ASTR 1210 (O'Connell) Study Guide

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11. PLANETARY SYSTEMS: OURS AND OTHERS

Comparison of the planets, based on NASA images.
Sizes are to scale, but separations are not.

The four large satellites of Jupiter discovered by Galileo in 1610 with his small telescope were the first new members of the Solar System identified in recorded history. They instantly increased the known membership of the Solar System from 8 to 12. Since that time, astronomers have identified hundreds of thousands of Solar System bodies (planets, satellites, and smaller rocky or icy objects) with telescopes and spacecraft.

Most remarkably, after thousands of years of speculation about other worlds like ours in the universe, astronomers have recently discovered planets in orbit around other stars---exoplanets.

This lecture describes the general properties of our planetary system and those around other stars and how we believe these originated.

A. Inventory of the Solar System

By terrestrial standards, the density of matter in the Solar System is extremely low, and the planets are separated by enormous gaps.

Contents of the Solar System:

• The Sun (99.8% of total mass)

• 4 "terrestrial" (Mercury, Venus, Earth, Mars) and 4 "Jovian" (Jupiter, Saturn, Uranus, Neptune) planets (0.1% of the mass). Jupiter's mass is greater than the masses of the other planets combined.

• Over 180 satellites of planets

• Hundreds of thousands of smaller rocky or icy bodies, ranging in size down to about 50 meters. The largest of these, including Pluto, are now called "dwarf planets." (We will postpone discussion of the controversy over the use of this terminology until Study Guide 20).
  Most of these are members of the asteroid belt between Mars and Jupiter or the "Kuiper Belt" in the outer solar system, beyond Neptune.
  Objects smaller than dwarf planets but larger than about 50-m diameter are called "asteroids" if they are composed of rocky materials or "comets" if they are icy.

• Meteoroids (rocky or icy bodies smaller than 50-m), dust, gas

• Other than the Sun, no solar system object is self-luminous at visible wavelengths, and all shine by reflected sunlight. Seen from the Earth, the second and third-brightest celestial objects are Earth's Moon and Venus.

For a diagram of the current location of the planets in their orbits, click here.

An oblique view of the planetary orbits drawn to scale
(though the planet sizes shown are not to scale).

B. Systematics of Planet Orbits

Systematic characteristics of the orbits of the terrestrial and Jovian planets:

• Orbits for all lie close to the plane of the Earth's orbit (the ecliptic plane)
  In the picture above, you can see the "cozy" inner solar system (Mercury through Mars) separated from the vast outer solar system by the asteroid belt.
  For an edge-on plot of the orbits showing the near-coincidence of the orbital planes, click here.
  The orbits of the "dwarf planets," including Pluto, can be more highly inclined to the ecliptic plane.

• The orbits, though technically ellipses, are nearly circular

• The direction of revolution of the planets in their orbits is the same (counterclockwise from above Earth's N. pole); the direction of spin on their rotation axis is the same for most.

• The orbits show systematic spacing (Bode's "Law"): the separation between orbits increases with orbit size from Mercury through Uranus. This is apparent in the figure above.

It is important to understand that none of the above is required by Newton's laws.

For example: Newton's laws imply the orbit of a given planet will be in a fixed plane, but the orbits of other planets could lie in different planes; revolution directions do not have to be the same; orbits can be highly elliptical rather than nearly circular; etc.

Instead, these systematics must be the product of special physical conditions prevailing during formation of the planets. That is, they provide clues to the process that forms planets.

C. Segregation of Physical Properties

The four "inner" or "terrestrial" planets (Mercury, Venus, Earth Mars) show a striking dissimilarity from the four large "outer" or "Jovian" planets (Jupiter, Saturn, Uranus, Neptune):

	INNER (TERRESTRIAL)	OUTER (JOVIAN)
Size & Mass**	Small	Large
Density	Large	Small
Composition	Si,O,Al,Mg,Fe Rocky	H,He Gas Giants

**See the image at the top of this page for a graphic comparison of planet sizes.

These differences constitute another major clue about the processes that formed the planetary system.

Note: we are deliberately omitting Pluto here, since it is not representative of either group.

D. Origin of the Solar System

Since the time of Galileo, there have been many models for the origin of the solar system. They all fall into two main categories:

• "Catastrophic/tidal theory": a passing star pulls material from Sun, which cools to form planets
  This would imply planets are rare, since close encounters between stars are extremely rare.
  The process is also physically unlikely: expelled solar material would be very hot and would diffuse quickly before it was able to condense.

• "Nebular theory": planets form from the cloud ("nebula") of cool debris surrounding a forming star. The theory was first described in 1755 by philosopher Immanuel Kant.
  This would imply planets are common because they are byproducts of normal star formation.
  There is now excellent supporting evidence for the nebular theory, not least of which is item "G" below

E. The Interstellar Medium and Star Formation

We know that stars are forming continuously out of the "interstellar medium" at a rate of about 1 solar mass per year throughout our Galaxy:

• The interstellar medium (ISM) is the dilute matter between stars. It constitutes a few % of the mass of our Galaxy

• Including the whole volume of the disk of the Galaxy, the average density of the ISM is about 1 atom per cubic centimeter.

• Contents of the ISM:
  Gas (atoms, molecules)
  Composition: hydrogen 71%; helium 27%; all other elements (C,N,O,Fe, etc) only 2%. When hot, or "ionized," this gas is visible as "gaseous nebulae" (producing optical spectra containing, among other features, bright emission lines of hydrogen, as discussed in the Supplements). Where the gas is cold, and in atomic or molecular form, we can detect it using radio telescopes.

  "Dust"
  Very small solid particles or "dust grains", mostly formed in the extended outer atmospheres of cool "red giant" stars and ejected into interstellar space. These are smoke-like. They absorb and redden light passing through them. Absorption by concentrations of dust creates "dark clouds" seen against bright background sources such as the Milky Way.
  Dust plays the essential role of a refrigerant for interstellar gas. Parts of the ISM, if well shielded by dust grains against heating by surrounding stars, can become very dense and cold (reaching only about 10^o K above absolute zero temperature). These are the regions which are primed to turn into nurseries for newly born stars.

A beautiful example of a likely stellar nursery is shown in the picture below:

This is the "Eagle Nebula" imaged by the Hubble Space Telescope. The extended, dark, sculpted "elephant trunk" running across the image is a cold, dusty region. It is surrounded by hot gas (greenish-blue), which is evaporating the cold material away. The small globules on the end of the finger-like protuberances are the densest regions of the cloud, possibly containing protostars with masses like the Sun. Click on the image for a full view. For more pictures and information, click here.

here is an MPEG video of a zoom into the Eagle Nebula.
For Hubble Space Telescope images of another spectacular star-forming region in the Carina Nebula, click here.

F. Planet Formation in the Nebular Theory

Star formation out of the interstellar medium is an amazing process. The compression of the dilute ISM into the body of a star occurs because of the combined effects of gas cooling, which reduces the thermal pressure that keeps clouds inflated, and relentless gravitational attraction. The compression in volume is an astonishing factor of about 10²⁴. The mass that ultimately resides in a star like the Sun originally occupied a volume about 10 light years on a side, a factor of 100 million larger across.

We now have a good, general understanding of how stars and planets form. The detailed physics and chemistry of the processes involved are still being worked out, but progress over the next decade or so should be rapid because of powerful new observational facilities like the Atacama Large Millimeter Array (ALMA, a radio telescope, which can detect molecules and dust grains in planetary systems) and the James Webb Space Telescope designed to attack these specific problems. ALMA is operated by the National Radio Astronomy Observatory here in Charlottesville. JWST, the successor to the Hubble Space Telescope, was launched in 2021.

Here is the sequence of steps in the formation of stars and their planetary systems:

1. Gas in an interstellar cloud cools down and slowly compresses. Dust grains shield the interior and allow it to fall to very low temperatures. After a certain point, a dense, cold cloud in the ISM will start to collapse faster under its own self-gravity:

   
   

2. As it collapses, the cloud spins up & flattens because of the conservation of angular momentum (first illustrated by Kepler's Second Law).
   A rotating, flattened "protoplanetary" disk is a natural consequence of the collapse of the interstellar cloud and is expected to accompany star formation in all enviroments. In the case of our solar system the disk is called the "solar nebula." In the densest parts of the disk, dust grains grow in size and begin to accumulate into larger solids.

   Note! The scale of this picture is much smaller, by several 1000x, than the scale of the previous picture.

3. The dense concentration of material in the center of the disk is the "protostar" ("protosun" in the illustration here).
   The protostar heats up, first from energy released by gravitational collapse, and later, once its core reaches a critical density and pressure, by nuclear reactions. The generated heat counterbalances the self-gravity of the protostar and prevents it from collapsing further.

4. The protostar heats the inner protoplanetary disk to a higher temperature than the outer disk. Here is a typical temperature profile for the disk. Because material in the disk is so dense, large parts of the disk can remain very cold for some time even if the inner regions are quite hot.

5. The heating determines the kinds of solids which can survive in a given part of the disk and generates the segregation of planetary properties:
   Only "refractory" (high melting point) solids survive in the inner disk. These tend to be heavy, rocky materials. Only a small fraction of the total inner disk is in this form since heavy elements are not abundant.
   "Volatile" materials are those with low melting points. They include the ices of water, methane, and ammonia (H₂O, CH₄, NH₃). These will be vaporized in the inner disk.
   On the other hand, these ices can persist in solid form in the cool outer disk. These are hydrogen-rich compounds, and because H is abundant, there is a large amount of such icy material in the outer disk.
   The innermost radius in the disk where icy materials can remain solid is called the "frost line".
   Solids in the outer nebula are more similar in chemical composition to the Sun than are inner nebula solids

6. Larger bodies grow initially from the solids, not from gas, through collisions and sticking together (or "accretion").
   Accretion produces solid bodies with a range of sizes in the sequence grains ==> pebbles ==> "planetesimals" ==> "protoplanets", where the distinction in size between the two latter classes is not firmly defined. A protoplanet is an object over about 500 km in diameter. For larger protoplanets (about 15x the mass of the Earth), gravitational fields can rapidly attract gas from the nebula.
   In the inner disk, small, rocky proto-planets form.
   In the outer disk, beyond the frost line, large, "gas-giant" proto-planets form.

   
   

   
   Computer simulation of protoplanetary disk

7. Final assembly: the violent infall of fragments heats the protoplanets. Collisions between protoplanets and large fragments can have drastic effects, producing extensive melting/resurfacing in a merged protoplanet or even shattering the originals into smaller pieces.

8. The elapsed time for proto-planet formation is now thought to be very short by cosmic standards, ranging from a few hundred thousand to a few million years.

9. The interiors of proto-planets that are large enough are heated and partially melted by the violent accretion and by the decay of short-lived radioactive isotopes. The melted interiors will differentiate, with heavy metallic materials settling to the center and lighter, rocky materials rising to the exterior.

10. Gravitational interactions between planets, or between planets and the residual protoplanetary disk (as in the image above), can drastically change the orbits of the new planets, moving large planets inward, tossing small bodies outward, or pushing planets into more strongly elliptical orbits.

11. Here is a pictorial summary of the nebular model.

Observational Support for the Nebular Model

• The nebular model successfully explains the systematics in the orbital geometry, motions, and compositions listed in Sections B and C above.

• We now have direct detections of protoplanetary disks around nearby stars by the Hubble Space Telescope, infrared telescopes, and ALMA. A montage of disk images made in the far-infrared bands, where cool dust glows brightly, is shown above. The physical and chemical properties of these disks are now being studied intensively with ALMA and other sensitive instruments.

• The expectation from the nebular model that planets should be common and that most stars should have accompanying planetary systems has now been confirmed in dramatic fashion by the discoveries described in the next section.

G. Exoplanets

Speculation about planets around other stars extends as far back in history as the ancient Greeks. The philosophical implications of discovering other planetary systems for the context in which we should view the Earth and the human race have been widely discussed. But for hundreds of years after the invention of telescopes, no planetary companions to other stars were found despite much effort.

Finally, extra-solar planets around other Sun-like stars were positively detected in October 1995. ("Extra-solar" means planetary systems other than that around the Sun, now usually abbreveviated simply to "exoplanets".) We have not only detected exoplanets, but we have established that they are relatively common around Sun-like stars in the Galaxy. And, using special techniques and highly sensitive detectors, we have begun to probe the composition and structure---even the meteorology---of some exoplanets.

Awarding credit for the discovery of exoplanets is, as in other famous cases in astronomy, complicated. The first report of an exoplanet that was ultimately confirmed was made by Campbell, Walker and Yang in 1988. But the confirmation did not come until 2002. In 1992, radio astronomers Wolszczan and Frail detected two exoplanets in orbit around a neutron star (whose pulsed radio emission allows high precision measures of stellar velocity). Whether these are "normal" planets or the product of the tremendous supernova explosion that produced the neutron star has yet to be established. The detection by Mayor and Queloz of the first Jupiter-like exoplanet (51 Pegasi b) around a normal, "main sequence" star like the Sun was announced in 1995.
Regrettably, the Nobel Prize, which is certainly justified in this case, can be awarded to a maximum of three scientists -- and in October 2019 it was won by Mayor and Queloz.

Detection Methods

The initial detections of exoplanets were technically very difficult (or they would have been found sooner!).

We cannot simply take a picture and see the planet. The images of the star and planet are blended together in an ordinary telescope (see the discussion of telescope "resolution" in Study Guide 14), and the feeble reflected light of the planet is completely overwhelmed by the bright star.

Instead, several sophisticated methods have been been developed for finding exoplanets (see this article). We discuss below only the two most widely used of those. The "Doppler method" is particularly important because it is the primary means by which we can obtain estimates of an exoplanet's mass.

Both of these techniques are biased in the sense they are much more sensitive to larger planets at small distances (say less than 1 AU) from a star.

Doppler Velocity Method
The Doppler method for finding exoplanets is based on detecting the tiny changes in the star's motion induced by the gravity of an orbiting planet. These amount to only a few 10's of meters per second.
Recall that in Newtonian gravity, a planet exerts the same force on its parent star as the star exerts on the planet. The star therefore accelerates in response, though the acceleration is very small because it is in inverse proportion to its mass. The animation at right shows how their mutual gravity causes both the star and its planet to move around a common "center of gravity." (The stellar wobble in the animation is greatly exaggerated compared to the motion induced by normal planets.)
The motions can be detected by the Doppler effect on the spectrum of the star (see the Supplements), although special spectrographs, with high sensitivity and stability, are required.

Shown at the right is the Doppler-derived velocity curve (velocity plotted against time) for the parent star of the first extra-solar planet identified around a Sun-like star (by Mayor and Queloz). Click for an enlargement. The amplitude of the velocity change is +/-50 meters/second, but the precision of the data is better than 10 meters/sec--- a velocity that can be achieved by a fast sprinter. So we can now detect stars moving at human speeds!
The shape of the velocity curve allows us to determine the planet's orbital shape. A markedly elliptical orbit will produce an asymmetrical curve.
By applying Kepler's Third Law to the observed orbital period and velocity amplitude, this method provides an estimate for the mimimum mass of the planet. (It is a minimum because we usually do not know the inclination of the plane of the planet's orbit to the line of sight; a tilt of this plane will reduce the observed radial velocities.)

Transit Method
After a number of planets were detected by the Doppler technique, astronomers realized that they could also find them by searching for planetary transits, that is, the very tiny change in light from a star when a planet crosses its disk seen from our point of view (i.e. a partial eclipse). In principle, astronomers could have detected these with many of the electronic devices available since the 1950's---but they had never configured their observing techniques to look for effects this small.
For a diagram showing the viewing configuration for a transit, click here.
The picture at the right shows a typical "light-curve" for a planetary transit --- i.e. the observed brightness plotted against time. Note that the amplitude of the eclipse shown here is only 1.5% of the star's normal brightness.
This method can catch only the small fraction of planets whose orbital planes have the right orientation such that eclipses occur from the Earth's point of view. However, with stable and sensitive digital cameras, it has proven possible to detect many transiting planets even with modest-sized telescopes. Many groups around the world, including amateur astronomers, are now surveying the sky for planet transits.
Normally, a transiting detection is not counted as a confirmed planet until a corresponding Doppler detection is made. However, in the case of systems with multiple transiting planets, the various phenomena that can lead to false positives can be confidently ignored, and the transiting objects are regarded as validated.
Aside from identifying new planets, the transit method is invaluable because, by determining the fraction of the parent star's surface that is occulted, it provides an estimate of the radius of the exoplanet. (We know the sizes of stars based on our understanding of their internal and atmospheric physics.) It also allows precision timing of exoplanet motions in their orbits and changes in those.

The Kepler Mission

Kepler was a small space telescope carrying a huge electronic camera (42 CCD detectors) which continuously monitored a single large patch of sky in the Milky way between Lyra and Cygnus searching for planetary transits in the tens of thousands of stars observable in the field. Planetary systems identified here are very distant (typically over a thousand light years away), but the strength of the mission was that it could potentially find a large number of planets. The Kepler survey field is shown at the right.
Kepler was launched in 2009 and identified thousands of planetary "candidates" --- but most of these must be confirmed by the Doppler velocity method before they are accepted as planet detections. By 2017, Kepler had found 5011 candidate planets, 2512 of which had been confirmed.
By design, Kepler was able to detect the very tiny changes in starlight (0.01%) caused by eclipses by Earth-sized planets. It identified scores of candidates with sizes less than 3 Earth radii.
In May 2013, Kepler lost a key component of its attitude-control system and its ability for precision pointing, regretfully just as it was exploring the Earth-like planetary regime around Sun-like stars in both size and orbital period. However, some clever engineering innovations to stabilize the spacecraft made it possible to continue the mission while observing fields other than the original one. Kepler made a number of additional exoplanet detections before it ran out of fuel in October 2018 and the mission had to be retired.

TESS

The Transiting Exoplanet Survey Mission (TESS), an orbiting imaging telescope, was launched in April 2018 and will continue the space-based search for transiting exoplanets begun by Kepler. It will survey most of the sky but only for periods of 27 days per field. It will emphasize study of about half a million nearby stars and especially types of stars significantly smaller than the Sun ("red dwarf" stars), where it is easier to find planets in the "habitable zone".

Exoplanet Count

As of 2020 we had found over 4300 confirmed planets in over 3100 planetary systems. 700 of these are multiple planet systems. Over 3000 are transiting planets. For a complete list, see the Extra Solar Planets Encyclopaedia.

Properties of Important Types of Exoplanets

Hot Jupiters: "Hot" Jupiters are gas giant planets (~ Saturn mass or larger) in very small orbits---less than 0.4 AU, the radius of the orbit of Mercury. The tightest orbits are less than 0.01 AU in radius. Hot Jupiter atmospheres are heated to high temperatures by their parent star; many are puffed-up or losing material. Under some circumstances, the atmospheres may evaporate altogether.
This was the first class of exoplanets to be discovered around Sun-like stars because they produce large Doppler signals. However, they were a great surprise because in our solar system the large planets are all at distances greater than 5 AU, and it is thought (see item F.6 above) that they cannot form at small distances from their parent star. Probably, these planets do form at large distances but, because of gravitational interactions with the protoplanetary disk, they migrate over time nearer the star.
Because early planet searchers thought massive planets would always be distant from their parent stars, with long orbital periods, most did not look for short-period oscillations of the stars (until after the 1995 detection).
[Note: objects with masses larger than 13 x Jupiter's are considered "brown dwarf" stars, not planets.]

Super-Earths: These are exoplanets with masses significantly larger than Earth's but smaller than 10 Earth masses. They are smaller than Uranus or Neptune. There are none in the Solar System. Scores of these have been detected so far around other stars. The exoplanet system Kepler-62 has four Super-Earths. Some Super-Earths have masses and radii that suggest they are made of rocky materials, like Earth, or of ice/water. A number are in or near their star's habitable zone, where surface temperatures allow the presence of liquid water. Water vapor and clouds were detected in the atmosphere of one such Super-Earth (K2-18b) in 2019. But its hydrogen-rich atmosphere makes it unlikely to host a biosphere.
Earth-Like Planets: A number of Earth-sized candidates have been found by the Kepler mission. In April 2014, Kepler announced the confirmation of Kepler-186f, the first Earth-sized planet in its star's habitable zone. K186f is 11% larger than Earth and orbits a so-called "M dwarf" star about 500 light years away with a period of 130 days. Because its star is fainter than the Sun, the small (0.4 AU) orbit of K186f places it within the habitable zone.

Another tantalizing Earth-mass exoplanet in the habitable zone is Proxima Centauri b, which was detected by the Doppler method in orbit around a small, red dwarf star. In this case, however, it happens to be the star nearest to the Sun (only 4 light years away), so the planet instantly became a target for extensive exploration. (Proxima Centauri is part of the triple-star system Alpha Centauri -- the third brightest star in the sky.)
The champion system for Earth-like planets was announced in February 2017, based on transit data from the Spitzer Space Telescope and terrestrial telescopes. It is "TRAPPIST-1", a very small, cool star, 36 light years away, which hosts a total of seven Earthlike planets in or near the habitable zone. The orbital periods range from 1.5 to 20 days. Spectroscopic searches for evidence of water in the atmospheres of the planets are already underway.

How Many Planets in the Galaxy?

Based on the excellent statistics from Kepler, astronomers estimate there are 100-400 billion planets in our Galaxy, though again most of these are not Earth-like nor in a terrestrial habitable zone. There are probably at least as many planets in the Galaxy as there are stars.
Think about that the next time you look at the sky on a clear night or a deep image of a Milky Way star field.

Exoplanet Art

The discovery of exoplanets inspired an explosion of artists' impressions of exoplanet systems and surfaces. Some nice ones are shown in the composite below. Bear in mind that no telescope is powerful enough to produce images like this, so they are all entirely speculative. Almost all contain some unphysical features (like showing the shape of other planets in the parent system).

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Reading for this lecture:

Alert! Most lectures from now on will cover more material in the text than has been the case up to now. Try to keep up with the reading.
Study Guide 11
Bennett textbook: Chapter 7 except pp. 202-212; Chapter 8; "Summary of Key Concepts" for Chapter 13.

Reading for next lecture:

Bennett textbook: Secs. 8.5, 9.1, 9.6
Study Guide 12

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Web Links:

Slides shown in class
Current coordinates, distances, brightnesses of the planets (Heavens Above)
More information on systematics of the Solar System
Java simulations of Solar System orbits (UMd)
Multimedia Tour of the Solar System
Links to good interstellar medium image sites
Earth May Have Formed From Tiny Pebbles (Alexandra Witze)
DSHARP: images of protoplanetary disks (from the Atacama Large Millimeter Array)
Early history of searches for extrasolar planets (ASU)
Extra Solar Planets Encyclopaedia
NASA Exoplanet Archive
Techniques for detection of extra solar planets
Detection of Extra Solar Planets by Transit Photometry (STARE Project)
Java simulations of orbits for selected extra solar planets (UMd)
MEarth Project (an automated transiting planet survey observatory)
The Kepler Mission (NASA)
TESS -- The Transiting Exoplanet Survey Satellite (NASA)

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Last modified January 2024 by rwo

Drawings of stages in the nebular theory from ASTR 161, University of Tennessee. Computer simulation of protoplanetary disk by G. Bryden. Velocity curve of 51 Peg from G. Marcy & P. Butler. Text copyright © 1998-2024 Robert W. O'Connell. All rights reserved. These notes are intended for the private, noncommercial use of students enrolled in Astronomy 1210 at the University of Virginia.