Download Do extrasolar planets go bang

Miller: Harold Jeffreys Lecture 2010
Do extrasolar planets
go bang?
In the 2010 RAS Harold Jeffreys Lecture,
Steve Miller discusses how a simple hydrogen
molecule controls the fate of the giants.
1: Artist’s impression of the Jupiter-size extrasolar planet HD 189733b being eclipsed by its parent star. (ESA, NASA, M Kornmesser [ESA/Hubble] and STScI)
I
t has existed for almost as long as molecules
have existed. It is the product of the most
abundant species in the universe. And it may
control the fate of giant planets, whether they
stay far away, like our solar system’s Jupiter, or
spiral in close to their central star, like many of
the extrasolar planets that have been discovered
in recent years.
“It” is H3+ and this year marks the centenary
of its discovery – at least as far as humankind is
concerned. The story of our coming to understand this simple molecular ion has already been
well told in the pages of A&G by Helge Kragh
(2010). Briefly, in the years leading up to the first
world war J J Thomson (figure 2) was studying
“rays of positive ions”. In 1911 he noticed that
he had an ion with a mass-to-charge ratio of
three produced alongside H+ and H 2+ in hydrogen discharge tubes. Candidates included a new
atomic species, that did not really fit into the
periodic table, carbon 4-plus, or a triatomic version of hydrogen, H3. By 1912 Thomson had
pretty much ruled out the first two options and
had decided on the ion being ionized H3 or H3+.
The downside of this choice was the difficulty
in conceptualizing a stable molecule of monovalent H in which one or more of the atoms had
somehow to become multivalent. Niels Bohr
attempted to calculate how this might happen
in 1918, using the “old”, semi-classical version
of quantum mechanics. His linear model of H3+
was unstable, however, and it was not until the
1930s that Joseph Hirschfelder and co-workers
A&G • October 2011 • Vol. 52 Harold Jeffreys Lectures
The Lectures commemorate Sir Harold
Jeffreys’ long career in mathematics and
the physics of the Earth. The Harold
Jeffreys Lecture is given annually on a
topic from solid-Earth geophysics, solar
physics, solar–terrestrial physics, or
planetary sciences.
– when “modern” quantum mechanics were
available – were able to produce a stable triangular H3+ molecule in which each of the three
hydrogen nuclei shared the two available electrons in a “delocalized” molecular orbital. In the
1960s it was shown that the ground electronic
state has “D3h symmetry” – i.e. an equilibrium
geometry that is an equilateral triangle. Later
calculations showed that there is an unstable
excited electronic state of H3+ that is linear, but
that transitions to this state are “forbidden”.
The best way to identify and study a molecule
is by its spectrum. The upshot of these calculations, however, is, firstly, that H3+ does not have
a measurable electronic, visible spectrum. Secondly, a centri-symmetric molecule composed of
three atoms of the same species does not have a
permanent dipole, and cannot have a pure rotational, microwave spectrum. In the absence of
a visible or microwave spectrum the hunt was
on for the infrared, rotation-vibration spectrum
of H3+. The development of infrared diode lasers
and discharge technology all played their part
in this hunt, and – in 1980 – Takeshi Oka (then
at the Herzberg Institute, Ottawa, now at the
University of Chicago) found the very first lines
(figures 3 and 4). And what a spectrum it was.
Ro-vibrational spectra
Normally, ro-vibrational spectral lines are
clumped into three groups around the central
frequency: P branch lines, in which the molecule
hops from a rotational state J to state J–1 as it
jumps up the vibrational ladder, are at lower
frequencies; a tightly clustered Q branch, with J
not changing, are found around the “vibrational
band origin”; and R branch lines are at higher
frequencies, with both the vibrational quantum
number, v, and the rotational quantum number,
J, increasing by 1. H3+ had lines all over the place,
and it was hard to sort out the pattern.
Normally, spectroscopists make use of a variant on quantum mechanics called perturbation
theory to explain ro-vibrational spectra. The
basic model is that the molecule vibrates as a
harmonic oscillator, regular as a watch-spring,
and rotates as a rigid rod of fixed length. Perturbations from this ideal model can be accommodated by letting the vibrations become a
bit anharmonic, allowing for the molecule to
stretch as it rotates faster and faster, and letting
the vibrations couple weakly to the rotations.
Perturbation theory works if the perturbations
represent a small deviation from the ideal harmonic-oscillator/rigid-rotor model. But not in the
5.11
Miller: Harold Jeffreys Lecture 2010
case of H3+ since the perturbations soon became
the determining feature, not the basic model.
Better understanding of what was happening came from an accurate calculation of the
electronic structure of the molecule, by Wilfred
Meyer, Peter Botschwina and Peter Burton, and
a calculation from first principles, not perturbation theory, of the highly coupled rotations and
vibrations that would result from this structure,
using a technique developed by Jonathan Tennyson and Brian Sutcliffe. These showed H3+ to be a
very “floppy” creature, liable to go from triangular to linear if given enough vibrational energy,
and to spin itself to destruction as the rotations
increased in ferocity. And as a result, H3+ broke
most of the rules of normal spectroscopy.
For a start, spun up enough, the molecule
would develop a small dipole and – theoretically
– develop a microwave spectrum. Secondly,
given just a quantum or two of vibrational
energy, it would give rise to “forbidden” lines in
which the normally infrared “dark” symmetric
stretch or breathing mode, which maintains the
equilateral triangle symmetry, lit up. Moreover
overtone bands, for which the vibrational quantum v number changes by two or more, turned
out to be (almost) as intense as the fundamental
bands, for which ∆v is just one.
That means that H 3+ can radiate from the
microwave through the infrared to the visible,
although it is brightest in the near-infrared
around 3–5 µm. In turn, that means that H 3+
can cool any gas cloud or atmosphere in which
it is found with temperatures ranging from a
few tens (albeit very slowly) to a few thousands
of degrees (very rapidly). This property is one of
the key features of H3+ in determining the role it
plays in astrophysical environments.
Hydrogen atoms make up 9 out of every 10
atoms in the universe, and molecular hydrogen
– H 2 – is the most abundant species. H3+ can be
formed whenever H 2 gets ionized, provided the
gas density is high enough (a few million mol­
ecules per cubic metre is more than enough).
Two Californian chemists, Thorfin Hogness
and E G Lunn, first came up with the required
sequence of reactions:
H 2 + 15.2 eV ionizing particle/radiation → H 2+ + e –
H 2+ + H 2 → H3+ + H
This ubiquitous reaction set can be found at
work in laboratory hydrogen discharges, such
as those used by J J Thomson and Takeshi Oka
and in space plasmas throughout the universe.
In the early universe, around 300 000 to
400 000 years after the Big Bang, temperatures
had dropped enough for electrons and atomic
nuclei to join up to form neutral atoms – the
recombination era. Matter and radiation became
decoupled, and the newly formed atoms could
take part in chemistry to make molecules. Since
helium nuclei combine with electrons at higher
temperatures than do protons, probably the first
molecule to form was HeH+, a molecular ion
5.12
2
3
4
2: J J Thomson discovered H3+ in 1911.
3: Takeshi Oka found the first lines of the infrared, rotation-vibration spectrum of H3+ in 1980.
4: The plasma tube used in Oka’s ‘Ion Factory’.
that was not very stable or productive. As the
temperature cooled further, H atoms formed,
and it became possible to form H 2 molecules.
This step was crucial to forming the earliest
stars. Atoms are not very efficient at cooling
the proto-stellar gas cloud below about 8000 K,
since they only have electronic transitions, with
energy gaps that are only accessed at high temperatures. But the ro-vibrational transitions of
molecules can get the gas temperature down
to 1000 K or less, at which point gravitational
attraction can overcome the kinetic forces and
a stellar nucleus can form.
In a universe consisting of predominantly H
and He atoms, plus a smidgeon of deuterium
and lithium, the main molecule to form up is
H 2 . H 2 is a very inefficient coolant. Nor was it
very abundant – some 100 million years after
the Big Bang only one out of every 200 000 of
the H atoms in the universe had combined to
form H 2. So cloud collapse to form the first stars
took something like 15 million years.
It was at this time that H 3+ made its first
appearance and showed some of the properties
that make it important today (Glover and Slavin
2009). Although it was never more than a billion times less abundant than H 2 , this molecular
ion could, under certain conditions, contribute
as much as 1% of the total gas cooling. Molecule for molecule, H 3+ is at least 10 million
times as effective as a coolant as H 2 , a property
that is crucial to understanding the atmospheres
of giant planets like Jupiter, where it was first
identified in 1988.
Models predict that the stars of the early
universe were either very large or very small,
depending on just how the gas clouds clumped
up. Very small, metal-poor stars, formed
before the many enrichments of the interstellar
medium by their larger cousins going supernova
or otherwise shedding their outer layers, would
have had H3+ in their stellar atmospheres. For
the very smallest of these, H3+ slows their evolution to the point that some of them may still be
around today.
In the interstellar medium (ISM) itself, H3+
plays a vital role in the initiation of chains of
chemical reactions that would otherwise never
get going (figure 5). Temperatures in the gas of
the Orion and Taurus molecular clouds, for
instance, can be as low as 10–20 K. Chemistry
between neutral atoms and molecules at those
temperatures is a painfully slow affair. There is
simply no energy available to get over the barriers to turning one chemical species into another.
But ion-neutral reactions are fast: ions attract
neutral atoms and molecules by polarizing their
electronic cloud structure; the closer they get,
the more polarization occurs and the faster they
want to get to know one another. Although the
A&G • October 2011 • Vol. 52
Miller: Harold Jeffreys Lecture 2010
5: H3+ in a web of chemical reactions in the
interstellar medium.
existence of H3+ in the ISM had been proposed
in the 1960s, it took another 30 years before
Oka and Tom Geballe (1996) first detected
key finger­print lines in gas clouds towards the
sources GL 2136 and W33A. As the child of
the most abundant of all molecules, H 2 , H3+ is
formed whenever ionizing rays and particles can
penetrate a molecular cloud. Once formed, it is
a very reactive species: almost everything has a
higher affinity for protons than H 2 , so reactions
that involve
H3+ + X → XH+ + H 2
where X might be a carbon, oxygen or nitrogenbearing species, can initiate sequences that end
up with some very complex chemistry occurring.
This may get as far as the formation of pre-biotic
molecules, the building blocks of life itself.
Detection on Jupiter
Although its astrophysical importance was first
considered in terms of its chemical role in the
ISM, it is the physical role played by H3+ in planetary atmospheres that is perhaps even more
important. And in its very first detection outside
of the laboratory, in the aurorae of the giant
planet Jupiter (figure 6), its rather particular
physical properties manifested themselves.
The detection of H3+ in Jupiter’s upper atmo­
sphere was, for a start, completely fortuitous.
In September 1988, a team of astronomers led
by Pierre Drossart of the Observatoire de Paris,
Meudon, had the idea of studying auroral emission from Jupiter – a massively supercharged version of Earth’s own northern and southern lights
– making use of the Canada–France–Hawaii
telescope at the Mauna Kea Observatory in
Hawaii. The team intended to look for infrared
auroral lines of molecular hydrogen: ultraviolet
emission had already been detected by the International Ultraviolet Explorer satellite (Clarke et
al. 1980) and the Voyager spacecraft (Hamilton
et al. 1980) some years earlier.
A&G • October 2011 • Vol. 52 6: H3+ emission from the auroral regions
of Jupiter, mapped by the NASA Infrared
Telescope Facility. (Jack Connerney and
Takehiko Satoh)
Drossart’s team was looking for very weak H 2
lines that are normally forbidden in the infrared, but that can occur as a result of a small
electrical property known as the quadrupole
moment. These quadrupole-induced changes in
the vibrational and rotational state of H 2 result
in transitions that emit infrared photons about
once every 100 000 seconds for an individual
molecule, or even slower. The team particularly
wanted to detect a line known as the v = 1 → 0
S(1) line that has a wavelength of 2.122 µm.
Indeed, this line was found. But it was surrounded by a series of sharp lines, some of
which were even stronger than the H 2 lines.
The lower regions of Jupiter’s atmosphere either
absorb radiation or give rise to broad emission
features; sharp lines can only come from high
in the atmosphere where the gas density is low,
and hence the collision rate that broadens lines
much lower. The upper atmosphere is almost
pure hydrogen – H atoms and H 2 molecules
– plus some helium. So the smart money had
to be on this series of lines being some form
of hydrogen molecule, and H3+ would seem a
natural candidate.
Except, the wavelengths were roughly half
the wavelengths that Oka had measured back
in 1980. By a roundabout route, news of the
Jupiter spectrum got to Jonathan Tennyson’s
group at University College London. The UCL
group had just been successfully calculating the
H3+ spectrum to high accuracy, and their calculations included not only wavelengths but line
strengths, which determine how fast the molecule can make transitions that give rise to rotation-vibration transitions and infrared spectra.
Normally, spectroscopists consider that only
transitions that involve the molecule changing
its vibrational state by one quantum (∆v = ±1)
should be allowed to occur. What the UCL calculations showed was that the line strengths of the
“forbidden” overtone spectrum, ∆v = ±2, were as
large as the allowed fundamental, ∆v = ±1, spectrum. And the wavelengths were roughly half
those of the fundamental spectrum that Oka
had measured in the laboratory. That meant
that, once excited into its v = 2 second vibrational level, an H3+ molecule could radiate back
down to the ground state roughly once every
0.01 seconds, at least 10 million times faster
than its excited H 2 neighbour. So even though
there was only roughly one H3+ for every million
H 2 molecules, the ion lines were equally strong,
if not stronger. And there were far more of them,
because infrared spectra become richer as the
number of atoms in a molecule increases.
Pretty soon it was realized that as much as
the overtone spectrum was very strong, the
fundamental spectrum would be even stronger,
as it is easier to excite molecules into the first,
v = 1, vibrationally excited state than the v = 2
state. What was soon discovered was that the
emission spectrum of Jupiter at wavelengths
between about 3 and 4 µm was dominated by
H3+ lines. Methane in the jovian middle atmo­
sphere absorbed both the incoming sunlight
and the upwelling infrared radiation from the
lower reaches of Jupiter, so all that could be
seen were sharp emission lines from high in the
upper atmosphere. The background was sufficiently dark and the lines sufficiently bright
that even at relatively low resolution, images of
Jupiter could be obtained that showed nothing
but H3+ emission.
These images showed a complex structure
around the high latitudes of the planet. Arcs
of bright aurorae – some hundreds of times
more intense that Earth’s northern and southern lights – ringed the poles. Poleward of these
“auroral ovals” were more diffuse emissions:
some – on the eastern, dusk side of the planet
– were sometimes as bright as the main auroral
ovals themselves; to the west, dawnward, the
polar regions looked relatively dark, although
many bright features could still be made out. At
latitudes just below the main oval, bright spots
and faint trails could be made out. All of these
features told stories about how Jupiter’s giant
magnetosphere was interacting with the planet’s
electrically charged upper atmosphere through
a series of multi-million-amp current systems.
Earth’s magnetic field carves out a region of
interplanetary space which it dominates. As
particles from the Sun – the solar wind – flow
past our home planet they crash into magnetic
field lines that flow from south to north to form
a “bowshock”, akin to that formed by an ocean
liner through the sea. The pressure of the solar
wind creates this stand-off about 60 000 km or
so from Earth in the direction of the Sun. In
the anti-sunward direction, Earth’s magnetic
field is swept downstream to form a wake – the
magnetotail – that stretches roughly a million
kilometres. This is the region known as the terrestrial magnetosphere.
5.13
Miller: Harold Jeffreys Lecture 2010
7: Simulations of
the bottom (left
panels) and top
(right panels) of the
upper atmosphere
of “Jupiter”
brought into 0.16 AU
from the Sun (top
panels) and 0.14 AU
from the Sun
(bottom panels).
The temperature
scales are on the
right of each panel.
Note that the scale
on the bottom right
panel runs from
19 000 K to 23 000 K.
1470
1468
1466
1464
1462
1460
distance = 0.16 AU
pressure = 121.62 nbar
distance = 0.16 AU, pressure = 5.52 pbar
1540
1530
1520
1510
1500
1490
distance = 0.14 AU
pressure = 121.62 nbar
Jupiter’s magnetism is approximately 1000
times greater than Earth’s. The jovian magnetosphere is consequently much larger: the stand-off
point is anything up to 7 million km from the
planet in the sunward direction, and the magnetotail has been observed to stretch anti-sunward
as far as the orbit of Saturn, some 750 million km
downstream. No wonder the jovian aurorae,
powered by its magnetosphere, are so much
brighter than their feebly flickering terrestrial
counterparts. There are other differences, too.
On Earth, the main auroral oval – roughly
speaking – maps to a magnetospheric region
where the magnetic field lines switch from being
closed, as around a schoolchild’s bar magnet, to
being open, swept away by the solar wind. On
Jupiter, however, there is a more complex system
at work. Jupiter’s closest large moon, Io, orbits
just 350 000 km above the surface of the giant
planet. As a result, Io has its innards continually stirred by the giant planet’s gravitational
field such that it is the most volcanic body in the
solar system. Gas and dust pour at the rate of
one tonne per second into the jovian magnetosphere. Charged up by solar ultraviolet radiation and collisions with other charged particles,
this gas and dust is swept up by the planet’s
magnetic field so that it rotates not once every
42 hours, like Io, but in just under 10 hours, like
the planet itself.
Jupiter and Io
The additional gas and dust momentum is supplied by Jupiter’s ionosphere – H+ and H3+ ions
– at the foot of the magnetic field lines: ionospheric ions drag the magnetic field through the
gas and dust torus created by Io; neutral atoms
and molecules in the upper atmosphere, rotating
at the normal rate of the planet, drag the ions
along with them. Gas and dust drift out centrifugally through the magnetosphere to form a
disc in the planet’s equatorial plane like a ballet
5.14
3800
3600
3400
3200
3000
2800
2600
2400
x10 4
2.3
2.25
2.2
2.15
2.1
2.05
2
1.95
1.9
distance = 0.14 AU, pressure = 5.52 pbar
dancer’s tutu. But there comes a point where the
momentum required to keep this skirt in corotation with the planet is too much for the coupled ionosphere–thermosphere to maintain. The
skirt lags behind, magnetic fields lines become
“bent”, ionospheric ions slip behind their neutral counterparts, and mega-amp currents flow
from plasmasheet to planet, firing high-energy
electrons into the upper atmosphere. In a ring
around the pole, and mapping magnetically to
the regions in the magnetosphere where co-rotation has broken down, bright aurorae glow.
This is Jupiter’s main auroral oval. Poleward
of this oval, on the dark, dawn side, there is a
region that is roughly equivalent to the terrestrial
oval. The brighter duskward emissions come
from regions on the flanks and down the tail of
the magnetosphere. The bright spots at lower
latitudes maps to the Galilean moons, especially
Io and Ganymede, and the trails they leave in the
magnetosphere as it sweeps past them. Enormous currents, driven by megavolt electric fields,
flow through the upper atmo­sphere, generating
temperatures hundreds of degrees greater than
sunlight alone as a result of Joule heating and
the friction of ionospheric ions dragged backwards through an otherwise intransigent neutral
thermosphere. Absolutely key in all these processes is our H3+ molecular ion.
It lights up the atmosphere where these processes are occurring. It provides the ions (and – by
electrical balance – the electrons) that allow currents to flow. Dragged against the natural rotation of the planet by straining magnetospheric
field lines, it crashes into the neutral atmosphere
to create more energy and heating.
H3+ is not only the major component of the
iono­sphere of Jupiter, but also of Saturn and
Uranus, although it has yet to be found on Neptune (Melin et al. 2011). Its heating effect may
help to explain why the upper atmospheres of
these giant planets are so hot. But its effect as a
strong radiator has another effect, too. Although
insufficient to balance the Joule heating and ion
drag inputs generated in Jupiter’s atmosphere,
and probably that of Saturn and Uranus, too,
it is enough to balance the energy that comes
into these planets as a result of electrons being
fired in from the magnetosphere. This “H3+ thermostat effect” plays an important role in some
extrasolar planets, particularly those that orbit
close to their central star.
Nowadays, exoplanets are everywhere you
look; at the end of July 2011, the Exoplanet
Encyclopedia lists 564 (http://exoplanet.eu), and
NASA’s Kepler satellite is claiming more than
1200 potential exoplanets, although only 1% of
them have so far been confirmed. Some exoplanets are around stars like our Sun, some around
stars that are a bit hotter or cooler, some are even
reported to be free-floating, detached from any
stellar-planetary system at all. But the first detection of such a planet only dates back to the 1980s
(Campbell et al. 1988, and this was not really
accepted at the time), the first credible detection
back to 1992 (Wolsczan and Frail 1992), and the
first detection that looked anything like what
people were expecting exoplanets to look like to
1995 (Mayor and Queloz 1995). This is a field
that has exploded in less than 20 years.
So, do (some of) the planets themselves explode
– “go bang”? Some might have every reason to
do so. Planets such as HD 209458b are Jupitersized affairs that orbit very close to their central
star – in this particular case, less than 1/100th
of the distance of Jupiter to the Sun. Since the
radiation field falls off as the square of the distance, this means that HD 209458b gets some
10 000 as much heating and ionization as does
Jupiter. As a result, this planet, which has about
70% of the mass of Jupiter, has a radius about
1.4 jovian radii. Even more importantly, it has
been shown to have a very extended atmo­sphere,
going out to three planetary radii and more, well
beyond the point where the planet’s own gravity
can stop gas being sucked into the star itself.
Given our observation of Jupiter, with its
tightly held atmosphere extending just a few
thousand kilometres, no more than 10% of its
notional planetary radius (for a gas giant, without a solid surface, this is usually defined at that
level in the atmosphere where the pressure is
1 bar), given our observation of HD 209458b,
with its bloated, escaping atmosphere that
extends 300 000 km into space, it is an interesting question to ask just where and when the
change might take place? And how?
This is where the H 3+ thermostat plays a crucial role. Consider this thought experiment: let
us move Jupiter in from its chilly 5.2 AU from
the Sun so that it now resides on the same orbit
as Earth (by definition, 1 AU). The radiation
flux from the Sun will have increased by some
27 times. The heating of the planet’s upper
atmo­sphere will have increased by this amount.
A&G • October 2011 • Vol. 52
Miller: Harold Jeffreys Lecture 2010
Importantly, there will also be 27 times the
ionization as a result of extreme ultraviolet
(EUV) radiation. In an upper atmosphere composed almost entirely of H 2 , the result will be
a much greater concentration of H 3+. And this
H 3+ will radiate out into space (most of) the
increased heating.
Bring Jupiter another 2.5 times closer to the
Sun, inside of the orbit of Mercury, and the
increased production of H3+ and its ability to
radiate heat away still keeps the planet Jupiter-like rather than HD 209458b-like. This
mechanism keeps working even if the planet
gets another 2.5 times closer, in to just 0.16 AU
(or 24 million km from the Sun). But, by this
point, the average temperature of the upper
atmo­sphere has reached a toasty 3000 K or
more, and molecular hydrogen is beginning to
break down to its atomic constituents.
If Jupiter gets just another 3 million km closer to
the Sun, then a vicious spiral occurs: H 2 breaks
down; H3+ forms less easily; cooling becomes less
efficient; the temperature increases; even more
H 2 breaks down, etc. At 0.14 AU from the Sun,
Jupiter would be transformed rapidly from being
jovian to being HD 209458b-like, a bloated version of its former self, with every chance of its
atmosphere escaping off into space (Koskinen et
al. 2007). But only if its orbit is circular.
HD 17156b is a remarkable planet. Its central
star is a bit older than the Sun, at 5.7 gigayears,
and about 2.5 times brighter. The planet is
about the same size as Jupiter, but three times
more massive, making it a very dense gas giant
indeed. On average, HD 17156b orbits at a distance of 0.16 AU, just inside the stability limit
for a circular orbit. But its orbit is not circular.
HD 17156b has one of the most eccentric orbits
of any planet known, with e = 0.67. This means
that at its furthest from its star, HD 17156b is
a little over 5% of the distance that Jupiter is
from the Sun (0.27 AU). But at its closest, the
planet is a mere 1% of the Jupiter–Sun distance
(0.052 AU). The effect is that the amount of
starlight HD 17156b receives during the course
of its 21-day orbit varies by a factor of 27; at
its closest approach the planet gets over 25 000
times as much radiation as does Jupiter.
Surprise stability
Amazingly, HD 17156b is still stable throughout
the course of the orbit (Koskinen et al. 2009).
If, as is quite probable, the planet is Jupiterlike in terms of the composition of the upper
atmosphere, then the H3+ keeps the temperature at the top to a comfortable 2000–3000 K,
cool enough for molecular hydrogen to remain
stable. But even if there is much more atomic
hydrogen in the mix, so less H3+ cooling, and the
upper boundary temperature is in the 20 000–
30 000 K range, HD 17156b does not spend
enough time during its orbit inside of 0.1 AU
for its atmo­sphere to escape.
A&G • October 2011 • Vol. 52 Table 1: The ‘Sun in Time’ targets and
thermospheric stability limits
name of star
EK Dra
1
p UMa
1
HD
type
age (Gyr)
FXUV (erg s–1 cm–2)
limit (AU)
129 333
G1.5 V
0.1
513.5
1.68
72 905
G1.5 V
0.3
129.3
0.84
k Cet
20 630
G5 V
0.65
51.1
0.53
b Com
114 710
G0 V
1.6
16.0
0.30
Sun
…
G2 V
4.58
4.64
0.16
b Hyi
2151
G2 IV
6.7
2.9
0.13
Characteristics of some of the “Sun in Time” stars and the stability of Jupiter-type planets.
What, then, of HD 209458b, with its extended
atmosphere? It turns out that, although H3+ cooling cannot play a role in the extended atmo­
sphere, which is mainly atomic hydrogen and
ions, there is always a molecular-hydrogen layer
where it does form and it does cool down the
atmosphere. And, coupled with other effects,
this is enough to stop the planet evaporating too
rapidly: HD 209458b-type planets are generally
stable at least for the lifetime of a stellar/solar
system (Yelle 2004). Extrasolar planets do not
go “bang”, or do they?
Which brings us back to our own Jupiter. Earth
today is bathed in a gentle sunlight that creates a
Goldilocks world, perfect for the development
and maintenance of life. But things were not
always so benign. In its early years, our Sun was
a much fiercer beast, delivering searing amounts
of radiation, particularly in the ultraviolet and
X-ray regions of the spectrum. Those are key
regions of the spectrum since they are responsible for ionizing planetary atmospheres, with the
potential to create H3+ in hydrogen-rich gas.
The “Sun in Time” project has attempted to
quantify the likely evolution of our home star
by looking at analogues of the Sun of known
ages (Ribas et al. 2005). When the Sun is about
half as old again as its current 4.58 billion years,
its output in the X-ray to EUV range (F XUV)
will have dropped to less than 60% of its current level. At a third of its current age, the Sun
was 3.5 times brighter than now. At a juvenile
100 million years old, the Sun’s XUV output
was 110 times fiercer.
During its lifetime, then, the “stability limit”
at which H3+ cooling could keep a giant planet
from going from Jupiter-like to HD 209458blike would gradually have shrunk from just
outside of the orbit of Mars, at a solar age of
100 million years, to the 24 million km that is
the “safe” distance now (see table 1). But you
only have to go back a bit further in time from
the 100 megayear-Sun represented by EK Draconis, and the stability limit would have been
even further out into the solar system (see table
1 for “Sun in Time” stars and their stability
limits, for Jupiter-type planets).
The results from the “Sun in Time” project
actually fit quite nicely to the formula
log10 [F EUV(t) / F EUV(4.58)] ~ 1.23 × log10 [4.58 / t]
where t is the age of the Sun in gigayears. So,
some time between a solar age of 10 million
years and 100 million years, at a time when
Jupiter would have been scrambling to grab
as much of the gas of the solar nebula as was
still available and Earth was little more than a
coagulating rubble pile, the stability limit would
have been outside of the current jovian orbit.
At that point, and for quite some considerable
time, the very existence of the Jupiter would
have been a battle between solar radiation blowing up the atmosphere and H3+ throwing that
radiation back out into space.
Without the cooling balm of H3+, how different
our solar system might have been! ●
Steve Miller is Professor of Science
Communication and Planetary Science at
University College London, UK. His book The
Chemical Cosmos: a Guided Tour is published by
Springer in its “Astronomers’ Universe” series.
This lecture was originally delivered at Burlington
House on 12 November 2010.
References
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Further reading
Much of the material and many of the key references
for this article can be found in these review articles:
Kragh H 2010 A&G 51 6.25–6.27.
Miller S et al. 2000 Phil. Trans. R. Soc. Lond. A358
2485–2502.
Miller S et al. 2006 Phil. Trans. R. Soc. Lond. A364
3121–3128.
Oka T 1983 Molecular Ions eds Miller T A and Bondeybev V E (North Holland, Amsterdam) 73–90.
Oka T 1992 Rev. Mod. Phys. 64 1141–1149.
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