Day 6
Inconstant Stars
Juliet: O! swear not by the moon, the inconstant moon,
That monthly changes in her circled orb,
Lest that thy love prove likewise variable.
Romeo and Juliet, Act II. Scene II
William Shakespeare (1564–1616)
The Oxford Shakespeare, 1914
Galileo and Bruno contended that the heavens change with time just like the base Earth. The appearance of comets and “new stars” were two examples. In the Dialogue, Galileo forcefully stated that Aristotle did not have this new information when he postulated that the heavens never change. Halley confirmed that the heavens do change when he detected the proper motion of stars (Figure 1).
Figure 1: Studies of the proper motions of stars revealed that star clusters are real groups. The stars in the open Taurus cluster move in essentially parallel paths relative to the Sun. Astronomers see their proper motion again the background of distant stars in 2-D like railroad tracks on a painting. The convergence point of the stars corresponds to the vanishing point of parallel lines on a painting. The Sun was part of an open cluster that has dispersed over the last 4.5 billion years. From Doig’s 1927 book Stellar Astronomy.
Yet finding that stars move around is a lot different than figuring out how they shine. Bruno contended that the stars exchanged light with each other. This perpetual motion did not make much sense then and was considered nonsense once conservation of energy became understood.
Gravitational energy from the Sun’s accretion is an obvious heat source, but a limited one. Lord Kelvin showed that it could keep the Sun going for about 20 million years. Unlike the Earth, ordinary radioactivity did not offer any help. There is little uranium, potassium, and thorium in the Sun. Significant amounts would have been obvious in the spectra even in 1900.
The Sun is mostly hydrogen with some helium (named because it was detected from solar spectra before it was found on the Earth). Only about 2% of the atoms are heavier elements. This fact presented the first key to figuring out how stars work. The second key came from radioactivity and the theory of general relativity. The total mass and energy of a closed system are conserved, rather than mass and energy separately. The conversion factor is the well-known formula E=mc2 where c is the speed of light. A small change in mass lets out lots of energy because the speed of light is large. Nuclear reactions involve changes between energy levels just like chemical reactions. In fact, precise measurements show that chemical and nuclear reactions are coupled to some extent. Nuclear reactions differ in that more energy is typically involved.
The change of mass in a nuclear reaction is large enough to detect with 1900’s technology. Four hydrogen atoms are more massive than one helium atom. There is enough hydrogen in the Sun for this reaction to power it for billions of years. Postulating that this reaction occurs, however, is different than showing that it occurs.
Until about 1950, scientists suspect that stars gradually cool and become less luminous as they use use their gravitational and nuclear energy. This natural idea, which sets the plot for H. G. Wells' War of the Worlds, proves to be grossly incorrect. As in all of science, intuition is often an unreliable guide.
After W.W. II, the energy levels at the center of the Sun are replicatable in atomic accelerators. The hydrogen bomb works on the first try. Physicists figure out how rapidly hydrogen becomes helium at the center of stars. It is obvious that the pressure and the temperature at the center of stars increase with their mass. The nuclear energy production and hence the light energy emitted by a star increase with about the fourth power of its mass. The hydrogen at the center of our Sun is already half used up. There is enough for the Sun to shine another 5 or 6 billion years.
The astrophysics of the center of stars explains the surface physics of stars. Hydrogen burning stars are in a (quasi) steady state with heat loss balancing heat generation. A massive star radiates more light than a small star. It does this partly by being larger and having more surface area. Its surface is hotter causing more light to be emitted per surface area. This effect is huge, the amount of energy per time per area scales with the fourth power of the absolute temperature. (The temperatures are so hot, thousands of degrees, that it does not matter much whether you think of them in Celsius rather than absolute Kelvin.) That is, small cool stars that radiate mainly in the red are much less luminous than massive hot stars that radiate in the violet and the ultraviolet.
Figure 2: Astronomers Hertzsprung and Russell plotted stellar luminosity plotted as a function of surface temperature. Note log-log scale and that temperature increases to the right. The Sun is part of the main sequence between red dwarfs and blue giants. These stars burn hydrogen to helium. Sun-sized stars evolve into red giants that burn helium. They become white dwarfs when these cease to burn. Blue giants evolve into super giants that then explode as supernovae.
This explains an observation from spectra studies. If one plots luminosity (total energy emission) as a function of surface temperature, most of the stars fall in a narrow band called the main sequence. These are hydrogen-burning stars. (Figure 2) Other classes of stars exist. There are luminous red stars called red giants and red supergiants. Their diameters measure in AU. There are small hot white stars with low luminosity, called white dwarfs. These uncommon classes of stars figure in the formation and ultimate fate of habitable planets.
Figure 3: Astronomers observe modern star-forming regions, here the Trifid Nebula. Light from young bright stars is dispersing the gas and dust and exposing very young stars. There are such stars near the top of the blue box. Star formation will end here once the gas and the dust are dispersed. The bright area is somewhat larger than a parsec. Hubble space photo. http://antwrp.gsfc.nasa.gov/apod/ap040618.html
Your fate is in the stars. Stars are now forming from gas clouds near (for astronomers) to the Earth (Figure 3). I follow the evolution of such a cloud. Initially the cloud is cool, about 10 degrees above absolute zero. It begins to collapse under its own gravitation. Some regions collapse faster than others. The collapsing regions rotate conserving angular momentum. In a few million years, some of the collapsing regions are dense enough to be optically thick. The trapped gravitational energy heats them up. Soon after, some of the dense regions collapse into rapidly rotating stars. Hydrogen begins to burn at their centers.
Figure 4: Hot gas diverges from the 1680 Supernova Cassiopeia A. A similar supernova occurred before the Solar System accreted. Our supernova material contained short-lived radioactive isotopes. It locally shocked the gas triggering the Sun’s collapse. The field of view is a few parsecs across. Hubble space photo. http://antwrp.gsfc.nasa.gov/apod/ap030830.html
We first follow the fate of a star that is 20 times the mass of the Sun. Its intense ultraviolet light heats the surroundings. From our simple scaling, this star has energy for 1/8,000 the life of the Sun or 1 million years. (A more precise calculation yields 7 million years.) It exhausts its interior hydrogen while much of the interstellar gas cloud is still collapsing. It does not go quietly. Instead the high temperatures at its center convert helium into heavier elements like carbon, nitrogen, and oxygen on up to silicon. This renewed energy source is huge. The star becomes a supergiant. The intense pressure from the light of the star expels its outer regions. This leaves the inside core (with no hydrogen) exposed. The star eventually has enough heavy elements at its center that nuclear reactions can produce iron, the most stable element. This process is unstable as the interior of the star becomes dense enough that electrons can combine with protons to form neutrons. Within seconds, the core of the star collapses into a few kilometer-wide region composed of neutrons. This releases vast amounts of neutrinos. Normally, neutrinos do not interact much with ordinary matter. (Most of those produced in our Sun escape unaffected.) But the interior of our star is quite dense and the high-energy neutrinos collide with the surrounding material ejecting it. Rebound of the shock wave from the initial collapse aids the ejection. The conflagration reaches the surface about an hour later. Over this time, elements heavier than iron form in the neutron-rich environment. The star is a supernova shining with a billion times the intensity of the Sun.
The expelled gas spreads in a shock wave through the gas cloud. This triggers further collapses in some places and disrupts the cloud in others. The debris enriches the cloud in elements heavier than helium. Some of these atoms have short half-lives.
Supernovas and bright massive stars heat our gas cloud. This often expels enough gas that the cluster of stars is no longer gravitationally bound. The stars disperse slowly in the galaxy, each going its own way. In other cases, a gravitationally bound “open” cluster persists after the gas disperses.
A sun-sized star has a more protracted history (Figure 5). First it collapses and becomes a star. Initially it rotates rapidly. Magnetic fields couple the rotating star to its solar wind. This transfers angular momentum to the wind and slows the rotation down. Gravitational energy is a powerful and, as Lord Kelvin suspected, short-term energy source. A sun-size star is initially 10 times as luminous as the Sun. After a few million years, the star settles down and joins the main sequence. It gradually burns hydrogen to helium. This causes the interior of the star to become more dense and hotter. Hydrogen burns at an increasingly faster rate. The luminosity of our Sun has increased by 30% over its lifetime.
After ten billion years our star exhausts the hydrogen at its center. Like the massive star, it does not go quietly. It contracts until helium can burn. This process is somewhat unstable. The outer regions of the star expand to around an AU. It is a red giant. Much gas gets expelled at times of energy surges. Eventually only the hot core remains. It has no more nuclear material to burn. It becomes a white dwarf and cools slowly. Depending on its initial size and the amount of gas expelled, it may end up composed mainly of helium or of carbon and oxygen.
Figure 5: Astrophysicists have predicted the Sun’s evolution the Hertzsprung-Russell diagram. Note that temperature is now linearly scaled. Gravitational energy makes the Sun 20 times more luminous than now during its collapse. The Sun joins the main sequence and starts to burn hydrogen. It gradually becomes more luminous. It is now about 4.5 billion years old. It will expand and become redder between 10.9 and 11.6 billion years after its formation. It then becomes more luminous as its interior contracts and becomes hotter, while its surface expands and becomes cooler. The curve ends at 12.2 billion years where helium ignites in the deep interior. After that the evolution is complicated by episodes of unstable helium ignition.
Minor amounts of heavy elements form in proton-rich and neutron-rich regions of red giants. Geochemists have been detected within pre-solar silicon carbide (grinding powder) grains in meteorites. They have also detected elements produced by supernovas soon before our solar system formed. All this supports the hypothesis that our sun formed in a region similar to modern gas clouds and open clusters.
Ice and rock. After the Big Bang, the universe had only hydrogen, helium, and a slight amount of lithium. The first stars formed from this mixture. The elements in rocks, like silicon, magnesium, and oxygen did not exist. Neither did the elements in ices, like oxygen and carbon. Since these elements did not exist yet, it was impossible for very old stars in our galaxy to have icy or rocky planets.
Figure 6: Astronomers can see clear signs that planets are now forming, in the protoplanetary dust and gas disk around star HD 141569A. The disk is 1200 AU across. Our Sun had a smaller disk. The black area in the center is an artifact of data collection. The astronomers plotted out the intense light from the star so that the faint disk was visible. Hubble space photo. http://hubblesite.org/newscenter/newsdesk/archive/releases/2003/02/image/b
Rock and ice forming elements built up in the galaxy over time as young massive stars and older red giants supplied light elements and supernovas supplied both light and heavy elements. (Astronomers call all elements heavier than lithium metals. This usage is a vestige of the fact that metal atoms in the usual chemical sense are easy to detect from spectra.) The fraction of metal atoms varies from place to place within our galaxy. It is easier to form earthlike rocky planets around some stars than others.
Just then how do planets form? The modern theory involves the rotating gas cloud that collapses to form a star (Figure 7). Early geologists were familiar with this hypothesis. Buckland discusses it in his 1837 book. Late in the 19th and early twentieth century, some scientists contended that the planets formed in the near collision of our Sun with another star. Since stars rarely come close in the vastness of space, this appealed to those who thought the Earth is special. The physics do not work out though. A near miss does not leave planets in its wake.
Lots of planets. A few years ago, astrophysicists had only our solar system as an example. They thought they understood that the formation of the planets occurred at about their present distance from the Sun. They understood the basic physics, which applies reasonably well to our solar system.
Figure 7: The protoplanetary dust and gas disk orbits the Sun at a time it was more luminous than at the present. The region near the Sun is so hot that only gas is present. Rock and iron metal condense farther out forming rocky planets like the Earth. Still farther out, it is cool enough for ice to condense. This leads to the formation of icy objects that accrete gas becoming giant planets. The gas orbits more slowly that planets. The effects of stellar winds and UV light from nearby bright stars limit the outer edge of the disk. Viewed obliquely with the top farther away, not to scale.
Our solar nebula was composed of elements similar to our Sun. For convenience, it contained 98% helium and hydrogen, 1.5% of material like water and carbon dioxide that form ices at low temperatures, and 0.5% of material that forms rock and iron metal. The Earth and other terrestrial planets formed from this half percent. It is obvious that it was hot near the Sun and cool further out. The contracting Sun was a lot brighter than the modern one. It was thus very hot at one AU. Rock and iron condensed outward of a fraction of an AU of the Sun, icy material condensed in the cool outer regions beyond 5 AU. Hydrogen and helium remained a gas. This arrangement yielded rocky terrestrial planets near the Sun.
Farther away, the collapse of icy objects contributed to the collapse of the surrounding gas in the outer solar system. Jupiter and Saturn contain much nebula gas. Uranus and Neptune are mostly icy and rocky material but have enough gas to be giant planets. Pluto is a small icy object that never collided with a larger planet.
Astrophysicists understood the basic physics of the collapse of (ice or rock) dust into planets. Gas rotates slower than solid material in Keplerian orbits because its pressure partly resists its fall into the Sun (Figure 7). Gas drag causes the rock orbits to become circular and to collapse to the plane of the rotating solar nebula. The solid particles become dense enough to collapse under their own gravitation in kilometer to 100’s of kilometer diameter planetesimals. There is a minimum size of object that can collapse for a given mass per area (surface density) of dust on the disk. The velocities imparted by the gravity of the collapsing region must exceed the random velocities of the dust. There is also a maximum size of the instability. The outer part of the nebula rotates more slowly than the inner part. A slowly collapsing instability will be sheared before it can collapse. No collapse can occur if the minimum size is greater than the maximum size. This situation prevails for gas, which cannot collapse unless a massive icy or rocky object is already present (its pressure resists compaction).
Once planetesimals are present, modeling of the formation of terrestrial planets becomes conceptually simple, but complicated. The bodies collide with each other eventually forming planets. The gravity of the largest plantesimals attracts smaller ones causing the process to accelerate. Formation of giant planets requires two steps. Massive icy objects grow until they can trigger gas collapse. Jupiter and Saturn accrete large amounts of gas. Uranus and Neptune accrete modest amounts.
Planet formation is complicated, involving turbulence in the gas, the tendency of dust to stick mechanically, and even gravitational effects and ultraviolet light of nearby stars in the nascent cluster. In retrospect, the 1990 astrophysical theory lacked predictability. It still cannot even hindcast our own solar system
This idea that all planets formed about where they sit collapsed when astronomers, Geoff Marcy, Paul Butler, Michel Mayor, and Didier Queloz began to detect planets around other stars. Their method is simple in concept. Planets revolve around the center of mass in their solar system. (See Figure 8.) The star is very massive so the center is typically within it. The star moves back and forth around the center of mass and hence flees and approaches the Earth. (This method observes only the motion along the line of sight.) For Jupiter-sized planets, the star velocities are meters per second, like those of a healthy jogger. The astronomers had to develop precise equipment before they could start looking.
In 2005, astronomers had detected planets around 5% of the stars examined, a total of over 100 out of over 2000. These are all giant planets. The mass of a rocky (terrestrial) planet is too small to have a measurable effect with current equipment. The detected giant planets are typically near their stars, often much closer than an AU. This is a sampling bias in that close-in planets produce the largest velocities. The year of close-in planets is short so it is easy to resolve that the star moves back and forth over a reasonable observation period. (Improved detection technology and continued effort has increased the fraction of stars with found planets along with decreasing the minimal detectable size and the maximum detectable year.) Still the result shocked astrophysicists. They did not realize that giant planets spiral in toward their star after they form.
Again the physics are simple, but extremely complicated to model. A giant planet cleans up the gas in the nebula near its orbit. Pressure variations in the gas cause some of it to flow into the void. This occurs irregularly at the edge of a donut-shaped region surrounding the planet’s orbit. Gravitational interactions set up waves in the gas, coupling the orbit of the planet to the gas. As the gas is revolving slower than the planet, the effect is like drag. The planet spirals inward, especially if the nebula becomes more dense inward. The process ends either when the planet collides with its star or the nebula disperses. Gravitational interactions between the planets remaining at that time may expel some of them from their solar systems, cause others to collide with their star, or scatter others to enter highly elliptical orbits. Astronomers have detected numerous giant planets in elliptical orbits.
There are subtle hints of this process in our solar system. Jupiter is enriched in the rare gas argon relative to solar abundance. This indicates that argon condensed as an ice, which could happen only in cold regions much farther from the Sun than Jupiter’s present position. That is Jupiter spiraled in. Uranus and Neptune appear to have spiraled out. Astronomers routinely detect 100’s of kilometer diameter objects beyond the orbit of Neptune. These “Kuiper belt” objects, however, have little total mass. This may indicate the effects of nearby stars forming with the Sun that kept the diameter of the nebula in check. The Kuiper belt objects have orbits that indicate they moved outward along with Neptune.
Let’s look. We would like to detect terrestrial planets around other stars and giant planets at Jupiter-like distances. As Bruno guessed, this is not an easy task. In addition to line of sight accelerations, three other methods seem practical.
Figure 8: Careful observations let astronomers detect planets around other stars. The planet and the star orbit around the center of mass M. A, B, C, and D denote positions of the planet and star around the orbit. Viewed obliquely from the Earth the circular orbits are ellipses. Astronomers observe the motion along the line of sight. The star moves toward the Earth through BCD and away from the Earth through DAB. Astronomers attempt to resolve the elliptical path of the star against the background of more distant stars. If the system is lined up so that we see it edge on, the planet transits the disk of the star dimming the light that we see. The situation with elliptical orbits and several planets is more complicated but analogous.
First, we can use the motion of the star perpendicular to our line of sight (Figure 8). The star revolves around the center of mass and sweeps an elliptical orbit. (a circle viewed at an oblique angle is an ellipse. You can see that with a sausage slice.) This method is most sensitive to giant planets that are well away from their star. It takes them several Earth years to complete their orbits. One needs to observe for over 10 years to separate the orbital motion from the unknown proper motion of the star. So far this method has worked only with already discovered planets.
Second one can wait for planets to transit their star, as long as the planet’s orbit is lined up right. Astronomers have observed the transit of planets already detected by line-of-sight velocities. A close-in planet is most likely to transit and the star dims slightly during the transit. Transits have the advantage that the spectrum of the star is slightly affected by light that passes through the planet’s atmosphere. This allows astronomers to determine the composition and the temperature of the planetary atmosphere. Sensitive space-based telescopes are needed to detect terrestrial planets in this way.
Third, one can try to see the reflected or emitted light of a planet directly. The Earth, Venus, and Jupiter are about a billionth as bright as the Sun in visible reflected light. This is plenty bright enough to see with modern telescopes at the distance of nearby stars. The difficulty is, as Bruno suspected, the glare of the star. One way around this is to take advantage of the fact that light is a wave. Instruments called interferometers are built to null out the light of a star in order to see planets. This works best in the thermal infrared where the emitted light of the planet is a millionth that of the star, rather than a billionth with visible light. This method provides spectra of the planet, particularly on the existence of ozone and methane in the atmosphere. Astronomers have observed emitted light from already known extrasolar planets.
The Sun also rises. Astrophysics tells us that our Sun will become a red giant in 5 to 6 billion years. Then the Earth will be incinerated if not consumed altogether. Life has taken a long time in evolving to its present state. What our are prospects of other earthlike planets? Where should we look?
Astrophysical theory is some help. The star-forming gas must contain “metals” to form rocky planets but the relationship of gas composition to rocky planet size is unknown. The first stars in our galaxy formed from metal-free gas. It took time - billions of years - for supernovas to build up metals in our galaxy, but local metal-rich regions exist in the oldest galaxies. About 10% of the stars have metal content close to the Sun. Many of these formed before the Sun. Fortunately for our search, the 10% includes many neighboring stars that we can actually study.
The other hard exception involves the time for planets to form and life to begin. We need not look at bright massive stars that meet a violent end within millions of years after they form. These stars are rare anyway so little living room is lost.
Other situations are unpromising to rocky planets but not exclusionary. Multiple star systems often preclude stable terrestrial planet orbits. The exceptions are when the stars are much closer than an AU or much more apart than an AU. Astronomers in fact have detected such planets. The 100 plus solar systems with giant planets near the star are also unpromising. Again there are no stable orbits for rocky planets near giant planets. The exceptions include icy and rocky moons of giant planets.
Going to the other end, faint red stars last almost forever. (None have yet entered the red giant stage in the observable part of the universe.) The smallest planets so far detected orbit red stars. This again is a sampling bias. The small mass of red stars makes it easier to see the feeble gravitational tug of planets. I address the habitability of their planets after I discuss climate and evolution.
Our search for other Earths hasn’t yet started. As in the time of Bruno, astronomers lack technology that would detect our Earth around nearby stars. They can barely detect another Jupiter at its distance from the Sun. This will soon change. In practice, this search will continue to be controlled by what we can detect, not by theory. It’s rather like a drunk looking for lost car keys only in the well-lit areas.
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