Figure 1Protostar system L1448 IRS3B, showing a 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.

The brighter companion star supports an alternative flip-flop formation mechanism, where the less-massive companion formed first at the center of the system, followed by a twin-binary spiral disk instability that ‘condensed’ a much-larger twin-binary pair from the twin arms of a spiral density wave. Then, equipartition of kinetic energy during subsequent orbital interplay caused the three stellar components to evolve into a hierarchical trinary system, where the former core evaporated into a circumbinary orbit around the more-massive twin-binary pair, which spiraled in to form a close-binary pair at the center of the system. The companion is brighter than the younger binary pair, due to being more evolved.

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


This alternative conceptual ideology suggests three novel mechanisms for the formation of gravitationally-bound objects:
– Flip-flop fragmentation (FFF)
– Trifurcation
– Hybrid accretion

– Flip-flop fragmentation (FFF)—a suggested mechanism for forming gaseous objects, ranging in size from gas-giant planets to brown dwarfs and companion stars:
    FFF suggests that excess angular momentum in a collapsing dark core may create an outsized accretion disk that is much more massive than its diminutive prestellar/protostellar core, such that the massive accretion disk inertially dominates the system.  Inertial dominance is suggested here to promote disk instability, ‘condensing’ either a solitary disk-instability (d-i) object or a twin-binary pair of d-i objects.  Disk instability presumably occurs by way of (spiral) density waves, either by way of an asymmetrical (m = 1 mode) density wave, condensing a solitary d-i object, or a symmetrical (m = 2 mode) density wave, condensing a twin-binary pair of d-i objects.  Inherent in FFF is an inertial ‘flip-flop’, where the diminutive prestellar/protostellar core is injected into a planetary satellite orbit around the much-more massive d-i object, or twin-binary pair of d-i objects, catastrophically projecting mass inward.  FFF suggests that gas-giant planets are former stellar cores that predate their stellar host.
    Asymmetrical FFF—Asymmetrical FFF condenses a solitary d-i object that automatically inertially displaces the diminutive former stellar core into planetary satellite orbit.
    Symmetrical FFF—Symmetrical FFF condenses a twin-binary pair of d-i objects around a diminutive stellar core, creating a dynamically unstable system, but the stellar core is not automatically inertially displaced into a circumbinary orbit.  Instead the diminutive core is progressively evaporated into a stable, hierarchical circumbinary orbit by way of orbital interplay with the more-massive d-i objects.  Symmetrical FFF is suggested to also form triple star systems such as Alpha Centauri, which is composed of a small companion star (Proxima Centauri) in a circumbinary orbit around the much-more-massive twin-binary pair (Alpha Centauri A&B).

– Trifurcation—a mechanism for forming twin-binary pairs, such as Jupiter-Saturn, Uranus-Neptune, & Venus-Earth by centrifugal fragmentation:
    Trifurcation is suggested to be a possible secondary effect of symmetrical FFF. During the orbital interplay phase of symmetrical FFF, orbital close encounters between a diminutive stellar core and its much-more-massive twin-binary d-i objects result in orbital energy and angular momentum transfer from the more massive d-i objects to the less-massive stellar core by the principle of equipartition of kinetic energy.
    Equipartition is also suggested to cause a rotational energy transfer, causing the diminutive stellar core to progressively increase its rotation rate, causing it to ‘spin up’ and distort into an oblate sphere. Continued spin up may distort the oblate core into Jacobi ellipsoid and then into a bar-mode instability, which may ultimately fail by centrifugally fragmenting into three components (hence trifurcation). During trifurcation, the opposing ends of the bar-mode arms gravitationally pinch off into gravitationally-bound Roche spheres in orbit around the diminutive ‘residual core’ of material remaining at the center of rotation.
    This newly trifurcated system, composed of a twin-binary pair in orbit around its ‘residual core’, is a diminutive version of the original symmetrical FFF system, and like the original system, the newly-trifurcated system is also dynamically unstable. First-generation trifurcation promotes second-generation trifurcation, and etc., potentially forming multiple-generations of twin-binary pairs of objects in diminishing sizes, like Russian nesting dolls. Trifurcation is the suggested origin of the four sets of twin-binary pairs in our solar system, namely, former ‘binary-Companion’, Jupiter-Saturn, Uranus-Neptune, and Venus-Earth, potentially with Mercury as the residual core of the 4th generation trifurcation.
    Similar to our solar system, the triple-star Alpha Centauri system is also suggested to have formed by symmetrical FFF; however, Proxima Centauri did not subsequently succumb to trifurcation.

– Hybrid accretion—a mechanism for forming super-Earths and giant-planet moons:
    Hybrid accretion is a suggested planet formation mechanism for forming planets by a hybrid mechanism (Thayne Curie 2005), combining planetesimal formation by streaming instability from an accretion disk, followed by the core accretion of these planetesimals into objects capable of both clearing their orbits and creating a gap in the accretion disk.
    Myriads of planetesimals condense by streaming instability at the inner edge of a protoplanetary disk. When core accretion reaches the nominal mass of a super-Earth around a dwarf star, the hybrid-accretion planet is able to clear its orbit and create a gap in the accretion disk, whereupon a second generation of planetesimals may condense by streaming instability against its outer resonances to form a second-generation hybrid-accretion planet. In this manor a cascade of hybrid-accretion super-Earths may form from the inside out. Cascades of hybrid-accretion moons may also form by this mechanism around gas-giant planets.

A brief history of the solar system:
1) Symmetrical FFF―binary-Sun (twin d-i objects) + Brown Dwarf* (protostellar core)
2) 1st-generation trifurcation―binary-Companion + SUPER-Jupiter* (residual core)
3) 2nd-gen. trifurcation―Jupiter-Saturn + SUPER-Neptune* (residual core)
4) 3rd-gen. trifurcation―Uranus-Neptune + SUPER-Earth* (residual core)
5) 4th-gen. trifurcation―Venus-Earth + Mercury(?) (residual core)
    A diminutive Brown Dwarf system with a much-more-massive accretion disk underwent symmetrical FFF, ‘condensing’ a twin-binary pair of d-i objects > 4,567 Ma. Brown Dwarf underwent four generations of trifurcation as a secondary effect of symmetrical FFF. And the resulting high-angular-momentum siderophile-depleted ‘trifurcation debris disk’ condensed hot classical Kuiper belt objects (KBOs) against Neptune’s outer 2:3 resonance.
    Following 4th-generation trifurcation, binary-Companion orbited binary-Sun at about 15 AU, with the 2nd, 3rd, and 4th-gen. components within its gravity well. Binary-binary resonances unwound the trifurcation generations, presumably by eccentricity pumping, causing Uranus-Neptune to be captured by binary-Sun by way of binary-Companion’s outer L2 Lagrangian point, and Jupiter-Saturn, with Venus-Earth-Mercury(?) in tow, were captured by binary-Sun via binary-Companion’s inner L1 Lagrangian point. Finally, additional eccentricity pumping caused twin-binary trifurcation pairs to separate. At this point the solar system consisted of, binary-Sun; Mercury(?), Venus, Earth, Jupiter, Saturn, binary-Companion, Uranus, Neptune, hot-classical KBOs. Mars is unaccounted for in this tally, with its size and density indicating likely formation by hybrid accretion around former Brown Dwarf, prior to symmetrical FFF, and as such Mars was likely in a circumbinary orbit around binary-Companion at this point.
    The twin-binary d-i objects spiraled-in to become our former binary-Sun, whose binary components continued spiraling in to merge at 4,567 Ma in a luminous red nova that created a low-angular-momentum ‘solar-merger debris disk’. The solar-merger debris disk, with stellar-merger short-lived radionuclides (SLRs), ‘condensed’ asteroids by streaming instability, likely against the Sun’s magnetic corotation radius. Slightly later, after the SLRs died away, chondrites condensed by streaming instability against Jupiter’s inner resonances. Mercury may be either the residual core of the 4th-gen. trifurcation, or alternatively, may be a hybrid accretion asteroid, compiled from the solar-merger debris disk.
    Similar to former binary-Sun, the super-Jupiter-mass components of former binary-Companion spiraled in and merged almost 4 billion years later, at about 650 Ma, in an asymmetrical merger explosion that gave the newly-formed Companion escape velocity from the Sun. The high-angular-momentum Companion-merger debris disk (which was not siderophile depleted) condensed cold classical Kuiper belt objects in situ against Neptune’s outer 2:3 resonance.

* Note, unorthodox capitalization indicates unorthodox definitions. ‘SUPER-Jupiter’, ‘SUPER-Neptune’ and ‘SUPER-Earth’ are the names for the former residual cores formed in the first three trifurcation generations, and ‘Brown Dwarf’ is the name of the original prestellar core of the solar system.


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 second collapse, 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 ~1013 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)

    The development of a bar mode and spiral structure is expected for rapidly rotating polytropic-like structures (e.g. Durisen et al. 1986). Such instabilities occur when the ratio of the rotational energy to the magnitude of the gravitational potential energy of the first core exceeds β = 0.274. Bate was also the first to point out that because a rapidly rotating first core develops into a disc before the stellar core forms, the disc forms before the star. Rather than hydrostatic cores, such structures are better described as ‘pre-stellar discs’.
    Without rotation (β = 0), the first core has an initial mass of ≈5 MJ and a radius of ≈5 au (in agreement with Larson 1969). However, with higher initial rotation rates of the molecular cloud core, the first cores become progressively more oblate. For example, with β = 0.005 using radiation hydrodynamics, before the onset of dynamical instability, the first core has a radius of ≈20 au and a major-to-minor-axis ratio of ≈4:1. With β = 0.01, the first core has a radius of ≈30 au and a major-to-minor-axis ratio of ≈6:1. Thus, for the higher rotation rates, the first core is actually a pre-stellar disc, without a central object. As pointed out by Bate (1998), Machida et al. (2010) and Bate (2010), the disc actually forms before the star. For the very highest rotation rates (β = 0.04), the first core actually takes the form of a torus or ring in which the central density is lower than the maximum density.
    In each of the β = 0.001–0.005 cases, the first core begins as an axisymmetric flattened pre-stellar disc, but after several rotations, it develops a bar mode. The ends of the bar subsequently lag behind and the bar winds up to produce a spiral structure. Spiral structure removes angular momentum from the inner parts of the first core via gravitational torques (Bate 1998).
(Matthew R. Bate, 2011)

    “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)

Protoplanetary disks have their highest masses at early times:
    “We find that the compact (< 100) dust emission is lower for Class I sources (median dust mass 96 M⊕) relative to Class 0 (248 M⊕), but several times higher than in Class II (5-15 M⊕). If this compact dust emission is tracing primarily the embedded disk, as is likely for many sources, this result provides evidence for decreasing disk masses with protostellar evolution, with sufficient mass for forming giant planet cores primarily at early times.” (Tychoniec et al. 2018)
    “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”. (Li et al. 2014)
    The discovery that accretion disks are born massive and rapidly diminish with age is counterintuitive and may be problematic for the accretion theory formation of gas-giant planets, where the precipitous falloff in mass is fighting against the logarithmically-increasing duration of successive protostellar classes, where Class 0 (with 248 M⊕ dust mass) lasts 104 yr, Class I (with 96 M⊕ dust mass) lasts 105 yr, Class II (with 5-15 M⊕ dust mass) lasts 106 yr, and Class III (? dust mass) lasts 107 yr.

Evidence for Kuiper belt objects (KBOs) formed by gravitational/streaming instability

    “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 [gravitational instability].” “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)

Hybrid accretion planets and moons:

    An alternative planet formation mechanism combines the formation of planetesimals at the inner edge of protoplanetary disks by streaming instability with their hierarchical accretion into cascades (series) of hybrid-accretion planets, with a nominal size of super-Earths, with the term ‘hybrid accretion’ referring to the hybrid mechanism that combines streaming instability and core accretion.
    The hybrid mechanism for planet formation was first proposed for the formation of gas giant planets (Thayne Curie, 2005), but the mechanism is instead suggested here for the formation of
terrestrial super-Earths that typically form in multiple-planet ‘cascades’.

    Gas pressure causes the gas in accretion disks to rotate slower than a Keplerian rate, and this gas drag on dust grains causes dust to spiral inward to the inner edge or nearest gap in an accretion disk, where the concentration of dust can result in gravitational instability, known as streaming instability.
    Planetesimals of indeterminate size condense by streaming instability at the inner edge of a protoplanetary disk, where the accretion disk is presumably truncated by the magnetic corotation radius of its young stellar object (YSO). A myriad of streaming-instability planetesimals merge by hierarchical accretion until the largest hierarchical component is able to open a gap in the accretion disk at a nominal super-Earth mass. The gap in the accretion disk precludes further planetesimal formation by streaming instability against the magnetic corotation radius of the YSO, but it begins the concentration of dust grains against the strongest outer resonances of the anchor super-Earth.
    Dust grains accumulate in the accretion disk dead zone beyond the anchor super-Earth that may repeatedly condense by streaming instability to begin the accretion of a second-generation super-Earth, and in this way, a cascade of super-Earths may form sequentially from the inside out.
    Giant planets may also form hybrid-accretion moons around giant planets. The 5 planemo moons of Uranus; Miranda, Ariel, Umbriel, Titania and Oberon, are perhaps the best example of a moony hybrid-accretion cascade in our solar system.
    Hybrid accretion objects may also form from massive debris disks resulting from cataclysmic events, such as the spiral-in merger of a former binary star. The planet Mercury may be a hybrid accretion planet formed from asteroids condensed by streaming instability from the solar-merger debris disk that formed from the aftermath of the spiral-in merger of our former binary-Sun at 4,567 Ma.

    Sourav Chatterjee and Jonathan C. Tan quantified this form of inside-out planet formation mechanism in a more general form, encompassing either pebble accretion or ∼1 M⊕ planet formation by gravitational instability. “Formation of a series of super-Earth mass planets from pebbles could require initial protoplanetary disks extending to ∼ 100 AU.” (Chatterjee and Jonathan, 2013)

    In cascades of super-Earths, the outermost planetary pair typically exhibit a greater period ratio than the other adjacent planetary pairs, which may give credence to inside-out formation if each super-Earth generation in turn experiences a significant degree of inward migration due to the ‘weight’ of truncating the inner edge of the protoplanetary disk to its outer resonances, except for the final super-Earth.

Relative orbital period ratios of adjacent super-Earths. Note the greater orbital period ratio between the outermost adjacent super-Earth pairs (red) compared to inner adjacent super-Earth pairs (blue).


Flip-Flop Fragmentation (FFF):

    ‘Flip-flop fragmentation’ (FFF) is an alternative conceptual ideology for the formation of gaseous satellites by catastrophic disk instability, indirectly forming satellites ranging in mass from gaseous planets to brown dwarfs and companion stars.

Asymmetrical FFF vs. Symmetrical FFF:
    FFF (disk instability) of massive disks surrounding diminutive prestellar or protostellar objects may occur by means of (spiral) density waves, where the mode of the density wave dictates the type of disk instability, forming either solitary disk instability (d-i) objects by ‘asymmetrical FFF’ or twin-binary d-i objects by ‘symmetrical FFF’.
    Asymmetrical density waves (asymmetrical FFF) are suggested to form solitary star systems with planetary former cores, while symmetrical density waves (symmetrical FFF) are suggested to form twin-binary star systems with larger former cores in circumbinary orbits, where some former cores attain dwarf-star status, forming trinary star systems. (Inoue & Yoshida, 2019) determined that spiral-arm instability (SAI) is driven by the self gravity of the density-wave (arms) and operates without rapid gas cooling, where self gravity is presumably the driving mechanism of FFF.
    1) Asymmetrical (m = 1 mode) density waves in massive accretion disks around diminutive prestellar/protostellar objects are suggested to condense solitary d-i objects, where the solitary d-i object is much-more massive than its diminutive stellar core. Asymmetrical FFF breaks the radial symmetry of the system and catastrophically projects mass inward by shifting the center of mass of the system toward the nascent d-i object, while inertially injecting the former core into a planetary satellite orbit around the d-i object. When an accretion disk is less massive than its stellar core, the core is presumably able to damp down disk inhomogeneities, whereas when an accretion disk greatly exceeds the mass of its prestellar/protostellar core, a disk inhomogeneity may cause the core to undergo inertial displacement from the center of mass, amplifying the inhomogeneity rather than dampening it down, resulting in a runaway disk instability that is necessarily more massive than the core. “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”. (Li et al. 2014) Asymmetrical FFF can apparently occur repeatedly, in succession, forming solar systems with multiple gaseous planets.
    2) Symmetrical (m = 2 mode) density waves in massive accretion disks around diminutive prestellar/protostellar objects are suggested to condense twin-binary d-i objects, where the twin d-i objects are much-more massive then their diminutive stellar core. In symmetrical FFF, the twin d-i objects create a bilateral symmetry that does not automatically inertially displace the core from the center of mass. Instead, the core is progressively displaced from the center of mass by the principle of equipartion of kinetic energy during orbital interplay with its much-more-massive twin d-i objects, eventually ‘evaporating’ the former core into a circumbinary orbit around the twin d-i objects, which spiral in to form a close-binary pair, conserving system angular momentum. Symmetrical FFF can promote centrifugal fragmentation of the former core by the mechanism of trifurcation, due to accompanying spin-up during orbital interplay. Presumably, symmetrical FFF can only occur once in a system. Note that the term ‘FFF’ without a ‘symmetrical’ or ‘asymmetrical’ modifier is assumed to be ‘asymmetrical FFF’, where ‘symmetrical FFF’ will always be called out as such.

Prestellar FFF vs. protostellar FFF, forming cold Jupiters and hot Jupiters respectively:
    Gas giant exoplanets exhibit a distinct bimodal distribution with respect to orbital distances from their host stars. ‘Hot Jupiters’ in low ‘hot’ orbits are defined as having orbital periods < 10 days (< .1 AU), whereas ‘cold Jupiters’, in high ‘cold’ orbits are centered around 2 AU, with a distinct desert of gas-giant planets at intermediate orbital distances.
    FFF ideology is strengthened by a counterintuitive discovery of decreasing accretion disk mass with protostellar evolution. (Tychoniec et al. 2018) measured a dramatic decrease in disk mass dust with increasing protostellar age, where measured dust mass is assumed to be a proxy for overall accretion disk mass. Disk dust mass was measured to decrease from 248 M⊕ in Class 0 protostars to 96 M⊕ in Class I protostars, to 5-15 M⊕ in Class II protostars.
    The Tychoniec study only evaluated the dust mass around protostars, not around prestellar objects, and the decreasing accretion disk mass with protostellar evolution must extend across the prestellar-protostellar boundary for the following hot and cold Jupiter hypothesis to be valid. If indeed prestellar accretion disks tend to be more massive than even Class 0 protostar accretion disks, and if the inertial displacement distance during asymmetrical FFF correlates with the accretion disk mass, then this evolutionary trend points to prestellar FFF forming cold Jupiters in cold distant orbits, while protostellar FFF forms hot Jupiters in low hot orbits.
    The recent discovery of a relative scarcity of gas-giant exoplanets at about 4 Mj (Santos et al. 2017), suggests a hiatus in asymmetrical FFF at a stellar core mass of 4 Mj. The appearance of the pithy first hydrostatic core (FHSC) at the final stage of the prestellar phase is suggested here to provide a viscous mechanism for physically impeding disk instability. As gas infalls onto a prestellar core, its potential energy is radiated away as infrared photons, but when prestellar core reaches a critical density, the gas temperature begins to rise, creating hydrostatic gas pressure, forming the FHSC. Gas infalling onto the hydrostatic core creates a shock front which extends out to radii on the order of ~5–10 AU (Tsitali et al. 2013), which may viscously engage with the accretion disk, damping down positive disk-core feedback necessary for runaway disk instability. The relatively-brief ~1,000 year FHSC stage marks the end of the prestellar phase, which concludes with an exceedingly-brief second collapse (~0.1 yr), mediated by endothermic dissociation of molecular hydrogen. The conclusion of the pithy FHSC stage marks the prestellar to protostellar transition, which is suggested to result in a disk-instability hiatus at a core mass of 4 Mj. Thus, prestellar asymmetrical FFF creates gaseous planets up to 4 Mj, which become cold Jupiters in high cold orbits, with a hiatus in asymmetrical FFF at a FHSC mass of 4 Mj, followed by protostellar asymmetrical FFF, creating hot Jupiters, > 4 Mj, in low ‘hot’ orbits.
    If accretion disks are most massive at earliest times, while stellar cores increase in mass over time, one would expect more-massive stars to host less massive gaseous planets in high cold orbits, while less-massive stars host more-massive gaseous planets in low hot orbits; however, stellar mass may not correlate well with hot and cold Jupiters due to significant stellar accretion following FFF. And the hot-cold Jupiter distinction itself may become muddied in multiple gaseous planet systems, having had multiple FFF occurrences, particularly if systems combine prestellar FFF and protostellar FFF; however, systems with multiple hot Jupiters are very rare, suggesting that multiple occurrences of protostellar FFF are rare.

Exoplanet mass vs. orbital distance illustrates the bimodal distribution of gas-giant planets into hot Jupiters in low ‘hot’ orbits and cold Jupiters in high ‘cold’ orbits

Image credit: Penn State, Eberly College of Science, ASTRO 140

Bimodal mass distribution of giant planets around solar-type stars (with blue and green representing different selection criteria) indicating a < 4 Mj low-mass population and a high-mass > 4 Mj populationImage credit: Santos et al., 2017

Hoptunes (hot Neptunes) and hot Saturns:
    A recent study (Dong et al., 2018) has identified a population of Neptune-size planets in low hot orbits, similar to hot Jupiters, separated in mass by a hot Saturn “valley” in the Saturn size range. The hot Saturn valley represents approximately an order of magnitude decrease in frequency compared to hot Jupiters and Hoptunes.
    If protostellar FFF inertially displaces > 4 Mj protostars into low hot orbits, forming hot Jupiters, then indeed there should not be any hot Saturns in low hot orbits, but neither should there be any Hoptunes either. This suggests either another (unimagined) formation mechanism for Hoptunes, or alternatively, suggests the possibility that Neptune-sized planets formed by prestellar FFF may be subject to inward planetary migration from interactions with their protoplanetary disk, after having been injected into high cold orbits during prestellar FFF.
    Additionally, the same article (Dong et al., 2018) makes another curious observation that the “radius distribution of planets around metal-rich stars is more ‘puffed up’ as compared to that around metal-poor stars”, again for unknown reasons.

    The probability of FFF is assumed to increase with the specific angular momentum of the collapsing gas cloud. The outcomes of asymmetrical FFF may range from sub-Neptunes with gaseous atmospheres up to brown dwarfs at the upper mass range. And symmetrical FFF may displace even larger stellar cores, such as the Alpha Centauri system, where the red dwarf star Proxima Centauri was presumably the original stellar core.
    Multiplicity of gas-giant planets formed by asymmetrical FFF requires successive instances of disk instability in the same system, presumably caused by continued infall of high angular-momentum gas from the envelope onto the accretion disk, regrowing the accretion disk after a previous disk-instability episode.


    First-generation trifurcation is the centrifugal fragmentation of a prestellar/protostellar core by orbital close encounters with a much-more massive binary pair formed by symmetrical FFF from a massive accretion disk.  Trifurcation implies centrifugal fragmentation into 3 components (hence TRIfurcation), forming a trinary subsystem, which locally decreases the subsystem entropy.
  Symmetrical FFF results in a dynamically-unstable trinary system, which is followed by orbital interplay to resolve the instability into a stable hierarchical system, and centrifugal-fragmentation trifurcation may occur as a result of the orbital close encounters occurring during orbital interplay.

    In a high angular momentum prestellar/protostellar system in which the accretion disk is much more massive than its diminutive stellar core, the disk has inertial dominance of the system.  And inertial dominance by an accretion disk is suggested here to promote disk-instability fragmentation at a stellar Jeans mass scale.  The type of disk instability fragmentation may depend on the mode of a (spiral) density wave resident in the accretion disk, with asymmetrical (m = 1 mode) density waves tending to gravitationally collapse to form solitary disk instability (d-i) objects in a process designated ‘asymmetrical FFF’, while symmetrical (m = 2 mode) density waves tending to gravitationally collapse to form twin-binary disk instability objects in a process designated ‘symmetrical FFF’.

    Asymmetrical FFF automatically inertially displaces the stellar core from the center of mass of the system as the system becomes progressively more asymmetrical during the incipient disk instability, but symmetrical FFF preserves bilateral symmetry of the system, maintaining the stellar core at the center of the system; however, the much-greater overlying mass of the twin d-i objects is dynamically unstable, resulting in chaotic orbital interplay, which progressively projects mass inward.
    In close orbital encounters between objects with dissimilar masses, the less-massive component receives an energy kick at the expense of the more-massive component by the principle of equipartition of kinetic energy, which is the same principle used to extract orbital energy from planets by interplanetary spacecraft, which is known as gravitational slingshot or gravity assist.  Gravitational slingshot or gravity assist is something of a misnomer, since the spacecraft is parasitizing the orbital energy of the planet by means of a gravitational interaction.
    In addition to this kinetic energy kick, equipartition in close orbital encounters is suggested here to also transfer rotational energy to the stellar core, causing an increase in its rotation rate, resulting in a ‘spin up’ 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.
    Rotational spin up in orbital close encounters causes a core to distort into an oblate sphere.  Additional spin up may cause the oblate sphere to distort into a triaxial Jacobi ellipsoid, and finally into a bar-mode instability.  The centrifugal failure mode of a bar-mode instability is suggested here to be trifurcation, in which progressive spin up causes the bar-mode instability to centrifugally fragment into into three components, with trifurcation mediated by the self gravity of the bar, wherein the opposing ends of the bar pinch off into twin gravitationally-bound Roche spheres in orbit around the diminutive residual core at the center of gravity and rotation.
  At the moment of trifurcation, the trifurcated trinary components resemble a smaller (Mini-Me) version of the original symmetrical FFF system, with both systems composed of a twin-binary pair orbiting a much-less-massive core. And like symmetrical FFF, the trifurcated trinary components constitute a dynamically unstable system that’s resolved by orbital interplay with accompanying spin up of the residual core, potentially resulting in next-generation trifurcation.
    Thus, trifurcation of a stellar core following symmetrical FFF fosters next-generation trifurcation, and etc., possibly extending to multiple generations, potentially creating a cascade of successively-smaller twin-binary pairs, like Russian nesting dolls, with the three sets of twin planets in our solar system (Jupiter-Saturn, Uranus-Neptune and Venus-Earth) as the trifurcation paradigm.
    Trinary star systems with diminutive companion stars orbiting similar-sized twin-binary pairs, such as Alpha Centauri and L1448 IRS3B, are also suggested to have formed by symmetrical FFF, but without subsequent trifurcation.  The companion star, Proxima Centauri, is the presumed former stellar core of the Alpha Centauri system, but Proxima may have been too massive in relation to Alpha Centauri A and B to have trifurcated.

Dynamical Bar-mode Instability

    In our own solar system, symmetrical FFF is suggested to have resulted in 4 generations of trifurcation, which created 4 sets of twin-binary pairs:
– 1st-gen trifurcation of Brown Dwarf (stellar core) >> binary-Companion + SUPER-Jupiter (residual core)
– 2nd-gen trifurcation of SUPER-Jupiter >> Jupiter-Saturn + SUPER-Neptune (residual core)
– 3rd-gen trifurcation of SUPER-Neptune >> Uranus-Neptune + SUPER-Earth (residual core)
– 4th-gen trifurcation of SUPER-Earth >> Venus-Earth + Mercury? (residual core?)
The question mark following Mercury indicated uncertainty in the origin of Mercury, which may either be the residual core of the 4th-generation trifurcation, or alternatively, Mercury may be a diminutive hybrid accretion asteroid formed from the solar-merger debris disk, at 4,567 Ma.
(Note, unorthodox capitalization indicates unorthodox definitions.  ‘SUPER-Jupiter’, ‘SUPER-Neptune’ and ‘SUPER-Earth’ are the names for the former residual cores formed in the first three trifurcation generations.  And ‘Brown Dwarf’ is the name of the original stellar core of the solar system.)

    Trifurcation is presumably a fractionation process, which pinches off more volatile components into the bar-mode arms, leaving behind a denser, more refractory residual core.  Thus in the trifurcation of the SUPER-Jupiter residual core, more of the volatile hydrogen and helium was pinched off into the Jupiter-Saturn twin-binary pair, leaving behind a higher ice and rocky-iron percentage in the SUPER-Neptune residual core. Thus each succeeding generation of twin-binary components is composed of higher-density elements, winding up with final residual core, Mercury(?), having a proportionately-larger iron-nickel core than its twin-binary siblings, Venus and Earth.
    If trifurcation is indeed a fractionation process, it predicts that later twin-binary trifurcation generations should tend to have heavier isotopic ratios, such that Venus and Earth should have identical isotopic ratios, which should be heavier than the isotopic ratios of Uranus and Neptune, for instance.  This should be true for oxygen isotopes as well; however, all the progeny of the original Brown Dwarf stellar core should lie on the 3-oxygen isotope ‘Brown Dwarf fractionation line, which we know as the terrestrial fractionation line (TFL), assuming no mass-independent fractionation of oxygen isotopes.
    The bar-mode instability pathway of trifurcation suggests that in the trifurcation of internally-differentiated objects, the residual core should acquire a relatively-larger iron-nickel core than its much-more-massive twin-binary siblings.  I.e., in the trifurcation of the rocky-iron SUPER-Earth with with its differentiated iron-nickel core, more of the lower-density mantle material should be preferentially centrifugally slung into the twin bar-mode arms that pinched off to form Venus and Earth, while a relatively-greater portion of the iron-nickel core should remain behind in the residual core.  And indeed Mercury has a proportionately-larger iron-nickel core, compared to Venus and Earth, although Earth slightly edges out Mercury in overall density, due to the compression of its much-greater gravity. Third-generation trifurcation-product Uranus also has lower density than second-generation trifurcation-product Jupiter, presumably for the same reason, with Uranus presumably also having a proportionately-larger iron-nickel core than Jupiter. So each generation of twin-binary pairs should be composed of denser elements and compounds, presumably extending to isotope fractionation.
    Thus, trifurcation makes makes predictions (unlike pebble/core accretion), such as multiple generations of twin binary pairs in size regression with density progression and presumed isotope fractionation.
    In our own solar system, the former symmetrical FFF d-i objects are suggested to have remained gravitationally bound to one another as our former binary-Sun, whose components spiraled in to merge at 4,567 Ma.  Similarly, the first-generation trifurcation twin-binary components are suggested to have also remained gravitationally bound, whose components spiraled in to merge around 650 Ma.  The twin-binary components of the second, third and fourth generations, however, spiraled out and separated to form our 3 sets of twin planets.

L1448 IRS3B (See Figure 1):
    The Class 0 protostar system, L1448 IRS3B, is suggested to have formed by symmetrical FFF. 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, and 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)
    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. Alternatively, the brighter tertiary companion, IRS3B-c, appears to refute the standard model and support the alternative asymmetrical FFF origin, attributing greater brightness to greater age, making the diminutive companion the progenitor of the younger, larger twin-binary pair.

    In addition to equipartition of kinetic energy and rotational spin-up during the orbital interplay phase of trifurcation, the configuration of our solar system in a trifurcation scenario suggests two additional dynamic elements in the form of binary-binary resonant coupling, resulting in 2 forms of orbit inflation; Type I, and Type 2 orbit inflation.

Type 1 orbit inflation:
    The first form of suggested orbit inflation occurs to the wide-circumbinary orbit in a quadruple system by way of binary-binary resonant coupling, with the quadruple system composed of a close-binary pair orbiting a much-more-massive binary pair in a wide-circumbinary orbit, such as a recently trifurcated system. Following trifurcation, the residual core is ‘evaporated’ outward by equipartition of kinetic energy in orbital close encounters with its twin-binary pair, and these orbital close encounters also induce rotational spin-up of the residual core, likely to the point of next-generation trifurcation. Once Uranus-Saturn induced spin-up trifurcation of its SUPER-Earth residual core into Venus-Earth + Mercury (residual core), the quaduple system (neglecting the residual core Mercury) was composed of the close-binary pair Venus-Earth in a wide-circumbinary orbit around the much-more-massive close-binary pair Uranus-Neptune. The outward evaporation of Venus-Earth from Uranus-Neptune presumably continued by means of binary-binary resonant coupling, likely by eccentricity pumping, transferring potential energy from the Uranus-Neptune close-binary pair to the wide-circumbinary orbit, progressively increasing the wide-circumbinary eccentricity between Venus-Earth and Uranus-Neptune.
    First, wide-circumbinary eccentricity pumping caused Venus-Earth to exceed the Uranus-Neptune Hill sphere, causing Venus-Earth to be captured from Uranus-Neptune by Jupiter-Saturn. Next, eccentricity pumping may have caused Uranus-Neptune to be captured from Jupiter-Saturn by binary-Companion. Then continued wide-circumbinary eccentricity pumping caused Uranus-Neptune to be captured by binary-Sun via binary-Companion’s far-side L2 Lagrangian point, injecting the the close-binary pair, Uranus-Neptune, into a heliocentric orbit beyond binary-Companion itself. By comparison, Jupiter-Saturn, with Venus-Earth-Mercury in tow, were captured via binary-Companion’s near-side L1 Lagrangian point. Finally, wide-circumbinary eccentricity pumping caused Venus-Earth-Mercury to be captured from Jupiter-Saturn by binary-Sun, via Jupiter-Saturn’s near-side L1 Lagrangian point.
    Another manifestation of wide-binary orbit inflation was the heliocentric eccentricy pumping of binary-Companion itself, wherein the Sun perturbed its binary components to spiral in, transferring the potential energy into eccentricity pumping, which was responsible for causing the late heavy bombardment by mean-motion resonance migration, and for overrunning Uranus’ orbit, causing its severe axial tilt.

Type 2 orbit inflation:
    The second form of suggested orbit inflation occurs to the close binary components of the smaller binary pair in a quadruple system. This second form of orbit inflation is suggested to have separated the twin-binary trifurcation pairs in our solar system after being captured into heliocentric orbits around binary-Sun. And like Type I orbit inflation, Type II orbit inflation is presumably in the form of eccentricity pumping by way of binary-binary resonant coupling.
    Type 2 orbit inflation is suggested to have separated the twin-binary planetary pairs (Jupiter-Saturn, Uranus-Neptune and Venus-Earth) after the twin-binary planetary pairs were captured into heliocentric orbits, presumably prior to the binary spiral-in merger of binary-Sun at 4,567 Ma.

Former binary-Companion:

    The twin-binary components of former Binary-Companion were most likely in the super-Jupiter-mass range, below the 13 Jupiter mass transition to brown dwarf where deuterium burning begins. The mass of former binary-Companion may be inferred from the mass regression of the 3 sets of twin-binary pairs

Mercury: mM = .055 mE
Venus: mV = .815 mE
Earth: mE = 1 mE
Uranus: mU = 14.54 mE
Neptune: mN = 17.15 mE
Saturn: mS = 95.16 mE
Jupiter: mJ = 317.8 mE
where m is mass, M, V, E, J, S, U, N are the planets in order, neglecting Mars, and BC is binary-Companion

Twin binary-pair mass, normalized to Earth mass:
mV + mE = 1.815 mE
mU + mN = 31.69 mE;
mJ + mS = 412.96 mE
mBC = ?

Relative mass progression between trifurcation generations:
(mU + mN) / (mV + mE) = 31.69 mE / 1.815 mE = 17.46
(mJ + mS) / (mU + mN) = 412.96 mE / 31.69 mE = 13.03
mBC / (mJ + mS) = ?

    The great disparity in the relative mass progression between trifurcation generations may indicate great variability in the combined twin-binary masses to that of their residual core, but more
likely the disparity represents decreasing relative mass loss with increasing trifurcation generations, such that relative trifurcation mass loss is inversely proportional to the metallicity of the trifurcating object. With only two ratio values (17,46 and 13.03), extending the mass-ratio progression to binary-Companion can only be surmised. A linear function suggests a (17.46 – 13.03) / 17.46 = 25% reduction between trifurcation generations, putting mBC / (mJ + mS) = 9.77. But more likely, the function is asymptotic, such that a more likely value for mBC/ (mJ+ mS) may be in the neighborhood of 12.

mBC / (mJ + mS) = mBC / 412.96 mE = 12(?)
mBC = 412.96 mE * 12 * (1 mJ / 317.8mE) = 15.6 mJ

    This suggests that the binary components of former binary-Companion were likely super-Jupiter mass, below the 13 Jupiter mass threshold for deuterium fusion, even with a > 3:1 mass disparity, such as in the Jupiter-Saturn trifurcation generation.
    The original Brown Dwarf core of the solar system prior to trifurcation incorporates the mass of the binary-Companion components + the SUPER-Jupiter residual core + 1st-generation trifurcation losses, putting Brown Dwarf somewhere on the low-mass end of the brown dwarf range, indicating symmetrical FFF during the protostar phase of the Brown Dwarf core, where the prestellar-protostellar FFF threshold presumably lies at 4 mJ.

    The solar system configuration of twin-binary planets in adjacent heliocentric orbits suggests that the planetary twin-binary pairs were captured by binary-Sun from binary-Companion prior to the twin-binary pairs separating, with Jupiter-Saturn & Venus-Earth having been captured by binary-Sun via the near-side L1 Lagrangian point of binary-Companion, while Uranus-Neptune were captured via the far-side L2 Lagrangian point. This arrangement places binary-Companion in a heliocentric orbit between Saturn and Uranus.
    Slotting binary-Companion between Saturn and Uranus provides a compelling mechanism for the perturbation of the Kuiper belt, giving rise to the late heavy bombardment (LHB), where a mean-motion resonance of binary-Companion migrated outward through the Kuiper belt, driven by eccentricity pumping of binary-Companion’s heliocentric orbit by the solar perturbation of binary-Companion’s components. Secular perturbation of binary-Companion by the Sun (after binary-Sun merger at 4,567 Ma) presumably transferred potential energy from the close-binary components of binary-Companion to its heliocentric orbit, progressively increasing the heliocentric eccentricity of binary-Companion. And a progressively-increasing heliocentric eccentricity implies a progressively-increasing heliocentric period, causing the mean-motion resonances of binary-Companion to migrate outward through the Kuiper belt over time. The mean-motion resonance presumed to cause the LHB may have been the 1:4 resonance, and if so, then the 9:2 resonance may have been instrumental in sculpting the trifurcation debris disk beyond Neptune, thereby influencing the locations of hot classical KBOs formed by streaming instability prior to 4,567 Ma.

Evidence for an early short-duration pulse in a bimodal LHB:
    Mean-motion resonance perturbation by binary-Companion predicts a bimodal late heavy bombardment, with a narrow early pulse, as the 1:4 resonance encountered Plutinos in a 2:3 resonance with Neptune at an average semimajor axis of 39.4 AU, followed by a much-broader main pulse, as the tidal inflection point encounters classical KBOs (cubewanos) that lie between the 2:3 resonance and the 1:2 resonance with Neptune, centered at about 43 AU. Indeed a bimodal LHB with a bright-line early pulse is supported by lunar regolith returned by Apollo missions.
    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 late heavy bombardment (LHB) melts and breccias, suggesting the date of the first of the early bimodal pulse. (Garrick-Bethell et al. 2008)
    Whole-rock ages of ~4.2 Ga from Apollo 16 and 17, a 4.23-4.24 Ga age of troctolite 76535 from 40-50 km depth of excavation of a large lunar basin (>700 km); a 4.23 Ga age was found in far-side meteorites, Hoar 489 and Amatory 86032; and samples from North Ray crater (63503) have been reset to 4.2 Ga, all support an early narrow pulse. Altogether, 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 a short-duration early pulse of a bimodal LHB occurring at about 4.22 Ga, possibly when binary-Companion’s outer 1:4 resonance passed through the Plutinos, in which binary-Companion’s 1:4 resonance overcame Neptune’s 2:3 resonance.

    The extreme obliquity of Uranus (98º), compared to the other planets, presumably also telegraphs the position of former binary-Companion, where the progressively-increasing heliocentric eccentricity of binary-Companion overran Uranus’ orbit, forcing Uranus outward, which torqued the ice-giant planet into its present extreme axial tilt as a mechanism for conserving system angular momentum. Notably, Uranus is missing its (oversized) trifurcation moon, presumably in a former prograde orbit, by symmetry to Neptune’s retrograde trifurcation moon, Triton. Apparently, Uranus’ former trifurcation moon was stripped by repeated close encounters of Uranus with binary-Companion. But while presumably missing a former prograde trifurcation moon, Uranus possesses a 4-moon cascade (Ariel, Umbriel, Titania and Oberon) of particularly-well-behaved moons in low-inclination (< 0.35º) and low-eccentricity (< 0.004) orbits. For a planet with an extreme 98º axial tilt caused by binary-Companion buffeting, the possession of such well behaved moons may telegraph the late in situ formation of a cascade of hybrid-accretion moons from the 650 Ma Companion-merger debris disk. And if Uranus spawned young hybrid accretion moons, the other giant planets may have also spawned young hybrid accretion moons as well.


Trifurcation moons:
    Since the iron core of Earth’s Moon is disproportionately small compared to Earth’s iron core, the Moon is evidently not the residual core of the SUPER-Earth trifurcation, captured by Earth. An alternative origin story is suggested by the visual depiction of computer models of bar-mode instabilities, where trifurcation is suggested to occur by way of bar-mode instabilities. A conspicuous component of the bar-mode instability structure is the twin pair of tails that stream behind the outer ends of the central bar, creating a pinwheel effect, as depicted in the following dynamical bar-mode instability video, Dynamical Bar-mode Instability
    ‘Trifurcation moons’ are suggested to form during trifurcation if the pinwheel tails streaming from the ends of the central bar gravitationally pinch off into their own moony Roche spheres while their associated bar-mode arms are gravitationally pinching off into their own twin-binary planetary Roche spheres. And the resulting trifurcation moons remain gravitationally attached to their twin-binary planets.
    In addition to Earth’s oversized Moon, Titan at Saturn and Triton at Neptune are also suggested to be trifurcation moons, with all other moons as hybrid-accretion objects, streaming instability objects (that did not experience merger accretion), or captured objects.
    Trifurcation moons are born with no net angular momentum with respect to their respective twin-binary (planetary) components, but the subsequent orbital interplay with their host twin-binary pair torques the trifurcation moons either clockwise or counter clockwise with respect to their twin-binary components, installing one moon in a prograde orbit, while its sibling is necessarily installed in a retrograde orbit. Thus because Luna acquired a prograde orbit around Earth, we know by symmetry that Venus’ corresponding trifurcation moon acquired a (decaying) retrograde orbit, where retrograde orbits ultimately spiral in and merge with their host planet.
    Jupiter-Saturn; If Titan is Saturn’s prograde trifurcation moon, then Jupiter presumably had a retrograde trifurcation moon that has long since merged with the planet, possibly at 4,562 Ma, forming enstatite chondrites that lie on the 3-oxygen isotope ‘terrestrial fractionation line’, with the moony merger explosion possibly melting water ice in nearby CI chondrites, forming dolomites in internal fissures.
    Uranus-Neptune; The retrograde orbit of Triton at Neptune presupposes a former prograde trifurcation moon at Uranus, which was presumably lost to binary-Companion. Triton will ultimately spiral in to merge with Neptune in about 3.6 billion years.
    Venus-Earth; Corresponding to Earth’s prograde trifurcation moon, Luna, was a former retrograde trifurcation moon around Venus that presumably spiraled in to merge at 579 Ma, fogging the inner solar system, causing the Gaskiers glaciation on Earth.

– Jupiter: former retrograde trifurcation moon that merged with the planet at 4,562(?) Ma
– Saturn: prograde trifurcation moon Titan
– Uranus: lost prograde trifurcation moon
– Neptune: retrograde trifurcation moon, Triton
– Venus: former retrograde trifurcation moon that presumably merged with the planet at 579 Ma
– Earth: prograde trifurcation moon, Luna

Hybrid accretion moons:
    Cascades of hybrid accretion moons apparently form around gas- and ice-giant planets, similar to the cascades of hybrid-accretion super-earths which form around dwarf stars. The Galilean moons of Jupiter and the large planemo moons of Uranus are the best examples of moony hybrid-accretion cascades in our solar system. Possession of a trifurcation moon does apparently does not preclude the subsequent formation of hybrid accretion moons, such as the planemo moons of Saturn inside the orbit of Titan, and likely including Iapetus beyond Titan.

Protoplanetary disk and three debris disks:

– Protoplanetary disk (> 4,567 Ma) – Brown Dwarf, Mars(?), Oort cloud comets(?), CI chondrites(?)
– Trifurcation debris disk [inferred] (> 4,567 Ma) – old hot-classical KBOs, and possibly hybrid-accretion moons
– Solar-merger debris disk (4,567 Ma) – asteroids, chondrites and likely hybrid-accretion moons
– Companion-merger debris disk [inferred] (650 Ma) – young cold-classical KBOs

– Protoplanetary disk, >4,567 Ma:
    Former Brown Dwarf is may have condensed trillions of kilometer-scale planetesimals from the protoplanetary disk by streaming instability against its magnetic corotation radius, many of which may have accreted to form Mars. Mars may have been one of a cascade of hybrid accretion planets around former Brown Dwarf, where Mars siblings were either lost from the solar system or merged with the Sun or with the components of binary-Companion.
    The vast majority of the leftover protoplanetary planetesimals were presumably scattered into the Oort cloud or out of the solar system altogether during the upheaval of symmetrical FFF followed by 4 generations of trifurcation, and small protoplanetary planetesimals of the inner solar system may have vaporized altogether in the luminous red nova phase of the binary-Sun merger at 4,567 Ma. Subsequently, a number of protoplanetary planetesimals may have been reintroduced into the inner solar system from the Oort cloud reservoir as CI chondrites.

– Trifurcation debris disk (Brown Dwarf reservoir) >4,567 Ma:
    Rotational fragmentation of a core by trifurcation is presumably an inefficient and messy process in which a sizable percentage of Brown Dwarf mass vaporized to form a trifurcation debris disk during 4 generations of trifurcation.
    The trifurcation debris disk had high angular momentum compared to the following solar-merger debris disk, forming a debris disk that extended beyond Neptune, ‘condensing’ planetesimals, presumably by streaming instability, against Neptune’s strongest outer resonances, principally against Neptune’s outer 2:3 resonance. Today, this reservoir presumably constitutes Plutinos and hot classical Kuiper belt objects (KBOs), as well as trans-Neptunian objects (TNOs) of the scattered disk and detached objects, scattered into their ‘hot’ perturbed orbits by the resonant effects of former binary-Companion.
    The trifurcation debris disk was derived from the homogenized Brown Dwarf reservoir defines the 3-oxygen-isotope terrestrial fractionation line (TFL), including all 6 trifurcation planets (excluding Mars and possibly Mercury), as well as the trifurcation debris disk condensates, including; hot classical KBOs, scattered disk, and detached objects. Mass-dependent fractionation during trifurcation, debris-disk processing and streaming instability may separate the trifurcation planets streaming-instability objects along the TFL, but only mass-independent fractionation could displace objects off the TFL, above or below it.
    Trifurcation of differentiated objects, with siderophile elements internally sequestered into iron-nickel cores created a siderophile-depleted trifurcation debris disk. Thus hot-classical KBOs condensed from the trifurcation debris disk were siderophile depleted. And siderophile depleted hot classical KBOs that lie on the terrestrial fractionation line plays into the alternative suggestion that gneissic continental basement rock is extraterrestrial, formed by ‘aqueous differentiation’ of KBOs, perturbed into the inner solar system by tidal effects of former binary-Companion during the late heavy bombardment. (See section, AQUEOUS DIFFERENTIATION OF KUIPER BELT OBJECTS (KBOs))

– Solar-merger debris disk (solar-merger reservoir) 4,567 Ma:
    The former binary-Sun components were perturbed by binary-Companion to spiral in and merge at 4,567 Ma, apparently elevating the temperature of the merging cores to the point of fusing r-process radionuclides, notably 26Al and 60Fe. The solar-merger debris was also variably enriched in the helium-burning stable isotopes, notably 20 Ne, 16O and 12C. Calcium aluminum inclusions (CAIs) apparently condensed from polar jets squirting from the merging cores with canonical 26Al concentrations, and chondrules appear to have formed episodically, as violent solar flares melted dust bunnies, during a circa 3 million year flare star phase of the Sun following its binary merger.
    The stellar merger created a luminous red nova (LRN) that may have briefly extended into the Kuiper belt, melting the surfaces of the hot-classical KBOS. The resulting low-angular-momentum solar-merger debris is suggested to have ‘condensed’ asteroids by streaming instability against the merger-expanded magnetic corotation radius of the Sun. Subsequently, infalling solar merger debris acquired angular momentum from Jupiter, forming a solar-merger debris disk in Jupiter’s inner resonances that condensed chondrites.
    Asteroids are suggested to have quickly condensed by streaming instability against the Sun’s post-merger super-intense magnetic field, while the short-lived radionuclides were still highly radioactive, causing these early condensates to ‘thermally differentiate’ (melt internally). Chondrites condensed over the course of the next 5 million years by streaming instability, against Jupiter’s strongest inner resonances, largely without live radionuclides.
    If the planet Mercury is not the residual core of the 4th-generation-trifurcation (Venus-Earth-Mercury), then Mercury may be a hybrid-accretion planet accreted from refractory asteroids condensed by streaming instability against the Sun’s greatly-expanded solar-merger magnetic corotation radius,
possibly near the orbit of Mercury.
    The stellar merger imparted very-little angular momentum to the nova debris, confining the debris disk to the inner solar system. An early debris disk may have formed near the orbit of Mercury, dragged into Keplerian rotation by the Sun’s magnetic field. Then gradually over the next several million years, the continuing infall of dust was imbued with angular momentum by Jupiter, forming a debris disk inside the orbit of Jupiter, with gaps caused by Jovian mean-motion resonances.
    At its greatest extent the LRN may have extended well into the Kuiper belt, melting an igneous crust on the surface of hot classical KBOs, as well as volatilizing the terrestrial planets and all trifurcation moons.

– Companion-merger debris disk, 650 Ma:
    The super-Jupiter components of former binary-Companion presumably spiraled in to merge at about 650 Ma, fogging the solar system with binary-Companion merger debris, causing the Marinoan glaciation on Earth. The binary-Companion merger presumably resulted in an asymmetrical merger explosion that gave the newly-merged Companion escape velocity from the Sun. While the binary-Sun merger at 4,567 Ma was vastly more energetic than the binary-Companion merger at around 650 Ma, the later Companion-merger debris disk inherited vastly more angular momentum, apparently creating a debris disk that extended beyond Neptune, which is suggested to have condensed a young population of cold classical KBOs.
    The proceeding Sturtian glaciation (715-680 Ma) of the Cryogenian Period points to a prolonged period of solar system fogging long before the actual binary-Companion merger at 650 Ma. This earlier Sturtian glaciation suggests a series of moony mergers with the binary-Companion components, as the components spiraled inward.
    A young, ‘cold classical KBO’ population presumably condensed in situ by streaming instability against the strongest outer resonances of Neptune from the Companion-merger debris disk, primarily against Neptune’s outer 2:3 resonance. Presumably the earlier moony mergers that fogged the solar system during the Sturtian glaciation did not eject sufficient mass to condense planetesimals.
    The young, cold-classical KBO population should lie on the TFL, like the old hot-classical KBO population, but the young population should have a siderophile signature, since the Companion-merger debris included siderophile material from the cores of the merging super-Jupiter-mass components.
    The companion-merger debris disk also inherited the Brown Dwarf D/H (deuterium/hydrogen) ratio. A measurement of the D/H ratio in the cold classical KBO population could determine if one or both binary-Companion components were above or below the brown-dwarf deuterium-burning threshold.

Orbital interplay of Mars and Earth during the Ediacaran Period:

    This is a working hypothesis for the origin of Mars and its suggested orbital interplay with Earth during the Marinoan glaciation and the succeeding Ediacaran Period, following the loss of binary-Companion at 650 Ma. This working hypothesis suggests an origin story and dynamic history for Mars, which was designed to explain terrestrial and solar system phenomena unaddressed by primary FFF-trifurcation ideology; however, the author has low confidence in this Mars origin story compared to FFF-trifurcation ideology.

    The Mars oxygen-isotope fractionation line appears to be incompatible with both the solar-merger debris disk (enriched in solar-merger-nucleosynthesis oxygen-16) and incompatible with the trifurcation debris disk (which lies on the 3-oxygen-isotope terrestrial fractionation line). Thus Mars apparently formed otherwise, presumably from the original protoplanetary disk by hybrid accretion. Had Mars formed around either former binary-Sun component, its expected scale would be in the super-Earth radius range, whereas Mars is only 7.2 times the mass of Io at Jupiter. Mars’ high density (3.933 g/cm3) and large iron core make it unlikely to be a trifurcation moon of one of the components of binary-Companion, since the 2nd-generation trifurcation moon Titan only has a density of 1.880 g/cm3; whereas Mars compares much-more favorably in density with the first Galilean hybrid-accretion moon, Io (3.528 g/cm3), at Jupiter, and at 7.2 times the mass of Io.

    The working hypothesis for Mars is a hybrid-accretion object formed around former Brown Dwarf, prior to its trifurcation by the former binary-Sun components. Because hybrid-accretion objects often form in multiple planet/moon cascades, Mars may have had one or more siblings that did not survive the dramatic dynamics of our solar system. All twin-binary pair trifurcation products (Jupiter-Saturn, Uranus-Neptune, and Venus-Earth-Mercury) were presumably captured by former binary-Sun from binary-Companion prior to the binary-Sun merger at 4,567 Ma, but solitary moons of binary-Companion, and possible circumbinary hybrid-accretion moon(s) presumably did not experience eccentricity pumping like the trifurcation binary pairs. Therefore, Mars was presumably still within the gravity well of binary-Companion when the binary-Companion components merged at 650 Ma.
    The asymmetrical merger explosion that gave newly-merged Companion escape velocity from the Sun did not take Mars with it, and, Mars apparently lost heliocentric angular momentum in the process of escaping from newly-merged Companion, apparently installing Mars in a low Earth-crossing orbit.

“Global preserved sedimentary rock volume increases by more than a factor of 5 across the Phanerozoic–Proterozoic boundary”
Image credit: Keller et al., 2019

     The Precambrian-Cambrian boundary marks a dramatic transition in the sedimentation record on Earth, “from roughly 0.2 km3/y of preserved sedimentary rock in the Proterozoic to ∼1 km3/y in the Phanerozoic” (Keller et al., 2018). The working hypothesis for this 5-fold increase in preserved sedimentation at the Cambrian boundary suggests that Earth may have been intermittently perturbed by close encounters with Mars that disrupted sedimentation preservation. And Earth may succeeded in clearing Mars from its orbit with a final close encounter at 541 Ma that kicked Mars into something close to its present orbit and issued in the Phanerozoic Eon on Earth. The Great Unconformity on Earth may have been partly attributable to perturbation by Mars, but the almost complete absence of terrestrial craters older than 650 Ma suggests that most of the Great Unconformity was attributable scouring of the continents by ice sheets during the global glaciations of the Cryogenian Period, where ice sheets may have extended almost to the edges of the continental shelves, as sea levels retreated during the Snowball Earth episodes. While it’s tempting to directly attribute the Great Unconformity to the gravitational effects of binary-Companion itself and/or its merger exodus, at its orbital distance beyond Saturn, the tidal influence of binary-Companion would have been barely 2% that of Earth’s Moon, Luna. Instead the effect was more likely indirect, by way of fogging the solar system, creating glaciations on Earth, and sending Mars into the inner solar system.

    A flood basalt dating to the end Proterozoic Eon may be evidence of the final close orbital encounter between Mars and Earth that kicked Mars into something close to its present orbit. The end Proterozoic Eon flood basalt is associated with a triple tectonic junction rift zone, known as the Southern Oklahoma Aulacogen (SOA), and a triple tectonic junction rift might be expected to occur at the summit of the tidal bulge caused by an orbital close encounter with Mars. The best available age constraints of the eruptive products of the Southern Oklahoma Aulacogen are ~ 535 to 540 Ma (Brueske et al., 2016).
    Closely coincident to the rift zone flood basalt on Earth is volcanism on Mars, circa 500 Ma. Arsia Mons, one of the largest volcanoes on Mars, has an eruptive episode dating to about 500 Ma (Werner, 2009), which could very well be 541 Ma.

    A 1998 numerical simulation of the asteroid belt suggests that the inner belt has been eroded by about half, by 3-way resonances with Mars and Jupiter, but this level of asteroid depletion is hard to reconcile with a nearly constant lunar cratering record over the last 3 billion years. (Nesvorný and Morbidelli, 1998, 1999) Alternatively, a late appearance of Mars to something close to its present orbit at 541 Ma predicts an increased cratering rate in the Phanerozoic Eon. Indeed, the lunar impact flux increases by a factor of 2.6 near 290 Ma (Mazrouei et al., 2019), which represents a 250 million year hiatus, from 541 Ma to ~290 Ma, before increased lunar and terrestrial cratering rates are evident. After falling from its circumbinary Companion orbit into Earth’s sphere of influence at 650 Ma, and after ejection from Earth’s orbit at 541 Ma, Mars apparently took an additional 250 million years to stabilize in orbital period, at about 290 Ma, resulting in 3-way resonances between inner belt asteroids, Mars and Jupiter that increased asteroid eccentricities, causing Mars-crossing and Earth-crossing orbits that increased Earth and Moon impacts by a factor of 2.6.

    The low-inclination moderate-eccentricity of Mars’ present orbit makes this dynamic orbital interplay seem unlikely; however, a trifurcation origin of 6 planets requires similar levels of radial displacement for the other 7 planets, which highlights the extremely coplanar nature of our solar system, considering the low orbital inclinations all planets except Uranus. As to eccentricity, Mars has twice the eccentricity of the next most eccentric planet (Mercury excepted), and Earth has 2.47 times the eccentricity of Venus.

Venusian cataclysm:

    Venus is suggested here to be Earth’s twin from a fourth-generation SUPER-Earth trifurcation that formed Venus with an oversized trifurcation moon in a retrograde orbit, where Venus’ retrograde moon spiraled in to merge with the planet during the Ediacaran Period, causing the Venusian cataclysm, resulting in Venus’ slight retrograde rotation.

    Orbital interplay between Uranus-Neptune and their residual SUPER-Earth core caused a 4th-generation trifurcation by means of bar-mode instability, complete with the ‘pinwheel’ tails trailing from the bar-mode arm that formed Venus-Earth. These pinwheel tails gravitationally collapsed to formed oversized trifurcation moons, one gravitationally bound to Earth and one gravitationally bound to Venus. Trifurcation moons are born with no net angular momentum with respect to their bar-mode arms and acquire their angular momentum by orbital interplay. Orbital interplay of the trifurcated quadruple system composed of close-binary Venus-Earth and close-binary Uranus-Neptune kicked Earth’s trifurcation Moon (Luna) into a prograde orbit around Earth, and by symmetry Venus’ trifurcation moon acquired a retrograde orbit around Venus. Venus’ oversized, retrograde trifurcation moon acquired a decaying orbit that was doomed to spiral in and merge with Venus, like Neptune’s retrograde trifurcation moon, Triton.
    Venus’ trifurcation moon may have spiraled in to merge with Venus at 579 Ma, causing a Venusian cataclysm that forever changed the planet. A Venusian cataclysm would neatly explain relatively ‘recent’ resurfacing of the planet. The nearly-random spatial distribution of Venus’ low crater count suggests 300-500 Myr resurfacing (Price & Suppe 1994), or 300-1000 Myr resurfacing (McKinnon et al. 1997).
    Pancake-shaped coronae on Venus caused by mantle upwelling may be direct evidence of a protracted digestion of its former moon, with Venus’ sulfurous atmosphere sustained by continued volcanic outgassing. “Sulfur dioxide is a million times more abundant in the atmosphere of Venus than that of Earth, possibly as a result of volcanism on Venus within the past billion years” (Marcq et al 2013). Additionally, the scorching temperatures recorded at the surface could be partly residual heat from the merger.

    For Venus’ retrograde orbit to be the result of a merger with a former retrograde moon requires that the moon’s retrograde orbit had greater angular momentum than Venus’ former prograde rotation. Part of the prograde-to-retrograde planetary rotation transition (angular momentum transfer) would have occurred progressively during 4 billion years of Venus-moon tidal interactions, but the majority of the angular momentum transfer would have been cataclysmic, at impact.
    An object in a circular orbit has only half the potential and kinetic energy necessary to achieve escape velocity, so presumably very few chunks of moon or planetary surface escaped Venus’ gravitational well. Volatile losses, however, creating a heliocentric debris ring centered on Venus, but the Venusian cataclysm debris ring did not directly fog the solar system. Instead, the accumulation of dust in Earth’s upper atmosphere from a greatly-increased rate of (Venusian) micrometeorites reduced the incident radiation at the surface by increasing the albedo of Earth’s upper atmosphere.

    A cataclysm the scale of a large moony merger with our closest planet will not have left Earth unscathed. A large moony merger with Venus would have created a heliocentric debris ring composed of micrometeorites that burned up in Earth’s upper atmosphere, creating high altitude dust that reflected sunlight back into space, causing a major glaciation on Earth. Two glaciations in the most-likely time frame present themselves; Gaskiers glaciation (between 579.63 ± 0.15 and 579.88 ± 0.44 Ma) in the Late Ediacaran Period, or Baykonurian glaciation near the Proterozoic-Phanerozoic boundary.

    The sudden appearance of all modern metazoa (animal) phyla in the Cambrian (Cambrian explosion) suggests another telluric effect, in the form of the possible contamination of Earth with Venusian fauna, but here again, either glaciation may be indicated, with Ediacaran fauna appearing shortly after the Gaskiers glaciation, and Cambrian fauna appearing some time after the Baykonurian glaciation. Molecular clocks indicate Metazoa originated in the range of 850-650 Ma (Cunningham et al., 2016), and if so, then the absence of earlier evidence of (soft bodied) Metazoa is inexplicable, given the abundant preservation of acritarchs from this period. Additionally, “recent molecular clock analyses estimate that the crown‐groups of most animal phyla did not originate until the Cambrian. The presence of crown members of most animal phyla in the Ediacaran is therefore not an expectation of most molecular clock studies” (Cunningham et al., 2016).
    Venusian contamination of Earth in a 579 Ma Venusian cataclysm explains the absence of earlier metazoa predicted by molecular clocks, and suggests that Ediacaran fauna, transplanted from Venus, were the stem groups of crown-group Cambrian phyla; however, Venusian cataclysm contamination also requires a degree of earlier protozoa interchange between Venus and Earth, before and after the Great Oxygenation Event of the Paleoproterozoic era.
    A Venusian cataclysm is not predicated on terrestrial contamination by Venusian lifeforms, but it would neatly explain the observed gap in the early fossil record.

    Most notably, trifurcation theory predicts a former retrograde moon at Venus, whose merger is neatly unifies;
1) the retrograde rotation of Venus,
2) the recent resurfacing of the planet,
3) the continuing volcanism and sulfurous atmosphere on Venus,
4) the Gaskiers glaciation on Earth,
5) and possibly the sudden origin of the Ediacaran biota.

Solar system summary:

    Four planets of our solar system exhibit a narrow range of axial tilts to their orbits, ranging from 23.44° for Earth to 28.32° for Neptune. This narrow range of axial tilts for half the planets suggests a solar system-wide effect. The greatest solar system wide effect was the suggested binary spiral-in merger of former binary-Sun at 4,567 Ma. The binary-Sun merger sloughed off a small percentage of the combined mass of the former binary components, reducing the central gravity well, which increased the orbital distance and orbital period of all heliocentric orbits. Conservation of angular momentum presumably caused axial tilts in the 20 degree range. Jupiter, however, is a notable exception, with its small 3.13° axial tilt.

    A massive accretion disk around a diminutive brown-dwarf-mass protostellar core underwent symmetrical FFF, ‘condensing’ a twin-binary pair of disk-instability (d-i) objects. The resulting system, comprised of a massive twin binary pair of prestellar d-i objects orbiting the diminutive Brown Dwarf, was dynamically unstable, resulting in orbital interplay that progressively ‘evaporated’ Brown Dwarf into a circumbinary orbit around the twin d-i objects, causing the d-i objects to spiral in to become binary-Sun. Orbital interplay caused Brown Dwarf to spin up and undergo 4 generations of trifurcation, forming binary-Companion, along with 3 generations of trifurcation planets. Perturbations from former binary-Companion caused the binary-Sun components to spiral in and merge at 4,567 Ma, creating a luminous red nova, which quickly retreated to leave behind the ‘solar-merger debris disk’. The solar-merger debris disk likely condensed asteroids against the Sun’s corotation radius with live short-lived radionuclides, and later condensed chondrites in situ against Jupiter’s strongest inner resonances.

Symmetrical FFF, followed by 4 generations of trifurcation:
    Our solar system at one time is suggested to have formed 5 transitory twin-binary pairs; binary-Sun, binary-Companion, Jupiter-Saturn, Uranus-Neptune, and Venus-Earth.
1) Symmetrical FFF – binary-Sun + Brown Dwarf (stellar core)
2) First-generation trifurcation – binary-Companion + SUPER-Jupiter (residual core)
3) Second-generation trifurcation – Jupiter-Saturn + SUPER-Neptune (residual core)
4) Third-generation trifurcation – Uranus-Neptune + SUPER-Earth (residual core)
5) Fourth-generation trifurcation – Venus-Earth + Mercury(?) (residual core)

    The suggested super-Jupiter-mass twin-binary components of binary-Companion did not separate like the binary components of the three subsequent trifurcation generations, briefly creating a quaternary system composed of binary-Sun and binary-Companion in a wide binary orbit around the solar system barycenter, with a Sun-Companion separation around 15 AU (between Saturn and Uranus).
    Following binary-Sun merger at 4,567 Ma, perturbations from the newly-merged Sun caused binary-Companion components to spiral in over time, progressively increasing the Sun-Companion eccentricity over time, eventually causing binary-Companion to overrun the orbit of Uranus, resulting in Uranus’ severe axial tilt.
    The progressively-increasing eccentricity caused binary-Companion’s heliocentric mean-motion resonance to migrate out through the Kuiper belt over time, perturbing Plutinos at 4.22 Ga, followed by cubewanos from 4.1-3.8 Ga, causing a bimodal late heavy bombardment of the inner solar system, with its short-duration early pulse.
    The spiral-in of the super-Jupiter-mass components eventually accreted their own moons, fogging the solar system, causing the Sturtian glaciation of Snowball Earth. Ultimately, the binary components merged at 650 Ma in an asymmetrical merger explosion, giving newly-merged Companion escape velocity from Sun, and causing the Marinoan glaciation of the Cryogenian Period.
    The resulting Companion-merger debris disk condensed the cold-classical KBOs against Neptune’s outer 2:3 resonance, and likely formed some of the giant planet’s hybrid-accretion moons.

    Mercury has two potential origin stories which seem equally plausible; first, as the fourth-generation residual core of the SUPER-Earth trifurcation, > 4,567 Ma, and second, as a hybrid accretion planet formed from the 4,567 Ma solar-merger debris disk. Both alternatives predict a large iron-nickel core, with trifurcation placing Mercury on the 3-oxygen-isotope terrestrial fractionation line (TFL), while a hybrid accretion origin suggests 16O enrichment, placing Mercury below the TFL.

    Venus is suggested to be the twin of Earth from the fourth-generation SUPER-Earth trifurcation, with identical bulk isotopic ratios. In another way, Venus is suggested to have been the mirror image of Earth, with a trifurcation moon similar in size and composition to Earth’s Moon, but in a decaying retrograde orbit that spiraled in to merge with the planet at 579 Ma, resulting in the ‘Venusian cataclysm’ that fogged the solar system and caused the Gaskiers glaciation on Earth.
    The Venusian cataclysm resurfaced the planet, and is responsible for ongoing volcanism in the form of pancake-shaped coronae and for the sulfurous component of Venus’ atmosphere. The moony merger imbued Venus with a slight retrograde rotation.
    Additionally, Ediacaran metazoa may be contamination from Venus, explaining the absence of earlier instances of metazoa on Earth predicted by molecular clocks.

    Earth is suggested to be the twin of Venus from the fourth-generation SUPER-Earth trifurcation. Earth is presumed to have acquired its trifurcation Moon as the trailing tail of the bar-mode arm which became Earth gravitationally pinched off into a separate Roche sphere, remaining gravitationally bound to the planet.
    Venus-Earth presumably escaped from Uranus-Neptune, prior to Jupiter-Saturn escaping from binary-Companion, such that Venus-Earth were still within Jupiter-Saturn’s gravity well. Binary-binary resonance presumably caused eccentricity pumping which caused Jupiter-Saturn to escape from binary-Companion by way of the binary-Companion’s (inside) L1 Lagrangian point. Similarly, additional eccentricity pumping caused Venus-Earth to escape from Jupiter-Saturn, also by way of Jupiter-Saturn’s L1 Lagrangian point. Finally, eccentricity pumping caused Venus-Earth to separate.
    The Great Unconformity may be the result of two Snowball Earth glaciations, with the first glaciation caused by the fogging of the solar system by moony mergers with the binary Companion components as the super-Jupiter-mass components spiraled in, and the second glaciation caused by the merger of the two components themselves at 650 Ma.
    Mars may be a hybrid accretion planet of former Brown Dwarf, hurled into the inner solar system on an Earth-crossing orbit at 650 Ma when newly-merged Companion escaped from the solar system. After about 100 million years, Earth finally kicked Mars into something close to its present orbit, during a particularly-close encounter at 541 Ma that may have caused the Southern Oklahoma Aulacogen flood basalt on Earth and volcanism on Mars at Arsia Mons. The volume of retained sedimentary rock on Earth increased by a factor of 5 at the Ediacaran-Cambrian boundary, presumably due to the absence of Martian orbital close encounters.
    Earth may be the recipient of Venusian metazoa from the Venusian cataclysm at 579 Ma in the form of Ediacaran biota, when Venus’ retrograde trifurcation moon spiraled in to merge with the planet.
    The continental tectonic plates on Earth are suggested to be cored by authigenic gneissic sediments, precipitated, lithified and metamorphosed in the cores of hot classical KBOs, which were perturbed into the inner solar system from the Kuiper belt by tidal effects of former binary-Companion. (See section, AQUEOUS DIFFERENTIATION OF KUIPER BELT OBJECTS (KBOs))

    Mars is not predicted by the FFF-trifurcation ideology, and thus its origin and dynamic history are comparative speculation, compared to the other planets; therefore its origin and orbital dynamics are merely a ‘working model’.
    As such, the working model for Mars is a hybrid-accretion planet formed around former Brown Dwarf prior to its trifurcation by binary-Sun. Binary-Companion presumably retained Mars as a circumbinary planet until escaping from the solar system in the binary-Companion spiral-in merger at 650 Ma. Mars was apparently hurled in a retrograde heliocentric direction when newly-merged Companion escaped from the Sun, causing Mars to lose heliocentric angular momentum, presumably injecting Mars into an Earth-crossing orbit in the inner solar system.
    Mars was presumably ejected from its Earth-crossing orbit at 541 Ma in final orbital close encounter between Earth and Mars. Mars may have taken an additional 250 million years to settle into its present orbit and orbital period, by about 290 Ma, after which 3-way resonances between Mars and Jupiter began strongly perturbing inner-belt asteroids into Mars-crossing and Earth-crossing orbits, which increased Earth and Moon impacts by a factor of 2.6.

    Jupiter is suggested to be a twin of Saturn from the second-generation SUPER-Jupiter trifurcation.
    Like Venus and Neptune, Jupiter presumably once possessed a former trifurcation moon in a doomed retrograde orbit that spiraled in to merge with the gas giant, perhaps at around 4,562 Ma. The cascade of 4 large Galilean moons, Io, Europa, Ganymede and Callisto, presumably formed by hybrid accretion, either from the trifurcation debris disk or the solar-merger debris disk.
    CI chondrites from the asteroid belt exhibit a thermal event that melted water ice and deposited dolomites in the 4,562 Ma age range, with a 53Mn-53Cr age of dolomites dated at 4,563.8-4,562.5) (Fujiya et al. 2013), suggesting a late heating event.
    The D/H (deuterium/hydrogen) ratio of Saturn is lower than that of Jupiter by a factor of 0.71 + 0.22% – 0.15, contrary to standard-model predictions of a higher ratio (Pierel et al. 2017). But when the suggested moony merger explosively overflowed Jupiter’s Roche sphere, hydrogen would have become particularly fractionated, due to the enormous 2 to 1 mass difference between deuterium and protium, depleting Jupiter’s outer layers in the much-more-volatile protium.
    Perhaps the most compelling evidence for a dramatic inner solar system event pointing to a Jupiter-moony merger around 4,562 Ma are enstatite chondrites, which are the only chondrites to lie on the terrestrial fractionation line, pointing to a Brown Dwarf reservoir origin, with a 29I-129Xe age for enstatite chondrites of 4,562.3 +/- 0.4 (Gilmour et al. 2009).

    Saturn, is suggested to be a twin of Jupiter from the second-generation SUPER-Jupiter trifurcation, with Titan as Saturn’s trifurcation moon. Saturn also exhibits a neat cascade of smaller planemo hybrid-accretion moons from one or more of the solar system debris disks.

    Uranus is suggested to be a twin of Neptune from the third-generation SUPER-Neptune trifurcation, and its, presumably former prograde trifurcation moon is missing.
    Uranus is telegraphing a significant dynamic event, due to its severe 98°axial tilt and its missing prograde trifurcation moon, which is suggested to have occurred when binary-Companion overran the orbit of Uranus, due to eccentricity pumping of binary-Companion by the Sun.
    If Uranus lost its trifurcation moon to binary-Companion, it likely also lost its former hybrid-accretion moons as well, suggesting that Uranus’ present cascade of well-behaved planemo moons likely date to the 650 Ma Companion-merger debris disk.

    Neptune is suggested to be a twin of Uranus from the third-generation SUPER-Neptune trifurcation.
    Triton is Neptune’s suggested retrograde trifurcation moon, which will one day spiral in to merge with the planet.
    The Kuiper belt presumably formed in situ against Neptune’s outer resonances, principally its strongest 2:3 resonance.

Asteroids and chondrites:
    Asteroids and chondrites are suggested to have condensed by streaming instability from a low angular momentum solar-merger debris disk, from the aftermath of the former spiral-in merger of former binary-Sun at 4,567 Ma.
    Early-forming asteroids with hot short-lived radionuclides (SLRs) may have primarily condensed by streaming instability against the Sun’s super-intense-stellar-merger magnetic corotation radius. The planet Mercury may or may not be a hybrid accretion planet formed from solar-merger debris disk asteroids. SLRs caused thermal differentiation, forming metallic cores in many asteroids.
    Chondrites formed over the next 5 million years, likely condensing in situ by streaming instability against Jupiter’s strongest inner resonances, with Jupiter’s orbit creating the necessary angular momentum. Chondrites are not internally differentiated, due to their formation after the radioactivity of the SLRs had largely died away.

Hot classical KBOs:
    Hot classical KBOs in are suggested to have condensed from the trifurcation debris disk from the Brown Dwarf reservoir against Neptune’s strongest outer resonances, shortly prior to 4,567 Ma. Hot classical KBOs are suggested to lie on the TFL and have a siderophile-depleted composition coincident with Earth’s continental crust, with the basement rock of Earth’s continental crust suggested to be extraterrestrial of hot classical KBO origin.
    Hot classical KBOs were presumably condensed against Neptune’s strongest outer resonances in ‘cold’, low-inclination low-eccentricity orbits, which were perturbed into their present ‘hot’, high-inclination high-eccentricity orbits by mean-motion resonances with former binary-Companion. And the scattered, extended scattered disc and detached objects represent KBOs that were severely perturbed.
    Large KBOs experienced ‘aqueous differentiation’ at formation by streaming instability that melted water ice and formed authigenic, gneissic sedimentary cores. Perturbation of KBOs into the inner solar system by mean-motion resonances with binary-Companion caused Earth impacts during the late heavy bombardment, with the gneissic cores becoming the basement rock of Earth’s continental tectonic plates.

Cold classical KBOs:
    Young, cold classical KBOs are suggested to have condensed in situ against Neptune’s outer 2:3 resonance from the young, 650 Ma, Companion-merger debris disk.
    Cold classical KBOs are often found in binary systems, composed similar-size and similar-color binary pairs, in ‘cold’ (unperturbed), low-inclination low-eccentricity orbits. Additionally, cold classical KBOs tend to be red in coloration, while hot classical KBOs are more heterogeneous, tending toward bluish hues.
    Presumably few if any cold classical KBOs in stable, low-inclination low-eccentricity orbits, have been perturbed into the inner solar system.

Pluto system:
    The Pluto system presumably formed in situ by streaming instability against Neptune’s outer 2:3 resonance. The geologically active surface of Pluto, revealed in 2015 by the New Horizons spacecraft, may possibly point to its membership in the young KBO population, condensed from the binary-Companion debris disk at 650 Ma.
    The binary Pluto system appears to have formed by symmetrical FFF, followed by 2 generations of trifurcation from a very-diminutive core, resulting in the central FFF binary pair, Pluto and Charon, orbited by the 1st-generation twins Nix-Hydra, and the 2nd-generation twins Styx-Kerberos. This formation sequence would make the Pluto system very similar to our solar system as a whole, despite being a heliocentric satellite. Pluto’s smaller moons are very much smaller than Pluto and Charon (circa 31,600 times less massive than Charon), which may point to differing dynamics between gaseous stellar systems in protoplanetary disks and dusty streaming-instability systems in debris disks.

Detached Objects:
    Detached objects, also known as extended scattered disc objects (E-SDO), distant detached objects (DDO) or scattered-extended objects, are a class of minor planets belonging to trans-Neptunian objects (TNOs), with perihelia sufficiently distant from Neptune to be considered detached from planetary influence.
    The relative aphelia alignment of detached objects, such as Sedna and 2012 VP-113, is suggested here to be a fossil alignment of KBO aphelia with the former Sun-Companion axis, where shorter period KBOs have randomized their orientations since the loss of binary-Companion, around 650 Ma.

The predictive and explanatory power of FFF-trifurcation ideology:

– Bimodal late heavy bombardment (LHB):
+++ Our former binary-Companion perturbed Plutinos in a brief, early bimodal pulse at 4.22 Ga, followed by the perturbation of cubewanos from 4.1-3.8 Ga in the broader, main bimodal pulse, presumably due to the outward migration of the 1:4 mean-motion resonance of binary-Companion that first passed through the Plutinos, followed by the cubewanos.
– – – Grand Tack dismisses LHB theory.

– Bimodal distribution of hot and cold Jupiters:
+++ Asymmetrical FFF explains the distinct gap between the bimodal distribution of gas-giant exoplanets into hot Jupiters in low ‘hot’ orbits and cold Jupiters in higher ‘cold’ orbits as a hiatus in the flip-flop mechanism during the brief formation of the pithy first hydrostatic core (FHSC), which marks the end of the prestellar phase. If the mass of the FHSC is about 4 Mj, then the hiatus in FFF during the FHSC phase could also explain the desert of gas-giant planets in this mass range.
– – – Hierarchical accretion theory suggests that planetary migration causes some gas-giant planets formed in the Goldilocks zone to migrate inward and become hot Jupiters; however, planetary migration does not explain the distinct gap between the two populations, and hierarchical accretion with planetary migration has no explanation for the 4 Mj desert.

– Bimodal distribution of hot and cold classical KBOs:
+++ The bimodal KBO populations ‘condensed’ by streaming instability from two separate debris disks, condensing old (> 4,567 Ma) hot classical KBOs from the trifurcation debris disk, and condensing young (650 Ma) cold classical KBOs from the Companion merger debris disk, with the hot classical KBOS having been perturbed into ‘hot’ high-inclination high-eccentricity orbits by the outward migration of the 1:4(?) mean-motion resonance of binary-Companion through the Kuiper belt. And the color difference between the two populations relates to their differing ages and differing reservoir compositions.
– – – The Grand Tack hypothesis explains the hot classical population as having been perturbed by the outward migration of Neptune and the cold classical population as being unperturbed by Neptune, where Neptune stopped just short of perturbing the cold classical population. Grand Tack, however, can not explain the observed color differences between the two populations.

– Three sets of twin planets in our unusual solar system:
+++ Asymmetrical FFF followed by 4 generations of trifurcation explains the 3 pairs of twin planets in our solar system and predicts a former binary-Sun and former binary-Companion, and if FFF-trifurcation is uncommon, it also explains why our solar system is unusual. Additionally, the trifurcation mechanism predicts that the 6 trifurcation planets and the hot classical KBOs lie on the 3-oxygen isotope ‘terrestrial fractionation line’, and that the hot classical KBOs are siderophile depleted.
– – – Hierarchical accretion followed by Nice model/Grand Tack does not predict and can not explain the 3 sets of twin planets in our unusual solar system.

– Short-lived radionuclides (SLRs) of the early solar system:
+++ In situ formation of stellar-merger SLRs may eliminate 3 ad hoc variables in the standard model of our early solar system, namely, timing, proximity, and dilution factor/mixing of SLRs from one or more external sources. Additionally, stars in the mass range of the Sun do not experience internal circulation, such that primordial lithium at the surface should be preserved through the life of the Sun; however, the binary-Sun merger at 4,567 Ma caused chaotic mixing, causing much of the primordial lithium to burn in the hot core, and indeed the Sun is depleted in lithium by two sigma compared to sister stars of the same age and mass. In addition to f-process nucleosynthesis of SLRs, helium-burning apparently formed stable-isotope enrichments as well, explaining the notable oxygen-16 enrichment of the Sun, asteroids, and chondrites, compared to Earth.
– – – A nearby supernova that contributed radionuclides and also precipitated the gravitational collapse of our protostar purports to eliminate the timing and proximity variables; however, core-collapse supernovae produce abundant 53Mn, which was relatively absent in our early solar system.

– Venusian cataclysm and the Ediacaran Metazoa:
+++ The suggested orbital decay and merger of a former retrograde moon of Venus at 579 Ma jolted the planet into retrograde rotation and resurfaced the planet, with continuing coronae eruptions accompanied by sulfurous outgassing. A Venusian cataclysm so near to Earth would have had a spillover effect, fogging Earth’s upper atmosphere with micrometeorite dust, presumably causing Gaskiers glaciation on Earth. Additionally, if the Venusian cataclysm seeded Earth with Ediacaran biota, then the absence of fossils older than the Gaskiers glaciation, predicted by molecular clocks, is explained away. A retrograde-moony-merger Venusian cataclysm unifies Venus’ retrograde rotation, its ‘recent’ resurfacing, its thick sulfurous atmosphere, and the origin of Ediacaran biota, and Gaskiers glaciation on Earth. And significantly, trifurcation theory predicts a former retrograde trifurcation moon around Venus in a doomed retrograde orbit.
– – – In the standard model, these various phenomena are explained by separate (ad hoc) causes, but absence of metazoa fossils older than the Ediacaran biota is unexplained.

– Relative aphelia alignment of detached objects:
+++ The relative aphelia alignment of detached objects, such as Sedna and 2012 VP-113, is suggested to be a fossil alignment of orbital aphelia with the former Sun-Companion axis, where shorter period KBOs have randomized their orbits since the loss of the Companion at 650 Ma.
– – – The favorite academic theory evokes an undiscovered Planet Nine to create and sustain this relative alignment.

– Bimodal Snowball Earth:
+++ The suggested spiral-in merger of a former binary-Companion at 650 Ma explains the Marinoan glaciation as the fogging of the solar system by the Companion-merger debris disk. And the earlier Sturtian glaciation resulted from earlier moony mergers with the binary-Companion components as they spiraled inward.
– – – Terrestrial theories for Snowball Earth can not explain its bimodal nature.

– Uranus’ 98° axial tilt:
+++ FFF-trifurcation ideology suggests that binary-Companion overran Uranus’ orbit, driven by the eccentricity pumping of binary-Companion’s heliocentric orbit by the Sun. The FFF-trifurcation clockwork ideology also unifies Venus’ retrograde rotation and the formation of Earth’s Moon.
– – – Canonical theories suggest 3 separate ad hoc impacts to explain the 3 phenomena, presumably requiring many more variables.

– Four planets with axial tilts in the 20–30° range:
+++ Three planets with 20–30° axial tilts points to a solar system wide event, explained as the binary spiral-in merger of binary-Sun at 4,567 Ma. The merger mass loss suddenly increased the radial distance of all heliocentric orbits and decreased their orbital periods, with the axial tilts preserving system angular momentum. Indeed, the axial tilts should enable the calculation of the spiral-in merger mass loss, and vice versa, the observed axial tilts should make a spiral-in merger hypothesis falsifiable.
– – – Canonical theories for planet formation offer no predictions, explanations, or falsifiability.


    The degree of consideration of theory should be heavily weighted on its unifying explanatory capacity (ability to reduce the overall variable count), its predictive capacity, and its falsifiability. Almost by definition, a deterministic clockwork ideology that unifies multiple phenomena with predictive primary mechanisms reduces the variables in the system, and is almost by definition is more falsifiable than multiple ad hoc secondary mechanisms.
    Grand Tack, proposes that Jupiter to migrated in before migrating out, with the inward migration able to explain the inner solar system configuration and the outward migration able to explain the outer solar system configuration; however, this self-serving redundancy gives the appearance of wheels within wheels to provide sufficient variables to explain the entire solar system. Secondly, Grand Tack lacks falsifiability in that it relies on a disappeared protoplanetary disk that had sufficient fine tuning to cause inward migration followed by outward migration.
    Ad hoc (accident) theories, such as,
– Giant Impact on Earth, responsible for Earth’s Moon,
– a giant impact on Venus, responsible for Venus’ retrograde rotation, and
– a giant impact on Uranus, responsible for its severe axial tilt,
that rely on fortuitous accidents, are particularly unfalsifiable and particularly burdened by high variable count.
    FFF-trifurcation was imagined to explain the 3 sets of twin planets in our unusual solar system (which is unexplained in any other theory or model), and surprisingly the deterministic clockwork mechanism inherent in converting symmetrical FFF with trifurcation into our present mature solar system offers predictive unifying explanations for numerous otherwise unrelated solar system phenomena.


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