Astronomy

What is the level of tidal heating between bodies that are already in mutual tidal lock?

What is the level of tidal heating between bodies that are already in mutual tidal lock?


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As I understood tidal heating, it comes from tidal force acting upon a body as it spins, distorting it; the wave of distortion travels along the surface (along with apparent travel of the other body on the sky) and continued friction as the matter is strained into the traveling wave is the source of tidal heating.

Now, if the two bodies are in a tidal lock, the distortion remains constant - it doesn't move. There's no new work done as the bodies remain immobile relative to each other. The tidal heating should be a flat zero.

Meanwhile, Io has immense volcanic activity attributed to tidal heating - despite it being tidally locked to Jupiter. While it still heats Jupiter, dragging its own tidal wave around it, Jupiter shouldn't contribute any heat to Io as its distortion remains constant over time, a stable equilibrium.

Is that just residual heat from times when Io was spinning or am I missing something?


There are actually several components of tidal forces which serve to distort a planet or moon - diurnal, nonsynchronous rotation, ice-shell thickening, orbit obliquity, and polar wander. A moon could be stressed by any combination of these mechanisms, leading to frictional forces and heating.

  • Diurnal Stress - Since orbits are ellipses, not circles, the moon will experience a differential gravitational field. When the moon is closer to the planet, the tidal stresses will be slightly larger than when it is closer away, since the gradient will be steeper. In addition, since Kepler's 2nd Law informs us that a body moves faster when it is closer to its primary, this means that the tidal locking is imperfect. When the moon is close to its primary, it is moving slightly faster than it is rotating. Likewise, when it is further away it is moving slightly slower than it is rotating. This leads to the moon seeing its primary as oscillating slightly in the sky. Source

  • Nonsynchronous Rotation Stress - If the moon's crust is decoupled from its core by a liquid layer (either liquid rock or liquid water), the crust can rotate freely over the core. The core will stay tidally locked to the primary, but the shell can move around. Since the core will have a tidal bulge, when the crust moves around it will become stressed. The crust feels a torque because its thickness varies across the moon's surface. Source

  • Ice-Shell Thickening - Icy moons, such as Europa, can experience stresses caused by their icy outer shells freezing and thickening. As the moon loses heat, the water at the bottom of the shell will freeze. This will increase its volume, creating extensional stresses. At the surface, the cooling of the ice will contract it, causing compressional stresses. While this is not a tidal stress, it is still a source of stressing which can act on these moons, so I thought I'd throw it in. Source

  • Orbit Obliquity - Most moons do not rotate exactly perpendicular to their orbital plane. Rather, their rotational axis has some amount of obliquity. This obliquity changes the latitudinal orientation of the tidal bulge as the moon orbits the planet. This creates additional stresses as the tidal bulge gets pulled on. Source

  • Polar Wander - Large impacts can cause a moon's lithosphere to rotate and reorient itself relative to its rotational axis. When this rotation changes the apparent location of the rotational poles, it is called "polar wander". Polar wander causes stress in a similar manner to nonsynchronous rotation. The lithosphere rotates over the core's bulge, pushing on the crust. Source

There may be other stress mechanisms that I am not aware of, but these are the main ones. If you want more information about the topic, or want to see some visualizations of what these various stresses look like, check out SatStressGUI, a program I helped developed which models stresses on icy moons.


Tides

TIDES
Tides are periodic rises and falls of large bodies of water. Tides are caused by the gravitational interaction between the Earth and the Moon. The gravitational attraction of the moon causes the oceans to bulge out in the direction of the moon.

Tides
The Earth and the Moon directly influence each other, so it is best to think of these two objects as part of one larger system, rather than two separate, individual objects. Compared to the Earth, the Moon is relatively large. It has 1% of Earth's mass, and has 1/4 the Earth's radius.

Tides and
Gravitational Locking
We have introduced tides in our earlier discussion of the Moon's observational characteristics through the effect of the Moon on the Earth's oceans, but the effect is much more general, and has a number of important consequences. Tidal Coupling and Gravitational Locking .

The Moon's role in the rhythmic rising and falling of the oceans along the shore was explained mathematically in 1687 by Isaac Newton.

Geologists find evidence of water throughout this image of Arda Valles, a region on Mars. Drainage channels empty into a plain at left, while the large crater to the right of center shows evidence that it was filled with muddy sediments.

would have the same amplitude.

have created the two types of surface features seen on Europa: cracks/ridges and chaotic areas, Greenberg said.
The ridges are thought to be built over thousands of years by water seeping up the edges of cracks and refreezing to form higher and higher edges until the cracks close to form a new ridge.

in convective zones have a significant effect on planetary orbits only during the PMS phase and only for fast-rotating stars. They have no significant effects during the PMS phase for initially slow-rotating stars and during the red giant branch phase, regardless of the initial rotation.

The tide-raising forces, acting over a number of hours, produce motions of the water that result in measurable tidal bulges in the oceans. Water on the side of Earth facing the Moon flows toward it, with the greatest depths roughly at the point below the Moon.

to Children
The appearance of the moon changes each month, which is known as phases of the moon.

(which was studied by Seleucus) can indeed hardly be explained in a geocentric system.

, particularly the spring tides where the gravitational pull of the Sun and Moon combine to give the greatest effect.

on the Earth which occur at full or new moon when the Moon and Sun are colinear with the Earth.

The Recession of the Moon .

. This is a factor only when determining what kinds of life will fill its biosphere.

Chapter index in this window " " Chapter index in separate window
This material (including images) is copyrighted!. See my copyright notice for fair use practices.

on Earth are caused by the stars
While the Flat Earth Society denies the existence of gravity, it does concede that something they call "gravitation" exists, and that it causes measurable tidal effects on Earth.

Now for a paradox: Suppose two particles orbit a planet in orbits whose semimajor axes differ by several hundred kilometers (1). The outer particle should have:
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are the result of the gravitational forces of the Sun and the Moon acting upon the planet.
Transit " The movement of a celestial body across another, from the viewpoint of an observer.

- Distortion of a body caused by the gravitational influence on another body.
Trans-Neptunion Object - Object in our solar system lying beyond the orbit of Neptune.
Transit - Passage of a smaller body in front of a larger body. Passage of a celestial body across an observer's meridian.

- Distortions in a body's shape resulting from tidal forces
Timelike Trip - A path in spacetime that can be followed by a body moving slower than the speed of light
Transform Fault - The boundary between two of the Earth's crustal plates that are sliding past each other .

You may have noticed that I used the phrase "tidally locked" above. What's that all about?

Neap tides - Neap tides occur when the gravitational forces of the Moon and the Sun are perpendicular to one another and occur during quarter moons.
NEAT - Abbreviation for Near-Earth Asteroid Tracking, which is a joint NASAJPL program that tracks near-earth asteroids (NEAs).

depends on the orientations of the Sun and the Moon relative to Earth.

on Earth. Rather, they are tidal bulges in the solid crust of the moon Io. Jupiter's gravitational field and the gravitational fields of its other large moons raise the bulges on Io as high as a 30-story building.

on Earth are caused by competing gravitational pull of the Moon and Sun on different regions of the Earth.

around the world with other useful info on weather and temperatures
The Old Farmer's Almanac Tidal Predictions for the U.S. and Canada
U.K. and Irish Tidal Predictions .

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The tidal motions of our oceans are a result of the Moon's gravity influence. The result of the ocean's motions provide energy for two very important effects:
Movement of the hot and cold ocean currents a result of a moving ocean.

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occur because of the gravitational pull of the moon. The oceans bulge in the direction of the moon. High tide happens when the moon is overhead, but it also happens on the opposite side of the planet because the moon is tugging on Earth as well.

are the rise and fall of sea level that is caused by the gravitational pull of the moon and the sun. They are one of the most reliable phenomena in the world. The difference between high and low tide is called the tidal range.
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modify the rotation and orbit of planets until an equilibrium is reached. Whenever the rotation rate is slowed, there is an increase of the orbit semi-major axis due to the conservation of angular momentum.

occur on every object in the Solar System (if it has "land"). They cause friction and affect the orientation of many satellites. Here's how.

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Low Cost Access to Space investigations may be science investigations in and of themselves or proof-of-concept experiments for techniques/detectors that enable new heliophysics science.

are magnified by other effects, such as frictional coupling of water to Earth's rotation through the ocean floors, the inertia of water's movement, ocean basins that get shallower near land, and oscillations between different ocean basins.

Sea Level Rise
Changing Planet: Ocean Temperature video
Changing Planet: Rising Sea Level video .

tidal tide Consider two points on the Moon, one the point closest to the Earth, the other the farthest from the Earth. The point closest to the Earth feels more gravitational force than the rest of the moon does. The farthest point feels less force.

of the ocean are at their highest when the earth, moon, and sun are in a line.
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Tail - Gas and dust left behind as a comet orbits close to the sun. The sunlight makes the tail bright.

occur when the Sun and the Moon pull at right angles to each other and their pulls partly cancel each other out.

, twin waves raised in the Earth's ocean by (mainly) the Moon's gravitational pull.

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The gravity from our sun and moon give us the low and high

of our oceans, seas, and water.
Our sun is thought to be an average-sized star and yet one million Earths could fit inside the sun.
For many years, scientists thought that the Earth might be the only planet in our solar system with liquid water.

Almanacs often contain astronomical data and information such as the times of the rising and setting of the sun and moon, eclipses, hours of full

as well as predications. Asterism: a group of stars that may form a picture. Asterisms are like constellations but generally contain fewer stars.

Moreover, the distortion of the two caused by

and rotation renders the binary continuously variable even when there is no actual eclipse going on, as we see different projections of the distorted surfaces as the stars go around each other.

The gravitational attraction between the Earth and the Moon gives rise to the lunar

in the ocean. Because the oceans are fluid, along the radial line from the Earth to the Moon they contain two bulges caused by the attraction.

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due to gravity. His impressive body of work made him a leader in scientific research.

we're familiar with on Earth. The gravitational fields of Jupiter and its large moons Europa and Ganymede cause tidal bulges in the solid crust of Io that are as high as 100 meters (330 feet).

. The Moon's gravitational attraction is stronger on the side of the Earth nearest to the Moon and weaker on the opposite side. Since the Earth, and particularly the oceans, is not perfectly rigid it is stretched out along the line toward the Moon.

Deoxyribonucleic acid (DNA) molecules consist of two long intertwined polymers of nucleo

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Proteins are sometimes referred to as macromolecular polypep

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on earth ?
The gravitational pull of the moon causes the earth's oceans to bulge. This bulge is the high tide. In fact the moon causes the oceans to bulge in two places, the oceans facing the moon and the oceans facing away from the moon.

The astrologer does at least inform us of his source --he was inspired by Fergus Wood and his eccentric tome on "The Strategic Role of Perigean Spring Tides" published c.1976. Ironically, this is the exact same author and source which inspired Donald Olson et al.

The notes include discussion of the Titan's clouds,

, and the possibilities of floating organics on Titan. Titan Master : book I. Image 56. 1981. Manuscript Division. Required reading for Carl Sagan's course, "Critical thinking in scientific and non-scientific contexts," at Cornell University.

Earth's gravity keeps the Moon in orbit around us and the Moon in turn causes the oceans'

. The side of Earth that faces the Moon feels a bit more gravity, while the side facing away feels less, creating a slightly oblong Earth.

"This is the reason we have ocean

on Earth, as tidal forces from both the moon and the sun can tug on the oceans, creating a bulge that we experience as a high tide. Luckily, on Earth it's really only the water in the oceans that gets distorted, and only by a few feet.

The tidal force (so named because it accounts for the

on the Earth) is due to a body receiving different amounts of gravitational force. If you were falling feet first into a black hole, your feet, being closer to the black hole, would receive a greater amount of gravitational force than your head.

A difference in gravitational attraction from the Moon and Sun causes

on Earth. If the Moon got too close to Earth the difference in gravitational attraction from Earth would rip the Moon apart, and we would be left with a prominent ring around Earth and stagnant harbours.

When the Moon is overhead or directly underfoot, the land surface is pulled about 1 foot higher by the Moon's tidal force. (Note that this means there are two high

are typically about 6 feet high.

The Voyager spacecraft found sulfur-spewing volcanoes on Jupiter's satellite Io that appear to be driven by the grinding

raised by the giant planet. These volcanoes are now monitored by earth-bound telescopes using cameras sensitive to the heat, or infrared radiation, from the volcanoes (Plate 2.2).

2. Long before the cause of

and looking for patterns. Was this what we now call science?

A highly conserved sequence of 180 nucleo

common to many regulatory genes and coding for the DNA-binding part of the corresponding regulatory proteins.

See Also: Homeotic gene, Transcription factor.
homeostasis - (n.) .

Ripping the star apart with intense

, the stellar material was then swept up into a disc and heated to millions of degrees. As some of the gas spirals into the jaws of the black hole, jets of matter form along the black hole's spin axis.

728 mi over the surface, moving so rapidly in its orbit that it orbits faster than Mars rotates.

from Mars are also altering its orbit, slowly lowering Phobos closer and closer to the surface.

As our planet's only natural satellite, the Moon has considerable pull - not only through its gravitational force, which sets the ceaseless rhythm of the

, but also as a nightly reminder that other worlds wait to be explored.

The Yolngu people in Arnhem Land, for example, have dreaming stories that explain

, eclipses, the rising and setting sun and moon and the changing positions of rising stars and planets throughout the year.

The center of a black hole, where the curvature of space time is maximal. At the singularity, the gravitational

diverge. Theoretically, no solid object can survive hitting the singularity.
Sirius
A star - Brightest. Apparent magnitude -1.46. Dog star .

Earth's axis of rotation is tilted with respect to its orbital plane, producing seasons on Earth. The gravitational interaction between Earth and the Moon causes

, stabilizes Earth's orientation on its axis, and gradually slows its rotation.

The heating of a planet or satellite because of friction caused by

.
Time Dilation
The slowing of time in curved space time, believed to occur as one approaches the speed of light or crosses the even horizon of a black hole.

Nearly every living thing on Earth is affected by celestial cycles, especially the diurnal motion of the Sun, the

of the moon, and the seasons of the year. So it is unsurprising that our distant ancestors were curious about the sky.

A vast ocean is theoretized to exist below Europa's icy crust. Though Europa is far from the Sun, strong gravitational

caused by Jupiter's powerful pull, could create internal heat necessary for maintaining liquid water.
Life .

Towards the end of Voyager's journey it was established that Tuvok's neural pep

were deteriorating due to an unspecified degenerative neural condition that could only be cured by Fal-tor-voh, a particularly intense mind-meld with a member of his family.

Enceladus: recent geological activity (lightly cratered regions), heated by

are greatly influenced by the Moon. As the Earth rotates on its axis, the Moon's gravitational pull draws the ocean toward it. So, when an ocean is closest to the Moon, it will be low tide and when a particular ocean is on the opposite side of the Earth from the Moon, it will be high tide.

which is the ratio of size to separation. The larger the value of &eta, the more important it will be to include the effects of extended mass distribution when we consider gravitational interactions in other words, the more significant gravitational torques and

might be.
Can you fill in the table below?

This calendar, known as a lunar calendar, has been used by many cultures throughout history. Some of the earliest records of lunar calendars are over 10,000 years old. The moon also causes the rise and fall of sea levels, known as

. This is due to the gravitational pull of the pull on our planet's bodies of water.

Our planet's Moon is the fifth-largest moon in the Solar System. Only three moons of Jupiter (Ganymede, Callisto, and Io) and Saturn's moon Titan are larger. The Moon's gravitational pull on the Earth is so strong that it affects our ocean's

number 37, is located about 3,600 light years away from us. As far as open star clusters go, NGC 2169 is a small one, spanning only 7 light years across. Its stars are about 8 million years old and are expected to disperse over time as they encounter other stars, interstellar clouds, and experience gravitational

A point at which space and time are infinitely distorted, such as the central point of a black hole where matter is concentrated into an area of zero volume and infinite density. The centre of a black hole, where the curvature of spacetime is at its maximum. At the singularity, the gravitational

Since B is now less massive than A, however, astronomers believe that B has lost much of its original mass. The two stars orbit so close to each other (0.062 AUs) that, as Star B swelled up to be a giant star, its companion Star A could produce

in Star B that causes gas in B's now swollen outer envelope to flow .

universe but without question continue into the present epoch as we observe many galaxies in the local universe, such as the M51 complex, showing the strong signatures of ongoing interactions. When encounters happen, the close proximity of the massive structures set up powerful gravitational forces known as


4 Answers 4

If the moon takes 7 years to do an orbit, relative to the surface, then it must be doing one orbit of the planet each day, relative to the centre of the planet (as it is nearly in geosynchronous orbit)

If the planet has about 86400 seconds in a day (like Earth), then the moon is orbiting at 36000km about the equator, much much closer than the moon really is. This would potentially lead to much bigger tides. However the way tides work is not simple bulges. There are tidal flows, the moon generates a flowing wave that moves around the Earth, and as this wave meets land it can be pushed up and that gives us large tides at the coast. The tidal range mid-ocean is much smaller (about a metre). If the moon isn't moving quickly, relative to the surface, then these flows will stop, and the coastal tide will be less.

I don't think that there would be significant tidal flows. The moon is moving so slowly, and the tide would rise so slowly that the required flow of water would be very little. You couldn't surf the world's tidal wave.

Tidal bulges are an idealisation, assuming a world in which there is no land. In reality the tidal flows are strongly determined by the shape of the land https://www.youtube.com/watch?v=ZEhm_ONTQKc

There would be two tidal bulges, just as on Earth. Except on Earth, tidal flows mean that in some places one tide is bigger than the other.

So I would expect the mid-ocean tide to be much larger, but the coastal effect is less, and there are no significant tidal flows. Also the tidal heating by the moon of the Planet's interior is much greater: I would expect lots more tectonic activity as the Planet bends and creaks with the nearby moon. The moon would also be massive: ten times larger than it appears in the sky. and eclipses would be commonplace.

dsimanek/scenario/tides.htm, the tidal bulge in the mid ocean is

1 meter. $endgroup$ &ndash Jay Lemmon Jul 9 '17 at 22:14

From the numbers you gave (planet and satellite of sizes comparable to Earth and Moon respectively, 7 years synodic month for the satellite) you cannot really infer the distance between the planet and the satellite and thence the magnitude of the tides.

The Moon is currently about 384000 km from Earth on average and is tidally locked to Earth for a mutual tidal lock to take place the Earth would have to decelerate its rotation and the Moon would have to recede a lot, a process that would take tens of billions of years. The Moon is obviously not on a geosynchronous orbit and as it recedes from Earth it will be even less so (if you take the value of today's GSO, of course!). As Earth's (or any planet's) rotation slows down due to tidal braking, the GSO will get farther from the planet.

The distance between two mutually tidally locked bodies depends on the sum of their angular momentum, which cannot increase or decrease. You can start with any value within a broadly reasonable range. Angular momentum depends on mass and rotational speed, and a planet could conceivably end up with almost zero rotational speed after it has formed.

On to your question: I would think that, irrespective of the magnitude of the tides, their extremely low frequency would make them almost unnoticeable. We're talking about an acceleration vector that takes seven years to go around an Earth-sized planet.

15meters, I think you would notice, even if it took almost 2 years to rise and another 2 years to fall. $endgroup$ &ndash Jay Lemmon Jul 10 '17 at 9:58

To expand on pablodf76's last sentence:

If your planet has an Earthlike circumference of 40,000 km, and your moon is orbiting once every seven years (relative to the surface), then, relative to the surface, the peak of your tides (i.e. the "groundspeed" of the moon) only travels at <1 km/hr. By comparison, the peak of Earth's tides (which effectively circle the planet each day) moves closer to 1700 km/hr. So, while local topography will of course cause variations on-the ground, in general, no, you're not going to see any appreciable tidal flow.

In fact, if the moon's orbital plane wasn't aligned with the plane of your planet's equator (geosynchronous but not geostationary), you'd probably see a stronger north-south tidal movement than east-west.

Your Tides would be HUGE, hundreds or thousands of feet high, but VERY slow. More like "Don't build anything permanent or expensive here, in three years it will be under water. Your moon will have to be about 10 times closer, all things being equal. Give the diminishing square laws, inverted, your moon, all things bing equal, will have 100 times the influence on the surface liquid. It would have so much influence that its gravity would have to be taken into account designing very tall structures. It also could very well have destructive effects on core heating and crust/mantle tectonics.

Other things to consider, IF you had something that you were not willing to leave every 2 years or so (figuring a tide every 3.5 years that is a year or or so long) Any mining could only be done for a couple of years at a time then all equipment pulled out and the mines allowed to flood till next 'low' tide. Any city would have to be built on towers tall enough to be higher than the water level at 'high' tide. OR you could build a city of inter connected structures, designed to float, tethered or moored on cables, thousands of feet long that would ride the tide up every time, or make a 'walking' city that would continue to move to stay ahead of the tide. You can also adjust the mass of your moon to adjust the tide to a manageable level. Your scenario, as given, would result is a single tide thousands of feet high (or deep as the case may be) every 7 years so explore how to make a civilization the avoids their equator (the place the gigantic blob of surface liquid would collect and move) or stay ahead of it. Do your equatorial latitudes have topography that would prevent a city sized machine from rolling/walking across it every 7 years? Do your movers have contingency plans for when a wheel/axle/leg goes down. How many, straight number or percentage can go down before speed or forward movement is impeded ect. have fin with this world.


Does Neptune's Moon Triton Have a Subsurface Ocean?

Triton was discovered in 1846 by the British astronomer William Lassell, but much about Neptune’s largest moon still remains a mystery.

A flyby by NASA's Voyager 2 spacecraft in 1989 offered a quick peek at the satellite, revealing a surface composition comprised mainly of water ice, along with some nitrogen, methane, and carbon dioxide.

As Triton’s density is quite high, it is suspected that the moon has a large core of silicate rock. It is possible that a liquid ocean formed between the rocky core and icy surface shell, and scientists are investigating whether or not this ocean could have survived until now.

Captured from the Kuiper Belt

Triton, which is about 1,680 miles (2,700 kilometers) wide, has a unique property among large solar system moons: a retrograde orbit. [Video: Fly By Neptune's Freezing Moon Triton]

Planets form from a circumstellar disc of dust and gas that surrounds a young star. This disc circles the star in one direction, and thus most planets and their moons orbit in this same direction. These orbits are known as prograde, and a rogue object that orbits backward is said to be in a retrograde orbit. The retrograde orbit of Triton means that it most likely did not form around Neptune.

The early solar system was a place of dynamic violence, with many bodies changing orbits and crashing into each other. Triton likely originated in the Kuiper Belt &mdash the ring of icy bodies beyond Neptune &mdash and was sent hurtling inward until it was captured by Neptune’s gravity.

Directly after capture, the moon would have been in a highly elliptical, eccentric orbit. This type of orbit would have raised large tides on the moon, and the friction of these tides would have caused energy to be lost. The energy loss is converted into heat within the moon, and this heat may have melted some of the icy interior and formed an ocean beneath Triton's ice shell.

The energy loss from tides is also responsible for gradually changing Triton’s orbit from an ellipse to a circle, researchers say.

Heating the interior

Friction from tides is not the only source of heat within a terrestrial body there is also radiogenic heating. This is heat produced by the decay of radioactive isotopes within a moon or planet, and this process can create heat for billions of years.

Radiogenic heating contributes several times more heat to Triton’s interior than tidal heating however, this heat alone is not sufficient to keep the subsurface ocean in a liquid state over 4.5 billion years.

But tidal dissipation causes heat to be concentrated at the bottom of Triton's ice shell, which impedes the growth rate of the ice and effectively acts as a tidal-heated blanket. This tidal dissipation is stronger for larger values of eccentricity, meaning it would have played a major role in heating Triton in the past.

"While the concentration of tidal dissipation near the bottom of ice shells was known for some time, we believe our work is the first to demonstrate that it indeed controls the rate of freezing and sustainability of subsurface oceans,"

said Saswata Hier-Majumder at the University of Maryland. "Radiogenic heating, in comparison, heats up the shell uniformly, and thus doesn't have as disproportionate an influence as tidal dissipation does."

Sustaining the ocean

The exact point in time when Triton was captured by Neptune and the length of time it took for the moon's orbit to become circularized are unknown.

Triton’s orbit is currently almost exactly circular. Investigating how the shape of the orbit evolved through time is important to determine the level of tidal heating that occurred, and thus if the subsurface ocean could still exist today.

As Triton cools, the ice sheet will grow to engulf the underlying ocean. The new research calculates how the thickness of the ice shell can influence the tidal dissipation and thus the crystallization of the subsurface ocean.

If Triton's ice shell is thin, then the tidal forces will have a more pronounced effect and increase the heating. If the shell is thick, then the moon becomes more rigid and less tidal heating will occur.

"I think it is extremely likely that a subsurface ammonia-rich ocean exists in Triton," Hier-Majumder said. &ldquo[But] there are a number of uncertainties in our knowledge of Triton's interior and past which makes it difficult to predict with absolute certainty."

For instance, the exact size of Triton’s rocky core is unknown. If the core turns out to be larger than the value used in the calculations, then there will be more radiogenic heating, with extra heating increasing the size of any existing ocean.

The depth of the ocean also may not be constant across the moon, as tidal dissipation concentrates energy near the poles, meaning that an ocean would likely be deeper there. In addition, recent calculations estimate that icy bodies in the outer solar system could be comprised of up to 15 percent ammonia. Ammonia-rich volatile material works to lower the temperature at which a solid turns to a liquid, and the presence of such volatiles may also help a liquid layer persist beneath the ice.

Life in the ocean

Subsurface oceans on icy solar system bodies could provide potential habitats for primitive extraterrestrial life. [5 Bold Claims of Alien Life]

Jupiter's moon Europa is currently the leading candidate for such a habitat, although there is still much debate about this. The probability of life existing within the depths of Triton's ocean is much smaller than for Europa, but it still can't be completely ruled out, researchers say.

The ammonia that is likely present in Triton's subsurface ocean might act to lower the freezing point of water, thus making it more suitable for life. The temperature of the ocean is still probably around minus 143 degrees Fahrenheit (minus 97 degrees Celsius), which would slow down biochemical reactions significantly, and impede evolution. However, terrestrial enzymes have been found to speed up biochemical reactions down to temperatures of minus 153 degrees Fahrenheit (minus 103 degrees Celsius).

A more remote possibility is that Triton could host silicon-based life, assuming that silicon can actually be used as a foundation for life instead of carbon.

Silanes, which are structural analogues of hydrocarbons, could be used as a building block for life under the right conditions. The frigid temperatures and the limited abundance of carbon on Triton could be suitable for silicon-based life, but there isn't enough known about the behavior of silanes in such unusual conditions to firmly state that such life could exist.

The research by Jodi Gaeman, Saswata Hier-Majumder and James Roberts was published in the August issue of the journal Icarus.

This story was provided by Astrobiology Magazine, a web-based publication sponsored by the NASA astrobiology program.


Planetary Satellites, Natural

IV.E The Satellites of Uranus

The rotational axis of Uranus is inclined 98°s to the plane of the Solar System observers on Earth thus see the planet and its system of satellites nearly pole-on. The orbits of Ariel, Umbriel, Titania, and Oberon are regular, whereas Miranda's orbit is slightly inclined. Figure 14 is a telescopic image of the satellites. The oretical models suggest the satellites are composed of water ice (possibly bound with carbon monoxide, nitrogen, and methane) and silicate rock. The higher density of Umbriel implies its bulk composition includes a larger fraction of rocky material. Melting and differentiation have occurred on some of the satellites. Theoretical calculations indicate that tidal interactions may provide an additional heat source in the case of Ariel.

FIGURE 14a . Telescopic view of Uranus and its five satellites obtained by C. Veillet on the 154-cm Danish–ESO telescope. Outward from Uranus they are as follows: Miranda, Ariel, Umbriel, Titania, and Oberon.

Water ice has been detected spectroscopically on all five satellites. Their relatively dark albedos ( Table I ) are probably due to surficial contamination by carbonaceous material. Another darkening mechanism that may be important is bombardment of the surface by ultraviolet radiation. The four outer satellites all exhibit large opposition surges, which may indicate that the regoliths of these objects are composed of very porous material.

The Voyager 2 spacecraft encountered Uranus in January 1986 to provide observations indicating that at least some of the major satellites have undergone melting and resurfacing. One feature on Miranda consists of a series of ridges and valleys ranging from 0.5 to 5 km in height ( Fig. 14b ). Ariel, which is the geologically youngest of the five satellites, and Titania are covered with cratered terrain transected by grabens, which are fault-bounded valleys. Umbriel is heavily cratered and is the darkest of the major satellites, which indicates that its surface is the oldest. Oberon is similarly covered with craters, some of which have very dark deposits on their floors. The satellites are spectrally flat, with visual geometric albedos ranging from 0.2 to 0.4, which is consistent with a composition of water ice (or methane-water ice) mixed with a dark component such as graphite or carbonaceous chondritic material.

FIGURE 14b . A mosaic of Miranda produced from images taken by the Voyager 2 spacecraft at 30,000–40,000 km from the moon. Resolution is 560 to 740 m. Older, cratered terrain is transected by ridges and valleys, indicating more recent geologic activity.

Voyager 2 also discovered 10 new small moons, including two which act as shepherds for the outer (epsilon) ring of Uranus ( Table I ). These satellites have visual geometric albedos of only 4–9%. They move in orbits that are fairly regularly spaced in radial distance from Uranus and have low orbital inclinations and eccentricities. Five additional small satellites (10–20-km radii) were subsequently discovered by ground-based observers (see Table I ).


Evolution of the Earth

D.C. Rubie , . H.J. Melosh , in Treatise on Geophysics , 2007

9.03.2.1 Accretion

The basic physics of planetary accretion are now reasonably well understood, although many details remain obscure (see Wetherill (1990) and Chambers (2003) for useful reviews). Growth of kilometer-sized objects (planetesimals) from the initial dusty, gaseous nebula must have been a rapid process (occurring within approximately 10 3 years), because otherwise the dust grains would have been lost due to gas drag. At sizes >1 km, mutual gravitational interactions between planetesimals become important. Furthermore, because the largest bodies experience the greatest gravitational focusing, they tend to grow at the expense of smaller surrounding objects. This ‘runaway growth’ phase, if uninterrupted, can potentially result in the development of tens to hundreds of Mars- to Moon-sized embryos in ∼10 5 years at a distance of around 1 astronomical unit (AU) from the Sun ( Wetherill and Stewart, 1993 ). However, runaway growth slows down as the initial swarm of small bodies becomes exhausted and the velocity dispersion of the remaining larger bodies increases ( Kokubo and Ida, 1998 ). Thus, the development of Moon- to Mars-sized embryos probably took ∼10 6 years at 1 AU ( Weidenschilling et al., 1997 ), and involved collisions both between comparably sized embryos, and between embryos and smaller, left-over planetesimals. Based on astronomical observations of dust disks ( Haisch et al., 2001 ), the dissipation of any remaining nebular gas also takes place after a few million years the dissipation timescale of gas has implications both for the orbital evolution of the bodies (e.g., Kominami et al., 2005 ), their volatile inventories (e.g., Porcelli et al., 2001 ), and their surface temperatures (e.g., Abe, 1997 ), and is currently a critical unknown parameter. Noble gas isotopes, in particular those of xenon, have been used to argue for a primordial, dense, radiatively opaque terrestrial atmosphere (e.g., Porcelli et al., 2001, Halliday, 2003 ), but this interpretation remains controversial (see Chapter 9.02 ).

Collisional growth processes lead to a peculiar size–frequency spectrum of the accumulating bodies. At first, the runaway accretional processes produce a spectrum in which the cumulative number of objects (the number of objects equal to, or greater, than diameter D) is proportional to an inverse power of their diameter, generally of form Ncum(D) ∼ Db , where b is often approximately 2 ( Melosh, 1990 ). One of the principal characteristics of such a distribution is that although the smallest bodies overwhelmingly dominate in number, most of the mass and energy resides in the very largest objects. Accretional impacts are thus catastrophic in the sense that objects at the largest end of the size spectrum dominate planetary growth. Later, during oligarchic growth at the planetary embryo scale, the large bodies represent an even larger fraction of the size spectrum and giant impacts, that is, impacts between bodies of comparable size dominate planetary growth history.

The subsequent growth of Earth-sized bodies from smaller Mars-sized embyros is slow, because the embryos grow only when mutual gravitational perturbations lead to crossing orbits. Numerical simulations show that Earth-sized bodies take 10–100 My to develop (e.g., Chambers and Wetherill, 1998 Agnor et al., 1999 Morbidelli et al., 2000 Raymond et al., 2004 ), and do so through a relatively small number of collisions between objects of roughly comparable sizes. A recent result of great importance is that geochemical observations, notably using the hafnium–tungsten (Hf–W) isotopic system, have been used to verify the timescales obtained theoretically through computer simulations of accretion processes (see Section 9.03.3.1 ).

It should be noted that an important implicit assumption of most late-stage accretion models is that collisions result in mergers. In fact, this assumption is unlikely to be correct ( Agnor and Asphaug, 2004 Asphaug et al., 2006 ) and many collisions may involve little net transfer of material, though both transient heating and transfer of angular momentum will occur. In fact nearly 80% of the mantle of Mercury may have been ‘lost’ by collisional erosion after core formation, thus explaining the huge size of its metallic core ( Benz et al., 1988 ). Such disruptive collisions may also have influenced the evolution of the Earth and could explain an excess of Fe in the Earth’s bulk composition relative to C1 chondrites ( Palme et al., 2003 ).

Figure 1(a) shows a schematic example (obtained by splicing together two different accretion simulations) of how a roughly Earth-mass (1Me) body might grow. Here the initial mass distribution consists of 11 lunar-mass embryos (≈0.01Me) and 900 smaller (≈0.001Me) noninteracting planetesimals centered around 1 AU. The solid line shows the increase in mass, and the crosses show the impactor:target mass ratio γ (both in log units). The early stage of growth is characterized by steady collision with small planetesimals, and occasional collisions with other, comparably sized embryos (e.g., at 0.068 and 1.9 My). Because the planetesimals do not grow, the impactor:target mass ratio γ of colliding planetesimals declines with time embryo–embryo collisions show up clearly, having γ ∼1. At 2 My, the growing object has a mass of 0.2Me and roughly half of this mass has been delivered by large impacts. The late stage of growth consists entirely of large impacts, between embryos of comparable masses (γ ∼ 0.5). This final stage takes place over a more extended timescale – in this case, the last significant collision occurs at 14 My, resulting in a final mass of 0.73Me.

Figure 1 . (a) Schematic growth of a proto-Earth, obtained by splicing two accretion simulations together. Early growth is from Agnor (unpublished) where the initial mass distribution consists of 11 embryos (≈0.01Me) and 900 noninteracting planetesimals (≈0.001Me) centred around 1 AU. Late growth is from particle 12 in run 3 of Agnor et al. (1999) . The vertical dashed line denotes the splicing time. The solid line shows the mass evolution of the body, and the crosses denote the impactor:target mass ratio γ. Circles denote embryo–embryo collisions squares late-stage giant impacts. The general reduction in γ prior to 2 My is a result of the fact that the planetesimals cannot merge with each other, but only with embryos. (b) Corresponding energy production (J kg −1 ). The cumulative energy due to impacts (crosses) is calculated using eqn [2] for each impact. The solid lines show the cumulative energy associated with the decay of radioactive elements 26 Al, 60 Fe, and 40 K. Half-lives are 0.73 My, 1.5 My, and 1.25 Gy, respectively initial bulk concentrations are 5 × 10 −7 , 2 × 10 −7 , and 4.5 × 10 −7 , respectively ( Ghosh and McSween, 1998 Tachibana et al., 2006 Turcotte and Schubert, 2002 ).

One of the most important outstanding questions regarding this late-stage accretion is the amount of water that was delivered to the Earth. The presence of large quantities of water in the early mantle would have profound implications for the oxidation state and composition of the core (see Williams and Hemley (2001) ) furthermore, a byproduct would be a thick steam atmosphere, which would be sufficiently insulating to ensure a magma ocean ( Matsui and Abe, 1986 ). Although the Earth formed inside the ‘snow line’, where water ice becomes unstable, some of its constituent planetesimals may have been derived from greater heliocentric distances and thus contained more water. Simulations ( Morbidelli et al., 2000 Raymond et al., 2004 ) suggest that a water-rich Earth is quite likely, but the stochastic nature of the outcomes precludes a firm conclusion. Radial mixing of planetesimals is clearly not completely efficient because of the differing oxygen-isotope characteristics of Earth and Mars (e.g., Clayton and Mayeda, 1996 ).


Effects of tidal forces

In the case of an infinitesimally small elastic sphere, the effect of a tidal force is to distort the shape of the body without any change in volume. The sphere becomes an ellipsoid with two bulges, pointing towards and away from the other body. Larger objects distort into an ovoid, and are slightly compressed, which is what happens to the Earth's oceans under the action of the Moon. The Earth and Moon rotate about their common center of mass or barycenter, and their gravitational attraction provides the centripetal force necessary to maintain this motion. To an observer on the Earth, very close to this barycenter, the situation is one of the Earth as body 1 acted upon by the gravity of the Moon as body 2. All parts of the Earth are subject to the Moon's gravitational forces, causing the water in the oceans to redistribute, forming bulges on the sides near the Moon and far from the Moon. [6]

When a body rotates while subject to tidal forces, internal friction results in the gradual dissipation of its rotational kinetic energy as heat. If the body is close enough to its primary, this can result in a rotation which is tidally locked to the orbital motion, as in the case of the Earth's moon. Tidal heating produces dramatic volcanic effects on Jupiter's moon Io. Stresses caused by tidal forces also cause a regular monthly pattern of moonquakes on Earth's Moon.

Tidal forces contribute to ocean currents, which moderate global temperatures by transporting heat energy toward the poles. It has been suggested that in addition to other factors, harmonic beat variations in tidal forcing may contribute to climate changes. However, no strong link has been found to date. [7]

Tidal effects become particularly pronounced near small bodies of high mass, such as neutron stars or black holes, where they are responsible for the "spaghettification" of infalling matter. Tidal forces create the oceanic tide of Earth's oceans, where the attracting bodies are the Moon and, to a lesser extent, the Sun. Tidal forces are also responsible for tidal locking and tidal acceleration.


Time, Tides and Habitability

Keep your eye on Gliese 581. Not that the news is necessarily good for our hopes for habitability around that star — in fact, a recent paper suggests quite the opposite. The red dwarf exploded into the public consciousness with the announcement that one of its planets — Gl 581 c — could conceivably support clement temperatures and water at the surface, at least in places. But in exploring that possibility, we’re getting a case study of world-class science at work, analyzing data, offering hypotheses, broadening options. It’s an exciting process to watch.

Gl 581 d is now being analyzed for habitability, while Gl 581 c begins to appear less and less likely as a home to life. It may take decades and new space-based observatories for the issue to be resolved, but we now have a new take on Gl 581 c, embedded in a broader study of tidal evolution as planetary systems evolve. The study has implications not just for rocky worlds but for planetary formation in many scenarios.

The work of Brian Jackson, Richard Greenberg and Rory Barnes (University of Arizona) draws on a key fact: A planet’s orbit can be greatly affected by tides that the planet raises on its star, and on the tides the star raises on the planet. In fact, tidal distortion and orbital evolution work together, tidal forces producing internal heating at the expense of orbital energy. Thus many close-in planets probably formed further out from their host star than their present position. In a typical case, say the authors, tidal heating increases as a planet moves inward and then decreases when the tides circularize the orbit and shut down the heat mechanism.

But each case will be different, the strength and timing of these effects determining a planet’s properties. The team’s intention is to construct heating histories for planets whose radii have been measured, sometimes with results that vary from theory. And that gets me back to Gl 581 c, for in terms of planets with masses less than ten times Earth’s, such heating could have played a role in the planet’s geophysical development. The Arizona team finds that the contribution of tidal energies on two ‘super Earths’ — Gl 581 c and GJ 876 d — should produce a heat flux with profound implications:

Among terrestrial-scale planets, we find that tidal heating may have dominated the geological and geophysical evolution of the planets and control their current character. The tidal heating rate for GJ 876 d may be orders of magnitude greater than the magnitude considered by Valencia et al. to be geophysically significant. For Gl 581 c tidal heating may yield a surface flux about three times greater than Io’s, suggesting the possibility of major geological activity.

Three times that of Io? Gl 581 c looks less hospitable all the time. The case of GJ 876 d is even more extreme. This ‘super-Earth’ of 5.89 Earth masses hasn’t been in the habitability picture because its two-day orbit keeps it far too close to its star for liquid water to exist. But while the planet has been considered vulnerable to tidal stresses, I don’t think anyone was prepared for what the Arizona team found:

…radiogenic heating of GJ 876 d might have been adequate to initiate plate tectonics, but our results indicate that tidal heating may have been a major contributor to the geological and geophysical character of the planet. Tidal heat has provided an important component of the heat budget for this planet, perhaps the dominant component during at least the past

10 8 yr. The tidal heating rate would be so large, in fact, that GJ 876 d is unlikely to be a solid, rocky body.

I’ve only focused on two super-Earths here, but the paper also offers interesting takes on planets like HD 209458 b, whose radius is larger than predicted, and HAT-P-2 b, whose radius is well below prediction. Tidal heating histories may help us understand these apparent anomalies. The paper is Jackson, Greenberg and Barnes, “Tidal Heating of Extra-Solar Planets,” accepted by the Astrophysical Journal (abstract).

Comments on this entry are closed.

Hmmm, doesn’t look well indeed for the Gliese planets. Tital forces were an early worry for red dwarf star planetary systems to begin with weren’t they Paul? Mainly if there were rocky worlds, they would be tidal locked with one face toward the primary.

What if one was a little further than the classical ‘sweet spot’? If the orbit isn’t too elliptic and the tidal forces was just enough for plate tectonics, the generated heat might make conditions somewhat livable(?)

dad2059, you’re right, we’ve had concerns voiced here about tidal forces and red dwarfs before, although the tidal lock isn’t necessarily a show-stopper when it comes to habitable conditions on at least part of the planet’s surface. It appears to me after reading the current paper that we have a long way to go in characterizing these forces and their potential effect over time. I know that Paul Shankland at the US Naval Observatory, a major player in the M-dwarf planet hunt, thinks these stars will offer up many potentially habitable planets, so I wouldn’t write anything off yet, except perhaps GJ 876!

Gl 581 c, we hardly knew ye!

Seriously, though, we need improvements that will allow not just identification but also observation of earth-like planets. Our science and culture will be totally altered (and, I venture to hope, for the better) by such advances.

Radiative Thrusters on Close-in Extrasolar Planets

Abstract: The atmospheres of close-in extrasolar planets absorb most of the incident stellar radiation, advect this energy, then reradiate photons in preferential directions. Those photons carry away momentum, applying a force on the planet. Here we evaluate the resulting secular changes to the orbit, known as the Yarkovsky effect. For known transiting planets, typical fractional changes in semi-major axis are about 1% over their lifetime, but could be up to

5% for close-in planets like OGLE-TR-56b or inflated planets like TrES-4.

We discuss the origin of the correlation between semi-major axis and surface gravity of transiting planets in terms of various physical processes, finding that radiative thrusters are too weak by about a factor of 10 to establish the lower boundary that causes the correlation.

Comments: 4 pages, accepted to ApJL

Subjects: Astrophysics (astro-ph)

Cite as: arXiv:0803.1839v1 [astro-ph]

From: Daniel Fabrycky [view email]

[v1] Thu, 13 Mar 2008 18:35:03 GMT (26kb)

Tidal heating may improve the chances of habitability on sub-Earth sized planets. One of the reasons Mars is so unihabitable is that it is geologically dead.

If you look at what we know of Earth’s and Mars’s history, the biggest factor in maintaining habitability appears to be is geological activity. It helps maintain a degree of stasis against external forcing of the environment and it also maintains a chemical disequilibrium, which can provide an energy source for life.

Tidal forces could provide useful energy for keeping planets warm – especially if those planets are moons! Look at Io and Europa, then imagine them a bit bigger. Could their tidal-heating help sustain a deep greenhouse atmosphere on a Mars or Earth sized moon?

This poses the question of just what kind of planet Gliese 876d actually is. If it’s rocky, perhaps there is a global magma ocean? What about on a planet where the main component by composition is icy material?

In addition, there’s the issue of how much energy goes into volcanism and how much energy goes into moving tectonic plates around on the planet’s surface.

One thing seems fairly certain – given the combination of high gravity and extensive melting, these planets are not places to expect significant vertical relief.

Once again, in the recent hype over M star planets folks forget how narrow the HZ is for a typical M red dwarf several THOUSANTHS or less of the sun’s luminosity. Tidal show stopers aside, the extremely low probability of finding a rocky planet in such tiny HZs works against even the large #s of M dwarfs.

Sadly, F stars have large HZs potentially containing multiple ‘Earthlike’ planet candidates, but their shorter lifetimes would tend to migrate the HZ outward too quickly for multicellular life to evolve, assuming (a big one) that Earth’s history is typical.

The fact we’ve found several planets in, or close to, the red dwarf CHZ, might mean there’s not a random distribution of planetary orbits. A lot of cosmogonists expect some kind of scaling dependent on the star’s mass, thus making planets in the CHZ more likely than chance alone.

The enhanced tidal forces might allow liquid water biocompatibility even further out than anyone has so far guessed. Definitely a process to watch out for as the tally of red dwarf planets goes up.

Adam,
I wasn’t so much thinking of moons but of a planet somewhere between Mars and Earth’s mass, tidally locked, and having its orbital eccentricity pumped by a larger planet.

There is evidence that tidally locked planets may be habitable the heat transfer is enough to keep the atmosphere from freezing out. And tectonic activity is certainly likely to help in this regard.

I could see tidal heating helping habitability in the following ways:
i) Creation and maintenance of a magnetic which would help prevent atmospheric loss (Though this argument is questionable as the planet’s orbital period and hence its rotational period would be in weeks, and Io, which rotates every 1.7 days doesn’t have a magnetic field for some reason.)
Anyhow, the primary, being a red-dwarf, would put out a lot less UV, which would slow atmospheric loss.

ii) Once the carbonate cycle thinned the atmosphere so the planet froze, a more active volcanism would reverse this process more quickly. Even if the planet froze over completely, active volcanism would maintain subsurface oceans and keep the overlaying ice cap thin enough so that cracks may open to the surface allowing photosynthesis.

I also think that tidally locked planets, because of their extremes, would have a broader HZ than planets with more equitable conditions over their entire surface. Because it’s difficult to freeze the sub-solar point of a tidally locked planet or melt the antisolar point, they would resist runaway greenhouse or freezing out.

Actually, given the differences or this type of planet to Earth, I think rather than use the term “Habitable Zone” which implies humans could live there, I’d use the term “Life Bearing Zone.”

Because Red dwarfs are very common and I assume smaller planets more common than larger ones, then this sort scenario has a reasonable probability.

“The fact we’ve found several planets in, or close to, the red dwarf CHZ, might mean there’s not a random distribution of planetary orbits. A lot of cosmogonists expect some kind of scaling dependent on the star’s mass, thus making planets in the CHZ more likely than chance alone.”

Although the science isn’t solid I also believe distribution’s NOT random and that it DOES scale with mass somewhat, but do the math. Let’s assume that the sun’s HZ for an Earthlike planet to survive several BILLION years without total freeze over or heat runaway allowing the evolution of complex multi-celled life is say 30 million miles, a decent window to have a terrestrial planet form within. However, given this the HZ of a typical M dwarf of less than a solar mass is under 1 million miles. Luminosity and SQRT. So, the fact that there are several tens of times more Ms than Gs is more than mitigated by the low probability of a terrestrial style planet hiting this really tiny HZ.

And that’s forgeting the troublesome tidal problems raised in this discussion.

If instead of jumping in with maths we take a look at the data…

If philw1776 is correct, then planets in the habitable zones of M dwarfs would be vanishingly rare, but instead we have two systems with planets in the HZ (both of which may have up to two planets in the HZ), out of a total of about eight planetary systems known around M dwarfs. This strikes me as staggeringly unlikely if such planets are as vanishingly rare as philw1776 makes out.

I took a look at the average planetary spacing around the habitable zone in an attempt to get a quantitative answer to the likelihood of planets falling into a red dwarf’s HZ. The calculations I did are very ad hoc and rough and there isn’t a statistically significant sized sample to conclude anything nevertheless, I think you can get some idea by looking at the situation.

If you take a look at the sun and assume like philw1776 did that the HZ is 30 million miles wide and if you look at the average planetary spacing around Earth (40 million miles) then you could assume that in any given sunlike system the would be a 75% chance of a planet falling into the habitable zone.

If you look at a M3/M4 dwarfs like GL 581 and GL 876, the HZ is from 3 to 4 million miles out. The planetary spacing at about this distance, if we look at the GL 581, GL 876 and 55 cancri sysyems (and assume there is at least one extra planet between GL 876 b & c) is in the order of 4 million miles so the likelihood of a planet falling in the HZ falls to 25%. While this is less frequent than for sunlike stars, it is not vanishingly rare.

In fact it is probably better to do this analysis in logarithmic space rather than linear: a spacing rule of the form a=A exp(Bn) fits both our own solar system (with the planets in positions n=1,2,3,4,6,7,8,9) and 55 Cancri (1,2,3,4,6).

The value of B, which represents the spacing of the planets in logarithmic space seems to range from about 0.6 to 1 for most of the known systems (including the red dwarf systems). The logarithmic width of the habitable zone is unaffected by scaling for luminosity. taking an HZ of 0.95 to 1.6 AU in our solar system corresponds to a logarithmic width of about 0.5. More liberal definitions of the HZ could take this figure up to 0.8 or more… thus systems with 1-2 planets in the habitable zone are quite plausible and should be fairly frequent, even around M dwarfs.

For reference, the planetary configurations I investigated for the M dwarf systems, together with the error on the linear regression in logarithmic space and the value of B:
Gliese 581 (1,2,3): err=0.27 B=0.9
Gliese 581 (1,2,4): err=0.02 B=0.6
Gliese 876 (1,3,4): err=0.24 B=0.8
Gliese 876 (1,4,5): err=0.08 B=0.6

Ground-based detection of sodium in the transmission spectrum of exoplanet HD209458b

Authors: I.A.G. Snellen, S. Albrecht, E.J.W. de Mooij, R.S. Le Poole (Leiden Observatory)

Abstract: [Context] The first detection of an atmosphere around an extrasolar planet was presented by Charbonneau and collaborators in 2002. In the optical transmission spectrum of the transiting exoplanet HD209458b, an absorption signal from sodium was measured at a level of 0.023+-0.006%, using the STIS spectrograph on the Hubble Space Telescope. Despite several attempts, so far only upper limits to the Na D absorption have been obtained using telescopes from the ground, and the HST result has yet to be confirmed.

[Aims] The aims of this paper are to re-analyse data taken with the High Dispersion Spectrograph on the Subaru telescope, to correct for systematic effects dominating the data quality, and to improve on previous results presented in the literature.

[Methods] The data reduction process was altered in several places, most importantly allowing for small shifts in the wavelength solution. The relative depth of all lines in the spectra, including the two sodium D lines, are found to correlate strongly with the continuum count level in the spectra. These variations are attributed to non-linearity effects in the CCDs. After removal of this empirical relation the uncertainties in the line depths are only a fraction above that expected from photon statistics.

[Results] The sodium absorption due to the planet’s atmosphere is detected at >5 sigma, at a level of 0.056+-0.007% (2ࡩ.0 Ang band), 0.070+-0.011% (2ࡧ.5 Ang band), and 0.135+-0.017% (2ࡦ.75 Ang band). There is no evidence that the planetary absorption signal is shifted with respect to the stellar absorption, as recently claimed for HD189733b. The measurements in the two most narrow bands indicate that some signal is being resolved.
[abridged]

Comments: Latex, 7 pages: accepted for publication in Astronomy & Astrophysics

Subjects: Astrophysics (astro-ph)

Cite as: arXiv:0805.0789v1 [astro-ph]

From: Ignas Snellen [view email]

[v1] Wed, 7 May 2008 07:44:22 GMT (79kb)

Tides and the Evolution of Planetary Habitability

Authors: Rory Barnes, Sean N. Raymond, Brian Jackson, Richard Greenberg

Abstract: Tides raised on a planet by its host star’s gravity can reduce a planet’s orbital semi-major axis and eccentricity. This effect is only relevant for planets orbiting very close to their host stars. The habitable zones of low-mass stars are also close-in and tides can alter the orbits of planets in these locations.

We calculate the tidal evolution of hypothetical terrestrial planets around low-mass stars and show that tides can evolve planets past the inner edge of the habitable zone, sometimes in less than 1 billion years. This migration requires large eccentricities (>0.5) and low-mass stars (<0.35 M_Sun). Such migration may have important implications for the evolution of the atmosphere, internal heating and the Gaia hypothesis.

Similarly, a planet detected interior to the habitable zone could have been habitable in the past. We consider the past habitability of the recently-discovered,

5 M_Earth planet, Gliese 581 c. We find that it could have been habitable for reasonable choices of orbital and physical properties as recently as 2 Gyr ago.

However, when we include constraints derived from the additional companions, we see that most parameter choices that predict past habitability require the two inner planets of the system to have crossed their mutual 3:1 mean motion resonance. As this crossing would likely have resulted in resonance capture, which is not observed, we conclude that Gl 581 c was probably never habitable.

Comments: 31 pages, 10 figures, accepted to Astrobiology. A version with full resolution figures is available at this http URL


Kirchoff et al. in Enceladus and the Icy Moons of Saturn 267–284 (Univ. of Arizona Press, 2018).

Lainey et al. New constraints on Saturn’s interior from Cassini astrometric data. Icarus 281, 286–296 (2017).

Ćuk, M., Dones, L. & Nesvorný, D. Dynamical evidence for a late formation of Saturn’s moons. Astrophys. J. 820, 97 (2016).

Asphaug, E. & Reufer, A. Late origin of the Saturn system. Icarus 223, 544–565 (2013).

Canup, R. M. Origin of Saturn’s rings and inner moons by mass removal from a lost Titan-sized satellite. Nature 468, 943–946 (2010).

Movshovitz, N., Nimmo, F., Korycansky, D. G., Asphaug, E. & Owen, J. M. Disruption and reaccretion of midsized moons during an outer solar system late heavy bombardment. Geophys. Res. Lett. 42, 256–263 (2015).

Charnoz, S. et al. Accretion of Saturn’s mid-sized moons during the viscous spreading of young massive rings: solving the paradox of silicate-poor rings versus silicate-rich moons. Icarus 216, 535–550 (2011).

Beuthe, M., Rivoldini, A. & Trinh, A. Enceladus’s and Dione’s floating ice shells supported by minimum stress isostasy. Geophys. Res. Lett. 43, 10088–10096 (2016).

Čadek, O. et al. Enceladus’s internal ocean and ice shell constrained from Cassini gravity, shape, and libration data. Geophys. Res. Lett. 43, 5653–5660 (2016).

McKinnon, W. B. Effect of Enceladus’s rapid synchronous spin on interpretation of Cassini gravity. Geophys. Res. Lett. 42, 2137–2143 (2015).

Tajeddine, R. et al. Constraints on Mimas’ interior from Cassini ISS libration measurements. Science 346, 322–324 (2014).

Tortora, P. et al. Rhea gravity field and interior modeling from Cassini data analysis. Icarus 264, 264–273 (2016).

Thomas, P. C. et al. Enceladus’s measured physical libration requires a global subsurface ocean. Icarus 264, 37–47 (2016).

Hsu, H.-W. et al. Ongoing hydrothermal activities within Enceladus. Nature 519, 207–210 (2015).

Waite, J. H. et al. Cassini finds molecular hydrogen in the Enceladus plume: evidence for hydrothermal processes. Science 356, 155–159 (2017).

Porco, C. C. et al. Cassini observes the active south pole of Enceladus. Science 311, 1393–1401 (2006).

Bland, M. T., McKinnon, W. B. & Schenk, P. M. Constraining the heat flux between Enceladus’ tiger stripes: numerical modeling of funiscular plains formation. Icarus 260, 232–245 (2015).

Howett, C. J. A., Spencer, J. R., Pearl, J. & Segura, M. High heat flow from Enceladus' south polar region measured using 10–600 cm −1 CASSINI/CIRS data. J. Geophys. Res. Planet. 116, E03003 (2011).

Spencer, J. R. et al. Enceladus heat flow from high spatial resolution thermal emission observations. Eur. Planet. Sci. Congr. Abstr. 8, 840–841 (2013).

Neveu, M. & Rhoden, A. R. The origin and evolution of a differentiated Mimas. Icarus 296, 183–196 (2017).

Rhoden, A. R., Henning, W., Hurford, T. A., Patthoff, D. A. & Tajeddine, R. The implications of tides on the Mimas ocean hypothesis. J. Geophys. Res. Planet. 122, 400–410 (2017).

Czechowski, L. & Witek, P. Comparison of early evolutions of Mimas and Enceladus. Acta Geophys. 63, 900–921 (2015).

Malamud, U. & Prialnik, D. Modeling serpentinization: applied to the early evolution of Enceladus and Mimas. Icarus 225, 763–774 (2013).

Schubert, G., Anderson, J. D., Travis, B. J. & Palguta, J. Enceladus: present internal structure and differentiation by early and long-term radiogenic heating. Icarus 188, 345–355 (2007).

Shoji, D., Hussmann, H., Sohl, F. & Kurita, K. Non-steady state tidal heating of Enceladus. Icarus 235, 75–85 (2014).

Travis, B. J. & Schubert, G. Keeping Enceladus warm. Icarus 250, 32–42 (2015).

Zhang, K. & Nimmo, F. Late-stage impacts and the orbital and thermal evolution of Tethys. Icarus 218, 348–355 (2012).

Meyer, J. & Wisdom, J. Tidal evolution of Mimas, Enceladus, and Dione. Icarus 193, 213–223 (2008).

Zhang, Z. et al. Cassini microwave observations provide clues to the origin of Saturn’s C ring. Icarus 281, 297–321 (2017).

Zhang, Z. et al. VLA multi-wavelength microwave observations of Saturn’s C and B rings. Icarus 317, 518–548 (2019).

Charnoz, S., Morbidelli, A., Dones, L. & Salmon, J. Did Saturn’s rings form during the late heavy bombardment? Icarus 199, 413–428 (2009).

Hyodo, R., Charnoz, S., Ohtsuki, K. & Genda, H. Ring formation around giant planets by tidal disruption of a single passing large Kuiper belt object. Icarus 282, 195–213 (2017).

Dubinski, J. A recent origin for Saturn’s rings from the collisional disruption of an icy moon. Icarus 321, 291–306 (2019).

Fuller, J., Luan, J. & Quataert, E. Resonance locking as the source of rapid tidal migration in the Jupiter and Saturn moon systems. Mon. Not. R. Astron. Soc. 458, 3867–3879 (2016).

Robbins, S. et al. Estimating the masses of Saturn’s A and B rings from high-optical depth n-body simulations and stellar occultations. Icarus 206, 431–445 (2010).

Grossmann, L. Saturn’s rings are surprisingly young and may be from shredded moons. Sci. News 193, 7 (2018).

Choblet, G. et al. Powering prolonged hydrothermal activity inside Enceladus. Nat. Astron. 1, 841–847 (2017).

Roberts, J. H. The fluffy core of Enceladus. Icarus 258, 54–66 (2015).

Tyler, R. Comparative estimates of the heat generated by ocean tides on icy satellites in the outer solar system. Icarus 243, 358–385 (2014).

Sekine, Y. et al. High-temperature water-rock interactions and hydrothermal environments in the chondrite-like core of Enceladus. Nat. Commun. 6, 8604 (2015).

Meyer, J. & Wisdom, J. Tidal heating in Enceladus. Icarus 188, 535–539 (2007).

Roberts, J. H. & Nimmo, F. Tidal heating and the long-term stability of a subsurface ocean on Enceladus. Icarus 194, 675–689 (2008).

Dermott, S. F. & Thomas, P. C. The shape and internal structure of Mimas. Icarus 73, 25–65 (1988).

Malhotra, R. Orbital resonances and chaos in the Solar System. In Solar System Formation and Evolution Vol. 149 (eds Lazzaro, D., Vieira Martins, R., Ferraz-Mello, S. & Fernandez, J.) 37 (ASP Conference Series, 1998).

Desch, S. J., Cook, J. C., Doggett, T. C. & Porter, S. B. Thermal evolution of Kuiper belt objects, with implications for cryovolcanism. Icarus 202, 694–714 (2009).

Rubin, M. E., Desch, S. J. & Neveu, M. The effect of Rayleigh–Taylor instabilities on the thickness of undifferentiated crust on Kuiper belt objects. Icarus 236, 122–135 (2014).

Neveu, M., Desch, S. J. & Castillo-Rogez, J. C. Core cracking and hydrothermal circulation can profoundly affect Ceres’ geophysical evolution. J. Geophys. Res. Planet. 120, 123–154 (2015).

Lodders, K. Solar system abundances and condensation temperatures of the elements. Astrophys. J. 591, 1220 (2003).

Tobie, G., Mocquet, A. & Sotin, C. Tidal dissipation within large icy satellites: applications to Europa and Titan. Icarus 177, 534–549 (2005).

Sabadini, R. & Vermeersen, B. in Global Dynamics of the Earth 1–44 (Springer, 2004).

Meyer-Vernet, N. & Sicardy, B. On the physics of resonant disk-satellite interaction. Icarus 69, 157–175 (1987).

Nakajima, A., Ida, S., Kimura, J. & Brasser, R. Orbital evolution of Saturn’s mid-sized moons and the tidal heating of Enceladus. Icarus 317, 570–582 (2019).

Henning, W. G. & Hurford, T. Tidal heating in multilayered terrestrial exoplanets. Astrophys. J. 789, 30 (2014).

Chambers, J. E. A hybrid symplectic integrator that permits close encounters between massive bodies. Mon. Not. R. Astron. Soc. 304, 793–799 (1999).

Greenberg, R., Wacker, J. F., Hartmann, W. K. & Chapman, C. R. Planetesimals to planets: numerical simulation of collisional evolution. Icarus 35, 1–26 (1978).

Zhang, K. & Nimmo, F. Recent orbital evolution and the internal structures of Enceladus and Dione. Icarus 204, 597–609 (2009).

Noyelles, B., Baillie, K., Lainey, V. & Charnoz, S. How Mimas cleared the Cassini division. AAS/DPS Meet. Abstr. 48, 121.07 (2016).

Dermott, S. F., Malhotra, R. & Murray, C. D. Dynamics of the Uranian and Saturnian satellite systems: a chaotic route to melting Miranda? Icarus 76, 295–334 (1988).

Tsiganis, K., Gomes, R., Morbidelli, A. & Levison, H. F. Origin of the orbital architecture of the giant planets of the Solar System. Nature 435, 459–461 (2005).

Barnes, R., Deitrick, R., Greenberg, R., Quinn, T. R. & Raymond, S. N. Long-lived chaotic orbital evolution of exoplanets in mean motion resonances with mutual inclinations. Astrophys. J. 801, 101 (2015).

Borderies, N. & Goldreich, P. A simple derivation of capture probabilities for the j+1:j and j + 2:j orbit-orbit resonance problems. Celestial Mech. 32, 127–136 (1984).

Wisdom, J. Tidal dissipation at arbitrary eccentricity and obliquity. Icarus 193, 637–640 (2008).

Greenberg, R. Orbit-orbit resonances in the solar system: varieties and similarities. Vistas Astron. 21, 209–239 (1977).

Sekine, Y. & Genda, H. Giant impacts in the Saturnian system: a possible origin of diversity in the inner mid-sized satellites. Planet. Space Sci. 63, 133–138 (2012).

Salmon, J. & Canup, R. M. Accretion of Saturn’s inner mid-sized moons from a massive primordial ice ring. Astrophys. J. 836, 109 (2017).

Iess, L. et al. The gravity field and interior structure of Enceladus. Science 344, 78–80 (2014).

Shoji, D. & Hussmann, H. Frequency-dependent tidal dissipation in a viscoelastic Saturnian core and expansion of Mimas’ semi-major axis. Astron. Astrophys. 599, L10 (2017).

Charnoz, S., Salmon, J. & Crida, A. The recent formation of Saturn’s moonlets from viscous spreading of the main rings. Nature 465, 752–754 (2010).

Salmon, J., Charnoz, S., Crida, A. & Brahic, A. Long-term and large-scale viscous evolution of dense planetary rings. Icarus 209, 771–785 (2010).

Howett, C. J. A., Spencer, J. R., Pearl, J. & Segura, M. Thermal inertia and bolometric bond albedo values for Mimas, Enceladus, Tethys, Dione, Rhea and Iapetus as derived from Cassini/CIRS measurements. Icarus 206, 573–593 (2010).

Thomas, P. C. Sizes, shapes, and derived properties of the Saturnian satellites after the Cassini nominal mission. Icarus 208, 395–401 (2010).

Jacobson, R. A. et al. The gravity field of the Saturnian system from satellite observations and spacecraft tracking data. Astron. J. 132, 2520 (2006).

Bland, M. T., Singer, K. N., McKinnon, W. B. & Schenk, P. M. Enceladus’ extreme heat flux as revealed by its relaxed craters. Geophys. Res. Lett. 39, L17204 (2012).

Bland, M. T., Beyer, R. A. & Showman, A. P. Unstable extension of Enceladus’ lithosphere. Icarus 192, 92–105 (2007).

Giese, B. et al. Enceladus: an estimate of heat flux and lithospheric thickness from flexurally supported topography. Geophys. Res. Lett. 35, L24204 (2008).

White, O. L. et al. Impact crater relaxation on Dione and Tethys and relation to past heat flow. Icarus 288, 37–52 (2017).

Hammond, N. P., Phillips, C. B., Nimmo, F. & Kattenhorn, S. A. Flexure on Dione: investigating subsurface structure and thermal history. Icarus 223, 418–422 (2013).

Nimmo, F., Bills, B. G., Thomas, P. C. & Asmar, S. W. Geophysical implications of the long-wavelength topography of Rhea. J. Geophys. Res. Planet. 115, E10008 (2010).


Time and Tides Have An Effect on Life

The creation of life on our planet was a long, drawn-out affair, taking more than a billion years of chemical and biochemical processing to accomplish after the planet formed some 4.5 billion years ago. Technically, life began some 3.8 billion years ago in some life-friendly oasis on the planet, meaning that the correct conditions were there for some chemically-rich soup to react to something like an influx of heat or a zap of lightning, producing the first living things. There’s enough ambiguity in there that just about anybody can come up with a theory about what happened (including some pretty jaw-dropping ones about LGMs, travelling deities, and so on), but the scientific consensus (based on verifiable research) is that the primal ooze finally combined in ways that led to the first life forms, and from there it was evolution all the way, baby.

Before all this happened, though, the planet had to form, and it had to do it in the right place. There’s the rub. If a planet forms too close to its star, its surface gets broiled. Mercury’s a good example here — its surface is alternately flame-roasted and then chilled as it rotates on its axis only 69 million kilometers from the Sun. Get too far away from the Sun, say out in the realm of the gas giants, and it’s too cold for a hard-body planet (i.e. rocky) to form life.

Distance isn’t the only characteristic you have to consider, however. There’s also a little thing called “tides” — and I’m not talking simply about the ocean tides we experience here on Earth, although they’re part and parcel of the same phenomenon.

Jupiter's moon Io is heated by tidal friction.

When two bodies interact with each other, gravitational interactions can push and pull on their surfaces, creating tides — and that also heats them.

Jupiter’s moon Io shows an extreme case of tidal heating — gravitational interactions between Jupiter and this tiny moon and its sibling moons Europa and Ganymede cause the surface to bulge up and down. This also heats Io’s interior, and the end result is a volcanic moon.

Tidal heating between a star and its planet (or even a planet and its moons) can drive plate tectonics. Earth has plates, is heated from within, and also has a “tidal” relationship with the Moon. Our planet’s “basement” is basically made up of seven major plates (and several smaller ones) and the continents and oceans ride along on top of them. (For more about plate tectonics on Earth, go here or here.). Among other things, tectonics keeps excessive carbon dioxide from accumulating in a planetary atmosphere. If it hadn’t performed this service on Earth, we might have a deadly greenhouse atmosphere like the one at Venus.

A group of scientists at University of Arizona is looking into the role that such tides play on planets and what influence they may have on whether life could evolve on rocky planets around other stars. Brian Jackson, Rory Barnes and Richard Greenberg of UA’s Lunar and Planetary Laboratory gave a paper at the Division of Planetary Sciences meeting in Ithaca, New York, and in it they say that tides can play a major role in heating terrestrial planets. Such tides could create scenes of unbelievable hellishnesson rocky alien worlds that would be livable if conditions were better. And tidal heat can work in reverse, creatiing conditions favorable to life on planets that would otherwise be unlivable.

A map of Earth's tectonic plates -- did they help life get started?

What this means is that as astronomers search out worlds on other planets, they might need to examine exoplanets in great detail to see if tidal heating (from their stars or interactions with possible moons) is playing a role in their livability factors. Recently there have been so-called “super Earths” discovered around other stars. These planets are somewhere between two and ten times as massive as Earth. If they really ARE Earthlike (meaning that they’re rocky bodies around the size of the Earth or bigger) then it’s possible that tidal heating from interactions with their star or nearby moons may be great enough to melt them, or at least produce volcanism at a level that we see at Io. This would make them pretty poor prospects for being life-bearing planets, and they’d be more like “super-Ios.”

The more massive a planet is, the greater the effects of tidal heating will be on its surface and interior. This means that the most easily detectable super-Earths could be dominated by volcanic activity, which is one of the big conclusions that the University of Arizona team came to in their research. So, the first Earth-like planets found are going to be the most easily spotted, and thus they’ll be big. This means they’ll probably going to be strongly heated and have big volcanoes.

A super-Earth with plate tectonics and experiencing tidal forces needs the right amount of both to support life.

And as astronomers find Earth-like planets in what they cal,l the “habitable zone” around other stars, those planets may well NOT be habitable if they’re gobsmacked by tidal heating.

On the other hand, if a planet is smaller than it should be, or maybe lies outside the habitable zone, it could still support life if it is heated by tidal interactions that could cause outgassing of volatiles (gases, ices) that enrich a planet’s atmosphere with the right stuff needed for life. Tidal heating also can generate sub-surface liquid oceans on water-rich rocky planets that would otherwise be frozen, just as tidal heating is believed to warm a sub-surface liquid water ocean on Jupiter’s moon Europa.

Also, tidal heating could produce enough heat to drive plate tectonics for billions of years, long enough for life to appear and flourish.

So, for those of you keeping score at home, the ingredient list for life is getting more and more refined. And, when we look at other planets in our search for life, we need at where the planet exists in relation to its star, how long it’s been around, whether it can supply the water, warmth, and “food” for life, and now, whether or not it is subject to the correct application of tidal force.