Innumerable as the Starrs of Night,
Or Starrs of Morning,
Dew-drops, which the Sun
on every leaf and every flouer
NGC3132 ©
Beauty is truth, truth beauty,
— that is all
Ye know on earth, and all
ye need to know.

E = M

Energy is eternal delight.
William Blake

Impearls: 2004-01-11 Archive

Earthdate 2004-01-17

“A Great Eye, lidless, (formerly) wreathed in flame…” – Chicxulub, the dinosaur-killer crater

Chicxulub crater, Yucatan peninsula, Mexico.  Remains of meteorite impact that 65 million years ago drove the dinosaurs into extinction.  Horizontal gradient of Bouguer gravity anomaly.

Figure 1.  Chicxulub crater, Yucatan peninsula, Mexico.  Remains of the meteorite impact which 65 million years ago drove the dinosaurs into extinction.  The white line cutting across the center of the crater (and figure) is the northwest Yucatan coastline.  Patterns of white dots indicate clustering of “cenotes”, water-filled sinkholes in the limestone “karst” bedrock.  As the indicated article in Nature lays out, this “image” of the ancient crater, stripped of up to a kilometer of enveloping sediments, was produced by measuring the “horizontal gradient of the Bouguer gravity anomaly.”  As it says, “Areas lacking gravity data appear blurred,” while “Darker shading corresponds to greater gradient magnitude.  The technique's sensitivity is illustrated by the detection of part of the Ticul fault [white diagonal lines near bottom of figure] that has only ~100 m [about 330 feet] of vertical displacement at the surface.”

Thanks to Nature article co-author and preparer of the figures Mark Pilkington (of the Geological Survey of Canada) and to the Nature Publishing Group for their kind permission to use the figure. 1

It's well accepted among scientists nowadays that the dinosaurs — along with three-quarters of all species on earth, land and sea — disappeared in the aftermath of the cataclysmic collision of a sizable asteroid or comet impacting the earth some 65 million years ago.  Though the huge, multi-ringed, some 180 kilometers (112 miles) in diameter crater resulting from that cosmic trainwreck was found over a decade ago — buried at the northwestern tip of the Yucatan peninsula in Mexico, beneath up to a kilometer of sediments — it's apparently invisible as far as any visible effect on the surface topography of that part of the Yucatan (which basically is about as flat as a pancake) is concerned.

The deeply buried crater's seeming irrelevance to affairs on the surface is more apparent than real, however.  The porous limestone (so-called “karst”) basement of the Yucatan is pierced by a plenitude of water-filled sinkholes, known locally as “cenotes”.  These cenotes fall into patterns (easily visible on detailed road maps, for example) which, it turns out, congregate along the buried outer wall of the stupendous concentric-ringed prehistoric crater.

(Thus, one can swim in a pool lying atop the old dinosaur-killer crater rim.  A fond remembrance: rather like the Pantheon in Rome, one might say, the underground cenote raised a vast dome vaulting through the rock ceiling into daylight for only a brief circle, through which sunlight poured to blaze in the otherwise dark, quiet pool, down the roof and along the sides of which stalactite and stalagmite columns marched….)

As A. R. Hildebrand and his colleagues (authors of the paper in Nature “Size and structure of the Chicxulub crater revealed by horizontal gravity gradients and cenotes” that is considered in this piece) describe it: 1

The cenote ring corresponds to (and was presumably created by) a zone of enhanced groundwater flow, as evidenced by a coincident low in the groundwater surface and the presence of freshwater springs where the cenote ring intersects the coast.  High hydraulic conductivity is also indicated in the surrounding near-surface rocks by low hydraulic gradients and widespread response to tides.  […]  The ring consists mostly of water- and reed-filled cenotes of larger size (typically up to ~300 m [~1,000 feet] diameter) than the cenotes and dry karst pits found elsewhere on the peninsula.  On the crater's east side, the size of the main ring's constituent cenotes allows it to be distinguished from the widespread karst features exterior to the crater.  The main cenote ring is up to ~5 km [~3 miles] wide, and corresponds to a topographic low of up to ~5 m [~16 feet] over some of its length.  Much of the permeability in karst terrains like the Yucatán peninsula is due to fracture systems, so it has been assumed that the cenote ring corresponds to a zone of enhanced fracturing.  Although fractures are not directly observable along the cenote ring, we presume that a fracture system of ≤5 km width with orientations preferentially parallel to the underlying crater structure created the permeability that lead to the ring's formation.  A zone of enhanced fracturing would also allow preferential erosion to create the topographic low associated with the ring.

The authors also note that, “The edges of the crater (and associated gravity-gradient features) correspond to bends in the coastline, and interior gradient features sometimes correlate with rocky points along the coastline.”

Beyond those surficial physical consequences of the subterranean crater's presence, the team assembling this marvelous figure and accompanying article, in effect — “merely” by careful measurement of seemingly trivial changes in gravity — have stripped the veil off this vast interred sepulchre, revealing the blasted hole in all its ruined glory!  Kudos to the group for putting together this dramatic portrait — which isn't an image at all in the sense of a photograph, but might as well be for the clarity of the scene it presents.

The authors interpret the spectacular visage of the ancient crater: 1

Figure 1 reveals a striking circular structure centred near the Yucatán shoreline at ~89.57° N, 21.29° W.  At least six concentric gradient features occur between ~10 and ~90 km [between ~6 and ~56 miles] radius.  These features are probably most distinct in the southwest owing to denser sampling of the gravity field.  Truncations of the gradient features often correspond to gaps in survey coverage.  […]  We interpret the outer four gradient maxima (at ~55 to ~90 km radii) to represent concentric faults in the crater's zone of slumping, as are also revealed by seismic reflection data.  The inner two maxima probably represent the outer margins of the central uplift (at 20-25 km radius) and the peak ring and/or collapsed transient cavity (at 40-45 km radius).  Radial gradients in the southwestern quadrant over the inferred ~40-km-diameter central uplift may represent structural ‘puckering’ as revealed at eroded terrestrial craters.  Gradient features related to regional gravity highs and lows are visible outside the crater, but no concentric gradient features are apparent at radial distances >90 km [>56 miles].  Note that the crater's outer gradient and karst features are linear near the northern and tangential part of the Ticul fault […].

Hildebrand et al. acknowledge that, “the peripheral strong gradient features are truncated or diverted for the northern third of the crater.  Magnetic and seismic data confirm that a completely circular basin and impact structure is present, and some weak circular structure appears in the gravity data north of the truncation of the peripheral gradient features, but the cause of the truncation of Chicxulub's gravity expression remains to be understood.”


Here's the Abstract from A. R. Hildebrand and colleagues' Nature article: 1

It is now widely believed that a large impact occurred on the Earth at the end of the Cretaceous period, and that the buried Chicxulub structure in Yucatán, Mexico, is the resulting crater.  Knowledge of the size and internal structure of the Chicxulub crater is necessary for quantifying the effects of the impact on the Cretaceous environment.  Although much information bearing on the crater's structure is available, diameter estimates range from 170 to 300 km (refs 1-7), corresponding to an order of magnitude variation in impact energy.  Here we show the diameter of the crater to be ~180 km [about 112 miles] by examining the horizontal gradient of the Bouguer gravity anomaly over the structure.  This size is confirmed by the distribution of karst features in the Yucatan region (mainly water-filled sinkholes, known as cenotes).  The coincidence of cenotes and peripheral gravity-gradient maxima suggests that cenote formation is closely related to the presence of slump faults near the crater rim.


1 A. R. Hildebrand, M. Pilkington, M. Connors, C. Ortiz-Aleman, and R. E. Chavez, “Size and structure of the Chicxulub crater revealed by horizontal gravity gradients and cenotes,” Nature, Vol. 376, Issue No. 6539 (dated 1995-08-03), pp. 415-417 [doi:10.1038/376415a0].  Requires pay-per-view for full text.

2 H. J. Melosh, “Around and around we go,” Nature, Vol. 376, Issue No. 6539 (dated 1995-08-03), p. 387.  Accompanying news piece; requires pay-per-view for full text.

UPDATE:  2004-01-19 19:00 UT:  Substantial rewording and material added from Hildebrand et al.

UPDATE:  2005-07-24 06:00 UT:  Compression on crater image decreased.

Impearls: 2004-01-11 Archive

Earthdate 2004-01-16

Through a Universe Darkly

The journal Science presented its annual “Breakthrough of the Year” special issue as usual in its final installment of the year.  This last year's No. 1 Breakthrough, however, would appear to deserve honors beyond a single year's acclaim.  It seems silly to talk about ”Breakthrough of the Century” this early in the 21st century, but the scientific results this last year in astrophysics are downright breathtaking.

Here's how Science's Charles Seife describes these illuminating advances: 1

A lonely satellite spinning slowly through the void has captured the very essence of the universe.  In February, the Wilkinson Microwave Anisotropy Probe (WMAP) produced an image of the infant cosmos, of all of creation when it was less than 400,000 years old.  The brightly colored picture marks a turning point in the field of cosmology:  Along with a handful of other observations revealed this year, it ends a decades-long argument about the nature of the universe and confirms that our cosmos is much, much stranger than we ever imagined.

Five years ago, Science's cover sported the visage of Albert Einstein looking shocked by 1998's Breakthrough of the Year: the accelerating universe.  Two teams of astronomers had seen the faint imprint of a ghostly force in the death rattles of dying stars.  The apparent brightness of a certain type of supernova gave cosmologists a way to measure the expansion of the universe at different times in its history.  The scientists were surprised to find that the universe was expanding ever faster, rather than decelerating, as general relativity — and common sense — had led astrophysicists to believe.  This was the first sign of the mysterious “dark energy,” an unknown force that counteracts the effects of gravity and flings galaxies away from each other.

Although the supernova data were compelling, many cosmologists hesitated to embrace the bizarre idea of dark energy.  Teams of astronomers across the world rushed to test the existence of this irresistible force in independent ways.  That quest ended this year.  No longer are scientists trying to confirm the existence of dark energy; now they are trying to find out what it's made of, and what it tells us about the birth and evolution of the universe.

Lingering doubts about the existence of dark energy and the composition of the universe dissolved when the WMAP satellite took the most detailed picture ever of the cosmic microwave background (CMB).  The CMB is the most ancient light in the universe, the radiation that streamed from the newborn universe when it was still a glowing ball of plasma.  This faint microwave glow surrounds us like a distant wall of fire.  The writing on the wall — tiny fluctuations in the temperature (and other properties) of the ancient light — reveals what the universe is made of.

Long before there were stars and galaxies, the universe was made of a hot, glowing plasma that roiled under the competing influences of gravity and light.  The big bang had set the entire cosmos ringing like a bell, and pressure waves rattled through the plasma, compressing and expanding and compressing clouds of matter.  Hot spots in the background radiation are the images of compressed, dense plasma in the cooling universe, and cold spots are the signature of rarefied regions of gas.

Just as the tone of a bell depends on its shape and the material it's made of, so does the “sound” of the early universe — the relative abundances and sizes of the hot and cold spots in the microwave background — depend on the composition of the universe and its shape.  WMAP is the instrument that finally allowed scientists to hear the celestial music and figure out what sort of instrument our cosmos is.

The answer was disturbing and comforting at the same time.  The WMAP data confirmed the incredibly strange picture of the universe that other observations had been painting.  The universe is only 4% ordinary matter, the stuff of stars and trees and people.  Twenty-three percent is exotic matter: dark mass that astrophysicists believe is made up of an as-yet-undetected particle.  And the remainder, 73%, is dark energy.

The tone of the cosmic bell also reveals the age of the cosmos and the rate at which it is expanding, and WMAP has nearly perfect pitch.  A year ago, a cosmologist would likely have said that the universe is between 12 billion and 15 billion years old.  Now the estimate is 13.7 billion years, plus or minus a few hundred thousand.  Similar calculations based on WMAP data have also pinned down the rate of the universe's expansion — 71 kilometers per second per megaparsec, plus or minus a few hundredths — and the universe's “shape”: slate flat.  All the arguments of the last few decades about the basic properties of the universe — its age, its expansion rate, its composition, its density — have been settled in one fell swoop.

As important as WMAP is, it is not this year's only contribution to cosmologists' understanding of the history of the universe.  The Sloan Digital Sky Survey (SDSS) is mapping out a million galaxies.  By analyzing the distribution of those galaxies, the way they clump and spread out, scientists can figure out the forces that cause that clumping and spreading — be they the gravitational attraction of dark matter or the antigravity push of dark energy.  In October, the SDSS team revealed its analysis of the first quarter-million galaxies it had collected.  It came to the same conclusion that the WMAP researchers had reached:  The universe is dominated by dark energy.

This year scientists got their most direct view of dark energy in action.  In July, physicists superimposed the galaxy-clustering data of SDSS on the microwave data of WMAP and proved — beyond a reasonable doubt — that dark energy must exist.  The proof relies on a phenomenon known as the integrated Sachs-Wolfe effect.  The remnant microwave radiation acted as a backlight, shining through the gravitational dimples caused by the galaxy clusters that the SDSS spotted.  Scientists saw a gentle crushing — apparent as a slight shift toward shorter wavelengths — of the microwaves shining near those gravitational pits.  In an uncurved universe such as our own, this can happen only if there is some antigravitational force — a dark energy — stretching out the fabric of spacetime and flattening the dimples that galaxy clusters sit in.

Some of the work of cosmology can now turn to understanding the forces that shaped the universe when it was a fraction of a millisecond old.  After the universe burst forth from a cosmic singularity, the fabric of the newborn universe expanded faster than the speed of light.  This was the era of inflation, and that burst of growth — and its abrupt end after less than 10-30 seconds — shaped our present-day universe.

For decades, inflation provided few testable hypotheses.  Now the exquisite precision of the WMAP data is finally allowing scientists to test inflation directly.  Each current version of inflation proposes a slightly different scenario about the precise nature of the inflating force, and each makes a concrete prediction about the CMB, the distribution of galaxies, and even the clustering of gas clouds in the later universe.  Scientists are just beginning to winnow out a handful of theories and test some make-or-break hypotheses.  And as the SDSS data set grows — yielding information on distant quasars and gas clouds as well as the distribution of galaxies — scientists will challenge inflation theories with more boldness.

The properties of dark energy are also now coming under scrutiny.  WMAP, SDSS, and a new set of supernova observations released this year are beginning to give scientists a handle on the way dark energy reacts to being stretched or squished.  Physicists have already had to discard some of their assumptions about dark energy.  Now they have to consider a form of dark energy that might cause all the matter in the universe to die a violent and sudden death.  If the dark energy is stronger than a critical value, then it will eventually tear apart galaxies, solar systems, planets, and even atoms themselves in a “big rip.”  (Not to worry; cosmologists aren't losing sleep about the prospect.)

For the past 5 years, cosmologists have tested whether the baffling, counterintuitive model of a universe made of dark matter and blown apart by dark energy could be correct.  This year, thanks to WMAP, the SDSS data, and new supernova observations, they know the answer is yes — and they're starting to ask new questions.  It is, perhaps, a sign that scientists will finally begin to understand the beginning.

Note:  The publishers of Science, the American Association for the Advancement of Science (AAAS), have made the “Breakthrough of the Year(2003-12-19) special issue of Science available without subscription or pay-per-view.  (Normally Science costs $125 per year, publishedly weekly — and totally worth it; $56 of that is tax deductible, by the way.)  Thus, the article in question is available for free online, all one must do is register for Science Online.

The online article (linked to below) ends with numerous links to abstracts and full text of recent online research reports and review articles in this area.  (I like the title of the article from last year, by A. Gangui:  “A Preposterous Universe”!)  Interesting results, indeed.


1 Charles Seife, “Illuminating the Dark Universe,” Science, Vol. 302, Issue No. 5653 (dated 2003-12-19), pp. 2038-2039.  Does not require subscription or pay-per-view; does require registration.

Impearls: 2004-01-11 Archive

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!


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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