The Massive Black Hole in the Center of the Galaxy

Tal Alexander
Faculty of Physics
Weizmann Institute of Science

1 Massive black holes in context

The phenomenon of black holes is one of the stranger consequences of General Relativity. The interest in these objects originates from two quite distinct perspectives.

From the perspective of basic theoretical physics, black holes are essentially elementary macroscopic objects, since their internal structure is causally disconnected from us. They can be fully characterized by three ``quantum'' numbers: mass, angular momentum and electrical charge. Black holes serve as ``gedanken-laboratories'' in attempts to reconcile quantum mechanics and General Relativity (e.g. Hawking radiation) and to explore the fundamentals of statistical mechanics and information theory (e.g. black hole entropy). Such thought experiments frequently require a microscopic black hole, where quantum effects are significant, or an isolated black hole in vacuum, where adiabatically slow thermodynamical processes can occur. Unfortunately, Nature does not appear to provide us with such black holes. All black holes that have been discovered so far are very massive, and are surrounded by, and interacting strongly with a hot radiating plasma (which also neutralizes any electric charge they may have). Thus, there is little hope of making an experimental connection between actual black holes and these fundamental questions of interest.

The questions of interest from the astrophysical perspective are very different from those of the fundamental physics perspective.

Two classes of black holes are known to exist. The first consists of stellar black holes of roughly $10$ solar masses, which emerge from the collapsing core of massive stars ($>30$ solar masses) that have exhausted their nuclear fuel. The second consists of super-massive black holes with masses in the range of $10^{6}$ to $10^{9}$ solar masses, which are found at the centers of galaxies, one in each galaxy. It is not exactly clear how super-massive black holes are formed. A third class of yet undiscovered intermediate mass black holes is also thought to exist. These may be the missing link between the stellar black holes and the super-massive ones. This web essay will focus on super-massive black holes, and specifically on the one in the center of our home galaxy, the Milky Way.

Black holes play a wide range of roles in current astrophysical research.

Massive black holes as extreme energy sources

The accretion of mass into black holes powers many astrophysical phenomena. It is a seeming paradox that black holes are in fact the most efficient persistent sources of energy in the universe (second in efficiency only to direct matter-antimatter annihilation). The source of the energy is the gravitational potential energy of the matter falling into the black hole. Since the matter reaches the speed of light as it crosses the event horizon (the ``edge'' of the black hole--the point of no return), its kinetic energy is of the order of its rest-mass energy. The effective friction of the inflowing gas on itself as it is squeezed into the small ``drain'' of the event horizon converts a significant fraction of the kinetic energy into radiation and energetic particles. Up to 42% of the gas rest-mass energy can be extracted until the gas finally reaches the point (close to the black hole but still outside the event horizon) where the orbits become unstable due to General relativistic effects and it plunges straight in and disappears forever inside the black hole. This high efficiency far exceeds the $<\!1\%$ efficiency of nuclear fusion that powers the Sun. The more massive a black hole is, the faster it can accrete before the radiation pressure of the accretion luminosity becomes so high that it wins over gravity and blows the gas away. Therefore of all black holes, it is the super-massive ones that achieve the highest luminosities. The most spectacular persistent accretion-powered phenomenon in the universe are quasars, which are super-massive black holes in the centers of distant galaxies. Quasars produce so much light that they outshine their entire host galaxy (Figure 1). Understanding the complex magneto-hydrodynamics of accretion flows and understanding why only a minority of massive black holes are luminous while the majority are dim is an important subfield of theoretical astrophysics.

Figure 1:

Left: A Hubble Space Telescope image of a disk of gas and dust in the inner 1000 light-years of active galaxy NGC4261. The gas is illuminated by an accreting massive black hole in the center. Right: The accretion also powers strong radio jets that extend well into intergalactic space. (Credits: National Radio Astronomy Observatory, California Institute of Technology, Walter Jaffe/Leiden Observatory, Holland Ford/JHU/STScI, and NASA. See Hubble Space Telescope press release.

Massive black holes, galactic dynamics and galaxy formation 

A super-massive black hole was found in every galactic center that was observed with high enough precision. It is now widely assumed that all galaxies contain one. The mass of the black hole is always about 0.1% of the mass of spheroidal component of the host galaxy (the galactic bulge in disk galaxies like our own, or the entire galaxy in elliptical galaxies like the one shown in Figure 1) (Magorrian et al. 1998; Häring and Rix 2004). This relation between the central black hole and the its host galaxy suggests a causal connection between the formation of the two. However, the physical mechanism behind this correlation is still unknown. The connection likely involves the feedback effect of the intense radiation from the accreting black hole on the star-forming gas in the galaxy around it. Galaxies grow by successive collisions and mergers with other galaxies, and the massive black holes in them must also eventually merge, while somehow preserving the black hole--bulge correlation. There is at present little direct evidence that black holes mergers actually occur. The next generation of space-borne gravitational wave observatories will hopefully detect the energetic bursts of gravitational waves that are emitted in the course of such mergers.

Massive black holes as astrophysical research tools

Irrespective of the unanswered questions about the formation mechanisms of the massive black holes, or the physics of accretion, massive black holes can serve as tools to study various other astrophysical questions. Two well-established techniques use quasar light to trace the distribution of matter in the universe. In one technique quasars serve essentially as lamps in a ``shadow theater'', which illuminate from behind filaments of inter-galactic gas, the left-over material from the epoch of galaxy formation. The gas is then detected by the absorption features it imprints in the quasar's spectrum. A second technique probes the gravitational potential of intervening galaxies, clusters of galaxies and the dark matter associated with them by the effects of gravitational lensing, where gravity causes light rays to bend. As a result, instead of seeing the actual quasar, several distorted images of the quasar are observed. A massive black hole, specifically the Galactic one, can also serve as a tool for studying stellar physics and stellar dynamics, since it is essentially a ``stellar collider''. This is further discussed below.

2 Infrared observations of the Galactic center

Figure 2:

Composite infrared image of the Milky Way and its center. Large scale: COBE/DIRBE satellite image (1.25, 2.2 and 3.5 micron). Small scale: a 2MASS survey (1.25 and 2.17 micron) image combined with one from the MSX/SPIRIT satellite (6-11 micron).

Like all galaxies, the Milky Way harbors a massive black hole. It is the lowest mass black hole discovered to date, with ''only'' $\sim\!4\!\times\!10^{6}$ solar mass (Eisenhauer et al. 2005; Ghez et al. 2005), in keeping with the atypically small bulge of the Milky Way. Like central black holes in many other galaxies, the Galactic black hole is very dim. What makes this black hole unique is its proximity. It is about 100 times closer than the black hole in the nearest large galaxy, Andromeda, and about 2000 times closer than those in the galaxies of the nearest cluster of galaxies, the Virgo cluster. For this reason it is possible to observe the environment of the Galactic black hole at a level of detail that will not be possible for any other galaxy in the foreseeable future.

The first hint of its existence was provided by the discovery, 30 years ago, of the unusual radio source Sagittarius A$^{\star}$ (SgrA$^{\star}$) at the dynamical center of the Galaxy (Balick and Brown 1974). It took almost three decades to obtain decisive observational evidence that SgrA$^{\star}$ is indeed a massive black hole. There were several reasons for the long wait. The faint radio luminosity of SgrA$^{\star}$ could be easily explained in terms of other, less exotic alternatives. Accreting massive black holes typically emit most of their luminosity in the UV to soft X-ray range of the spectrum (the more massive the black hole, the less energetic the typical wavelength). However, most of this spectral range is not accessible to observations, since the line of sight to the Galactic center is completely opaque to optical to UV light (Figure 2) due to the large amount of intervening interstellar dust (smog-like micron-sized particles made of graphite and silicates). To see anything, it is necessary to observe in either longer or shorter wavelengths. It is only recently that the Galactic black hole was observed in the IR (Genzel et al. 2003a) and X-ray (Baganoff et al. 2001) bands. Unfortunately, even these impressive observational achievements are insufficient determine the nature of SgrA$^{\star}$--the physics of accretion are still not understood well enough for the detection of this emission to be considered strong evidence of the existence of a black hole.

Figure 3:

Adaptive optics-assisted infrared images of the the central light year taken by the Very Large Telescope (Genzel et al., 2003a). The false colors correspond to temperature. Blue stars are hot and short-lived (therefore must be young). Red stars are old, less massive giant stars at the last stages of their lives. It should be emphasized that what seems to be the size of the stars is just an artifact due to light ``leaking'' around bright sources. At a distance of about 24000 light year all the stars are actually point-like sources well below the telescope's angular resolution.

Most of the light emitted by the stars that orbit the black hole is also obscured by the inter-stellar dust. However, stars can be observed in the infrared, albeit with more difficulty (Figure 3). Recent technological advances in infrared astronomy enabled deep and precise observations of these stars as they orbit the black hole (Eisenhauer et al. 2005; Ghez et al. 2005). It was these observations that finally delivered the most convincing evidence for the existence of the massive black hole. This is because the stars are clean, direct probes of the gravitational potential, whereas gas can be affected by other forces, such as radiation pressure, thermal pressure and magnetic fields.

3 Probing the dark mass in the Galactic center

Figure 4:

Stellar orbits around the massive black hole in the Galactic center, observed in the infrared (2.2 micron) with the Very large Telescope (Schödel et al. 2002; Eisenhauer et al. 2005). The actual measurements (points with error bars) are shown only for the star named ``S2''. S2 has the shortest orbital period (15.2 years) of the stars detected to date. Its distance of of closest approach to the black hole is only 17 light-hours, at which point it is traveling at almost 2% of the speed of light. For more information see MPE's Galactic Center web page.

Figure 4 shows the reconstructed orbits of several of the stars near SgrA$^{\star}$ that were monitored over about a decade. The stars appear to be in orbit around an empty spot in space. The one star with the shortest period, S2, (15.2 yr) singly provided enough information to resolve several key question about the mysterious dark mass in the center of the Galaxy (Figure 5).

Figure 5:

What is the dark mass?		or		?
Where is the dark mass?
How far is the dark mass?

Using stellar orbits to answer fundamental questions about the dark mass in the center of the Galaxy. Top: The perfect (to within measurement errors) Keplerian elliptical orbit implies that the central mass is fully enclosed inside the point of closest approach, leaving few viable options other than a black hole to explain the central mass. Middle: the acceleration vectors from several orbits should all point to the center of acceleration, thereby identifying the position of the dark mass (this subsequently enabled a targeted search for the infrared emission from the accretion on the massive black hole, see Figure 6). Bottom: By combining measurements of line-of-sight velocity (in km/s) and angular velocity in (rad/yr) with the orbital solution, it is possible to measure the distance between the solar system and the black hole, that is, the distance to the Galactic center.

What is the dark mass?

Can it be a compact, but non-singular distribution of dark objects? Any spherical distribution of mass will affect the motions of the stars as if it were all concentrated in the center, as long as they do not pass through it. Possible candidates range from dark stellar objects: stellar black holes, neutron stars, white dwarfs or planets to particle dark matter, perhaps the same dark matter that is indirectly detected on cosmic scales. The good fit of the orbit of S2 to a Newtonian (Keplerian) orbit--a closed ellipse--implies that all the mass that is pulling on S2 ( $3.6\!\times\!10^{6}$ solar masses, as derived from the orbital solution) is entirely enclosed inside the point of closest approach, 17 light-hours from the center. If it were not so, the orbit of S2 would have displayed signs of retrograde precession (rosette-like orbits) because the gravitational force on it would have deviated from exact $r^{-2}$ dependence. Such a tight upper limit on the volume containing the central mass rules out any dense cluster made of stellar mass objects on the grounds of dynamical stability (Maoz 1998). S2's orbit also rules out some elementary particle alternatives, such as the ``universal Fermi ball'', where all dark matter is explained by heavy fermionic particles, and where the central massive objects are in fact dense concentrations (``balls'') of fermions held against gravity by quantum degeneracy pressure (Munyaneza et al. 1998).The only remaining viable explanation for the dark central mass is that it is a black hole (Schödel et al. 2002).

Where is the dark mass?

Until very recently there was no sign of accretion emission from the black hole in any other band apart for the radio. A blind search for the faint infrared emission that is expected to accompany the radio emission is very difficult because there are so many faint stars at the center. Stellar orbits can pinpoint the position of the black hole, since the measured projected acceleration vectors should all point to the central mass. The close proximity between the dynamically detected center of acceleration and the position of the recurrent infrared flares (Figure 6) that were discovered a few years later was key evidence in confirming that the flares are indeed coming from an accreting massive black hole (Ghez et al. 2000).

How far is the dark mass?

Because we observe our Galaxy from the inside (Figure 2), it is actually harder to reconstruct its structure than it is to reconstruct the structure of other galaxies seen from the outside. The distance of the solar system from the center of the Galaxy is a key parameter for Galactic cartography and for calibrating the luminosities of bright stars that can be used as ``standard candles'' to measure distances on cosmological scales. Stellar orbits can measure the distance to the MBH by a classical method long-used for measuring distances to binary stars (Salim and Gould 1999). The essence of the idea is that the motion of the star on the plane of the sky (the ``apparent motion'') is measured in terms of radians/year, whereas the line-of-sight velocity is measured via the Doppler shift of the stellar spectrum in terms of km/s. The orbital solution ties the angular and true velocities together through the distance to the black hole. The latest orbital determination fixes the distance to the Galactic center at 25000$\pm$1000 light years (Eisenhauer et al. 2005).

4 Probing post-Newtonian gravity

One of the prime motivations for exploring the Galactic black hole is to observe General relativistic phenomena close to a super-massive object. The accretion luminosity is emitted by gas at distances only a few times larger than the event horizon (the strong-field limit). Not long after the center of acceleration was pinpointed, the black hole was finally revealed when it flared in the infrared (Figure 6). Such flares are now known to be fairly frequent, occurring a few times per day, and typically lasting about an hour. It is thought that the flares are triggered by temporary peaks in the mass supply rate to the black hole, perhaps due to the presence of a denser than average clump of gas in the accretion flow. Two of these flares displayed an almost periodic fluctuation in their luminosity while the flare lasted (Figure 7). The quasi-period of about 17 minutes is almost half as short as would be expected for gas orbiting at the last stable circular orbit of a $3.6\!\times\!10^{6}\, M_{\odot}$, non-spinning black hole. The black hole's spin affects the structure of space-time around it in a way that draws the last stable circular orbit closer and shortens its period. Thus, if indeed the flares arise from gas orbiting for a few periods close to the last stable orbit, and if the quasi-periodicity indeed reflects the orbital period, it is possible to translate the 17 minutes period to a lower limit the spin of the black hole, which must be spinning at half of its maximal possible value (Genzel et al. 2003a). This is not surprising; since the black hole absorbs the angular momentum of the matter that falls in it, it is expected to spin quite substantially. Thus, it is possible that the temporal structure of the flares is probing how spacetime is twisted by the spinning black hole.

Figure 6:

First observed infrared (2.15 microns) flare from the Galactic black hole, as detected by the Very Large Telescope. The animation is looped: one cycle corresponds to half an hour (Genzel et al. 2003a).For more information see MPE's Galactic Center web page.

Figure 7:

A 17 minute quasi-period in the flux during an accretion flare, possibly originating in a hot clump of gas that orbits right at the last stable orbit for a few times before finally falling into the black hole. The period at the last stable orbit of a non-rotating black hole with the mass of the Galactic black hole is predicted by theory to be 27 minutes. The shorter 17 minutes period is explained by the fact that spacetime warps differently when the black spins, resulting in a smaller last stable orbit and a shorter orbital period. (Genzel et al. 2003a)

Typical stars cannot approach the Galactic black hole as close as the emitting gas without being destroyed by the tidal field of the black hole. Thus, stars can mostly probe the weak-field limit of General relativity. Though less spectacular than the strong-field limit, stars orbiting a million solar mass class object at up to a few percents of the speed of light nevertheless probe a virtually unexplored regime of relativistic celestial mechanics. One effect that will be hopefully detected with continued monitoring is the slow-down of time near the black hole (gravitational redshift), as expressed by the Doppler shift of the stellar spectra. This effect is substantially larger at the orbits' point of closest approach than it is on the surface of a white dwarf. Another effect that may be eventually detected is the advancing rosette-like orbits that are predicted by General Relativity (Figure 7) as a consequence of the deviation from the Newtonian $r^{-2}$ gravitational force law.

Figure 8:

A schematic comparison of a classical Newtonian orbit around a point central mass (red) and a General Relativistic one (blue). In Newtonian physics the gravitational force falls exactly as the distance squared, and the orbital ellipse closes on itself. Close enough to the central black hole General Relativistic effects deviating from Newton's law of gravitation cause the point of closest approach to advance, leading to a rosette-shaped orbit (blue).

5 Stellar phenomena near a massive black hole

Figure 9:

Gravito-hydrodynamic simulations of fast stellar collisions in the dense stellar cusp near a massive black hole. Left: two equal mass stars (orange) in a grazing collision are momentarily deformed and evaporate a few percents of their mass (yellow clouds). Right: A neutron star (blue) in a penetrating collision with a normal star.

Dynamical studies of the way stars respond to the growth and presence of a massive black hole in a galactic center all predict that the stellar density will grow toward the center and settle into a (formally) diverging, high density ``stellar cusp''. The observed stellar density near the black hole is about a billion times higher than near the Sun, and the stars move up to a 100 times faster relative to each other than they do elsewhere in the Galaxy (Alexander 1999; Genzel et al. 2003b). Such extreme and unique conditions effectively make the inner stellar cusp into a ``stellar collider'', where stellar properties can be probed when stars closely interact with each other or with the black hole. Many theoretical ideas involving stellar dynamics and stellar physics have been proposed to explain various aspects of the unusual stellar population that is observed near the Galactic black hole. The picture is still far from clear. We conclude this article by briefly mentioning just three of the many possible processes.

Tidal destruction

Stars that approach too close to the black hole are destroyed. They are either swallowed whole, or, as is more typical of the relatively small massive black hole in our Galaxy, first disrupted by the strong tidal field and then get accreted. Figure 10 show a Gravito-hydrodynamic simulation of an extreme case of tidal disruption where the tidal ``squeeze'' raises the central density of the star by so much that the resulting accelerated nuclear reactions may cause the star to explode as a supernova (Carter and Luminet 1982).

Collisional destruction

Physical star-star collisions (Figure 9) are predicted to be frequent in the high density cusp. Such destructive collisions may be responsible for the absence of bright, large giant stars in the very central region around the black hole (cf Figure 3) (Alexander 1999).

Exchange interactions

One of the consequences of the steep gravitational potential around the black hole is ``mass segregation'', a dynamical process whereby massive stars tend to ``sink'' to the bottom of the potential well, whereas the light stars ``float'' out. As a consequence, the inner light-year of the Galaxy is expected to contain a large, dense cluster of stellar black holes (of about $10\, M_{\odot}$). Such black holes may be responsible for the presence of young stars of about $10\, M_{\odot}$ very close to the black hole (S2 is one of them), by capturing there via the dynamical process of ``3-body exchange'' (Figure 11), where the young star ``knocks out'' a stellar black hole of a similar mass and takes it's place (Alexander and Livio 2004).

Figure 10:

A gravito-hydrodynamic simulation of an extreme tidal interaction between a star and a massive black hole, that may lead to a nuclear run-away and a supernova explosion. Top left: a view of the stellar trajectory (orange) around the black hole (red dot) from above the orbital plane. Top right: An edge-on view of the orbit. Note how the star (black blob) is squeezed into a two-dimensional pancake as it passes through the point of closest approach. Bottom: a plot of the changes in the central density as function of time. The higher the central density, the faster the nuclear reaction rates.

Figure 11:

A schematic depiction of a celestial billiards ball game. The orbit of a hot young star (blue dot following dashed trajectory) approaching close to the black hole (big central black dot) intersects with the tight orbit of a stellar mass black hole (small black dot following solid trajectory) of roughly the same mass. As a result of a 3-body exchange, the young star ``knocks'' the stellar black hole away (the interaction is gravitational--the two don't actually touch each other) and takes its place in a tight orbit very close to the massive black hole.

6 Conclusion

The Galactic black hole provides a uniquely accessible laboratory for studying in detail a massive black hole in its interactions with its environment: how it feeds and grows by accreting gas and stars and how the extreme density, high velocity and strong tidal fields affect the stars near it. The gas and stars probe the nature of the central dark mass and probe post-Newtonian gravity in the weak- and strong-field limits. These issues are relevant for understanding the massive black hole phenomenon in general. The wealth of observed phenomena near the Galactic black hole provides the impetus to study the physics of gas and stellar processes in such an extreme environment. These studies prove to be very fruitful, yielding valuable insights even in cases where they do not fully succeed to explain the observations (Alexander 2005). Many questions remain--the most exciting science still lies ahead.

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