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Impearls: Galactic Central - The Black Hole at the Center of the Galaxy

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Earthdate 2004-01-13

Galactic Central – The Black Hole at the Center of the Galaxy

A recent issue (2003-10-30) of the journal Nature contains a pair of articles, a research report titled “Near-infrared flares from accreting gas around the supermassive black hole at the Galactic Centre” by R. Genzel (of the Max-Planck-Institut für extraterrestrische Physik) et al., and a news item by Harvard astronomer Ramesh Narayan on the same topic, called “Black holes: Sparks of interest.” 1, 2

I vividly remember reading decades ago one of the first books to come out on the quasars, those seemingly starlike (though stars impossibly brilliant to be seen at their distance) ‘quasi-stellar objects’ that were such a puzzle at the time.  The book, as I recall, carefully considered the characteristics of the light spectrum emitted by quasars and came to the then-controversial conclusion (it seemed to me that the evidence, as the author presented it, practically screamed) that the terrific engines powering those gargantuan, universe-illuminating beacons were black holes — gigantic, what are now called supermassive, black holes.  How can a black hole release energy, you may ask?  As matter ‘infalls’ into a black hole, a portion of the matter's Einsteinian E = mc2 energy — i.e., nuclear energy — may be liberated, and the process can be far more efficient than what the stars, and we on Earth, use to produce nuclear power or explosions.

Nowadays the existence of black holes can scarcely be doubted, and any number have been located, from so-called ‘stellar-mass’ black holes incorporating a few times the sun's mass (relatively tiny in size, with a Schwarzschild ‘event horizon’ only a few kilometers across) to the ‘supermassive’ black holes, containing millions of times the mass of our sun, which drive the brilliant quasars as well as quieter, more lurking variants of these exotic beasts that occupy the centers of many of the galaxies.

New details about the light spectrum of one particular supermassive black hole — the closest to us, our own galaxy, the Milky Way's stupendous central black hole — promise to repeat this history of unfolding knowledge, by uncovering the precise modus operandi of this fabulous monster, the gigantic Hole at the heart of the Galaxy.  The two Nature articles together describe detection of flares in the pattern of near-infrared light emission from the Galaxy's supermassive black hole, which has already provided illuminating details concerning it.

Harvard astronomer Ramesh Narayan describes the latest news, in his accompanying piece in Nature:

At the centre of the Milky Way is a supermassive black hole called Sagittarius A* (Sgr A*).  As supermassive black holes go, Sgr A* is a relatively small one: it's four million times more massive than the Sun, but black holes up to 1,000 times more massive are known to exist in other galaxies.  What makes Sgr A* special is that it is by far the closest supermassive black hole to Earth, making it a prime target for study.  And, of course, it is our black hole, at the centre of our own Galaxy.  Another, curious, feature is that Sgr A* is one of the dimmest black holes known.

Sgr A* has been studied extensively at long wavelengths, through the detection of radio- and millimetre-wavelength radiation from it; only recently has that information been complemented by images at shorter wavelengths, taken by the space-borne Chandra X-ray Observatory.  On page 934 of this issue, Genzel and colleagues add more detail, with their detection of Sgr A* at infrared wavelengths, using the Very Large Telescope in Chile's Atacama Desert.  Genzel et al., and another group led by Ghez, find that the brightness of Sgr A* at infrared wavelengths is highly variable, and flares frequently.  These observations, reflecting similar patterns seen earlier in X-rays, open a new window on this enigmatic source.

Some supermassive black holes in distant galaxies are observed as very bright quasi-stellar objects, or quasars, that often outshine an entire galaxy of stars.  Those black holes accrete (absorb) a lot of gas from their surroundings and in so doing convert a good fraction, say 10%, of the mass energy of that gas to radiation.  Their luminosities are nearly equal to the maximum allowed — the so-called Eddington limit, which is proportional to the mass of the object.  Sgr A*, in contrast, is extremely dim, radiating at only a billionth of the Eddington limit for its mass.  In this respect it resembles the vast majority of black holes in the Universe, which are mostly very dim.

Why is Sgr A* so dim?  It is true that it has less gas to accrete, compared with the bright black holes in quasars — but this is only around 10,000 times less, not a billion times.  Two other factors are believed to contribute to its dimness.  First, in contrast to the accretion flows in quasars, the gas flow in Sgr A* is radiatively inefficient: only a very small fraction of its mass energy is converted to radiation.  Second, as a direct consequence of this radiative inefficiency, only a small fraction of the available gas actually accretes onto the black hole, the rest being ejected from the system.

This still leaves the fundamental question of exactly how an accretion flow converts mass energy to radiation and why the process is very efficient in bright quasars but highly inefficient in Sgr A*.  Something is clearly different about the physics in bright black holes and in dim ones.  Unfortunately, the relevant effects are complex and poorly understood, and it has become clear in recent years that real progress will be achieved only when we have more detailed observational clues.  The infrared detections of Sgr A* by Genzel et al., coupled with Chandra's X-ray observations, may be the breakthrough we have been looking for.

The fact that the emission from Sgr A* varies over tens of minutes, and is almost periodic, indicates that the radiation comes from gas orbiting close to the black hole.  This is not unexpected.  What is surprising is that Sgr A* emits frequent massive flares of radiation at both infrared and X-ray wavelengths, suggesting that the conversion of mass to radiation is not steady and continuous, but very erratic.  There are several possible explanations.  One is that the radiatively inefficient accretion flow ejects gas in spurts rather than continuously, and that each ejection of a blob of gas is accompanied by a spurt of radiation.  Another is that the amount of gas accreting onto the black hole itself fluctuates, causing the emission to vary.  A third idea, perhaps the simplest, is that the accretion engine shorts out once in a while.  Lines of magnetic field pervade the accretion disk, and occasionally these may become so distorted that they ‘snap’ and new lines form.  These magnetic reconnection events would produce streams of energetic particles and sparks of radiation (Fig. 1).

It is not clear at present which, if any, of these ideas is correct, or how the radiation processes actually work in detail.  But the beauty of having a flaring source such as Sgr A* is that each flare provides a new and independent view of the underlying physical processes.  So by collecting and studying data on many flares, we may learn much more than from a steady source.

After chewing on that ‘supermassive’ entree, try this meaty excerpt from Genzel et al.'s research report:

The flares' location close to the central black hole, as well as the temporal substructure, poses a serious challenge to models in which the flares originate from rapid shock cooling of a large-scale jet, or are due to passages of stars through a central accretion disk.

The few-minute rise and decay times, as well as the quasi-periodicity, strongly suggest that the infrared flares originate in the innermost accretion zone, on a scale less than ten Schwarzschild radii (the light travel time across the Schwarzschild radius of a 3.6-million-solar-mass black hole (1.06 × 1012 cm) is 35 s).  If the substructure is a fundamental property of the flow, the most likely interpretation of the periodicity is the relativistic modulation of the emission of gas orbiting in a prograde disk just outside the last stable orbit (LSO).  If the 17-min period can be identified with this fundamental orbital frequency, the inevitable conclusion is that the Galactic Centre black hole must have significant spin.  The LSO frequency of a 3.6-million-solar-mass, non-rotating (Schwarzschild) black hole is 27 min.  Because the prograde LSO is closer in for a rotating (Kerr) black hole, the observed period can be matched if the spin parameter is J/(GMBH/c) = 0.52 (± 0.1, ± 0.08, ± 0.08, where J is the angular momentum of the black hole); this is half the maximum value for a Kerr black hole.  (The error estimates here reflect the uncertainties in the period, black-hole mass (MBH) and distance to the Galactic Centre, respectively; G is the gravitational constant.)  For that spin parameter, the last stable orbit is at a radius of 2.2 × 1012 cm.  Recent numerical simulations of Kerr accretion disks indicate that the in-spiralling gas radiates most efficiently just outside the innermost stable orbit.  Our estimate of the spin parameter is thus a lower bound.

Other possible periodicities, such as acoustic waves in a thin disk, Lense-Thirring or orbital node precession are too slow for explaining the observed frequencies for any spin parameter.  (The 28-min timescale of the quiescent emission corresponds to a radius of 3.2 × 1012 cm for a prograde orbit of J/(GMBH/c) = 0.52; the last stable retrograde orbit for that spin parameter has a period of 38 min at a radius of 4 × 1012 cm).  Lense-Thirring precession and viscous (magnetic) torques will gradually force the accreting gas into the black hole's equatorial plane.  Recent numerical simulations indicate that a (prograde) disk analysis is appropriate to first order even for the hot accretion flow at the Galactic Centre.

To extract some fascinating details from this piece, the Schwarzschild radius (radius of the event horizon) of the 3.6 million solar mass ‘Galactic Centre’ (as they call it) black hole is 35 light seconds, or some 10.6 million kilometers (about 6.6 million miles); this is about 15¼ times the size of the sun (695,000 km radius), and (at 0.07 Astronomical Unit) about one-sixth the radius of the orbit of Mercury (0.4 AU) in our solar system.  As the authors conclude, “the most likely interpretation of the periodicity” in the observed flaring in the infrared emission of the black hole — including a 17-minute periodicity — is “the relativistic modulation of the emission of gas orbiting in a prograde disk just outside the last stable orbit (LSO).”  ‘Prograde’ means orbiting in the direction of spin of the black hole.  The period of the ‘last stable orbit’ of a non-rotating black hole of this mass is 27 minutes; thus a 17-minute orbital periodicity could not exist if the black hole were not rotating.

For a rotating black hole, Genzel et al.'s article points out, “the observed period can be matched if the spin parameter” is about 0.52 (52%) of the maximum spin such a black hole could possibly possess.  “For that spin parameter, the last stable orbit is at a radius of 2.2 × 1012 cm” from the ‘center’ of the black hole — which is 22 million km (13 million miles), or some 31 times the size of the sun, and (at about 0.15 AU) more than one-third the radius of Mercury's orbit.  Something in this ‘prograde last stable orbit’ would orbit some 11 million km (7 million miles) above the ‘Galactic Central’ (as we'll call it) black hole's event horizon.  If I understand the physics correctly, something like a spaceship could venture below the ‘last stable orbit,’ but an unpowered trajectory would inevitably spiral into the event horizon, from whence no return is possible; a spaceship would have to expend power (if it had enough) to return from below the ‘last stable orbit.’

As Genzel and his colleagues wrote, “Recent numerical simulations of Kerr accretion disks indicate that the in-spiralling gas radiates most efficiently just outside the innermost stable orbit.  Our estimate of the spin parameter is thus a lower bound.”  The piece also notes that “The 28-min timescale of the quiescent emission corresponds to a radius of 3.2 × 1012 cm.”  This ‘quiescent emission’ gas is thus orbiting at a radius of 32 million km (about 20 million miles), which is some 0.21 AU or a little over half the size of Mercury's orbit.  The article additionally points out that the last stable retrograde orbit for that Galactic Central black hole spin parameter (0.52) “has a period of 38 min, at a radius of 4 × 1012 cm,” or 40 million km (about 25 million miles), which is some 57 times the size of the sun, and (at about 0.26 AU) approximately two-thirds the radius of Mercury's orbit.

Even though the last stable orbit, in any direction, around the ‘Galactic Central’ black hole lies below the height of Mercury's orbit in our solar system, if a planet such as Mercury were to swing by at a similar distance from the ‘center’ of Galactic Central, it would have to possess a far greater velocity to successfully orbit, due to the enormously greater mass and thus gravitational strength of the central attractor in that system, or else it would simply plop into the black hole.  Notice the difference in orbital period: 38 minutes for the (retrograde) last stable orbit (which would orbit Galactic Central at two-thirds the distance of Mercury) versus Mercury's period of 88 days to circle our sun.

Disregarding complications such as tidal forces which tend to pluck apart a too-closely-orbiting planet, and presuming an appropriately large enough orbital velocity, an object or planet would be able to stably orbit the ‘Galactic Central’ black hole — at or beyond the so-called ‘last stable orbit’ for the direction in which it is orbiting.  How fast would that orbital velocity have to be?  Taking the prograde direction, and ignoring relativistic effects, the circumference (2πr) of a 22 million km radius circular orbit is about 138 million km.  This distance must be traversed during each 17 minute orbital period, requiring a speed of some 136,000 km/second (84,000 miles/second), or approximately 45% of the speed of light!
 

References

1 R. Genzel, R. Schödel, T. Ott, A. Eckart, T. Alexander, F. Lacombe, D. Rouan, and B. Aschenbach, “Near-infrared flares from accreting gas around the supermassive black hole at the Galactic Centre,” Nature, Vol. 425, Issue No. 6961 (date 2003-10-30), pp. 934-937 [doi:10.1038/nature02065].  Requires subscription or pay-per-view.

2 Ramesh Narayan, “Black holes: Sparks of interest,” Nature, Vol. 425, Issue No. 6961 (date 2003-10-30), pp. 908-909 [doi:10.1038/425908a].  Requires subscription or pay-per-view.



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