Search
for Other Worlds
Project 29, HET608B
Jose Ribeiro
11/ 2003
Abstract
This project reviews the present and future efforts in the detection of extra-solar planets, their properties at the actual state of knowledge, and the changes that this knowledge introduced in our early conception of the planetary formation.
Keywords: Extra-solar
planets, planetary formation
I –
Introduction
The possibility that intelligent life, other than ours, may exist elsewhere in the Universe has interested philosophers and scientists throughout time. From Aristotle and Ptolemy up to Hubble, mankind understood that its existence in the Universe might not be unique. The acceptance of this fact has not always been pacific and men beyond their time have often suffered the consequences of their opinions. “As in this space, equal to the World’s dimension (to which platonics call matter), this World exists, another one may exist in that space as well, and in uncountable space beyond this one, and similar to this one”. So wrote Giordano Bruno in his book “De L’Infinito, Universo E Mondi”. From the Hubble’s discovery that some nebulosities were in fact galaxies like the Milky Way, all the remnant ideas that mankind was the centre of the existence definitively lost sustain.
Many forms of life may exist out of the Earth. Yet, life as we know it should exist in environments not very different from our own. This implies the existence of a planet around a star, with characteristics to harbour life, such as atmosphere and liquid water.
The aim of this work is to review the past, state-of-the-art and future trends on the extrasolar planetary methods of detection, the properties of the extrasolar planets and host stars, and the theories of formation of these planetary systems.
II
– Concepts
Before entering the theme, some concepts must be presented.
1 – the most controversial one is the definition of “planet”. For example, all the polemics around Pluto are paradigmatic: is Pluto a planet or a transneptunian body? Even the most recent definition of “planet” proposed by the Working Group on Extrasolar Planets (WGESP) of the International Astronomical Union leaves this issue opened. According to this group, the borderline between a planet and a non-planet is the limiting mass for thermonuclear fusion of deuterium. This limiting mass is 13 Jupiter masses for objects of solar metallicity [2]. Such objects must orbit stars or stellar remnants in order to be considered planets. The minimum mass proposed by this group doesn’t resolve the polemic around Pluto: “the minimum mass/size required for an extrasolar object to be considered a planet should be the same as that used in our Solar System” [2]. Geoff Marcy and Buttler are more objective in their definition of “planet”: “an object that has mass between that of Pluto and the deuterium-burning threshold [7]. However, these authors state that planets must orbit objects that “can generate energy by nuclear reactions”, which excludes stellar remnants such as pulsars and white dwarfs, should this definition be taken literally.
2 – according to the WGESP a brown dwarf, that is an object with mass inferior to 0.08 solar masses, unable to begin hydrogen nuclear fusion in its core, must have a limiting mass above the thermonuclear fusion of deuterium (masses between 12 Jupiter masses and 80 Jupiter masses).
At the borderline it is sometimes difficult, or even impossible, to assess if a detected object is a planet or a brown dwarf.
3 – Since the Solar System is the planetary system we know best, it is interesting to mention the most accepted theory of the Solar System formation and its properties in order to compare them later with the observed in the extrasolar planetary systems.
The Sun and planets formed from the same cloud of gas and dust. This cloud began to contract due to some sort of instability, as for example the radiation pressure of a nearby recently formed star in the interstellar medium. Due to angular moment conservation, the cloud contraction is associated to an increase in rotation, resulting in the shape of a disc. This disc is the protoplanetary disc (proplyd) where the future Sun will begin its life at the centre, and the planets will form around it. An inflow of gas and dust from the disc will take place onto the central protostar, by self-gravitation, until the temperature of the gas, due to the pressure increase, is enough to begin the thermonuclear fusion in the new-born Sun. The surrounding molecular cloud will go on feeding the proplyd with matter [3]. The temperature in the proplyd decreases from the centre outwards. Due to this fact, the various substances in the disc may exist in the solid or gaseous state depending on their condensation point temperatures. The different temperature distribution in the disc favours the existence of more stable matter at high temperatures in the inner part of the disc whereas the more volatile matter tends to dominate in the outer colder parts.
During condensation, more dense regions
tend to agglomerate more matter due to gravitational effects. Dust grains begin
to collide and stick together, forming objects of the size between 0.01 and
At the outer part of the disc, the volatile matter, the water, methane, and ammonia, could condense into ices. As these lighter elements are more abundant, the result was the accretion of rocky and ice materials, giving birth to bigger bodies than the ones near the Sun. These massive bodies could accrete gas molecules, mainly hydrogen, because at such low temperature the kinetic energy of the gases was very low, not escaping to the bodies’ gravity.
The end of accretion happens when there is no more matter along the planet’s orbit. A gap will result in the proplyd.
The jets and the solar wind of the new-born Sun finally cleaned the unaccreted debris out of the planetary orbits. Many of this unaccreted material forms the asteroids and the transneptunian objects.
This theory of the Solar System formation explains very well the observed properties of the Solar System:
- all planets orbit the Sun in the same direction, which is the direction of the Sun’s rotation.
- Solid planets are near the Sun
- Gaseous planets orbit in the outer part of the system
The theory does not explain the orbit of Pluto, the planetary satellites formation, nor the 7º tilt of the solar axis relative to the mean orbital plane.
III - Exoplanets
1 – Methods of detection
Exoplanets cannot be detected directly with our actual technology. The host stars are many orders of magnitude brighter than the planets, remaining the planets unresolved inside their brightness.
The detection of exoplanets was first mentioned in a work by Otto Struve in 1952, “Proposal for a Project of High-Precision Stellar Radial Velocity Work” [1], where he refers to the radial velocity and to the transit methods. Curiously, using the accuracy of that epoch equipment, Struve wrote “a planet ten times the mass of Jupiter would be very easy to detect”.
Fig.1
Present and future exoplanetary detection
methods. (Perryman, Sep.2003)
Until now, some 117 exoplanets were detected [9]. The totality of them, with the exception of the planetary system, orbiting a millisecond pulsar, were detected through the method of radial velocity. One of these planets was also later detected by the transit method.
i ) Methods based on the dynamical perturbation of the star.
When a star is orbited by other bodies, it will wobble around the common centre of mass. In the case of a two-body system, the orbital radius “a” and masses “M” are related by a*M*=apMp. Being a* the mean orbital radius of the star, then it will have a periodical motion corresponding to the orbital period of the system, as seen from Earth. This star motion may be measured by some methods, being the radial velocity method the one with practically all the positive results since 1995 with the discovery of the first planet orbiting the main sequence star 51 Peg by Mayor and Queloz.
a ) Radial Velocity
The radial velocity method consists in the measurement of the Doppler shift of the host star due to its motion around the system centre of mass. As the star approaches the line of sight (LOS), the spectral lines shift towards shorter wavelengths; when the star recedes the LOS its spectral lines will shift towards longer wavelengths. The Doppler shift is given by Dl¤l=v/c=1/R, being Dl the shift of the line with wavelength l, c the speed of light, v the velocity of the source, and R the resolution power of the spectrometer with which the Doppler shift is measured. The resolution of modern spectrometers such as the SARG of the TNG, the CORALIE, the ELODIE, the Keck HIRES [14][15], may attain 144,000 which are able to measure directly source velocities in the order of 20 km/s and with integration and accurate comparative methods they can achieve 2 m/s precision in the range of 510-1010 nm in radial velocity measurements [10]. An accuracy better than 15 m/s is needed for this detection method.
The radial velocity amplitude of the star is given by
K = (2 p G / P)1/3 Mp sin i / (Mp + M*)2/3 1/(1-e2) 1/2
Being G the gravitational constant, P the orbital period, Mp and M* the mass of the planet and star respectively, i the angle of the orbital plane relative to the LOS (90º as seen edge on) and e the eccentricity of the orbit. Knowing K, P, M* by spectral class and the orbital eccentricity from the velocity curve shape, one may know Mp sin i. This limits the assessment of the planetary mass to the unknown angle of the orbit relative to the LOS.
The actual precision of this method may allow the detection of planets with minimum mass of about 33 Me / sin i (Me = Earth mass), orbiting at one astronomical unit (AU) from a one solar mass star [8].
The major limitations of this method are related with the spectral characteristics of the host stars. Main sequence stars hotter than F5 rotate fast, show less spectral structure and have more coronal activity jeopardising the Doppler shift measurements. The method is confined to the detection of planets orbiting main sequence stars from M to mid F spectral types [8].
b) Pulsar timing
The first exoplanetary system ever found
was in
Pulsars are spinning neutron stars emitting strong radio beams that due to the rotation seem to pulsate at the reception. There are two types of pulsars: slow rotating pulsars and millisecond pulsars. The pulses of the pulsars are so accurate that even a very small delay in the pulse arrival due to the pulsar motion can be easily detected. The method to measure the pulsar timing can detect dynamical perturbations caused by jovian or terrestrial planets on slow pulsars, and dynamical perturbations caused by Moon-sized or large asteroids on millisecond pulsars [3].
Yet, planetary systems around pulsars may be rare.
c) Astrometry
Astrometry consists in the measurement of positions, parallaxes, and proper motions of bodies in the sky. The motion of a planet host star orbiting the system’s centre of mass may be detected through the astrometric position method. The star’s motion will appear projected in the sky plane as an ellipse with angular semi-major axis a (arcsec) given by
a = (Mp /M*) (a /d)
with a the semi-major axis in AU and d the distance to Earth in pc [3].
From the above equation one can see that the star’s motion angular size decreases with the decreasing mass of the planet and its distance to the star, and with the increasing distance to Earth. For Jupiter-Sun systems seen at 10 pc, a corresponds to 0.5 milliarcsec. and for an Earth-Sun system at 10 pc a will be 0.3 microarsec. This method will not be useful for the detection of distant Earth-like planets.
With the development of adaptive optics and visual interferometry, ground based astrometric measurements may achieve in the near future accuracy levels of the order of 20 microarcsec. either in Keck or in VLT interferometers. This will allow the detection of 66 Me planets with 1 AU orbits at 10 pc.
This method may have the following advantages:
- It is independent of the spectral type of the star. It can then study the behaviour on all main sequence stars.
- If M* is known from spectral type, d from parallax, and a from radial velocity measurements (a3 = Const. M* P2), then Mp will be known independently of the system orbital angle with LOS.
These two advantages make this method a good complement of the radial velocity method.
This method shows some limitations:
- Measurement accuracy must be better than 1 milliarcsec.
- The stars’ small wobble angle for distant Earth-like planets
- The atmospheric perturbations may limit ground-based measurements
- The brightness variability of the stellar discs due to stellar activity, such as dark spots, may induce measurement errors, as the astrometric techniques use the star’s photocentre for plotting the orbital points.
ii ) Transits
Transits happen when a body passes in front of a larger one, as seen by an observer. In the case of a planetary system, a planet transiting its star will cause a luminosity decrease, that can be measured through photometric techniques. An observer at 10 pc would see a Sun’s luminosity decrease of 2% (0.02 mag.) during the transit of Jupiter across the solar equator [3].
If transits happen at the centre of the disc and the surface brightness of the star is uniform, as seen from the observer, then the following relation is valid:
(DL/L*) @ (Rp/R*)2
with DL the luminance difference, L* the luminance of the star, Rp and R* the radius of planet and star respectively.
The duration of the transit is given by
T = P/p ((R* cos d + Rp) / a) hours
with d the latitude of the transit in the stellar disc [3].
This relation can be simplified to
T @ 13 SQR (a) hours
for transits across the centre of the star and a in AU [8].
One planet before detected by radial velocity was latter detected by the photometric transit method. The planet was HD209458, and make this method a confirmed detection method.
Small aperture systems such as STARE and ASP can screen determined fields of stars in order to detect transit events.
Some limitations, however, are reported:
- The method efficacy depends on the orbital plane orientation relative to the LOS.
- The utilisation of the method in ground-based locations limits its accuracy due to atmospheric perturbations, mainly extinction.
- The method is sensitive to star variability namely rotational behaviour causing brightness variations due to magnetic processes.
On the positive side, a planet that transits it’s star sin i≈1 so, from the transit method one can calculate accurately the planet’s mass.
Space missions are thought to be the best application for this planetary detection method, due to the absence of atmosphere. It is expected the detection of planets less massive than Jupiter and even Earth-like planets.
iii ) Microlensing
If the light of a bright and
distant object passes sufficiently near a massive object ahead it, the image of the bright object
will be altered. The curvature of the spacetime near the massive object will
deflect the beams of light giving the idea to an observer standing in the same
line of sight, that the distant object has been amplified as if it had passed
through a lens. The massive object that deflects the beams of light is named as
“lens”, and the object that is amplified is named as “source”. The effect
varies, depending on the mass of the lens, and on the relative positions of the
lens and of the source;
thence, its importance in the detection of dark matter and of
faint objects. Theoretically, if we have a point-like mass as lens exactly on
the line of sight of a distant galaxy or quasar, a circular image of the source
will be seen by the observer; that circular image is known as Einstein ring.
The Einstein ring radius, the Einstein radius, is given by
RE = SQRT[(4GM / c2)(DOL DLS / DOS)]
Fig.2 Gravitational lens representation. A massive object L (could be a planetary system) passes in the
line of sight of a distant object, changing its bright
Where G = Gravitational
Constant, M = Lens Mass, D = Distance, O = Observer,
L = Lens, S = Source.
The Einstein angular radius is given by
qE = RE / DOL = SQRT
[(4GM / c2) (DLS / (DOL DOS))]
These formulas are valid for the co-linearity among source, lens, and observer, as well as for point-like source and lens, which is an improbable situation to occur. Yet, this simplification helps to best understand the issue.
When the gravitational field of the lensing object is not strong enough to form distinct images of the source, one says that a microlensing event is happening. When it does, it causes an apparent brightening of the source (left part of figure 3).
Fig.3
A microlensing event. A massive object passing
in front of a distant object increased its bright. (Sackett,P)
With the passage of time,
the lens moves across the observer-source line and the apparent brightness
changes.
The most important
properties of lensing are:
- Surface brightness is conserved by lensing
-
Polarisation of light is unaffected by lensing
-
Lensing is achromatic. The light curves are the same
in blue and red filters
The distance observer-source can be normally calculated with some accuracy, due to the fact that the source object can be seen. As the object lens cannot normally be seen, its mass, distance and velocity are unknown.
Fig.4
A caustic caused by a binary system lens (the 2
dots), and respective brightness curves in function of the distance of the
lens to the line-of-sight. (Sackett,P)
Sometimes, some alterations
to the normal microlensing light curve can help to best define the lens,
allowing a better assessment of the lens parameters. Microlensing
anomalies are alterations of the normal microlensing
light curve due to a peculiar geometry or to the non-linear motion of a source
or lens object.
The most frequent case of
microlensing anomaly is the one observed when the lens is a close binary object
such as a planetary system (Fig.4). In this case, the magnification pattern is
altered and for certain positions of the binary each individual lensing
strength can reinforce each other. These positions are known as “caustics”.
Whenever a source passes behind a caustic, the magnification reaches high values .
The detection of distant planets has been carried out by the PLANET team. In this case, a sufficiently massive planet around a star is a binary system, and may cause an anomaly in the event (caustic). Yet, the angular size of the caustic structure is smaller for the planetary lensing system than for a binary star system; this will lead to the fact that the anomaly part of the light curve will be more short-lined for a planetary anomaly. Detectable anomalies from Jupiter-like planets would last 1 to 3 days. This method is only suitable for very distant planets, some Kpc [11].
No planet was detected through this method, although some candidates exist[12].
This method has the disadvantage to happen just once for each star.
iv ) Imaging
Actually, it is not possible to detect an exoplanet by direct imaging. For a Jupiter-like exoplanet around a Sun-like star the ratio of luminosities LJ/L* is 10-9. At very small angular distances between the star and the planet, the star’s luminosity prevails over the planet’s luminosity. On the other hand, the technology to overcome the atmospheric turbulence is still under development and even in the big telescopes cannot yet resolve the angular sizes of exoplanetary systems. The only space telescope, Hubble, is not also big enough to resolve the angular sizes involved.
In a near future, when VLT,
Keck, and Large Binocular Telescope will be using in a routine procedure the
visual/IR interferometry, then it will be possible to detect giant planets
around nearby stars.
Some steps in order to
improve the imaging techniques to future imaging exoplanet detection are:
- Development of adaptive
optics such as the tomography (MCAO) techniques in order to minimise the
atmospheric turbulence.
- To achieve better angular
resolutions, in order to reduce the angular size of the star, by increasing
telescopes’ apertures, and by building visual interferometer arrays with long
baselines.
- The development of
coronographic masks to suppress scattered light from the star.
- As the thermal curve of
the planet may peak at the IR, observing at these wavelengths may increase the
contrast between the star and the planet. The planet is cooler than the star.
This technique may be very
promising in the future with the construction of Extremely Large Telescopes in
ground and with large baseline interferometers in space.
v ) detection of
proplyds
As said before, the proplyd
is a stellar system under development. Detecting proplyds is a way to detect
planetary systems in the evolutionary phase. The detection and observation of
proplyds is relatively easy with our actual technology. The study of the discs
may improve our knowledge about the planetary systems’ evolution.
vi ) future
The constant development of
observing and detection techniques, as well as the improvement in data
management gives exoplanets detection a good future perspective.
In the ground, the
construction of Extremely Large Telescopes as the Overwhelmingly Large
Telescope with a
Yet, the future of this
science is mainly in space missions, out of the atmospheric/pollution
disturbances. The construction of medium/large space interferometers will
improve the required angular resolution for this job. Missions as SIM [13],
scheduled for 2009, consists on a space-based
One technique to improve
exoplanetary imaging using space interferometry will be the interferometric
nulling of the star, and consequent enhancement of the planet.
Arrays of interferometers
with baselines of
Photometric techniques will
also improve from space missions.
Some missions already
scheduled are COROT,
2 – Properties of Extrasolar
Planets
i ) Properties of
the host stars
the probability for
a stellar system to produce a planetary system seems to be related to its iron
abundance [4][6][16].
Fig.5 Histogram showing that planets
are more numerous in stars with more iron abundance. (Nuno Santos et al. 2004)
Some authors [16] defend
that “the metals are the seeds from which planets form”. This fact may be
explained on the basis that heavier elements accrete easier creating
planetesimals and then planets in a more efficient way. A recent study from
Nuno Santos et al. [4] compares metal abundance of 2 star populations, one with confirmed
planetary companions and another without known giant planets. They conclude
that host stars have higher iron content than stars without planets. However,
that does not apply to many other metals such as Si, Ca, Ti, Sc, V, Cr, Mn, Co,
and Ni. An immediate conclusion from the above is that the actual proplyds,
with more iron abundance fabricated by ancient dead stars, may probably produce
planetary systems, making their study valuable for the understanding of the
planetary formation.
However, a certain care must
be taken, because until now only gaseous planets were detected. Perhaps the
distribution of host stars with Earth-like planets shown a different trend. Our
Sun, for instance, and according to Fig.5, belongs to an iron abundance
group not very efficient in planetary formation. Yet, four terrestrial planets
were formed.
ii ) Mass
distribution
the exoplanets mass
distribution in function of the distance to the host stars, led to some
questions on the accepted model of planetary formation. Observed giant planets
orbiting near the host star is not consistent with the accretion model of volatile matter for gaseous
planets. If in-situ formation takes places then the accepted theory is wrong or
incomplete. However, an explanation may not contradict our knowledge on
planetary formation: the migration of the planets from the outer parts of the
disc into inside [5].
Until now, the orbital
distribution of planets relative to their masses has been measured as:
There are not massive
planets on short orbits. The reasons may be related with the migration process: it is less
effective for massive planets [5][17]; the migration may end inside the star;
the planet may transfer mass to the star due to its proximity; tidal
interactions with the star may disrupt the planet; planet evaporation.
There is a shortage of
planets in orbits with periods between 10 – 100 days.
Lack of lighter planets (M
sin i £ 0.75 MJ)
in more distant orbits. The reason for this is still unknown and may be related
to the detection limitations. Simulations, however, tend to confirm that the
outer regions of the discs are empty of lighter planets [5].
iii ) Orbits
Fig.6
Eccentricity distribution vs. Distance to the
star (California-Carnegie planet
search team)
The studied orbits of
exoplanets, through the Doppler surveys, revealed many different
eccentricities. However, planets orbiting at small distances from the star
(<0.1 AU) have almost circular orbits. At larger distances the orbits may be
either circular or showing high eccentricity (Fig.6).
The high eccentric orbits
may result from the interactions such as angular momentum changes between
planets and planetesimals in multiple planetary systems [19], or interactions
between a giant planet and the protoplanetary disc [20].
iv ) Migration
Planetary migration may
explain some observed characteristics of exoplanetary systems, complementing
our knowledge of planetary systems formation.
The causes for planetary
migration may be due to some mechanisms [17]:
- The generation of density
waves by the planet in the proplyd, causing the planet to lose energy to the
disc and migrating inwards.
- Orbital instability due to
the interactions between near massive planets
The migration process may be
halted due to:
- Tidal or magnetic effects
from the star.
- Collision with the star
- The planet opens a gap in
the disc, coincident with its orbit, ceasing the angular momentum exchanges
with the disc.
IV – Conclusions
The search for planets outside our Solar System is today a reality, a conquer of the humanity over the prejudice of conservative mentalities that pretended to defend the idea that the Universe was created for mankind.
As science, all the work
done helped us to improve our theories on planetary formation. Eleven years
pasted since the first discovery of a planetary system outside our own.
Scientists are dealing with the lack of information due to the technological
limitations in sensing
Earth-like planets. The future will bring more knowledge, as the hardware will
improve. Ground-based giant telescopes as well as space-based long baseline
interferometers will unveil all the myriad of small planets, today out of
reach. It will be then that mankind will know for sure if life is exclusive of
planet Earth.
References
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Stellar Radial Velocity Work, Otto Sturve,
1952, http://astron.berkeley.edu/~gmarcy/struve.html
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http://www.eiw.edu/IAU/div3/wgesp/definition.shtml
[3] Review Article: Extra-solar Planets, M A C
Perryman, Rep. Prog. Phys, 2000,
Vol. 63, 1209-1272
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Santos et al., astro-ph/0304360 v1
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[6] Statistical properties of exoplanets II, Nuno Santos et al., astro-ph/0211211 v1
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http://www.kepler.arc.nasa.gov./Capabilities.html
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[13] Space Interferometry
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http://exoplanets.org/metalicity.html
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astro-ph/9801138 v2
[18] http://exoplanets.org/ecc_vs_a_col.html
[19] Eccentricity Evolution of Extrasolar
Multiple Planetary Systems due to the
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al.
http://es.arxiv.org/abs/astro-ph/0205104
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