Figure 1. All planets
and dwarf planets orbiting within 6 astronomical units (AU) of our Sun, shown
at their relative diameters.
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From afar, our Solar System looks regular and
well-organized. At its center is a large, massive sphere of incandescent gases
(the Sun) surrounded by eight smaller and less massive spheres of heavier
elements (the planets) distributed in concentric orbits out to a distance of
about 4.5 billion km/2.8 billion miles.
The orbital distribution of the eight planets also seems
regular, at least at first glance. Smaller, rocky worlds are confined to the
inner system, while larger, gaseous worlds dominate the outer system. Planet
sizes follow a curve, rising from the inner to the middle planets and then
declining again from the middle to the outer planets.
In more specific terms, mass and radius increase along
with distance among the three planets closest to the Sun (Mercury through
Earth). Both parameters peak at the orbit of the fifth planet, Jupiter, which is
almost a dozen times the radius and more than 300 times the mass of Earth. Then,
from Jupiter through Uranus, the seventh planet, both mass and radius decline
substantially along with distance from the Sun.
But this orderly progression of planet sizes has two
notable interruptions: Mars and Neptune. If the distribution of planets were truly
regular, Mars would be larger and more massive than Earth, and Neptune would be
smaller and less massive than Uranus. Instead, the Red Planet has only 53% of
Earth’s radius (0.53 Rea) and 11% of its mass (0.11 Mea), while the Azure
Planet, at 17.2 Mea and 3.9 Rea, has about 98% of the radius of Uranus but 119%
of its mass.
How did that happen?
In the present post I’m going to ignore the oddity of
Neptune and concentrate on the Martian half of the question. My rationale is
that Mars occupies our system’s classical habitable zone, and therefore – along
with Earth and Venus – plays a critical role in theories of the habitability of
extrasolar planets. If mass had been more uniformly distributed in the inner
Solar System, Mars would be more massive than it is. If its mass were in the
range of 1 to 2 Mea, Mars would likely be able to sustain a magnetic field,
plate tectonics, surface water, and long-term habitability. Therefore, if we
want to understand the potential system architectures that might support
life-bearing planets, we need to understand why Mars is so small.
Figures
1 and 2 highlight the Small
Mars Problem and the Great Martian Gap, which is the name I just invented for the
general depletion of mass between Earth and Jupiter. The planet Mars and the
dwarf planet Ceres orbit within this gap at 1.52 AU and 2.77 AU, respectively. With
a little more than 1% of the mass of our Moon, Ceres accounts for fully one-third
of all mass in the Asteroid Belt, which is concentrated between 2.2 and 3.3 AU
(the latter boundary provided by the 2:1 resonance with Jupiter's orbit; Jewitt
et al. 2009). The entire region between the orbits of Earth and Jupiter
contains less than 0.12 Mea, with little Mars accounting for 99% of the total. By
contrast, the region extending inward from Earth’s orbit to the Sun contains
1.87 Mea, yet Earth, the most massive object, accounts for only 53% of the
total.
Figure 2. The
Great Martian Gap
Blue numbers along the bottom refer to
astronomical units (AU), where the Earth/Sun separation = 1. Planets are shown
at their relative sizes and relative distances from the Sun, with separate
scales for radius and distance. As astronomers have long noted, mass is
severely depleted between the orbit of Jupiter at 5.2 AU and the orbit of Earth
at 1 AU (see Weidenschilling 1977).
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zigzag
migration
Recent studies by Konstantin Batygin & Greg Laughlin
(2015) and by Sean Raymond & colleagues (2016) have presented conflicting scenarios
to explain the Small Mars Problem and the Great Martian Gap. Both involve
zigzag migratory paths for Jupiter during the primordial phase of system
evolution.
Batygin &
Laughlin based their approach on earlier models
by Kevin Walsh & colleagues (2011) and Pierens & Raymond (2011), in
which Jupiter formed in the outer Solar System (somewhere beyond 3 AU) and then
migrated first inward and then outward again. The popular name for this scenario
(blogged here and here) is the Grand Tack. According to Batygin & Laughlin,
these maneuvers not only swept most solid mass out of the region exterior to
Earth’s present orbit, but also created an instability that emptied the region interior
to 0.7 AU.
Raymond &
colleagues took a very different approach based
on the “inside out” model of planet formation presented by Chatterjee & Tan
(2014). Contrary to his own earlier work, Raymond’s group proposed that Jupiter
formed in the inner Solar System near the Sun, and then migrated first outward,
then inward, and finally outward again, depleting the region inward of Venus
and wreaking havoc beyond Earth.
sweeping secular resonances
While the Grand Tack has been more widely discussed and
endorsed than the inside-out scenario, both explanations have been faulted. Now
Benjamin Bromley & Scott Kenyon (2017) present an alternative approach in
which “sweeping secular resonances” with Jupiter’s orbital motion, rather than
any migratory scenario, become the mechanism for clearing the Great Martian
Gap. Their model implies a less dramatic but equally consequential role for
Jupiter, and I suspect that it can be extended to explain similar gaps observed
in the architecture of multiplanet systems around other stars.
To develop their model, Bromley & Kenyon (hereafter
BK17) conducted extensive numerical simulations based on earlier work by and
with their collaborators Makiko Nagasawa and Edward Thommes (Nagasawa et al.
2007, Thommes et al. 2008). They also note recent work on the same problem by Xiaochen
Zheng & colleagues (2017).
BK17 begin with the familiar theoretical construct of the
Minimum Mass Solar Nebula (blogged here). They assume that a dusty gas nebula (generally known
as a protoplanetary
disk) is present at the outset of their
simulations. Jupiter is fully formed at its current semimajor axis of 5.2 AU (Figure 2), having cleared a gap in the
disk for 1 AU on either side of its orbital path. A swarm of planetesimals orbits
inward of this gap, while Saturn orbits well beyond it. Both gas giants exert
gravitational effects on their surroundings, and the disk itself has gravity. In
addition, the orbit of Jupiter is slightly eccentric, but probably less so than
its present value of 0.05. BK17 assume an eccentricity of 0.03 in their
simulations.
The key factor in their approach is the n5 resonance (“nu-5,” Greek letter nu with superscript 5), a
“secular” or “very long-term” resonance between the motion of the
protoplanetary disk and Jupiter’s orbital period. BK17 define the nu-5
resonance as the location “where the local apsidal precession rate matches
Jupiter’s rate of precession,” and note that a planetesimal or protoplanet at
this location will be perturbed by Jupiter’s gravitational influence onto a
highly eccentric orbit. The likely result will then be either collision with
another planet or protoplanet, engulfment by the Sun, or ejection from the
Solar System.
In the early Solar System, when the gas disk was still present,
the nu-5 resonance was located in the vicinity of the present Asteroid Belt
(Zheng et al. 2012). As the gas dissipated, the resonance moved inward,
destabilizing (“shaking up”) the orbits of protoplanets and planetesimals and
effectively clearing out a substantial mass in solids. After the gas was
completely depleted, the nu-5 resonance reached its present position inside the
orbit of Venus. This sweeping shake-up created the Great Martian Gap while
leaving behind enough mass to build Earth and Venus, as well as their two
by-blows, Mercury and Mars.
BK17 discovered that several different factors were
critical to reproducing the mass of Mars and the present-day Asteroid Belt
within the time constraints provided by the known age of Mars. These include the
mass of the perturbing planet, its distance from the system habitable zone, and
the timing and speed of the sweeping secular resonance generated by its orbital
motion.
Regarding mass,
BK17 find that only a “Jupiter-mass planet” can produce the magnitude of
perturbation required to induce a shake-up in the protoplanetary disk of a
Sun-like star. Unfortunately, they don’t provide a precise value for the necessary
mass – for example, would an object of Saturn’s mass (95 Mea) be sufficient?
They also note that a “super-Earth” would be massive enough to produce sweeping
secular resonances in an M dwarf system, likely referring to an object in the
range of 1-10 Mea (see, e.g., Kenyon & Bromley 2009).
Regarding orbital location,
they find that the masses of Earth and Mars depend sensitively on the semimajor
axis of Jupiter at the time of the sweeping resonance. If Jupiter had been
substantially farther from the Sun, the resonance would never have reached the
orbit of Mars, and Mars would have grown much bigger than it actually did –
presumably massive enough to support a habitable environment. But if Jupiter
had been substantially closer to the Sun, and thus closer to the system
habitable zone, the resonance would have inhibited the formation of Earth in
the same way that it stunted the growth of Mars when Jupiter was at 5.2 AU. Instead
of one living planet, our system would have none at all.
Regarding the timing
of the sweeping secular resonance, BK17 note that its schedule is determined by
the lifetime of the protoplanetary disk. As we saw in an earlier
post, the system age when gas dissipation commences can fall anywhere
between 1 and 10 million years. At the early end of that range, according to
BK17, dissipation accompanied by shake-up would have extremely negative
consequences for rocky planet formation, as it would destroy planetesimals
before they had time to accrete into protoplanets. At the latter end, however,
the effects would be modest, since accretion would already be well advanced,
potentially permitting the growth of Earth-size planets out to a distance of 3
AU. In the case of our Solar System, we can assume that the shake-up happened
before a system age of about 4 million years, given radiometric evidence that
Mars was fully formed by then.
The rate of disk dispersal also matters. Although many studies
have found that gas dissipation happens rapidly, requiring less than half a
million years from start to finish (Williams & Cieza 2011), variation is
inevitable: some disks take longer than others to disperse. BK17 find that the
relative speed of dissipation strongly affects the outcomes of secular
resonance sweeping. If the gas dissipates quickly, the resonance sweeps inward at
the same rate, resulting in minimal disruption of the planetesimal population. If
the gas dissipates more slowly, the resonance becomes increasingly more destructive,
clearing larger and larger quantities of solid mass from the system.
Figure 3. Calaveras street sweepers on the Day of the Dead
From a print by José Guadalupe Posada
(1852-1913)
-----------------------
extrasolar
asteroids and orbital gaps
Although BK17 are interested primarily in the evolution
of our Solar System, they attempt to generalize some of their results to
extrasolar locales. Their chief concern is the occurrence of extrasolar analogs
of the Asteroid Belt. They argue that most systems with a gas giant in
Jupiter’s approximate location (i.e., just outside the system ice
line, where accretion is maximized) will experience a sweeping secular
resonance whose outcome will be a ring of rocky debris in the inner system. While
they concede that few such structures have been discovered to date (HD 69830 is most familiar),
they attribute these limited findings to the difficulty of discerning modest
aggregations of warm debris even around nearby stars. In the future, they predict,
more sensitive searches will be more successful.
I suggest that the implications of their model are much
broader than their relevance to extrasolar asteroid belts, and far more dispiriting.
If sweeping secular resonances are common in systems with cool gas giants, then
the outlook for habitable planets is even less promising than I thought. Here’s
why.
An important focus of this blog is the possibility of
Solar System analogs – that is, exoplanetary systems containing cool giants
whose orbital parameters would permit the survival of Earth-mass planets (0.5-2
Mea) in the local habitable zone. (For recent posts on this topic, see here
and here.)
My January search of the Extrasolar Planets Encyclopaedia identified
17
such systems located within 60 parsecs/196 light years. All center on
Sun-like stars in the range of 0.85-1.15 Solar masses, so their habitable zones
have boundaries similar to those proposed for our own system (0.99-1.70 AU;
Kopparapu et al. 2013).
Among the Jupiter analogs in these systems, semimajor axes
range from 3 AU to 5.2 AU, and more than half orbit inside 4 AU. According to the
findings of BK17, virtually all these systems will have experienced a sweeping
secular resonance very similar to the one they propose for the Solar System.
Because all but one of the 17 confirmed Jupiter analogs orbits closer to the local
habitable zone than does our own Jupiter, the depletion of mass in this favored
region is likely to be even more extreme than it was at home. Therefore,
habitable planets appear to be less likely in the existing sample of Solar System
analogs than they are in the Solar System.
To put it another way: BK17 have just shown that gas giant
planets are even more unfriendly to the formation and survival of habitable
planets than we already
suspected. It’s not enough for the giant to reside outside the system ice
line in a configuration that permits an Earth-like planet to maintain an
Earth-like orbit. The giant must also be distant enough from the central star that the sweeping
secular resonance generated by its orbit was insufficient to clear solid mass
from the local habitable zone. Even Jupiter managed to evacuate mass from more
than half of the radial extent of our own habitable zone, drastically reducing
our system’s potential to produce life-bearing planets. Now it looks like
extrasolar Jupiters might be still more likely to foreclose the possibility of
life around other stars.
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