GALAXIES, STARS, PLANETS, MOONS, MINOR PLANETS AND COMETS

Suggested outward sweep of the Sun-Companion solar system barycenter (SSB) through the Kuiper belt at an exponential rate, driven by the spiral in of the brown dwarf components of former binary-Companion. The ‘tidal threshold’, associated with the SSB, perturbed Kuiper belt objects into the inner solar system during the late heavy bombardment:

– 35.8 AU at 4,567 Ma

– 39.4 AU at 4,220 Ma, 1st pulse of LHB by Plutinos

– 43 AU at 3,900 Ma, 2nd pulse of LHB by cubewanos

– Binary-Companion merges in an asymmetrical binary spiral-in merger explosion at 542 Ma, giving our newly-merged Companion escape velocity from the Sun

Abstract:

This alternative conceptual ideology attempts to suggest alternative primary mechanisms for the formation of gravitationally-bound objects and their subsystems, with the intention of creating more predictive, more falsifiable and less ad hoc ideologies than the standard models.

The following planetesimal to stellar formation mechanisms will be examined conceptually:
– Flip-flop fragmentation (FFF)
– Trifurcation
– Density-wave core spin off (core spin off)
– Streaming instability and hybrid accretion

– FFF suggests that excess angular momentum in the collapsing dark cores may create accretion disks which are much more massive than their diminutive cores with accretion disks which inertially dominate the system. A spiral density wave of a massive accretion disk may cause a bilateral disk instability, condensing a twin-binary-pair of ‘disk instability objects’, which are much more massive than the ‘stellar’ brown-dwarf or red-dwarf core at the center of the system. Following the disk instability, equipartition of kinetic energy causes a flip-flop to occur between the much-greater overlying mass of the twin-binary (stellar-mass) disk instability objects and the diminutive (brown-dwarf- or red-dwarf-mass) core, creating a hierarchical system in which the former core is ‘evaporated’ into a circumbinary orbit around the twin binary pair which spiral inward to conserve system energy and angular momentum. FFF is a catastrophic mechanism for projecting mass inward and increasing system entropy, compared to the gradualism of gas infalling onto a young stellar object from its accretion disk. Our own solar system is suggested to have undergone FFF in which our former binary-Sun spiraled in to merge at 4,567 Ma. The binary-Sun merger created a primary debris disk which condensed asteroids and chondrites against Jupiter’s strongest inner resonances and Kuiper belt objects against Neptune’s strongest outer resonances.

– Trifurcation suggests that FFF not only transfers kinetic energy and angular momentum from the orbits of more massive disk-instability objects to their central cores in a flip-flop process, but it also transfers rotational kinetic energy and angular momentum to the central cores, causing them to ‘spin up’. This spin up of a core may progress to the point of becoming a bar-mode instability which may undergo ‘trifurcation’, in which the self gravity of the bar-mode arms causes them to pinch off to form a twin binary pair in Keplerian orbit around the much-smaller but higher-density residual core. Thus our former brown-dwarf or red-dwarf-mass core is suggested to have trifurcated to form a former binary-Companion composed of a twin pair of brown-dwarf components, along with a super-Jupiter-mass residual core. Additionally, equipartition following trifurcation can cause next-generation trifurcation in the residual core, causing the super-Jupiter-mass residual core to trifurcate to form Jupiter-Saturn, whose residual core trifurcated to form Uranus-Neptune, whose residual core trifurcated to form Venus-Earth, with Mercury as the final residual core of 4 generations of trifurcation in our solar system.

– Density-wave core spin off is a less catastrophic mechanism than FFF by which an inertially dominant accretion disk may gravitationally couple with its prestellar or protostellar core by way of a lopsided m = 1 mode density wave, causing the core to spiral out from the center of rotation of the accretion disk. Core spin off may occur repeatedly to form multiple planets in a size range of mini-Neptunes to super-Jupiters.

– Hybrid accretion (Thayne Curie 2005) is suggested to form super-Earths just beyond the magnetic corotation radius of young stellar objects. Zillions of planetesimals presumably condense by streaming instability against the magnetic corotation radius at the inside edge of protoplanetary disks, followed by core accretion to form a super-Earth, with ‘hybrid’ referring to the combination of streaming instability and core accretion in the formation of hybrid-accretion objects. ‘Cascades’ of super-Earths may form in succession from the inside out when the first super-Earth creates a gap in the accretion disk and begins condensing planetesimals by streaming instability against its outer resonances. Hybrid-accretion moons may also form by this mechanism, such as the larger planemo moons of Uranus. Additionally, asteroids are suggested to have ‘condensed’ by streaming instability against Jupiter’s strongest inner resonances, and Kuiper belt objects (KBOs) are suggested to have condensed by streaming instability against Neptune’s strongest outer resonances.

Flip-flop perturbation of minor planets by a tidal threshold:
Flip-flop perturbation by a ‘tidal threshold’ is related to the barycenter between two massive objects, such as the Sun and former binary-Companion. When a heliocentric object is orbiting inside the tidal threshold its aphelion is attracted to the companion object, and when a heliocentric object is orbiting outside the tidal threshold, its aphelion will be centrifugally slung away from the Companion by 180°. In our early solar system our former brown-dwarf binary-Companion spiraled out from the Sun as its binary brown-dwarf components spiraled inward, causing the tidal threshold (which was associated with the solar system barycenter but not coincident with it) to spiral out through the classical Kuiper belt from about 4,100–3,800 Ma, perturbing Kuiper belt objects (KBOs) into the inner solar system, causing the late heavy bombardment. Then binary-Companion also spiraled in to merge at 542 Ma in an asymmetrical merger explosion that gave the newly-merged Companion escape velocity from the Sun, creating a secondary debris disk which condensed young, cold classical KBOs in low-eccentricity low-inclination orbits which have not been perturbed by the tidal threshold.
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Introduction:

Star formation stages:
1) Starless core: May be a transient phase or may progress to gravitational instability infall
2) Prestellar core: A gravitating prestellar core ends with the formation of the second hydrostatic core when hydrogen gas endothermically dissociates into atomic hydrogen at around 2000 K.
3) Protostar (Class 0, I, II, III): Begins with the formation of the second hydrostatic core.
4) Pre-main-sequence star: A T Tauri, FU Orionis, or larger (unnamed) pre-main-sequence star powered by gravitational contraction
5) Main-sequence star: Powered by hydrogen fusion

“Starless cores are possibly transient concentrations of molecular gas and dust without embedded young stellar objects (YSOs), typically observed in tracers such as C18O (e.g. Onishi et al. 1998), NH3 (e.g. Jijina, Myers, & Adams 1999), or dust extinction (e.g. Alves et al. 2007), and which do not show evidence of infall. Prestellar cores are also starless (M⋆ = 0) but represent a somewhat denser and more centrally-concentrated population of cores which are self-gravitating, hence unlikely to be transient.” (André et al. 2008)

In Jeans instability, the cloud collapses at an approximately free-fall rate nearly isothermally at about 10 K until the center become optically thick at ~10-13 g/cm3 after 105 yr (Larson 1969), at which point when the temperature begins to rise, forming a ‘first core’ or first hydrostatic core (FHSC). Supersonically infalling gas in the envelope is decelerated and thermalized at the surface of the first core (Masunaga et al. 1998).

When the temperature reaches about 2000 K, the hydrogen begins to dissociate endothermically, forming a ‘second core’, the birth of a protostar. The protostar grows in mass by accreting the infalling material from the circumstellar envelope, while the protostar keeps its radius at ~4 R☉ during the main accretion phase. (Masunaga et al. 1998)

“Enoch et al. (2009a) discovered a massive circumstellar disk of ∼1 M☉ comparable to a central protostar around a Class 0 object, indicating that (1) the disk already exists in the main accretion phase and (2) the disk mass is significantly larger than the theoretical
prediction.” (Machida et al. 2011)

“The size of the first core was found to vary somewhat in the different simulations (more unstable clouds form smaller first cores) while the size, mass, and temperature of the second cores are independent of initial cloud mass, size, and temperature.
Conclusions. Our simulations support the idea of a standard (universal) initial second core size of ~ 3 × 10−3 AU and mass ~ 1.4 ×10−3 M☉.”
(Vaytet et al. 2013)

“Class 0 objects are the youngest accreting protostars observed right after point mass formation, when most of the mass of the system is still in the surrounding dense core/envelope (Andre et al. 2000).”
(Chen et al. 2012)

“The compact components around the Class 0 protostars could be the precursors to these Keplerian disks. However, it is unlikely that such massive rotationally supported disks could be stably supported given the expected low stellar mass for the Class 0 protostars: they should be prone to fragmentation”.
(Zhi-Yun Li et al. 2014)
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Hybrid accretion planets and moons:

An additional planet formation mechanism proposed by Thayne Curie 2005, designated ‘hybrid accretion’, marries gravitational instability with core accretion, suggesting that zillions of planetesimals form by gravitational instability, which subsequently combine by core accretion to form planets.

Super-Earths are suggested to form by ‘hybrid accretion’ of planetesimals ‘condensed’ by streaming instability at the inner edge of accretion disks, presumably against the magnetic corotation radius of young stellar objects. The ‘hybrid’ term in ‘hybrid accretion’ refers to the juxtaposition of planetesimals formed by gravitational (streaming) instability, followed by the core accretion of those planetesimals into super-Earths.

Cascades of super-Earths are suggested to form in sequence from the inside out, with the innermost super-Earth of a cascade forming first. When hybrid accretion nominally reaches the size of a super-Earth, it creates a gap in the accretion disk, effectively truncating the inner edge of the accretion disk to its outer resonances where a next generation of planetesimals may condense from by streaming instability to form the next super-Earth in a possible cascade.

Streaming instability presumably can occur at the inner edge of accretion disks around giant planets as well, but the hybrid-accretion moon apparently clears a gap in the accretion disk long-long before reaching the scale of a super-Earth or even a super moon, presumably because proto gas-giant planets have relatively-weak magnetic fields compared to protostars, even correcting for their much-lower mass. And a comparatively-weak magnetic field puts the magnetic corotation radius comparatively close to gas-giant planets, which creates diminutive hybrid-accretion moons.

The 5 planemo moons of Uranus; Miranda, Ariel, Umbriel, Titania and Oberon appear to be the best example of a moony hybrid-accretion cascade in our solar system, with Mimas, Enceladus, Tethys, Dione, Rhea, and presumably Iapetus at Saturn as the second best.

The observed pattern of Uranian moons, tending to increase in size with orbital distance but not tending to decrease in density is suggested to be the pattern of hybrid accretion, where the most distant planemo hybrid accretion moon of Uranus (Oberon) hasn’t quite reached hybrid accretion maturity before the gravitational instability mechanism was shut down by the dissipation of the Uranian accretion disk.

See:
– Hybrid Mechanisms for Gas/Ice Giant Planet Formation (Thayne Currie 2005),
– And section; CASCADE FORMATION OF SUPER-EARTHS BY HYBRID CORE ACCRETION OF PLANETESIMALS ‘CONDENSED’ BY GRAVITATIONAL INSTABILITY AT THE INNER EDGE OF ACCRETION DISKS
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Flip-flop fragmentation (FFF):

This is an alternative conceptual ideology for the formation of similar-sized (twin) binary pairs by disk instability, followed by ‘flip-flopping’ the diminutive core at the center of the accretion disk into a circumbinary orbit around the much-larger twin-binary pair of disk instability objects, creating a hierarchical system. During the flip-flop process, the twin binary pair to spiral in to a tighter orbit around the center of gravity of the system or subsystem. This disk instability fragmentation followed by the inertial flip-flop is designated, flip-flop fragmentation (FFF).

When an accretion disk supported by rotation is much more massive than its central core, the accretion disk inertially dominates the system and dictates the dynamics, and the diminutive core may be unable to damp down disk inhomogeneities from amplifying into runaway disk instability.

In a massive accretion disk the differential mass of the disk increases with distance to the point where the outer portion of the disk may contain much more mass with near-zero-angular-momentum-with-respect-to-itself than its diminutive core and thus the outer portion of the disk will inertially dominate the system. Angular momentum merely forestalls inward gravitational attraction, where the inward projection of mass is suggested to be a proxy for increasing the system entropy, so any mechanism which promotes the inward projection of mass is suggested to be thermodynamically favorable. And catastrophic mechanisms for the inward projection of mass should be thermodynamically favored over the gradual infall of gas onto the core.

L1448 IRS3B:
The Class 0 protostar system, L1448 IRS3B is suggested to have formed by FFF, from an accretion disk with a spiral density wave. This triple system is composed of a similar-sized binary pair (IRS3B-a & IRS3B-b), with a combined mass of ~ 1 M☉ in a 61 AU binary orbit, with a distant tertiary companion (IRS3B-c) that has a minimum mass of of ~ 0.085 M☉ at a separation of 183 AU from the binary pair. This system may become more hierarchical over time, coming to resemble the Alpha Centauri system at half the mass. “Thus we expect the [L1448 IRS3B] orbits to evolve on rapid timescales (with respect to the expected stellar lifetime), especially as the disk dissipates. A natural outcome of this dynamical instability is the formation of a more hierarchical system with a tighter (few AU) inner pair and wider (100s to 1,000s AU) tertiary, consistent with observed triple systems.” (Tobin et al. 2016)

L1448 IRS3B (continued):
The tertiary star, IRS3B-c, is embedded in a spiral arm of the outer disk, where the spiral arm has an estimated mass of 0.3 M☉. The standard model of companion star formation expressed by Tobin et al. suggests that IRS3B-c formed in situ by gravitational instability from the spiral disk, making IRS3B-c younger than IRS3B-a & IRS3B-b, but problematically, circumbinary IRS3B-c is brighter at at 1.3 mm and 8 mm than its much more massive siblings, as is clearly apparent in the image above. Instead, the brighter (apparently more evolved) tertiary companion, IRS3B-c, appears to support an alternative FFF origin, in which a diminutive central core was surrounded by a much more massive accretion disk that underwent FFF disk instability. Presumably the disk instability condensed a twin binary pair that was much more massive than the central core and hierarchically displaced the older core into a circumbinary orbit, causing the twin binary pair to spiral inward. This is a fortuitously young system in which the smaller circumbinary star is still apparently more evolved than its twin-binary-pair (host) stars, since more massive stars evolve faster such that the twin-binary-pair stars will likely reach the main sequence before the smaller, older circumbinary star.

Protostar system L1448 IRS3B, showing central binary pair of protostars (IRS3B-a & IRS3B-b) orbited by a less massive but much brighter companion protostar (IRS3B-c) in a circumbinary orbit.

Image Credit: Bill Saxton, ALMA (ESO/NAOJ/NRAO), NRAO/AUI/NSF – Publication: John Tobin (Univ. Oklahoma/Leiden) et al.

Galactic FFF:
FFF may occur over a wide range of scales, from the gas-giant planet scale up to perhaps the galactic scale. Galactic FFF is suggested to be the mechanism by which proto-spiral-galaxies with excess angular momentum catastrophically projected mass inward to become stable spiral galaxies with flattened disk planes and sufficiently large galactic bulges to prevent further disk instability and spiral-galaxy core spin off. Our proto-Milky-Way is suggested to have experienced runaway disk instability, condensing a twin-binary-pair of disk instability objects that were much more massive than the diminutive core. Hierarchy emerged, causing the twin disk instability objects to spiral in, inertially ejecting the former core into a circumbinary orbit, perhaps as the Large Magellanic Cloud, with Triangulum Galaxy as the corresponding former FFF core of proto-Andromeda Galaxy. The twin disk instability objects flip-flopped with the core and spiraled in to form central bulge of the Milky Way, but not without retaining a fossil memory of their former binary origin in the form of a peanut/box-shaped central bulge, with an off-centered X structure. If the twin-binary-pair disk instability objects each formed a supermassive black hole (SMBH) by direct collapse, this may explain the origin of binary supermassive black holes in smaller and younger (spiral) galaxies that underwent galactic FFF, where the former twin-binary-pair SMBHs spiraled in to merge and form Sagittarius A* in the central galactic bulge of the Milky Way.
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Trifurcation:

This alternative ideology attempts to explain the origin of the 3 twin pairs of planets in our solar system (Jupiter-Saturn, Uranus-Neptune, Venus-Earth) and the suggested former brown-dwarf binary-Companion by the repetitive application of a suggested mechanism which fragments solitary gravitationally-bound objects into three components in Kelerian rotation around their mutual center of gravity in a mechanism designated, ‘trifurcation’.

Trifurcation is a suggested dynamic mechanism for pumping energy and angular momentum into a gravitationally-bound object, causing the object to ‘spin up’ to the point of inducing a bar-mode instability followed by fragmentation into three components: a twin (similar-sized) binary pair and a smaller residual core. In the flip-flop dynamic of FFF a diminutive core is inertially displaced into a circumbinary orbit around the much-larger twin binary pair of disk-instability objects condensed from the accretion disk, and the resulting energy and angular momentum transfer from the larger, younger twin-binary-pair disk-instability objects to the smaller, older central core is suggested to also pump energy and angular momentum into the rotation of the diminutive core, causing it to spin up.

The centrifugal force of a progressive spin up distorts a core from a radially-symmetrical oblate spheroid into a bilaterally-symmetrical bar-mode instability. As the bar-mode arms become increasingly displaced from the center of gravity, the self gravity of the bar-mode arms increases until it dominates and causes gravitational fragmentation, where the arms pinch off from the core to form a twin binary pair of discrete gravitationally-bound objects within their own Roche spheres in Keplerian orbits around a much-smaller residual core.

Following trifurcation pinch off, the much-greater inertial mass of the twin binary pair dominates the nascent trinary system, where the much-greater overlying twin-binary-pair mass is dynamically unstable, which initiates a transfer of kinetic energy and angular momentum from the twin binary pair to the residual core in a dynamic flip-flop mechanism akin to FFF.

In addition to FFF induced trifurcation, trifurcation itself is suggested to induce next-generation trifurcation of the residual core by means of the flip-flop mechanism the two mechanisms have in common. Following trifurcation, the dynamic interplay between the three trifurcated components transfers orbital energy and angular momentum from the larger twin binary pair to the smaller residual (tertiary) core until the core is evaporated into a circumbinary orbit around the larger twin binary pair. This orbital energy and angular momentum transfer is suggested to accompany a rotational energy and angular momentum transfer into the core, tending to induce a next-generation trifurcation in the core.

At the instant of trifurcation, when the twin bar-mode arms pinch off into separate gravitationally-bound objects within their own Roche spheres, the residual core is at the trinary center of gravity, orbited by the twin binary pair. The much-greater overlying mass of the twin binary pair constitutes an unstable system which amplifies chaotic inhomogeneities to create orbital ‘interplay’ between the trinary components. During interplay, orbital close encounters between the core and its twin-binary-pair components tends to equalize the kinetic energy by the process known as ‘equipartition’ of kinetic energy, transferring orbital energy and angular momentum from the more-massive twin components to the less-massive core. In this way, orbital interplay gradually gives way to a hierarchical system in which the less-massive core is ‘evaporated’ into a circumbinary orbit around the twin binary pair, while the twin binary pair sinks inward to conserve subsystem energy and angular momentum; however, the trifurcation subsystem itself may be orbiting within a larger system undergoing FFF or within a previous-generation trifurcation system, so while a twin binary pair is induced to spiral inward due to dynamic interactions with its less-massive core, the twin binary pair may be simultaneously induced to spiral outward due to dynamic interactions with a much-larger twin-binary disk-instability objects, or much-larger previous-generation-trifurcation twin-binary pair. So twin binary components may ultimately either spiral in to merge (like former binary-Companion), or may spiral out to dynamically separate, like Jupiter-Saturn, Uranus-Neptune, and Venus-Earth. Presumably diminutive cores rarely if ever spiral in to merge with much-larger twin components, even if their twin binary-pair components do so, but instead evaporate out to become permanent satellites of their immediate subsystem or larger system.

During interplay, hyperbolic-trajectory close encounters between a core and its more-massive twin binary components also tends to increase the rotation rate of the core. Scheeres et al. 2000 calculates that the rotation rate of asteroids tends to increase in close encounters of asteroids with larger planemo objects. Thus kinetic energy and angular momentum are not only pumped into the orbit of the core around the center of gravity of the trinary subsystem but also pumped into the rotation of the residual core, perhaps to the point of inducing a next-generation trifurcation. In this way a next-generation (higher-order) trifurcation is suggested to possibly evolve from the previous-generation (lower-order) trifurcation by way of spin up of the core.

Trifurcation leaves behind a much-smaller higher-density (higher-metalicity) residual core by spinning off the gaseous volatiles into the bar-mode arms, where the bar-mode arms condense into the next-generation twin binary pair. But while the densest solids gravitationally sequester in the core, the heaviest gaseous isotopes are presumably fractionated into the bar-mode arms by the centrifugal centrifuge effect. So while the residual core acquires the highest metallicity solids of the trifurcated components, the twin binary pair presumably acquires the heaviest gaseous isotopes, where gravity wins inside a certain threshold radius of a bar-mode instability and centrifugal force wins beyond the threshold radius.

Jupiter apparently also underwent (pinch-off) FFF during Jupiter-Saturn trifurcation, forming a super moon which apparently underwent two generations of moony trifurcation. (See the following subsection for an explanation of ‘pinch-off FFF’. Indeed, Io (3.528 g/cm3) and Europa (3.013 g/cm3) are considerably denser than Ganymede (1.936 g/cm3) and Callisto (1.8344 g/cm3), in line with residual cores having higher density then their twin binary pair siblings. But if so, Jupiter is missing a residual core of second-generation moony trifurcation of twin-binary-pair Io and Europa.

FFF and trifurcation are suggested catastrophic mechanisms for catastrophically projecting mass inward and increasing system entropy by way of increasing system asymmetry. While trifurcation of a core increases its energy and angular momentum and reduces its entropy, the top-level system must conserve energy and angular momentum and must experience a sufficient increase in entropy to drive the system forward.
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‘Pinch-off FFF’ accompanying trifurcation, forming binary planets and oversized moons:

Since Earth’s Moon has a proportionately smaller iron core than Earth itself, the Moon apparently did not form by trifurcation of proto-Earth, otherwise it should have a proportionately-larger iron core than Earth, as Mercury has. Alternatively, the lower-density of the Moon compared to the Earth suggests an alternative mechanism: ‘pinch-off-FFF’ in the bar-mode arm constituting proto-Earth during the suggested trifurcation of the super-Earth-sized object that formed the twin binary pair Venus & Earth, with the residual core, Mercury.

During trifurcation pinch off, if a pinched-off bar-mode arm possess excess angular momentum such that it can’t directly condense into a solitary object, a pinched-off bar-mode arm with excess angular momentum may undergo a form of FFF, condensing a twin binary pair of disk-instability objects around a diminutive pinch-off-FFF core. Then the diminutive FFF core spirals out into a circumbinary orbit around the twin binary pair as they spiral in to ultimately merge and form a solitary planet with an oversized moon. Titan at Saturn and Moon at Earth are presumably ‘pinch-off-FFF’ moons. Even after Titan lost most of its gaseous component by volatile evaporative loss, it still formed into a much larger pinch-off-FFF moon than the subsequently-formed hybrid-accretion moons, namely, Mimas, Enceladus, Tethys, Dione, Rhea, and Iapetus.

Binary spiral in merger is suggested to condense chondrules and chondrites, primarily from polar jets squirting from merging cores. Enstatite chondrites, which lie on the terrestrial fractionation line, presumably condensed from polar-jet material that squirted from the cores of the binary spiral-in merger of former binary-Earth and/or former binary-Venus, with their highly-chemically-reduced and super-enriched sulfur composition pointing to proto-Earth core material, presumably squirting out in polar jets from the merging cores. If so, then ordinary chondrites, with their elevated ∆17O values, may have condensed from the binary spiral-in merger of another binary trifurcation planet, perhaps former binary-Jupiter and/or former binary-Saturn. The wide range of carbonaceous chondrites presumably condensed from the ‘primary debris disk’ formed from the binary spiral-in merger of former binary-Sun.

Analyzing the Jupiter system from a ‘pinch-off-FFF’ perspective reveals multiple oversized moons, suggesting that a pinch-off-FFF core may undergo one or more generations of trifurcation. Apparently, the Jovian pinch-off-FFF core underwent two generations of trifurcation, to form the first-generation twin binary pair of Ganymede & Callisto and the second-generation twin binary pair of Io and Europa, with a missing second-generation trifurcation core (possibly having merged with Io).

Additionally, Triton appears to be Neptune’s oversized pinch-off-FFF moon, in which case Venus and Uranus are missing pinch-off-FFF moons, suggesting that Venus and Uranus either didn’t undergo pinch-off FFF, or subsequently lost their pinch-off-FFF moons. While the dwarf-planet Eris could correspond to Uranus’ lost pinch-off-FFF moon, Venus is out in the cold without a likely former moon in the inner solar system, with Ceres, presumably too small and icy, and Mars, presumably too large and ‘isotopy’ (with Mars having the wrong oxygen-isotope signature). ………………..

Density-wave core spin off:

What follows is a working ideology for a ‘density-wave core spin off’ mechanism (abbreviated, ‘core spin off’) for forming giant planets, whereby a massive disk inertially displaces its gas-giant-mass core from the center of rotation as a means of ‘projecting mass inward’ (as in mass segregation in globular clusters), where ‘projecting mass inward’ is a suggested proxy for increasing system entropy.

When an accretion disk is much more massive than its diminutive core, the disk inertia dominates the system. And an accretion-disk dominated system will evolve in a manor which maximizes system entropy over time, while conserving system energy and angular momentum.

This working ideology suggests that a massive accretion disk with a diminutive gas-giant-mass core may assume a lopsided m = 1 density wave that gravitationally couples with the core like a binary pair orbiting its common barycenter, causing the core to spiral out from the center of rotation of the accretion disk.

Presumably the lopsided densification of an m = 1 mode density wave gravitationally couples with the core, creating an orbiting, binary-pair ‘odd couple’, with its barycenter presumably residing at the center of rotation of the accretion disk. An m = 1 mode density wave is a lopsided (bilaterally asymmetrical) density wave (see image).

Density waves rotate with the galaxy or accretion disk. At the ‘corotation radius’ of a density wave, the stars and gas rotate together. Inside the corotation radius, the stars and gas rotate faster than the density wave, resulting in an inner Lindblad resonance, whereas beyond the corotation radius, the stars and gas rotate slower, resulting in an outer Lindblad resonance.

For a core to progressively spiral out from the center of rotation suggests a gradual appearance of a presumed m = 1 mode density wave, perhaps gradually transitioning from a more common, (nominally bilaterally symmetrical) m = 2 mode density wave, or from a superposition of a nascent m = 1 mode over an existing m = 2 mode density wave.

Binary asteroids orbiting a common barycenter consitute a stable system coupled by gravitational feedback, but this type of suggested binary-pair odd couple require additional coupling (feedback) elements, such as orbital period coupling and presumably a gradually increasing moment of inertia as the core progressively spirals out from the center of rotation.

Core spin off by means of density-wave coupling is presumably driven by an inward projection of mass, but the that portion of the ideology is a mere tenet.

Once the core spirals out to its maximum extent, the m = 1 mode density wave may dissapate when the inward projection of mass, which presumably drives the process, dwindles away. Core-spin-off planets presumably spiral out many AU, only to gradually spiral back in to its final orbit as a stellar mass finally forms at the center of rotation. The subsequent substantial spiral in of core-spin-off proto-planets presumably occurs in an angular-momentum-conserving fashion, unlike non-angular-momentum-conserving ‘planetary migration’ theory espoused by core accretion theory, where angular momentum is supposedly trasferred to or from the accretion disk, depending on the type of planetary migration.

Exoplanet systems with mutiple gaseous planets apparently indicates that the process can occur repeatedly, with earlier generations of core-spin-off planets presumably not gravitationally coupling with an incipient m = 1 mode density wave like a binary-pair odd couple orbiting a mutual barycenter. There also must also be a an (unknown) trigger mechanism to initiate core spin off, which allows a core to reach a gas-giant size before initiating, and allowing the process to occur repeatedly to form multiple core-spin-off planets.

Presumably the final core attains a sufficient mass relative to the accretion disk to prevent (damp down) further instances of core spin off, where the formation of the final stellar-mass core is presumably aided by the inward projection of accretion-disk mass during one or more episodes of core spin off.

Mini-Neptunes (also known as gas dwarf planets) in a mass range of about 6–10 Earth masses may be the most common type of exoplanet in the universe, and their hydrogen/helium atmospheres suggest the lower limit of spin off planets around dwarf stars, although there may be no bright-line cut off between high-end super-Earths formed by hybrid accretion and low-end mini-Neptunes with tenuous H-He atmospheres formed by core spin off. The rocky cores of mini-Neptunes are presumably formed by sedimentation of dust and ice during the circa 100,000 year prestellar phase, forming super-Earth-sized cores of rock and ice that survive core spin off, even when the vast majority of the hydrogen and helium of their extended atmospheres dissipates back into the accretion disk following core spin off.

Flip-flop fragmentation is suggested to form solar systems such as ours with a former binary-brown-dwarf-Companion at many 100s to several 1000s of AU, or the Alpha Centauri system with red-dwarf Prxima Centauri at 12,950 AU, or the L1448 IRS3B system with red-dwarf IRS3B-c at 183 AU, by flip-flopping brown dwarf or red dwarf cores into circumbinary orbits around much-larger twin-binary-pair disk-instability-object stars, whereafter secular perturbation may cause the twin binary pairs to spiral in and merge, as is suggested to have occurred in our solar system with the binary-Sun components merging at 4,567 Ma. By comparison, hot Jupiter exoplanets have an orbital period of under 10 days and ‘cold Jupiters’ have a median semi-major axes of about 2 AU. The paucity of brown dwarf orbits of less than 5 AU, known as the ‘brown-dwarf desert’, may indicate that brown dwarfs are apparently above the upper-limit cut off for objects formed by the core-spin-off mechanism, at least around yellow dwarf stars such as our own. But by simple mass extrapolation, accretion disks around giant stars may routinely form brown dwarfs and red dwarf stars by the core-spin-off mechanism.

Globular clusters as proto-spiral-galaxy core-spin-off objects:
The analogy between suggested core-spin-off planets around dwarf stars and globular clusters around the central bulge of spiral galaxies suggests a formational analogy. Presumably proto-spiral-galaxies with excess angular momentum and massive spiral disks spun off a succession of former cores in the form of globular clusters as the most efficient mechanism for projecting spiral-disk mass inward and winding down excess angular momentum. But the growing inertial mass of the collective globular clusters may have ultimately terminated the galactic core-spin-off phase, perhaps causing a switch to an m = 2 mode spiral density wave which culminated in a single instance of galactic FFF, converting our former proto-Galaxy into a mature spiral galaxy with a sufficiently-large central bulge to damp down further instances of galactic core spin off or galactic FFF.
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Hot Jupiter and cold Jupiter core-spin-off planets:

What follows is a working ideology to explain the distinct bimodal distribution of gas-giant exoplanets into hot Jupiters in low ‘hot’ orbits and ‘cold Jupiters’ in much-higher ‘cold’ orbits. Hot Jupiters are suggested to spin off during early prestellar freefall phase, while cold Jupiters are suggested to spin off during the later protostellar phase, with a circa 1000 year core-spin-off hiatus during the intervening hydrostatic core (FHSC) phase. Presumably the difference in accretion disk size and mass between the early prestellar phase and the later protostellar phase dictates the ultimate spin off distance, with the circa 1000 year FHSC hiatus explaining the distinct bimodal grouping.

In the core of a prestellar object, the potential energy released by gas undergoing freefall accretion is radiated adiated away, largely by dust and chemical compounds, notably carbon monoxide, maintaining the core temperature at around 10 K. When the core density reaches about 10^13 g cm-3, it becomes optically thick to infrared radiation, causing the internal temperature to rise. This rise in temperature creates a ‘first hydrostatic core’ (FHSC), with compression becoming approximately adiabatic. The FHSC phase is thought to last about 1000 years, by which time the core temperature rises to about 2000 K. At around 2000K, the core undergoes a brief ‘second collapse’, on the order of 0.1 yr, caused by the endothermic dissociation of molecular hydrogen. Following the fleetingly-brief second collapse, the prestellar object transitions to a ‘second hydrostatic core’ (SHSC) wherein it becomes known as a protostar.

The outer shock front of the FHSC phase extends out to radii on the order of ~ 5–10 AU (Tsitali et al. 2013). This enormous hydrostatic diameter of the FHSC phase is suggested to create sufficient viscous drag between the core and the inner edge of the accretion disk so as to largely preclude core spin off during this puffy transitional phase, thus creating a circa 1000 year hiatus in core spin off.

By comparison, the initial radius of the SHSC is only about 1.3 solar radaii (Larson 1969), albeit initially with an extended hydrostatic shock front characteristic of the FHSC, so the core-spin-off hiatus may extend into the SHSC phase until its radiation pressure dissapates or collapses the extended hydrostatic envelope.

“The [second hydrostatic] core then begins to lose a significant amount of energy through the combined effects of convective energy transport from the interior and radiative energy losses from the surface layers; as a result the core contracts by a significant factor in radius. This phase of the evolution, represented in Fig. 3 by the section of the curve between approximately 10 and 100 years after the formation of the stellar core, is quite analogous to the pre-main sequence contraction of a star along the ‘Hayashi track’.” (Larson 1969)

So if accretion disk size dictates the spin-off distance of core spin off planets, then the accretion disk size range typical of FHSC systems may explain the bimodal orbital gulf between hot Jupiters and cold Juipiters.

Protostar system L1448 IRS3B, showing central binary pair of protostars (IRS3B-a & IRS3B-b) orbited by a less massive but much brighter companion protostar (IRS3B-c) in a circumbinary orbit.

Image Credit: Bill Saxton, ALMA (ESO/NAOJ/NRAO), NRAO/AUI/NSF – Publication: John Tobin (Univ. Oklahoma/Leiden) et al.

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Solar system evolution:

A massive accretion disk around a small red-dwarf-sized core distorted by spiral-density wave underwent FFF, condensing a twin pair of disk-instability objects, binary-Sun, that flip-flopped with the much-smaller red-dwarf-sized core. During the FFF flip-flop, the core underwent 4 generations of trifurcation, forming 4 twin binary pairs, plus the residual core, Mercury:
1) Binary-Companion (former)
2) Jupiter-Saturn
3) Uranus-Neptune
4) Venus-Earth + residual core, Mercury.

Smaller higher-generation trifurcation components tend to cause twin binary pairs to spiral in, while larger lower-generation trifurcation components tend to cause twin binary pairs to spiral out, so the multi-generation trifurcation components conspired to cause the twin binary-Sun components to spiral in and merge at 4,567 Ma, creating a ‘primary debris disk’, while the twin binary-Companion components spiraled in to merge 4 billion years later, at 542 Ma, creating a ‘secondary debris disk’. Supernova explosions are known to create run away stars, so an asymmetrical binary spiral-in merger explosion of our former binary-Companion at 542 Ma is suggested to have given the newly-merged Companion escape velocity from the Sun.

Flip-flop perturbation:
The tidal threshold between the Sun and former binary-Companion is suggested to have perturbed Kuiper belt objects (KBOs), most notably during the late heavy bombardment (LHB)(4000–3800 Ma) by means of aphelia precession. As the brown-dwarf binary-Companion components spiraled in, the brown-dwarf orbital potential energy was transferred to the Sun-Companion system, causing the Sun-Companion orbits around their common center of gravity, the ‘solar system barycenter’ (SSB), became progressively more eccentric, causing the ‘tidal threshold’, associated with the SSB, to spiral out into the classical Kuiper belt, perturbing KBOs by causing aphelia precession. The major axes of KBO orbits were aligned with the Sun-Companion axis, with their aphelia gravitationally attracted toward binary-Companion inside the tidal threshold and with their aphelia centrifugally slung away from the Companion beyond the tidal threshold. So as the eccentric tidal threshold reached a KBO for the first time it begin periodic aphelia-precession perturbation, with the period of Sun-Companion around the SSB. The tidal threshold reached the Plutinos at 4,220 Ma, causing the first (narrow) spike in a bimodal late heavy bombardment, followed by the more prolonged and heavier second pulse centered around 3,900 Ma, as the tidal threshold spiraled through the classical KBOs (cubewanos).

Primary (4,567 Ma) and secondary (542 Ma) debris disks:
Binary-Sun is suggested to have merged at 4,567 Ma in a luminous red nova that created a primary debris disk which condensed asteroids against Jupiter’s strongest inner resonances, presumably by streaming instability, and condensed Kuiper belt objects (KBOs) against Neptune’s strongest outer resonances. Polar jets from the binary merger condensed calcium-aluminum-rich inclusions (CAIs) with a canonical r-process aluminum-26 concentration from the merging cores. The polar jets apparently took several million years to flatten into a debris disk to condense chondrites, some of which formed several million years after the rocky-iron asteroids with live radionuclides. The binary brown-dwarf components of binary-Companion presumably merged at 542 Ma, creating a ‘secondary debris disk’ around the Sun which apparently condensed a young population of cold classical KBOs by gravitational instability against Neptune’s outer resonances in unperturbed (‘cold’) low-inclination low-eccentricity orbits, with a high incidence of similar-sized binary pairs. Primary debris disk KBOs also originally condensed in ‘cold’ low-inclination, low-eccentricity orbits, with a high incidence of similar-sized binary pairs, but were subsequently perturbed into ‘hot’ high-inclination high-eccentricity orbits by flip-flop perturbation (apsidal precession) by the tidal threshold between the Sun and former binary-Companion. Flip-flop perturbation apparently also either dissociated binary KBOs, or caused binary components to spiral in and and merge. So the old, first-generation, hot classical KBO population in dynamically-excited ‘hot’ (high-inclination high-eccentricity) orbits presumably condensed from a primary debris disk from the ashes of the spiral in merger of former binary-Sun at 4,567 Ma and were subsequently perturbed into their ‘hot’ orbits by binary-Companion. And the young, second-generation, cold classical KBO population in unperturbed, ‘cold’, low-inclination low-eccentricity orbits, with frequent similar-sized binary pairs, presumably condensed from a secondary debris disk created from the ashes of the spiral-in merger of former binary-Companion at 542 Ma. If a young second generation asteroids/chondrites condensed from the secondary debris disk (542 Ma) against Jupiter’s inner resonances, they haven’t been identified in the meteorite population found on Earth.

Mars:
Mars stands out as the only suggested hybrid accretion planet in our solar system, even though suggested hybrid-accretion super-Earths are commonplace in the exoplanet tally. Our early solar system may bear a resemblance to the twice as massive Alpha Centauri system, with Proxima Centauri comparing with our former binary-Companion, and Alpha Centauri A & B stars comparing with our former binary-Sun. While the Alpha Centauri system did not undergo the 4 generations of trifurcation that are suggested to have occurred in our solar system, both systems may contain a hybrid accretion planet. Perhaps our former binary-Sun B-star component formed a hybrid-accretion planet, Mars, comparable to the unconfirmed super-Earth exoplanet, Alpha Centauri Bc (unconfirmed), around the Alpha Centauri B star.

The Pluto system:
The Pluto system presumably formed in situ by streaming instability against Neptune’s strongest outer 2:3 resonance, either from the primary debris disk resulting from the spiral-in merger of former binary-Sun at 4,567 Ma or more likely from the secondary debris disk resulting from the spiral-in merger of former binary-Companion at 542 Ma since the geologically active surface of Pluto and its intact (unperturbed) trifurcation moons point to the younger formation date. The Pluto system presumably formed by FFF, followed by 3 generations of trifurcation, very similar to our FFF and 4-generation trifurcation solar system, in which FFF disk instability presumably condensed a twin-binary-pair of disk instability objects (binary-Pluto) from a ‘disk’ around a proto-Charon core. The first-generation trifurcation of the core created a twin binary pair (binary-Charon) and a residual core. The second-generation trifurcation of the core created the twin-binary-pair, Nix (50 x 35 x 33 km) & Hydra (65 x 45 x 25 km), with a residual core, and the third-generation trifurcation created the twin-binary-pair, Styx (16 x 9 x 8) & Kerberos (19 x 10 x 9 km), with a residual core which hasn’t been discovered, but a much-smaller residual core would likely be too dim to be seen by the Hubble Wide Field Camera that found Styx & Kerberos. Then like our solar system, the two largest twin binary pairs, binary-Pluto and binary-Charon, spiraled in and merged. The Pluto system apparently puts streaming instability against a giant-planet resonance on the same footing as the collapse of a stellar-mass dark core in a giant molecular cloud, but since densities of the smaller Pluto moons are unknown, the density progression of the trifurcation generations is still only a prediction.

Cambrian Explosion:
A number of Phanerozoic events may be correlated with the suggested binary brown-dwarf merger explosion, as well as the loss of the SSB, even though Earth would likely have accreted only a thin veneer of material from the secondary debris disk. The Cambrian Explosion, with the sudden appearance of most major animal phyla, is suggested to result of the disbursal of free-swimming brown-dwarf lifeforms, likely from a water-vapor cloud layer (similar to Jupiter) in the upper cloud decks of a room-temperature spectral-class-Y brown dwarf or super-Jupiter binary component of former binary-Companion, presumably with lightening between water-vapor clouds creating free oxygen.

Venus retrograde rotation and the Great Unconformity:
The loss of the Companion at 542 Ma would correspond with a loss of centrifugal force of the Sun around the former SSB, causing all heliocentric objects to fall into slightly-lower shorter-period orbits. If Venus had been in a synchronous orbit prior to the loss of the Companion, its slight retrograde rotation today might be the result of having dropped into a slightly shorter-period orbit, with conservation of rotational angular momentum. Venus also apparently underwent a global resurfacing event, some 300–500 million years ago. The corresponding upheaval on Earth is suggested to be the cause of the global erosion event known as the ‘Great Unconformity’.
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‘Flip-flop perturbation’ of KBOs:

Secular perturbation of our former binary-Companion’s brown-dwarf components caused them to spiral in for 4 billion years, translating close-binary potential energy into wide-binary potential energy. This energy transfer increased the Sun-Companion eccentricity over time around the solar system barycenter (SSB), progressively increasing the maximum wide-binary Sun-Companion separation (at apoapsis), presumably at an exponential rate over time. By Galilean relativity with respect to the Sun, SSB could be said to have spiraled out through the Kuiper belt at an exponential rate for 4 billion years, fueled by the orbital potential energy of the binary-Companion brown-dwarf components.

(Negative) gravitational binding energy is an inverse square function with distance, such that an orbit 100 times further away will have 1/10,000 the binding energy. Angular momentum, by comparison, is an inverse square root function of the semimajor axis, such that an orbit 100 times further away will have 10 times the angular momentum. Since the binding energy function is much steeper than the angular momentum function with respect to distance, the brown-dwarf components of binary-Companion could dramatically reduce the negative Sun-Companion binding energy of the system without much affect its angular momentum. Periapsis of an orbit is a good measure of its relative angular momentum, while apoapsis is a good measure of its relative binding energy, so the 4 billion year spiral-in of the binary components of binary-Companion effectively increased the Sun-Companion apoapsis at an exponential rate, (by Galilean relativity) causing the SSB apoapsis to spiral out through the Kuiper belt and into the scattered disc over time.

Tidal perturbation of KBOs by the Sun-Companion system can be visualized with the example of lunar tides on Earth. Earth has two lunar high tides, a high tide on the Moon side of Earth, gravitationally pulled into high tide by the Moon, and a high tide on the far side of Earth, centrifugally slung away from it. The Earth-Moon barycenter is inside the Earth, and it can be stated that the centrifugal force of the Earth around the Sun-Moon barycenter creates the far-side lunar tide by centrifugal force. But while the near side and far side high tides are relatively symmetrical, they are not symmetrical around the Sun-Moon barycenter axis, but instead symmetrical around a point we’ll call the ‘tidal threshold’, which is associated with the Sun-Moon barycenter, but not coincident with it. Similarly, the tidal threshold of the solar system was not coincident with the SSB, but associated with it.

The tidal threshold on Earth is low tide, across which the ocean is either pulled toward the Moon or centrifugally slung away from it. And by analogy, when the semi-major axes of KBOs crossed the Sun-Companion tidal threshold, KBOs underwent aphelia-precession perturbation from having their aphelia gravitationally attracted toward binary-Companion to being centrifugally slung away from it (centrifugally slung 180° away from binary-Companion).

In the Sun-Companion system (prior to 542 Ma) all heliocentric object aphelia were aligned with the Sun-Companion axis, with either their aphelia pointing toward binary-Companion or 180° away from binary-Companion. And note that the tidal threshold is defined with respect to the semi-major axes of KBOs, such that KBOs with their semi-major axes closer to the Sun than the tidal threshold had their aphelia gravitationally attracted toward binary-Companion, while KBOs with their semi-major axes further from the Sun than the tidal threshold had their aphelia centrifugally slung 180° away from binary-Companion. And when the tidal threshold crossed the semi-major axis of a KBO, it cause aphelia precession, either toward or 180° away from binary-Companion, depending on whether tidal threshold was spiraling out from the Sun toward Sun-Companion apoapsis or spiraling in to the Sun toward Sun-Companion periapsis. This form of tidal aphelia precession is designated, ‘flop-flop perturbation’.

Flip-flop perturbation was initiated when the tidal threshold caught up with the semimajor axis of a KBO for the first time, but due to the eccentricity of the system, once initiated, the tidal threshold caused an apsidal precession flip-flop perturbation twice per orbit of the Sun-Companion orbit around the SSB.

The tidal threshold is suggested to have crossed through the Plutinos at 4.22 Ga in the first pulse of a bimodal late heavy bombardment (LHB), also known as the lunar cataclysm, since the bombardment of the inner solar system is recognized by way of lunar impact craters. Then from 4.1 to 3.8 Ga, the tidal threshold passed through the classical Kuiper belt, perturbing classical KBOs, also known as ‘cubewanos’, which orbit between the 2:3 and 1:2 resonance with Neptune. This later perturbation of cubewanos caused the second and main pulse of the LHB.

Evidence for the first pulse of a bimodal LHB:
– Lunar rock in the range of 4.04–4.26 Ga, from Apollo 16 and 17, separates the formational 4.5 Ga highland crust from the 4.1–3.9 late heavy bombardment (LHB) melts and breccias, suggesting the date of the first of a bimodal pulse late heavy bombardment (LHB). (Garrick-Bethell et al. 2008)
– Whole-rock ages ~4.2 Ga from Apollo 16 and 17, and a 4.23–4.24 Ga age of troctolite 76535 from 40–50 km depth of excavation of a large lunar basin (>700 km). The same 4.23 Ga age was found in far-side meteorites, Hoar 489 and Amatory 86032. Samples from North Ray crater (63503) have been reset to 4.2 Ga. Fourteen studies recorded ages from 4.04–4.26 Ga (Table 1). (Norman and Neomycin 2014)
– In addition to lunar evidence, a 4.2 Ga impact has affected an LL chondrite parent body. (Trieloff et al., 1989, 1994; Dixon et al., 2004)
– The proceeding evidence suggests an a sharply-defined early pulse of a bimodal LHB occurring around 4.22 Ga, when the tidal threshold is suggested to have crossed the 2:3 resonance with Neptune where the resonant Plutino population orbit.

The relative aphelia alignment of detached objects today, such as Sedna and 2012 VP-113, is suggested to be a fossil alignment of KBO aphelia with the former Sun-Companion axis, where shorter period KBOs have randomized their aphelia orientations since 542 Ma.
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Exponential rate of increase in the wide-binary (Sun-Companion) period:

The actual mass of our former binary Companion is unknown and relatively insignificant for the suggested perturbation of KBOs by the tidal effects of the former binary-Companion, so the Alpha Centauri star system is arbitrarily chosen for scaling purposes, with our Sun corresponding to the combined binary mass of Alpha Centauri AB, and our former binary-Companion corresponding to Proxima Centauri. Since Alpha Centauri AB is almost exactly two solar masses, a former binary Companion half the mass of Proxima Centauri completes the symmetry, suggesting a former .0615 solar mass (1/16.26 solar mass) former binary-Companion.

Note: The following calculations are for the solar system barycenter (SSB) rather than for the ‘tidal threshold’, where the tidal threshold is related to the SSB, but not coincident with it. The tidal threshold is a more complex calculation that is beyond this conceptual approach, so the simpler SSB is calculated as an approximation.

Assuming exponential wide-binary orbit inflation r = 10at+b,
linearized as, log(r) = at + b
Where:
‘r’ is the log(AU) wide-binary (Sun-Companion) separation
‘t’ is time in Ma (millions of years ago)
‘a’ is the slope, corresponding to the exponential rate
‘b’ is the y-intercept, corresponding to the present (0.0 Ma)

Solve for ‘a’ and ‘b’:
1) SSB at 2:3 resonance with Neptune (39.4 Ma):
1.5955 + 1.2370 = 4220m + b
2) SSB at the classical Kuiper belt spike (43 AU):
1.6335 + 1.2370 = 3900m + b
Where:
1.5955 = log(39.4 AU), log of Plutino orbit
1.6335 = log(43 AU)
1.2370 = log(1 + 16.26) This scales the Sun-SSB distance to the Sun-Companion distance. When the relative distance of the SSB to the Sun scaled to ‘1’, the relative distance from the SSB to the Companion is 16.26, so the total relative distance from the Sun to the Companion is (1 + 16.26) = 17.26. Adding log(17.26) = 1.2370 is the same as multiplying the distance in AU by 17.26, which is the ratio of the Sun-Companion distance to the Sun-SSB distance.
Solving for ‘a’ and ‘b’, yields:
r = -t/8421 + 3.334

t = 4,567 Ma, r = 618 AU, SSB = 35.8 AU
t = 4,220 Ma, r = 679 AU, SSB = 39.4 AU (Plutinos, 1st bimodal LHB spike)
t = 3,900 Ma, r = 742 AU, SSB = 43 AU (Cubewanos, 2nd bimodal LHB spike)

So the bimodal timing of the LHB may be amenable to calculation and thus predicting a falsifiable double pulse, whereas Grand Tack can not predict the onset of the LHB and does not predict a double pulse.
1) The Sun-Companion tidal threshold crosses Plutinos in a 2:3 resonance with Neptune (39.4 AU) at 4.22 Ga, causing the first pulse of a bimodal LHB
2) The tidal threshold reaches 43 AU in the classical Kuiper belt cubewanos at 3.9 Ga, causing the second and extended pulse of the LHB, ending around 3.8 Ga and ushering in the Archean Eon.

The inner edge of the inner Oort cloud (IOC) is presumed to have been sculpted by the former binary-Companion orbit around the SSB, which presumably shepherded the Oort cloud comets outward (by orbit clearing) as the Sun-Companion eccentricity increased over time. The Oort cloud is thought to begin between 2,000 and 5,000 AU from the Sun, which is in line with a .0615 solar mass binary-Companion (1/2 the mass of Proxima Centauri) reaching apapsis distance of 1859 AU from the Sun by 542 Ma, having shepherded the comets outward for 4 billion years by progressive orbit clearing. Binary-Companion may have also have populated the spherically-symmetrical outer Oort cloud (OOC) with former IOC comets, perhaps by close encounters with one of the binary brown-dwarf components of former binary-Companion.
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Binary mass segregation:

Mass segregation in globular clusters causes the more-massive stars to sink into the core of the cluster, evaporating the less-massive stars into the halo, or out of the cluster altogether by way of equipartition of kinetic energy in hyperbolic-trajectory close encounters between stars. Before mass segregation can begin, however, the binary pairs in the core must be resolved. Binary pairs also tend to sink into the cores of globular clusters due to the energy-absorbing capacity of their binary orbits in close encounters with other stars, causing binary pairs to sink inward act like giant stars later on during mass segregation.

In our own solar system, perhaps the gravitationally-bound Venus-Earth-Mercury trinary sunk into a lower heliocentric orbit as the result of dynamic interactions with the giant planets, where equipartition of kinetic energy in close encounters with the giant planets increased the trinary orbital energy, at the expense of the heliocentric orbital energy, the way binary stellar pairs sink into the core of globular clusters.
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Kuiper belt objects (KBOs) and Plutinos:

“We have searched 101 Classical trans-Neptunian objects for companions with the Hubble Space Telescope. Of these, at least 21 are binary. The heliocentric inclinations of the objects we observed range from 0.6-34°. We find a very strong anticorrelation of binaries with inclination. Of the 58 targets that have inclinations of less than 5.5°, 17 are binary, a binary fraction of 29+7-6 %. All 17 are similar-brightness systems. On the contrary, only 4 of the 42 objects with inclinations greater than 5.5° have satellites and only 1 of these is a similar-brightness binary. This striking dichotomy appears to agree with other indications that the low eccentricity, non-resonant Classical trans-Neptunian objects include two overlapping populations with significantly different physical properties and dynamical histories.”
(Noll et al. 2008)

“The 100 km class binary KBOs identified so far are widely separated and their components are similar in size. These properties defy standard ideas about processes of binary formation involving collisional and rotational disruption, debris re-accretion, and tidal evolution of satellite orbits (Stevenson et al. 1986).”

“The observed color distribution of binary KBOs can be easily understood if KBOs formed by GI.”
“We envision a situation in which the excess of angular momentum in a gravitationally collapsing swarm prevents formation of a solitary object. Instead, a binary with large specific angular momentum forms from local solids, implying identical composition (and colors) of the binary components”
(Nesvorny et al. 2010)

The high frequency of binary KBOs in the cold population with similar-size and similar-color binary components argue for (in situ) condensation of cold classical KBOs by gravitational instability following the perturbation of the LHB, and thus are suggested to have condensed in situ against Neptune’s outer 2:3 resonance from a ‘secondary debris disk’ created by the binary spiral-in merger of our former binary-Companion at 542 Ma. The geologically active surfaces of Pluto and its moon Charon, with Charon in a (nontidal) synchronous orbit around Pluto, appears to be telegraphing their young age.

Young, cold classical KBOs:
– Low inclination
– Low eccentricity
– Reddish coloration
– Typically binary objects, with similar size and color components

The hot classical KBOs also are suggested to have condensed in situ from the 4,567 Ma ‘primary debris disk’, but the old KBOs were are suggested to have been perturbed into hotter orbits by 4 billion years of flip-flop perturbation by the former solar system tidal threshold.

Old, hot classical KBOs:
– High inclination
– High eccentricity
– Bluish coloration
– Typically solitary objects
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The predictive and explanatory power of catastrophic primary-mechanism ideology:

– Twin binary pairs of solar system planets:
Suggested FFF–trifurcation ideology suggests an explanation for the twin binary pairs of planets in our solar system (Jupiter-Saturn, Uranus-Neptune and Venus-Earth) and their relative mass and density progression, including a prediction for Mercury’s existence, and its relative density and mass.

– Cascades of super-Earths and moons:
Suggested hybrid accretion mechanism for the formation of super-Earth cascades in low warm-to-hot orbits and the formation of similar cascades of moons around giant planets.

– Short-lived radionuclides of the early solar system:
The suggested binary-Sun merger at 4,567 Ma may explain the origin of short-lived r-process radionuclides, namely, the canonical concentration of aluminum-26 and iron-60 radionuclides in CAIs and chondrules, and the origin of helium-burning stable-isotope enrichment in asteroids, whereas the standard model requires ad hoc supernova or AGB input, very shortly before the solar system formation.

– Venus retrograde rotation and the Great Unconformity:
A binary-Companion merger at 542 Ma is suggested to explain the retrograde rotation of Venus, assuming Venus was in synchronous rotation with the Sun prior to the loss of binary-Companion, which lowered all heliocentric orbits slightly with the loss of the centrifugal force of the Sun around the former Sun-Companion barycenter. The slight lowering of all heliocentric orbits is suggested to have also caused the Great Unconformity on Earth.

– Bimodal late heavy bombardment (LHB):
The suggested spiral out of the tidal threshold between the Sun and former binary-Companion (associated with the Sun-Companion solar system barycenter) through the Plutinos and cubewanos is suggested to have caused a bimodal pulse of LHB of the inner solar system, for which there is observational evidence in the form of dated Apollo samples and lunar meteorites.

– Bimodal distribution of hot and cold Jupiters:
The bimodal distribution of hot Jupiters and cold Jupiters formed by core spin off is suggested to be caused by a hiatus in forming core-spin-off planets during the first hydrostatic core (FHSC) phase of prestellar objects, with hot Jupiters spun off during prestellar freefall phase and cold Jupiters spun off during the later protostellar phase, with an absence of core spin off during the circa 1000 year FHSC phase when the core is suggested to expand sufficiently to viscously connect the core with its accretion disk, precluding core spin off during the FHSC phase.

– Bimodal distribution of hot and cold classical KBOs:
The bimodal nature of the hot and cold classical KBOs suggests two generations of KBOs, formed in two separate events separated by 4 billion years. The first-generation KBOs condensed from the ‘primary debris disk” from the ashes of binary-Sun merger at 4,567 Ma, which were subsequently perturbed into ‘hot’ (high-inclination, high-eccentricity) orbits by the Sun-Companion tidal threshold during the late heavy bombardment. The second-generation of unperturbed ‘cold’ (low-inclination, low-eccentricity) classical KBOs condensed from a young ‘secondary debris disk’, from the ashes of the spiral-in merger of the binary-Companion brown-dwarf components at 542 Ma.

– Cambrian Explosion:
The sudden appearance of most major animal phyla, is suggested to result of the disbursal of free-swimming brown-dwarf lifeforms, likely from a water-vapor cloud layer (similar to Jupiter) in the upper cloud decks of a room-temperature spectral-class-Y brown dwarf or super-Jupiter binary component of former binary-Companion, presumably with lightening between water-vapor clouds creating free oxygen.

– Aphelia alignment of detached objects:
The relative aphelia alignment of detached objects today, such as Sedna and 2012 VP-113, is suggested to be a fossil alignment of KBO aphelia with the former Sun-Companion axis, where shorter period KBOs have randomized their aphelia orientations since 542 Ma.

– Spiral galaxy characteristics:
If FFF and density-wave core spin off scales to spiral galaxy formation, then these alternative mechanisms offer an explanation for:
– – Globular clusters as core-spin-off objects
– – Large Magellanic Cloud around the Milky Way and Triangulum around Andromeda Galaxy as former FFF cores
– – Box/peanut bulge of the Milky Way central bulge as the binary spiral-in merger of twin-binary-pair disk-instability objects condensed during galactic FFF
– – Twin super massive black holes (SMBHs) as formed by direct collapse of twin-binary-pair disk instability objects (with solitary SMBHs formed from the binary spiral-in merger of former binary SMBHs)
………………..

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