 2004). More re ently, Zhi-Qiang Shen etal. (2005), arried out observations with the VLBA at 3.5 mm of Sgr A ∗ . Theyreport a radio image of Sgr A ∗ , demonstrating that its size is 1 AU. This high-resolution image of Sgr A ∗ , made at 3.5 mm, also exhibits an elongated stru ture.When ombined with the lower limit on its mass, the lower limit on the massdensity is . × M ⊙ p − , whi h provides strong eviden e that Sgr A ∗ is asuper-massive BH.Near-infrared (cid:29)ares from Sgr A ∗ Dete tion of variable infrared (3.8 mi ron)light oin ident to within 18 mas (1 σ ) of the super-massive BH at the entreof the Milky Way galaxy and the radio sour e Sgr A ∗ was reported by Ghez etal. (2004). The brightness variations, whi h o ur on times ales as short as 40minutes, reveal that the emission arises quite lose to the BH, within 5 AU, or80 r Sch . Two K-band (cid:29)ares observed on the 15th and 16th of June 2003 showa quasi-periodi ity of about 17 min (Genzel et al. 2003). The only reasonableexplanation for this so short period is that the os illations are produ ed byDoppler boosting of hot gas near the last stable orbit of a spinning Kerr BH.The spin of the BH will allow for a last stable orbit loser to the event horizonand thus with a shorter orbital frequen y. From the observed 17 min quasi-periodi ity it is estimated that the super-massive BH Sgr A ∗ has a spin thatis half of the maximum possible spin of su h an obje t (Genzel et al. 2003).Additional observations of (cid:29)ares and their quasi-periodi ity will be needed inorder to on(cid:28)rm this result.X-ray (cid:29)ares from Sgr A ∗ In the X-ray regime, SgrA ∗ was found to exhibit twodi(cid:27)erent states. In the quies ent state, weak X-ray emission appears to omefrom a slightly extended area around the BH that appears to be eviden e ofhot a reting gas in the environment of SgrA ∗ . SgrA ∗ shows X-ray (cid:29)ares witha re urren e of about one per day. During these (cid:29)ares, the emission rises byfa tors up to 100 during several tens of minutes and a distin tive point sour ebe omes visible at the lo ation of SgrA ∗ . The short rise-and-de ay times of the(cid:29)ares suggest that the radiation must originate from a region within less than10 r Sch of a . × M ⊙ BH (Bogano(cid:27) et al. 2001).Lensing of orbital shapes The frame(cid:21)dragging that auses matter and light to o(cid:21)rotate with the spa e(cid:21)time has e(cid:27)e ts in the orbits around BHs. Mueller(2007) shows relativisti ally distorted images of tight orbits around BHs for dif-ferent in lination angles and for S hwarz hild and Kerr BHs. When viewed by adistant observer at in(cid:28)nity, in nearly edge(cid:21)on situations the observer would de-te t di(cid:27)erent apparent orbit shapes depending on BH spin. These orbit shapesbe ome asymmetri in the ase of rotating BHs. The maximum relative spatialo(cid:27)set predi ted is 0.08 r g = 0 . r Sch . This means that it might be possible todete t it by observing the Gala ti entre BH but not by observing an stellar BH.The reason is that the angular size orresponding to an S hwarzs hild radius of0 J. M. Paredesa super-massive BH is about three orders of magnitude larger than the an stellarmass BH. The angular size orresponding to an S hwarzs hild radius is given by: θ Sch = 2 arctan ( r Sch /d ) ≃ r Sch /d ≃ . × (cid:16) M M ⊙ (cid:17) × (cid:16) d (cid:17) µ as (14)For a mass M = 3 . × M ⊙ at a distan e d = 7 . kp one obtains θ BH =18 . µ as . Then, the angular size of the relative spatial o(cid:27)set predi ted is . µ as .In ontrast, for a lose stellar BH like Cygnus X − M =10 M ⊙ and d =2.2 kp ,the angular size is θ Sch ≃ − µ asas