PoS(Multif2019)028 https://pos.sissa.it/ ∗ [email protected] Speaker. In this review, I have tried tothe focus current on lines the of development research. of According therelatively to field, simple Einstein’s from objects theory the of and first general completely speculations relativity,and to characterized black electric holes charge, by are but their the mass, latter canSearch spin be for angular ignored black in holes momentum, the in the case sky of startedmass astrophysical in of macroscopic the objects. the early compact 1970s with object the in dynamicalsome Cygnus measurement techniques X-1. of for the measuring In the the black hole past spins. 10-15black Recently, years, holes we for astronomers have started testing have using developed fundamental astrophysical physics. ∗ Copyright owned by the author(s) under the terms of the Creative Commons c Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). Multifrequency Behaviour of High Energy Cosmic3-8 Sources June - 2019 XIII - MULTIF2019 Palermo, Italy Cosimo Bambi Astrophysical Black Holes: A Review Center for Field Theory and Particle200438 Physics Shanghai, and China Department of Physics, FudanE-mail: University, PoS(Multif2019)028 ]. ]: 7 [ 10 (1.1) , 9 , 8 Cosimo Bambi ]. The simplest 1 . There are certain , but actually it is a Q ]. Note, however, that the Kerr-Newman solution 4 , 3 [ ]. This was a very important dis- 6 [ if the radius of the body is smaller c no-hair theorem . M and in the framework of Newtonian mechanics, 2 N because they had to appear dark being unable to Kerr solution c 1 , and their electric charge M G J 2 = R dark stars Reissner-Nordström solution ]. It describes the spacetime of a spherically symmetric and 2 [ , their spin angular momentum M Schwarzschild solution ]. 5 At the end of 1915, Albert Einstein proposed the theory of general relativity [ The solution describing the spacetime of a rotating and electrically uncharged black hole was Since the late 1960s, people realized that the black holes of general relativity are simple ob- Roughly speaking, a black hole is a region of the spacetime in which gravity is so strong emit radiation from their surface. Apparentlylevel of the a proposal theoretical of speculation Michell and and nobody Laplace tried remained to at look the for similar objects in the sky. Such hypothetical objects were called actual nature of these solutionsing was for not the understood spherically for symmetric agravitational vacuum while. field solution of of Schwarzschild a Einstein’s was equations spherically simplymately describing look- that symmetric the of and a exterior electrically star or unchargedand a body, planet. Nordström like Reissner solved it solved the Einstein’s is equations equationswere approxi- for for singular a a point-like on charged spherically a mass symmetric surface,nature and charged which the mass. is implications now of These known suchFinkelstein solutions to a realized surface be the were the actual not location nature understood.way of of In membrane, these was the so only solutions that event in whatever and horizon, crosses 1958 described thelonger but that the event [ David the horizon event cannot horizon influence as the a exterior region one- any found in 1963 by Roy Kerr and is now called the jects, in the sense that they are completely specified by a small number of parameters [ black hole solution was discovered immediatelycalled after, the in 1916, by Karlelectrically Schwarzschild uncharged black and hole. is The now solutiona describing possible a spherically non-vanishing symmetric electric black charge holeström was with in found 1918 by and Hans is Reissner now in called 1916 the and Gunnar Nord- covery for astrophysical applications, because astronomicalspin bodies angular have momentum. naturally a The non-vanishing completefound solution in describing 1965 a by Ezra rotating Newman and and charged collaborators black and hole is now was called the their mass that nothing can escape orof communicate similar systems with can the be exteriorindependently, dated Pierre-Simon region. Laplace back in to 1796 Speculations discussed the on the possibility endcompact the of of objects, the existence existence the so of XVIII extremely compact century. thatlight. John the For Michell a escape spherically in velocity symmetric 1783 body on and, of their mass surface could exceed the speed of Astrophysical Black Holes 1. Introduction 1.1 Historical overview one finds that the escapethat velocity exceeds the speed of light assumptions behind and the result goes under the name of family of theorems because there are different versions and different extensions. The name no-hair PoS(Multif2019)028 ]. In 15 Cosimo Bambi , above which ]. More recently, 23 , 22 ] and supermassive black , so these are their hairs, but 18 Q ]. However, their idea was not 14 , , and Chandrasekhar mass ]. Once again, it was advocated the J 13 , 12 M 2 ]. From the study of the orbital motion of the companion ]. 17 19 , 16 ] and X-ray reflection spectroscopy (or iron line method) [ 21 , ]. Such a scenario was criticized by many physicists, arguing the existence of a yet un- 20 11 Cygnus X-1 is one of the brightest X-ray sources in the sky and was discovered in 1964 [ For astrophysical black holes, the electric charge should be completely negligible and there- Quasars were discovered in the 1950s and their nature was unknown for a while. In 1964, The Schwarzschild solution describes the exterior gravitational field of a spherically sym- there have been efforts to use astrophysical black holes to test fundamental physics, in particular taken very seriously at the beginning.supermassive stars, Other were proposals, initially like considered the more possibility promising. that these sources were fore these objects shouldmentum. be completely The characterized mass only isor relatively by gas, easy their as to mass it measure, was andholes. by done spin studying with angular In Cygnus the mo- X-1 the orbital andwith motion past later different of 10-15 methods. with nearby years, other stars The stellar-mass there twomethod and have leading [ supermassive techniques been black are significant currently efforts the to so-called measure continuum-fitting black hole spins 1971, Thomas Bolton and, independently, Louise Websterhad and a Paul Murdin massive found stellar that companion Cygnus [ star, X-1 it was possible to estimatevalue the for mass the of mass the of a compactas neutron object. star, the The and latter therefore first exceeded the stellar-mass compact the black objectphysics maximum in and hole Cygnus helped candidate. X-1 to was convince identified the SuchUniverse. astronomy a community Since then, about finding we the is have existence obtained of a anexistence black increasing milestone of holes number in in stellar-mass of the astronomical black black data holes hole pointingholes out in astro- at the the some center X-ray of binary many systems galaxies [ [ known mechanism capable of stopping theexceeding collapse. the It Chandrasekhar was limit then had found tosure that transform a of into dead neutrons a star could neutron with stop star a thethat and mass collapse. even that In neutron the 1939, quantum stars Robert pres- have Oppenheimerstop a and the maximum George collapse Volkoff mass if found the and mass that of the the quantum body pressure exceeds this of limit neutrons [ cannot Yakov Zel’dovich and, independently, Edwin Salpeteraccretion proposed material that orbiting quasars around were supermassive powered black by holes the [ Astrophysical Black Holes comes from the fact thatblack/brown/blond, people etc.). are Black mainly holes characterized are by characterized their by hairs (short/long, straight/curly, existence of a yet unknown mechanism capable of stopping the collapse. metric body like, withSchwarzschild a solution was good initially approximation,coordinate thought a is to much star have smaller no or thanexterior physical a the solution implications physical planet. should because radius be its oftional pasted The radial any field with singular typical inside the the astronomical surface object. interior body, in Inshrinks where non-vacuum the to the the solution 1920s, find it describing a was new the known equilibriumelectrons gravita- that configuration, stops when and the a that collapse star at and finishes a its the certaindrasekhar nuclear point object showed fuel the becomes that it quantum a there pressure white is of dwarf. a In critical 1931, mass, Subrahmanyan now Chan- called the since these are just three parameters it follows that black holes have almost no hairs. the quantum pressure of electronsa cannot point stop [ the process and the whole body had to collapse to PoS(Multif2019)028 (1.3) (1.2) (1.4) (1.5) 5 s. If the ]. ∼ ]. The impact Cosimo Bambi τ 28 ] and the Event 29 27 1 hr. Variability in ∼ km and τ ]. Thanks to significant 6 26 10 , ∼ 25 km and g , r 9 . 24 10 . km s ∼ , µ  g r 

 , we find 2 ∗

M a

M M . M − M 10 1 6 M 10  N cJ , we find q 10  3 77 G

. + ∼ 23 M . 1 = 14 9 M  ∗ 49 = a g 10 r = M ∼ 2 = g c N c r H M G r , sets the size of the system. The gravitational radius is defined , only affects the strong gravity region. Indeed in Newtonian = J = M τ g r ]. Any initial non-vanishing electric charge can be almost neutralized 31 , 30 ]. is the dimensionless spin parameter defined as 32 ∗ a The spin of the black hole, The mass of the black hole, It is curious that the term “black hole” is relatively recent and its origin is unknown. We do Astrophysical black holes should be well described by the “ideal” Kerr solution of general For a supermassive black hole withsupermassive black a hole mass has a mass The characteristic timescale is thus the electromagnetic and gravitational wave spectraof associated to the modifications system in in the the configuration strong gravity region follows these timescales. gravity the spin of a bodyof has Universal no Gravitation. gravitational effects, and Thisanalogies only with is its a not mass rotating appears true charge in in inthe Newton’s electrodynamics. Law event general For horizon. example, relativity, In the where spin Boyer-Lindquist ahole changes coordinates, is the rotating the position radius mass of of has the some event horizon of a Kerr black where as technological progress and new observational facilities,time the the LIGO experiment gravitational detected waves for from theHorizon the first Telescope coalescence collaboration released of the two first black “image” holes of in a black 2015 hole [ in 2019 [ of the gravitational field of thenear accretion the disk black or hole of [ nearbyvery stars quickly is because normally of completely the negligible equilibrium highly electric ionized charge host environment is aroundobjects extremely black [ small, holes and and thus the residual completely negligible, for macroscopic not know who used the termin a first. publication. In It 1964, was the onafter journalist a it report Ann was on Ewing used Science was by News the John Letter. first Wheeler The to term at use became a quickly this lecture1.2 very in term popular New Physical York properties in 1967. relativity. When aquickly collapsing reduces object to the enters Kerr inside solution through its the own emission of event gravitational horizon, waves [ the spacetime metric Astrophysical Black Holes Einstein’s theory of general relativity in the strong field regime [ PoS(Multif2019)028 . For the ∗ shows the a 1. A non- . The orbits 1 Cosimo Bambi | ≤ ∗ ISCO ]. In this model, r a | 33 . Fig. . Heuristically, we 1 ) 3 ISCO r 1 < (or ISCO), r 0.8 0 and a maximally rotating black hole = ∗ 0.6 a * a 4 0.4 1, there is no event horizon and the Kerr metric describes 0.2 innermost stable circular orbit > | ∗ a | 0 ), the spin parameter is subject to the constraint 0 8 6 4 2

10

g 1. For 1.4 r/r ± and unstable (or they do not exist at all) for = ∗ a ISCO r > r 1 and ignore the possibility of naked singularities. Radius of the ISCO (red solid line) and of the event horizon (blue dashed-dotted line) of a Kerr | ≤ ∗ a | Once the particles reach the ISCO, they quickly plunge onto the black hole. In the interpretation of astronomical observations of accreting black holes, a relevant quantity The Novikov-Thorne model is the standard framework for the description of thin accretion 1 can say that near a blackThis hole implies the gravitational that force the is innersuch so edge strong a that of property stable a can orbits thin are be accretion not exploited possible. disk to is measure at black the hole ISCO spins or (see at Section a larger radius, and is the accretion luminosity ofEddington the luminosity source, is which the is maximum convenient luminosity tobody of measure a and generic in is spherically Eddington found symmetric units. astronomical when The the pressure of the radiation luminosity balances the gravitational force ISCO radius, the upper curve refers to counterrotating orbits and the lower curve to corotating orbits. As we can see from Eq. ( has spin parameter radial coordinate of the ISCO radiusthe and ISCO of radius, the we event have horizon twoangular in curves Boyer-Lindquist momentum because coordinates. the parallel lower For one to(orbits refers the with to black corotating angular orbits momentum hole (orbits antiparallel spin) with toeffect to the and reduce black the hole the upper spin). strengthget of one Heuristically, the the closer to gravitational spin to counterrotating field has the and, the orbits blackISCO in radius hole, this increases way, while as corotating for the stable spin counterrotating orbits parameter orbits can increases. we have the opposite effect and the the spacetime of a nakedcase singularity. In astrophysical contexts, it is common to consider only the disks around black holes and is largely employed to interpret astronomical data [ rotating (Schwarzschild) black hole has spin parameter the disk is assumed to begas on follows the nearly-geodesic circular equatorial orbits plane in perpendicular thealways to equatorial stable the plane. but black Interestingly, there these hole is orbits spin. are the Theare not so-called particle stable for Figure 1: black hole in Boyer-Lindquist coordinates as a function of the dimensionless spin parameter Astrophysical Black Holes PoS(Multif2019)028 , 38 , (1.6) 37 [

M , there is no Cosimo Bambi

M 3 ). There is probably −

M , s 10 / 10 erg −  5

10 M M ∼ 10 M is the proton mass.  p 39 m 10 · is 5 26 . M 1 ]. = 36 c p Mm Th N σ G π 4 = ) and supermassive black holes ( Edd

L M ]. It is currently unclear whether there is a mass gap between the populations 35 (the exact limit depends on the unknown matter equation of state at high densities 100 ,

− 34 M 3 3 is the electron Thomson cross section and ≈ − Th M σ ]. Such an upper bound crucially depends on the metallicity of the progenitor star, namely The maximum mass for a stellar-mass black hole is expected to be around 100 The search for black hole candidates in the Universe started in the 1970s. Today we have a A comment is in order here. There is no “conclusive” proof that the objects that we call Stellar-mass black holes are the natural product of the complete gravitational collapse of heavy 40 , of stellar-mass black holes andmost neutron theoretical stars, models because do observations not may predict suggest it such [ a gap while 39 the fraction of mass of theremnant star formed made from of the elements collapse heavierduring than of the collapse, helium. a which The star increases with mass depends the ofsection indeed metallicity the and because on heavier black thus elements the hole evaporate have mass faster. larger cross loss In the rate case by of stellar low wind metallicity stars, some models predict a mass body of observational evidence for the existence ofholes at least ( two classes of objects: stellar-mass black where 2. Search for Black Holes black holes are reallyexperimental black science. holes. We can However, onlybut generally disprove only a speaking, get model/theory. this some Wethat is bounds. cannot these confirm because objects a For physics are model/theory, the black is holesfind moment, an and that all these therefore objects we observational have call data some themname, properties are black but not holes. consistent belonging for to with If the black at moment the holes,waves some we and we idea point are black may we change hole in will idea imaging the and are opposite confirming case, what and we expected all2.1 from recent the Stellar-mass data theory. black including holes gravitational stars. When a starforce exhausts any all its longer, nuclear and fuel,away the the by body gas this collapses. pressure violent cannot process. balance A the If significant gravitational the faction mass of of material the is collapsing usually core expelled exceeds 2 Astrophysical Black Holes towards the object. Assuming thatthe the Eddington emitting luminosity material of is an a object of ionized mass gas of protons and electrons, a third class ofstellar-mass objects, and intermediate the mass supermassive ones, black butyet holes, their robust mass nature with measurements. is a still mass controversial filling and they the do gap not between have the known mechanism capable of stopping theminimum collapse mass and of we a have the stellar-massthus creation black be of hole 2 a formed black from hole. the The collapse of a progenitor star should and on the rotationor of neutrons the can body), stopneutron because the star for collapse, [ lower leading masses to the the formation quantum of, pressure respectively, of a electrons white dwarf or a PoS(Multif2019)028 , . )

M M ( (2.1) f 150 > > M Cosimo Bambi M or disappear because

M M 50 stellar-mass black holes ]. Since the discovery in 9 . < i 150 41 10 are all in the Milky Way with M > 2 − and M to infer the mass of the compact 8 c i M is the inclination angle of the orbital , is the mass of the compact object. In and i 2 i is the orbital period of the companion ) M c 3 q M orb sin + P 1 M ( = are low-mass X-ray binaries, i.e. the companion 6 N orb 2 shows 22 X-ray binaries with a stellar-mass black G P 3 c π 2 2 K exceeds the maximum mass for a neutron star we can ) ). These 4 systems are persistent X-ray sources, namely ) = M

( M f M ] ( f 42 10 > ), and they are transient sources: the mass transfer is via Roche Lobe

M M 3 is the velocity of the companion star, c < is the mass of the companion star, and v c , M i does it too even if we do not have estimates of M , sin M c M v / c = M . If the latter exceeds the maximum mass for a neutron star, the compact object is classified c K M = q Currently we know about 20 stellar-mass black holes in the Milky Way and a few more stellar- Currently we also know more than 50 X-ray binaries with a stellar-mass black hole candidate, From stellar evolution studies, we expect a population of 10 mass black holes in nearby galaxies. Fig. and therefore if theconclude mass that function object as a black hole and we say that it has a dynamical measurement of the mass. Note that namely with a compact objectsurement that of is its thought mass to isstellar-mass be lacking. black a The hole, black spectra but hole it of but is these for possible sources which that suggest in a that some dynamical the sources mea- compact there object is is no a black hole but a neutron where plane with respect to thestar, line of sight ofgeneral, the it observer, is necessary to have independent estimates of the exception of LMC X-1 andresiding LMC in the X-3, nearby residing small in galaxy the M33. Large Magellanic Cloud, and M33 X-7, hole confirmed by dynamical measurements.figure), Among LMC these systems, X-1, Cygnus LMC X-1companion X-3, (Cyg star and X-1 in is M33 the X-7 heavythey are ( are high-mass bright X-ray X-ray binaries, sourcescompanion in star in the to the sense the sky that black atprocess. hole the any originates The time: from other the 18 this wind binary is of systems because the in former the Fig. and mass is transfer a from relatively the stable star is not heavy ( overflow and is not continuos, so thea system few may be days a to bright a X-ray few sourcequite months for a and a peculiar then period case ranging be from because in it a1992, is quiescent so state a for for low-mass more X-ray years than or binary 25material decades. but years, to it probably GRS1915+105 the because is is black of a hole the persistent at very X-ray any large time. source accretion since The disk 22 that X-ray can binaries provide in Fig. Astrophysical Black Holes gap in the remnant population, and the black hole mass can either be the early 1970s of Cygnusidentification X-1, of the compact search objects for stellar-mass inneutron black X-ray stars. holes binaries In has with these mainly masses systems, focused exceedingdisk the on the around X-ray the maximum the radiation mass compact originates of object. frommay the measure From inner the the part mass study function of [ the of accretion the orbital motion of the companion star, we As the metallicity of the progenitor star increases, remnants with of the higher mass loss ratesuch during a the mass black gap, hole finding formation. that very However,destroys heavy other the stars models undergo body, do a without not runaway leaving predict nuclear any explosion black that hole. completely in the Milky Way as the final product of the evolution of heavy stars [ PoS(Multif2019)028 Cosimo Bambi ], while in the case of small galaxies the 19 7 ]. Ground-based gravitational wave detectors now 27 Sketch of 22 X-ray binaries with a dynamically confirmed stellar-mass black hole. For every Astronomical observations show that at the center of every large and middle-size galaxy there In September 2015, the LIGO experiment detected for the first time the gravitational wave is a large amount of mass in a relatively small volume [ promise to discover a largecoalesce number of of two stellar-mass stellar-mass black black holesquite holes a or rare in of event the in a a next stellar-mass singlesensitivity black few galaxy, to current hole years. monitor gravitational with wave many antennas a While galaxies, have neutron making the reachedat the star the detection the necessary can of level be of this kind one of event every event relatively few frequent, days. 2.2 Supermassive black holes signal from the coalescence ofto two the stellar-mass search black for holes, these opening objects a in completely the new sky window [ Figure 2: system, we see the accretionThe disk color of around the the stellar black companionincreases). hole refers to on the The the surface orientation left temperature (from and ofsystem brown the the Sun-Mercury to stellar white in accretion as companion the disks the on top temperature reflectsand the left the the corner right. radius of inclination of the angles the figure: Sun of is the the about distance binaries. 0.7 Sun-Mercury millions is km. Note about Figure the 50 courtesy millions ofstar. km Jerome Every Orosz. year the number ofone X-ray binaries or with two, a because stellar-mass we blackand hole observe start candidate new emitting increases X-ray by radiation sources due that toobject. they the were transfer previously of material in from a the quiescent companion state star to the compact Astrophysical Black Holes PoS(Multif2019)028 ;

M ]. At 5 01 pc, . 50 ]. Such 0 10 ]. Similar 46 − < 2 , 47 R Cosimo Bambi 10 45 ∼ ]. For example, these ]. However, the nature 49 51 within a radius

M 6 . ].

10 54 · erg/s and thus exceeds the Eddington M , 4 from stellar-mass to supermassive black 10 40 53 = M in very distant galaxies, when the Universe 10 10 / M

− > 5 M X 8 L 10 10 ∼ 10 ∼ M M ]. In particular, the dark image commonly called the shadow (even if the ]. It is unclear how it was possible for such black holes to grow so fast in 28 48 ]. Their X-ray luminosity is 52 ]. In the case of the center of the Milky Way, it is possible to study the orbits of 44 , 43 Intermediate mass black holes would be black holes with a mass in the range The recent image of the center of the galaxy M87 obtained by the Event Horizon Telescope Some intermediate mass black hole candidates are associated to the so-called ultra-luminous Quasi-periodic oscillations (or QPOs) are narrow features in the power density spectrum of a While stellar-mass black holes in the Universe are expected as the final product of heavy objects may have formed fromwas a the few collapse order of of magnitudefrom heavy above the primordial the merger clouds; mass of of several if black stellar-massof so, holes. black super-Eddington holes. their They accretion, may initial They which have may is mass grown havethe possible faster formed within moment, by experiencing some we some particular do period accretion notmechanisms models contributed know [ together. which of these mechanisms is the2.3 correct Intermediate one, mass black nor holes if two or more collaboration confirms the presence of acannot supermassive be black ruled hole out) (even if [ some exotic alternatives X-ray sources [ source. While their exactvariability origin of is the source currently and unknown, their they frequency scales are as associated 1 to the short timescale a large amount of massbrown dwarfs, in and such the natural a interpretation volumeconclusions is that cannot can there be be is inferred explained a by supermassive withother black studying a hole the galaxies, [ cluster gas it of orbiting is neutron thepossibilities center not stars like of or possible the the presence to galaxy of NGC obtainsystems a are 4258. sufficiently cluster supermassive For black of stringent holes neutron measurements with stars, to but exclude it is other thought that all these massive a relatively short time. There are a few possibilities under investigation [ that is, filling the gap between theof stellar-mass and these the objects supermassive is ones [ stillblack controversial. holes It and is other likely candidates are the not. some candidates are really intermediate mass luminosity of a stellar-masswe object. cannot exclude However, that without they asuper-Eddington are rate dynamical neutron and measurement with stars a of or non-isotropic their stellar-mass emission black mass, [ holes accreting at a moderate name may be misleading, becauserays) it is consistent is with not the created predictions for as a a black normal hole shadow instars, by general relativity. the a exact body origin stopping of light understood. the Heavier supermassive objects black naturally holes tend ateasy to to the move imagine center to that the of an center original galaxiesit of black is is a hole not puzzling can multi-body to completely grow system, see by and objects swallowing it the with is material masses around. However, was only 1 Gyr old [ holes, which is exactly what one should expect in the case of a common origin of these features Astrophysical Black Holes situation is more uncertain: somedo small not galaxies probably [ do haveindividual too, stars while and other conclude small that galaxies thewhich central is mass the is smallest distance of the orbit of one of those stars from the center [ PoS(Multif2019)028 , the ˙ ]. M and the 57 , M 56 and the mass Cosimo Bambi ∗ a ]. 1 keV) for stellar-mass black 59 − , , the mass accretion rate 1 . 58 M ]. ]. Since the shape of the spectrum is 21 , 60 ]. Future space-based gravitational wave are required, and if they are available it [ i 20 ∗ 23 , a ], we assume that the disk is on the equatorial 22 ] and X-ray reflection spectroscopy (applicable , and 33 9 21 D , , M 20 ]. 55 . A direct or indirect mass measurement is often the key-quantity that J , the inclination angle of the disk with respect to the line of sight of the D , and the black hole spin parameter i . This is the continuum-fitting method [ ˙ M This technique is normally used for stellar-mass black holes only, because the disk temperature Geometrically thin and optically thick accretion disks around black holes have a blackbody- Intermediate mass black holes may be expected at the center of dense stellar clusters as the In the absence of new physics, astrophysical black holes should be described by the Kerr distant observer to both stellar-mass and supermassive black holes)antennas [ promise to provide veryfrom accurate the measurements detection of of the extreme spin mass ratio of inspirals supermassive (or black EMRIs) holes [ black hole distance quite simple, it is notof possible a to source. determine all Independentis these measurements possible parameters of to by fitting fit the the observational thermal data spectrum and infer the black hole spin parameter depends on the blackthermal hole spectrum mass. of the For disk is a peaked black in hole the soft accreting X-ray at band 10% (0 of its Eddington limit, the plane perpendicular to the blackorbits hole and spin. the The inner gas in edgeof the of the disk the disk moves disk on depends is nearly on set geodesic five circular at parameters: the ISCO the radius. black hole Eventually mass the thermal spectrum like spectrum locally, whichradially. becomes Employing a the multi-temperature Novikov-Thorne model blackbody [ spectrum when integrated 3.1 Continuum-fitting method accretion rate result of collisions andpresence mergers. of an Studies intermediate on massvelocity the dispersion. black dynamics Some hole observations of at are multi-body consistent the withholes systems center the in presence show some of of stellar that a intermediate clusters, mass the cluster but black other should explanations increase cannot the be stellar completely ruled out [ solution and thus be completely characterized by two parameters; that is, the mass Astrophysical Black Holes for all these sources.suggest the Observations presence of of objects QPOs heavier than insupermassive normal stellar-mass black some black holes holes ultra-luminous [ and X-ray lighter than sources normal at a few Hz 3. Spin measurements spin angular momentum allows us to classifyindirect a mass measurement), compact as object we haveis as discussed more a in the challenging black previous because hole section.requires the (or The the spin spin black study measurement has hole ofcompact no candidate intrinsic object. effect in relativistic The in effects the development occurring Newtonian case of15 in techniques gravity of years aiming the and ago. at strong thus measuring gravity black Currently, its(suitable hole region the for estimate spins near stellar-mass two started black the leading 10- holes techniques only) are [ the so-called continuum-fitting method PoS(Multif2019)028 . 2 line is 998 in . 30 keV. 0 α − = complex at Th ∗ α Cosimo Bambi a , respectively. It is 2 100 keV) cloud near the black hole. ∼ (third column) and Tab. ]. For lower mass accretion rates, the disk may 1 63 10 line is very weak as a result of fully ionized iron atoms. α 100 eV) for supermassive black holes. In the latter case, dust − ]. Supermassive black holes can thus have a spin parameter very 113 ]. This technique is also called the iron line method because the iron K 23 ]. , 62 22 , 61 shows a summary of current spin measurements of stellar-mass black holes. close to 1, because they maytion have disk. swallowed This a is significant not amount theto of case have mass for a from stellar-mass their value black close accre- holes, to whose that spin at parameter the is expected time of the formation of the black hole. For objects with the case of a thin disk [ this is not crucial forimportant stellar-mass for black supermassive holes, black as holes an they introduces are and already observational quite bias. bright sources, it is 7 keV (depending on the ionization of iron atoms), and by the Compton hump at 20 1 A summary of current spin measurements of stellar-mass and supermassive black holes using Despite that, there are efforts to apply the continuum-fitting method even to measure the spin of supermassive Thermal photons from the accretion disk can inverse Compton scatter off free electrons in the In the past 10-15 years, the spin parameter of about 10 stellar-mass black holes have been 2 − 2. Accretion from disk can spin a black hole up, potentially to the Thorne limit 1. Fast-rotating black holes are brighter and therefore it is easier to measure their spin. While 4 . X-ray reflection spectroscopy are reported in Tab. black holes [ usually the most prominent featurethe in analysis the reflection of spectrum, the butpotentially whole any possible reflection spin even when spectrum, measurement the requires not iron K only of the iron line. Spin measurements are be truncated at abecomes radius important: larger than the the diskTab. ISCO. is For not higher thin mass any accretion longer rates, and the its gas inner pressure edge may be inside the ISCO. surely remarkable that thethese spin objects measurements are of rotating supermassive very blackprobably fast, the holes while combination this suggest of is a that few not most effects: the of case for stellar-mass black holes. This is 3.2 X-ray reflection spectroscopy so-called corona, which is a generic name to indicate a hotter ( estimated with this method. Itaccreting is at important 5% to to select 30% sources of with their a Eddington strong limit thermal [ component and Astrophysical Black Holes holes and in the optical/UV band (1 absorption prevents an accurate measurement of the spectrum and, in turn, an estimate of the spin The corona may be thebase accretion of the flow jet, between or the some atmosphere innerThe above process edge the accretion produces of disk, a the but power-law other disk spectrumthe geometries and with are coronal the also an temperature. possible. black exponential cut-off, hole, This whose the component. power-law value component depends In on illuminates the the rest-frame disk,narrow fluorescent of producing emission the a lines reflection gas in in6 the the soft X-ray disk, band, the in reflection particular spectrum by is the iron characterized K by These fluorescent emission lines are broadened andcombination skewed of when relativistic observed effects occurring far in from the thepoint strong source of gravity as region emission a and in depending the on disk. thecomponent exact [ X-ray reflection spectroscopy refers to the analysis of this reflection PoS(Multif2019)028 ]. ] 114 71 , ] 70 81 ] , ] ] , ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] 65 69 74 77 80 87 Cosimo Bambi , , , , , , 89 90 91 92 93 94 95 72 75 82 83 84 85 86 87 88 [ [ 64 68 73 76 79 85 [ , , 67 78 , 66 ]. 63 98 [ 01 [ 030603 [ [ [ . 02 25 15 22 11 15 ...... 95 [ [ 0 0 0 0 0 0 0 0 0 0 0 96 [ 959898 [ [ [ ...... + − + − + − 0 0 ∼ ± ± ± ± 0 0 0 0 —[ —[ (Iron) Principal References 97 55 76 > < ∗ . . . > > > > 98 95 92 88 84 a . . . . . 11 ? ? 06 0 05 —28 [ 153 0 19 — — — [ [ [ 10 10 19 16 ...... 2 — [ . . . . . 7 — [ 9 0 0 0 0 0 0 0 0 0 9898 0 . . 0 0 0 . . − + 0 0 ± ± ± ± ± ± 0 0 − ± ± 2 63 < & . . > > < 25 12 92 84 34 80 70 . . . . . (Continuum) . . ∗ a error estimates are doubled following [ σ M33 X-7 0 Summary of current spin estimates for stellar-mass black holes. The second column refers to the IC10 X-1 LMC X-3 0 LMC X-1 0 GX 339-4 A0620-00 0 BH Binary H1743-322 0 4U 1543-47 0 Cygnus X-1 GS 1124-683 0 GS 1354-645 – Swift J1753.5 — 0 Swift J1658.2 — from the fit of the spectrum.tic Only effects when in the the value of reflection the spectrum spin are parameter strong is enough very to high break relativis- parameter degeneracy [ a low mass companion star, thestellar spin value companion. cannot increase For much objects evenlifetime with swallowing and the a the whole black high hole mass cannotat swallow companion enough the star, material Eddington the to limit. change latter its has spin even a accreting too short GRO J1655-40 0 GRS 1915+105 XTE J1550-564 0 XTE J1650-500XTE J1652-453 — — 0 XTE J1752-223 — 0 MAXI J1836-194 — 0 MAXI J1535-571 — XMMU J004243.6 3. Reflection models are characterized by a large number of parameters that must be inferred These sources were studied in an early work of the continuum-fitting method, within a more simple model, Table 1: spin estimates via thereflection continuum-fitting spectroscopy method. (iron? line The method). third column See is the for referencesand the therefore in the spin the published estimates last 1- using column X-ray for more details. Note: Astrophysical Black Holes PoS(Multif2019)028 Cosimo Bambi ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] 99 104 110 111 101 , , 96 , , 96 96 96 97 98 96 , 96 96 96 107 108 109 112 100 102 105 106 [ [ [ [ [ 96 96 96 96 103 [ [ [ 01 06 04 04 02 09 10 13 10 18 01 04 06 07 2 2 ...... 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9999989898 [ 98 [ [ 97 [ 96 [ [ 96 [ 9595 [ [ [ 84 [ 56 [ [ 9999 [ [ ...... 12 + − + − + − + − + − + − + − − + 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 (Iron) Principal References 6 . 96 93 91 83 81 97 91 ∗ ...... > > > > > > > > > > > > > > > a ], while we know that most supermassive black holes have higher 63 ]. When the mass accretion rate is high, the disk becomes geometrically 115 Object 3C120 Mrk 79 Ark 120 0 Ark 564 0 Fairall 9 Mrk 335Mrk 841 0 Mrk 509 Mrk 110 PDS 456 Ton S180 0 RBS 1124 NGC 5506 0 NGC 4051 NGC 3783 NGC 1365 0 1H0707-495 1H0419-577 MCG-6-30-15 0 Swift J0501-3239 IRAS 00521-7054 IRAS 13224-3809 Swift J2127+5654 0 Summary of current spin estimates for supermassive black holes. See the references in the last accretion rates [ to be infinitesimally thin and withof the the inner disk edge is at the finite ISCO anddisk radius. increases is thought However, as the to the thickness be mass at accretion theof rate ISCO the radius increases. Eddington when The limit the inner [ accretion luminosity edge is of between the 5% to 30% Low spin measurements of supermassivestrong black assumptions holes on are often the obtained valuewith by great of imposing caution. other some model parameters and they should thus be taken 4. Current spin measurements employ reflection models in which the accretion disk is supposed Table 2: column for more details. Astrophysical Black Holes PoS(Multif2019)028 ], ]. 118 59 , 58 ]. There are Cosimo Bambi 122 , 121 , 120 , 119 cycles, leading to a very good 5 10 ∼ ]. ]. However, at present we do not know the exact 13 124 116 , 123 ]. Future observations with space-based laser interferometers 117 , 27 thick and the inner edge canignore be the inside radiation emitted the by ISCO the radius. materialthe Moreover, in disk current the and reflection plunging the region, models black between hole. the inner These edge two of effects can lead to overestimate the black hole spin. Current gravitational wave data of the coalescence of stellar-mass black holes with ground- Black hole systems are ideal laboratories for testing fundamental physics in strong gravita- Let us note it is not true, as instead it is often believed, that tests of general relativity require the The measurement of the QPO frequencies could potentially provide quite precise measure- Einstein’s theory of general relativity has been extensively tested in weak gravitational fields [ scenarios motivated by the needdeparture to in electromagnetic avoid signatures information [ loss that can potentially lead to significant based laser interferometers already providewith estimates a of precision the of order spin 10% parameter [ of the final black hole tional fields. This canthe be two done methods either are with complementary electromagnetic becausenetic or they tests, test gravitational strictly different wave speaking, sectors techniques, can of verifygravitational and the the field theory. motion around Electromag- of a massive black andgeneral massless hole relativity. particles and in Gravitational check the wave whether strong testsand it thus are is can sensitive consistent directly to with check thebetween the the evolution the predictions predictions matter of of and of the the Einstein’s spacetime gravity equations.of sectors metric leading For fundamental to example, constants departure a from may new geodesicand leave coupling motion not an or in variations observational the signature gravitationalare in wave still the one. described electromagnetic by Modified the spectrum gravityrelativity Kerr theories but solution in have may which a predict uncharged different the black gravitationalbut same the wave holes electromagnetic field signal, spectrum equations because as are the general different. spacetime metric is the same study of small effects in the electromagnetic or gravitational wave spectra, difficult to observe and mechanism responsible for these QPOsthe and technique is different not models yet provide matureis to different measure the measurements, black correct so hole one. spins because we do not which model, if any, Similar measurements will be possibleLISA from the will observations be of able EMRIs, since to an observe experiment the like signal of an EMRI for promise excellent spin measurements of supermassive black holes at the level of 0.01% [ 3.3 Other approaches ments of black hole spins, see for instance [ Astrophysical Black Holes signal-to-noise ratio. 4. Testing Fundamental Physics With Black Holes 4.1 Motivations while the strong gravityblack regime holes is should still be largelytions well unexplored. can described The be by spacetime the possible aroundexotic Kerr if fields, solution, astrophysical general or in but relativity the deviations is case from not of macroscopic standard the quantum predic- correct gravity effects theory [ of gravity, in the presence of PoS(Multif2019)028 , 141 ], the , 146 140 , ]. Cosimo Bambi 145 136 , 135 ]. Usually, in these tests one 133 , ]. 132 , 127 131 ], the observation of jets powered by the , 147 130 , ]. Gravitational waves predicted by other theories ]. However, this technique can only be used to test 14 ]. Current efforts are devoted to improve the theo- 129 , 126 138 , 134 , 128 125 137 ], etc. 148 ]. 139 ]. However, the current image can only rule out very exotic scenarios [ ], the analysis of QPOs in the spectrum of accreting black holes [ 28 144 , 143 Other electromagnetic tests proposed in literature include the study of pulsars orbiting black The detection of the shadow of the supermassive black hole in M87 with the Event Horizon In principle, any astrophysical model requiring the Kerr metric to describe some component As of now, the most promising electromagnetic technique for testing fundamental physics with Like X-ray reflection spectroscopy, even the continuum-fitting method can be extended to test ] and it is not clear the future progress in this direction considering that the inclination angle of detection of blobs of plasmarotational energy orbiting of a black black holes [ hole [ holes [ the spin of the blackimage hole in will M87 likely with be our veryalternative line circular, solutions. of which sight makes is it presumably impossible very to small distinguish and the any Kerr shadow metric from 142 retical models to reduce andselect quantify the current most systematic suitable uncertainties. sources and Itmaximize data is relativistic to also features minimize very the in important systematic the to uncertainties reflectionto of spectrum. select the clean For model sources, and this without reason, intrinsic itpossible absorption, is to and extremely the with important compact the object. inner For edge more of details, the see disk the as discussions close in to Refs. [ stellar-mass black holes, it requiresand independent inclination measurements angle of of theoften the black affected disk hole by (three systematic mass, effects), quantities distance, andthat that the it thermal are component seems currently of difficult difficult the tofrom disk to break the has estimate Kerr the a solution and so degeneracy [ simple are among shape the spin parameter andTelescope possible has deviations opened the possibilityhole of shadow testing [ the Kerr metric with accurate detections of black of the electromagnetic spectrum ofphysics with an black accreting holes. black From holemodel the with can comparison the be data of extended of the the to theoreticalparameters source, of predictions test it the of fundamental is model. the potentially astrophysical possible to probe new physics by measuringblack the holes is probably X-ray reflection spectroscopy,servational and constraints surely already the published only [ one with quantitative ob- the nature of astrophysical black holes [ 4.2 Electromagnetic tests assume geodesic motion and comparepossible the deviations from theoretical the model Kerr withalence metric. observational Principle data by However, to it verifying that is constrain is atomic also the physics possible same in to as the test in strong the our gravity laboratories Einstein region on Equiv- around Earth a [ black hole of gravity can be very differentpossible from to those obtain expected very in strong general constraint relativity, on and some even models in [ this case it is Astrophysical Black Holes subdominant with respect to theof uncertainties electromagnetic of tests the we can theoretical note models.or that reflection wormholes For spectra can example, from be in accretion qualitatively disks the differenteasy around case from to boson those rule stars out around some Kerr extreme black scenarios holes [ and it is relatively PoS(Multif2019)028 Cosimo Bambi , 189 (1916) [physics/9905030]. , 517 (2005)]. 1916 ]. 14 151 15 , 1238 (1918). 20 ]. In model-dependent tests, we compare the theoreti- 117 , 769 (1916) [Annalen Phys. 49 , 106 (1916). ]. The disadvantage of model-dependent tests is that there are many 59 127 ]. Future space-based laser interferometers promise to detect gravitational 150 , 149 Black holes are among the most amazing objects that can be found in the Universe today and This work was supported by the Innovation Program of the Shanghai Municipal Education Current observations of gravitational waves from black holes are limited to the detection of Gravitational wave tests are the only method to probe the dynamical strong field regime. [2] K. Schwarzschild, Sitzungsber. Preuss. Akad. Wiss. Berlin [3] H. Reissner, Ann. Phys. [1] A. Einstein, Annalen Phys. [4] G. Nordström, Proc. Kon. Ned. Akad. Wet. represent ideal laboratories for testingcommunity has fundamental convinced physics. about the existence In ofmore the these candidates objects past and employing 50 has different started years, looking detection thehave for techniques. been more astronomy devoted and In to measure the the paststandard spin 10-15 physics. of years, these In objects many the and efforts past studyto their use few astrophysical host years, black environment there assuming holes have tobe been test an fundamental the physics. increasing beginning It number of is of a possiblethe studies that beginning “Golden devoted the of Age” next a decade golden for will age observationalfacilities for and black observational cosmology, unprecedented holes, thanks high-quality the just data. advent like of new 20 observational years ago it was Acknowledgments Commission, Grant No. 2019-01-07-00-07-E00035, and Fudan University, Grant No. IDH1512060. References 5. 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Astrophysical Black Holes COSIMO BAMBI: In the astronomy community, it ismeasurement common to of call its “black mass hole” and amass compact when for object the a with latter neutron a star. exceeds dynamical “Black threethought hole to Solar be candidate” masses, a is black which usually hole, is used butcannot to we the exclude do indicate maximum it not a have is compact dynamical a object measurement neutronof of that its star. is its mass In mass and the therefore and we case thisa of is Cygnus dynamically X-1, about confirmed we 14 black have Solar hole aand masses, dynamical this to so measurement exceeds stress Cygnus the that X-1 maximum thereimpossible is mass to is firmly classified for a confirm a as that dynamical neutron a an measurement object star).being, black is the of hole a astrophysical As black its objects (or physics hole, that mass as is but are wethe called an can available black empirical observations only holes are disprove science, are consistent it. with thought it For such to is a theturns be conclusion. time black out If, holes to at because be some all point, inconsistent some withobjects. observation this conclusion, we will need to revise our undesratnding of these