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Mass Dependence Mass – Luminosity relationship: More massive stars are brighter. To be brighter, they spend more energy. Massive stars live shorter. Luminosity = Mass4 (roughly) Lifetime = Mass / Luminosity Lifetime = 1 / Mass3 (roughly) Example: A star 5 times more massive than the Sun (5)4 = 625 times brighter than the Sun But it will live for (1/5)3 = 125 times shorter 1010/125 = 80,000,000 years
Stages of Life Gas Cloud Main Sequence Red Giant Planetary Nebula or Supernova Remnant How long each star will last in each stage and what kind of remnant will form depends on the initial mass and composition of the star.
Protostar Over a long period of time, the gases in the giant molecular cloud begin to condense. There are no nuclear reactions in these regions, but they are hot enough to glow in the infrared. When fusion starts at the core, it stops the gas from collapsing further. But gas from the gas cloud still continues to fall: Most of the energy of a protostar comes from this gravitational energy.
Protostar Clusters Young stars are social: Inside the molecular clouds, usually more than one star is born. They are also born at around the same time. Giant cloud is blown away or evaporated by a nearby, powerful star and we can see the young stars forming.
T-Tauri stage When the young star is “ripe”, it will produce strong winds and blow away the surrounding cocoon gas and dust. After the gas is blown away, the star becomes visible for the first time.
Main Sequence Stage Because of the Hydrostatic Equilibrium, all stars become stable. They spend 90% of their life on the main sequence buring hydrogen in their cores. They start their lives in clusters, however with the gravitational influences from other stars they wander away from their clusters. Pleiades cluster in the Taurus constellation
Subgiants and Red Giants Finally, all the hydrogen in the core is converted to helium, and the temperature is not high enough to fuse helium (to convert helium into carbon). Hydrodynamic Equilibrium is destroyed, the core shrinks because of gravity. The layers outside of the core fall onto the core and heat it up to a temperature where helium fusion can start. The luminosity increases immensely. The heat generated in the core expands the star to become a subgiant and then a red giant. Large area, not enough heat red surface
Life of a Red Giant This process takes about 1 billion years for a star like our Sun. The radius increases 100-fold. Temperature of the core increases.
Helium Flash But the thermal pressure is not high enough to counteract gravity. -> new source needed -> electron degeneracy pressure -> but this does not depend on the temperature -> heats up the core without expanding it -> helium fusion rate increases enormously -> HELIUM FLASH
Supergiants Our Sun will also go thru the Red Giant stage. During this stage the Sun will swell to be as large as Venus’ orbit, and maybe even engulf the Earth (in a few billion years). However, as we have seen, the Sun is an ordinary star, there are more massive stars than the Sun, and when they go through the Red Giant stage, they will not be just giants, but Supergiants: Betelgeuse is one of these supergiants, and not the biggest one of them. Giants have strong winds. They lose material with these winds. Their surfaces are colder than their main sequence equivalents. But their cores are much denser and warmer.
Smaller Stars Once helium is converted into carbon, the star is not massive enough to go through the same cycle again. Weak grip on its outer layers -> matter flows away from the surface (Planetary) Nebula
Red Giant again (Massive Stars) At the next stage, the collapse of the outer layers will heat the core up even further, and this time carbon atoms will fuse to form Oxygen, Neon, Magnesium, etc. With each kind of fuel exhausted, the core will collapse and than the gravitational energy will be converted into heat once again, and the temperature of the core will increase to fuse even heavier elements. This creation of heavier elements from lighter elements is called stellar nucleosynthesis. Stellar nucleosysnthesis continues until all of the core is converted to Iron. After Iron, there is no energy production possible, so the core collapses. This time, no energy production can stop the collapse. What happens??
Big Stars – Small Stars Both big and small stars live most of their lives on the Main Sequence. They both go through the Red Giant Stages. But for stars there exists a limit, called the Chandrasekhar limit. Chandrasekhar limit: 1.4 Msun Stars with M > 1.4 Msun are big stars, with M < 1.4 Msun are small stars. At the stars under the Chandrasekhar limit, electron degeneracy pressure is strong enough to stop the collapse of the star. Electron degeneracy pressure: You cannot put two electrons into the same place (state), they will resist.
White dwarfs The shrinkage stops at a radius equal to Earth’s radius (Sun compressed into a volume as large as the Earth). White Dwarf Leftover heat has to be radiated thru a small surface, so white dwarfs are very small, very hot and very bright. The light pressure pushes the outer layers further away forming a planetary nebula. Planetary nebula have regular shapes and better defined colors coming from the emission from hydrogen, oxygen and nitrogen.
Novae Isolated white dwarfs are boring, they just fade to become brown dwarfs first, and then black dwarfs. However, if the white dwarf has a companion from which it can “steal” some material, then things get interesting: White dwarf H + He stolen from the companion The surface of the white dwarf is normally not at the fusion temperature of hydrogen. However the accumulated H + He increase the temperature where H fusion starts at the surface of the white dwarf. With a major explosion which can be seen from the Earth (novae = new star in the sky) the H + He layer is blasted outwards, then the whole cycle begins anew.
Supernovae Type I If a white dwarf with mass very close to 1.4 Msun steals some more hydrogen from its companion, then the star goes over the Chandrasekhar limit. The electron degeneracy pressure cannot hold the star. The core collapses very fast and the resulting explosion disrupts the star (the star blows itself apart). Nothing is left as a remnant of this supernova.
Supernovae Type II Sandeulet in the Large Magellanic Cloud: 40 Msun Main sequence 9-10 million years (H burning) Red supergiant 1 million years (He burning) Blue supergiant 1000 years (C burning) few years (N burning) few days ( Fe) Electron degeneracy pressure is not strong enough to hold up the gravitation the star collapses further Electrons and protons fuse to form neutrons and neutrinos are released. From our Sun which is 0.000016 lightyears away we detect 1 neutrino every three days. During this collapse, from Sandeulet, which is 170,000 ly away we detected 11 neutrinos in 13 seconds.
Neutron Degeneracy The star will collapse until the neutron degeneracy pressure is reached. The star is composed of only neutrons. White dwarf Earth diameter, Neutron star about 30kms in diameter It takes 0.2 seconds to collapse from the white dwarf to neutron star. Heated core starts to expand immediately outwards. The outer layers are falling inwards at relativistic speeds (comparable to the speed of light) When the expanding core collides with the outer layers we have a BIG explosion. Type II Supernova. So much energy is released that all nuclear reactions can occur simultaneously. This is how the heavier elements (than iron) are created.
How big is the explosion? Crab Nebula In July 4th, 1054, the Chinese astronomers reported that there is a new Sun in the sky, visible during the daytime as well. The same event is recorded by every tribe on the world.
After the Explosion Now the outer layers are gone, what happens to the star?? The answer depends on the initial mass: Minitial < 3 Msun Neutron star Minitial > 3 Msun Black Hole
Neutron Stars If the star has more mass than 1.4 Msun, electron degeneracy pressure is not strong enough against the gravity, so the star collapses rapidly. Electrons fuse with protons to form neutrons and a huge number of neutrinos are generated as a byproduct. The star shrinks until all the electrons and protons are converted to neutrons. But there is a limit to the volume you can squeeze the neutrons into Neutron Degeneracy Pressure. Finally, the star becomes about 30kms in diameter, and about 1,000,000 degrees at the surfaces. In the 1930s, the existence of neutron stars were proposed, however as they were very small, they were only (it was) observed after the HST.
Pulsars 1967 – graduate student Bell radio source with a short, periodic signal jumped to a very logical conclusion and named it LGM. • LGM: Little Green Men Later, other sources were found too natural source • Renamed: Pulsating Stars, or pulsars. Source is unknown: Normal stars change their brightness towards the end of their lives (expanding and contracting), however the period of these changes are never in the seconds’ range. To pulsate with a high frequency, the star must be very dense and very small, so the only likely known source are the Neutron Stars.
Strong Magnetic Fields When the star becomes smaller, it starts to rotate faster gives stronger magnetic field. Faster rotation when the size gets smaller is a result of conservation of angular momentum.
Lighthouse Model Electrons and protons get caught in this field and strike the neutron star with a high velocity, giving out a very strong radiation. But this does not explain the high frequency of the pulsar. Actually the pulsar does not “pulse”, however it radiates a sharp beam from the magnetic poles. Because the whole star rotates quickly, only from time to time the Earth stands on the path of this sharp beam, hence we see the pulsar as pulsating.
… and then nothing is left… If the star’s mass is larger than 3 Msun, nothing can stop the collapse and the star shrinks… Force of Gravitation: FG = GmM / r2 On Earth, if we have to leave the planet we have to shoot a rocket up, and if the rocket can overcome this force it can escape from Earth. If shoot the rocket up with a speed greater than 11km/s, it can leave the Earth. To leave the surface of the Sun, you need a speed of 620km/s. When the Sun becomes a white dwarf, you will need 6400km/s. If the Sun became a neutron star, you would need 94,300 km/s. The speed of light is 300,000 km/s, so if we could squeeze even the Sun to about 3 kms radius, even light would not be able to escape. AND, much bigger stars are squeezed into almost nothingness… so nothing can escape from the surface.
Curvature of Spacetime Gravitation is a manifestation of the curvature of spacetime. Mass changes the curvature of spacetime around itself. The more massive is the object the higher will be the curvature of space. All objects follow the shortest path of the curvature of spacetime. Earth does not revolve around the Sun because of gravitation, but because it follows the shortest path around the Sun.
Deflection of light Light, just like all the other moving objects, follow the curvature of spacetime. In our daily life, we do not observe any such curvature of spacetime, hence it is very difficult to believe such theoretical concepts. However, astronomers observe this curvature by the deflection of light around the Sun.
Detecting Black Holes The event horizon of black holes is too small to be optically observed from the Earth. Instead we must rely on indirect methods of observation. First, if a star seems to be rotating around “nothing”, that nothing is probably very small to be observed from the Earth, but very massive, hence it can be a black hole. Also, the black holes will steal material from their normal companions, and this gas, while falling into the black hole, will emit X-rays.
Hawking Radiation Particle – antiparticle pairs are created almost everywhere in the universe. However, they annihilate each other very quickly, hence we do not observe these event routinely. But when this particle – antiparticle pair creation occurs right along the boundary of the event horizon, one of the pair might be caught by the black hole whereas other one escapes and can be observed by outside sources.