Innumerable as the Starrs of Night,
Or Starrs of Morning,
Dew-drops, which the Sun
on every leaf and every flouer
Beauty is truth, truth beauty,
— that is all
Ye know on earth, and all
ye need to know.
E = M
Energy is eternal delight.
Impearls: Galactic Central - The Black Hole at the Center of the Galaxy
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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:
After chewing on that ‘supermassive’ entree, try this meaty excerpt from Genzel et al.'s research report:
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!
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.
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