Lecture 6

Lecture 6

Topic 4B:
ARE WE UNIQUE?

Planet Hunters:

S.E.T.I.:

Reading:

Other Planetary Systems, The New Science of Distnat Worlds, Chapter 10

Astronomers have always thought that the process of Solar System formation is one of the natural outcomes of the star formation process so that our home, the Solar System, is just a typical example of one of many planetary systems in our home galaxy, the Milky Way. Are we really though?
The Nebular Theory offers a nice explanation for the formation of our Solar System. How universal is the Nebular Theory? Can it describe adequately planet formation everywhere in our home galaxy, the Mlky Way?
We are now in a position to start addressing these types of questions. Astronomers have discovered many extra-Solar planets and planetary systems over the last 25 years using a variety of methods. The methods may be broken down into direct searches for planets and indirect searches for planets.

Indirect (ID) searches are based on the fact that the members of a planetary system orbit about something known as the center-of-mass of the system. This includes the star. The motion of the star may be detectable.
Direct (D) planetary searches look for eclipses (transits) of stars by planets.

Here, we consider the following methods,

astrometric searches (ID)
spectroscopic searches (ID)
searches for transits (eclipses) (D)
searches using gravitational microlensing (D)

The methods writen in magenta have found extra-Solar planetary systems. Spectroscopic and Transit (eclipse) searches have been the most successful and are the ones we concentrate on here.

SEARCH METHODS: INDIRECT SEARCHES
In a planetary system, the planets do not orbit about the star. The planets, as also does the star, orbit about what is called the center-of-mass of the system. We can see what the center-of-mass means by looking at a seesaw:

The center-of-mass is where the sawhorse (fulcrum) must be placed in order for the two riders to balance each other. On a seesaw, the more massive person sits closer to the fulcrum than does the less massive person if we want to keep the seesaw in balance.
In planetry systems, we define the center-of-mass in the same way, however, because the star is usually much more massive than the planets, the center-of-mass lies very close to the star,
In our Solar System, the center-of-mass lies just outside the surface of the Sun. The Sun and planets all orbit about the center-of-mass of the Solar System. In our Solar System, the Sun and Jupiter dominate the motion ===>The orbital period of the Sun is roughly 11.9 years and the Sun's orbital speed is 13-14 meters per second, the speed of a very fast human. Indirect planetary searches look for the small changes in the position of the star (astrometric searches) or for effects due to the fact that the star is moving ( spectroscopic searches).
I. Astrometric Searches
Astrometric searches try to detect directly the motion of the star. To get a feel for the difficulty of astrometric searches , suppose that we lived on the nearest star to the Earth (excluding the Sun), Proxima Centauri. Could we see our Solar System? Proxima Centauri is at a distance of 4.3 light years or 40 trillion kilometers from the Earth. This is a long way away -- the average distance the Earth is from the Sun is 1 Astronomical Unit which is 8.3 light minutes or 150 million kilometers -- Proxima Centauri is 270,000 Astronomical Units from the Sun.
Jupiter orbits in our Solar System in an orbit of size 5.2 A. U. with orbital period of 11.9 years. From the distance of Proxima Centauri this would correspond to an orbit of angular size ~ 0.004 arc-seconds. Recall 1 degree = 60 arc minutes. 1 arc-minute = 60 arc-seconds ===> 1 arc-second = 1/3,600 of a degree!! Given current technology for ground-based observatories, this is not do-able.
There are currently no good candidates based on astrometric searches. In the future, we will develop space-based experiments which will have pointing accuracies of better than 0.00001 arc seconds and thus will be able to see nearby planetary systems.
II. Spectroscopic Searches
Spectroscopic searches try to detect evidence of the motion of the star by looking at changes in the light spectrum the star produces because of its orbital motion. To understand what is done, we introduce the phenomenon of Doppler Shift,
"When a body that is emitting light has a velocity towards or away from an observer, the wavelength of the light will be shortened (blueshifted) if the body is moving towards the observer or will be lengthened (redshifted) if the body is moving away from the observer. This change in observed wavelength, or frequency, is known as the Doppler shift"
To show how this relates to planet searches, I will remind you of something about sunlight. Even though sunlight appears colorless, it is actually a blend of many different colors (wavelengths) as can be seen if we pass the light through a prism. We see the same effect naturally when the light from the Sun is spread out into a rainbow by water droplets in the air (acting as prisms).

Red light has a longer wavelength than does blue light.

Spectroscopic Method (Doppler Method)
At left, we show a schematic view of an observer (green spot) observing a planet (red object) orbiting a star (blue object). We are looking at the system from overhead. The star and planet orbit about the center-of-mass of the system (small red dot). Because of its orbital motion, the star periodically approaches and recedes from the observer. This means that the light from the star will be periodically blueshifted and redshifted over the orbital cycle of the star.
The amount of stretching or contraction of the wavelengths is determined by how fast the star moves compared to how fast the wave moves. For example, consider the analogous case of sound waves. Sound waves move at speeds of around 330 meters per second. To make a noticeable change in wavelength (frequency) the sound source must move at speeds of tens or so of meters per second. The faster the source moves the more apparent will be the effect. For light, it is a completely different ballgame. Light waves travel at a speed of 300,000 kilometers per second! That's fast.
How easy (or difficult) will it be to detect Doppler shifts in the light from stars?
The orbital speed of the Sun is on the order of 13-14 meters per second. This motion leads to a fractional change in the wavelength of about 0.00000004! The amazing thing is that this tiny change is detectable with current technology!

The Doppler shift method (spectroscopic method) is best at detecting systems where the stars move the fastest, that is, have the largest orbital speeds. This means that the spectroscopic method is most sensitive at finding massive Jupiter-like planets and, especially, massive Jupiter-like planets orbiting well inside the Snow lines of their systems (Hot Jupiters). The spectroscopic method indeed produced the first discovery of an extra-Solar planet around a Sun-like star when it discovered the Hot Jupiter, 51 Pegasi b, a Jupiter-like planet 0.46 times the mass of Jupiter in a 4.23 day orbit in 1995. 51 Pegasi moves at the brisk speed of 70 meters per second. The discovers Michel Mayor and Didier Queroz shared the Nobel Prize in Physics in 2019.

SEARCH METHODS: DIRECT SEARCHES
III. Transits (Eclipses) of Stars by their Planets

Kepler and TESS
The current NASA mission TESS (shown to the left) was launched in 2018. TESS observes around 200,000 bright, nearby stars distributed over around 85 % of the sky to search for transits in extra-Solar planetary systems ( 2012 transit of Venus). To date, TESS has found over 5,000 planet candidates. The Kepler mission was launched in 2009 and retired in 2018 having acquired data on roughly 156,000 nearby stars similar to the Sun, but not as bright as those sampled by TESS and distributed in only 0.25 % of the sky, in its search for extra-Solar planets. Overall Kepler observed over a half-million stars of all types. Kepler detected over 2,600 planets over its lifetime. Kepler and TESS suggest that between 10-20 % of stars have planetary systems!

The big problem with direct detections of planets is that stars are very bright and planets are very faint. This means that it is very difficult to see planets in the glare of the stars. Furthermore, because planets are small, direct detections of planets from eclipses (transits) of stars by planets are not likely to lead to large changes in the light output and so will be hard to see.^* Kepler was able to see changes in the brightness of a star to around 0.01 %, TESS is not as sensitive as Kepler for individual stars, but TESS sampled a much wider swath of the sky, 85 % coverage compared to 0.25 % coverage. Kepler and TESS (Transiting Exoplanet Survey Satellite) have been very successful having discovered thousands of planets and candidates.
Given the strengths of the missions, Hot Jupiters were the first type of planet found (by Kepler). Since then, however, Kepler and TESS have discovered most of the known super-Earths and mini-Neptunes, exploiting their greater ability to detect earth-like planets compared to the spectrocscopic methods.
An aim of TESS, beyond discovery of planets, is to identify targets for future observations by ground-based telescopes and the Webb space telescope.
Beyond utility as a path to planetary discovery, transits observed by Kepler and TESS lead to further information such as planetary radii, planetary masses, orbital properties, information on the atmospheres of the planets. A key result is that densities of the planets may be found from transits and potentially (when used in conjunction with ground-based and space-based telescopes) may shed light on the atmospheric composition of the planets.

Click on image for a Kepler Orrery

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^We don't really see a planet during an eclipse, we see its shadow as it moves across the star; we may be able, however, to see the planet's atmosphere as the light from the star shines through the atmosphere during the transit or as it reflects off the planet's atmosphere.
IV. Gravitational Microlensing*
An interesting discovery of an Earth-like planet in the constellation Sagittarius was made during a Dark Matter search. The planet was discovered using a technique that used gravitational microlensing. An Earth-like planet 5 times the mass of Earth with an orbital period of ~10 years was made.

DETECTIONS AND IMPLICATIONS OF THE DETECTIONS OF EXTRA-SOLAR PLANETS

As of October 1, 2022, 5,197 exoplanets in 3,833 planetary systems have been confirmed with 840 systems having more than one planet. The latest results suggests that a large fraction of stars have planetary systems and that around one-sixth of stars have Earth-like planets. However, most are found in orbits smaller than the orbit of Mercury. No twin of the Solar System with an Earth-twin has yet been found. If we are more liberal as to what we mean by a Solar System twin, and ask "Have we seen twins of Jupiter?" what are the results? There may be several Jupiter twins but no system has been observed long enough to be able to claim to that a twin has been found. For example. Epsilon Indi Ab is a Jupiter-like object 3.25 times the mass of Jupiter, orbiting a star a little less massive than the Sun in an 11.55 A.U. orbit (45.2 year period). Kepler expected to see perhaps 50 or so Earth-like planets in orbits of around 1 Astronomical Unit in size. Some have been found, for example, KOI-456.04 a planet whose radius is 1.9 times that of the Earth in an orbit of 378 days around a Sun-like star in the system Kepler 160. Kepler 160 is not in a twin of our Solar System, KOI-456.04 has earth-like planet companions in very small orbits. The answer to the question of whether we are unique or not is unanswered.
To see the properties and relationships between the properties of the discovered planets, e.g., their orbital eccentricities, their masses and radii, the relation between their orbital periods and their orbital sizes (the semi-major axes of their orbits), and other correlations, go to the Exoplanets website and use their plotting tool to play with the data, as was done on Homework 3.
Bottom left: we show a plot of planetary masses versus how far the planets sit from their stars. Bottom right: we show how the planet's densities compare to their masses.

planet masses with respect to their orbital sizes
planetary radii with respect to the masses

You noticed several things from the plots:

The size of Jupiter's orbit is 5 A.U. lying just outside the snow line; there are many Jovians far inside their system's snow lines, the Hot Jupiters
Most of the newly discovered planets have masses between the most massive Terrestrial, the Earth, and the lowest mass Jovians, Uranus and Neptune, the so-called super-Earths and mini-Neptunes.
...

Do these things mean that our current understanding of Solar System formation and evoluton is in trouble?

For further information that may be gleaned from your homework plots, click on this tab.

Planetary Migration
Before the onslaught of the extra-Solar planets, the party line was that planets formed at particular radii in the Solar Nebula and essentially spent their lives at around the same distance from the Sun. This position is no longer held by most people. The snowline in our planet forming disk is around 3-4 AU and it was expected that all Jovian planets in extra-Solar planetary systems would be found outside the snowlines of their disks. The discovery of so-many Jupiter-like planets close to their stars, inside the snowlines, suggested that planets likely migrate around their systems over their lifetimes. This notion has also influenced the modeling of our Solar System. Shown below is one of the proposed models for how our Solar System formed. The model is known as the Grand Tack Hypothesis.

223 Kepler

The current lore is that our basic notions about planetary system formation are probably okay in that we think the general ideas are correct. However, the current results suggest that after planets start to form, their orbits must somehow be modified so that Jupiter-like planets will be found close to their stars, within the zones where water would be in vapor form not solid form, that is, inside the snowlines in their systems. More extreme orbital migration than thought to happen in our Solar System must occur in planetary systems in general and is a topic of current research.