Or how to measure the radius of an exoplanet

At least ten research teams in various countries have taken upon themselves the task of finding exoplanets by means of the transit method. Analysis of the light-curves of the millions of stars studied has revealed hundreds of candidate events which might be ascribed to exoplanets. Velocimetry is then introduced, using powerful instruments such as the Very Large Telescope (VLT) of the European Southern Observatory. With this method it can be determined whether these events are caused merely by binary stars or by transits of exoplanets. Big telescopes are essential, because most of the candidate stars are very distant and faint. Their identity as star-planet systems can be confirmed, and the masses of the planets estimated. This tireless hunt has begun to bear fruit, and ten of the

3.7 Dark hints of planets 55

Mass/radius relationship for exoplanets detected by the transit method (in red), and the giants of the solar system (in blue). The exoplanets resemble solar system giants.

many suspects are now known to have planets. Painstaking dedication to this work has proved itself worthwhile, and reveals two important factors. The first, as we have seen, is the radius of the planet, deduced from the relative dimming during the transit being proportional to the square of the ratio of the radii of the planet and the star, (Rp/R»)2. The second is that the planetary system must be observed practically edge-on, else no transit will be seen. Remember that the radial velocity method determines only the minimum mass of the planet, M sin i. For all the planets detected by the transit method and subsequently confirmed by the radial velocity method, we know that i is close to 90° and sin i = 1. We therefore have two quantities: the mass and the radius of the planet. With these, we can embark upon some physics!

We can say for certain that these exoplanets are giants, as their radii are comparable to that of Jupiter; and, like Jupiter and Saturn, they are composed mainly of gases. Their mean density is of the order of 0.8 gm/cm3 - less than that of water, and far less than that of the terrestrial planets (the mean density of Earth is 5.5 gm/cm3). If we could find a sufficiently large bowl of water and put the exoplanets into it, they would all float, with the exception of OGLE-TR-113 b! The giants of the solar system are a little denser, but only Saturn is, overall, less dense than water. In the final analysis, all this strongly suggests that exoplanets are similar in constitution to the giant planets of the solar system. There do not seem to be any rocky 'super-planets'.

Giants, and very hot giants at that... The nine planets in question share the

ESO's GIRAFFE spectrograph obtains high-resolution spectra of several objects, simultaneously. The transit method requires complementary velocimetric observations with powerful telescopes in order to establish whether candidate stars really have exoplanets, as many of these stars are very distant and faint.

ESO's GIRAFFE spectrograph obtains high-resolution spectra of several objects, simultaneously. The transit method requires complementary velocimetric observations with powerful telescopes in order to establish whether candidate stars really have exoplanets, as many of these stars are very distant and faint.

characteristic that they are very close to their central stars, with mean distances ranging from 0.022 AU to 0.047 AU, and orbital periods between 1.2 and 4 days. The planet that is closest to its star must have a surface temperature of about 1,600° C! Because all these planets are 'hot Jupiters' there is certainly an effect of selective bias in the method of detection, and we have seen that the probabilty of a transit varies as R* la, where a is the radius of the orbit. These planets are at just a few tens of stellar radii from their stars.

3.8 Close-p of a hot Jupiter; HD 209458 b 57

3.8 CLOSE-UP OF A HOT JUPITER: HD 209458 b

Is this planet evaporating?

HD 209458 b is also known as Osiris: two names for an exoplanet which has become, for astronomers, the exoplanet, most of whose physical and orbital parameters have been determined. This exoplanet, 47 parsecs (153 light-years) away in the constellation of Pegasus, is obliging enough to have an orbit which presents itself edge-on across its star, as seen from Earth. It is therefore susceptible to observation by both transit and radial velocity techniques.

Since it was first observed in 1999, this 'star among stars' and its companion have been scrutinised as no other, from Earth and by means of the Hubble Space Telescope. We therefore know quite a lot about planet HD 209458 b. Its orbital period is 3.52474 days, and it is 0.045 AU from its star. We know that its radius is 1.347 Rj + 0.06 Rj, and its mass is 0.69 Mj + 0.05 Mj. These are indeed remarkable findings for a body so far away.

Although HD 209458 b is less massive than Jupiter, it has a greater diameter. This set astronomers thinking. Might this planet, so close to its star, be in the process of losing its atmosphere? Could they learn more about that atmosphere? Visible and ultraviolet spectroscopic analyses of the star were carried out, both during the transit and when no transit was occurring. In this way, various teams sought possible spectral signatures of the planet itself - and they were successful. Evidence of the presence of sodium atoms suggested that clouds of sodium were present deep within the planet's atmosphere. Moreover, absorption features due to hydrogen, carbon and oxygen were detected. These were more intense than might have been expected, leading to the conclusion that the atmosphere is

Computer simulations of atmospheric circulation on exoplanet HD 209458 b. (After Cho, Menou et a!., Ap. J., 587, L11 7.)

An artist's impression of the oxygen/carbon atmosphere surrounding exoplanet HD 209458 b. Alfred Vidal-Madjar and his team at the Paris Astrophysical Institute were the first to detect the signal of oxygen and carbon in the atmosphere of an extrasolar planet. The nearness of the planet to its star is thought to cause the evaporation of the atmosphere into space, with the radiation pressure of the star forming an immense 'tail' reminiscent of the train of a comet.

An artist's impression of the oxygen/carbon atmosphere surrounding exoplanet HD 209458 b. Alfred Vidal-Madjar and his team at the Paris Astrophysical Institute were the first to detect the signal of oxygen and carbon in the atmosphere of an extrasolar planet. The nearness of the planet to its star is thought to cause the evaporation of the atmosphere into space, with the radiation pressure of the star forming an immense 'tail' reminiscent of the train of a comet.

indeed expanding, or even evaporating! The proximity of the star, just 7 million km away (0.05 the distance from the Earth to the Sun), is causing the evaporation. The radiation pressure of the star pushes the evaporated gas away from the planet, creating an immense 'tail' like that of a comet. Computer models suggest that in certain circumstances the whole atmosphere could be stripped away over a few billion years, leaving behind a small rocky remnant.

3.9 How many stars have planets? 59

Thus the name Osiris. The dismembered body of this Egyptian deity was scattered all over Egypt in an attempt to deny him immortality.

Some astronomers have undertaken studies of the 'climate' of HD 209458 b; a singular kind of climate, to be sure - not only because of the nearness of the star, but also because it is certain that the planet always keeps the same face turned towards it. Intense tidal effects have locked the star-planet system into a configuration like that of the Earth and its Moon; and this is probably the case with all exoplanets with orbital periods of a few days or less. The difference in temperature between Osiris's 'day' and 'night' sides is likely to engender violent winds, of the order of several thousand km/h. In spite of these winds, which would tend to homogenise atmospheric temperatures a little, the 'daytime' side no doubt experiences a scorching 1,500° C, some 600° hotter than the night side. These results are obviously much debated, as meteorology is a complex science even when applied to the Earth!

3.9 HOW MANY STARS HAVE PLANETS? Planetary systems are common - but how common?

The detection of planets utilising the radial velocity method cannot be referred to as 'highly productive'. As we have seen, if the Sun and its planets were to be among those so far studied by this method, it might still be some years before we could detect Jupiter. Saturn might be found, but not for about twenty years. Nevertheless, the list of known exoplanets has now passed the 200 mark.

So, is it likely that many stars have planets? Initially, the answer is 'no'. Only a small percentage of stars observed with the velocimetric method have planets, and the transit method has produced far fewer results. In reality, however, the proportion of stars possessing planets is certainly much greater. There are several explanations for this. First among them is that we are not detecting all types of

Annual numbers of discoveries of exoplanets since 1995 (including the first seven months of 2006 only). In spite of the introduction of new instruments in the last few years (up to and including 2006), the radial-velocity method is unable to reveal hundreds of extra planets in the future. Nearly all observable stars are now studied, and the short-period planets are already detected. Long-period planets are found as studies proceed, but fewer of these have been detected. Fewer planets with periods between 500 and 510 days have been discovered than planets with periods between 0 and 10 days.

JLJL

1995 1996 1997 1998 1999 3000 3001 3002 2003 2X11 300 5 2006

Our galaxy, the Milky Way - seen here above one of the telescopes of the Australian National University - contains approximately 300 billion stars. If we suppose that only one in every 100 of these stars has a planetary system, then there must be several billion such systems in our galaxy!

planet. There are the small ones, whether or not they orbit close to their stars; and large ones, if they are in remote orbits like Jupiter's. It may be no coincidence that of those stars which have been observed for the longest period of time (some fifteen years), more than 10% are known to possess planets.

There is no kind of star, even of solar type, which is easy to observe. A small degree of variability, involving just the odd eruption, will contaminate the spectral signature of a star and considerably increase the difficulty of detecting any planets. Moreover, if we restrict ourselves only to stars of very limited variability, one in four will yield results. Other targets offering a high probability of discovering exoplanets are those stars with a higher than average content of heavy elements. At a metallicity level twice that of the Sun, one star in four has a detectable planetary companion. In summary: of a sample of ordinary solar-type stars, only 5% will possess planets; and in carefully selected subsamples the figure can rise to one in four. However, the method used is not sensitive. Finally, there is nothing to prevent us from imagining that nearly all these stars have planets, and certain researchers already consider this to be so. Yet how are we to discover all those planets? In time, the radial velocity method will reveal all 'Jupiters', 'Saturns' and 'Neptunes' in long orbits, but Earth-like planets will be forever outside their range. These questions have given rise to projects, both on the ground and in space, with the avowed object of finding exoEarths.

It is worth noting that, effectively, nearly all the stars which can be observed by this method are being observed, and often by more than one team. Here we have some thousands of stars under scrutiny, of spectral type similar to that of the Sun and of suitable magnitudes. The sample can be enlarged if fainter objects are included, through the use of telescopes more than 2 metres in aperture. This is the aim of the HARPS (High Accuracy Radial Velocity Planet Searcher) spectrograph, currently mounted on a 3.6-metre telescope.

3.10 FAILED STARS OR SUPERMASSIVE PLANETS?

Planet or brown dwarf: a question of mass

Star or planet? This is not as easy a distinction as one might think, although theoretically a star produces energy from thermonuclear fusion reactions and a planet does not do so. The Sun shines because, like most other stars, it transforms hydrogen into helium, while the light of the planets accompanying it is merely reflected sunlight. Let us start from the beginning, from the birth of a star. A small 'knot' of matter within an interstellar cloud is drawn inwards upon itself by its own gravity. Its core becomes more and more dense, and ever warmer. If the initial knot of matter is sufficiently large, the core of the resulting protostar will become hot enough to switch on the thermonuclear reactions. The fusion process which turns hydrogen into helium requires a temperature of about 10 million degrees, implying a mass of the order of 0.08 times that of the Sun (about 80 times the mass of Jupiter). If this value is attained, a star will be born. The smallest hydrogen-burning stars are the red dwarfs.

Below this mass the hydrogen fusion reaction will not proceed, but deuterium - a heavy isotope of hydrogen - may instead come into play. We

The Trapezium, in the Orion Nebula. The points of light seen here, with the exception of the main (young) stars, are brown dwarfs and 'drifting' planets unattached to any star. This false-colour photomosaic is based on a combination of infrared and visible-light images obtained by the Hubble Space Telescope.

The Trapezium, in the Orion Nebula. The points of light seen here, with the exception of the main (young) stars, are brown dwarfs and 'drifting' planets unattached to any star. This false-colour photomosaic is based on a combination of infrared and visible-light images obtained by the Hubble Space Telescope.

are now in the realm of brown dwarfs, about which it might be said: 'When is a star not a star?'

Brown dwarfs shine feebly (0.0001 the luminosity of the Sun), but have lifetimes of billions of years. If a body has less than thirteen times the mass of Jupiter (about 0.01 of the mass of the Sun), then its core temperature will not be high enough to trigger the fusion of deuterium. Any object below this crucial mass of 13 Mj will therefore remain a planet.

The number of companion objects of a solar-type star as a function of mass (M sin /'), from planets (<0.01 solar mass) to ordinary stars (>0.08 solar masses). There are very few objects in the 'brown dwarf desert' between 0.01 and 0.08 solar masses. (After Santos et al., A. & A., 392, 215 (2002).

This definition, however, might be considered a little bizarre. Surely a planet is, by its very nature, in orbit around a star. Could there be planets drifting in interstellar space, not associated with any other body? Some astronomers claim to have discovered 'floating planets'; but in the absence of any accurate measurements of these bodies it is difficult to reach a conclusion.

Might a planet merely be a failed brown dwarf - a kind of 'doubly failed' star? Observations suggest that brown dwarfs and planets are rather different, and evidence of this is the 'brown dwarf desert'. When we investigate the types of companion that solar-type stars have, we find far fewer objects in the range 0.010.08 times the mass of the Sun, between the zone of planets (below 0.01 solar mass) and the zone of stars (more than 0.08 solar mass). This clear separation of stars from planets reminds us that the two types of body are formed in different ways - stars via gravitational collapse, and planets by accretion of matter onto a rocky embryo within a disk of gas and dust.

But beware! Some of the most massive exoplanets may indeed be brown dwarfs, as the radial velocity method determines the mass only to within a factor of the inclination.

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