“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.” (Andre et al. 2008)
Star formation stages:
1) Starless core: May be a transient phase or may progress to gravitational instability infall
2) Prestellar core: A gravitating prestellar core ends with the formation of the second hydrostatic core when hydrogen gas endothermically dissociates into atomic hydrogen at around 2000 K.
3) Protostar (Class 0, I, II, III): Begins with the formation of the second hydrostatic core.
4) Pre-main-sequence star: A T Tauri, FU Orionis, or larger (unnamed) pre-main-sequence star powered by gravitational contraction
5) Main-sequence star: Powered by hydrogen fusion
In Jeans instability, the cloud collapses at an approximately free-fall rate nearly isothermally at about 10 K until the center become optically thick at ~10-13 g/cm3 after 105 yr (Larson 1969), at which point when the temperature begins to rise, forming a ‘first core’ or first hydrostatic core (FHSC). Supersonically infalling gas in the envelope is decelerated and thermalized at the surface of the first core (Masunaga et al. 1998).
When the temperature reaches about 2000 K, the hydrogen begins to dissociate endothermically, forming a ‘second core’, the birth of a protostar. The protostar grows in mass by accreting the infalling material from the circumstellar envelope, while the protostar keeps its radius at ~4 R☉ during the main accretion phase. (Masunaga et al. 1998)
“Enoch et al. (2009a) discovered a massive circumstellar disk of ∼1 M☉ comparable to a central protostar around a Class 0 object, indicating that (1) the disk already exists in the main accretion phase and (2) the disk mass is significantly larger than the theoretical
prediction.” (Machida et al. 2011)
“However, if the evolution is followed to the higher density regime where the gas becomes adiabatic, a disk-like structure forms which allows another mode of binary formation to develop, i.e., disk fragmentation around the central protostar. For example, calculations based on a piecewise polytropic equation of state show that the central portion of a collapsing core becomes adiabatic and forms a disc-like structure around the central object, which subsequently fragments into “satellite” objects (Matsumoto & Hanawa 2003).” (Andre et al. 2008)
“The size of the first core was found to vary somewhat in the different simulations (more unstable clouds form smaller first cores) while the size, mass, and temperature of the second cores are independent of initial cloud mass, size, and temperature.
Conclusions. Our simulations support the idea of a standard (universal) initial second core size of ~ 3 × 10−3 AU and mass ~ 1.4×10−3 M☉.”
(Vaytet et al. 2013)
“Class 0 objects are the youngest accreting protostars observed right after point mass formation, when most of the mass of the system is still in the surrounding dense core/envelope (Andre et al. 2000).”
(Chen et al. 2012)
“The compact components around the Class 0 protostars could be the precursors to these Keplerian disks. However, it is unlikely that such massive rotationally supported disks could be stably supported given the expected low stellar mass for the Class 0 protostars: they should be prone to fragmentation”.
(Zhi-Yun Li et al. 2014)
Solar system evolution:
Massive prestellar envelopes (nominally accretion disks) supported by rotation surrounding diminutive cores in prestellar objects are suggested to be vulnerable to disk instability that breaks the radial symmetry. In a prestellar object with excess angular momentum (prior to the formation of the first hydrostatic core), the bulk of the mass is contained in a doughnut-shaped envelope, supported by rotation, surrounding a diminutive core undergoing freefall collapse. The combination of a greater inertial mass in a radially-symmetrical envelope partially disconnected from its core by freefall conditions is suggested to promote disk instability, causing the envelope to clump and inertially displace the gravitationally-bound core into a satellite status. Clumping of the envelope begins to precipitate a new, younger core. This process by which a prestellar object spins off its core by disk instability is designated, ‘flip-flop fragmentation’ (FFF), with the core and envelope flip-flopping in position, when the former core becomes the satellite of the clumped envelope.
‘Flip-flop fragmentation with bifurcation’ is suggested to occur in prestellar objects with particularly-high specific angular momentum, which may dictate bifurcation of the envelope during disk instability to conserve system energy and angular momentum in the lowest possible energy state following fragmentation, with the former core displaced into a circumbinary orbit. And observational evidence suggests that the bifurcated envelope forms a similar-sized binary pair and that the ‘FFF w/bifurcation’ displaces an oversized core (with FFF without bifurcation typically displacing a smaller core). Thus an oversized satellite (oversized moon around a gas-giant planet or oversized brown dwarf around a solar-sized star) may indicate FFF w/bifurcation, suggesting the existence of a former similar-sized binary pair if the oversized satellite presently orbits a solitary object. The prototype of FFF w/bifurcation is the Alpha Centauri system, with the former oversized core Proxima inertially displaced (‘spun off’) into a circumbinary orbit around the similar-sized (bifurcated) Alpha Centauri A and B stars. Titan is suggested to be the former oversized core in the Saturnian system, suggesting Saturn formed as a similar-sized binary pair which has subsequently merged. By comparison, Jupiter appears to missing its Titan moon, unless Mars is the former Titan moon of Jupiter. This would suggest that Mars was stripped from Jupiter when Jupiter transitioned from a circumprimary orbit (around the larger A star binary-Sun component) into a circumbinary orbit as the binary-Sun components spiraled in. But unlike Jupiter, which formed around the larger A star and had to pass the smaller B star in transitioning to a circumbinary status, Saturn formed around the outer B star and thus had no such obstacle in its circumbinary transition and thus didn’t lose its Titan moon. (Not all FFF w/bifurcation may form and displace a core, however, since circumbinary objects are less common than similar-sized binary stars.)
Not only may prestellar objects undergo FFF, spinning off gas-giant-sized cores (designated ‘proto planets’), but the proto planets themselves will typically undergo FFF w/bifurcation, spinning off one or more generations of ‘proto moons’. After bifurcating, the twin bifurcated proto gas giant will typically undergo another episode of FFF without bifurcation, spinning off moons into circumprimary and a circumsecondary orbits around the binary gas giant components. Then core collapse of the binary gas-giant system causes the bifurcated gas-giant binary pair to spiral in, injecting the circumprimary and circumsecondary moons into circumbinary orbits before ultimately merging to form a solitary gas-giant planet.
Binary spiral-in mergers of binary stars and binary gas-giant planets are suggested to undergo a process similar to FFF within a common envelope phase of a spiral-in merger. When the cores reach a ‘common envelope’ stage of in-spiral, they are suggested to spin off diminutive twin cores, forming twin satellites, such as Venus and Earth from the binary-Sun merger, or twin moons, such as Io and Europa from the binary-Jupiter merger, in a process designated ‘merger fragmentation’. While a contact binary configuration, in which the stellar atmospheres touch one another, can be stable over millions or even billions of years, the common envelope configuration is understood to be short lived, either expelling the stellar envelope or merging the binary pair in a ‘timescale of months to years’. So the difference between contact-binary stability and common-envelope instability is suggested to require a catastrophic mechanism of outward angular momentum projection.
Merger planets proto Venus and proto Earth briefly orbited inside the greatly-expanded red giant phase of the Sun during the stellar-merger luminous red nova (LRN). And outward diffusion of proto-planet volatility along with inward diffusion of helium-burning, stellar-merger, nucleosynthesis metallicity enrichment (notably carbon-12 and oxygen-16), resulted in the ‘terrestrial fractionation line’, below that of presolar Mars, where Mars was presumably a rocky planet by 4,567 Ma which was vastly less susceptible to stellar-merger nucleosynthesis contamination than proto Venus and proto Earth in their pithy proto-planet phase.
A third planet formation mechanism was proposed by Thayne Curie in 2005, designated ‘hybrid accretion’, which suggests the formation of planets by core accretion from planetesimals condensed by gravitational instability, hence hybrid, resulting in a more rapid formation process than by (the myth of) pebble accretion. Hybrid accretion is suggested to form icy or rocky terrestrial super-Earths in low hot orbits, whereas gassy ice-giant planets like Uranus and Neptune are suggested to have formed by FFF. ‘Super-Earth’ is redefined here as any planet formed by hybrid accretion, regardless of its size, although most hybrid accretion planets are apparently larger than Earth. Super-Earths often form in ‘cascades’ (groups) in low warm-to-hot orbits. Cascades of super-Earths are presumed to form from the inside out, with the oldest super-Earth in the lowest hottest orbit having accreted from planetesimals that condensed against a solitary star’s magnetic corotation radius. The next oldest super-Earth in the cascade forms from planetesimals condensed against the outer resonances of the first super-Earth, and so on. (Diminutive) super-Earths may also form by hybrid accretion from debris disks, such as Mercury in our own solar system.
So some time prior to 4,567 Ma, our collapsing prestellar object is suggested to have undergone FFF w/bifurcation, forming twin stellar components (binary-Sun) orbited by the former core which also underwent FFF w/bifurcation to form binary-Companion. Binary-Sun and binary-Companion were in ‘hard’ close-binary orbits, in a ‘soft’ wide-binary Sun-Companion separation. ‘Close binary’ orbits are defined here as ‘hard’ orbits that tend to spiral in due to external perturbation, whereas ‘wide binary’ orbits are defined here as ‘soft’ orbits that tend to spiral out due to external perturbation, becoming softer over time. The two close binary systems, binary-Companion and binary-Sun, orbited the solar system barycenter (SSB) in a wide-binary separation. And resonant feedback between the close-binary pairs is suggested to have promoted core collapse, transferring potential energy and angular momentum from the close-binary orbits to the wide-binary orbits, causing the close binary orbits to decay over time, transferring their orbital energy and angular momentum to the wide binary system, causing Sun and Companion to spiral out from the SSB over time.
Following FFF w/bifurcation into similar-sized binary-Sun components, the binary prestellar components of binary-Sun still had too much angular momentum to collapse into protostars, requiring two additional generations of FFF (without bifurcation) to catastrophically rid themselves of sufficient angular momentum to reach the main sequence. The first generation FFF spun off proto Uranus & Neptune into circumprimary and circumsecondary orbits respectively, with the progressive in-spiral of binary-Sun leaving Uranus and Neptune behind in circumbinary orbits. The second generation FFF spun off proto Jupiter and Saturn into into circumprimary and circumsecondary orbits which likewise also transitioned into circumbinary orbits with continued binary orbital decay. Finally, binary-Sun spiraled in to merge at 4,567 Ma, spinning off twin merger planets, proto Venus and proto Earth.
And each of the four spin off planets underwent FFF w/bifurcation themselves to spin off a oversized ‘Titan moon’, followed by one or more generations of FFF without bifurcation. And each of the binary giant planets likewise spiraled in to merge and spin off twin merger moons. Uranus and Jupiter, however, apparently lost their oversized ‘Titan moons’ in bypassing the smaller ‘B star’ component of binary-Sun, with the Jupiter ‘Titan moon’ likely becoming Mars(?) and the Uranus ‘Titan moon’ perhaps becoming Eris(?).
Giant planet resonances are suggested to create pressure dams which promote GI condensation of planetesimals, but only Jupiter’s inner resonances and Neptune’s outer resonances may have been sufficiently unperturbed by overlapping giant planet resonances to have condensed objects from the primary debris disk formed from the ashes of binary-Sun merger at 4,567 Ma, with chondrites condensing against Jupiter’s strongest inner resonances and hot classical Kuiper belt objects (KBOs) against Neptune’s strongest outer resonances, principally against Neptune’s 2:3 resonance. The inner edge of the primary debris disk was likely sculpted by the super-intense stellar-merger corotation radius of the Sun, condensing asteroids near the present orbit of Mercury which contained live short-lived stellar-merger radionuclides (most importantly, aluminum-26 and iron-60). Mercury is suggested to be a hybrid accretion super-Earth, formed by core accretion of rocky-iron asteroids. Some of the leftover asteroids were apparently evaporated into the relative protection of Jupiter’s inner resonances by orbit clearing by the 4 terrestrial planets, with many or most of the leftover asteroids crashing into the Sun or into Jupiter.
The binary-Companion (presumably brown-dwarf) components are suggested to have continued to spiral in for another 4 billion years, presumably increasing the Sun-Companion apoapsis (greatest separation) at an exponential rate over time. The binary-Companion components contained a significant amount of potential energy compared to the Sun-Companion wide-binary gravitational potential well, but a negligible amount of angular momentum compared to the Sun-Companion wide-binary angular momentum, so while the apoapsis (which is energy sensitive) is suggested to have increased at an exponential rate over time, the Sun-Companion periapsis (which is angular momentum sensitive) remained relatively unchanged over time. Thus the maximum Sun-Companion system is suggested to have become progressively eccentric over time.
The solar system barycenter (SSB) was the gravitational balance point around which Sun-Companion orbited for 4 billion years, and by Galilean relativity with respect to the Sun, the SSB can be said to have spiraled out through the Kuiper belt at an exponential rate over time. The lunar ocean tides in the Earth-Moon system are suggested to be an analogy for tidal disruption of the Kuiper belt by the SSB. As Earth rotates, the ocean facing the Moon is pulled to high tide by Moon’s gravity, followed by low tide, followed by high tide on the opposite side of the Earth. High tide on the far side of the Earth can be thought of as due to the centrifugal force of the Earth around the Earth-Moon barycenter, slinging the far side tide away from the Moon. Similarly in the solar system, Kuiper belt objects (KBOs) will experience an attractive tide toward the Companion and a repulsive tide away from the Companion when KBOs cross the ‘tidal threshold’, associated with the SSB, but not coincident with it. KBOs will not experience significant tidal perturbation until the tidal threshold crosses their semimajor axes for the first time, causing ‘aphelia precession’ of their orbits, in a process designated, ‘flip-flop perturbation’. Thus KBO aphelia will have their aphelia attracted toward the Companion until the tidal threshold catches up with the semimajor axis of the KBO, after which it will experience aphelion precession as its aphelion is centrifugally slung 180° away from the Companion. As tidal threshold spiraled out from the Sun along with the SSB it moved through the main concentration of KBOs, the cubewanos, from 4.1 to 3.8 Ga, perturbing binary KBOs to spiral in to merge. Flip-flop perturbation also perturbed KBOs into the inner solar system, causing the late heavy bombardment (LHB).
The binary brown dwarf components of binary-Companion are suggested to have spiraled in to merge at 542 Ma in an asymmetrical merger that gave the newly-merged Companion escape velocity from the Sun. The merger created a ‘secondary debris disk’ which is suggested to have condensed ‘cold classical KBOs’ in situ in low-inclination low-eccentricity orbits, many in binary pairs, including binary Pluto. The suggested solitary (not binary) ‘hot classical KBO’ population in high-inclination high-eccentricity ‘hot’ orbits presumably resembled the present cold classical KBO population prior to flip-flop perturbation during the LHB. The recent New Horizons flyby of Pluto revealed a geologically-young surface on a tidally-locked (synchronous orbit) binary planet, having no tidal heating contributed by rotation, but a young origin might explain the geological activity, particularly if a former binary-Pluto in-spiraled to merge and form solitary Pluto some time after 542 Ma.
A number of Phanerozoic events may be correlated with the suggested binary brown-dwarf merger, as well as the loss of the solar system barycenter, even though Earth would likely have accreted only a thin veneer of material directly from the secondary debris disk. The Cambrian Explosion is suggested to result from the disbursal of free-swimming brown-dwarf lifeforms, likely from a water vapor layer on a room-temperature spectral class Y brown dwarf, perhaps with lightening creating free oxygen. The large negative δ13C excursion at the Cambrian boundary is suggested to represent an accretionary veneer of presolar brown-dwarf material, lacking solar-merger Carbon-12 enrichment.
The loss of Companion implies the loss of the centrifugal force of the Sun around the former SSB, causing all heliocentric objects to fall into slightly lower shorter-period orbits, which is suggested to have been responsible for Venus’ slight retrograde rotation, if Venus had previously been in a synchronous orbit where its day equaled its year. Venus also apparently underwent a global resurfacing event, some 300–500 million years ago. Earth’s upheaval at dropping into a lower orbit may have caused the global erosion known as the ‘Great Unconformity’, where in the Grand Canyon area eroded as much as a billion years’ worth of continental rock.
Oort cloud comets may have condensed in circum-quaternary obits beyond binary-Companion from a circum-quaternary protoplanetary disk, which were progressively shepherded outward by the exponentially-increasing Sun-Companion apoapsis for 4 billion years, from > 4,567 Ma until 542 Ma.
Flip-flop fragmentation (FFF):
‘Flip-flop fragmentation’ (FFF) is a suggested catastrophic mechanism for forming (subsystem) objects by gravitational instability which are smaller than a Jeans mass within a Jeans mass system. An alternative description for FFF is ‘spinning off’ planets or moons, as ‘spin off’ planets or moons.
During freefall collapse of a self-gravitating cloud with sufficient angular momentum, a diminutive core forms, surrounded by a much-more-massive, radially-symmetrical doughnut-shaped envelope supported by angular momentum. If the overlying envelope becomes self gravitating, with a Toomre Q parameter of order unity, and if the ratio of the core mass to the incipiently-self-gravitating envelope mass is too small to dampen dynamic inhomogeneities in the envelope, then the envelope may undergo disk instability, causing it to catastrophically clump and form a new more-massive core, which inertially displaces the former core to a satellite status.
In the freefall collapse of a dark core within a giant molecular cloud, the catastrophic FFF mechanism is presumed to occur during the prestellar phase, prior to the central core becoming a Class 0 protostar, when the diminutive densifying core is only on the order of a Jupiter mass. And a dark cloud undergoing freefall collapse may spin off 2 or more diminutive cores in succession before achieving a sufficiently-massive core to dampen inhomogeneities in the residual envelope, resulting in a stable system.
When the overlying envelope mass to core mass exceeds an unknown ratio (with a self-gravitating envelope), the diminutive core is unable to dampen the envelope inhomogeneities, presumably resulting in positive feedback between the envelope and the core. This positive feedback may result in runaway disk instability that breaks the radial symmetry of the envelope, causing it to clump and form a new, larger core which is radially offset from the smaller former core. And since the newly forming core is more massive than the former core, the former core becomes its satellite.
As a simplistic analogy, imagine a Slinky made into a doughnut ‘envelope’ by joining the two ends around a golf ball ‘core’ in the center. Releasing the ends of the Slinky breaks the radial symmetry of the envelope, causing the slinky to clump into a central mass, catastrophically projecting system mass inward, while offsetting the golf ball as its satellite to conserve angular momentum.
FFF turns Jeans mass systems undergoing freefall collapse inside out, spinning off gas-giant planet/brown dwarf subsystems in primary FFF. And gas-giant planet subsystems may themselves undergo secondary FFF, spinning off moon sub-subsystems. Additionally, primary or secondary FFF may undergo one or two generations of FFF, such as the larger binary-Sun component spinning off Uranus in a first generation (primary) event and spinning off Jupiter in a second generation (primary) event.
The rocky-icy nature of gas-giant planet moons in our solar system suggests that sedimentation of mineral grains and ice grains occur within central cores, which are spun off as gas-giant proto planets in primary events, and as moons in secondary events. Sedimentation greatly increases the density of spun off objects even in the earliest prestellar phase of freefall collapse when the surrounding envelope still has a volatile solar composition of circa 99% hydrogen and helium, long before the appearance of a late-forming dusty/icy accretion disk.
Volatile evaporation during the pithy proto phase of spin-off cores will also increase their metallicity, particularly in small moons which can’t compress or hold on to significant volatile atmospheres, but even proto gas-giant planets would suffer considerable volatile loss following FFF in the prestellar phase of the spin-off core.
In addition to a much greater overlying mass and a self-gravitating envelope, disk instability may require the additional element of a physical disconnect between a rotationally-supported envelope and its core, in order for inhomogeneities to amplify by positive feedback into runaway disk instability. The distinct bimodal clumping of gas-giant planets into ‘hot Jupiters’ (with a median semimajor axes below about .1 AU) and ‘cold Jupiters’ (with a median semimajor axes around 2 AU), suggests an FFF hiatus, with higher specific-angular-momentum prestellar objects spinning off cold Jupiters and lower specific-angular-momentum prestellar objects spinning off hot Jupiters.
And if the suggested freefall gap necessary for envelope instability disappears with the formation of a ‘first hydrostatic core’ (FHSC)–establishing a viscous gaseous connection between the core and envelope which damps oscillations–then FFF can only occur during the prestellar first collapse phase, spinning off cold Jupiters, and in the exceedingly brief ‘second collapse’ stage, between the FHSC and the formation of the second hydrostatic core (SHSC).
“When the central density exceeds 10−13 g cm−3
the radiative cooling ceases to be efficient and an opaque, adiabatic
core forms at the centre. The rise in temperature results in
an increase of the thermal pressure, and finally, when the pressure
balances the gravitational force the collapse ceases and the
first hydrostatic core is formed. The initial central temperature of
the FHSC is estimated to be around 170 K with an initial central
density of 2×10−10 g cm−3.
The so-called second, more compact
(protostellar) core is formed after the dissociation of H2 and subsequent
collapse, when the central temperature and density reach
2 × 104 K and 2 × 10−2 g cm−3, respectively (Larson 1969).”
(Tsitali et al. 2013)
So in the ‘first collapse’ of a Jeans instability, nearly-isothermal freefall conditions prevail as long as the cloud remains nearly transparent to infrared radiation, presumably opening a freefall gap between the densifying core and its rotationally-supported envelope. This freefall gap presumably permits the amplification of oscillations between the core and envelope, possibly ending in disk instability.
When the core temperature reaches about 170 K, at a density of 2×10−10 g cm−3, the thermal pressure balances the gravitational force, forming a FHSC, where the hydrostatic core may make a viscous connection with its rotationally-supported envelope, damping out oscillations between the core and envelope, which may largely prevent envelope inhomogeneities from running away into full-fledged disk instability for the lifespan of the FHSC.
Prior to the formation of the FHSC, radiative cooling allows infalling gas to radiate away its potential energy in the form of infrared radiation, but when the density reaches around 10-13 g/cm-3, the gas becomes opaque to infrared radiation, rendering the gas nearly adiabatic, causing the temperature to rise. This temperature rise creates an outward gas pressure which balances the inward force of gravity. The FHSC is thought to last a few hundred years to a few thousand years, until the temperature reaches about 2000 K when molecular hydrogen dissociates endothermically, causing a brief second collapse lasting less than a year and ending in the formation of a second hydrostatic core (SHSC).
“First cores are characterized by radii and masses of the order of ~ 5 AU – 10 AU and 0.05 M☉ – 0.1 M☉, respectively (Masunaga et al. 1998; Saigo et al. 2008). Their lifetimes range from a few 100 yr to a few 1000 yr, increasing with the rate of rotation.”
(Tsitali et al. 2013)
When the core temperature reaches about 2000 K, molecular hydrogen begins to dissociate into atomic hydrogen endothermically, promoting a very brief nearly-isothermal ‘second collapse’,
The dynamical timescale of the second collapse is of the same order as the free-fall time, corresponding to a density of 10-7 g cm-3, which is 0.1 yr.
(Masunaga and Inutuka, 2000)
Assuming bimodal FFF with a FHSC hiatus, the astonishingly-brief second collapse (~ 0.1 yr), which suggests that the endothermic mediated second-collapse shockwave would have to act as an exceedingly-efficient trigger of disk instability in an self-gravitating envelope with sufficient angular momentum.
FFF may have also occurred even in stars without gas/ice giant planets, particularly in low metallicity stars if the spun off gas cores can dissipate (evaporate) instead of continuing to collapse to form planets.
An interesting sidelight of a dynamic mechanism which repeated turns (sub)systems inside out is that the first-generation FFF moon around the first-generation FFF gas-/ice-giant planet in a solar system is likely to be the oldest object in the system, older than its so called progenitor star. However, depending on rate of dynamic evolution, such a scenario might not necessarily create a first-generation FFF planet older than its central star, if the central star spun off a second-generation planet before the first-generation planet spun off its first- and second-generation moon(s) and spiraled in to merge, if the planet formed as a similar-sized binary pair and the star did not. So relative brightness anomalies in prestellar/protostar systems may point to subsystem satellites which are more highly evolved (older) and therefore possibly brighter than their central stars.
FFF is suggested to work over a wide range of scales, from the gas-giant planet scale up to perhaps the galactic scale. FFF is suggested to be the mechanism by which proto-spiral-galaxies wound down their excess angular momentum in the early universe to the characteristic angular momentum of spiral galaxies with flattened disk planes and galactic bulges (cores). If proto-spiral-galaxies also suffered from the instability of massive envelopes overlying diminutive cores, then FFF may have been the mechanism for catastrophically projecting mass inward to create a sufficiently-large central galactic bulge which could damp down disk inhomogeneities to create a stable spiral galaxy. So perhaps our proto-Milky-Way underwent two generations of FFF (without bifurcation), spinning off two former cores in succession which became the Small and Large Magellanic Clouds. In (at least) the final FFF generation, disk instability clumping of the former envelope created a direct-collapse supermassive black hole in the center of the galactic bulge, Sagittarius A*.
‘Flip-flop fragmentation with bifurcation’ (FFF w/bifurcation):
The triple-star Alpha Centauri system suggests an alternate FFF pathway, when envelope instability occurs with particularly-high specific angular momentum. Similar-sized binary pairs with an ‘oversized’ circumbinary satellite, such as Proxima Centauri (Alpha Centauri A) in a circumbinary orbit around the similar-sized binary pair (Alpha Centauri A & Alpha Centauri B), suggests binary fragmentation (‘bifurcation’) of envelopes with particularly-high specific angular momentum. A system with particularly-high angular momentum may dictate fragmentation into a triple system to conserve energy and angular momentum in a system with the lowest resulting energy state, by causing the envelope to fragment into a similar-sized binary pair around an oversized core. Then hierarchy prevails, inertially slinging the former oversized core into a circumbinary orbit, causing the binary pair to drop into slightly lower orbits. So while FFF without bifurcation typically spins off ice giants or gas giants, FFF w/bifurcation typically spins off oversized brown dwarfs or red giant stars, as in the case of Proxima Centauri.
This alternative particularly-high-angular-momentum pathway is designated, ‘flip-flop fragmentation with bifurcation’, or ‘FFF w/bifurcation’ for short, with ‘bifurcation’ indicating envelope fragmentation into a similar-sized binary pair. In our own solar system the following FFF w/bifurcation systems are suggested to have formed by FFF w/bifurcation, followed by spiral-in merger:
– oversized Companion in a circumbinary orbit around former binary-Sun,
– oversized gas giant planet around binary-Companion,
– oversized Mars(?) around binary-Jupiter,
– oversized Titan around binary-Saturn,
– oversized Eris(?) around binary-Uranus, and
– oversized Triton around binary-Neptune.
Oversized Titan cores:
‘Titan’ is chosen as the prototypical FFF w/bifurcation spin-off core, due to its namesake as a mythical race of (oversized) giants, so the existence of a Titan Companion (such as Proxima Centauri) or a Titan moon may point to a (former) FFF w/bifurcation, followed by a spiral-in merger of the former similar-sized binary pair if they’re no where to be found. Oversized Titan cores suggests that FFF w/bifurcation may be delayed, compared to FFF (without bifurcation), due to the greater radial distance of their higher angular-momentum envelopes which give the core longer to form.
The Class 0 protostar system, L1448 IRS3B, is another suggested star system formed by FFF w/bifurcation. This triple system is composed of a similar-sized binary pair (IRS3B-a & IRS3B-b), with a combined mass of ~ 1 M☉ and a binary separation of 61 AU, orbited by a distant (oversized) companion (IRS3B-c), with a minimum mass of of ~ 0.085 M☉ at a separation of 183 AU. Compared to the Alpha Centauri system, the relative mass of the tertiary IRS3B-c to its similar-sized binary pair compared to the Alpha Centauri system is 38% over-oversized, using the minimum estimated mass for IRS3B-c, making it nearly a twin to the Alpha Centauri system at half the overall mass, particularly considering that secular perturbation of the system will likely cause an orbital energy transfer from the close binary pair (IRS3B-a—IRS3B-b) to the tertiary separation. “Thus we expect the [L1448 IRS3B] orbits to evolve on rapid timescales (with respect to the expected stellar lifetime), especially as the disk dissipates. A natural outcome of this dynamical instability is the formation of a more hierarchical system with a tighter (few AU) inner pair and wider (100s to 1,000s AU) tertiary, consistent with observed triple systems.” (Tobin et al. 2016)
L1448 IRS3B (continued):
The tertiary star, IRS3B-c, is embedded in a spiral arm of the outer disk, where the spiral arm has an estimated mass of 0.3 M☉. The standard model of companion star formation expressed by Tobin et al. suggests that IRS3B-c formed in situ by gravitational instability from the spiral disk, making IRS3B-c younger than IRS3B-a & IRS3B-b; however, the smaller tertiary star 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, if IRS3B-c is older than its larger siblings, having formed by FFF, then by its greater age it would be expected to be more highly evolved, and therefore possibly hotter and brighter than its younger much-larger siblings. Thus FFF w/bifurcation predicts a more highly evolved tertiary star, whereas the standard model would have to evoke secondary mechanisms (such as dimming by dust) to explain away the brighter tertiary star. Finally, the hierarchical inertial displacement of the former core to a circumbinary orbit could neatly explain the spiral nature of the spiral disk, as IRS3B-c spiraled outward to its current orbit.
FFF w/bifurcation evolution:
If the Sun and gas-giant planets in our solar system all underwent FFF w/bifurcation, as is suggested, we can only infer the typical number of FFF w/bifurcation generations at two, as in the larger binary-Sun component spinning off Uranus in the first generation and spinning off Jupiter in the second generation. Some exoplanet systems, however, have 3 or even 4 gas giant planets with no Titan object, and therefore presumably not having undergone FFF w/bifurcation. This either means that FFF (without bifurcation) may undergo as many as 3 or 4 FFF generations, or more likely that continued infall of gas from beyond the envelope induces extra (artificial) FFF generations, not inherent in the original envelope. By comparison, in FFF w/bifurcation, the extra turbulence generated by a similar-sized binary pair and an oversized core, along with the extra delay of forming an oversized core and the extra distance of its high-angular-momentum envelope may preclude continued infall of gas from beyond, clamping the number of subsequent FFF generations at 2.
The Pluto system appears to have an oversized ‘Titan moon’, Charon, which is well short of being the smaller component of a similar-sized binary pair, suggesting FFF w/bifurcation, where a former binary-Pluto spun off two generations of moons, perhaps spinning off Nix and Hydra in the first generation and Styx and Kerberos in the second generation (or vice versa), before binary-Pluto spiraled in to merge to form solitary Pluto.
Merger fragmentation planets and moons:
Binary in-spiral mergers of stars and binary gas-giant planets are suggested to undergo a catastrophic process for ridding themselves of angular momentum, designated, ‘merger fragmentation’, spinning off their former twin cores to become twin ‘merger planets’ or twin ‘merger moons’.
A binary spiral-in merger first becomes a ‘contact binary’ followed by a ‘common envelope’. Contact binaries, in which the stellar atmospheres are in contact, can be stable over millions or even billions of years, but the the common envelope configuration is understood to be short lived, either expelling the stellar envelope or merging the binary pair in a ‘timescale of months to years’.
Suggested merger fragmentation is an attempt to understand the catastrophic loss of angular momentum in the short-lived common-envelope phase of binary in-spiral mergers of gaseous objects. Merger fragmentation is not suggested to occur in icy or terrestrial objects, like ‘contact-binary’ asteroids and comets, which don’t go through a common-envelope phase (where ‘contact-binary’ asteroids and comets refers to their final post-merger (peanut-shaped) state, whereas contact-binary stars are far from their final state).
Suggested merger fragmentation is suggested to be analogous to flip-flop fragmentation with a slingshot mechanism to kick the former stellar cores into high heliocentric orbits, with Venus and Earth as twin ‘merger planets’ formed by the in-spiral merger of former binary-Sun at 4,567 Ma.
Within a common envelope, inward tidal and outward centrifugal forces radially elongate in-spiraling objects. As the twin cores slowly spiral inward, the inward tidal component may be reflected outward into the outward centrifugal bulges. In spiraling within a common envelope may take the form of the cores sloughing off gas into their outward centrifugal bulges as a means of ridding the twin cores of angular momentum. This may continue until the overlying outward bulges become much more massive than the diminishing cores, whereupon the system becomes unstable.
The instability of the greater overlying mass creates a catastrophic flip-flop, wherein the centrifugal bulges presumably merge by centrifugally slinging the former twin cores outward into high orbit, ridding the merging bulges of excess angular momentum. And similar to the triple object formed by FFF w/bifurcation, merger fragmentation may also require the formation of a triple object to conserve both energy and angular momentum.
In the pithy ‘preplanetary’ phase of merger planets when their evaporating atmospheres filled their Roche spheres, preplanetary-Venus and preplanetary-Earth suffered heavy volatile losses, but the outward diffusion of volatiles necessarily included an inward diffusion of solar-merger metallicity, first from the enveloping red giant phase of the LRN (which lasted a few months), and then from the primary debris disk, injecting helium-burning stellar-merger nucleosynthesis stable isotopes, notably carbon-12 and oxygen-16 into the gravitationally-bound proto-planets. If Mars was an older FFF w/bifurcation moon of preplanetary-Jupiter, then it likely would have already had its present rocky form at the time of the 4,567 Ma solar merger, explaining why the terrestrial fractionation line of Earth is depressed below essentially presolar Mars on the 3-oxygen-isotope plot of ∆17O vs. δ18O, since Earth/Moon has a solar-merger 16O enrichment.
In the Jupiter system, Io and Europa are suggested to be merger planets, presumably with Mars as Jupiter’s former Titan moon, spun off during FFF with/fragmentation that formed binary Jupiter. And Ganymede and Callisto were presumably spun off from Jupiter’s two former binary components.
Finally, solar mergers of low metallicity stars may fail to condense merger planets from spun off cores, if the cores dissipate (evaporate).
Suggested solar system formation mechanisms:
Prestellar object—FFF w/bifurcation—Binary-Sun + Companion
— Binary-Sun—FFF x 2—Binary-Sun + Uranus & Neptune + Jupiter & Saturn
—— Neptune—FFF w/bifurcation—Binary-Neptune + Triton
——— Binary-Neptune—FFF x 2—Binary-Neptune + perhaps Makemake(?) & Haumea(?) +
2007 OR10(?) & Quaoar(?)
———— Binary-Neptune—Merger fragmentation—Neptune + Proteus & Nereid
—— Uranus—FFF w/bifurcation—Binary-Uranus + Eris(?)
——— Binary-Uranus—FFF x 2—Binary-Uranus + Oberon & Titania + Umbriel & Ariel
———— Binary-Uranus—Merger fragmentation—Uranus + Miranda & Puck(?)
—— Saturn—FFF w/bifurcation—Binary-Saturn + Titan
——— Binary-Saturn—FFF x 2—Binary-Saturn + Iapetus & Rhea + Dione & Tethys
———— Binary-Saturn—Merger fragmentation—Saturn + Enceladus & Mimas
—— Jupiter—FFF w/bifurcation—Binary-Jupiter + Mars(?)
——— Binary-Jupiter—FFF x 1—Binary-Jupiter + Ganymede & Callisto
———— Binary-Jupiter—Merger fragmentation—Jupiter + Io & Europa
— Companion—FFF w/bifurcation—Binary-Companion + circumbinary gas-giant planet
– FFF x 1: one generation of FFF
– FFF x 2: two generations of FFF, as in the larger binary-Sun component spinning off Uranus in the first generation and Jupiter in the second generation
Gravitational instability (GI) within accretion disks:
Pebble accretion does not appear to be borne out in chondrites, which do not appear to have an internal accretionary structure above that of chondrules and CAIs. Chondrules may have been melted by super-intense solar flares from a circa 3 million year flare-star phase of the Sun following its spiral-in merger, suggesting the scale of accretionary dust clumps in the inner solar system. And thus if chondrites (and asteroids) didn’t form by pebble accretion, then the alternative is suggested to be gravitational instability.
The locations of the two planetesimal belts in the solar system (excluding comets) suggests the formation of primary debris disk-dust rings against the strongest planetary resonances which weren’t disrupted by the resonances of other giant planets, namely, Jupiter’s inner resonances (condensing the chondrites of the asteroid belt) and Neptune’s outer resonances (KBOs) were precluded by mutual resonant interference. Rocky-iron asteroids are suggested to have condensed against the Sun’s magnetic corotation radius, near the present orbit of Mercury, whereafter some of the leftover asteroids cleared by the terrestrial planets were captured by Jupiter’s inner resonances. Alternatively, if dust rings formed around other giant planet resonances which also condensed planetesimals from the primary debris disk, the resulting planetesimals have since drifted away, like the centaurs, due to relative orbital instability of overlapping giant planet resonances.
Presumably comets condensed by GI against Sun-Companion’s outer resonances from the > 4,567 Ma protoplanetary disk, with the additional pressurizing condition of the Sun-Companion spiraling out from the SSB. Perhaps the typical small kilometer-scale size of comets, compared to the larger scale of asteroids, chondrites and KBOs was partly due to the increased compression of binary-Companion spiraling out from the solar system barycenter which promoted condensation by GI.
So presumably, when infall of dust from a protoplanetary disk or debris disk is compressed against a giant planet or super-Earth resonance or against a wide-binary (stellar) resonance, or against the magnetic corotation radius of a young star, or against a reactivated magnetic corotation radius following a binary spiral-in merger, repeated instances of gravitational instability may occur. Super-earths may form by hybrid accretion of smaller planetesimals, not by GI alone, so gravitational instability from an accretion disk appears to occur not at all or in great multiplicities, so belts of objects or hybrid accretion objects capable of clearing their orbit(s) of leftover planetesimals are suggested to point to former instances of ‘accretion disk GI’.
Primary debris disk at 4,567 Ma:
Asteroids are suggested to have condensed by GI from the ‘primary debris disk’, against the magnetic corotation radius of the Sun at about the orbit of Mercury. The super-intense stellar-merger magnetic field created a greatly-expanded magnetic corotation radius which is suggested to have condensed asteroids near the orbit of Mercury. Secondly, carbonaceous chondrites are suggested to have condensed in situ against Jupiter’s strongest inner resonances, and finally, Plutinos and hot classical Kuiper belt objects (KBOs) are suggested to have condensed against Neptune’s strongest outer resonances.
Secondary debris disk at 542 Ma:
Cold classical KBOs (along with binary Pluto) are suggested to have condensed in situ against Neptune’s outer 2:3 resonance from the ‘secondary debris disk’ ashes of the suggested binary-Companion merger at 542 Ma. Low inclination, low eccentricity cold classical KBOs, typically occurring in binary pairs, are suggestive of in situ condensation following the cessation of flip-flop perturbation by the solar system barycenter following the loss of the Companion, whereas hot classical KBOs had been perturbed to spiral in to merge to form solitary objects and also perturbed into high inclination high eccentricity ‘hot’ orbits. The lack of young (circa 542 Ma) meteorites suggests that the secondary debris disk didn’t condense any planetesimals in the inner solar system against Jupiter’s inner resonances.
The Pluto system appears to have a ‘Titan moon’, Charon, suggesting FFF w/bifurcation, requiring a former binary-Pluto which created 4 smaller Galilean moons: presumably FFF moons Nix & Hydra, and merger moons Styx & Kerberos. And many of the much-smaller cold-classical KBOs have similar-sized binary pairs as well, including kilometer-scale comets as well, from their peanut-shaped contact-binary shapes.
Hybrid accretion (super-Earths):
When planetesimals are condensed by GI in sufficient quantity and density from a protoplanetary disk (or subsequent debris disk), gravitational accretion may form planets by ‘hybrid accretion’ (Thayne Curie 2005), with hybrid referring to core accretion of planetesimals formed by gravitational instability, hence hybrid. Super-earths often form in cascades (multiples), formed sequentially from the inside out, with the first super-Earth hybrid presumably accreting from planetesimals condensed against the magnetic corotation radius of the star. The initial super-Earth of a cascade not only clears its orbit of leftover planetesimals, but also disrupts the accretion disk as far out as its strongest outer resonances, whereupon the next generation of planetesimals condense the next-generation super-Earth in the cascade. ‘Super-Earth’ is defined here as any planet formed by hybrid accretion, regardless of size or location. By this definition, Mercury is also a (diminutive) super-Earth, which is suggested to have formed by the hybrid accretion of asteroids condensed against the super-intense magnetic field of the Sun immediately following its binary spiral-in merger from the primary debris disk. See section, CASCADE FORMATION OF SUPER-EARTHS BY HYBRID CORE ACCRETION OF PLANETESIMALS ‘CONDENSED’ BY GRAVITATIONAL INSTABILITY AT THE INNER EDGE OF ACCRETION DISKS.
‘Flip-flop perturbation’ mechanism of the solar system barycenter (SSB) on KBOs:
Secular perturbation of our former binary-Companion’s brown-dwarf components caused them to spiral in for 4 billion years, translating close-binary potential energy into wide-binary potential energy, increasing the Sun-Companion eccentricity over time, presumably increasing the maximum wide-binary Sun-Companion separation (at apoapsis) at an exponential rate over time. By Galilean relativity with respect to the Sun, the solar system barycenter (SSB) could be said to have spiraled out through the Kuiper belt at an exponential rate for 4 billion years, fueled by the orbital potential energy of the binary-Companion brown-dwarf components.
(Negative) gravitational binding energy is an inverse square function with distance, such that an orbit 100 times further away will have 1/10,000 the binding energy. Angular momentum, by comparison, is an inverse square root function of the semimajor axis, such that an orbit 100 times further away will have 10 times the angular momentum. Since the binding energy function is much steeper than the angular momentum function with respect to distance, the brown-dwarf components of binary-Companion could dramatically reduce the negative Sun-Companion binding energy of the system without materially affecting its angular momentum. Periapsis of an orbit is a good measure of its relative angular momentum, while apoapsis is a good measure of its relative binding energy, so the 4 billion year spiral-in of the binary components of binary-Companion effectively increased the Sun-Companion apoapsis at an exponential rate, (by Galilean relativity) causing the SSB apoapsis to spiral out through the Kuiper belt and scattered disc over time, perturbing planetesimals with progressively greater semi-major axes over time.
Tidal perturbation of KBOs by the Sun-Companion system can be easily visualized with the example of lunar tides on Earth. Earth has two lunar high tides, a high tide on the Moon side of Earth, gravitationally pulled into high tide by the Moon, and a high tide on the far side of the Earth, centrifugally slung away from it. The Earth-Moon barycenter is inside the Earth, and it can be stated that the centrifugal force of the Earth around the Sun-Moon barycenter creates the far-side lunar tide by centrifugal force. But while the near side and far side tides are relatively symmetrical, they are not symmetrical around the Sun-Moon barycenter axis, but rather symmetrical around a point we’ll call the ‘tidal threshold’, which is associated with the Sun-Moon barycenter, but not coincident with it. Similarly, the tidal threshold of the solar system was not coincident with the SSB axis, but was associated with it. Note that the ‘tidal threshold’ is defined with respect to the semimajor axis of a KBO.
If the lunar tidal threshold on Earth is the low tide threshold across which the ocean is either pulled toward the Moon or centrifugally slung away from it, the solar system analogy for KBOs may be orientation of the major axis, which is suggested to nominally undergo apsidal precession as the semimajor axis crosses the tidal threshold, flip-flopping from having its aphelion gravitationally attracted toward the Companion to having its aphelion centrifugally slung 180° away from the Companion, in a process designated ‘flip-flop perturbation’, by which operates by means of ‘apsidal precession’. Flip-flop perturbation was initiated when the tidal threshold caught up with the semimajor axis of a KBO for the first time, but due to the eccentricity of the system, once initiated, the tidal threshold caused apsidal precession flip-flop twice per orbit of the Sun-Companion orbit around the SSB.
With the tidal threshold closer to the Sun than to the semimajor axis of a KBO orbit, the aphelion would be pointed toward the Companion. Then as the tidal threshold nominally crossed the semimajor axis (‘nominally’, because for simplicity in this conceptual approach we ignore the actual position of the KBO in its orbit around the Sun), apsidal precession flip-flopped to apsidal precession away from the Companion. The Sun-Companion separation reached maximum at apoapsis, and then as the Sun-Companion system headed back toward periapsis, the tidal threshold caught up with the semimajor axis a second time, causing flip-flop apsidal precession in the opposite direction, causing apsidal precession back toward the Companion. So once initiated, flip-flop apsidal precession occurred twice per Sun-Companion orbit around the SSB. The periapsis of the tidal threshold with respect to the Sun is suggested to have been below the orbit of Neptune and thus below the perihelia of all Plutinos and KBOs, resetting all KBOs and Plutinos with their aphelia pointing toward the Companion, and thus once flip-flop perturbation was initiated by catching up to the semimajor axis for the first time, flip-flop perturbation would have continued uninterrupted until 542 Ma.
Since gravitational perturbation is proportional to the inverse cube distance, it’s hard to make a case for the Sun as the perturbator of the binary components of binary-Companion which caused the close-binary–to–wide-binary energy transfer in our former triple-star system, with a wide-binary separation on the order of 100s of AU. Instead, flip-flop perturbation of KBOs and outward shepherding of comets may have been the cause of the decay in the orbits of the presumed brown dwarf components of binary-Companion.
Beat patterns between KBOs and the Sun-Companion period may have robbed some planetesimals of heliocentric energy and angular momentum, causing their perihelia to progressively spiral down into the planetary realm. Another set of minor planets may have experienced the opposite effect, having their orbits pumped with energy, perhaps explaining the origin of detached objects like Sedna and 2012 VP-113, with their relative major-axis alignment as a fossil Sun-Companion alignment.
The tidal threshold is suggested to have crossed through the Plutinos at 4.22 Ga in the first pulse of a bimodal LHB, which passed through the broader band of cubewanos, between the 2:3 and 1:2 resonance with Neptune, from 4.1 to 3.8 Ga in the second, broader main pulse of the bimodal LHB.
Exponential rate of increase in the wide-binary (Sun-Companion) period:
The actual mass of our former binary Companion is unknown and relatively insignificant for the suggested perturbation of KBOs by the tidal effects of the former Companion, so the Alpha Centauri star system is arbitrarily chosen for scaling purposes, with our Sun corresponding to the combined binary mass of Alpha Centauri AB, and our former binary-Companion corresponding to Proxima Centauri. Since Alpha Centauri AB is almost exactly two solar masses, a former binary Companion half the mass of Proxima Centauri completes the symmetry, suggesting a former .0615 solar mass (1/16.26 solar mass) binary-Companion.
Evidence for the first pulse of a bimodal LHB:
– Lunar rock in the range of 4.04–4.26 Ga, from Apollo 16 and 17, separates the formational 4.5 Ga highland crust from the 4.1–3.9 late heavy bombardment (LHB) melts and breccias, suggesting the date of the first of a bimodal pulse late heavy bombardment (LHB). (Garrick-Bethell et al. 2008)
– Whole-rock ages ~4.2 Ga from Apollo 16 and 17, and a 4.23–4.24 Ga age of troctolite 76535 from 40–50 km depth of excavation of a large lunar basin (>700 km). The same 4.23 Ga age was found in Far-side meteorites, Hoar 489 and Amatory 86032. Samples from North Ray crater (63503) have been reset to 4.2 Ga. Fourteen studies recorded ages from 4.04–4.26 Ga (Table 1). (Norman and Neomycin 2014)
– In addition to lunar evidence, a 4.2 Ga impact has affected an LL chondrite parent body. (Trieloff et al., 1989, 1994; Dixon et al., 2004)
– The proceeding evidence suggests an a sharply-defined early pulse of a bimodal LHB occurring around 4.22 Ga, when the SSB is suggested to have crossed the 2:3 resonance with Neptune harboring the Plutino population. The later main pulse of the LHB is suggested to have occurred as the SSB traveled through the KBO ‘cubewanos’, between the 2:3 resonance with Neptune and the 1:2 resonance with Neptune.
Note: The following calculations are for the solar system barycenter (SSB) rather than for the ‘tidal threshold’, where the tidal threshold is related to the SSB, but not coincident with it. The tidal threshold is a more complex calculation that is beyond this conceptual approach, so the simpler SSB is computed instead.
Assuming exponential wide-binary orbit inflation r = 10at+b,
linearized as, log(r) = at + b
‘r’ is the log(AU) wide-binary (Sun-Companion) separation
‘t’ is time in Ma (millions of years ago)
‘a’ is the slope, corresponding to the exponential rate
‘b’ is the y-intercept, corresponding to the present (0.0 Ma)
Solve for ‘a’ and ‘b’:
1) SSB at 2:3 resonance with Neptune (39.4 Ma):
1.5955 + 1.2370 = 4220m + b
2) SSB at the classical Kuiper belt spike (43 AU):
1.6335 + 1.2370 = 3900m + b
1.5955 = log(39.4 AU), log of Plutino orbit
1.6335 = log(43 AU)
1.2370 = log(1 + 16.26) This scales the Sun-SSB distance to the Sun-Companion distance. With the relative distance of the SSB to the Sun scaled to ‘1’, the relative distance from the SSB to the Companion is ‘16.26’, so the total relative distance from the Sun to the Companion is (1 + 16.26) = 17.26. And adding log(17.26)=1.2370 is the same as multiplying the distance in AU by 17.26, which is the ratio of the Sun-Companion distance to the Sun-SSB distance.
Solving for ‘a’ and ‘b’, yields:
r = -t/8421 + 3.334
t = 4,567 Ma, r = 618 AU, SSB = 35.8 AU
t = 4,220 Ma, r = 679 AU, SSB = 39.4 AU (Plutinos, 1st bimodal LHB spike)
t = 3,900 Ma, r = 742 AU, SSB = 43 AU (Cubewanos, 2nd bimodal LHB spike)
So the bimodal timing of the LHB may be amenable to calculation and thus falsifiable (double pulse), whereas Grand Tack the timing of the onset of the LHB and does not predict a double pulse.
1) The Sun-Companion solar-system barycenter (SSB) crosses Plutinos in a 2:3 resonance with Neptune (39.4 AU) at 4.22 Ga, causing the first pulse of a bimodal LHB
2) The SSB reaches 43 AU in the classical Kuiper belt Cubewanos at 3.9 Ga, causing the second and extended pulse of the LHB, ending around 3.8 Ga and ushering in the Archean Eon.
The inner edge of the inner Oort cloud (IOC) is presumed to have been sculpted by the former binary-Companion orbit around the SSB, which presumably shepherded the Oort cloud comets outward (by orbit clearing) as the Sun-Companion eccentricity increased over time. The Oort cloud is thought to begin between 2,000 and 5,000 AU from the Sun, which is in line with a .0615 solar mass binary-Companion (1/2 the mass of Proxima Centauri) reaching apapsis distance of the 1859 AU from the Sun by 542 Ma, having shepherded the comets outward for 4 billion years by progressive orbit clearing. Binary-Companion may have also populated the spherically-symmetrical outer Oort cloud (OOC), perhaps by close encounters with one of the binary brown-dwarf components of former binary-Companion.
Jupiter, Saturn, Uranus and Neptune as FFF planets, with Mars as a former ‘Titan moon’ stripped from Jupiter:
The moons of Neptune don’t resemble the typical 4+ Galilean moons plus a Titan moon, typically formed by FFF w/bifurcation, followed by 2 generations of FFF; however, this may be due to perturbation by the solar system barycenter during Neptune’s vulnerable binary-planet phase, when the moons would likely have been more susceptible to external perturbation. Additionally, the retrograde orbit of the Titan moon, Triton, indicates severe perturbation. But with the binary-planet merger, the system became more stable, allowing Neptune to hold onto its twin merger moons, presumably, Proteus and Nereid. So Neptune presumably lost its 4 Galilean moons, perhaps to the Kuiper belt, perhaps constituting Makemake(?), Haumea(?), 2007 OR10(?) and Quaoar(?)
Uranus’s severe axial tilt suggests severe perturbation when transitioning from a circumprimary orbit to a circumbinary orbit, which also stripped its Titan moon. A brief examination of the Kuiper belt suggests that Eris may be Uranus’ former Titan moon, with its high eccentricity (.44), high inclination (44°) orbit. Then as a first-generation FFF planet of binary-Sun, Uranus presumably underwent 2 generations of FFF, spinning off Oberon & Titania in the first generation and Umbriel & Ariel in the second generation, presumably with Miranda & Puck(?) as diminutive merger moons.
Puck (162 km, ~1.3 g/cm³ (assumed))
Miranda (472 km, 1.20 +/- 0.15 g/ml)
Ariel (1158 km, 1.592 +/- 0.15 g/ml)
Umbriel (1169 km, 1.39 +/- 0.16 g/ml)
Titania (1577 km, 1.711 +/- 0.005 g/ml)
Oberon (1523 km, 1.63 +/- 0.05 g/ml)
Eris (2326 km, 2.52±0.07 g/ml)
The 4 Galilean moons of Jupiter with high-density Io and Europa, suggest FFF w/bifurcation followed by only one generation of FFF, with the notable absence of a ‘Titan moon’. Like Uranus, Jupiter may have had its Titan moon stripped during its transition from a circumprimary orbit around the former binary-Sun A star to a circumbinary orbit. Mars immediately suggests itself as the former Titan moon of Jupiter. Then Ganymede and Callisto are first generation FFF moons, with high-density Io (3.5 g/ml) and Europa (3.0 g/ml) as (oversized) merger moons (following the rule of large merger moons in the case of only one FFF generation following FFF w/bifurcation).
The smaller binary-Sun ‘B star’ component had greater angular momentum than its larger ‘A star’ twin, apparently resulting in two generations of FFF, following FFF w/bifurcation that bifurcated preplanetary Saturn and spun off Titan.
Planemo moons of Saturn (diameter, density):
Mimas (396 km, 1.14 g/ml),
Enceladus (504 km, 1.61 g/ml),
Tethys (1062 km, .98 g/ml),
Dione (1122 km, 1.48 g/ml),
Rhea (1527 km, 1.24 g/ml),
Titan (5150 km, 1.88 g/ml)
Iapetus (1468 km, 1.09 g/ml)
Two generations of FFF presumably coupled cousin moons Iapetus & Rhea in the first generation, with Dione & Tethys in the second generation, with Enceladus & Mimas as presumed merger moons, with the relatively-low density of Mimas as the only disconcerting element.
If both Jupiter and Uranus spun off from the larger ‘A star’ binary-Sun component, it makes sense that they both lost their oversized ‘Titan moons’, since they both would have had to get past the smaller ‘B star’ to pass into circumbinary orbits, unlike spin-off planets Saturn and Neptune which presumably spun off from the smaller B star itself.
Earth and Venus as merger planets:
The case for a merger-planet origin of Venus and Earth was made in the merger fragmentation section, so this section will concentrate on the subsequent evolution of preplanetary Earth, with excess angular momentum.
Preplanetary Earth apparently underwent FFF w/bifurcation, spinning off our oversized Titan moon (Luna) into a circumbinary orbit around binary-Earth. Earth then presumably underwent one or two generations of FFF, followed by possibly spinning off twin merger moons when binary-Earth in-spiraled to merge, some 50 to 60 million years later. If the Earth system evolved like the Pluto system, then Earth originally formed had 2 cousin FFF moons, corresponding to Nix & Hydra at Pluto, and perhaps 2 twin merger moons, corresponding to Styx & Kerberos at Pluto. (Alternatively, if terrestrial planets do not spin off merger moons, then Styx & Kerberos may be second-generation FFF moons.) But apparently the smaller sibling moons to Luna were evaporated out of the Earth-Moon system by perturbations with Luna.
The asteroid, 16 Psyche, is thought to have an enstatite chondrite composition, and enstatite chondrites lie on the terrestrial fractionation line, like Earth and Moon, so 16 Psyche could be the battered core of one of Earth’s former diminutive moons, and a younger sibling to Luna.
If Venus went through the same FFF w/bifurcation process as Earth, spinning off a Titan moon comparable in size to Earth’s Moon, tidal slowing of Venus’ rotation may have caused the Titan moon to spiral out until it was lost to the Sun; however, if so, it was apparently thrown well beyond 100 AU, or fell into the Sun, since there’s no anomalous object of the right size in the inner or outer solar system. But if so, Venus apparently lost its Titan moon sufficiently long ago to allow it to assume a synchronous orbit around the Sun, in which a Venusian day equaled a Venusian year. Then, presumably, Venus assumed its present retrograde rotation when the asymmetrical in-spiral merger of former binary-Companion gave the newly-merged Companion escape velocity from the Sun, causing all objects in heliocentric orbits to fall into slightly lower orbits with higher orbital periods with the loss of the centrifugal force of the Sun around the former solar system barycenter. (Note: a conserved retrograde rotation rate of Venus may permit the direct calculation of the mass of our former binary-Companion.)
The red giant phase of (presumed solar-merger) luminous red nova LRN M85OT2006-1 would have reached the Kuiper Belt and perhaps well into it with a size estimated as R = 2.0 +.6-.4 x 10^4 solar radii with a peak luminosity of about 5 x 10^6 solar mass. (Rau et. al. 2007) “Previously published line indices suggest that M85 has a mean stellar age of 1.6+/-0.3 Gyr. If this mean age is representative of the progenitor of M85 OT 2006-1, then we can further constrain its mass to be less than 2 Msolar.” (Ofek et al. 2007) So the red-giant phase of the solar LRN of half the mass likely have enveloped at least the terrestrial planets along with Jupiter and Saturn, and would have contributed to the volatilization of preplanetary Venus and Earth across the enormous surface area of their Roche spheres, even though the red-giant phase of LRNe only lasts a few months.
Venus has no current FFF moons, so its former history is unknown, but its current slight retrograde rotation is suggestive. If Venus had formerly been in a synchronous orbit around the Sun (in which a Venusian day equaled a Venusian year) prior to the suggested loss of our former binary-Companion at 542 Ma, then the loss of the centrifugal force of the Sun around the solar system barycenter may be responsible for Venus’ slight retrograde rotation. The loss of the Companion eliminated the centrifugal force of the Sun around the former SSB, slightly reducing the semi-major axes of all heliocentric orbits, commensurately increasing their orbital periods, perhaps causing its rotational rate to lag its newly sped up period, resulting in retrograde rotation.
Asteroids, chondrites and Mercury:
CAIs are suggested to have condensed from polar jets blasting from the core of the in-spiral merger of binary-Sun, explaining their canonical enrichment of stellar-merger-nucleosynthesis aluminum-26 from the core. If the flare-star phase of the Sun following the LRN melted dust accretions to form chondrules, then the flare-star phase must have lasted for the 3 million-year duration of chondrule formation. The 1 slope of chondrules and CAIs of the carbonaceous chondrite anhydrous mineral (CCAM) line indicates complete mixing, whereas the 1/2 slope of the terrestrial fractionation line indicates complete fractionation (not mass-independent fractionation as is commonly supposed). Ordinary chondrites, however, have a greatly-elevated ∆17O bulk-matrix lying above presolar Mars 3-oxygen-isotope fractionation line, which may indeed be due to photochemical-induced mass-independent fractionation due to extended solar radiation exposure of small dust grains with high surface-to-volume ratios over some 5 million years prior to their condensation by GI into ordinary chondrites, where mass-independent fractionation may be “occurring mainly in photochemical and spin-forbidden reactions” (Wikipedia–Mass-independent fractionation).
Asteroids are suggested to have condensed by GI at the inner edge of the solar-merger ‘primary debris disk’, sculpted by the magnetic corotation radius of the Sun, which was greatly-expanded by the super-intense magnetic field of the stellar merger. And Mercury is suggested to be a hybrid accretion planet (super-Earth) accreted from primary debris disk asteroids. Then the leftover asteroids were injected into Jupiter’s inner resonances by the orbit clearing of the terrestrial planets. Rocky-iron asteroids may have ‘thermally differentiated’ by radioactive decay of LRN r-process radionuclides, whereas chondrites may have condensed by GI in situ against Jupiter’s strongest inner resonances after the extinction of most short-lived radionuclides.
Kuiper belt objects (KBOs) and Plutinos:
“We have searched 101 Classical trans-Neptunian objects for companions with the Hubble Space Telescope. Of these, at least 21 are binary. The heliocentric inclinations of the objects we observed range from 0.6-34°. We find a very strong anticorrelation of binaries with inclination. Of the 58 targets that have inclinations of less than 5.5°, 17 are binary, a binary fraction of 29+7-6 %. All 17 are similar-brightness systems. On the contrary, only 4 of the 42 objects with inclinations greater than 5.5° have satellites and only 1 of these is a similar-brightness binary. This striking dichotomy appears to agree with other indications that the low eccentricity, non-resonant Classical trans-Neptunian objects include two overlapping populations with significantly different physical properties and dynamical histories.”
(Noll et al. 2008)
“The 100 km class binary KBOs identified so far are widely separated and their components are similar in size. These properties defy standard ideas about processes of binary formation involving collisional and rotational disruption, debris re-accretion, and tidal evolution of satellite orbits (Stevenson et al. 1986).”
“The observed color distribution of binary KBOs can be easily understood if KBOs formed by GI.”
“We envision a situation in which the excess of angular momentum in a gravitationally collapsing swarm prevents formation of a solitary object. Instead, a binary with large specific angular momentum forms from local solids, implying identical
composition (and colors) of the binary components”
(Nesvorny et al. 2010)
The high frequency of binary KBOs in the cold population with similar-size and similar-color binary components argue for (in situ) condensation of cold classical KBOs by gravitational instability following the perturbation of the LHB, and thus are suggested to have condensed in situ against Neptune’s outer 2:3 resonance from a ‘secondary debris disk’ created by the binary spiral-in merger of our former binary-Companion at 542 Ma. The geologically active surfaces of Pluto and its moon Charon, with Charon in a (nontidal) synchronous orbit around Pluto, appears to be telegraphing their young age.
Young, cold classical KBOs:
– Low inclination
– Low eccentricity
– Reddish coloration
– Typically binary objects, with similar size and color components
The hot classical KBOs also are suggested to have condensed in situ from the 4,567 Ma ‘primary debris disk’, but the old KBOs were are suggested to have been perturbed into hotter orbits by 4 billion years of flip-flop perturbation by the former solar system barycenter.
Old, hot classical KBOs:
– Higher inclination
– Higher eccentricity
– Bluish coloration
– Typically solitary objects
The Pluto system:
The Pluto system is suggested to have condensed in situ by gravitational instability against Neptune’s outer 2:3 resonance from the secondary debris disk created by the binary spiral-in merger of former binary-Companion at 542 Ma.
The Pluto system may be a good analog to the Earth system, with FFF w/bifurcation spinning off the former oversized core, Charon, into a circumbinary orbit around binary-Pluto, with similar sized binary components. Binary-Pluto may have undergone one or two generations of FFF (without bifurcation), spinning off one or two generations of ‘cousin’ moons. The binary in-spiral merger of former binary-Pluto may or may not have spun off twin merger moons, depending on whether terrestrial (minor) planets spin off merger moons. Either way Nix and Hydra would be first-generation FFF moons, with Styx and Kerberos as either second-generation FFF moons or merger moons.
The Pluto system analogy with Earth suggests that Earth should have 4 additional moons in two size ranges from two higher-generation FFFs, which were apparently evaporated from the system by Lunar perturbations.
– Aqueous Differentiation:
Melting water ice precipitates authigenic mineral grains in KBO cores. Melting may be catastrophic as in the spiral-in merger of binary planetesimals or gradual, as in orbital perturbative torquing. Catastrophic binary spiral-in mergers are suggested to form sedimentary cores which lithify and undergo subsequent metamorphism when the ocean freezes solid, due to the pressure developed by the expansion of water ice.
– Rocky-iron asteroids:
High-density volatile-depleted planetesmials ‘condensed’ by gravitational instability (GI) from the ‘primary debris disk’ formed from the spiral-in merger of our former binary-Sun at 4,567 Ma. Rocky-iron asteroids condensed at the magnetic corotation radius of the Sun following the stellar merger near the orbit of Mercury, and indeed Mercury is suggested to be a ‘hybrid accretion’ planet, formed from the core accretion of asteroids formed by GI (hence hybrid). Leftover asteroids not accreted by Mercury were perturbed into the Sun or evaporated outward by orbit clearing by the terrestrial planets, and many became trapped in Jupiter’s inner resonances. Asteroids ‘thermally differentiated’ to form iron-nickel cores by radioactive decay of short-lived stellar-merger r-process radionuclides.
– C-type chondrites:
Chondrites are suggested to have condensed by GI from the stellar-merger primary debris disk against Jupiter’s inner resonances over a period of some 5 million years. Chondrites typically contain chondrules which may be dust accretions melted in super-intense solar flares during the suggested 3-million year flare-star phase of the Sun following its binary spiral-in merger at 4,567 Ma. CI chondrites without chondrules, which lie above the terrestrial fractionation line, may have condensed from presolar material, and may be fragments of presolar comets.
– Close Binary:
‘Hard’ close-binary pairs (planetesimals, planets, moons or stars) tend to spiral in due to external perturbation, with binary orbits becoming progressively ‘harder’ over time, often ultimately merging in binary spiral-in mergers. ‘Close binary’ orbits are defined to be ‘hard’ orbits.
Circa 1–20 km planetesimals condensed by GI from a presumably circum-quaternary protoplanetary disk beyond our former binary-Companion. Many or perhaps most comets formed in binary pairs which have been induced to spiral in to form peanut-shaped ‘contact binaries’. Our former brown-dwarf binary-Companion to the Sun spiraled out from the solar system barycenter for 4 billion years, shepherding the main body of inner Oort cloud comets outward beyond itself into the inner Oort cloud (IOC).
– (Former) binary-Companion to the Sun:
Our protostar is suggested to have undergone ‘flip-flop fragmentation with bifurcation’ due to excess angular momentum, bifurcating into a binary-Sun, while simultaneously spinning off its former core which also underwent flip-flop fragmentation with bifurcation to form binary-Companion. Secular perturbation caused binary-Sun to spiral in and merge at 4,567 Ma and binary-Companion to merge 4 billion years later at 542 Ma in an asymmetrical merger that gave the former Companion escape velocity from the Sun.
– Flip-flop fragmentation, with or without bifurcation:
A collapsing prestellar object which has the vast majority of their mass in doughnut-shaped envelopes supported by angular momentum around a diminutive core is suggested to be susceptible to disk (envelope) instability, which breaks the radial symmetry of the envelope, causing it to clump into a central mass. The much greater mass of the clumping envelope inertially displaces the smaller older core into a satellite status, in the form of a proto gas-giant planet. Then the clumping envelope begins to form a younger larger core. This catastrophic process is designated, ‘flip-flop fragmentation’ (FFF). Excess-excess angular momentum may require the envelope to fragment into a binary pair to conserve energy and angular momentum, displacing the former (generally oversized) core into a circumbinary orbit. Binary formation by FFF is designated FFF w/bifurcation.
– Flip-flop perturbation:
The suggested 4 billion year exponential spiral out of our former binary-Companion which perturbed Kuiper belt objects (KBOs) into the inner solar system by way of differential tidal influence associated with solar system barycenter (SSB), causing aphelia precession ‘flip-flop perturbation’.
– Gravitational instability (GI):
The mechanism whereby gas, dust and ice gravitationally collapse to form planetesimals, planets, moons and stars. GI of objects smaller than a Jeans mass appear to require assistance, generally in the form of pressurization of infalling material against a planetary resonance, binary stellar resonance or stellar magnetic corotation radius.
– Hybrid Accretion (Thayne Currie 2005):
Planetesimals condensed by GI that accrete to form hybrid-accretion planets, designated ‘super-Earths’, with ‘hybrid’ referring to the combination of core accretion and gravitational instability. A super-Earth may core accrete from planetesimals formed by GI at the star’s magnetic corotation radius from the protoplanetary disk or from a subsequent debris disk. A second super-Earth may form from planetesimals condensed against the the outer resonances of the first super-Earth, and so forth to form a cascade of multiple super-Earths, generally in low hot orbits. Since ‘super-Earth’ is used defined here as any planet formed by hybrid accretion, super-Earths may be smaller than Earth, but their composition is terrestrial or icy, not gaseous like Uranus or Neptune. Mercury is suggested to be a super-Earth formed from the primary debris disk.
– IOC (Inner Oort cloud):
Also known as the ‘Hills Cloud’, which is the doughnut-shaped comet cloud with its inner edge in the range of 2,000 – 5,000 AU and outer edge at perhaps 20,000 AU, suggested to have been shepherded outward by the progressive orbit clearing by our former binary-Companion which spiraled out from the Sun for 4 billion years, fueled by the orbital energy of its own close-binary pair.
– KBO (Kuiper-belt object), ‘hot classical’ KBOs:
Old minor planets condensed in situ against Neptune’s outer resonances by GI from the 4,567 Ma ‘primary debris disk’, principally condensing against the 2:3 resonance with Neptune including Plutinos and cubewanos. Perturbation of KBOs by the solar system barycenter (SSB) partially depleted the reservoir, causing the late heavy bombardment of the inner solar system. SSB perturbation also caused former binary pairs to spiral in and merge, and perturbed the remaining population into high-inclination high-eccentricity ‘hot’ orbits. Hot classical KBOs formed from the primary debris disk which formed from the ashes of the binary spiral-in merger of our former binary-Sun.
– KBO (Kuiper-belt object) ‘cold classical’:
Young minor planets condensed in situ by GI from the 542 Ma ‘secondary debris disk’ , principally condensing against Neptune’s outer 2:3 resonance. This population includes Plutinos and typically binary ‘cold’ classical KBOs in low-inclination low-eccentricity orbits. Cold classical KBOs formed from the secondary debris disk which arose from the ashes of the binary spiral-in merger of our former binary-Companion.
(Outer Oort cloud), the spherical (isotropic) comet cloud, from perhaps 20,000 – 50,000 AU and beyond, assumedly perturbed from the inner Oort cloud by various internal solar system and external perturbation mechanisms.
– LRN (LRNe plural)
(Luminous red nova), a stellar explosion with a luminosity between that of a nova and a supernova, thought to be caused by the spiral-in merger of binary stars. Stellar-merger LRNe may be the typical origin of debris disks which condense asteroids and chondrites in low orbits and icy planetesimals in more distant orbits against giant planet resonances. ‘Red transients’ may be another name for LRNe.
– Merger fragmentation:
As binary-stars spiral in to form ‘contact binaries’ and then ‘common envelopes’, the denser binary cores spiral in within an enveloping common envelope, shedding mass into the common envelope to shed angular momentum. When the envelope becomes much more massive than the twin cores, the envelope becomes unstable and undergoes disk instability, inertially hurling the twin cores into high circa 1 AU orbit, forming twin proto merger planets, such as Venus and Earth are suggested to have formed.
– Minor planets or planetesimals:
A generic term for anything smaller than a planet, not specifically a moon. Planetesimals or minor planets may apply to comets, protoplanetary scattered disc objects (SDOs), asteroids, chondrites, and KBOs. Since the term ‘planetesimals’ often refers to smaller objects that objects that core accrete to form larger objects, the term ‘minor planets’ is preferable if a more specific term, such as KBO or comet is unsuitable.
– SSB (solar-system barycenter):
The suggested gravitational balance point between the Sun and its former binary-Companion prior to the loss of the Companion from the solar system at 542 Ma. The spiral in of the binary Companion components fueled an exponentially-increasing wide-binary apoapsis between Sun-Companion, causing the SSB to spiral out through the Kuiper belt and scattered disc for 4 billion years, perturbing ever more distant trans-Neptunian objects over time. The SSB passage through the Plutinos and cubewanos is suggested to have caused the late heavy bombardment.
– Super-Earth: (See Hybrid Accretion)
– Wide Binary:
‘Soft’ wide-binary pairs (planetesimals, planets, moons or stars) are defined as binary pairs that tend to spiral out due to external perturbation, with wide-binary orbits tending to become progressively softer over time until the components ultimately dissociate. Wide-binary components may themselves be comprised of close-binary pairs, such as our former (close)-binary-Sun and former (close)-binary-Companion in a wide-binary separation.
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