Explanation: Light rays from accretion disks around a pair of orbiting supermassive black holes make their way through the warped space-time produced by extreme gravity in this stunning computer visualization. The simulated accretion disks have been given different false color schemes, red for the disk surrounding a 200-million-solar-mass black hole, and blue for the disk surrounding a 100-million-solar-mass black hole. That makes it easier to track the light sources, but the choice also reflects reality. Hotter gas gives off light closer to the blue end of the spectrum and material orbiting smaller black holes experiences stronger gravitational effects that produce higher temperatures. For these masses, both accretion disks would actually emit most of their light in the ultraviolet though. In the video, distorted secondary images of the blue black hole, which show the red black hole's view of its partner, can be found within the tangled skein of the red disk warped by the gravity of the blue black hole in the foreground. Because we're seeing red's view of blue while also seeing blue directly, the images allow us to see both sides of blue at the same time. Red and blue light originating from both black holes can be seen in the innermost ring of light, called the photon ring, near their event horizons. Astronomers expect that in the not-too-distant future theyâll be able to detect gravitational waves, ripples in space-time, produced when two supermassive black holes in a system much like the one simulated here spiral together and merge.
Re: APOD: The Doubly Warped World of Binary... (2021 Apr 16)
Posted: Fri Apr 16, 2021 4:42 am
by alter-ego
You can't touch this.
Re: APOD: The Doubly Warped World of Binary... (2021 Apr 16)
Posted: Fri Apr 16, 2021 4:46 am
by Ann
Wow. Very cool.
So...how about diving into a black hole in the hopes of finding a wormhole inside?
Any takers?
Ann
Re: APOD: The Doubly Warped World of Binary... (2021 Apr 16)
Posted: Fri Apr 16, 2021 4:50 am
by Chris Peterson
Ann wrote: ↑Fri Apr 16, 2021 4:46 am
Wow. Very cool.
So...how about diving into a black hole in the hopes of finding a wormhole inside?
Any takers?
Ann
At the least, you'd want to dive into a supermassive black hole, since that's the only kind that you might safely cross the event horizon. Unfortunately, you'll have to keep your discovery to yourself.
Re: APOD: The Doubly Warped World of Binary... (2021 Apr 16)
Posted: Fri Apr 16, 2021 5:06 am
by shaileshs
Sorry to say, today's APOD content might be "super cool and/or extraordinarily amazing" for some but for me (a lay person), honestly, I am not enjoying it much. Seems some *random imagination of super complex things we really don't know much about*.. And the music (background score) makes it even worse.. arbitrary mysterious sounds and patterns as if they are trying to narrate/convey some meaning and carry some importance.. Feels made for some Sci-Fi hollywood movie.. Sorry, I'm not questioning anyone's interest/knowledge/beliefs/feelings as such, I don't want to offend anyone, just expressing my personal thoughts.
Re: APOD: The Doubly Warped World of Binary... (2021 Apr 16)
Posted: Fri Apr 16, 2021 8:52 am
by JohnD
Thank you, APOD, and thnak you, NASA!
A recent BH simulation video on the APOD (https://apod.nasa.gov/apod/ap210411.html ) puzzled me by the apparent duplication of the BH's event horizons, which members here explained to me were caused by the space-time distortion in that part of space.
If I had seen this video first, I would not have needed to ask the question! It makes that distortion so clear, even to someone who has only the vaugest notion of the "super complex things we really don't know much about."!
The music, shaileshs, is very personal. It could have had the Blue Danube, if that wasn't a hackneyed trope since 2001!
John
Re: APOD: The Doubly Warped World of Binary... (2021 Apr 16)
Posted: Fri Apr 16, 2021 9:15 am
by rj rl
shaileshs wrote: ↑Fri Apr 16, 2021 5:06 am
*random imagination of super complex things we really don't know much about*
no more random than any image of atomic nucleus you've ever seen. And while black holes are certainly complex, they're not complex to the point where we absolutely can't even imagine what one would look like: we can and that's roughly what you see in the APOD. An actual image of a black hole was produced just a couple years ago remember, and it looked pretty close to what models predicted.
Re: APOD: The Doubly Warped World of Binary... (2021 Apr 16)
Posted: Fri Apr 16, 2021 10:17 am
by Knight of Clear Skies
rj rl wrote: ↑Fri Apr 16, 2021 9:15 am
no more random than any image of atomic nucleus you've ever seen. And while black holes are certainly complex, they're not complex to the point where we absolutely can't even imagine what one would look like: we can and that's roughly what you see in the APOD. An actual image of a black hole was produced just a couple years ago remember, and it looked pretty close to what models predicted.
Yes, we have direct evidence that binary black holes exist and that we can calculate the visual effects of their gravitational lensing. I think it's good that APOD tries to cover a variety of subjects.
Merging masses: chart showing the ten black-hole mergers (top) and one neutron-star merger (bottom). Also shown are black holes and neutron stars observed using electromagnetic (EM) radiation. (Courtesy: LIGO-Virgo/Frank Elavsky/Northwestern)
I agree the music was distracting but my mute button took care of that.
Re: APOD: The Doubly Warped World of Binary... (2021 Apr 16)
Posted: Fri Apr 16, 2021 12:38 pm
by orin stepanek
I don't think I like black holes! But I guess they are like a land fill, gobbling up all the waste & then some!
Re: APOD: The Doubly Warped World of Binary... (2021 Apr 16)
Posted: Fri Apr 16, 2021 1:06 pm
by Chris Peterson
orin stepanek wrote: ↑Fri Apr 16, 2021 12:38 pm
I don't think I like black holes! But I guess they are like a land fill, gobbling up all the waste & then some! :shock:
They really don't gobble up much. Even truly massive black holes like the one in M87, massing more than a billion suns and active enough to have jets, still take a decade just to suck in one additional solar mass. And the overwhelming majority of black holes pretty much suck in nothing at all.
Re: APOD: The Doubly Warped World of Binary... (2021 Apr 16)
Posted: Fri Apr 16, 2021 1:07 pm
by De58te
alter-ego wrote: ↑Fri Apr 16, 2021 4:42 am
You can't touch this.
There is the APOD understatement of the year. lol, So far no human has even figured out how to touch the surface of our own sun yet - and live!
Re: APOD: The Doubly Warped World of Binary... (2021 Apr 16)
Posted: Fri Apr 16, 2021 1:10 pm
by Chris Peterson
shaileshs wrote: ↑Fri Apr 16, 2021 5:06 am
Sorry to say, today's APOD content might be "super cool and/or extraordinarily amazing" for some but for me (a lay person), honestly, I am not enjoying it much. Seems some *random imagination of super complex things we really don't know much about*.. And the music (background score) makes it even worse.. arbitrary mysterious sounds and patterns as if they are trying to narrate/convey some meaning and carry some importance.. Feels made for some Sci-Fi hollywood movie.. Sorry, I'm not questioning anyone's interest/knowledge/beliefs/feelings as such, I don't want to offend anyone, just expressing my personal thoughts.
Except that this is a subject that we know a LOT about. The physics of the actual black hole itself, the singularity or tiny particle that lies inside the event horizon is not well understood. But outside of that? Black holes are weird with respect to our intuition, but they are not poorly understood, and their effects on the surrounding spacetime follow directly from GR and are observationally verified with multiple lines of evidence.
Re: APOD: The Doubly Warped World of Binary... (2021 Apr 16)
orin stepanek wrote: ↑Fri Apr 16, 2021 12:38 pm
I don't think I like black holes! But I guess they are like a land fill, gobbling up all the waste & then some!
They really don't gobble up much. Even truly massive black holes like the one in M87, massing more than a billion suns and active enough to have jets, still take a decade just to suck in one additional solar mass. And the overwhelming majority of black holes pretty much suck in nothing at all.
Thanks Chris!
Re: APOD: The Doubly Warped World of Binary... (2021 Apr 16)
Posted: Fri Apr 16, 2021 1:42 pm
by sillyworm 2
I find black holes fascinating .Basically the extreme biproduct of gravity, a process we experience daily,and as far as I can tell,we still don't know much about it.
Re: APOD: The Doubly Warped World of Binary... (2021 Apr 16)
Posted: Fri Apr 16, 2021 1:51 pm
by Chris Peterson
sillyworm 2 wrote: ↑Fri Apr 16, 2021 1:42 pm
I find black holes fascinating .Basically the extreme biproduct of gravity, a process we experience daily,and as far as I can tell,we still don't know much about it.
Given the number of different lines of evidence that continue to be found and which continue to support GR, I'd say we know almost everything about gravity. The only hole is how (if?) it is connected to the other forces/fields, all of which are described by QM.
Re: APOD: The Doubly Warped World of Binary... (2021 Apr 16)
Posted: Fri Apr 16, 2021 2:44 pm
by E Fish
That's an excellent video, and I appreciate that they anticipated my own questions about the distorted secondary image I was noticing during the orbit. I think I've found another video to show my astronomy class.
The first book I read on black holes was back in the 90s in my high school library. It was the only one they had and it was written back in the 60s. So it took me a while to get up to date on what black holes were and the fact that we've detected them. But I've long been fascinated by them and I love introducing students to them because it's a way to get their brains a little stretched.
Re: APOD: The Doubly Warped World of Binary... (2021 Apr 16)
orin stepanek wrote: ↑Fri Apr 16, 2021 12:38 pm
I don't think I like black holes! But I guess they are like a land fill, gobbling up all the waste & then some!
They really don't gobble up much. Even truly massive black holes like the one in M87, massing more than a billion suns and active enough to have jets, still take a decade just to suck in one additional solar mass. And the overwhelming majority of black holes pretty much suck in nothing at all.
Like the Milky Way's own supermassive black hole, I think.
Not that it couldn't get hungry in the future, when the Milky Way is getting too close for comfort to the Andromeda galaxy.
Ann
Re: APOD: The Doubly Warped World of Binary... (2021 Apr 16)
orin stepanek wrote: ↑Fri Apr 16, 2021 12:38 pm
I don't think I like black holes! But I guess they are like a land fill, gobbling up all the waste & then some! :shock:
They really don't gobble up much. Even truly massive black holes like the one in M87, massing more than a billion suns and active enough to have jets, still take a decade just to suck in one additional solar mass. And the overwhelming majority of black holes pretty much suck in nothing at all.
Like the Milky Way's own supermassive black hole, I think.
Not that it couldn't get hungry in the future, when the Milky Way is getting too close for comfort to the Andromeda galaxy.
Ann
Hungrier, maybe. But it will still not absorb very much. How could it? Its size does not exceed that of Neptune's orbit- a volume so small that any collisions with passing stars is extremely unlikely, even in the densest parts of the collision zones.
Re: APOD: The Doubly Warped World of Binary... (2021 Apr 16)
<<The Brodie helmet is a steel combat helmet designed and patented in London in 1915 by John Leopold Brodie. A modified form of it became the Helmet, Steel, Mark I in Britain and the M1917 Helmet in the U.S. Colloquially, it was called the shrapnel helmet, battle bowler, Tommy helmet, tin hat, and in the United States the doughboy helmet. It was also known as the dishpan hat, tin pan hat, washbasin, battle bowler (when worn by officers), and Kelly helmet. The German Army called it the Salatschüssel (salad bowl).
At the outbreak of World War I, none of the combatants provided steel helmets to their troops. Soldiers of most nations went into battle wearing cloth, felt, or leather headgear that offered no protection from modern weapons. The huge number of lethal head wounds that modern artillery weapons inflicted upon the French Army led them to introduce the first modern steel helmets in the summer of 1915. The first French helmets were bowl-shaped steel "skullcaps" worn under the cloth caps. These rudimentary helmets were soon replaced by the Model 1915 Adrian helmet, designed by August-Louis Adrian. The idea was later adopted by most other combatant nations.
At about the same time, the British War Office had seen a similar need for steel helmets. The War Office Invention Department was ordered to evaluate the French design. They decided that it was not strong enough and too complex to be swiftly manufactured. British industry was not geared up to an all-out effort of war production in the early days of World War I, which also led to the shell shortage of 1915.
John Leopold Brodie (1873–1945), born Leopold Janno Braude in Riga, was an entrepreneur and inventor who had made a fortune in the gold and diamond mines of South Africa, but was working in London at that time. A design patented by him in August 1915 offered advantages over the French helmet. It was constructed in one piece that could be pressed from a single thick sheet of steel, giving it added strength and making it simple to manufacture. Brodie's patent deals mainly with the innovative lining arrangements; an engineer called Alfred Bates of the firm of Willis & Bates of Halifax, Yorkshire, manufacturer of Vapalux paraffin pressure lamps, claimed that he was asked by the War Office to find a method of manufacturing an anti-shrapnel helmet and that it was he who had devised the basic shape of the steel shell. Aside from some newspaper articles, there is nothing to substantiate
Brodie's design resembled the medieval infantry kettle hat or chapel-de-fer, unlike the German Stahlhelm, which resembled the medieval sallet. The Brodie had a shallow circular crown with a wide brim around the edge, a leather liner and a leather chinstrap. The helmet's "soup bowl" shape was designed to protect the wearer's head and shoulders from shrapnel shell projectiles bursting from above the trenches. The design allowed the use of relatively thick steel that could be formed in a single pressing while maintaining the helmet's thickness. This made it more resistant to projectiles but it offered less protection to the lower head and neck than other helmets.>>
Re: APOD: The Doubly Warped World of Binary... (2021 Apr 16)
They really don't gobble up much. Even truly massive black holes like the one in M87, massing more than a billion suns and active enough to have jets, still take a decade just to suck in one additional solar mass. And the overwhelming majority of black holes pretty much suck in nothing at all.
Like the Milky Way's own supermassive black hole, I think.
Not that it couldn't get hungry in the future, when the Milky Way is getting too close for comfort to the Andromeda galaxy.
Ann
Hungrier, maybe. But it will still not absorb very much. How could it? Its size does not exceed that of Neptune's orbit- a volume so small that any collisions with passing stars is extremely unlikely, even in the densest parts of the collision zones.
Point taken, but what about Andromeda's black hole? It's a lot bigger than out own, and our two galaxies are set to merge in the future.
Ann
Re: APOD: The Doubly Warped World of Binary... (2021 Apr 16)
Posted: Fri Apr 16, 2021 4:55 pm
by johnnydeep
There are at least two statements here I don't quite understand:
1. "...material orbiting smaller black holes experiences stronger gravitational effects that produce higher temperatures."
Is this due to the tidal effects being greater for smaller black holes? Meaning that the gravity gradient is steeper around a smaller black hole and thereby tears at orbiting matter more greatly?
2. "...relativity causes the black holes to appear smaller and brighter as they approach the camera and larger and fainter as they recede."
This I don't get at all. Does it matter which BH is closer to the camera and/or whether they are eclipsing each other or not? And either way, I still don't get it
Re: APOD: The Doubly Warped World of Binary... (2021 Apr 16)
Chris Peterson wrote: ↑Fri Apr 16, 2021 1:06 pm
They really don't gobble up much. Even truly massive black holes like the one in M87, massing more than a billion suns and active enough to have jets, still take a decade just to suck in one additional solar mass. And the overwhelming majority of black holes pretty much suck in nothing at all.
Like the Milky Way's own supermassive black hole, I think.
Not that it couldn't get hungry in the future, when the Milky Way is getting too close for comfort to the Andromeda galaxy.
Hungrier, maybe. But it will still not absorb very much. How could it?
Its size does not exceed that of Neptune's orbit- a volume so small that any collisions with passing stars is extremely unlikely, even in the densest parts of the collision zones.
"[Recent] observations of the star S14 showed the mass of Milky Way's Sgr A* to be about 4.1 million solar masses within a volume with radius no larger than 45 AU or about 6.7 billion kilometres. S175 passed within a similar distance. For comparison, the Schwarzschild radius is 0.08 AU."
The Schwarzschild radius of Milky Way's Sgr A* is only 12.25 million kilometers.
(As of its last perihelion on 17 January 2021,
the Parker Solar Probe's closest approach to the Sun was at 13.5 million kilometers.)
However, the Andromeda Galaxy is thought to harbor two massive
black holes of radii 0.8 AU & 3.2 AU orbiting about 4.9 ly apart.
(The Schwarzschild radius of Messier 87's black hole is ~125 AU.
Voyager 1&2 are currently at 152.5 AU & 126.8 AU from the Sun.)
<<The Andromeda Galaxy is known to harbor a dense and compact star cluster at its very center. In a large telescope it creates a visual impression of a star embedded in the more diffuse surrounding bulge. In 1991, the Hubble Space Telescope was used to image the Andromeda Galaxy's inner nucleus. The nucleus consists of two concentrations separated by 1.5 pc (4.9 ly). The brighter concentration, designated as P1, is offset from the center of the galaxy. The dimmer concentration, P2, falls at the true center of the galaxy and contains a black hole measured at 3–5 × 107 M☉ in 1993, and at 1.1–2.3 × 108 M☉ in 2005. The velocity dispersion of material around it is measured to be ≈ 160 km/s.
Chandra X-ray telescope image of the center of the Andromeda Galaxy. A number of X-ray sources, likely X-ray binary stars, within the galaxy's central region appear as yellowish dots. The blue source at the center is at the position of the supermassive black hole.
It has been proposed that the observed double nucleus could be explained if P1 is the projection of a disk of stars in an eccentric orbit around the central black hole. The eccentricity is such that stars linger at the orbital apocenter, creating a concentration of stars. P2 also contains a compact disk of hot, spectral-class A stars. The A stars are not evident in redder filters, but in blue and ultraviolet light they dominate the nucleus, causing P2 to appear more prominent than P1.
While at the initial time of its discovery it was hypothesized that the brighter portion of the double nucleus is the remnant of a small galaxy "cannibalized" by the Andromeda Galaxy, this is no longer considered a viable explanation, largely because such a nucleus would have an exceedingly short lifetime due to tidal disruption by the central black hole. While this could be partially resolved if P1 had its own black hole to stabilize it, the distribution of stars in P1 does not suggest that there is a black hole at its center.>>
https://en.wikipedia.org/wiki/Sagittarius_A* wrote:
<<Since the 1980s it has been evident that the central component of Sgr A* is likely a black hole. Infrared and submillimetre spectroscopy by a Berkeley team involving Nobel Laureate Charles H. Townes and future Nobelist Reinhard Genzel showed that the mass must be very tightly concentrated, possibly a point mass.
On October 16, 2002, an international team led by Reinhard Genzel of the Max Planck Institute for Extraterrestrial Physics reported the observation of the motion of the star S2 near Sagittarius A* throughout a period of ten years. According to the team's analysis, the data ruled out the possibility that Sgr A* contains a cluster of dark stellar objects or a mass of degenerate fermions, strengthening the evidence for a massive black hole. The observations of S2 used near-infrared (NIR) interferometry (in the K-band, i.e. 2.2 μm) because of reduced interstellar extinction in this band. SiO masers were used to align NIR images with radio observations, as they can be observed in both NIR and radio bands. The rapid motion of S2 (and other nearby stars) easily stood out against slower-moving stars along the line-of-sight so these could be subtracted from the images.
The VLBI radio observations of Sagittarius A* could also be aligned centrally with the NIR images, so the focus of S2's elliptical orbit was found to coincide with the position of Sagittarius A*. From examining the Keplerian orbit of S2, they determined the mass of Sagittarius A* to be 2.6±0.2 million solar masses, confined in a volume with a radius no more than 17 light-hours (120 AU). Later observations of the star S14 showed the mass of the object to be about 4.1 million solar masses within a volume with radius no larger than 6.25 light-hours (45 AU) or about 6.7 billion kilometres. S175 passed within a similar distance. For comparison, the Schwarzschild radius is 0.08 AU. They also determined the distance from Earth to the Galactic Center (the rotational center of the Milky Way), which is important in calibrating astronomical distance scales, as (8.0±0.6) kiloparsecs. In November 2004 a team of astronomers reported the discovery of a potential intermediate-mass black hole, referred to as GCIRS 13E, orbiting 3 light-years from Sagittarius A*. This black hole of 1,300 solar masses is within a cluster of seven stars. This observation may add support to the idea that supermassive black holes grow by absorbing nearby smaller black holes and stars.
After monitoring stellar orbits around Sagittarius A* for 16 years, Gillessen et al. estimated the object's mass at 4.31±0.38 million solar masses. The result was announced in 2008 and published in The Astrophysical Journal in 2009. Reinhard Genzel, team leader of the research, said the study has delivered "what is now considered to be the best empirical evidence that supermassive black holes do really exist. The stellar orbits in the Galactic Center show that the central mass concentration of four million solar masses must be a black hole, beyond any reasonable doubt."
On January 5, 2015, NASA reported observing an X-ray flare 400 times brighter than usual, a record-breaker, from Sgr A*. The unusual event may have been caused by the breaking apart of an asteroid falling into the black hole or by the entanglement of magnetic field lines within gas flowing into Sgr A*, according to astronomers. On 13 May 2019, astronomers using the Keck Observatory witnessed a sudden brightening of Sgr A*, which became 75 times brighter than usual, suggesting that the supermassive black hole may have encountered another object.>>
Re: APOD: The Doubly Warped World of Binary... (2021 Apr 16)
Posted: Sat Apr 17, 2021 6:15 pm
by neufer
johnnydeep wrote: ↑Fri Apr 16, 2021 4:55 pm
There are at least two statements here I don't quite understand:
1. "...material orbiting smaller black holes experiences stronger gravitational effects that produce higher temperatures."
Is this due to the tidal effects being greater for smaller black holes? Meaning that the gravity gradient is steeper around a smaller black hole and thereby tears at orbiting matter more greatly?
Presumably. Tidal effects scale as M/r3 or 1/R2.
johnnydeep wrote: ↑Fri Apr 16, 2021 4:55 pm
2. "...relativity causes the black holes to appear smaller and brighter as they approach the camera and larger and fainter as they recede."
This I don't get at all. Does it matter which BH is closer to the camera and/or whether they are eclipsing each other or not? And either way, I still don't get it
Light from the most distance edge of an approaching accretion disk has to catch up with the black hole in order to pass it (both above & below) and, hence, requires minimal bending at a distanceimpact parameter for forward scattering. Minimal bending would also minimize the brightness of an optically thick nearly horizontal accretion disk even if the radiation wasn't spread out over a larger impact parameter.
Light from the most distance edge of a receding accretion disk has to avoid an oncoming black hole in order to pass it (both above & below) and, hence, requires maximal bending at a close impact parameter for forward scattering. Maximal bending would also maximize the brightness of an optically thick nearly horizontal accretion disk even if the radiation wasn't concentrated within a smaller impact parameter.
Re: APOD: The Doubly Warped World of Binary... (2021 Apr 16)
johnnydeep wrote: ↑Fri Apr 16, 2021 4:55 pm
There are at least two statements here I don't quite understand:
1. "...material orbiting smaller black holes experiences stronger gravitational effects that produce higher temperatures."
Is this due to the tidal effects being greater for smaller black holes? Meaning that the gravity gradient is steeper around a smaller black hole and thereby tears at orbiting matter more greatly?
Presumably. Tidal effects scale as M/r3 or 1/R2.
johnnydeep wrote: ↑Fri Apr 16, 2021 4:55 pm
2. "...relativity causes the black holes to appear smaller and brighter as they approach the camera and larger and fainter as they recede."
This I don't get at all. Does it matter which BH is closer to the camera and/or whether they are eclipsing each other or not? And either way, I still don't get it
Light from the most distance edge of an approaching accretion disk has to catch up with the black hole in order to pass it (both above & below) and, hence, requires minimal bending at a distanceimpact parameter for forward scattering. Minimal bending would also minimize the brightness of an optically thick nearly horizontal accretion disk even if the radiation wasn't spread out over a larger impact parameter.
Light from the most distance edge of a receding accretion disk has to avoid an oncoming black hole in order to pass it (both above & below) and, hence, requires maximal bending at a close impact parameter for forward scattering. Maximal bending would also maximize the brightness of an optically thick nearly horizontal accretion disk even if the radiation wasn't concentrated within a smaller impact parameter.
Thanks for trying, but that didn't help me, even after sleeping on it What's an "impact parameter"?
Re: APOD: The Doubly Warped World of Binary... (2021 Apr 16)
johnnydeep wrote: ↑Fri Apr 16, 2021 4:55 pm
2. "...relativity causes the black holes to appear smaller and brighter as they approach the camera and larger and fainter as they recede."
This I don't get at all. Does it matter which BH is closer to the camera and/or whether they are eclipsing each other or not? And either way, I still don't get it
Light from the most distance edge of an approaching accretion disk has to catch up with the black hole in order to pass it (both above & below) and, hence, requires minimal bending at a distanceimpact parameter for forward scattering. Minimal bending would also minimize the brightness of an optically thick nearly horizontal accretion disk even if the radiation wasn't spread out over a larger impact parameter.
Light from the most distance edge of a receding accretion disk has to avoid an oncoming black hole in order to pass it (both above & below) and, hence, requires maximal bending at a close impact parameter for forward scattering. Maximal bending would also maximize the brightness of an optically thick nearly horizontal accretion disk even if the radiation wasn't concentrated within a smaller impact parameter.
Thanks for trying, but that didn't help me, even after sleeping on it What's an "impact parameter"?