The Grand Tack is a scenario for early inner Solar System evolution, published in 2011 in the journal
Nature([arXiv]).
The Grand Tack model of terrestrial planet formation has emerged in recent years as the premier scenario used to account for several observed features of the inner solar system. It relies on the early migration of the giant planets to gravitationally sculpt and mix the planetesimal disk down to ∼1 au, after which the terrestrial planets accrete from material remaining in a narrow circumsolar annulus. While making use of a recent model of the protosolar disk that takes into account viscous heating, including the full effect of type 1 migration, and employing a realistic mass–radius relation for the growing terrestrial planets, the results show that the canonical tack location of Jupiter at 1.5 au is inconsistent with the most massive planet residing at 1 au at greater than 95% confidence. This favors a tack farther out at 2 au for the disk model and parameters employed. Of the different initial conditions, we find that the oligarchic case is capable of statistically reproducing the orbital architecture and mass distribution of the terrestrial planets, while the equal-mass embryo case is not.
Type I planetary migration was the starting point of planetary migration theories, generally applicable to all planets unless special circumstances are met. Still, it is the most troublesome because it indicates that all planets should disappear in their host stars and further research in the nature of protoplanetary disks has to be made to explain why this isn’t the case in at least thousands of cases where we indeed can observe (exo)planets.
Type II applies for massive planets that form a gap, which frees it from the most Lindblad resonance torques and lets it wander through the disk slower. Type II migration timescales are of the same order as disk lifetimes, so a lot of massive planets survive and occupy a wide range of possible semi-major axes around their stars.
Type III is quite an obscure migration mechanism, only applying to a small domain of planets and disks but probably including Saturn. It is by far the fastest of these three modes but doesn’t pose the same danger Type I does. If we assume that the Grand Tack model applies to our solar system, we can assume that the Sun’s protoplanetary disk was much more dense and turbulent than the simple models assume - this can explain the survival of the terrestrial planets and giant planet cores via stochastic migration and/or turbulences, as well as enable Saturn to migrate via Type III.
Semi-major axis development of a Saturn-sized planet during Type III migration. We note the abrupt ending of the fast Type III migration regime at ≈ 52 orbits. [Peplin ́ski et al., 2008]
Walsh et al. (
2011) proposed the so-called Grand Tack scenario, wherein the early, gas-driven coupled migration of Jupiter and Saturn sculpts the planetesimal disk and truncates it near 1 au (astronomical unit: the distance from the Earth to jolly old Mr Sun).
The Grand Tack, taken from sailing*, at least partially explains the formation of a high-density region in the inner disk, although it cannot explain the existence of an inner cavity inside roughly 0.7 au. The inclusion of this scenario leads to a broad outline of how the early solar system evolved. First, Jupiter is assumed to form before Saturn, clearing the gas in an annulus with a width comparable to its Hill radius, and undergoing inward Type 2 migration (Lin & Papaloizou
1986). The inward migration of Jupiter shepherds material toward the inner portion of the disk while also scattering other material outward, creating an enhanced density region for terrestrial planet formation and mixing planetesimals from the innermost and outer portions of the protoplanetary disk. Once Saturn grows to about half of its current mass (Masset & Casoli
2009), it is assumed to partially clear the disk in its vicinity, migrate rapidly at first to catch up with Jupiter, and subsequently become trapped in a mean-motion resonance near Jupiter, presumably the 2:3 resonance (Masset & Snellgrove
2001; Pierens & Raymond
2011) but it may also have been the 2:1 (Pierens et al.
2014). In this process, these two giant planets clear the disk together. The torque from the interaction with the disk is stronger for a shorter separation between the planet and the disk edge. Since Jupiter and Saturn are interacting and Jupiter is more massive, it is reasonable to think that Saturn is pushed outward by Jupiter's perturbation, and the separation from the disk edge is smaller for Saturn than for Jupiter. Thus, the torque on Saturn can be larger despite the planet's lower mass. The interaction with Jupiter prevents Saturn from creating a cleared annulus in the disk and allows gas from the outer disk to flow past Saturn and into the inner disk. If the gap-crossing disk gas flow is large enough, then the Jupiter-Saturn pair can migrate outward (Masset & Snellgrove
2001; Pierens & Nelson
2008).
Consequently, the planets reverse their migration: they tack as a sail boat would change its direction by steering into and through the wind. Once the giant planets have completed this early migration phase, have left the inner solar system, and settled in the vicinity of their present positions, terrestrial planet formation could proceed as before, but only (as advocated by Hansen
2009) from material in a narrow circumsolar annulus. In this manner, Walsh et al. (
2011) successfully reproduced the mass-semimajor axis distribution of the inner planets if the reversal of Jupiter occurred at 1.5 au because they truncated the inner edge of their planetesimal disk at 0.5 au. A successful feature of their model is that it also accounts for the apparent compositional differences across the asteroid belt (DeMeo & Carry
2014).
The `Grand Tack' model thereafter proposes that the inner Solar System was sculpted by the giant planets' orbital migration in the gaseous protoplanetary disk. Jupiter first migrated inward then Jupiter and Saturn migrated back outward together. If Jupiter's turnaround or "tack" point was at ~1.5 AU the inner disk of terrestrial building blocks would have been truncated at ~1 AU, naturally producing the terrestrial planets' masses and spacing. During the gas giants' migration the asteroid belt is severely depleted but repopulated by distinct planetesimal reservoirs that can be associated with the present-day S and C types. The giant planets' orbits are consistent with the later evolution of the outer Solar System. Some uncertainties remain regarding the Tack mechanism itself; the most critical unknown is the timing and rate of gas accretion onto Saturn and Jupiter. Current isotopic and compositional measurements of Solar System bodies -- including the D/H ratios of Saturn's satellites -- do not refute the Grand Tack model.
In the last few decades we have learned that planets have the capability to move around - their orbits are not static. While the discovery of interesting planets around other stars really demonstrate dramatic migration effects (Hot Jupiters for example), we now find signs all over our own Solar System that point to sometimes violent migration of our own planets. Understanding when and how our own planets migrate is a major goal of dynamicist studying the formation and evolution of our Solar System. We know of three major types of planetary migration: gas migration, planetesimal scattering migration and planet-planet scattering.
After a star forms a disk of gas survives around for for a few (1-10) million years. The disk of gas far outweighs the total amount of solid material that could form, and thus given the right conditions can push planets rapidly and great distances. There are a handful of studied types of gas migration, each of which depend on many hard to study parameters, such as the viscosity of the gas or the temperature gradients existing in the proto-planetary disk. However, knowing that gas is required fundamentally restricts these modes of migration to the earliest 1-10 million years of a Star's lifetime. For context, in our own Solar System it is thought that the giant planets formed in a few million years (before the gas disk was disipated by radiation pressure and increasing radiant heat), while the terrestrial planets took 10-100 million years to form.
In some scenarios, including our own Solar System, it is thought that there are regions where large disks of small planetesimals (km to 100s of km size objects) form rather than a few large planets. These smaller bodies can easily be tossed around the Solar System if they come into contact with a planet (Jupiter easily scattering an asteroid out of the Solar System). Each time a planet scatters a smaller planetesimal there is an exchange of angular momentum, which given enough encounters with small bodies can change the orbit of the planet in a significant way. This is called planetesimal scattering migration, and is thought to have played a major role in the evolution of Neptune. This type of migration can happen any time in the history of a Solar System, as long as there remains a sizeable population of small bodies -- for example the today's asteroid belt would not nearly be massive enough to move any planets.
Finally, the most dramatic events in a Solar System's history happens when planets end up on crossing orbits. In these cases planets orbits can become very eccentric (elongate) and they can excite and remove otherwise stable resevoirs of planetesimals and planets in a Solar System. These instabilities are thought to have numerous causes, distant stellar companion (Kaib et al. 2013), long-term interactions with massive disks of planetesimals (Levison et al. 2011) or simply inheritly unstable and chaotic orbits. It is generally thought that most instabilities happen after the gas-disk has dissipated, as the gas has a damping affect on the orbits of the planets keeping their eccentricities low and stable. This type of migration results in a rapid reconfiguring of a planetary system and probably results in short episodes of violent collisions of any small body populations.
An important piece of scientific data from the Apollo missions was radiometric dates for major impacts events on the Moon. With no atmosphere to erode away impact histories, the lunar surface can report on most of the history of the Solar System. The data from those missions, and also from lunar meteorites (chunks of the Moon liberated during impacts that eventually hit the Earth), suggest that the Moon (and therefore the Earth) suffered a surge of impacts around 4 billion years ago. This bombardment is relatively "late" in the history of the Solar System, as nearly 600 million years would have passed from its formation 4.56 billion years ago, before this "late heavy bombardment" (LHB) would have taken place. Such an impact spike is hard to explain in a quiescent and stable Solar System. This LHB has been linked to an instability and episode of planet-planet scattering among our giant planets -- commonly referred to as the "Nice Model" (Tsiganis et al. 2005, Gomes et al. 2005, Levison et al. 2011). This instability has been used to explain numerous properties of the Solar System (Jupiter's Trojans, Irregular Satellites, the structure of the Kuiper Belt etc.), and its violent nature makes it a viable and attractive cause of the LHB.
Thus planetary migration by way of planet-planet scattering (and also planetesimal scattering migration of Neptune) is thought to be responsible for the final reshaping of our Solar System 4 billion years ago. However, there are many problems with our understanding of the inner Solar System that may be explained with earlier gas-migration of our planets. Given the relatively short lifetime of the gaseous disk around our Sun, these events are restricted to the first few million years of our Solar System's lifetime, but the power of gas migration to push giant planets large distances rapidly makes for significant consequences.
Numerical simulations then produce two big earth-mass planets equivalent to Venus and Earth inside this annulus. Mars only accretes a small fraction of this. The same applies to Mercury on the inner side of the disk. The Grand Tack doesn’t attempt to explain the inner truncation, and models often ignore Mercury. Simulations often fail to produce Mercury-like planets since the planetary embryos at the start of the simulation already have a big portion of Mercury’s mass. Since collisions are treated as perfect mergers with no scattered material, most resulting planets are more massive than Mercury [Jacobson and Morbidelli, 2014].
An overview of the development of the giant planets in terms of their masses (top) and semi-major axes (bottom). They start further in than they are today, and begin migrat- ing inwards. Jupiter is the first as it forms earliest, then the others follow. As Jupiter has fully cleared a gap around it, it accretes almost no mass during this. Fulfilling the requirements for Type III migration, Saturn catches up very rapidly and subsequently gets in resonance with Jupiter and they mi- grate outwards. After 200 kiloyears, they reach Uranus and Neptune and all four plan- ets are in resonance together. (From [Walsh et al., 2011])
We now look at Jupiter. The giant planet starts to form his gap at his current mass and at a distance from the sun of roughly 3.5 AU. When its gap has fully formed, Jupiter starts his inwards migration of Type II. We might speculate if Jupiter has formerly undergone Type III migration and thus might originate from farther outside, but this makes no difference for the Grand Tack. As mentioned above, migration speed doesn’t change the outcome of the simulations much, but usually a migration time of 0.1 Myr is given [Brasser et al., 2016]. In this time, Jupiter moves from his initial location at 3.5 AU to the tacking position at 1.5 AU [Walsh et al., 2011]. This is equivalent to a disk truncated at 1 AU and therefore in accordance to [Hansen, 2009]. If we include Type I migration of our embryos and employ a more realistic disk model ([Brasser et al., 2016] called the one from [Walsh et al., 2011] ’artificial’) we see that all our planets are too close to the Sun. This means that Jupiter’s tacking location must be farther out, probably at 2 AU. Also of importance is the age of the disk. As the disk becomes older, more and more planetesimals become lost and dynamical friction gets weaker. So, the formation time of Jupiter, the time it takes for Jupiter to reach the inner disk respectively has an influence on the eccentricity and inclination of the embryos and planetesimals.
When Jupiter marches inwards, what happens to the objects (S-type planetesimals/asteroids, embryos) it encounters? Most of these are being transported inwards. [Walsh et al., 2011] explain this with resonance trapping by Jupiter, with excitation of their eccentricity, which brings them closer inside and then lets these objects stay there as the gas damps their eccentricity, and with gas drag. A fraction of the matter gets scattered outside Jupiter’s orbit when it is gravitationally disturbed by Jupiter. Meanwhile, the higher concentrated mass in the inner disk leads to a sustainably accelerated planet formation process.
Giant planets form faster if they are more massive because their gravitational cross-section enhances their mass accretion rate. The higher accretion rate increases the planet mass further. So, when Jupiter has formed and is on its way towards the inner disk, Saturn has still less than the mass it has today. The exact value of Saturn’s mass is not known since the minimum mass for Type III migration depends on the disk parameters which in turn are also not well constrained. [Walsh et al., 2011] and [Brasser et al., 2016] give a value of approximately half of today’s Saturn mass. [Masset and Papaloizou, 2003] put it at one Saturn mass, making it accrete almost no matter during its migration. This is an unrealistic assumption, and in the most simulations Saturn actually gains a big portion of its mass.
Saturn’s migration happens really fast, and can be taken as instantaneous compared to the slow migration of Jupiter (a few hundred years opposed to about 100 kyr). As Saturn approaches Jupiter it crosses a few lines at which they fall into mean-motion resonance to each other. At these points their eccentricity increases rapidly, but their inwards migration does not stop. This is because the eccentricities need to be higher than a certain value to couple the two planet’s orbits together [Masset and Snellgrove, 2001]. This only happens when they finally reach the 2:3 resonance which is the most cited resonance, although sometimes 1:2 is also considered. The 1:2 resonance applies for disks with low overall mass and low viscosity, implying a low aspect ratio of disk height to radius [Pierens et al., 2014]. This also is the resonance for which the Nice model, that explains the later evolution of the solar system millions of years after the Grand Tack, works better. We will use the value of 2:3 here since we are assuming a more massive disk.
When Jupiter and Saturn are in their final resonance, their orbital period ratio is 2:3 and therefore, according to Kepler’s laws, their semi-major axes have a ratio of aS : aJ = 1.31. These ratios are conserved until the gas disk dissipates and Jupiter’s and Saturn’s migration stops.
Mean-motion resonance can let planets move together as one. And not just two planets, but even a whole chain of planets. It is assumed that Uranus and Neptune also formed nearer to the sun than they are today. As Jupiter and Saturn move outwards, they fall into resonance with Uranus and then Neptune too, producing a line of planets moving outwards together and enlarging the scale of the planetary system [Walsh et al., 2011].
The orbits of the four outer planets and the positions of the outer planetesimal disk particles at different times of the nice model, measured from beginning of planetary formation. a) The start of the simulation at 100 megayears. b) The beginning of the LHB at 879 megayears. c) during the LHB, only three million years later at 882 megayears. d) After the end of the LHB at 1082 megayears. At this point, 97 % of the planetesimal disk mass has been depleted, either through accretion or through scattering. Taken from one of the three papers that first proposed the Nice model in 2005, [Gomes et al., 2005].
But, how does this work? To avoid complexity we take a look only at our more important planets, Jupiter and Saturn. Consider Type II migration again. As the gap drives the gas out of those points in the disk where the strongest Lindblad resonances lie, their torques vanish and only the weaker ones farther away from the planet remain. We also note that, according to (8), the torque on a planet is proportional to its mass squared. Jupiter, as it has more mass, experiences stronger torques than Saturn at every possible Lindblad resonance. The resonance locked planets can be thought of as two planets sharing one large gap in the disk. Would there be only one planet, lets say Jupiter, it would rest in the middle of the gap. Approaching the inner edge would increase the outwards torques, since then stronger Lindblad resonances would appear and would push Jupiter back out again. The reverse would happen when the planet approaches the outer gap edge - it would be pushed inwards.
Now there are two of them. As Jupiter lies on the inner side, it experiences a positive net torque proportional to MJ. Saturn on the contrary receives negative net torque proportional to MS [Masset and Snellgrove, 2001]. Because Jupiter is much more massive than Saturn, the positive torque overweighs and the system of planets migrates outwards. The absolute torque acting on the system has to be corrected for the different distances of Jupiter and Saturn to the inner, outer edge respectively since different masses cause different gap widths, but this is only a small correction to the effect the mass difference between the planets causes (MJ/MS2 ≈ 10).
The largest population of remnant planetesimals still found in the inner solar system is the Main Asteroid Belt, "the Main Belt", located between 2.1-3.2 astronomical units (AU).
According to meteorite studies, many of the largest bodies there formed ~4.56 Ga during planet formation processes. Since that time, however, they have been subject to collisional and dynamical evolution. A problem in interpreting what we know about asteroids, however, is that collisonal and dynamical evolution are coupled to one other. For example, assuming a given dynamical excitation state for a small-body population, more collisional evolution takes place when a population is large than when it is small. Thus, if dynamical effects suddenly remove bodies from a population, disruption and cratering events must drop as well. Similarly, a population with low eccentricities and inclinations will undergo little collisional grinding, while one with large values will grind much faster. For this reason, we must examine what has been inferred about the collisional evolution of the asteroid belt. How it has been affected dynamically by the processes that led to the origin of our planets. Given the enormous number of possibilities that can take place in collisional evolution models for given assumptions, and the importance of dynamical excitation, dynamical removal, and stochastic breakup events, it is critical that planetesimal formation and collisional/dynamical evolution models be tested against as many constraints as possible. This potentially allows us to rule out certain scenarios and place higher degrees of confidence in successful solutions.
Collisional mechanisms were suggested previously and offer attractive solutions to many chondrule features (Krot et al., 2005;Sanders and Scott, 2012;Stammler and Dullemond, 2014;Dullemond et al., 2014Dullemond et al., , 2016Marrocchi et al., 2016). From a dynamical point-of-view, collisional interactions of planetesimals and embryos during accretion are inevitable and expected to create a vast amount of continuously reprocessed debris (Bottke et al., 2006;Carter et al., 2015;Jacobson and Walsh, 2015;Asphaug, 2017; Bottke and Morbidelli, 2017) that inherits the geochemical features from previous planetesimal generations.
16 Psyche makes its home in the
Asteroid Belt that lies between
Mars and
Jupiter. This giant metal asteroid is one of the most massive objects in the Asteroid Belt, categorised as a minor planet.
Astronomers think that 16 Psyche is the exposed core of a full planet that failed to further coalesce. NASA will be sending a probe to check it out in the next few years, and in the meantime, scientists are working to glean what they can from Earth.
If 16 Psyche is a protoplanetary core, it's possible that repeated impacts stripped it of its accumulating material. Planets are thought to form when their stars are very young -
possibly even in tandem - and are surrounded by a thick cloud of dust and gas. Material in this cloud starts to stick together, first electrostatically, then gravitationally as the object grows more massive.
As these bodies grow, they become hot and a bit molten, allowing material to move around. Core differentiation is the process whereby denser material sinks inwards towards the centre of the object, and less dense material rises outwards. For 16 Psyche to be a differentiated core, the protoplanet would once have had to have been much bigger than it is now.
Now, for the first time, 16 Psyche has been studied in ultraviolet wavelengths using the Hubble Space Telescope, revealing that, just as we thought, the dense chunk of space rock is remarkably metallic.
"We were able to identify for the first time on any asteroid what we think are iron oxide ultraviolet absorption bands," Dr. Tracy Becker said. "This is an indication that oxidation is happening on the asteroid, which could be a result of the solar wind hitting the surface."
All the standard planetary formation models, when applied to the solar system, are stymied by the “Mars Problem” and the “Main Belt Problem.” Most solar system formation models can explain the masses and orbits of the solar system’s four gas giant planets (Jupiter, Saturn, Uranus, and Neptune) as well as the masses and orbits of Mercury, Venus, and Earth. They predict, however, Mars should be 1.1–1.5 times more massive than Earth, that the Main Belt of asteroids should be much larger in terms of total mass and should include a few bodies as massive or nearly as massive as Mars (Mars = 0.11 Earth masses), and (3) the Main Belt should extend from Jupiter’s orbit to just outside Earth’s orbit.
Many have searched for a solution to the "Mars Problem." This problem is essentially the inability of modern computer simulations of terrestrial planet formation to create correct-size Mars analogs at the location, 1.5 AU, where we find Mars today. Typically the Mars-analogs are produced at 0.5 to 1.0 the mass of the Earth - much larger than its actual mass at 0.1 times the mass of the Earth. The figure to the right shows a plot from
Raymond et al. 2009 with the actual planets as the filled squares (with Mars at 1.5 AU), and the results from many simulations plotted as gray circles. At the location of Mars, the planets being formed in the simulations are 5-10 times too massive.
Simulated Mars always grows too big. They’re typically about the mass of Earth, about nine times more massive than the real Mars.
To date there are two viable solutions to the small Mars problem. The first is the
Grand Tack model, which proposes that the inner Solar System was sculpted by Jupiter’s migration. The second is the
Low-mass Asteroid belt model, which instead proposes that there was never sufficient rocky planetesimals between Earth and Jupiter’s orbits in the first place.
When planetary instability is triggered after 10 million years (Myr) in the proto-planetary disc, the asteroid belt gets really excited and so does Mars’ feeding zone. This has the effect of stunting Mars’ growth and simultaneously depleting the asteroid belt. The instability has little effect on the growth of Earth and Venus, so those planets end up much more massive than Mars, as in our actual Solar System. A nice solution to the small Mars problem.
After several hundred simulations. It was found that simulations that match the rocky planets best are those that also match the giant planets best. That is really nice because it’s simple: one event can explain the inner and outer Solar System in one fell swoop.
So now there are three competing models to explain the Solar System: the
Grand Tack,
Low-mass asteroid belt and Early Instability models.
* Grand or long tack - When you can't find a pattern to the wind shifts, sailing the long tack might become your primary strategy. Tack on the large headers, but don't be a slave to your compass. If you're not pointed at the mark, think about tacking. One side is advantaged - if due to more wind or a persistent shift, you may end up sailing the short tack first to get to that side. However, once you reach that advantage, continuing further on the short tack becomes much riskier.
See:
https://www.planetary.org/articles/20180601-mars-growth-stunted
See:
https://www.planetary.org/articles/20180601-mars-growth-stunted
See:
https://www.sciencealert.com/this-a...re-of-a-failed-planet-and-it-s-slowly-rusting
See:
https://www.researchgate.net/public...o_constrain_planetesimal_and_planet_formation
See:
https://static.uni-graz.at/fileadmi...atzka_thorsten/BachelorarbeitFelixTischer.pdf
See:
https://static.unigraz.at/fileadmin...atzka_thorsten/BachelorarbeitFelixTischer.pdf
See:
https://iopscience.iop.org/article/10.3847/0004-637X/821/2/75
See:
https://www.researchgate.net/publication/266024250_The_Grand_Tack_model_a_critical_review
See:
https://www.arxiv-vanity.com/papers/1409.6340/
Establishing the chain of events as the photo-planetary disc coalesces is very complicated as a result of the many variables involved: time, gravity, the mass of the planetesimals and the later planets themselves and their changing orbits. I hope the foregoing will serve to further flesh out the various theories at large concerning the planets, their formation and final alignment. In any case, had the bombardments not slowed and had Earth a different history in our solar system, we wouldn't be discussing these ideas here.
Hartmann352
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