15. Stars 2

Transcript: The laws of microscopic physics are invariant with respect to time which is to say that microscopic interactions can move backwards or forwards equally well. The laws of physics really say nothing about the arrow of time, and yet when a movie is run backwards it’s obviously silly and nonsensical. Smashed wine glasses do not leap whole up onto the table. So where does the strong perception of the arrow of time come from? It comes from the second law of thermodynamics and the tendency for disorder to increase over time, and this is related to the fact that disorder is statistically a much more likely outcome so tends to increase when changes occur in a system. The deck of cards is the best example. The initially ordered deck of cards when shuffled will gradually approach a random sequence, and no amount of shuffling will reconstruct the initial high degree of order. You may shuffle the deck over and over, and you will see sequences of two or three or maybe four cards appear in sequence, but the large amount of order or the low amount of entropy is never recreated no matter how much you shuffle the deck.

Transcript: Disorder or entropy tends to increase because disordered states are usually the most common outcome in an experiment or any situation. Take the artificial but simple example of four coins, each of which has two outcomes when it’s tossed and is independent of the other. There are two to the power four or sixteen possible states. The most orderly is either four heads or four tails which occurs two out of sixteen times or thirteen percent of the time. The most disorderly or mixed outcome is two heads and two tails which occurs six times, three times as often. This situation becomes more extreme with a hundred coins tossed. There the probability of all heads or all tails is only one in ten to the power thirty whereas the probability of equal numbers of heads and tails is one in twelve, a hugely more likely outcome. The German physicist Ludwig Boltzmann made the mathematical definition of entropy in terms of the number of microscopic states, and he was so proud of his work that he had it engraved on his tombstone.

Transcript: The third law of thermodynamics states that it’s impossible to remove all the heat from a physical system. At the temperature absolute zero there is no heat, and there is no atomic motion. So there would be no friction, and perfect machines with perpetual motion would be possible. This can never be achieved in the real universe. Imagine taking a cold gas. If you expanded it its temperature would cool further, and its molecular or atomic motions would reduce. But no matter how much you expanded it there would always be some motion because it would take an infinite amount of expansion to theoretically reduce it to absolute zero temperature.

Transcript: The second law of thermodynamics states that as energy changes form the amount of heat energy will tend to increase. Another way of saying this is that the entropy or disorder of a system will tend to increase. We are familiar with this systematic change from order to disordered energy with the simple example of an automobile. Gasoline is a place where the ordered energy in chemical bonds in hydrocarbons are converted into ordered mechanical energy in the motion of an engine. But the ultimate result is the release of heat or disordered energy, and that’s the inefficiency in a car. Stars are also creating disorder from order. They are fusing atomic nuclei to make heavier and heavier forms, but they’re releasing the energy as disordered radiant heat energy into space.

Transcript: The first law of thermodynamics states that energy can change forms, but the total amount of energy in a system is always conserved. This is the familiar statement of the conservation of energy familiar for example in gravitational physics with the situation in an orbit where gravitational potential energy is continually trading off between kinetic energy, but the sum or the total is always constant. It seems as if we get starlight for free from nowhere, but in fact starlight comes from the creation of radiant energy from the binding energy of the atomic nucleus. Essentially stars are fusion factories steadily converting mass into energy according to E = mc2.

Transcript: Thermodynamics is the study of heat and the way it flows. In this field of physics a strong connection is made between large scale or macroscopic behavior and small scale or microscopic behavior. On the large scales we can study behavior of a perfect gas and the well known relationships between the temperature, density, and pressure of the gas when it undergoes changes. These laws extend simply to the behavior of stars. On the small scale the idea of temperature is related to the microscopic motion of atoms and molecules where temperature is simply a measure of the instantaneous velocity of subatomic particles.

Transcript: The most spectacular type of mass loss occurs in post-main sequence stars undergoing their planetary nebula phase. The name comes because the pale bubbles of gas looked like planets as seen through early small telescopes, but it’s a misnomer. Planetary nebulae have nothing to do with planets. They are the evolved states of stars where the gas is glowing in sheets or spheres around the central stellar core. The gas glows for two reasons: first the large amount of ultraviolet radiation from a hot star at the center and second because the gas is being ejected, and it can be raised in energy in shocks as it hits the interstellar medium. The resulting morphologies can be complex: shells, rings, arcs, or more complicated patterns. The colors are indicative of the chemical elements involved in the gas: the red glow coming from the hydrogen alpha line, and the blue-green glow typically from doubly ionized oxygen. Emission lines of nitrogen, oxygen, carbon, sulfur, chlorine, and iron are routinely seen in planetary nebula indicating the recycling of heavy elements into the interstellar medium from evolved stars.

Transcript: In both the early and late phases of stellar evolution a star can lose mass. The mass in the outer envelope can be ejected into interstellar space where it can form material to take part in the creation of a new generation of stars. Mass loss is most spectacular among evolved stars where the behavior of the outer atmosphere becomes decoupled from the behavior of the hot, dense stellar core. For example in blue supergiants the mass loss rate is enormous. Roughly one solar mass of gas can be lost every hundred thousand years of the star’s main sequence lifetime, and so the star can lose a total of one third to one half of its total mass by ejection into interstellar space. For red giants the mass loss rates are smaller, and such stars can be thought to have a smooth stellar wind that slowly leaks gas and dust into the interstellar medium. For stars like the Sun and main sequence stars in general mass loss occurs at a very small rate.

Transcript: In the late eighteenth century the young English amateur astronomer John Goodricke discovered brightness variations in the star Algol while he was only seventeen years old. Soon afterwards he observed Delta Cephei carefully enough to find regular brightness variations with a timescale of five days and eight hours. The Royal Society awarded him a medal for his work, and he quickly became noted in the scientific community. Goodricke was born deaf and unable to speak in an age when most deaf-mutes were consigned to asylums and rarely did any useful work. Unfortunately Goodricke died of pneumonia at age twenty-one due to his excessive time spent outside making difficult observations. Goodricke had discovered regular short period variable stars. The two most notable categories of these stars are Cepheid variables with periods of one to fifty days, Polaris is a prime example, and RR Lyrae variables with periods in the range of one to twenty-four hours.

Transcript: Just like a bell or any mechanical object, stars have a particular frequency or timescale when they tend to vibrate in response to an external disturbance. If the time that it takes for energy to dam up in the atmosphere of a giant star corresponds to the natural frequency the star will oscillate or pulsate. These are regular variables. In stars where the timescale of the damming of radiation in the atmosphere and the oscillation timescale are not synchronized the variations are irregular. The complex behaviors of variable stars have led to a zoo of categories of variable stars.

Transcript: In 1595 the amateur astronomer and Lutheran pastor David Fabricius noticed the bright star in a constellation Cetus fading until it became invisible and was amazed several months later to see it reappear. The star Mira, called wonderful, has a period of eleven months and is a classic example of a long period variable star. Most stable stars are in hydrostatic equilibrium. They act like a thermostat, but giants have atmospheres that trap some fraction of the energy as it’s released. The energy dams up causing the outer layers to heat up and expand. The expansion lowers the pressure and then the layer can contract again, and the process is repeated. Notice that a variable star in a long period situation is not due to any variation in the rate of energy generation in the core. It’s due to a variation in the rate of energy release. Think of a boiling pan of water with a lid on it. The energy flow through the pan is constant, but steam builds up under the lid and the lid periodically tips to release the steam. This is a similar type of mechanism.

Transcript: When Shakespeare talked about love that was as constant as the pole star he was taking artistic license. Polaris is in fact a variable star along with many other bright stars in the night sky. Chinese astronomers were the first to note systematic variations in stars visible to the naked eye. Modern astronomers using digital surveys and high quality detectors have cataloged hundreds of thousands of variable stars in at least twenty eight different types. There are stars that vary regularly or periodically and stars that flare up regularly. There are stars that vary with light intensity variations of only a few percent and some that vary by orders of magnitude in their brightness. Variable star science is complex and has led to many insights into the way that stars work.

Transcript: After the main sequence the core and the envelope of a star often follow utterly different evolutionary paths. For example consider the fact that in a red giant the outer envelop becomes cooler than the Sun, or redder, while the core is actually more than ten times hotter. Remember also that when we observe stars in the sky we are only every seeing the photospheric temperature reflecting the color and the energy in the outer diffuse envelope. Often the conditions in the deep core of the Sun or any other star are vastly different. Material can also be lost into space during stellar evolution so the final mass of a star or a stellar remnant is always less than the initial mass.

Transcript: The core of an evolving star like a red giant contracts until the temperature reaches roughly two hundred million Kelvin. At this point a new energy source is available from the fusion of helium nuclei by the triple alpha process. This is a two stage reaction. In the first stage two helium four nuclei combine to form a beryllium 8 nucleus with a photon, and in the second stage a beryllium 8 nucleus combines with a helium 4 nucleus to form a carbon 12 nucleus with a photon released. Beryllium is unstable, and so the decay of beryllium before it can combine with another helium nucleus reduces the efficiency but does not quench the process. In low mass stars the energy released can rapidly heat the core and cause what’s called a helium flash. This can consume the helium fuel in only a few seconds although the effects are seen at the outer cool envelope of the star hundreds or thousands of years later and can last thousands of years. The Sun faces a helium flash roughly three hundred million years after it leaves the main sequence.

Transcript: Eventually all main sequence stars must exhaust their hydrogen fuel supply. This is true whether or not they are high mass and live their lives quickly or low mass and live their lives very slowly. The star must then eventually pass through either the red giant or the white dwarf stage. For a star like the Sun and more massive than the Sun it goes to a red giant stage. The Sun will spend roughly a billion years in this phase of evolution. As a star leaves the main sequence the core collapses because there is no pressure support from nuclear reactions. Meanwhile a shell of hydrogen is still fusing into helium. The core releases gravitational energy which drives an expanding envelope. Thus the outer part of the star turns into a huge, thin, and diffuse envelope with a low effective temperature, hence the name red giant, while the core becomes smaller, hotter, and denser than it was before. The size of the red giant envelope is huge, up to a thousand times the size of the Sun itself. If the Sun turns red giant its envelope would extend to the orbit of Jupiter. On the HR diagram stars leave the main sequence and have properties to place them in the upper right of the diagram.

Transcript: Conceptually we can divide the evolution of stars into three rough stages: the early stages or pre-main sequence stages of evolution, the main sequence itself when hydrogen is converted into helium, and post pain sequence stages which vary depending on the mass of a star. To take the example of the Sun, the Sun has spent roughly thirty million years reaching the main sequence, will spend nine billion years in total on the main sequence, followed by about a billion years as a red giant, and then a large or essentially infinite amount of time as a cooling white dwarf. What this implies for censuses of stars outside the main sequence is that the visibility of a star depends roughly on the amount of time that it spends in each evolutionary stage. So if a star like the Sun spends less than one percent of its time reaching the main sequence and about ten percent of its time as a red giant, then if we surveyed a hundred stars like the Sun at different stages of their evolution we’d find only about one on its way to the main sequence, ninety percent we’d find on the main sequence, and about ten percent we’d find as red giants. This is not the whole truth however because the different evolutionary stages have different luminosities, and short-lived but luminous stages of stellar evolution are much more visible than long-lived or dim stages of stellar evolution. Thus the stellar catalogs are over represented in the short-lived luminous stages such as red giants and of course supernovae.

Transcript: We say that the Sun is a typical star, and that’s not precisely true. The Sun is indeed intermediate in mass range between the lowest mass and highest mass stars, but it’s not typical numerically. The distribution of stellar masses is called the initial mass function. This is the relative numbers of stars of different masses that emerge average over star formation regions throughout the Milky Way. The initial mass function is a power law, and it’s quite steep which means that there are many more low mass stars for every high mass star. The highest mass stars, about a hundred times the mass of the Sun, live a very short time on the main sequence, only about a million years, whereas the lowest mass stars, much larger in number, live a very long time, trillions of years. None of these stars have ever left the main sequence, but because they’re intrinsically very dim they’re hard to see at large distances and they’re underrepresented in most stellar catalogs.

Transcript: The fusion process that dominates stars of less than about one and a half times the mass of the Sun and core temperatures less than fifteen million Kelvin is called the proton-proton chain. There are three steps in this reaction which converts hydrogen into helium. In the first step that lasts about ten million years per proton, two protons combine to form deuterium with the release of a positron and a neutrino. In the second step which occurs relatively quickly the deuterium atom has a proton added to become a helium 3 nucleus with the release of another photon. In the third step which takes about a million years two helium 3 nuclei combine to form a single helium 4 nucleus with two protons left over and the emission of a photon. Thus mass energy is converted at every step, and energy emerges in three separate forms: neutrinos which flee at the speed of light, protons which help further nuclear reactions, and photons themselves.

Transcript: Stellar fusion cannot be understood without the quantum theory of matter. In classical physics the electrical repulsion force between two protons as they approach each other is an insurmountable barrier, but in the quantum theory there’s a finite probability that the protons will ignore the barrier and be able to fuse. This problem was worked out in the 1930s by Hans Bethe, a German physicist who immigrated to Cornell University. Bethe calculated the probability that protons would fuse and then was able to realize that the small amount of mass-energy released was sufficient to power the fusion reaction in the Sun and other stars. The paper he wrote on the subject gave him a prize with which he helped his parents and family escape from Nazi Germany. The same work subsequently won him the Noble Prize.

Transcript: Imagine a set of stars with different masses, all of which are just reaching the main sequence and beginning to consume hydrogen for the first time. This is called the zero age main sequence. In theory it would be a line across the HR diagram, but in practice the properties of such stars form a band because stars of different ages have different chemical compositions which gives them slightly different observed properties.

Transcript: Star formation in molecular clouds occurs more slowly and less efficiently than the simple theory of gravitational collapse would predict. Regions of star formation do not only contain gas and dust however. They are threaded by weak magnetic fields. When the clouds begin to collapse the magnetic field lines are trapped and entrained and so the magnetic field increases as the cloud collapses. The gravity is opposed by magnetic pressure as the field lines are compressed and magnetic forces play an important role in any successful theory of star formation. Magnetic fields are also essential in explaining the bipolar outflows exhibited by young stellar objects.

Transcript: When a new star turns on in the center of a disk shaped cocoon of gas and dust material is blown out along the rotation axes at speeds that range from twenty kilometers per second all the way up to two hundred kilometers per second. Bipolar outflows or jets are distinctive features of young stellar objects. When these jets hit the interstellar material or gas they create bright shocks and regions of emission.

Transcript: Star formation results in a young star embedded in a disk of gas and dust. In its early stages every young star has a higher luminosity than its eventual main sequence luminosity. The disk of gas and dust is equally important. This infrared emitting material extends hundreds of astronomical units, and protostellar disks form the missing link between the initial collapsing gas cloud and the formation of planets themselves. Starting in the mid-1980s astronomers used infrared and other techniques to discover large numbers of dust disks around young stars. Beta Pictoris is perhaps the most famous example. Detailed infrared studies of these objects are providing us with vital insights as to the way in which planets form.

Transcript: The most important pre-main sequence stars are called T Tauri stars, named after the twentieth cataloged variable star in the constellation of Taurus. T Tauri stars are transitions between infrared stars in opaque cocoons or nebulae and stable stars settling for the first time onto the main sequence. The density of T Tauri stars in a rich star forming region like the Orion nebula exceeds the density of all stars in the solar neighborhood. T Tauri stars vary irregular in their brightness and are very young in the range twenty thousand to only a million years old.

Transcript: Stars must be hot enough in their cores for fusion to occur, a temperature of about ten million Kelvin or higher. Objects lower than this boundary which corresponds to a mass of eight percent the mass of the Sun are called brown dwarfs. Brown dwarfs have a mass range from a few times the mass of Jupiter up to eighty Jupiter masses at which point an object becomes a star. If you imagine the hypothetical experiment of adding mass to a gas giant planet the following occurs. As the mass is increased from the size of Jupiter to several times the mass of Jupiter the object continues to get larger. From two or three times Jupiter mass up to eighty Jupiter masses, as more mass is added the brown dwarf actually gets smaller because of gravitational compression. At eighty Jupiter masses as more mass is added nuclear reactions kick in and the star puffs up and starts to become larger again with increasing mass. Thus there are natural divisions between planets, brown dwarfs, and stars.

Transcript: Japanese theorist Chushiro Hayashi did the detailed calculations to show how stars change their properties as they evolve towards the main sequence when they are still pre-main sequence stars. In terms of the HR diagram they start at regions of high luminosity and low effective temperature, few thousand Kelvin. The time taken to collapse onto the main sequence depends on the stellar mass. The highest mass stars take a shorter amount of time than the lowest mass stars. For example a fifteen times the solar mass star with an initial luminosity of thirty thousand solar luminosities takes only a hundred thousand years to reach the main sequence. A star five times the mass of the Sun with an initial luminosity three hundred times the Sun’s luminosity takes about a million years, and the Sun with an initial luminosity twenty times its present luminosity takes a few times ten to the seven years. The lowest mass stars take even longer to reach the main sequence.

Transcript: After the freefall gravitational collapse phase, a pre-main sequence star emerges. The collapse is inside out which is to say that the material near the center of the cloud collapses first followed by material further out. After only a few thousand years gravitational contraction releases sufficient energy to raise the temperature of the cloud, still not yet a star, to a few thousand Kelvin, and thus it can emit light. Convection also helps transmit energy to the outer regions of the cloud. In the case of a star like the Sun this process took less than a thousand years to produce a cloud about twenty times the size of the present day Sun and with a luminosity a hundred times that of the present Sun’s luminosity.

Transcript: A protostar is a cloud of interstellar gas and dust that’s dense enough and cool enough to contract gravitationally to form a star. An interstellar cloud may be close to the state of collapse for millions of years and be triggered by a nearby disturbance such as the death or birth of a nearby star. The collapse occurs extremely quickly on an astronomical timescale in about a hundred thousand years. This is a hundred thousand times less than the lifetime of the Sun. In the first stage of collapse it is freefall. The collapse is as rapid as gravity will allow.

Transcript: Star formation is very complex. Thus when astronomers talk about the theory of star formation they’re talking about a theory that is not yet highly refined where many details remain to be worked out. Star formation occurs in dense regions from which light cannot emerge. There are four basic stages. In the first, cores form within a molecular cloud. A giant molecular cloud could potentially form hundreds or thousands of stars. In the second stage the cores collapse to form protostars and surrounding disks. In the third stage fusion begins, initially hydrogen fusing to form deuterium, and a wind blows out from the star along the rotation axes. In the fourth stage the wind fans out to form a wind in all directions, and the young star becomes visible, still surrounded by its nebular disk.

Transcript: Over sixty different types of molecules have been found in interstellar space. Most of them are simple molecules with two or three atoms. However some of them are complex, and they include organic materials that make people very interested in the possibilities of life in deep interstellar space. For example the amino acid glycine, NH2CH2COOH, has been found, and acetone CH3CH3CO, and ethyl alcohol CH3CH2OH. Astronomer Ben Zuckerman calculated that the Sagittarius B2 molecular cloud if cleared of impurities would yield ten to the power twenty-eight fifths of pure alcohol at two hundred proof. However the density of interstellar space is very low. A business man once calculated that a one kilometer wide funnel being dragged at ten times smaller than the velocity of light would take a thousand years to fill a single shot glass of the alcohol that exists in space. The molecules in space are important because they show that complexity can be derived from simple atomic collisions provided the density is sufficiently high.

Transcript: The birth of radio astronomy and the development of millimeter and submillimeter astronomy has opened up the capability of astronomers to detect molecules in space. Dozens of molecular species are routinely detected in molecular clouds in the interstellar medium. Radio astronomy is necessary because most of the energy transitions in molecules have low energies and therefore produce spectral features in the submillimeter or far infrared regions of the electromagnetic spectrum. These transitions can be changes of energy level, or changes of vibration, or rotational states of the molecules. Most spectral features are found between a hundred microns and a few millimeters in the electromagnetic spectrum. These spectral transitions are energetically very important in the process of star formation because much energy is contained in the spectral lines, and these spectral transitions become a way in which energy is lost from the center of a molecular cloud allowing the cloud to cool and collapse.

Transcript: The typical environment of the space between stars is a very thin and very cold gas. The interstellar medium typically has about a million particles per cubic meter, and the temperatures are only ten to twenty degrees Kelvin. However there are some regions with densities a thousand or ten thousand times higher than this. In these regions collisions can occur between the atoms and the temperatures are low enough so the atoms will stick together to form molecules. These regions of space are called molecular clouds, and they are the classic birthplaces of stars. Even though the density is higher than pure interstellar space, it’s still an almost perfect vacuum with a density ten to the power fifteen or a thousand trillion times less than the air you are breathing.

Transcript: Ancient astronomers once thought that stars were eternal and unchanging. We now know that stars evolve. They are born, they live, and they die. Well with stellar lifetimes so much longer than a human lifetime how do we actually know that stars evolve? The Sun is 4.6 billion years old, and astronomers have evidence that the system of stars in which the Sun sits, the Milky Way, is much older, perhaps ten or eleven billion years old. Thus the Sun is not the first generation of stars to live in the Milky Way. We also know from the theory of stellar evolution that the most massive stars must have short lives. So the most massive stars we see in the sky cannot have lived for very long, and they will not live for long. The most massive stars have total main sequence lifetimes that are less than the span of the human species so far.

Transcript: Astronomers are interested in the true population of stars in the sky. However the visibility of stars is affected by their luminosity. The more luminous stars can be seen to larger distances than the less luminous stars, and this causes them to be overrepresented in catalogs that are limited by apparent brightness. An example will make this clear. Consider a star that’s the luminosity of the Sun and one that’s five times more luminous than the Sun. Suppose we can see stars that are luminosity of the Sun out to a distance of one parsec. By the inverse square law we can see the five times more luminous stars out to the square root of five or about 2.2 parsecs, and the volume enclosed is the cube of the distance so the ratio of the volumes is 2.24 cubed or a factor of eleven. Thus if there were truly equal numbers of one solar luminosity and five solar luminosity stars we would count ten times more of the more luminous stars. If there were ten times less numbers of the high luminosity stars we would still count about equal numbers hugely over representing their situation in true space.

Transcript: When we look at the lists of the brightest stars in the sky and the nearest stars to the Sun we see that there are almost no stars in common. In fact, among the first few dozen stars in each list only Sirius is in common. Why are the lists so different? When we look at the brightest stars in the sky we are looking preferentially at high luminosity stars. Hertzsprung called these the whales among the fishes. So when we search for the apparent brightness of a star we preferentially see the most luminous stars because we can see them to the largest distance, and so we sample a larger volume for them than for low luminosity stars. Thus samples of stars limited by apparent brightness will over represent the whales, or the more massive stars, relative to the fishes, the much more abundant low mass stars.

Transcript: The brightest stars in the night sky are not exactly like the Sun. In fact almost all of them are hotter, more massive, and more luminous. Most of the brightest stars in the sky are luminous main sequence stars, red giants, or supergiants. Each of the seventeen brightest stars in the sky is more luminous than the Sun. The brightest ten in order are Sirius, Canopus, Arcturus, Alpha Centauri, Vega, Capella, Rigel, Procyon, Achernar, and Hadar.

Transcript: Surveying the volume around the Sun for the nearest stars reveals something interesting. If we look in the volume around the Sun, the nearest few lightyears, for the nearest one hundred stars most of them are actually not like the Sun at all. Almost all of them are cooler, less massive, and less luminous. In fact only five are more massive and more luminous than the Sun. This means that the Sun is not typical of the nearest stars. The very nearest star to the Sun is Alpha Centauri, second nearest is Barnard’s Star, the third nearest is called Wolf 359. Among the nearest twenty or so stars, the famous star Sirius and Procyon also feature.

Transcript: There’s a simple formula to give an approximation for the lifetime of a main sequence star. The lifetime is the mass divided by the luminosity of the star, both in solar units, times nine billion years. However the lifetime does not depend exclusively on mass. As shown by theorists Russell and Vogt in the 1920s the final state of a main sequence star depends both on its mass and its chemical composition. For example a one solar mass star of three quarter hydrogen one quarter helium by mass composition can only form one stable configuration. However it will be a slightly different configuration from a one solar mass star made of half helium and half hydrogen. They will have different positions on the HR diagram. The Russell-Vogt theorem allows astronomers to calculate stellar evolution more accurately because as a star evolves it is continually changing its chemical composition by the conversion of hydrogen into helium, and thus the stable configuration of the star is also evolving with time.

Transcript: Intuitively we might expect a more massive star to last longer than a less massive star because it has more hydrogen to consume in the fusion process, but intuition does not work for stars because of the very steep and sharp relationship between luminosity and mass. If we want to use the analogy of a fuel tank, a large mass star does indeed have a larger fuel tank than a low mass star. However the efficiency or the rate of using that fuel is much, much faster and so the more massive star lasts far less long than the low mass star. It’s as if the most massive stars in the universe were extremely fuel inefficient gas guzzling cars that burn through their fuel at an enormous rate and don’t get very far on their tank full of gas even though the tank is large whereas the lowest mass stars in the universe are extremely gas efficient or fuel efficient. They’re miserly with their fuel, and although their fuel tank is small it lasts far longer than the gas guzzlers. Thus if we have a population of stars of different masses that form at the same time the most massive stars will die first. The least massive stars will last substantially longer.

Transcript: The steep relationship between mass and luminosity for main sequence stars has an important consequence for the lifetime of the stars. Consider a star that’s a tenth the mass of the Sun. In round numbers the luminosity is ten to the minus four times the luminosity of the Sun. Thus the size of the fuel reservoir is ten times smaller, but the rate of evolution is ten thousand times smaller. This means the star will last about a thousand times longer than the Sun. Instead of a total main sequence life of ten to the ten years, we have a total main sequence life of ten to the thirteen or ten trillion years. Compare it to the other end of the main sequence. A star of a hundred times the mass of the Sun in round numbers has a luminosity a million times that of the Sun. Although the fuel reservoir is a hundred times larger than the Sun, the rate of burning the fuel is a million times larger which means the star lasts ten thousand times less long than the Sun. Instead of a main sequence lifetime of ten billion years, we have a main sequence lifetime of roughly a million years.

Transcript: The Sun is a typical main sequence star by which astronomers mean that the Suns properties lie in the middle of the range of stellar properties on the main sequence. It’s intermediate in mass, in size, in temperature, and luminosity compared to the most and least massive main sequence stars. The Sun has a spectral type G2 which gives it a photosphere temperature of fifty-seven hundred Kelvin. Spectral types O, B, A, F, G, K, and M are subdivided on a decimal scale running from O1 to O8 to O9 to B0, B1, etcetera. The Sun as a G2 star is a little cooler than a G0 star. The Sun is typical in most properties, but most stars are less massive than the Sun and the very highest mass main sequence stars are extremely rare.

Transcript: Main sequence stars are classified according to the system of spectral types developed almost a hundred years ago. Going from the hottest to the coolest stars there are O type main sequence stars whose mass is about fifty times that of the Sun, radius about twenty times, a temperature of forty thousand degrees, and a luminosity a million times that of the Sun. B stars have masses twenty times that of the Sun and radii seven times that, photospheres are thirty thousand Kelvin and the luminosity is about twenty thousand times that of the Sun. A stars masses three times that of the Sun and radius three times, ten thousand degree atmospheres, and eighty times the Sun’s luminosity. F stars mass of 1.7 times the Sun’s mass and radius 1.4 times, seventy-five hundred degree Kelvin for the photosphere, and six times the luminosity of the Sun. G stars, similar to the Sun, 1.1 times the mass and the radius, six thousand degree atmospheres, and 1.3 times the Sun’s luminosity. K stars 0.8 times the mass of the Sun and the same factor for the radius, five thousand degree atmospheres, and 0.4 solar luminosities. And the coolest M stars about a half the mass of the Sun, 0.6 times the solar radius, a photosphere of thirty-five hundred Kelvin and luminosity of 0.03 times the Sun’s luminosity.