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Astronomy C10/L&S C70U Stellar Life Cycles and Supernovae Nicholas McConnell Like many aspects of nature, star formation and destruction is a cycle. Stars form from clouds of gas, remain stable for long periods of time, and then expel gas back into space, where it can later form new stars. Below are four stages in the life of a massive star. Describe what happens in each stage, and how energy is generated and used up. Initial formation from a cloud of gas Description: Once a gas cloud (or a particularly dense region of a much larger cloud) reaches a certain mass, it begins to collapse in on itself. As it collapses, it heats up. The collapse continues until the center of the cloud is hot enough to fuse hydrogen into helium. Energy Source: Gravitational energy Energy Released As: Heat in the contracting cloud, light Main Sequence lifetime Description: At the center of the star, it so hot that hydrogen nuclei (protons) are moving fast enough to overcome their electrostatic repulsion and fuse together. Through a series of nuclear reactions, four protons become one helium nucleus (2 protons, 2 neutrons). A small amount of mass is lost in this process; it is converted to pure energy. Because the interior of the star is very hot, it exerts enough outward pressure to match the inward force of gravity. This state of balance is known as hydrostatic equilibrium. Throughout its Main Sequence lifetime, the star is basically stable. Energy Source: Mass (E = mc2 ) Energy Released As: Light, some neutrinos Red Giant/Supergiant Phase Description: Eventually, there is no hydrogen left in the center of the star, and fusion stops. With no way to maintain outward pressure, the core begins to collapse again, getting hotter and denser. Eventually, it is hot and dense enough to fuse helium into carbon and oxygen. In a massive star, this process (contraction, then fusion of new elements) repeats for heavier and heavier elements. During this phase, the temperature of the core creates enough pressure to push out on the outer layers of the star. They expand and cool, creating an enormous, red surface. We view the star as a red supergiant. Energy Source: Gravitational energy, then mass ( E = mc2 ) once fusion starts again Energy Released As: Heat, until fusion can occur again. Then, light, and work done to expand the outer layers Supernova Description: The final fusion product in the center of a massive star is iron. Iron nuclei cannot fuse together without losing energy (all previous fusion steps created energy), so fusion stops altogether. Now, the collapse of the core under gravity is inevitable. Within instants, the center is compressed into pure nuclear material (neutrons with very little space between them: much less than the width of an atom). Quantum mechanics dictates that this state must extert an enormous degeneracy pressure. The rest of the collapsing core bounces off this neutron center, and the star explodes. Energy Source: Gravitational energy. As the core collapses to very high density, neutron degeneracy pressure provides the "bounce." Energy Released As: Mostly neutrinos. The explosion also ejects gas (what used to be the star) at very high speeds. Light makes up about 0.01% of the total energy released. What happens in low-mass stars (less than about 10 solar masses) instead of a supernova? In low-mass stars, the core never gets hot or dense enough to fuse carbon and oxygen into heavier elements. Once the helium is used up, the core is able to stave off gravitational collapse with a new source of pressure: electron degeneracy pressure. This is a quantum mechanical effect similar to the neutron degeneracy pressure that creates the "bounce" for a supernova, except electron degeneracy pressure is less powerful. Therefore, the core of the low-mass star ultimately stable as a very dense glowing mass of carbon and oxygen. En route to this final state, instabilities during helium fusion create winds that gradually blow away the outer layers of the red giant star. In the intermediate phase, we see a so-called planetary nebula: these escaping layers are illuminated and excited by UV radiation from the core. Eventually, the layers have been entirely blown away and all that remains is the bare core: a white dwarf, which cools off over billions of years. Here's a quick list of qualities that should test your knowledge of two different supernova types. Mark whether the qualities listed apply to Type Ia supernovae, Type II supernovae, or both. Try to keep in mind how these relate to the ways in which the two types above are physically different from one another. Type Ia Strong hydrogen lines in spectrum X No hydrogen lines in spectrum X Only occurs in a binary system X Requires a star more massive than 10*MSun Completely destroys the exploding star Type II X X Leaves behind a neutron star or black hole X Creates heavy elements (including stuff humans are made of) X Almost always has a standard, predictable luminosity X X We haven't learned the last one yet, but it will be important later. Alex's research team has used this fact to show that the universe is expanding faster and faster, rather than slowing down as initially expected. Supernovae are extraordinarily energetic events. This next exercise will allow us to compare the luminosity (energy output per second) of a light bulb, the Sun, all the stars in the Milky Way, and a typical supernova. Light bulb vs. Sun: We know the formula for an object's brightness: b = L / 4d2 . This describes how much light we see, but the same concept can also describe how much energy we feel as heat. By this token, we can approximate that a light bulb is as "bright" as the Sun, when we stand close enough to it to feel the same amount of heat as we would feel from sunlight. If this is true, then bbulb = bSun, so Lbulb / 4dbulb2 = LSun / 4dSun2 . Or, (LSun / Lbulb ) = (dSun / dbulb )2 . There is a 100-Watt light bulb at the front of the classroom. 1 Watt is one Joule of energy released per second, so Lbulb = 100 J/s. dSun is 1 A.U., or 1.5 x 1013 cm. Our experiment will give us dbulb. Hold your hand out and approach the light bulb until its warmth feels about the same as sunlight. Then measure the distance from the bulb to your hand, in centimeters. This is subjective, but let's say we measure 7.5 cm. Now you have Lbulb, dbulb, and dSun. You can plug these values into the bold equation above and calculate the Sun's luminosity in J/s. Do it! From (LSun / Lbulb ) = (dSun / dbulb )2 , we get LSun = Lbulb * (dSun / dbulb )2 = 100 J/s * (1.5 x 1013 cm / 7.5 cm )2 = 102 J/s * ( 2 x 1012 )2 = 4 x 1026 J/s , which is very close to the actual value of LSun. Sun vs Milky Way: Your answer above for LSun will depend on what distance you chose for dbulb. The actual value of LSun is about 1026 Joules per second (!!!). Hopefully your answer was close (1024 - 1028 J/s might be reasonable, given our method). In any case, the Milky Way galaxy contains about 100 billion (1011) stars. Some are much more luminous than the Sun, and many are less luminous, but an acceptable approximation is that the average luminosity per star is 1 LSun . Therefore, the Milky Way has an approximate luminosity of 1011 * 1026 J/s. So, LMW = 1037 J/s (one easy step). Milky Way vs Supernova: Now, a typical Type II supernova explosion releases 1044 Joules of light (and hundreds or thousands of times more energy in the form of neutrinos and high-speed gas!) Suppose this release occurs over a single second. For that initial second, how many times brighter will the supernova be than the entire Milky Way galaxy? LSN = 1044 J / 1 s = 1044 J/s LSN / LMW = (1044 J/s ) / (1037 J/s ) = 107 . In that first second, the supernova is 10 million times as luminous as the entire Milky Way galaxy! Wow!!