Farther afield Extrasolar planets

Up until 1988, the Solar system was the only field of play for students of planetary climate, and it provided the only example against which theories of planetary formation could be tested. Revolutionary improvements in detection methods led to the first confirmed detection of a planet orbiting another star in that year, and instrumentation for planetary detection has continued to improve by leaps and bounds. As of the time of writing, over 228 planets orbiting stars within 200 parsecs (652.3 light years) of Earth have been detected, and the rate of detection of new planets is if anything accelerating. Certainly, much of the excitement surrounding the new zoology of planets has revolved around the prospect for detecting a planet that is habitable for life as we know it - or have known it to be in the past few billion years of Earth history. Perfectly aside from the habitability question, though, the rich variety of new planets discovered offers the student of planetary climate stimulus for thinking well outside the box of how the climates of known Solar System planets operate and have evolved over time.

Planets have been detected in orbit about a variety of different kinds of stars, so it is necessary to learn something of how stars are characterized. At the most basic level, stars are classified according to their luminosity (i.e. their net power output) and the temperature of the star at the surface from which the starlight escapes to space. The luminosity is determined by measuring the brightness of the star as seen from Earth's position, and then correcting for the distance between the star and the Earth. For relatively nearby stars, the distance can be measured directly by looking at the tiny shift in angular position of the star as seen from opposite ends of the Earth's orbit, but for stars farther than 500 parsecs (1630.8 light years), more indirect inferences are required. The stellar effective temperature is determined by measuring the spectrum of the starlight - how the brightness changes when the star is observed through different filters. Hotter stars have colors towards the blue end of the spectrum, while cooler stars tend toward the red. Hot stars emit more energy per unit surface area, but a reddish cool star can still have very high luminosity if it is very large, since it then has more surface area that is emitting. The energy sustaining the emission of starlight comes from the fusion of lighter elements into heavier elements. Since hydrogen is by far the most common element in the Universe that can participate in thermonuclear fusion, the overwhelming majority of stars ignite by fusing hydrogen into helium. These stars are known as Main Sequence stars, and stellar structure models predict that there is a distinct relation between the luminosity and emission temperature for stars that get their energy in this way. The stellar structure theories imply that the position of a star on the Main Sequence is determined primarily by its mass, with more massive stars being both hotter and more luminous. Moreover, stars spend most of their lifetimes on the main sequence, so that a scatter plot of luminosity vs. temperature of stars - a Hertzsprung- Russell diagram shows most stars to be clustered along the main-sequence curve. Indeed, the Main Sequence was discovered by plotting catalogs of stars in this way long before the energy source of stars was discovered.

Stars do not evolve along the main sequence. Rather, they enter it at a certain position when fusion ignites, remain near the same point for a certain amount of time while gradually brightening, and then leave the main sequence for a comparatively short afterlife as a brighter star with a more rapidly evolving spectrum. What happens when a star leaves the Main Sequence depends on the star's mass. The Sun will spend a billion years or so as a Red Giant, before collapsing into a gradually fading white dwarf. Main Sequence stars are thought to be the best candidates for hosts of habitable planets, since they provide relatively long-term stable stellar environments. Once a star leaves the main sequence, the climates of any unfortunate planets the star may have had will have been radically disrupted, if indeed the planets continue to exist at all; there will be relatively little time for any new form of life to establish itself. Nonetheless, planetary systems do exist off the main sequence, and these planets, too have their points of interest. The first confirmed detection of a planet orbiting a Main Sequence star did not occur until 1995.

Just as the luminosity of the Sun increases over time, the luminosity of other Main Sequence stars increases during their time on the Main Sequence. However, the lifetime of a star on the Main Sequence varies greatly with the mass of the star. The mass of the star determines the amount of nuclear fuel available to sustain the star's life on the main sequence, while the luminosity give the rate at which this fuel is consumed. The Main-Sequence lifetime of a star with mass M and luminosity I, scaled to values for the Sun, is estimated by

MSun 1

Main sequence stars have a power law mass-luminosity relationship I a M3 5, so on the Main Sequence the lifetime scales with luminosity according to the law

Bright, hot, blue massive stars thus have a much shorter lifetime on the Main Sequence than dim, cool reddish dwarf stars. The Sun has a Main Sequence lifetime of about 10 billion years, and is nearly halfway through its time on the Main Sequence.

Figure 1.2 shows the Hertzsprung-Russell diagram for stars that are known to host one or more planets. Astronomers designate the color (equivalently surface temperature) of stars according to spectral classes given by the letters O, B,A,F,G,K,M extending from hottest to coldest, with numbers appended to indicate subdivisions within a spectral class. Our Sun is a class G2 Main Sequence star. The diagram shown in the Figure represents a tiny subset of the many millions of stars that have been catalogued, and none of these stars (so far) have spectral classes hotter than F. The stars cluster along the Main Sequence simply because there are more stars in general along the Main Sequence than elsewhere. There is also a selection bias due to the technologies available at present for detecting planets, which work better for some kinds of stars than for others. Thus, the gap in detections between K and M0 stars may be an artifact of detection bias rather than a reflection of some basic feature of planetary formation.

There is a rich supply of planets orbiting stars between spectral classes G0 and K, as well as a good handful of planets around bright red giant stars off the main sequence. The cluster of detections around M5 dim red-dwarf stars are particularly interesting, as many of these turn out to represent the most Earthlike planets to date - again a detection bias, because it is easier to detect low-mass Earthlike planets around low mass stars using present technology. These M-dwarf stars are very dim, so a planet has to be in a very close orbit about its star in order to be as warm as Earth. In compensation, these systems have very long lifetimes compared to the Sun and other brighter stars. According to Eq. 1.3, an M5 dwarf spends about 100 times as long on the main sequence as the Sun does, and so this kind of star will brighten only very slowly over time. Such a star provides a very stable climate to its planet, and requires much less adjustment of atmospheric s s

4 Blue

4 Blue

7000 6500 6000 5500 5000 4500 4000 3500 3000 Effective Stellar Temperature

Figure 1.2: Scatter plot of luminosity vs. effective surface temperature for stars about which at least one orbiting planet has been detected as of 2007. Luminosity is given as multiples of luminosity of the Sun. The colder stars are redder while the hotter stars are more blue in color. The letters at the top indicate the standard spectral classification of stars in this temperature range, and the dashed line approximately locates the Main Sequence. The Sun is a class G2 Main Sequence star.

conditions than the Earth had to accomplish to resolve the Faint Young Sun problem. In contrast, an F0 star would spend under a billion years on the Main Sequence, and if the history of life on Earth is anything to go by, life around an F0 star would be snuffed out at the prokaryotic stage, before it could even begin to think of making oxygen. Aside from affecting the lifetime, the spectral class of the star affects the degree of absorption of stellar radiation by whatever atmosphere the star's planet may have, and this too provides a lot of novel things to think about when pondering the climates of extrasolar planets.

That takes care of the stars, but what is known about the extrasolar planets themselves? Here, too, there is a detection bias, since it is much easier to detect massive planets comparable in mass to Jupiter than it is to detect more Earthlike planets. Most planets detected to date are very massive planets which, according to theories of planetary formation, are likely to be gas-giants like Jupiter or Saturn, or ice giants like Neptune or Saturn. The full variety of planetary climates offered by the various combinations of planetary mass, orbital characteristics and stellar characteristics is hard to convey by looking at just a few graphs. We'll give a small sampling of this variety below. In the course of the exercises in this book the student will have ample opportunities to explore the wider universe of exoplanets.

One of the key determinants of planetary climate is the rate at which the planet receives energy from its star. This is a function of the luminosity of the star and the distance of the planet from the star, which varies to some extent in the course of the planet's year (as discussed in Chapter 7). Planets that receive more stellar energy flux than the Earth will tend to be hotter, all other things being equal, whereas planets that receive less will tend to be colder. The left panel of Fig. 1.3 shows the mass of the planets discovered so far and plotted against the stellar flux heating the planet at the time of the planet's closest approach to its star. The masses are measured relative to the mass of Jupiter and the fluxes are measured relative to Earth's solar heating. One Earth mass is 0.00315 times the mass of Jupiter. On this diagram, a planet with a relative flux of unity would have an Earthlike temperature if its atmosphere were like Earth's. We see that a great many planets with a mass one tenth Jupiter mass or greater have been discovered; these are all likely to be gas giants or ice giants made mostly of hydrogen and helium. Though these are in some ways like Jupiters, their climate has no real analog in the Solar system, since most of them are in orbits where the planet receives at least as much stellar energy as the Earth receives from the Sun. These are all "hot Jupiters," and represent climates very different from anything in the Solar System. Could Jupiters receiving Earthlike stellar radiation be habitable for life? That is certainly a Big Question, requiring understanding of the climate of such planets. Even more exotic are the giant planets receiving vastly more stellar flux than the Earth - up to one thousand times as much, in fact. These are "roasters" - very hot gaseous planets in close orbits about their host stars. Planetary formation theory gave no inkling that such things should exist, and indeed the existence of roasters poses real challenges for the theory.

Another way that the new extrasolar planets offer novel climates is in the nature of their orbits. Solar System planets, except for Pluto, have fairly circular orbits. However, most exoplanets have highly elongated orbits with a considerable difference between the distance of closest approach to the star (the periastron) and the distance of farthest remove from the star (the apastron). The range of orbital elongation is shown in the right panel of Fig. 1.3. Since the stellar energy goes down like the square of the distance from the star, the planets with highly elongated orbits will have novel seasonal cycles unlike any encountered in the Solar System. They would tend to heat up to a great degree at periastron and cool down, perhaps freezing over any ocean, at apastron. Could such a planet be habitable? The answer depends a lot on the thermal response time of the planet's atmosphere and ocean, which could average out the orbital extremes. The relevant physics is discussed in Chapter 7.

0.01

0.001 0.01 0.1 1 10 100 1000 Stellar Flux at Periastron (Relative to Earth)

to f

0.001 0.01 0.1 1 10 100 1000 Stellar Flux at Periastron (Relative to Earth)

Figure 1.3: Left panel: Scatter plot of mass of extrasolar planets in units of Jupiter masses vs. the flux of stellar energy impinging on the planet at the time of closest approach (the periastron). Right panel: Scatter plot of the ratio of farthest (apastron) to closest (periastron) distance of the planet from its star in the course of the planets orbit vs. the stellar energy at the time of closest approach. The stellar energy flux is given as a multiple of the corresponding flux for the Earth.

The orbital period, or "year", of the extrasolar planets also varies widely, as shown in the left panel of Fig. 1.4. Planets have been discovered with a wide range of orbital periods, ranging from as little as two Earth days to as much as 6000 Earth days. Planets in close-orbits with short orbital periods are likely to be tide locked and always present the same face to the star, just as the Moon always presents the same face to the Earth. The Super Earths to be discussed shortly are mostly in this category. Tide-locked planets offer novel possibilities for planetary climate. The night-side could get very cold, and if the planet has an ocean, it might freeze over completely. The day side would be hot, but there could be a habitable zone near the ice margin. Further, the transport of moisture and heat from the day side to the night side poses interesting questions; the answers are important, since such transports in large measure will determine the nature of the planet's climate.

Low mass planets are of particular interest because according to theories of planetary formation they have the best chance to have a rocky composition similar to that of Earth, Mars or Venus. Relatively few planets with a mass of 10 Earth masses (0.03 Jupiter masses) or less have been discovered, but there has been recent progress in this area. The planets discovered so far in this range are all considerably more massive than Earth, and are therefore called Super Earths. The left panel of Fig. 1.3 shows that a handful of Super Earths have been discovered with stellar fluxes ranging from .25 that of Earth (yielding a too-cold planet) to 1000 times that of Earth (yielding a planet far too hot. The closest to being "just right" is Gliese 581c, with a flux of about three times that of Earth. Would such a planet be habitable, or would it turn into a Venus? The physics needed to answer such questions will be developed in Chapter 4.

The right panel of Fig. 1.4 gives an indication of the masses of planets that have been discovered about stars having various temperatures. The stellar temperature is of interest to climate since it determines the spectrum - the redness or blueness - of the starlight, which in turn affects the absorption of starlight by various atmospheric constituents. Hotter stars also put out more of the energic ultraviolet radiation, which can have a profound effect on atmospheric chemistry. We see that a few low mass Super Earths have been found around class G or K stars, but examination of the associated planetary data reveals that these planets are in close orbits and receive several hundred times as much stellar energy as the Earth receives from the Sun. They

S3 100 r

0.001 0.01 0.1 1 10 100 1000 Stellar Flux at Periastron (Relative to Earth)

Blue

0.01

Blue

7000 6500 6000 5500 5000 4500 4000 3500 3000 Effective Temperature of Host Star

Figure 1.4: Left panel: Scatter plot of orbital period (in Earth days) vs. the flux of stellar energy impinging on the planet at the time of closest approach (the periastron). Right panel: Scatter plot of the mass of the planets (in units of Jupiter masses) vs. the effective radiating temperature of the host star.

will unquestionably be extremely hot places, and unlikely to be able to sustain an atmosphere or liquid water. There is, however, a small cluster of Super Earths orbiting very cool stars with temperatures under 3700K. These stars are Main Sequence "M-dwarfs." They are very red, very small, and very dim, but by virtue of their dimness planets in close-orbits can still have a chance to be habitable. Moreover, dim stars like M-dwarfs have a long lifetime, and therefore provide a stable environment for their planets. Gliese 581 is such a system, but it appears that the two most Earthlike planets still miss being habitable - one likely to turn into a Venus if it has an ocean and the other likely to freeze into a Snowball. Part of the reason for interest in M-dwarfs comes purely from detection technology. It is comparatively easy to detect low-mass planets in close orbit around a low-mass star, and at the same time low-mass dim stars give a planet in a close orbit a chance to be habitable. As time goes on, it is likely that a habitable world around an M-dwarf will be discovered. As detection technology improves, the possibility for discovering Earthlike habitable planets will expand to other spectral classes of stars.

Naturally, one is at this point intensely curious as to the composition of these planets, whether they have water, and what their atmospheres (if any) are made of. Some information can be inferred from planetary formation theory and theories of atmospheric evolution , but there is as yet no great ability to determine atmospheric composition from observations. That will change in the next decade or two, as satellite-borne instruments come online which will be able to determine the spectrum of emission and reflection from extrasolar planets. The anticipated instruments will only return a single spectrum averaged over the whole visible surface of the planet, but a great deal can nonetheless be inferred about atmospheric composition from such data. Learning how to make the most of this single-pixel planetary astronomy, in which the Earth would appear as a pale blue dot (in Carl Sagan's words) opens a whole range of Big Questions. Much of the same radiative transfer used in calculating planetary climate bears on the interpretation of planetary spectrum as well.

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  • Regina Lightfoot
    How does temperature of a planet change with the distance from the sun?
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