a (very) short and (very) partial introduction to black ... · pdf filea (very) short and...

A (very) short and (very) partial introduction to

black hole astrophysics

Giovanni Miniutti

Institute of Astronomy, University of Cambridge

Lezioni del corso

Contents

1 Black hole accretion and X–ray emission 1

1.1 Some basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.1 Accretion discs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.1.2 X–ray emission from accreting black holes . . . . . . . . . . . . . . . . . 4

1.2 Black hole binaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.3 Active Galactic Nuclei . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

1.3.1 Optical spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131.3.2 The central engine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151.3.3 The unified model of AGN . . . . . . . . . . . . . . . . . . . . . . . . . 17

1.4 The relativistic Fe line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191.4.1 Dependence on disc inclination and emissivity . . . . . . . . . . . . . . . 211.4.2 Self–consistent ionized reflection models . . . . . . . . . . . . . . . . . . 221.4.3 Dependence on the inner disc radius . . . . . . . . . . . . . . . . . . . . 23

2 Observational evidence for black holes 25

2.1 The Galactic centre . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.1.1 The radio source Sgr A* . . . . . . . . . . . . . . . . . . . . . . . . . . . 262.1.2 Stellar motions in the GC region . . . . . . . . . . . . . . . . . . . . . . 282.1.3 Weighting Sgr A* . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302.1.4 Sgr A* fast variability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

2.2 Supermassive black holes in other galaxies . . . . . . . . . . . . . . . . . . . . . 352.2.1 Stellar kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352.2.2 Gas kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372.2.3 Water Maser emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

2.3 Stellar–mass black holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402.3.1 Identification of black holes in X–ray binaries . . . . . . . . . . . . . . . 41

iii

Chapter 1

Black hole accretion and X–rayemission

The observational evidence for the existence of black holes is overwhelming and two familiesof black holes are currently known. Stellar–mass black holes (with typical masses of ∼ 10 M⊙)are known to exist in 20 X–ray binaries in the Milky Way. On the other hand, supermassiveblack holes with masses in the range of 106 M⊙ − 109 M⊙ are thought to be present in thenuclei of most, if not all galaxies. Here we review some of the basic properties of these systemsmainly focussing on X–ray observations.

1.1 Some basics

The extraction of gravitational potential energy from matter accreting onto a compact objectis now known to be the main source of power in several types of luminous astrophysical sources.For a body of mass M and radius R, the gravitational energy released by the accretion of amass m onto its surface is simply ∆Eaccr = GMm/R and most of it is expected to be releasedin the form of electromagnetic radiation. By differentiating, the luminosity produced by theaccretion process is thus Laccr = GMm/R ≃ ηmc2, where η is the efficiency for converting therest mass energy into radiation and m is the mass accretion rate (the mass accreted per unittime). If matter could be accreted onto a black hole infinetesimally slowly, η = 1, obviouslyan unrealistic assuption. However, the current consensus is that, for typical accreting blackholes, η ∼ 0.1, i.e. the efficiency is about 10 %. This can be compaired with the rest–massto energy efficiency of nuclear fusion of H into He which is only η = 0.007, i.e. less than 1 %.It is therefore quite clear that accretion onto black holes is the most efficient way to convertrest–mass into luminosity and the mechanism is indeed widely believed to power among themost luminous sources of radiation in the Universe.

However, there is a limit on the luminosity that can be extracted from the accretion.Consider for simplicity a spherically simmetrical accretion process in which the accretingmaterial is mainly fully ionized hydrogen (a very good approximation to real situations). Theradiation produced through the accretion process produces radiation pressure which mainly actas a repulsive force on the free electrons via Thomson scattering. The attractive electrostatic

2 BH accretion

Figure 1.1: Schematic view of a binary system comprising a companion star loosing gas to a compactobject. The gas accretes preferentially along circular orbits in the binary equatorial plane forming anaccretion disc which slowly spirals inwards. The accretion disc radiates large amounts of energy in theprocess. In the case of a black hole (or neutron star), most of the emission is in the X–rays.

Coulomb force means that the free electrons which are repelled from the compact objectand effectively stop accreting will drag the protons with them. In fact, the radiation pressurepushes away the electron–proton pairs against the gravitational interaction which is responsiblefor the accretion process. It is clear that if the luminosity released by the accretion mechanismsproduces a force on the electron–proton pairs which is greater than the gravitational one,accretion stops altogether and we have rather an outflow of matter driven by radiation pressure.This balance sets the maximum luminosity that can be extracted via accretion, the so–calledEddinton luminosity

LEdd = 4πGMmpc/σT ≃ 1.26 × 1038M/M⊙ erg s−1 , (1.1)

where M is the compact object mass, mp is the proton mass, and σT is the Thomson cross–section. We remind here that the luminosity of the Sun is L⊙ ∼ 4 × 1033 erg s−1 whichmeans that accretion potentially provides almost five order of magnitude more power than thenuclear reactions occurring in the Sun for an object of the same mass.

1.1.1 Accretion discs

Accretion discs are the basic and fundamnetal structure through which matter (gas) is accretedonto compact objects. They can be thought of as geometrically thin structures orbiting the

1.1 Some basics 3

central black hole (or other compact object) wich allow the accreting matter to loose itsangular momentum and therefore to be accreted. Since circular orbits have the least energyfor a given angular momentum, we expect that the gas slowly spirals inwards through a seriesof approximately Keplerian (or geodesical) circular orbits transferring angular momentumoutwards1. A schematic view of a black hole accreting matter from a companion star (a blackhole binary) through an accretion disc is seen in Fig. 1.1.

The binding energy of a gas element with mass m in a Keplerian orbit grazing the surfaceof the compact accretor (of size R) is 1/2GMm/R, and since the gas element starts its inspiralat large distances with negligible binding energy, the total luminosity of a disc (in a steadystate) must be Ldisc = 1/2GMm/R (where m is the mass accretion rate) which is half of theavailable energy (Laccr, see discussion above). In other words, an accretion disc can be anefficient machine for slowly lowering gas in the gravitational potential of the central compactobject and for extracting large amounts of energy in the process. A vital part of this processis clearly the mechanism which converts the orbital energy into heat and thus radiation. Infact. this is the main problem for disc structure theories.

Keplerian rotation implies differential rotation, i.e. gas iat neighbouring radii moves with adifferent angular velocity (ΩK(r) = (GM/r3)1/2). Because of the cahotic thermal or turbulentmotions that will always be present, viscous stresses are generated in the disc which producea local loss of mechanical energy which is dissipated into internal heat. In the case of a steadyKeplerian disc, it can be shown (Frank, King & Raine 2002) that the local dissipation rate ishowever independent on the viscosity and can be written

D(r) =3GMm

8πr3

[

1 −(rin

r

)1/2]

, (1.2)

where rin is the inner edge of the disc. If the disc is optically thick (i.e. the optical depthis large) in the z–direction, each element of the disc radiates roughly as a blackbody with atemperature T (r) given by equation the dissipation rate D(r) to the blackbody flux (Planck’slaw), i.e. D(r) = σT 4(r), where σ is the Stefan-Boltzmann constant. Thus

T (r) =

3GMm

8πσr3

[

1 −(rin

r

)1/2]1/4

, (1.3)

and the emitted spectrum will be the superposition of blackbodies with temperature T (r)emitted from narrow annuli at r and integrated over the whole disc surface. To get a roughidea of the maximum temperature that is achieved in a standard accretion disc around a blackhole T (r) can be expressed as a function of total emitted luminosity (L) and black hole mass:

T (r) ∼ 1.06 × 106

(

L

LEdd

108 M⊙

MBH

)1/4 (

r

rg

)−3/4

K , (1.4)

where rg = GMBH/c2 is the gravitational radius and L the overall luminosity of the system.The maximum temperature is clearly reached for the smallest radii, i.e. at the inner edge of

1For an excellent review of accretion theory and some applications the book Accretion power in astrophysics

by Frank, King, & Raine is suggested.

4 BH accretion

0.1 1 10 100

110

E F

(E)

Energy (keV)

Blackbody (BB)

Comptonized BB

Figure 1.2: The effect of inverse Compton on the blackbody emission from the accretion disc. Theoriginal photons from the disc (red) are upscatterd up to energies ∼ 4kTe/mec

2 by scattering withthe more energetic electrons in the corona. This provides significant X–ray flux at energies where noblackbody emission would be in principle expected.

the accretion disc. This is generally assumed to coincide with the innermost stable circularorbit (ISCO) around the black hole, beyond which matter plunges ballistically onto the eventhorizon. The ISCO radius is 6 rg for a non–rotating Schwarzschild black hole and ∼ 1.24 rg

for a maximally rotating Kerr black hole (Kerr black holes are thus slightly hotter thanSchwarzschild ones).

1.1.2 X–ray emission from accreting black holes

The accretion disc thermal spectrum is not the only component in the observed spectra fromaccreting black holes. In particular, a power law spectral component2 is ubiquitous in the X–ray spectra of black hole binaries and active galactic nuclei. The most promising mechanismto produce such a power law component is inverse Comptonization of the thermal disc photonsby a population of energetic electrons above the accretion disc itself (the so–called corona inanalogy with Sun’s corona). The idea is based on Compton scattering, i.e. the electron–photoninteraction (Rybicki & Lightman 1979; Haardt & Maraschi 1991). For a non–relativisticpopulation of electrons with energy kTe, the average change in photon energy for each single

2When the photon flux per unit energy (photons cm−1 s−1 keV−1) can be described in the form F (E) ∝ E−Γ

the spectrum is said to have a power law form with photon index (or slope) Γ.

1.1 Some basics 5

scattering is

< ∆E >= (4kTe − E)E

mec2. (1.5)

If the photon energy is initially much lower than the electron energy kTe, the photon gainsenergy in the scattering and this process is generally called inverse Compton scattering. Hence,as long as E ≪ kTe, the photon continues to gain energy after each scattering with an electronwith ∆E/E ∼ 4kTe/mec

2. After N scatterings, the final photon energy Ef , compared to theinitial energy Ei is then

Ef ∼ Eiexp

(

N4kTe

mec2

)

. (1.6)

The number of scattering depends of course on the properties of the electron population (itsoptical depth) but, in general, the exponential gain of photon energy (eq. 1.6) leads to aspectrum which has a power law form with Γ ∼ 2 and a high energy cutoff at the energy inwhich no more scatterings are possible (i.e. when the photon reaches the electron energy).Therefore the combined spectrum for the accretion disc plus electron corona system can bedescribed as a modified black body, i.e. a blackbody with a power law tail at high energies(due to the scattering of photons to higher energies). An illustrative example is given inFig. 1.2 where we show the disc blackbody emission and its Comptonized version (assuminga population of electrons with energy ∼30 keV).

There are two principle uncertainties in applying coronal models to observed black holesystems, and both are substantial. First, the mechanism for heating the electrons up to thehigh energies needed to exaplin the observations (10–100 keV or even more) is currently un-known. Current hypotheses invoke magnetic processes, perhaps akin to solar flares on the Sunor heating of the solar corona. Second, the geometry of the corona is also completely unknown.However, Comptonization models have proved so far very successful in explaining X–ray ob-servations of accreting black hole. There is vast consensus that the current understanding isfar from definitive, but such models seem to catch the basics of the observed phenomena. Wenow have a situation in which the accretion disc is not the only source of radiation. There is acorona somewhere above the disc that upscatters the low energy disc photons and produces asubstantial fraction of the observed flux. Obviously the corona also re–irradiates the accretiondisc and thus a balance between the two systems has to be found.

A second effect is that irradiation of the dense disc material gives rise to a characteristic“reflection” spectrum which is the result of i) Compton scattering by free electrons associ-ated with fully ionized hydrogen (and helium) and/or by outer bound electrons of the heavierelements; ii) photoelectric absorption followed either by fluorescent line emission or Augerde–excitation (see e.g.George & Fabian 1991). This produces an emission line spectrum wherefluorescent narrow Kα lines from the most abundant metals are seen. Thanks to a combinationof large cosmic abundance and high fluorescent yield, the iron (Fe) Kα line at 6.4 keV is themost prominent fluorescent line in the X–ray reflection spectrum. Photoelectric absorptionis obviously an energy–dependent process, so that incident soft X–rays are mostly absorbed,whereas hard photons tend to be Compton scattered back out of the disc. However, above afew tens of keV, Compton recoil reduces the backscattered photon flux and produces a broadhump–like structure around 20–30 keV (the so–called Compton hump). An example of the X–ray reflection spectrum from a neutral and uniform density semi–infinite slab of gas is shown

6 BH accretion

Figure 1.3: Left panel: Monte Carlo simulations of the reflection spectrum from a slab of uniform

density neutral matter with solar abundances. The incident power law continuum is also shown.

Figure from Reynolds (1996). Right panel: The main components of the X–ray spectra of accreting

BH are shown: soft quasi–thermal X–ray emission from the accretion disc (red); power law from

Comptonization of the soft X–rays in a corona above the disc (green); reflection continuum and narrow

Fe line due to reflection of the hard X–ray emission from a slab of dense gas (e.g. the accretion disc

itself).

in the left panel of Fig. 1.3 where fluorescent emission lines dominate below about 8 keV andthe Compton hump is seen above 20 keV. In the right panel of Fig 1.3, we show the maincomponents of the X–ray spectrum of accreting black holes.

Summarizing, accreting black holes emit thermal quasi blackbody radiation from the accre-tion disc. This is thought to be upscatterd to higher energies by inverse Compton scatteringin the corona, a distribution of hot electrons above the disc itself probably heated by magneticreconnection events (in analogy with the Sun). Comptonization gives rise to a high energytail which can be well approximated by a power law with high energy cutoff (where the pho-ton energy reaches the electron energy and thus cannot be upscattered anymore). This powerlaw emission irradiates the accretion disc (and other material in the surroundings) and isreprocessed, giving rise to a characteristic reflection spectrum whose main properties are a Feemission line at 6.4 keV and a Compton hump at 20–30 keV.

1.2 Black hole binaries

As discussed in Chapther 2, there are 20 confirmed black hole in the Milky Way with massesof about 10 M⊙ and at least 20 more black hole candidates thought to be representative ofa very large population of about 108 − 109 black holes in the Galaxy. They are observedas members of binary systems in which the black hole accretes gas from the outer layers of

1.2 Black hole binaries 7

Figure 1.4: Drawings of 16 black hole binaries in the Galaxy. The estimated inclination angle of theorbit with respect to us is indicated by the tilt of the accretion disc, while the color of the companionstar roughly indicates its surface temperature.

its stellar companion. In Fig. 1.4, we show scale drawings of 16 black hole binaries in theMilky Way. The Sun–Mercury distance of 0.4 AU is shown as a reference. The differencesbetween the systems is clear for the Figure. Some are long–period systems with large orbitalseparation containing both hot (Cyg XX-1) and cool (GRS 1915+105) supergiants, and othersare instead compact systems with dwarfs companions, and finally there are also intermediatesystems (e.g. GS 2023+338).

From eq. 1.4, for a typical (non–rotating) stellar mass black hole with mass 10 M⊙ radiatingat the Eddington luminosity, T (rin = 6 rg) ∼ 1.5 × 107 K which corresponds to an energyof kT ∼1.3 keV, i.e. in the X–ray regime of the elctromagnetic spectrum. We thus expectthat stellar–mass black holes accreting gas from a companion star in a binary system willpredominantly emit in the X–ray regime. This is indeed what is observed and, in fact, the first

8 BH accretion

Figure 1.5: X–ray light curves for six black hole binaries (X–ray count rate as a function of time indays (the corresponding year is also indicated). The bottom panels in each figure are the hardnessratio (HR2) light curves, i.e. the ratio between the flux in a hard (high energy) X–ray band and thatin a soft (low energy) one.

detection of a stellar–mass black hole in the Milky Way is associated with the X–ray binaryCygnus X–1, which was discovered in the X–rays (very roughly defined as electromagneticradiation with energy in the range of 200 eV–100 keV).

Most black hole X–ray binaries are so–called X–ray novae, i.e. transient X–ray sourceswhich spend most of their lifetime in a state of quiescence with little X–ray emission becauseaccretion is somehow quenched. However, these source occasionally exhibit very large lumi-nosities, the so–called outbursts. The commonly accepted view is that the accretion rate fromthe companion star is normally too low to support a continuous viscous flow to the black holeand therefore the accretion disc cannot form and X–ray emission is at very low levels (often


Figure 1.6: GX 339–4 during in the 1996–2005 period during which 3 outbursts were detected. Panla shows the X–ray lightcurve and the 3 outbursts. The symbols colors denote the X–rays state: soft(red), hard (blue), and intermediate (green, black).

even undetectable). However, matter starts to fill the outer disc during that time until a crit-ical surface density is reached which triggers a disc instability giving rise to the fast buildingup of the inner accretion disc with the associated X–ray luminosity (e.g. Smak 1971; Dubus etal 2001). Current models predict recurrent outbursts. Indeed half of the black holes observedso far have shown recurrent outbursts with a typical timescale of 1–20 years. The increase influx during outbursts means that these event are the ones one should look for to discover newX–ray binaries. In fact, the discovery of new X–ray binaries relies on monitoring large portionsof the sky in the X–rays (e.g. the Rossi X–ray Timing Explorer, RXTE) to catch their firstoutburst. Each single outburst typically last between ∼ 20 days to few months depending onthe source. In Fig. 1.5 we show typical X–ray light curvse (from RXTE) of such events.

The properties of black hole binaries during their outbursts exhibit an exceptionally com-plex and fascinating phenomenology leading to the definition of the so–called X–ray states.

10 BH accretion

Here we briefly mention some of their most important properties (see e.g. Remillard & Mc-Clintock 2006 for a much more extensive review). During outbursts black hole binaries exhibittwo main very different main spectra states, the hard state, and the soft state. They are de-fined on the basis of which part of the X–ray spectrum contributes the most to the X–ray flux.X–rays can be roughly devided in two categories: soft X–rays with energies below ∼ 2 keV andhard X–rays, whith higher energy. A useful quantity to describe the contribution of the softand hard photons in the X–ray spectrum is the so–called hardness ratio (HR), i.e. the ratiobetween the flux in hard and soft photons. The higher the HR, the more the hard photonscontribute to the total flux with respect to soft ones. X–ray states can be roughly classifiedby the HR, i.e. soft states have low HR, hard states have high HR. In general, soft photonswill be dominated by the thermal disc emission, while hard ones are mainly representative ofthe high energy power law tail due to the Compton upscattering of the soft disc photons bythe electrons in the corona (see Fig. 1.2). Therefore, X–ray states with low HR are dominatedby disc emission, while in those with high HR, it is the powe law emission that dominates,and the disc contributes only marginally.

In Fig. 1.6 we show the behaviour of one of the best–studied black hole binaries, GX 339–4, during its three outbursts. Panles (a) and (b) show the X–ray lightcurve and the flux asobtained from spectral fits to the X–ray data during a long monitoring from 1996 to 2005,comprising theree outbursts. Blue symbols refer to hard states, red ones to soft states, whilegreen and black symbols are representative of states which are intermediate between the two.As clear from panel (b) the outburst always starts in the hard state (blue), where the disccontribution is minimal and progreeses into soft states (red) which are reached close to theoutburst peak and continue during the outburst decay.

As can be seen in panel (d), the outbursts all trace a characteristic path in the intensity–hardness (HR) diagram. By considering the time evolution of the outburst (panels (a) and (b)for comparison), it can be seen from panel (d) that the ouburst starts in the hard state (blue)and the flux rapidly increases. Towards the flux/intensity peak there is a transition to thesoft state (red) via intermediate states (green, black). Such a characteristic anti–clock wisepattern in the intensity–hardness diagram (d) is common to almost all outbursts of black holebinaries. In the bootom panels, spectral information is also given. As can be seen in panel(e) the power law is dominant in the hard states (blue), while the disc is the main spectralcomponent in soft states (red), as expected from the hardness ratios. In panels (e), (f), and(g), the evolution of the power law index Γ, the disc contribution to the total flux, and theamplitude of X–ray variability is seen as a function of the hardness ratio.

X–rays are not the only electromagnetic emission emitted in black hole binaries. Radioobservations have shown that black hole binaries are also sources of Synchrotron emission,thought to be associated with the presence of jets. In fact, relativistic jets are a fundamen-tal aspect of accreting black hole on all scales (from stellar–mass black holes in black holebinaries to supermassive black holes in active galactic nuclei). For black hole binaries, thepresence/absence of jets is associated with the X–ray state. In particular hard states are asso-ciated with the presence of steady jets, while no jets are generally observed during soft states.It has been shown that during the transition between the hard and the soft state, black holebinaries cross the so–called jet line (dividing the region in which jets are persistent and steadyin the hard state to that in which they are absent or very much suppressed in the soft state).


jet l

ine

HS LSVHS/IS

Soft Hard

Γ > 2 Γ < 2

i

ii

iii

jet

Jet L

oren

tz fa

ctor

iiiiv

iv

iii

inte

nsity

hardnessX−ray

Dis

c in

ner

radi

us

no

Figure 1.7: A schematic of a simplified model for the jet-disc coupling in black hole binaries. Thecentral box panel represents an X-ray hardness-intensity diagram (HID); ’HS’ indicates the ‘high/softstate’, ’VHS/IS’ indicates the ’very high/intermediate state’ and ’LS’ the ’low/hard state’. In thisdiagram, X-ray hardness increases to the right and intensity upwards. The lower panel indicates thevariation of the bulk Lorentz factor of the relativistic jet and of the inner radius of the accretion discwith hardness ratio (smaller inner radii correspond to enhanced thermal emission). In the LS andhard-VHS/IS the jet is steady with an almost constant bulk Lorentz factor Γ < 2, progressing fromstate i to state ii as the luminosity increases. At some point Γ increases rapidly producing an internalshock in the outflow (iii) followed in general by cessation of jet production in a disc-dominated HS (iv).The solid arrows indicate the track of a simple X-ray transient outburst with a single optically thin jetproduction episode. Sketches around the outside illustrate the concept of the relative contributions ofjet (blue), ’corona’ (yellow) and accretion disc (red) at these different stages.

As the binary approaches the jet line in its outburst, the jet is observed to become more andmor relativistic. When the jet line is crossed, the jet emission is very much suppressed.

Such a characteristic behaviour has prompted the search for a unified model that couldexplain the time–evolution of the properties of black hole binaries during outbursts takingalso into account the relativistic jet emission (radio). The outburst evolution is schematicallyrepresented in Fig. 1.7 where HS and LS are the soft (often called high state) and hard (oftenlow state) states respectively, while intermediate states are indicated with VHS/IS. The time–evolution foolows the solid arrows in the anti–clock wise direction (see Fender, Belloni &Gallo 2005 from which the following discussion is taken). The main idea that well describes

12 BH accretion

Figure 1.8: Spectrum of a Carbon star, made of a thermal continuum and absorption lines.

most observations is represented by the sketches around the outside. At the beginning of theoutburst (i) the emission is dominated by the power law component probably produced in thecorona (yellow) through inverse Compton, and by the steady jet observed in the radio (blue).The luminosity increases from i to ii but no qualitative changes are required to explain thedata. As the outburst starts to track the horizontal path at the top of the Figure and to makethe transition in the soft state 1) the velocity of the jet increases sharply until the jet–lineis crossed (and no jet is seen afterwards) and 2) the disc (red) thermal emission starts todominated the X–ray spectrum (iii). Finally the disc completely dominates the emission withno visible jet (iv).

The complex phenomenology outlined (and significantly simplified) above makes it clearthat the study of black hole binaries is providing and will provide in the future importantinformation on the nature of the accretion mechanism onto black holes. Most remarkable, itseems clear that all main components (disc, corona, jet) are coupled together and that thesystem must be considered as a whole. Further observational studies of black hole binariesin outburst are likely to clarify the most important connections between the mentioned threemain components and to raise new questions which will in turn make our understanding ofthese fascinating processes much deeper than it is at present.

1.3 Active Galactic Nuclei

In general the term “active galactic nucleus” (AGN) refers to the existence of energetic phe-nomena in the nuclei of galaxies which cannot be attributed clearly and directly to stars. Thetwo largest subclasses of AGNs are Seyfert galaxies and quasars. The fundamental difference

1.3 Active Galactic Nuclei 13

Figure 1.9: The optical spectrum of a type 1 AGN (top) shows both narrow and broad emissionlines. On the other hand, type 2 AGN (bottom) only exhibit narrow emission lines. The x–axis in thewavelength in A.

between these two subclasses is in the amount of radiation emitted by the compact centralsource. In the case of a typical Seyfert galaxy, the total energy emitted by the nuclear sourceat visible wavelengths is comparable to the energy emitted by all of the stars in the galaxy,while in a typical quasar the nuclear source is brighter than the stars by a factor of 100 ormore (and in fact the stars of the galaxy are typically undetectable). The typical luminositiesof AGN span the wide range of 1042 − 1047 erg s−1. A comparison with eq. 1.1 already showsclearly that these objects are most likely powered by accretion onto supermassive black holes.

1.3.1 Optical spectra

The optical spectrum of a star normally consists of a continuum of thermal emission (from thestar surface) with a pletors of absorption lines superimposed to it which are caused by coolergas surrounding the hot surface (see Fig. 1.8). Obviously, spectra of normal galaxies are thesuperposition of the spectra of the star’s in the galaxy and are dominated by absorption lines.Some emission lines due to hot gas in the galaxy are also present, but they do not dominatethe spctrum (generally speaking).On the other hand, AGN optical spectra are dominated byadditional emission lines, most of which are broadened up to significant velocities (thousandskm s−1). The emission lines are produced by hot gas, but its temperature can be estimated tobe ∼ 104 K, too low to produce also the broadening of the lines. The alternative explanation is

14 BH accretion

Figure 1.10: A radio image of the radio galaxy Cygnus A. All radio components are seen: a brightpoint–like radio core, a bright jet (right) and a fainter counter–jet (left), radio lobes and the hot–spots.

that the lines are produced in gas clouds which are moving with high velocities thus producingthe broadening of the lines. The optical spectra of AGN reveal that they can be broadlyclassified into two types

• Type 1: they have two sets of emission lines, namely both narrow (widths of ∼400 km s−1) and broad emission lines (widths up to 10000 km s−1).

• Type 2: only have narrow lines. Broad lines are very weak or totally absent in theoptical spectra.

The two sets of lines are thought to originate from two distinct regions: a low density region(the narrow–line region, NLR) with little velocity produces the narrow lines, while denser andhigher velocity one (the broad–line region, BLR) is responsible for the broad emission lines.In Fig 1.9 we show the typical spectra of a Type 1 and a Type 2 AGN. AGN sometimes alsoexhibit radio emission which is associated with the presence of jets (radio galaxies). In fact,the radio emission from radio galaxies often comprises several components, namely a compactradio core at the center, jets and radio lobes. The jets are relativistic and beaming effectsmake the jet pointing towards the observer much brighter than the opposite counter–jet. Atypical example is shown in Fig. 1.10. Despite the dramatic difference between radio galaxiesand AGN which do not emit in the radio, the optical spectra of radio galaxies are very similarto other AGN and they are classified into the classes of broad–line radio galaxies (BLRG)and narrow–line ones (NLRG) which are nothing else than type 1 and type 2 AGN. Opticalspectra of a BLRG and a NLRG are shown in Fig. 1.11 to compaire with the spectra of typicaltype 1 and 2 AGN (Fig. 1.9).


Figure 1.11: The optical spectrum of a BLRG (top) shows both narrow and broad emission lines.On the other hand, NLRGs (bottom) only exhibit narrow emission lines. The x–axis in the wavelengthin A. By comparison with Fig. 1.9 it is clear that BLRG and NLRG are the radio–active analogous oftype 1 and type 2 AGN.

1.3.2 The central engine

From the discussion above we have seen that the optical spectra of AGN share commonproperties and that they can be broadly classified into two main categories, type 1 and type2 AGN. Some ehibit very powerful jets and radio emission, some don’t. In any case, theluminosity from the point–like nucleus is comparable or even much larger than the integratedluminosity of all stars in the host galaxy.

It is instructive to consider the size of the emitting region. One possible approach is toconsider the variability of AGN. Consider a familiar analogy, a electric light bulb surroundedby a spherical lampshade. When the elctric bulb is turned on the light from the bulb travelsat speed c and reaches the lampshade after a certain time ∆t = R/c where R is the radius ofthe spherical lampshade. If the lampshade is large, say the size of Earth’s orbit oround theSun (1AU = 1.5 × 1013 cm), this delay is about 500 s. Now suppose the light bulb flickerseveral times a second: what will an observer see? It is clear that the lampshade will flickerat the same rate as the electric bulb, but this will have little effect on the observed brightnessof the lampshade because each individual flicker will take 500 s to reach the lampshade sothat subsequent flickers are mixed together and the variability is completely washed out. Theargument can be inverted to say that if the observer is able to detect variability in a timescale

16 BH accretion

0 5×104 105

010

2030

Cou

nts/

s

Time (s)

Figure 1.12: X–ray light curve of the type 1 AGN MCG–6-30-15 as observed with the XMM–Newtonsatellite.

∆t, then the source size must be smaller than R = c∆t.

Now, let’s consider AGN variability, for example in the X–rays. In Fig. 1.12, we show theX–ray light curve from the AGN MCG–6-30-15. Form the Figure it canbe seen that significant(50 %) variability is detected down to timescales as short as few thousands seconds. To beconservative, let assume a ∆t ∼ 104 s. This means that the size of the X–ray emitting regionmust be R < 3× 1014 cm, only 20 times Earth’s orbit around the Sun. It should be remindedhere that we are talking of enornous amounts of power radiated from such a tiny volume ofspace. In fact, as discussed earlier, AGN often outshine the whole galxy which means thattheir luminosity is something like the luminosity of 1010 stars. It is clearly impossible to puttogether 1010 stars in such a tiny volume.

Such large amount of luminosity can only be provided by accretion onto a supermassiveblack hole in the center of the galaxy. If we consider a 107 M⊙ black hole, a size of 3×1014 cmcorresponds to about 200 rg, a totally reasonable size for e.g. the inner regions of an accretiondisc around a black hole. In fact, the black hole in MCG–6-30-15 is most likely smaller, whichlimits the X–ray emitting region to a mere ∼ 50 rg.

AGN are therefore clearly powered by accretion onto supermassive black holes. As dis-cussed in Chapter 2, supermassive black holes are thought to be present in the center of allgalaxies (icluding ours). AGN are simply galaxies in which the central black hole is able toaccrete gas from its surroundings in an efficient way. To create an AGN, gas must be presentin the inner regions of the galaxy to feed the black hole. Once the black hole fuel is exhausted,the black hole become dormant and the galaxy is not an AGN anymore, just an ordinaryinactive galaxy.


Figure 1.13: Popular schematic unification model for AGN. The supermassive black hole is sur-rounded by a thin accretion disc providing most of the power. At larger scales, a dusty molecular torusis present providing the gas supply. Jets are sometimnes formed in the direction perpendicular to theaccretion system. The narrow line region if made of clow density clouds far off from the center, whilethe broad line region clouds are denser and closer to the black hole (hence they have higher velocitiesand produce broad lines). The type 1/2 difference is mainly an orientation effect. In type 2 AGN theline–of–sight intercepts the torus which obscures the broad line region so that the optical spectrumonly contains the narrow lines. Type 1 AGN are seen more face–on and therefore both the narrow andthe broad line region are visible.

1.3.3 The unified model of AGN

In Fig, 1.13 we show a schematic view of the most popular ideas for a unified model for AGNs.The supermassive black hole at the center accretes matter in an accretion disc which producesthe observed huge luminosity. The accretion disc is then surrounded by a dusty torus. The gapbetween the torus edge and the black hole is filled by the broad–line region clouds which havethus high velocities and account for the broad emission lines seen in the optical spectra of type

18 BH accretion

Figure 1.14: NGC 5252 is a relatively nearby type 2 AGN. The colored area show emission from thenarrow–line region. Blue and red regions indicate gas moving towards and away from us respectively.The shape of the emitting region reveals that the gas is most likely illuminating by radiation escapingfrom the poles of the obscuring torus.

1 AGN. Further away, the lower density narrow–line regions are responsible for the narrowemission lines seen in the optical spectra of both type 1 and type 2 AGN. A jet is sometimespresent as well. In this scheme, the most important difference between type 1 and type 2AGN is simply due to orientation effects. When the line–of–sight intercepts the torus, thebroad–line region cannot be seen directly and therefore the optical spectrum only comprisesnarrow emission lines (type 2 AGN). On the other hand, when the system is seen face–on (i.e.with a line–of–sight close to the axis of symmetry and which does not intercept the torus) theobserver can see both the narrow and the broad line regions: the optical spectrum comprisesboth narrow and broad emission lines and the AGN is classified as a type 1 AGN.

This simplified picture can thus explain the difference between type 1 and type 2 AGN.Moreover, it also explains the infrared emission (seen in the spectra of AGN) as reprocessingof the higher energy emission from the accretion by the dust in the molecular torus. Also,the gas clouds in the narrow and broad line region emit their emission lines because they areheated and irradiated by the central engine. If the torus block this radiation, what escapeshas a cone–like geometry and one may expect that the narrow–line region also exhibit such

1.4 The relativistic Fe line 19

Figure 1.15: In the left panel we show the galaxy NGC 4261 (grey) and its radio jet (and lobes). Inthe right panel a zoom of the central region is obtained with the HST and shows the presence of adusty torus surrounding the bright AGN. Compare with Fig. 1.13.

a cone–shaed geometry that should be particularly clear in AGN seen edge on, i.e. in type2 AGN. Indeed, observations confirmed that picture. In Fig. 1.14 we show the shape of theemission from the narrow line region in a type 2 AGN (NGC 5252) confirming the cone–like geometry expected is the unification scheme represented in Fig. 1.13 holds. Many otherobservational aspects have been used to build the unification scheme only sketched above, andmany subsequent results have shown that the picture is correct at least at first order. Oneexample is provided by NGC 4261, a nearby radio galaxy. In the left panel of Fig. 1.15 weshow the superposition of the optical image of the galaxy (grey) and the radio emission fromthe jets and lobes (yellow). In the right panel we show an optical image from the HubbleSpace Telescope which reveals the presence of a very small scale dusty torus surrounding thenucleus of the AGN. The similarities with Fig. 1.13 are striking.

1.4 The relativistic Fe line

We have seen that irradiation of the disc material by the power law originating in the coronaabove the disc gives rise to a characteristic reflection spectrum (see left panel of Fig. 1.3).However, if the reflection spectrum, and therefore the Fe line, originates from the accretiondisc, the line shape is distorted by Newtonian, special and general relativistic effects (see e.g.

20 BH accretion

0.5 1 1.5

Line profile

Gravitational redshiftGeneral relativity

Transverse Doppler shift

Beaming

Special relativity

Newtonian

Figure 1.16: The profile of an intrinsically narrow emission line is modified by the interplay of

Doppler/gravitational energy shifts, relativistic beaming, and gravitational light bending occurring in the

accretion disc (from Fabian et al 2000). The upper panel shows the symmetric double–peaked profile from

two annuli on a non–relativistic Newtonian disc. In the second panel, the effects of transverse Doppler shifts

(making the profiles redder) and of relativistic beaming (enhancing the blue peak with respect to the red) are

included. In the third panel, gravitational redshift is turned on, shifting the overall profile to the red side and

reducing the blue peak strength. The disc inclination fixes the maximum energy at which the line can still

be seen, mainly because of the angular dependence of relativistic beaming and of gravitational light bending

effects. All these effects combined give rise to a broad, skewed line profile which is shown in the last panel,

after integrating over the contributions from all the different annuli on the accretion disc.

Fabian et al 2000; Fabian & Miniutti 2007).

This is illustrated schematically in Fig. 1.16. In the Newtonian case, each radius on thedisc produces a symmetric double–peaked line profile with the peaks corresponding to emissionfrom the approaching (blue) and receding (red) sides of the disc. Close to the BH, where orbitalvelocities become relativistic, relativistic beaming enhances the blue peak with respect to thered one, and the transverse Doppler effect shifts the profile to lower energies. As we approachthe central BH and gravity becomes strong enough, gravitational redshift becomes importantwith the effect that the overall line profile is shifted to lower energies. The disc inclination


Figure 1.17: Left panel: The dependence of the line profile from the observer inclination is shown.

Right panel: The dependence of the line profile from the emissivity profile on the disc is shown. The disc

emissivity is assumed to scale as ǫ = r−q . The steeper the emissivity, the broader and more redshifted

the line profile, because more emphasis is given to the innermost radii where gravity dominates.

fixes the maximum energy at which the line can still be seen, mainly because of the angulardependence of relativistic beaming and of gravitational light bending effects. Integrating overall radii on the accretion disc, a broad and skewed line profile is produced, such as that shownin the bottom panel of Fig. 1.16. It is clear from the above discussion that the detailed profileof a broad relativistic line from the accretion disc has the extraordinary potential of revealingthe dynamics of the innermost accretion flow in accreting BHs and even of testing Einstein’stheory of General Relativity in a manner that is unaccessible to other wavelengths.

1.4.1 Dependence on disc inclination and emissivity

The relativistic line profile exhibits a dependence for many physical parameters. The energyof the blue peak of the line is mainly dictated by the inclination of the observer line of sightwith respect to the accretion disc axis. This is clear in the left panel of Fig. 1.17 where weshow the result of fully relativistic computations (e.g. Fabian et al 1989; Laor 1991; Dovciak,Karas & Yaqoob 2004 among many others). The three profiles have all the same parametersbut different observer inclination i. From the figure, it is clear that the higher the inclinationthe bluer the line is, providing a quite robust tool to measure the inclination of the accretiondisc.

Another important parameter is the form of the emissivity profile, i.e. the efficiency withwhich the line is emitted as a function of the radial position on the disc. This depends mainlyon the illumination profile by the hard X–rays from the corona which is in turn determined bythe energy dissipation on the disc and by the heating events in the corona (possibly associatedwith magnetic fields see e.g. Merloni & Fabian 2001a,b). The emissivity profile is generallyassumed to be in the form of a simple power law ǫ(r) = r−q, where q is the emissivity index(but see e.g. Beckwith & Done 2004). By assuming that the emissivity is a good tracer ofthe energy dissipation on the disc, the standard value for the emissivity index is q = 3 (e.g.

22 BH accretion

Figure 1.18: Left panel: Computed X–ray reflection spectra as a function of the ionization parameterξ (from the code by Ross & Fabian 2005). The illuminating continuum has a photon index of Γ = 2and the reflector is assumed to have cosmic (solar) abundances. Right panel: Relativistic effects on theX–ray reflection spectrum. We assume that the intrinsic rest–frame spectrum (dotted blue) is emittedin an accretion disc and suffers all the relativistic effects discussed above (see text for details). Therelativistically–blurred reflection spectrum is shown in red.

Pringle 1981; also Reynolds & Nowak 2003 and Merloni & Fabian 2003 for a discussion on thedependence of the emissivity profile on boundary conditions). In the right panel of Fig. 1.17,we show the dependence of the line profile from this most important parameter. We show thecases of a uniform (q = 0), standard (q = 3), and steep (q = 6) emissivity profile. A steepemissivity profile indicates that the conversion of the X–ray photons from soft to hard in thecorona is centrally concentrated thereby illuminating more efficiently the very inner regions ofthe accretion disc. As shown in the figure, steeper emissivity profiles produce much broaderand redshifted lines because more weight is given to the innermost disc, where gravitationalredshift dominates.

1.4.2 Self–consistent ionized reflection models

So far, we have assumed that the disc (or to be more precise its outer layers) is a slab ofuniform density gas where hydrogen and helium are fully ionized, but all the metals areneutral. The real situation is likely to be much more complex. One first important steptowards the accurate model of accretion disc atmospheres is made by considering thermal andionization equilibrium. Results of such computations have been published over the last tenyears or so with different degrees of complexity (e.g. Ross & Fabian 1993; Matt, Fabian &Ross 1993, 1996; Zycki et al 1994; Nayakshin, Kazanas & Kallman 2000; Rozanska et al 2002).See Ballantyne, Ross & Fabian 2001 for a comparison between different hypothesis such asconstant–density atmospheres and atmospheres in hydrostatic equilibrium. The recent workby Ross & Fabian (2005) extending and improving previous computations (e.g. Ross, Fabian& Young 1999; Ballantyne, Ross & Fabian 2001) is described here in some detail since it isused extensively in comparing X–ray data to theoretical models.


The illuminating radiation is assumed to have an exponential cut–off power law form withhigh–energy cut–off fixed at 300 keV and variable photon index Γ between 1 and 3 roughlycovering the observed range. The ionization parameter ξ is defined as the ratio between theisotropic total illuminating flux and the comoving hydrogen number density of the gas; resultsare produced for ξ ranging from 1 erg cm s−1 to 104 erg cm s−1. The local temperatureand fractional ionization of the gas are computed self–consistently by solving the equations ofthermal and ionization equilibrium and ions from C, N, O, Ne, Mg, Si, S, and Fe are treated.The available model grids allow for a variable Fe abundance.

In the left panel of Fig. 1.18 we show X–ray reflection spectra produced by the code forthree different values of the ionization parameter (all other parameters being fixed). Theionization parameter has clearly a large effect on the resulting spectrum, most remarkablyon the emission lines. For ξ = 104 erg cm s−1 (top black) the surface layer is very highlyionized and the only noticeable line is a highly Compton–broadened Fe Kα line peaking at7 keV. The overall spectral shape closely resembles that of the illuminating continuum (acut–off power law with photon index Γ = 2). For ξ = 103 erg cm s−1 (middle blue) thestrong Fe Kα line is dominated by the Fe XXV intercombination line, while Kα lines fromthe lighter elements emerge in the 0.3-3 keV band. Further reducing the ionization parameterto ξ = 102 erg cm s−1 gives rise to a spectrum dominated by emission features below 3 keVatop a deep absorption trough. The most prominent feature is the Fe Kα one at 6.4 keV. Noresidual Compton broadening of the emission lines is visible.

In the right panel of Fig. 1.18 we show two versions of a model with ionization parameterof ξ = 2 × 102 erg cm s−1. The blue one is the X–ray reflection spectrum in the absence ofany relativistic effect, whereas in red we show the relativistically–blurred version of the samemodel, i.e. the spectrum that is observed if reflection occurs from the accretion disc. All sharpspectral features of the unblurred spectrum (blue) are broadened by the relativistic effectsexplained above which makes it difficult to identify clear emission lines in the soft spectrum.Below about 2 keV the situation is often complicated by the presence of absorption/emissionfeatures due to photoionized gas complicating the soft part of the spectrum (see Fig. 1.18,left panel). Thanks to its strength, isolation, and to the fact that it occupies a region of theX–ray spectrum relatively free from absorption, the Fe line is however clearly seen. This iswhat makes this particular emission feature a remarkable and unique tool that allows us toinvestigate the dynamics of the innermost accretion flow via relativistic effects in accretingBH systems.

1.4.3 Dependence on the inner disc radius

Einstein’s equations imply the existence of an innermost radius within which the circularorbit of a test particle in the equatorial plane is no longer stable. This radius is known as theInnermost Stable Circular Orbit (ISCO), sometimes referred to as the marginal stable orbit(Bardeen, Press & Teukolsky 1972). Beyond the ISCO, test particles rapidly plunge into theBH on nearly geodesic orbits with constant energy and angular momentum. By making thestandard assumption that the accretion disc is made of gas particles in circular, or nearlycircular, orbital motion, the disc extends down to the ISCO, and emission from the plungingregion is ignored. We shall discuss further this assumption in the next Section.

24 BH accretion

Figure 1.19: Left panel: The dependence of the ISCO from the BH spin. We consider the allowed

spin range from a/M = 0 (Schwarzschild solution) to a/M = 0.998 (Maximal Kerr solution). For these

extremal cases, the ISCO is located at 6 rg (a/M = 0) and ≃ 1.24 rg (a/M = 0.998). Right panel: The

line profiles dependence from the inner disc radius is shown for the two extremal cases of a Scwarzschild

BH (red, with inner disc radius at 6 rg) and of a Maximal Kerr BH (blue, with inner disc radius at

≃ 1.24 rg)

The actual radius of the ISCO depends on the BH spin parameter a/M which can takeany value for 0 (Schwarzschild BH) to 1 (maximally spinning Kerr BH). As pointed out byThorne (1974), the maximal value for the spin parameter is likely to be about 0.998 and weshall refer to that case as “Maximal Kerr”. The dependence of the ISCO from the BH spinparameter is illustrated in the left panel of Fig. 1.19. The ISCO lies at 6 rg from the centrefor a Scwarzschild BH, and at ≃ 1.24 rg for a Maximal Kerr one, where rg = GM/c2 is thegravitational radius. It should be stressed that the dependence is quite steep. If emission fromsay 3 rg can be detected the implied BH spin would be a/M > 0.78. Notice that accretionnaturally causes a BH to spin up provided the disc angular momentum is oriented as that ofthe hole (the possible history of the spin of massive BHs is discussed e.g. by Volonteri et al2005 and references therein).

The inner boundary of the accretion disc, i.e. the location of the ISCO, has a large impacton the shape of the line profile, especially on its broad red wing. This is shown in theright panel of Fig. 1.19 where the cases of a Schwarzschild (red) and Maximal Kerr BH(blue) are computed. The line is much broader in the Kerr case because the smaller innerdisc radius implies that the line photons are suffering stronger relativistic effects (such asgravitational redshift) which is visible in the resulting line profile. To summarise, the detectionand modelling of a relativistic broad Fe line via X–ray observations of accreting BH potentiallyprovides crucial information on the system inclination, the radial efficiency of the coronal hardX–ray emission, and also on one of the two parameters that characterise the Kerr solution,i.e. the BH spin.

Chapter 2

Observational evidence for blackholes

The current observational evidence for black holes in the Milky Way and in other galaxies isbriefly reviewed.

2.1 The Galactic centre

The inner few parsecs around the centre of our Galaxy, the Milky Way, have been extensivelyexplored observationally in recent years. The Galactic Centre (GC) is complex and comprisesseveral different components ranging from a cluster of young and evolved stars, to diffusehot gas and a powerful supernova remnant (the full list being longer). At a distance of only8 kpc, the GC is obviously the closest nucleus of a galaxy, 100 to 1000 times closer than thenearest extragalactic systems. It is therefore a unique laboratory for the study of the physicalprocesses occuring there and which are likely to occur also in the unuclei of extragalacticsystems. Despite its proximity, observations of the GC are very challenging. This is due tothe presence of interstellar gas and dust which is opaque to optical and ultraviolet (UV) light.The extinction is so severe that approximately only 1 : 1012 photon is trasmitted and can bedetected in the optical. On the other hand, absorption is much less severe in the radio, infrared(IR) and X–ray regimes. These portions of the electromagnetic spectrum are therefore themost important tools for the observational study of the GC.

Here we focus on the very inner region around the GC and, more specifically around thecompact radio source Sgr A*, discovered in 1974 (Balick & Brown). Observations of thisinnermost region in the radio, IR, and X–ray bands, coupled with theoretical arguments, haveled to the widely accepted conclusion that Sgr A* is located at the dynamical centre of theGalaxy and that it is associated with a massive, compact and dark mass concentration, bestexplained by the presence of a supermassive black hole. At present, Sgr A* and its immediateenvironment offer the strongest observational evidence for the existence of supermassive blackholes in the Universe. The arguments and observations that led to this conclusion are brieflyreviewed here.

26 Evidence for BHs

Figure 2.1: Left: A 2 pc× 2 pc radio (at λ = 2 cm) image around Sgr A* (brigth central spot). Thefilamentary structure surrounding SGr A* is known as Sgr A West and is associated with gas and dust,most likely ionized by bright stars. Right: An HST NICMOS image of roughly the same field seen inthe left panel. Sgr A* is right in the middle but not seen at these wavelengths (1.6 µm). The centraldistribution of bright stars is likely to be the most important ionizing source of Sgr A West.

2.1.1 The radio source Sgr A*

Radio observations of the GC region by Balick & Brown (1974) led to the discovery of acompact radio source, a discovery later confirmed by Ekers et al (1975) and by Lo et al(1975). Later on, the source was named Sgr A* to distinguish it from the extended radioemission in the surrounding region (see left panel of Fig. 2.1), which is most likely ionized by adistribution of bright stars (right panel). Higher resolution observations with the Very LargeArray (VLA) indicated that Sgr A* is located near the dynamical center of the hot gas (seeFig. 2.1, left panel), as already inferred from infrared spectroscopy (Lacy et al 19080; Brown,Johnston, & Lo 1981). In fact, the ionized gas spiral–like structure seen in the left panel ofFig. 2.1 rotates in the counter–clock wise direction around Sgr A* with a velocity of about150 km s−1 (Serabyn et al 1988).

Early on, Sgr A* was also found to be unresolved in size, i.e. smaller than the availablespatial resolution of the observations, ruling out an extended nature of the radio source. Radiovariability was also detected (Brown & Lo 1982), which is also inconsistent with an extendedsource or with the suprposition of many different radio sources, suggesting a compact natureof Sgr A*. The size of Sgr A* is actually difficult to measure directly from radio observations.This is mainly because the true structure is washed out by scattering of the radio emission inthe interstellar medium. However, by performing observations at very high frequency (wherethe scattering angle is reduced) a size of ∼ 1 AU (≃ 1.5×1013 cm) for the radio source Sgr A*

2.1 The Galactic centre 27

Figure 2.2: A composite image of the innermost parsec of the Galaxy obtained at the VLT (Genzelet al 2003). The image is a composite of the H, K, and L infrared bands (from 1.65 to 3.76 νm). Theposition of Sgr A* is marked by arrows.

has been recently derived (Shen et al 2005).

Another important factor in determining the nature of Sgr A* is its precise position inthe Galaxy. If Sgr A* is really located at the GC and represents the dynamical centre of thewhole Galaxy, its proper motion should be consistent with the apparent motion induced bythe Galactic rotation of our own Solar system. One possible way to determine the positionof a radio source is to measure the relative position of Sgr A* with respect to very distantextragalactic sources. Since the extragalactic sources have little motion on the sky (due totheir cosmological distances), one can infer the proper motion of Sgr A* which turns out to be1) constant over time, and 2) entirely consistent with 220 km s−1, which is nothing else thanthe Galactic rotation of our Solar system around the GC (Reid et al 1999). After removalof the Galactic rotation, any proper motion intrinsic to Sgr A* is limited to have a velocityof only 0 ± 15 km s−1. This implies the Sgr A* is indeed located at the GC with very littleuncertainty.

Summarizing, Sgr A* is a compact and variable radio source with a size of ∼ 1.5×1013 cmand located, with almost no ambiguity, at the dynamical centre of the Galaxy. In the following,we shall see how detailed studies of the stellar motions in its immediate vicinity stronglyindicate that Sgr A* is powered by a supermassive black hole sitting at the GC. For a reviewon the radio properties and on the mechanisms producing the radio emission of Sgr A*, seee.g. Melia & Falcke (2001).

28 Evidence for BHs

2.1.2 Stellar motions in the GC region

The most remarkable results about the nature of Sgr A* come from the analysis of stellardynamics in the innermost region of the GC. The idea is that by following the motion ofindividual stars close to Sgr A*, one could in principle be able to 1) verify that the the radiosource really coincides with the dynamical center of the Galaxy, and 2) estimate its mass inorder to obtain clues on its nature.

As mentioned, the observed properties of Sgr A* already suggested that the radio source isassociated with a massive compact dark matter distribution sitting at the dynamical centre ofthe Galaxy, pointing towards the presence of a supermassive black hole. However, definitiveproof regarding the existence of a black hole and its association with Sgr A* lies in theassessment of the real mass distribution in the few central parsecs of the Galaxy. If gravityis the dominant force, the motion of the stars in the vicinity of the putative black hole willpotentially reveal the mass enclosed within their orbits, providing vital tests of the black holehypothesis for Sgr A*. Stars are good tracers of the gravitational potential because, unlike gas,their motion is not strongly affected by non–gravitational forces (e.g. thermal and radiationpressure, magnetic fields), but it is obvious that probing the motion of individual stars in avery crowded region such as the GC presents significant challenges.

Firstly, as mentioned above, observing stars in the innermost GC region proves very chal-lenging: stars normally emit most of their luminosity in the optical and UV, but the extinctiondue to gas and dust in the GC means that these wavelengths are almost unobservable. Ex-tinction is still large but much less important in the IR. On the other hand, IR radiation is ab-sorbed by the Earth atmosphere. However, the presence of atmospheric transmission windows(primarily in the K–band at 2.2µm) enables to observe the IR emission from ground–basedtelescopes. This is demonstarted by the false color composite image of the central pc of theGalaxy (see Fig. 2.2), obtained with the Very Large Telescope (VLT) in the H, K, and Linfrared bands (Genzel et al 2003a). The GC comprises a mixture of old red giant and young(hot) blue stars, while in the very inner region (< 0.05 pc or so), no bright giants are seenand only faint blue stars are detected. This population of stars is known as the S–stars (orthe S–cluster). They are identified as massive main sequence stars (with masses in the rangeof 3–15 M⊙) and are the most important stellar population for the dynamical study of theimmediate vicinity of Sgr A*.

A second technical challenge is represented by the need for very high angular (spatial)resolution to avoid confusion between stars. High resolution is in general difficult to achieveeven from the largests available ground–based telescopes, mainly because of time–variableatmospheric distortions that limit the image resolution (seeing). In practice, atmospheric tur-bulence distorts the otherwise planar incoming wavefronts and is responsible for producinga time–variable spread of the image of a point–like source on the detector plane. However,different techniques have been devised to correct for the atmospheric distortions and to recoveroptimal resolution in the IR. Among these, Speckle imaging and adaptive optics are very ef-fective. The former involves taking hundreds (or even thousands) very short exposures imagesof an object to freeze the distortions, and later combine them to recover a high resolutionimage. On the other hand, adaptive optics works by measuring the distortion on a referencestar (or a laser beam used to generate a reference source), and by rapidly compensating for it


Figure 2.3: An image of a double star demonstrating some of the capabilities of the PUEO AdaptiveOptics Bonnette of the Canada-France-Hawaii Telescope. The double star separation is 0.276 arcsec,roughly a factor 2 smaller than what is possible to resolve given the typical seeing at the telescopelocation (see the uncorrected image on the left). As can be seen from the right image, such an angularseparation is however an easy target once adaptive optics techniques are implemented.

using deformable mirrors or material with variable refractive properties (see Fig. 2.3 for oneexample).

Two major groups have carried out extensive observations of the central S–cluster stars inthe IR (respectively based at the Max-Planck-Institut fur extraterrestrische Physik in Germanyand at the University of California, Los Angeles). In order to determine the mass enclosedwithin a certain volume from stellar dynamics, two approaches are possible. One is statisticalin nature, and typically requires a very large large sample of stars, but not many data on eachsingle star (and so was the first to be applied). The second involves the derivation of partialor full orbital solutions for individual stars. In principle, a single well sampled stellar orbit isall that is needed to obtain the mass and location of the central dark mass.

Following initial attempts to probe the potential of the central dark mass by gas kinematics(Lacy et al 1980), the use of stellar kinematics progressed to include radial velocities (e.g.Genzel et al 1997), stellar proper motions (Eckart & Genzel, 1996; Ghez et al 1998), andstellar accelerations (Ghez et al 2000; Eckart et al 2002). Finally, it is now possible, using high-precision infrared astrometry and spectroscopy, to follow the trajectories and radial velocitycurves of individual stars as they orbit Sgr A*. Here we focus on this latter technique and, inparticular, on the work of the European–based group of Genzel and collaborators.

Before considering more specifically the stellar dynamics around Sgr A*, it should bementioned that, Sgr A* is a radio source, but is very faint in the IR, where stellar dynamicsobservations are carried out. Therefore, the accurate position of Sgr A* in an IR image is notnecessarily known with the required accuracy. It is thus necessary to pinpoint the location ofthe radio source Sgr A* in the IR frame, where the stars are observed and where the dynamicalcenter is identified. This was achieved by the important discovery of 7 red giant stars whoseextended envelopes emit radio maser radiation from a molecular transition of SiO (the maser

30 Evidence for BHs

Figure 2.4: Projected acceleration vectors and their 2σ error cones for the stars S 1, S 2, S 8, S 12,and S 13 of the S–cluster. The grey scale is a χ2 map of the position of the center of accelerationwhere 1 and 2σ contours are plotted as white contours (fits exclude the more uncertain oS 13 data).The position of Sgr A* is marked with a crossed white circle and is totally consistent with being thedynamical center of the system.

emission is a coherent emission analogous to laser light). Since these stars are also brightIR sources, it was possible to align with very high accuracy the radio and IR maps of theGC obtaining two coincident reference frames in the two bands. This enabled to recover theprecise position of Sgr A* relative to the IR frame of the stellar observations. Subsequently,the knowledge of the precise position of Sgr A* in the IR allowed Genzel et al (2003b) andGhez et al (2004) to detect IR emission from Sgr A* itself.

2.1.3 Weighting Sgr A*

The first step toward orbital reconstruction is to detect accelerations (curvature) in the stellarmotion. Accelerations play two major roles: firstly, the projected acceleration vectors pointtoward the position of the center of the acceleration, i.e. the dynamical center of the system;secondly, when associated with Keplerian laws, they provide tight constraints on the densityof the dark mass (m) enclosed within the radius r of the orbit via:

ρ =3

4π

m

r3=

3

4πG

r

r=

3

4πG

p

p. (2.1)


Figure 2.5: Projection on the sky (left) and radial velocity (right) of the six stars included in theorbital fitting (Eisenhauer 2005)

When the inclination i of the orbit is not known, the acceleration provides a lower limit forthe mass (assuming its distance to us is R)

m ≥R3pp2

G≡ m cos3 i . (2.2)

As for the acceleration vectors, Schodel et al (2003) have shown that, for the best sam-pledfour stars in the S–cluster, they all point toward Sgr A*. This is shown in Fig. 2.4. Thestar S 13 acceleration vector does not seem to point to SGR A*. However, this is one of thefaintests star in the sample and the orbital parameters were derived from epochs in which thestar was very close to S 1, making the acceleration much more uncertain. The contours inthe Figure show the best estimate of the dynamical center for the remaining 4 stars whichis totally consistent with SGR A* (indicated by the crossed circle). On the other hand, themeasure of the acceleration of a few stars in the innermost 0.5 arcsecond from Sgr A*, provideda lower bound of m ≥ 106 M⊙ for the enclosed mass assuming a distance of 8 kp for the GC(Ghez et al 2000; Eckart et al 2002; Schodel et al 2003).

This lower limit on the mass of the central object can be refined if more orbital information(than simply accelerations) are available. In fact, the stars S 2, S 12 and S 14 orbit Sgr A*sufficiently close that observations in the last decade have made possible to obtain uniquesolutions for their Keplerian orbits. Other stars, such as S 1, S 8, and S 13 do not allow foran independent unique solution, but the partial orbits that have been observed can be usedin combination with the others to obtain a global solution for the orbits of up to six stars.However, as clear from eq. 2.1 and 2.2, there is a remaining degeneracy: only the ratio m/R3

is constarined, but not the two quantities separately. This degeneracy can be resolved with

32 Evidence for BHs

Figure 2.6: IR (1.65µm) images of the GC before and during the flare detected in 2003. Time (t) isin minutes. The images clearly show the variability of the IR emission from the black hole location(marked with a circle).

radial velocity information: in practice the radial velocity (i.e. the velocity in the line of sight)is determined via the Doppler shift of a given spectral feature in terms of an absolute velocity,whereas the proper motion p is measured in terms of an angular velocity. The two are tiedtogether by the orbital solution which relates the line of sight (z) and projected (p) velocitiesthrough the distance R as

〈z2p〉 = R2〈

(

2

3p2‖ +

1

3p2⊥

)

p〉 . (2.3)

Fig. 2.5 shows the best–determined orbits for the six S–stars mentioned above as projectedon the sky (left). In the right panel, the radial velocities as a function of time are shown.The solid lines in both panels indicate the best–fitting orbital results which only assume theKeplerian nature of the motion. By making use of the derived radial velocities and propermotions, the distance of the dynamical center can be estimated to be R = 7.62 ± 0.32 pc(Eisenhauer 2005) and by combining this information with the orbits derived via the fttingprocedure, the mass of center of the acceleration turns out to be m = 3.6 ± 0.3 × 106M⊙.

Such a mass estimate can be combined with the size of Sgr A* which was obtained (atleast as an upper limit) via radio observations. As mentioned, a size of ∼ 1 AU≃ 1.5×1013 cmhas been recently derived by Shen et al (2005) for the radio source. For a ∼ 3.6 × 106M⊙

black hole, the Scwarzschild radius is RS ≃ 1.06 × 1012 cm. This means that radio activityfrom Sgr A* is detected as close as ∼ 14 RS from the center. Any alternative to a black holefor Sgr A* must be able to concentrate a mass of ∼ 3.6 × 106M⊙ within that small radius,which seems highly unlikely. In fact, almost all alternatives to a supermassive black hole inthe GC have been ruled out in the past decade as observations became more accurate. The


Figure 2.7: Flux densities light curves for Sgr A* (blue) and for the star S 1, shown for comparison(and multiplied by a factor 2 for better presentation). The IR flares of Sgr A* are clearly seen. Thearrows mark the temporal structure which may suggest the presence of a quasi–periodic modulationwith period of ∼17 min.

observational evidence for the presence of a black hole is indeed overwhelming and there isnow a wide consensus on the idea that out Galaxy hosts a supermassive black hole at its verycenter.

2.1.4 Sgr A* fast variability

As mentioned, Sgr A* is very faint in the IR. The precise location of the putative sourceobtained thanks to the alignement of radio and IR images (see above) was crucial for itsdetection. However, during routine observations of the GC in 2003, a powerful IR flare wasdetected at the location of the black hole (Genzel et al 2003b). Within a few minutes, theflux increased by a factor of 5-6 and fainted again after about 30 min. The short variabilitytimescale can be immediately associated with a source size. The light travel time across theSchwarzschild radius of a 3.6×106M⊙ black hole is about 35 s. Therefore, the few minutes riseand decay timescale of the flare would suggest that emission is coming from within 10–20 RS

only, providing further evidence for the black hole nature of the source. Moreover, a temporalstructure was observed in subsequent flare with a (tentative) periodicity of about 17 min.Athough the statistical significance of the periodicity is not impressive, it is interesting tocompaire it with a natural periodic modulation, i.e. with the orbital period of matter matterorbiting the black hole in an accretion disc. It is in fact likely that the flares are due tooccasional events in which gas is accreted onto the black hole, forming a temporary accretiondisc structure and releasing IR emission in the process. The orbital timescale for a geodesic

34 Evidence for BHs

.Figure 2.8: Relation of MBH versus (1 − a). Each curve represents one period assigned to a specificgravitational mode, coded by a label (LT: Lense–Thirring; K: Keplerian; R: radial epicyclic; V: verticalepicyclic). The error region is enclosed by the dashed polygon and points to a ∼ 2.7×106M⊙ maximallyspinning Kerr black hole.

circular orbit in the equatorial plane of around a black hole is given by

Torb = 310[

a + (r/rg)3/2

]

M7 s , (2.4)

where a is the black hole spin and M7 is the black hole mass in units of 107M⊙. If theblack hole is a non–rotating Schwarzschild one (a = 0), the innermost stable circular orbit(ISCO) is at 6 rg, beyond which the motion is almost ballistic. For the black hole massthe GC black hole, the orbital period at the ISCO is therefore Torb ≃ 27 min, longer thanthe observed quasi–periodic modulation of ∼ 17 min. Baring in mind that this is only thesimplest (and not necessarily the rigth) interpretation, this implies that the orbital motionmust occur closer to the black hole, which is allowed by General Relativity only if the blackhole is spinning. Considering the dependency of the ISCO from the black hole spin, a lowerlimit of a > 0.5 on the black hole spin can be set. Although only tentative, the detection ofthe quasi–periodic IR modulation from the GC black hole, together with the most obviousinterpretation, suggests therefore that the GC black hole is a Kerr one, with a spin parameterat least half of the maximum allowed. MOreover, subsequent observation revealed even shorterquasi–periodicities down to 13 min (Trippe et al 2007). By applying the same arguments asbefore, the spin parameter of the black hole would be constrained to be a > 0.7.

The GC black hole has been observed also in the X–rays that can pierce through the gasand dust that characterizes the GC region. X–ray emission from the GC black hole has been

2.2 Supermassive black holes in other galaxies 35

detected and, most remarkably, X–ray variability is present down to very short timescales.In particular bright X–ray flares have been detected, which seem analogous the the IR flaresdiscussed above. Aschenbach et al (2004) have identified some characteristic quasi–periodicoscillations during the X–ray flares. Their statistical significance is rather low, but the sametimescales have been observed in different observations, providing some support for their real(as opposed to noise) nature. The authors identify groups of characteristic timescales withperiods ranging from 100 s to 2180 s and try to assign to each group one of the characteristictimescales expected to be present in an accretion disc due to General Relativity (the Keplerian,vertical and radial epicyclic, and the Lense–Thirring frequencies). Since the characteristicfrequencies depend on the black hole mass and spin, the idea is to infer a best–fitting mass andspin for the black hole based on the assumption that the observed periodicities are associatedwith the General Relativistic characteristic frequencies. What is intersting in this work is thata solution with the same black hole mass and spin does indeed exist for 3 (out of 5) of thegroups identified (see Fig. 2.8). The inferred values are MBH ≃ 2.7 × 106M⊙ and a ≃ 0.99and it is indeed quite remarkable that the black hole mass is so close to that estimated viastellar dynamics, suggesting that the identification of the observed quasi–periodicities withsome of the General Relativistic frequencies (specifically the Keplerian, the vertical, and theradial epicyclic frequencies) is a viable possibility.

Summarizing, the observational evidence for the presence of a supermassive black hole withMBH ≃ 3.6 × 106M⊙ at the GC is overwhelming. Its location coincides with the dynamicalcenter of the stars in the innermost region of the GC and also with the position of the radiosource Sgr A*. The size of the radio source corresponds to only 10–20 Schwarzschild radii fora black hole with that mass. We are thus witnessing emission from close to the event horizonof the GC black hole. Moreover, IR and X–ray variability strongly suggest that the GC blackhole is in fact a spinning Kerr one.

2.2 Supermassive black holes in other galaxies

The GC obviously represents the best opportunity we have to investigate the stellar dynamicsin the sphere of influence of a supermassive black hole. However, a great deal of observationaleffort is devoted to study the inner nuclear region of other galaxies as well to search for thesignature of a supermassive black hole. It is now widely accepted that supermassive blackholes are present in the nuclei of all galaxies and we briefly review here the main observationalresults that led to this conclusion.

2.2.1 Stellar kinematics

The exquisite angular resolution that made it possible to resolve the orbits of individual stars inthe GC is clearly not enough to do the same in extragalactic objects. One has therefore to relyon information on much larger distances from the central putative black hole. Dynamical massmeasurements are conceptially simple. To very good approximation, galaxies can be treatedas collisionless stellar systems in which each star is moving in the combined gravitationalpotential of all other stars. This makes it possible to describe the system analytically throughthe Collisionless Boltzmann Equation (CBE) which relates the distribution function of the

36 Evidence for BHs

Figure 2.9: The velocity dispersion (top) and rotation curve (bottom) profiles from HST observationsof M 31 (Andromeda galaxy). The symmetry point of the rotation curve coindides with the sharp peakin the dispersion, as expected if a supermassive black hole sits at the center of the star motions.

stars (the number of stars in a given volume in the position–velocity phase–space) to thegravitational potential Φ and the velocity field. Obviously, Φ is then linekd to the mass densityvia the standard Poisson’s equation. However, the mass density comprises contributions fromboth the stars themselves and from any other mass distribution which may be dark and thusunobservable. It is precisely the difference between the mass distribution as inferred fromthe direct observation of the stars and the total one, derived from the stellar kinematics, thatwould indicate the need for a central dark mass, possibly a supermassive black hole. In theory,the distribution function can be reconstructed from the stellar mass density and the velocityfield. Once the distribution function is obtained, Φ is derived from the CBE, and the totalmass density (and hence the putative supermassive black hole mass) follows from integrationof the Poisson’s equation. Unfortunately, the procedure is far from trivial because not all thevariables of the system can be retrieved from the data. Therefore, any analysis has to rely onassumptions and modelling (see Ferrarese & Ford 2005 for a critical review).

However, despite the theoretical uncertainties and the observational difficulties, the HubbleSpace Telescope (HST) high resolution allowed to obtain extremely reliable measurements ofthe rotation curves and velocity dispersions in several nearby galaxies. In most (if not allwell studied cases) the rotation curves and peaked velocity dispersion rquires the presence ofa central mass which does not contribute to the galaxy emission (i.e. a dark mass) and thepresence of supermassive black holes in these galaxies seems the simplest explanation. One is


Figure 2.10: HST image of M 87. In the right panel, the galaxy is seen together with its well knownoptical jet. The left inset is an expanded view of the central region, showing the gas and dust disk–likefeature.

shown in Fig. 2.9, where the cusp in the velocity dispersion at the center of the galaxy andthe rotation curve suggest the presence of a central black hole with a mass of ∼ 3 × 107M⊙

in the galaxy M 31 (Andromeda). Many other examples (about 18 so far, see e.g. Kormendy& Richstone 1995; Ferrarese & Ford 2005) of this kind have been observed and almost anygalaxy that has been observed in detail with HST does require a supermassive black hole witha mass of 107 − 109M⊙ in its nucleus.

2.2.2 Gas kinematics

As discussed in the GC Section, the hot gas was soon suspected to orbit Sgr A* hinting at thepresence of a large mass concentration well before the spectacular and conclusive results onproper motions and accelerations of the S–stars. It is thus natural to look for gas kinematics inother galaxies to search for confirmation of the idea that supermassive black holes are presentin the nuclei of most, if not all galaxies. In general, gas kinematics is thought to be lessreliable than stellar motions because gas, unlike stars, is possibly subject to non–gravitationalaccelerations (e.g. radiation pressure). However, spectacular HST spectra of the ellipticalgalaxy M 87 have convinced the community that gas motion can also be used reliably toestimate the gravitational potential and the putative black hole mass.

As can be seen in Fig. 2.10, images of the inner regions of M 87 revealed the presenceof a gas/dust disk–like structure. Spectroscopy carried out at diffrent locations from thecenter of the disk showed that the gas velocity was as large as 500 km s−1 either side of thenucleus (with different sign) strongly suggesting a Keplerian–like rotation curve, such as that

38 Evidence for BHs

Figure 2.11: Rotation curve from emission–lines of the disk–like structure in M 87. The curve isbeautifully Keplerian as demonstrated by a fit with a Keplerian disk model (lower panel) and impliesa central (3.2 ± 0.9) × 109M⊙ supermassive black hole.

seen in the bottom mpanel of Fig. 2.9 (Harms et al 1994). A few years later, a much moreextensive observational campaign was carried out and the quality of the data allowed for verydetailed dynamical modelling to be performed, leaving virtually no doubt as to the presenceof a (3.2± 0.9)× 109M⊙ supermassive black hole in the nucleus of M 87. In Fig. 2.11 we showthe rotation curve that was derived (top) together with the residuals to a fit with a Kepleriandisc model (Macchetto et al 1997).

As for stellar kinematics, other examples followed and at least 11 supermassive blackholes have been discovered to date thanks to gas motion (Ferrarese & Ford 2005) providingcomplementary evidence (with respect to stellar dynamics studies) that black holes are indeedpresent in the nuclei of the galaxies studied so far in enough detail.

2.2.3 Water Maser emission

Besides the compelling case for a supermassive black hole in the GC, the second best evidencecomes from the galaxy NGC 4258 via the study of the 22 GHz maser emission from watermolecules. A maser (microwave/molecular amplification by stimulated emission of radiation) isa device that produces coherent electromagnetic waves through amplification due to stimulatedemission. The most important characteristics of masers is that they are monochromatic,having the frequency corresponding to the energy difference between two quantum-mechanical


Figure 2.12: The spiral Seyfert galaxy NGC 4258 in the constellation of Canes Venatici. Opticalimage from the Kitt peak telescope.

energy levels. In the astrophysical context, masers lack the resonant cavity engineered forterrestrial laboratory masers. Indeed, the emission from an astrophysical maser is due to asingle pass through the gain medium and therefore generally lacks the spatial coherence andpurity expected of laboratory realizations.

Maser emission has been detected in many astrophysical systems from srellar atmospheresand star–forming regions to supernova remnants. Here we specifically focus on maser emissionfrom molecular discs orbiting an accreting supermassive black hole. The huge luminosityreleased by the accretion processes near the black hole acts as the pump source exciting theouter disc molecules responsible for the maser emission. Given the monochromatic nature ofmasers, their study at very high angular resolution potentially provides a unique tool to studythe motion of the molecular disc surrounding the black hole. If the motion is found to beKeplerian or quasi–Keplerian, the mass of the central object can be computed with accuracyand clues on its black hole nature can be obtained.

The most spectacular results in this area come from observations of the spiral active galaxyNGC 4258 (also M 106) shown in Fig. 2.12 in an optical image. The maser emission frequencyof 22 GHz allows to use the Very Long Baseline Array (VLBA) interferometer which canachieve exquisite angular resolution, about 100 times better than that delivered by the HST.Since NGC 4258 is relatively closeby (6 Mpc away), the angular resolution translates intoa remarkable linear resolution of 0.017 pc only (1 pc=3.086×1018 cm), only one order ofmagnitude worse than that obtained in the GC. In Fig. 2.13 we show the spatial and velocitydistribution of the water maser clouds (Miyoshi et al 1995).

The clouds are clearly part of a warped disc–like structure (left panels) and their radialvelocities are extremely well fitted by a Keplerian model (right). The reconstructed structurecan be seen in Fig. 2.14. The high velocities imply the presence of a compact distribution ofmatter with a mass of 3.6× 107M⊙. Moreover, the fact that the radial velocity is so preciselyKeplerian implies that the central mass must be extremely compact and, in fact, comparable

40 Evidence for BHs

Figure 2.13: Left: The spatial distribution of the water maser clouds in NGC 4258 (bottom).The clouds are color–coded according to their measured velocity so that blue and red correspond toblueshifted (moving towards us) and redshifted (moving away from us) clouds. The clouds are clearlydistributed in a narrow ring which is warped. The top panel shows an expanded view of the centralregion which does not show significant signs of a warp. Right: Line of sight velociy as a function ofthe distance along the major axis. The solid line is a fit with a Keplerian model. The velocity near theinnermost region is magnified in the inset.

to the limits on the density of the GC black hole. This is clear evidence that NGC 4258 hostsa supermassive black hole at its very center.

2.3 Stellar–mass black holes

After the rigorus calculation of black hole formatin following the gravitational collapse of mas-sive stellar cores (Oppenheimer & Snyder 1939), the first strong evidence for the astrophysicalexistence of such objects came from X–ray and optical observations of the X–ray binary CygnusX–1 (Bolton 1972; Webster & Murdin 1972). Today, a total of 20 similar binary systems inthe Milky Way are known to contain a compact object believed to be too massive (> 3 M⊙) tobe a neutron star (or indeed a degenerate star of any kind). These systems are now known asGalactic black hole binaries or, in some more uncertain cases, Galactic black hole candidatesand they are thought to be just the tip of the iceberg of a very large population of 108 − 109

black holes in the Milky Way (see Remillard & McClintock 2006 for an excellent review).

2.3 Stellar–mass black holes 41

0.5 ly

Figure 2.14: The warped disc of NGC 4258 modelled from the water maser emission. The black dotin the center marks the dynamical center of the system (i.e. the position of the supermassive blackhole). The shaded color contours are due to jetted emission from the active galaxy.

2.3.1 Identification of black holes in X–ray binaries

Hundreds of point–like luminous X–ray sources are present in our Galaxy (see Fig. 2.15).Their luminosity is typically too high by orders of magnitude to be stellar in nature (theSun luminosity is L⊙ ∼ 1033 erg s−1) but compaires well with the luminosity that can beextracted from the accretion process onto a stellar–mass object. As mentioned elsewhere, thisis the so–called Eddington luminosity LEdd = 1.26× 1038M/M⊙ erg s−1. Such objects, calledX–ray binaries, are now identified with binary systems comprising a massive compact objectaccreting gas and matter from its companion star. Spectra and variability properties can beused to some extent to distinguish between different types of accretion and to gain insights onthe nature of the compact object (a white dwarf, a neutron star or a black hole). However,distinguishing between an accreting neutron star and a black hole is far from unambigous and,in that case, we must consider more secure ways to properly identify the compact object.

The most secure method relies on mass determination. In fact, we know on theoreticalground that the mass of a neutron star cannot exceed ∼ 2.5 M⊙ because for larger masses,the Fermi pressure cannot balance gravity anymore and the neutron star collapses to form ablack hole. Hence, if the mass of the compact object in an X–ray binary can be estimated tobe > 2.5 − −3 M⊙, one can be reasonably certain that the compact object is indeed a blackhole and not a neutron star. The question is thus how to measure the mass of the compactobject in a binary system.

Consider a binary system comprising a star with mass M∗ and a compact object with massMx with orbital separation a and distances from the center of mass a∗ and ax respectively.

42 Evidence for BHs

Figure 2.15: The central region of the Milky Way as seen by the Chandra X–ray observatory.Besides emission from diffuse hot gas, the X–rays reveal hundreds of point–like X–ray sources, mostlikely associated with accreting white dwarfs, neutron stars, and black holes. The GC black hole iswithin the bright central patch.

Obviously, a = a∗ + ax, and M∗a∗ = Mxax, so the third Kepler’s law can be written as

GM∗ + Mx

a3=

(

2π

P

)2

= GM3

x

(M∗ + Mx)2 a3∗

=

(

2π

P

)2

, (2.5)

where P is the orbital period. However, there are still too many unknowns in the equationand we must find a way to measure observationally at least a few of them. The period Pand orbital separation a∗ can be obtained if information about the velocity of one of the twocomponents can be gained via observations. Obviously the compact object velocity cannot bemeasured (especially if it is a black hole!), but we can use spectral features (lines) from thecompanion star to obtain that information. Doppler shifts caused by the orbital velocity ofthe star induce a periodic modulation of the energy of the line (see Fig. 2.16). This can beused to infer the orbital period velocity of the star (projected on the line of sight). Assumingthe orbital plane has an inclination i, the projection of the star velocity on the line of sight issimply

v∗ =2π

Pa∗ sin i , (2.6)

which can be inserted in eq. 2.5 to define the so–called mass function f(M∗,Mx, i):

f(M∗,Mx, i) =(Mx sin i)3

(M∗ + Mx)2=

Pv3∗

2πG, (2.7)

which only depends on the observable on the right–hand–side of the equation. Both P andv∗ can be obtained from the observed periodic Doppler shifts of the star spectral lines (seeFig. 2.16).

2.3 Stellar–mass black holes 43

Figure 2.16: A spectral line from the companion star’s atmosphere has fixed energy (wavelength)in the rest–frame. However, as the star orbits the center of mass, Doppler effects induce a periodicmodulation which is used to obtain its radial velocity.

Figure 2.17: Radial velocity light curves of the companion stars in the X–ray binaries GS 2000+251(left) and Cyg X–1 (right). The observed velocity and orbital period imply a mass function of 5 M⊙

and 0.24 M⊙ respectively.

Moreover, it is easy to see from eq. 2.7 that f(M∗,Mx, i) < Mx, i.e. the mass function isa lower limit on the mass of the compact object. Therefore, if Doppler meaurements from thevisible stellar companion produce a mass function larger than the maximum possible mass fora neutron star, the conclusion is that the compact object must be a black hole. This is the casefor 15 systems in which the presence of a black hole is directly inferred from the mass function.One example (GS 2000+251) is shown in the left panel of Fig. 2.17 for which the orbital data

44 Evidence for BHs

Table 2.1: Twenty confirmed black holes and twenty black hole candidates.

Coordinate Common Year Porb f(M) M1

Name Name/Prefix (hr) (M⊙) (M⊙)

0422+32 (GRO J) 1992 5.1 1.19±0.02 3.7–5.00538–641 LMC X–3 – 40.9 2.3±0.3 5.9–9.20540–697 LMC X–1 – 93.8 0.13±0.05 4.0–10.00620–003 (A) 1975 7.8 2.72±0.06 8.7–12.91009–45 (GRS) 1993 6.8 3.17±0.12 3.6–4.71118+480 (XTE J) 2000 4.1 6.1±0.3 6.5–7.21124–684 Nova Mus 91 1991 10.4 3.01±0.15 6.5–8.21354–64 (GS) 1987 61.1 5.75±0.30 –1543–475 (4U) 1971 26.8 0.25±0.01 8.4–10.41550–564 (XTE J) 1998 37.0 6.86±0.71 8.4–10.81650–500 (XTE J) 2001 7.7 2.73±0.56 –1655–40 (GRO J) 1994 62.9 2.73±0.09 6.0–6.61659–487 GX 339–4 1972 42.1 5.8±0.5 –1705–250 Nova Oph 77 1977 12.5 4.86±0.13 5.6–8.31819.3–2525 V4641 Sgr 1999 67.6 3.13±0.13 6.8–7.41859+226 (XTE J) 1999 9.2 7.4±1.1 7.6–12.01915+105 (GRS) 1992 804.0 9.5±3.0 10.0–18.01956+350 Cyg X–1 – 134.4 0.244±0.005 6.8–13.32000+251 (GS) 1988 8.3 5.01±0.12 7.1–7.82023+338 V404 Cyg 1989 155.3 6.08±0.06 10.1–13.4

indicate a mass function of 5 M⊙, well in excess of the maximum mass of a neutron star.For other 5 systems, such as the famous Cyg XX-1, the mass function is not itself conclusive.For example, the mass function of Cyg X–1 is 0.24 M⊙ only, thereby leaving room for a nonblack hole identification. However, in these 5 cases the nature of the stellar companion isaccurately known and the mass can be derived with very little uncertainty from its spectralproperties. In the case of Cyg X–1, the star’s mass is M∗ > 6.8 M⊙ which, combined withthe mass function, implies that Mx > 9 M⊙, leaving no doubts about the black hole nature ofthe compact object. In Table 2.3.1 we give a list of the 20 confirmed black holes in the MilkyWay with a summary of their main properties.

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