Age and Origin of our Planetary System as a Supernova-Remnant
Wolfgang G. Gasser
Original discussion on International Skeptics Forum
The age of our planetary system is assumed be around 4.6 x 109 = 9p46 = nine.po four six years. This value can be derived under the reasonable premises that half-lives of radioactive decay have not relevantly changed and that the oldest inclusions found in meteorites are indicative of the age of our planetary system.
The currently prevailing theory of the origin of our planetary system seems to me almost as implausible as the the giant-impact hypothesis concerning the origin of our moon. So I present here an alternative based on the distinction of first- and next-generation stars.
A first-generation star emerges by gravitational attraction from normal galactic matter (primarily hydrogen). First-generation stars can emerge alone or in groups. They grow from randomly generated small seed objects by absorbing further mass and by fusing together with other objects having evolved in the same way. Thus, even the most giant first-generation star has passed through all sizes (i.e. from smaller than Moon to final). A higher mass density in a region of star formation increases the probability of big stars.
In principle, there is a continuous transition from moons to planets to stars. A lonely rogue planet with a moon can be considered a binary star system where one star is small and the other very small.
First-generation stars cannot lead to planetary systems similar to ours. In a multiple object system, where one object has grown to a real sun with thermonuclear fusion whereas the smaller objects remain at the size of planets, all is possible: from completely arbitrary rotation planes of the "planets" to even retrograde orbits. Yet it is highly unlikely that all "planets" lie by chance in more or less the same plane.
The chaotic movements of lots of different
masses forming one star ultimately lead to one rotation axis. The corresponding
angular momentum can range from close to zero to high. In order to get
something similar to our planetary system, a supernova-like explosion of a previous-generation
star with substantial angular momentum (rotation speed) is needed.
During gravitational collapse preceding a supernova explosion, the
previous-generation star (or at least the star's massive core) becomes a more
and more oblate spheroid (due to conservation of angular momentum). The
highest pressure and temperature obviously reigns in the center of the star,
where a new kind of nuclear chain reaction is eventually triggered.
The pressure (resp. weight) at the center is the same in direction of the
vertical rotation axis as in directions on the horizontal equatorial plane. Yet
there is more mass between the center and a point on the equatorial plane than
between the center and the poles. On the equator, strong centrifugal forces
compensate gravitational attraction so that compressing forces (weight,
pressure) at the center are the same from all directions.
The supernova chain reaction spreads from the center, and resulting heat and pressure try to accelerate outwards the matter outside this explosion region. The more oblate (flat) the spheroid, the more difficult to accelerate masses outwards in the equatorial plane and the easier are outbursts on the poles.
Depending on chain-reaction type, oblateness and other parameters, this may lead to rather spherical explosions, to bipolar outflows or astrophysical jets through the rotation poles.
In case of favorable conditions, such an explosion can lead to a proto-planetary disk in the equatorial plane of the previous-generation star. During the explosion, much or most of the stellar material is definitively lost into space, since it is expelled at velocities higher than escape velocity. In the equatorial plane, stellar material is expelled at the lowest velocities, because momentum and energy in these directions are distributed among more mass, and explosive power dissipates more easily in polar directions.
A central part of the core of the previous-generation star will probably remain where it is, as explosive forces outwards can lead by actio-reactio (i.e. momentum conservation) to inward forces. Also not all of hydrogen and other elements from outer star layers is accelerated enough to leave the newly created next-generation solar system. A next-generation star can at least in principle also grow further by absorbing matter during its journey through the galaxy.
If this hypothesis presented here is true then our sun is a next-generation star. Its previous incarnation, a substantially bigger star, exploded around 4.6 billion = 9p46 years ago as a supernova and ejected (among lots of material having disappeared in space) more or less homogeneously around its equatorial plane the material which is still gravitationally bound to our sun. This material cooling down and giving rise to meteoroids, asteroids and so on coincides with the start of ticking of what we use as radioactive clocks.
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Argumemnon in #3:
If there was a "predecessor" star at all, where's the resulting black hole or neutron star?
The remnant of the previous-generation star is our Sun. There is no reason to assume that every exploding star must turn into a neutron star (let alone into a logically impossible black hole). A lot of pressure is needed in order to compress atomic nuclei and electrons into neutrons. The more mass a star loses during an explosion, the less likely is the outcome of a neutron star.
Are there arguments suggesting that normal stars (such as our sun) cannot have at its center a pure neutron-core?
According to common sense, every neutron star must have outer layers consisting of conventional stellar matter. Surface neutrons of neutron stars would simply decay into atomic nuclei and electrons because of lacking pressure from outside. Own weight cannot be enough, even in case of extremely high gravity.
smartcooky in #13:
Solar systems like ours require supernova remnant material to make the heavy elements that lead to rocky planets. I speculate (and I'm happy be corrected) that solar systems formed by first generation stars could only have contained gas giant-like planets.
My use of first-generation star and next-generation star does not depend on whether stars are formed from "fresh" or from "remnant" material. Every star having (more or less continuously) grown from galactic matter is considered a first-generation star. Next-generation stars can only emerge by explosions of previous-generation stars.
wogoga in #20:
According to common sense, every neutron star must have outer layers consisting of conventional stellar matter. Surface neutrons of neutron stars would simply decay into atomic nuclei and electrons because of lacking pressure from outside. Own weight cannot be enough, even in case of extremely high gravity.
Lukraak_Sisser in #22:
By that same common sense the core of Jupiter should have nuclear fusion, or be as dense as interstellar hydrogen.
By 'common sense' I mean 'simple, transparent, logically consistent reasoning'. It should not be confused with 'superficial reasoning' or 'prejudiced reasoning'.
High pressure resp. temperature is obviously a prerequisite for nuclear fusion. So, it is a very simple common sense conclusion that Jupiter's core cannot have nuclear fusion, if pressure and temperature are not high enough.
According to common sense, neutrons consist of protons and electrons plus mass-equivalent of compression energy. Neutrons are not stable outside atomic nuclei, and they decay into protons and electrons. Neutrons do not decay into quarks, and the involvement of neutrinos is only inferred from dogmatic premises.
wogoga in #1:
During gravitational collapse preceding a supernova explosion, the previous-generation star (or at least the star's massive core) becomes a more and more oblate spheroid (due to conservation of angular momentum).
For a time I have become suspicious of whether this is actually true.
Three principles are relevant for contraction of rotating stars under conservation of angular momentum:
o Since angular momentum is proportional to r ∙ v, our rotation speed v becomes inversely proportional to r (radius, distance from rotation axis). During contraction, gravity-potential energy is converted into kinetic energy of rotation.
o Since concerning centrifugal forces we have F = m ∙ v2 / r, these forces turn out to be inversely proportional to the third power of r.
o Gravitational forces are inversely proportional to the second power of radius.
If this is correct, then contraction of a star increases centrifugal forces more than gravity, entailing star oblateness.
There are even "normal" stars with substantial equatorial bulges:
Achernar is a bright, blue star about 3,150 times more luminous than the Sun. As of 2003, Achernar is the least spherical star in the Milky Way studied to date. It spins so rapidly that it has assumed the shape of an oblate spheroid with an equatorial diameter 56% greater than its polar diameter. Since it is actually a binary star, its highly distorted shape may cause non-negligible departures of the companion's orbital trajectory with respect to a Keplerian ellipse. (Wikipedia)
Some neutron stars may even resemble more discs than spheres.
By the way, spin up (rotation speed increase) of a neutron star could simply be the result of further contraction (not yet fully accomplished).
Binary Pulsars as Remnants of Fast Rotating Single Stars
What will happen to Achernar after definitively having burned out? Independently from intermediate states (such as red-giant phase or star explosion), transformation into a neutron star is a reasonable hypothesis. Neutron stars have densities in the order of atomic nuclei (~ 1017 x 3 kg/m3 = 17p3 kg/m3) and have typical radii in the order of 10 km = 4p1 meter. Equatorial radius of Achernar is ~ 10 solar radii ≈ 8 million km = 9p8 m ≈ 10p1 m.
Since centrifugal forces increase proportionally with decreasing radius (#28), a reduction in radius by 6 decimal powers (i.e. from 10p1 m by factor 6p1 to 4p1 meter) would lead to an increase in rotation speed by the same factor 6p1. In case of Achernar, equatorial rotation speed is already ~ 0.1% of light-speed = 7n1 c ≈ 5p3 m/s = 300 km/s. An increase by 106 = 6p1 would therefore lead to a "theoretical" rotation speed in the order of 1000 c = 3p1 c (i.e. thousand times faster than the speed of light).
It is obvious that one neutron star alone cannot take over all the angular momentum. What can happen is the following: During the process of shrinkage, the original star decays into a central part and an orbiting ring. The ring condenses more and more into discontinuous fragments until in the end only one such fragment remains. Thus we get a binary pulsar, with both components within the surface of the original star.
Even if the new companion originating from the ring has enough mass to turn into a neutron star, its axial rotation speed should be substantially lower than the one of the central remnant. The latter consists of the central and polar parts of the original star. Most of the angular momentum of the ring remains orbital momentum (as opposed to axial), also when condensing to one single companion.
Maybe binary pulsar PSR J0737-3039 with orbital period of only 2.4 hours could be the remnant of one single fast-rotating star such as Achernar.
Reality Check in #34:
Special relativity also applies to stars - it is relativistic angular momentum that you have to use. In SR no massive object can reach the speed of light. So there is not an increase of speed by 6 orders of magnitude corresponding to a radius decreasing by 6 orders of magnitude.
The simplest hypothesis concerning high-speed momentum is the one of Einstein: Momentum p equals relativistic mass m[v] times velocity v. This relation p = m[v] ∙ v is enough to assess angular momentum well enough for our situation.
During star contraction, gravity-potential energy is transformed into other energy forms such as heat, kinetic and compression energy. Thus, relativistic mass m[v] remains in principle unchanged, since it is proportional to total energy (see Controversy over Mass-Energy-Equivalence & Photon Mass).
Angular momentum of a given sample (particles of a small region) of a collapsing star is L = p ∙ r = m[v] ∙ v ∙ r, where velocity v is orthogonal to distance from rotation axis r. Since an increase of v cannot (relevantly) change relativistic mass of the sample m[v], a reduction of r by factor 106 = 6p1 = six.po one could only be compensated by an increase of v by the same factor. And this is obviously impossible in our situation.
Reality Check:
It is gravity that holds a star together - ignoring that is ignorant.
Let us again assume a star rotating as fast as Achernar and with a mass high enough for a neutron star to form. My claim: Gravity cannot hold such a star together, because due to conservation of angular momentum, contraction to a neutron star would lead to rotation speeds v >> c. If you think that a neutron star can take over the whole angular momentum of such a collapsing star, please explain!
Reality Check:
Achernar is a main sequence star with a mass of about 7 solar masses.
It will become a white dwarf not a neutron star.
Neutron stars form from the collapse of large (1029 solar masses)
stars.
As far as I understand, approximate size, oblate form and rotation speed of Achernar are more or less empirical facts derived from straightforward (optical) principles, whereas its mass is derived from a complex theory, i.e. from less secure premises. In any case, the difference between 7 and 10 solar masses is not really big. And I used Achernar only as an illustration.
wogoga in #35:
During star contraction, gravity-potential energy is transformed into other energy forms such as heat, kinetic and compression energy. Thus, relativistic mass m[v] remains in principle unchanged, since it is proportional to total energy (see Controversy over Mass-Energy-Equivalence & Photon Mass).
Reality Check in #37:
As any body contracts, conservation of angular momentum means that the speed of its surface increases. The relativistic mass of that surface thus increases.
Relativistic mass is equivalent to total energy. So your claim implies that huge amounts of energy are transferred from elsewhere to the equatorial surface particles in order to increase relativistic mass as much as needed. The slowly rotating matter near the center and the poles of the star actually can lose energy during contraction due to decreasing gravity potential. Yet even if all this mass/energy were transferred to the fast rotating particles close to the equator, this could never be enough to take over all the angular momentum, even if speed v of this resulting equatorial ring would reach c. And we agree on the impossibility of v ≥ c.
Reality Check in #37:
Neutron stars always "take over" the whole angular momentum of their collapsing star because of a basic law of physics - the conservation of angular momentum!
What would be the minimal radius rmin to which our Sun could shrink without rotating at v ≥ c, assuming conservation of (relativistic) mass m and angular momentum L?
o The suns mass: m = 1030 x 1.99 kg = 30p199 kg ≈ 30p2 kg = thirty.po two kilogram
o "On average, helioseismology yields S = 1.92 1041 kg m2 s-1 for the angular momentum of the Sun" (Source). Thus: L ≈ 41p2 kg ∙ m/s ∙ m
o Max. angular momentum at given r and m can be reached by distributing the whole mass m close to the equator, i.e. on a rotating ring resp. circle: L = m ∙ vmax ∙ r where vmax = c
o We get: rmin = L / (m ∙ c) ≈ 41p2 kg ∙ m/s ∙ m / (30p2 kg) / (8p3 m/s) = 11p1 / 8p3 m = 3p1 / 0p3 m ≈ 2p33 m = 330 m
This means: Even by fully transforming into a rotating ring, momentum conservation alone would prevent our Sun from shrinking below a radius of ~ 330 m.
Equatorial rotation speed of the sun is ~ 2 km/s = 3p2 meter. Equatorial rotation speed of Archernar is ~ 300 km/s = 5p3 m, more than 100 times higher. Equatorial radius of Achernar is ~ 10 times the radius of our Sun. Thus (assuming differential rotation not too different from our Sun's) we get:
o L/m = v ∙ r is at least 3p1 = 1000 times higher, and rmin for Achernar thus ~ 1000 times bigger than for the Sun
This means: Even if Achernar turned by contraction into a ring rotating at c, a minimal radius of ~ 2p33 m ∙ 3p1 = 5p33 m = 330 km would be necessary in order to take over the original angular momentum. In the case of a uniformly rotating sphere, radius must even be bigger (probably in the order of 6p1 m = 1000 km). For comparison, radius of a corresponding neutron star is only ~ 4p1 meter = 10 km)!
phunk in #36:
You are basing your math on the equatorial radius and velocity, but the neutron star won't be formed by the star shrinking, it will be formed by the star exploding and blowing away all of those outer layers while compressing the core. What will become the neutron star is just the core of the current star, not the whole thing.
I agree. If all the outer parts containing the highest "density" of angular momentum are blown away then the problem disappears. Yet there may be situations where all the excessive angular momentum cannot escape from such a star's gravity.
Even if we assume that only the innermost 10% = 9n1 of radius (with 0.1% = 7n1 of volume) of such an Achernar-like star turn into a neutron star (without transferring angular momentum to the outer layers), my rough calculation of #32 would still result in an equatorial rotation speed of 10 c. And a rotation speed of 10 c is as impossible as of 1000 c.
phunk in #40:
As Reality Check pointed out, you are using classical momentum in a case where you need to think relativistic.
Already in #35 I pointed out that I use Einstein's relativistic momentum based on relativistic mass. Einstein in The principle of Conservation of Motion of the Center of Gravity and the Inertia of Energy, 1906:
It turned out that to an energy change of magnitude ΔE there must correspond to a change of mass of the same sign and of magnitude ΔE/c2, where c denotes the velocity of light.
In the present paper I want to show that the above theorem is the necessary and sufficient condition for the law of the conservation of motion of the center of gravity to be valid (at least in first approximation) also for systems in which not only mechanical, but also electromagnetic processes take place.
Let us assume a loss-free bidirectional explosion of 10 kg of a very explosive material at the center of a coordinate system: After explosion, 1 kg moves at speed 9/10 c in positive x-direction and 9 kg at speed 1/10 c in negative x-direction. This situation agrees with conservation of relativistic mass (resp. total energy), because we have 10 kg both before and after explosion. And "center of gravity" remains where it is, because the distance of the 1 kg piece is always 9 times farther from the center than the distance of the 9 kg piece.
With respect to "center of gravity" and momentum, it is irrelevant how much of the two pieces is invariant mass and how much is kinetic energy (or radiation), since only relativistic mass resp. total energy is relevant. (See also Controversy over 'Invariant Mass'.)
Independently from any distribution between invariant mass minv and mass-equivalent of kinetic energy mkin = Ekin / c2, a given relativistic mass of mrel = minv + mkin entails an upper limit for momentum: pmax = mrel ∙ c. A higher momentum is only possible if relativistic mass from elsewhere is added.
phunk in #40:
It's not a linear relationship, momentum approaches infinity as v approaches c. You can conserve any amount of momentum without v exceeding c.
This is only valid if we ignore conservation of relativistic mass. Let us assume an object with relativistic mass mrel orbiting a given point at constant distance r. Then angular momentum is theoretically limited to Lmax = mrel ∙ c ∙ r, since speed cannot exceed c.
Your claim implies that this situation would also allow a momentum of e.g. L = 10 Lmax, since relativistic mass can in principle increase from 1 mrel to ~ 10 mrel in accordance with the Lorentz-factor of an increased speed. But where could this huge amount of additional energy ΔE ≈ 9 mrel ∙ c2 come from? The energy needed to increase relativistic mass of rotating parts during star-contraction cannot magically emerge but must already be present as relativistic mass somewhere in the original star.
If not even a ring (containing the whole relativistic mass of the original star) of radius r and rotating at c could absorb the original angular momentum, then contraction to one single neutron star of radius r is obviously far from possible.
wogoga in #1:
During gravitational collapse preceding a supernova explosion, the previous-generation star (or at least the star's massive core) becomes a more and more oblate spheroid (due to conservation of angular momentum). The highest pressure and temperature obviously reigns in the center of the star, where a new kind of nuclear chain reaction is eventually triggered.
The pressure (resp. weight) at the center is the same in direction of the
vertical rotation axis as in directions on the horizontal equatorial plane. Yet
there is more mass between the center and a point on the equatorial plane than
between the center and the poles. On the equator, strong centrifugal forces
compensate gravitational attraction so that compressing forces (weight,
pressure) at the center are the same from all directions.
The supernova chain reaction spreads from the center, and resulting heat and pressure try to accelerate outwards the matter outside this explosion region. The more oblate (flat) the spheroid, the more difficult to accelerate masses outwards in the equatorial plane and the easier are outbursts on the poles.
Depending on chain-reaction type, oblateness and other parameters, this may lead to rather spherical explosions, to bipolar outflows or astrophysical jets through the rotation poles.
An asymmetry in debris expansion of this kind has been found in THE EXPANSION ASYMMETRY AND AGE OF THE CASSIOPEIA A SUPERNOVA REMNANT, 2006. Some quotes from the study:
Fig. 2-Top: Plot of extrapolated 320 yr proper motions for the 1825 identified outer knots based on actual proper motions ... Central white circle has a radius of 5′′ and marks the remnants estimated center of expansion.
expansion and spatial distribution of its highest velocity debris 1825 high-velocity, outlying ejecta knots The distribution of derived transverse expansion velocities for these ejecta knots shows a striking bipolar asymmetry with the highest velocity knots confined to nearly opposing northeast and southwest jets The jets have about the same maximum expansion velocity In addition, we find significant gaps in the spatial distribution of outlying ejecta in directions which are approximately perpendicular to the jets.
However, despite current uncertainties about the specific engine that drives core-collapse explosions, a variety of observations and hydrodynamic modeling make a compelling case that high-mass supernovae are intrinsically aspherical events.
While the presence of a jet and counterjet in this high-mass progenitor supernova-remnant might indicate an aspherical supernova expansion, the nature of these jet features is controversial.
Asymmetries in Cassiopeia A's outermost debris may offer clues as to the nature of the supernova explosion engine.
A chain reaction starting either from the center or from a surface close to the center is enough to explain star explosion. In order to explain "aspherical sometimes even jet-like supernova explosions" we only have to add the principle of rotation-caused oblateness.
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Reality Check in #55:
That the "nature of these jet features is controversial" does not support an imaginary "principle of rotation-caused oblateness".
Take the left side of this figure:
Assume that this is a contracted fast-rotating star and that a chain reaction is spreading in the red-colored center. Isn't it obvious that effects from the central explosion will reach the surface at first close to the poles, and that the equator is best protected against the effects from the central explosion?
In fast rotating stars, excess pressure created by e.g. normal nuclear fusion might even steadily escape towards the poles, thus giving rise to bipolar jets:
"An astrophysical jet is a phenomenon often seen in astronomy, where streams of matter are emitted along the axis of rotation of a compact object. While it is still the subject of ongoing research to understand how jets are formed and powered, "
In any case, we know that contraction increases oblateness of a rotating star. And we know that such a deviation from spherical form entails an asymmetry in dissipation of (explosive) energy (resp. pressure and temperature) to the surface.
Lurch in #54:
I only skimmed after the first several posts, but feel much corrective commentary has been supplied. I'll just throw this in there.
"Corrective commentary" would only be possible if something were wrong. It is obvious that some of my premises and conclusions disagree with currently accepted theories. Yet such calling into question of accepted beliefs is at the heart of fundamental scientific progress.
Lurch in #54:
For a core collapse supernova, the only relevant mass which goes to making up the remnant is that in the roughly Earth-sized, solar-mass core, which collapses into a neutron star. The rest of the envelope outside this is blasted away. And so calculations of angular momentum must be restricted to this pretty miniscule object, not the entirety of the star just prior to obliteration of the envelope.
Sun density at the center is assumed to be ~ 5p15 = 150,000 kg/m3. Mean density of the Earth is ~ 3p55 = 5500 kg/m3. Thus the Earth-sized core of the sun has less than 30 terrestrial masses, far too low for even becoming a white dwarf ("A white dwarf is very dense: its mass is comparable to that of the Sun, while its volume is comparable to that of Earth."). It seems to me that you confuse sizes before and after the onset of contraction. (See also end of #38.)
Lurch in #54:
In shrinking down from Earth- to city-sized, the surface gravity will be astoundingly high; the object is very deep in its gravity well and so can have its surface compressed to the same density as at the center.
For the surface your "deep in its gravity" means high acceleration (unit: m/s2) and low gravity potential (unit: m2/s2). Pressure (unit: kg ∙ m/s2 per square meter) is a completely different category. Independently from gravity, pressure on an ideal (upper) surface is always zero. (See also #20.)
Lurch in #54:
Essentially the entirety of the envelope is accelerated to beyond escape velocity and thoroughly dispersed, leaving nothing of note from which to build another star/planet system.
Look again at the debris expansion after the Cassiopeia star-explosion:
If we explain the asymmetry of the ejected material by rotation-caused deviation from spherical form then we have to conclude that the "jets" move in direction of the rotation axis and the "gaps in the spatial distribution of outlying ejecta" are rather in the equatorial plane.
How do you exclude this hypothesis: Ejected material lacking nearby the equatorial plane at big distances is still gravitationally bound to the remnant at small distances, possibly giving rise to a planetary system in this equatorial plane.
TRAPPIST-1 with exoplanets paradigm of next-generation planetary system
From Wikipedia:
TRAPPIST-1 is an ultra-cool dwarf star located 39 light-years away from Earth in the constellation Aquarius [17p37 meter since 1 light-year ≈ 15p946 m ≈ 16p1 m].
In 2015 astronomers discovered three Earth-sized planets orbiting the dwarf star. On 22 February 2017, astronomers announced four additional exoplanets around TRAPPIST-1.
[The star] is approximately 8% the mass of and 11% the radius of the Sun. It has a temperature of 2550 K. In comparison, the Sun has a temperature of 5778 K.
The star is metal-rich, with a metallicity [Fe/H] 109% the solar amount. This is particularly odd as such low-mass stars near the boundary between brown dwarfs and hydrogen-fusing stars are expected to have considerably less metallic composition than the Sun.
It seems that the current theories of stellar classification and evolution have become as outdated as the epicycle theories at the times of Johannes Kepler (1571-1630).
Mass of Trappist-1 is given as 84 ± 10 Jupiter masses, resulting in ~ 1029 ∙ 1.6 kg = 29p16 kg. For comparison Earth: 24p6 kg, Jupiter: 27p19 kg, Sun: 30p2 kg.
A normal process of accretion could not have compressed this small mass of ~ 10% = 9n1 of our sun into such a dense star.
Mean density of Trappist-1 turns out to be ~ 4p76 = 76000 kg/m3, and is thus ~ 55 times higher than mean density of both Jupiter (~ 3p13 = 1300 kg/m3) and Sun (~ 3p14 = 1400 kg/m3), and ~ 14 times higher than mean density of the Earth (~ 3p55 = 5500 kg/m3). Mean density of Trappist-1 is also higher than the density of any material on or in the Earth.
The most obvious hypothesis for such a strongly compressed star with relatively high metallicity is formation by star-explosion from a previous-generation star as presented in #1.
From Seven temperate terrestrial planets around the nearby ultracool dwarf star TRAPPIST-1, 2017:
The derived planets' orbital inclinations are all very close to 90°, indicating a dramatically coplanar system seen nearly edge-on.
We have to conclude: The planetary plane representing this "dramatically coplanar system" comes close to the equatorial plane of the rotating previous-generation star of Trappist-1, which gave rise to the current Trappist-1 planetary system by means of a huge star explosion.
By the way, also the brown dwarfs Epsilon Indi Ba and Bb must be remnants of star explosions, if currently assumed values for mass and radius are correct, since these values entail stars smaller than Jupiter but with mass densities similar to or even higher than Trappist-1.
Thus, we have two completely different kinds of brown dwarfs: 1) first-generation stars not massive enough to sustain substantial nuclear fusion and 2) small remnants of explosions of big previous-generation stars possibly containing neutron-star cores (see #28).
Lurch in #54:
Finally, as I understand it, the solar system's chemistry requires that it incorporated not just the debris from one or more supernovae, but also the contributions of the effluvia from less massive stars that expired less violently. In other words, numerous previous stars had to already have 'polluted' the primordial gas, so that three kinds of contributors left their imprint; primordial gas, red giant effluvia and supernova-enriched products.
A major problem of such an origin from matter of multiple stars consists in short-lived radionuclides (SLRs) present in the early solar system, especially those with mean lives τ of less than 5 million years such as: 10Be (6p22 year), 26Al (6p103 yr), 36Cl (5p43), 41Ca (5p15), 60Fe (6p22).
Half-life t1/2 is mean lifetime τ times natural logarithm of two. Thus we get: t1/2 ≈ 0.7 τ. A mean life of e.g. 6p1 = 106 years entails a half-life period of 5p7 = 105 ∙ 7 yr. After 10 times this period, i.e. after only 6p7 years, the quantity of such a short-lived radionuclide decreases to 1 / 210 = 1 /1024 ≈ 0.001 = 7n1 of its original quantity. After further 10 half-life periods, the quantity is further reduced from 0.001 to 0.000001, i.e. from 7n1 to 4n1.
For comparison: "The oldest inclusions found in meteorites, thought to trace the first solid material to form in the pre-solar nebula, are 4568.2 million years old [~ 9p457 yr], which is one definition of the age of the Solar System." (Source)
Quotes from INJECTION OF SHORT-LIVED RADIONUCLIDES INTO THE EARLY SOLAR SYSTEM FROM A FAINT SUPERNOVA WITH MIXING FALLBACK, 2008:
Several short-lived radionuclides (SLRs) were present in the early solar system. Stellar nucleosynthesis has been proposed as the mechanism for the production of SLRs in the solar system, but no appropriate stellar source has been found that explains the abundances of all solar system SLRs.
The SLRs with relatively long mean lives, such as 107Pd, 129I, 182Hf, and perhaps 53Mn, may have been products of steady state nucleosynthesis in the Galaxy, while those with mean lives (τ) of <5 Myr, 10Be (τ = 2.2 Myr), 26Al (τ = 1.03 Myr), 36Cl (τ = 0.43 Myr), 41Ca (τ = 0.15 Myr), 60Fe (τ = 2.2 Myr), and possibly 53Mn (τ = 5.3 Myr), should have been produced either by energetic-particle irradiation in the early solar system or by stellar nucleosynthesis just prior to or shortly after the birth of the solar system.
The paper concludes:
However, in either case, the supernova explosion should have occurred near the solar system materials, which supports the idea that the solar system was born in a star cluster containing massive stars. The lifetime of the star cluster is several to 10 Myr, within which only massive stars (>20-25 Msun) explode. The proportion of massive stars in a cluster is low, and thus it may be highly unlikely that multiple supernovae brought SLRs into the solar system materials within the lifetime of the star cluster.
In the [proposed] model for a faint supernova with mixing fallback, solar system SLRs with mean lives of <5 Myr [six.po five years] could be from a single supernova.
This "single supernova", this "faint supernova" of the paper was our Sun itself which exploded ~ 9p46 = 4.6 billion years ago giving rise to the protoplanetary disk of our planetary system.
Such star-explosions of fast rotating stars also explain the commonness of debris disks which are circumstellar disks of dust and debris in orbit around both "mature" and "young" stars. The assumption that such gravitationally bound debris stems from explosions of other stars is rather difficult to defend.
Supernova fallback origin of a debris disk
From the abstract of A debris disk around an isolated young neutron star, 2006:
Pulsars are rotating, magnetized neutron stars that are born in supernova explosions following the collapse of the cores of massive stars. If some of the explosion ejecta fail to escape, it may fall back onto the neutron star or it may possess sufficient angular momentum to form a disk. Here we report the discovery of mid-infrared emission from a cool disk around an isolated young X-ray pulsar. The disk does not power the pulsar's X-ray emission but is passively illuminated by these X-rays. The estimated mass of the disk is of the order of 10 Earth masses, and its lifetime (>∼106 yr) significantly exceeds the spin-down age of the pulsar, supporting a supernova fallback origin. The disk resembles protoplanetary disks seen around ordinary young stars, suggesting the possibility of planet formation around young neutron stars.
This 2006 paper shows that the hypothesis protoplanetary disks originating from star explosions isn't even novel, since it is essentially the same as supernova fallback origin of a debris disk.
Only the central role of such explosive star metamorphosis for cosmic evolution in general, and for formation of our planetary system in particular seems to have remained unrecognized.
Essentials of Star-explosions
According to classical mechanics, a sufficiently small piece ejected away from the surface of a spherically symmetric star has only two possibilities (in absence of effects from third bodies):
1) The piece falls back onto the surface (on a highly elliptical path or straight line)
2) The piece escapes the star's gravity (on a slightly curved path or straight line)
In case of an explosion of a spherically symmetric star without rotation, the explosion is spherically symmetric (apart from inhomogeneous clumping), and we get primarily* three categories of matter:
1) Matter remains more or less where it was before explosion since pressure from outside remains bigger than pressure from inside
2) Matter falls back after explosion since ejection velocity is smaller than escape velocity
3) Matter leaves the star's gravity since ejection velocity is higher than escape velocity
* Matter can at least in principle reach an orbital path around
the remnant by collisions with other ejecta, or by further explosions outside
the exploding star.
Only if the star loses a relevant part of its mass during explosion, pieces
having been ejected (or later deflected) in non-radial directions may remain on
(highly) elliptical orbits around the star, since diminished gravity can no
longer accelerate the ejected pieces back to the surface. Yet since
distribution of such orbital planes is fully random with zero total angular
momentum, (most of) these ejecta will ultimately fall back onto the star by
mutual interactions (collisions).
Something like a debris resp. protoplanetary
disc can only emerge from the explosion of a rotating star. The bilateral and
circular symmetry of a rotating star obviously
leads in principle to a bilaterally and circularly symmetric explosion. Both
theoretical arguments and astronomical data suggest that the concentration of
ejected mass and its kinetic energy is lowest at low altitudes near the equator
and highest at high altitudes near the poles.
An example of a star explosion is the Homunculus Nebula, which originated from
an Eta Carinae outburst which became visible on Earth in 1841. Quotes from THE STRUCTURE OF THE HOMUNCULUS: I. SHAPE
AND LATITUDE DEPENDENCE FROM H2 AND [Fe II] VELOCITY MAPS OF ETA
CARINAE, 2006:
"The maximum radial expansion speed does not occur at the pole, but at latitudes around 6570° (Fig. 5a)."
"Figure 5b indicates
that most mass lost during the Great Eruption was aimed to high
latitudes. Only 25% of the total Homunculus mass was ejected at 0° < θ < 45°, with the remaining 75% ejected between 45° and the pole.
The latitudinal distribution of the ejecta's kinetic energy is even more
extreme, with almost all the mechanical energy (∼94%) escaping between 45° and the pole. The efficiency of imparting
mechanical energy to the ejecta seems to peak at latitudes around 60-65°, while
the peak mass loss occurs around 5060°."
"[T]he concentration of mass at high latitudes suggests that the original
explosion itself directed the mass and momentum toward the poles. An
alternative way to express same result is that perhaps much of the mass that
would have been ejected at 040° failed to reach escape velocities and fell
back onto the star.
In any case, having the majority of the mass a significant fraction of the
total mass of the star lost at polar latitudes will affect the star's angular
momentum evolution. A polar explosion will tend to take away less than its
share of angular momentum, leaving the post-outburst star with higher angular
momentum per unit mass."
"The differences between a spherical shell and the Homunculus are
striking. This latitudinal behavior strongly refutes the idea that a bipolar
nebula like the Homunculus was caused by an otherwise spherical explosion or
wind that is simply pinched by a pre-existing circumstellar torus, because in
that case we would expect to see more mass at low latitudes."
Ejecta at high altitudes (close to the poles) from rotating stars
behave as ejecta from non-rotating stars do. They normally either fall back
onto the surface or escape from the star's gravity. Distance from explosion to
surface contains the least mass at the poles, and inertial resistance to
explosive pressure resp. energy is smallest. Thus ejection energy from the
surface is maximal at the poles.
Concerning total ejected mass of the 1841 outburst of Eta Carinae we have to
conclude:
o The majority of the corresponding material ejected at altitudes higher than ~ 70° has dissipated into space, due to higher and more variable speeds. Maybe the explosion even started with bipolar jets from the poles.
o Relevant parts of the confirmed "H2 layer" close to the poles consist of material deviated from lower latitudes, e.g. 6070°. This explains that the "maximum radial expansion speed does not occur at the pole, but at latitudes around 6570° (Fig. 5a)".
wogoga in #81:
Something like a debris resp. protoplanetary disc can only emerge from the explosion of a rotating star. The bilateral and circular symmetry of a rotating star obviously leads in principle to a bilaterally and circularly symmetric explosion. Both theoretical arguments and astronomical data suggest that the concentration of ejected mass and its kinetic energy is lowest at low altitudes near the equator and highest at high altitudes near the poles.
Let us assume an idealized explosion of a fast-rotating star (where altitude 0° means equator and 90° is used for both rotation poles):
00° 20° : almost all
ejecta fall back
20° 30° : relevant mass remains in orbit
30° 90° : almost all ejecta leave the star remnant
After short-term stabilization (when gravity of leaving ejecta becomes negligible), relevant mass is primarily orbiting at latitudes 20° 30°, mostly on highly elliptical paths. Due to the rotation before star explosion, total (resp. maximum) angular momentum of this orbiting material corresponds to the equatorial plane (because of mutual compensations of e.g. latitude -25° and +25°). Disappearing pressure from outside, lingering heat and the decay of short-lived radionuclides produced during the explosion transform such orbiting ejecta into a cloud of hot gases and dust particles.
Due to the circular symmetry before and during explosion, collisions between cloud particles from the 20° 30° latitudes will fill more and more the empty region in the equatorial plane. Orbits also become more and more spherical. The result is a still hot, regularly orbiting protoplanetary disk.
The Earth has an orbital radius of r ≈ 1 AU ≈ 11p15 meter and an orbital velocity of v ≈ 30 km/s = 4p3 m/s. Angular momentum Lm per mass around the Sun results in Lm ≈ v ∙ r ≈ 4p3 m/s ∙ 11p15 m ≈ 15p45 m/s m. It is a reasonable assumption that the material eventually having formed the Earth had on average a similar angular momentum at the moment of star explosion. If we assume a distance of one solar radius r = 1 Rsol ≈ 8p7 m from rotation axis for such "future Earth material", the material should have rotated at a speed v ≈ Lm / r ≈ 15p45 / 8p7 m/s ≈ 6p64 m/s = 6400 km/s.
The planet with the highest angular momentum per mass Lm is Neptune. Orbital radius of Neptune is r ≈ 30 AU ≈ 12p45 meter and mean orbital velocity is v ≈ 5.4 km/s = 3p54 m/s. We get Lm = v ∙ r ≈ 16p24 m/s m. At a distance of one solar radius, such "future Neptune matter" would have rotated at v ≈ Lm / Rsol ≈ 16p24 / 8p7 ∙ m/s ≈ 7p23 m/s = 23,000 km/s, and at a distance of 10 Rsol at ~ 6p23 m/s = 2300 km/s. For comparison, light speed is ~ 8p3 m/s = 300,000 km/s.
Under the premise of solid-body rotation before explosion, the conclusion seems reasonable that the material having led to Neptune was on average ~ 0p55 = 5.5 times more distant from the rotation axis of the exploding star than the material having led to the Earth, since orbital angular momentum per mass of Neptune is ~ 16p24 / 15p45 ≈ 0p55 = 5.5 times higher than the one of Earth.
From all this follows: The previous incarnation of our Sun was a fast-rotating big star with quite substantial angular momentum. Angular momentum per mass must have been bigger for the outermost equatorial layers than now for Neptune. Most of the mass and of total angular momentum got lost during the explosion. Thus even the majority of ejecta from the equator must have left the remnant. The highly compressed matter rotating at relatively low speeds close to the center of the old star then started to expand as outside pressure from disappearing outer layers decreased. The result was a star capable of further evolving into our present Sun.
The Triple-Ring Nebula around Supernova 1987A
Quotes and picture from The Triple-Ring Nebula: Fingerprint of a Binary Merger (or Supernova 1987A: a Mystery Solved):
Supernova 1987A (SN 1987A), the first naked-eye supernova observed since Keplers supernova in 1604, was an anomalous supernova that has confounded astronomers for many years. Its anomalies have long been attributed to the merger of two massive stars that occurred some 20,000 years before the explosion, but so far there has been no conclusive proof that this merger took place.
Figure 2: The triple-ring nebula around SN 1987A. Left Panel: Hubble Space Telescope image of the nebula. Right Panel: Three-dimensional geometry of the three rings. The supernova is at the center of the inner ring, the outer rings are displaced above and below the central ring plane. The rings are seen in projection by the observer (us) as indicated. All of the material in the rings was ejected some 20,000 years before the explosion.
The nebula is almost axisymmetric. This generally suggests that rotation may have played an important role in the shaping of the nebula. However, any star that was rapidly rotating early in its evolution could not have been rapidly rotating as a supergiant. This essentially ruled out that the progenitor star could have been a normal single star and strongly suggested that the progenitor was a member of a binary system, where two stars orbit each other.
A main problem of the presented binary-system hypothesis is the main inner ring. Two quotes from the corresponding article published in Science, 2007:
We modeled the red supergiant as a poly-trope with a central point source of 8 MSun, representing the compact core of the star and the immersed companion, and an envelope mass of 12 MSun; the initial radius of the star was taken to be 1500 RSun. We then mimicked the initial spin-up phase by adding angular momentum to the envelope over a period of ∼6 years until all of the angular momentum from the initial binary was deposited in the envelope. Because of this spin-up, the envelope became highly nonspherical and took on a disklike shape.
In our best model, no matter was ejected in the equatorial direction. However, because the merged object has much more angular momentum than a more compact blue supergiant could have, the merged object has to lose this excess angular momentum, most likely in the form of a slow equatorial outflow, as it shrinks to become a blue supergiant.
Summary of this hypothesis: The inner ring has been caused by a slow equatorial outflow due to necessity of losing excess angular momentum. Isn't this purely ad-hoc? In order to move away and to leave the star "envelope" (with a radius of 1500 RSun ≈ 7 AU ≈ 12p1 meter), the material now forming the inner ring (at a distance of 0.66 light year ≈ 42,000 AU ≈ 4p42 AU ≈ 15p6 meter) must have gained energy. From where could this energy have come from? Due to gravity darkening, also solar wind is normally weakest on the rotational equator. And only very special cases allow such a transfer of angular momentum at a distance.
Mass transfer and star-mergers in binary systems are much less
common than currently assumed. Conservation of energy and momentum makes it
very unlikely that matter from one star or the whole star of a binary system
can reach the other. The belief in the commonness of spiraling in and out of
moons, planets and stars is also a result of the belief in the Apollo "moon rocks" samples, some or most of which stem from the Earth's crust. Part of the solution to the problem "Earth crust brought
back by Apollo from the Moon" became the "fact" that our moon
spiraled out from an orbit very close to the Earth. And spiraling in
(outside an atmosphere) is even more unlikely then spiraling out.
An alternative to the proposed
binary-star-merger is the hypothesis of a simple star-explosion caused by
contraction around 4p2
= 20,000 years before Supernova 1987A. Gravitational collapse had increased oblateness (flatness) of the
fast rotating precursor of Sanduleak -69° 202. Gravity-potential energy transformed into thermal energy during
contraction eventually triggered some kind of chain reaction leading to a
supernova-like "primary explosion". Already ~ 4p2 = 20000 years after this
"primary explosion", the still huge remnant (a contracting blue
supergiant with a luminosity of ~ 5p1 = 100,000 times the Sun's luminosity) exploded anew as SN 1987A.
According to this hypothesis, the three rings are density enhancements of
ejected materials from the older "primary explosion". Essential
principles of such density enhancements are:
1) Ejection speeds of materials leaving the star depend on latitude. The closer to the poles the higher are ejection-speed averages.
2) Mean ejection speeds are distributed around such latitude-dependent values. The more clumped-together ejection-speeds at given latitudes are (for whatever reason), the more pronounced are ejection density enhancements and the more likely become distinct rings and surfaces such as hourglass nebulas (moving away from the center).
3) Ejection materials from different ejection depths, times and latitudes collide and thus form discontinuous density enhancements (by mutually adapting kinetic energy and momentum).
Mixing caused by the previous "primary explosion" also explains the anomalously high abundance of helium found on Sanduleak -69° 202 before SN 1987A.
By the way, before the fact it was generally accepted that blue supergiant stars like Sanduleak -69° 202 cannot explode as a supernova. This too shows that our understanding of star evolution is still far more hypothetical than generally admitted.