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Lecture

ASTR 1P02 Lecture Notes.docx

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Department
Astronomy
Course Code
ASTR 1P02
Professor
Bozidar Mitrovic

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ASTR 1P02 January 7 2013 Star Formation To find out about the process of star formation one should look at the young stars. Mass luminosity relation for main sequence stars L=M 3.5 L= luminosity M=Mass of a star Lifetime of a star= amount of fuel/energy output =M/L =M/M 3.5 =1/M 3.5 The youngest stars are located at the top left corner of the main sequence – they appear as bluish (high surface temp) and they have very high luminosities. The observations show that such stars are surrounded by gas and dust of interstellar material (ISM) Gas: 1. 74% by mass is hydrogen (H) 2. 24% by mass is helium (He) 3. 2% by mass all other elements Dust: - 10-100 nanometers - 1nm= 10^-9 nm - Core- Silicate Material - Mantle-ices of water, ammonia and methane January 9, 2013 When the clouds of interstellar material are observed in the visible part of the spectrum (wave lengths: 400mm – 700mm). They are called Nebulae. There are general types of nebulae: -Dark Nebula The starlight is absorbed by dust particles in the Nebula. Reflection Nebula (Bluish in color) - They are Bluish for the same reason that the sky appears to be blue on a clear sunny day- molecules (and dust) in the air scatter blue light more efficiently than the longer wavelengths. The star appears as reddish but the nebula itself is bluish in color. Emission Nebula (Reddish in color) - This process where a proton of one wavelength is absorbed by an atom and then the atom and then the atom emits a photon of a different wavelength is Fluorescence. - The stars are formed in a particular type of Dark Nebula – the giant molecular cloud (example: eagle nebula M16). Giant- because they can be several hundreds of light-years in size. Molecular- the temperature inside the dense cloud is low enough so that the atoms of hydrogen combine into molecules of hydrogen H . 2 In addition to Molecular hydrogen they also contain small amounts of more complex molecules: -Carbon monoxide (CC) -Water (H O2 -Ammonia (NH 3) -Methanol (CH OH3 -Ethyl Alcohol (C 2 5H) These clouds are not uniform in density- there are clumps (regions of higher density) inside the clouds. January 11, 2013 Some Clumps (regions of higher density) start contracting under their own gravity As the material falls in its speed increases and the temperature at the center of the collapsing clump increases. During the Protostar, stage the star generates energy via gravitational contraction; protostars can be observed at infrared wavelengths- their temperature is such that they emit most of the energy in the infrared part of the spectrum. -whether a protostar becomes a star depends on its mass: if the mass is less than 1/12M.=0.08M (M.=solar mass) the temperature in the core will never get high enough (it would be less than 10,000,000 K) to fuse hydrogen into helium with release of energy. They produce so-called Brown Dwarfs. For higher mass (>0.08 M.) the temperature in the core becomes high enough so that the hydrogen fuses into helium with release of energy. The star becomes the main sequence star. Just before it becomes a main sequence star it goes through a phase of instability (T-Tauri phase). -During this stage gas and dust surrounding the newly formed star are blown away. -While on the main sequence star in hydrostatic equilibrium: the inward gravitational force (weight) is balanced by the outward gas pressure within the star. In stars with masses from 0.08M. to 2M. the fusion of hydrogen into helium proceeds via proton-proton chain. In stars with masses over 2M. the fusion of hydrogen proceeds via so-called CNO ( carbon-nitrogen-oxygen) cycle. High mass stars contract faster than the low mass stars end up higher on the main sequence (higher temp and lumen) compared to lower mass stars. January 14, 2013 The life story of a star depends on its mass. Low mass stars (mass ranges from 0.08M. to 0.5M. Result in red dwarfs- -lower main sequence stars with low surface temperature and low luminosity. 2 4 (Stefan-Boltzmann Law L=const. R T ) L=luminosity Const.= universal constant T=Surface temperature They are hard to detect because of their low luminosity but could represent the largest class of stars in the universe). Medium Mass stars: (masses range from 0.5M. to about 8M.) After some time all the hydrogen in the core is fused into helium and that signals the beginning of the end. The suns main sequence life is about 9 billion years old and it is halfway through its life cycle. While on the main sequence, the luminosity of a star slowly increases over time (now the sun is 30% more luminous than when it became a main sequence star). Pressure in the core: - particle number density x temperature (reduced by a factor of 4) (has to increase to keep the same pressure needed to support the top layers) Increased temperature implies higher rate of energy production and hence higher energy output (luminosity). As a result in about 0.5-1 billion years the surface temperature on the earth would become so high that all oceans would evaporate. When all the hydrogen in the core is fused into Helium the energy production in the core stops (for a while) -The core is not hot enough for the helium nuclei to fuse into heavier nuclei ( C and 16O). The fusion of helium requires temperatures of at least 100 billion K Proton Fusion . --> . Repulsive electrical force Helium Fusion  HE 4HE The nonfusing helium core shrinks and heats up. January 16, 2013 First red giant stage of a medium mass star (M=0.5M. – 8M.): Nonfusing HE core which shrinks and heats up. Hydrogen Fusing shell Non fusing hydrogen over layers Because of its proximity to very hot HE-core the rate of hydrogen fusion in hydrogen fusing shell is greater than the fusion rate during the main sequence phase. The energy transport to the surface cannot catch up with all that energy produced in the fusing shell and the thermal pressure builds in the interior of the star. This pressure causes the star to expand. Increase in the surface area causes the surface temperature to drop, and its color changes from white-yellow to orange or red. When the temperature of the shrinking helium core increases to 100 million K the HE nuclei start fusing into C (and some O) nuclei with release of energy (so- called helium flash). This fusion occurs via so-called triple alpha process. 4 (“Alpha Particle” = Nucleus of HE) The star has entered the yellow giant phase. Now more energy is produced by fusing core and fusing shell, the star is again near the equilibrium and it shrinks in size. More energy production and smaller surface imply higher surface temperature and the color becomes yellow. Since the energy produced in HE fusion is less (per fusion reaction) than in H fusion the rate of HE “burning” must be high in order to produce enough energy to support the star. As a result this phase does not last very long (about 1 million years in the case of 1 solar mass star). When all of the helium in the core is used the star enters the final red giant stage. nonfusing carbon core (with some O nuclei) HE Fusing Shell The medium mass star does not have enough mass for the contracting carbon core to start fusing carbon into silicon. January 18, 2013 Remnants of a medium mass star: -Planetary nebula and the whit dwarf. Planetary nebula: their name comes from the fact that they often have blue-green color (e.g. the ring nebula), similar to that of Uranus and Neptune, but they have nothing to do with planets. They are formed from the star’s material pushed out by radiation pressure (the central core is hot (10000-30000 K) and produces a lot of high-energy UV photons. The material in the ejected shell of gas grows due to fluorescence. White Dwarf: is the dead core of the star. Consists of carbon and some oxygen nuclei in a sea of negatively charged electrons. Density is about 1000 kg/cm . 3 The object emits light because it is still very hot (carbon and oxygen nuclei move with high speeds). The gravitational collapse of this very dense object is prevented by the pressure created by degenerate electrons. So called Pauli Principle: -one can put at most two electrons into a given energy state. The degenerate matter such as white dwarfs has some unusual properties: 1) The pressure depends only on density but not on temperature. 2) The bigger the mass, the smaller the radius of the object. The maximum mass that an object composed of degenerate matter can have is called Chandrasekhar limit. For a white dwarf (compiled of mainly C in a sea of degenerate electrons) it is 1.4M. NOTE: More massive white dwarfs have a smaller radius. For the white dwarf that the sun will produce one day it is estimated that it would have a radius comparable to that of Earth. Many white dwarfs have been observed (e.g. Sirius B) January 21, 2013 Life story of a high mass star (M>8M.) Every stage in life (protostar, main sequence) is shorter as a resul2.5f high mass. (faster gravitational contraction, main sequence lifetime = M/L=1/M ) L=M 3.5 While on Main sequence the hydrogen is fused into HE via so-called CNO cycle. Once the hydrogen in the core is fused into Helium, the fusion of helium into carbon starts right away since the temperature of the HE-core is high enough. Because of the high mass of the star-the star becomes a yellow giant. Once the helium in the core is fused into carbon, the high core temperature results in the fusion of carbon into heavier nuclei with release of energy. Stellar Nucleosynthesis: HHE HEC CNe, Na, Mg, Al NeO, Mg OSi, S, Ar, Ca SiFe (Iron) last stop Energy is released To fuse nuclei heavier than iron (such as silver and gold) the energy needs to be supplied. The nucleus of iron has the largest binding energy per nucleon (proton or neutron) – it is the most stable nucleus). To fuse nuclei which are heavier than Iron the energy must be supplied. The structure of the core of a massive Red Giant. -Iron Silicon fusing into Iron Helium fusing into Carbon Hydrogen fusing into Helium (from core to outer shell) -Each successive fusion reaction releases less energy than the previous one. As a result the reaction rates speed up (more Si nuclei must be consumed per unit time than, say carbon nuclei) -As a result each phase in the fusion chain lasts a shorter period of time. -example: M=25M -HHE (10 million years) -HEC (1 million years) -CNe, Na, Mg, Al (1000 years) -NeO, Mg (3 years) -O Si, S, Ar, Ca (4 months) -Si Fe (5 days) -The mass of the intert Iron core grows. It is supported against the gravitational collapse by the pressure exerted by degenerate electrons. Once the Chandrasekhar limit for the iron core is reached the core collapses and the star explodes in type II Supernova. January 23, 2013 The iron core of a massive red giant is supported (against gravitational collapse) by the pressure created by degenerate electrons. Iron Nuclei ………… ………… …………. Degenerate Electrons Once the Chandrasekhar limit is reached the electrons cannot hold the core stable and it collapses. Electrons combine with protons in the nuclei to form neutrons plus neutrinos. The support for the top layers of the red giant is required once the core collapses and they start to fall in. The neutron core rebounds and collides with the infalling layers. A shock wave is created which passes through the star and rips it apart. Also the hot neutron core (temperature – 100 billion K) produces a higher number of thermal neutrinos that cause, via interaction with the material in the top layers, the violent explosion. The importance of type II Supernovae: 1) As the shock wave passes through the top layers it supplies the energy needed for the nuclei heavier than iron (e.g. platinum, silver, gold) to be formed. 2) The explosion disperses all of the material of the star and it becomes a part of interstellar material out of which new stars and planets around them are formed. The energy output of supernovae is about 10 times the luminosity of the sun- this is greater than the energy produced by all the stars in all galaxies in the observable universe. 99% of this energy is taken up by the neutrinos. Most of the remaining 1% of energy is taken up by the ejected material. Only 0.1% of the energy created during the explosion is carried by light! January 25, 2013 There are several types of supernovae: Type II- single exploding massive star; they are identified from the presence of hydrogen spectral lines (produced by “unburned” hydrogen in the outer layers of the red giant) Type I a – In a binary system where one star is a white dwarf (initially with a mass less than 1.4.) and the other is a red giant. Strong gravitational field of the white dwarf causes material transfer from red giant to the white dwarf. Once the white dwarf gets close to the Chandrasekhar Limit of 4M. , it heats up, the runaway fusion reactions starts and so much energy is released that the entire system is blown up. All hydrogen is fused and hence there are no hydrogen spectral lines in the spectra of the type 1a supernovae. Type 1a supernovae are extremely important in determining distances to the most distant galaxies: They all have the same Luminosity (L), because the explosion occurs near the Chandrasekhar Limit. Then their distances (d) is found from the observed brightness (B) using B= ¼ Pi L/d 2 Supernovae in our own galaxy: -These recorded were AD 1006 (recorded by Arab Astronomer) 1054 (recorded by Chinese Astronomer; They also marked its position in the sky) 1572 (Tycho Brahe) 1604 (Johannes Kepler) It is estimated that there is one Supernova somewhere in our Galaxy every 25-50 years. Most of them cannot observe because their light is blocked by the gas and dust in the plane of the Milky Way. The estimate is that there is a supernova every second in the universe (the number of galaxies and stars in those galaxies in the observable universe is “Astronomical”) Supernova Remnants: The gas ejected by the supernova explosion expands and it compresses the surrounding interstellar material; growing and expanding cloud of stellar debris is called supernova remnant. Example: crab nebula, which is the remnant of the supernova from 1055. January 28, 2013 What happens to the collapsed core which consists of degenerate neutrons (density=10 kg/cm 3 If its mass is less than about 3M. it will be stable and form a neutron star (degeneracy pressure cannot prevent gravitational collapse) 2a) Neutron Stars Evidence for neutron stars comes from so-called pulsars (discovered in 1967 by J. Bell) She detected regular pulses (every 1.33 seconds) of radio pulses coming from outer space (LGM – for little green men) Evidence for the neutron stars: -Pulsars-observed first in 1967 by a graduate student Jocelyn Bell oShe noted that there is a source of regular radio pulses (Every 1.33728 Seconds) oLater several more such sources were discovered and they were called pulsars. oBy now over 1500 pulsars have been discovered. oPulsars are fast spinning neutron stars. -They are fast spinning neutron stars (T. Gold, Cornell) and they also emit radiation of other wavelengths including the visible light The spin is fast because a contracting spinning object will increase the rate of spin [due to conservation of angular momentum = mass (M) x average radius (R) x rotation speed (v)] The density of a neutron star is about 10 11 Kg/cm 3 (larger than the density of atomic nucleus) It is supported against gravitational contraction by the pressure of degenerate neutrons Contraction of the core results in tremendous increase of its magnetic field (from 1 gauss to 10 12 gauss) The magnetic North-South axis is off the rotational axis The changing magnetic field (due to rotation) produces electric field which accelerates the charges at the surface along North-South axis (neutrons at the surface decay into protons and neutrons) The spin rate of a spinning contracting object increases with decreasing size C because of the concentration of angular momentum: The pulse rate of the pulsars slows down over time as they lose energy via radiation (the period increases by a few seconds in a million years). The observed pulse rates range from 0.001 seconds to 10 seconds. Some Pulsars have “Planets” orbiting around them. January 30, 2013 Black Holes and Einstein’s general theory of Relativity Black Holes: If the core of a high mass star has mass above about 2M. the degenerate neutrons cannot prevent its gravitational collapse and it collapses into a single point (so called singularity). The escape velocity from a body (Earth, Moon, Sun, Star etc.) is the velocity that an object has to have so that it can escape the gravitational confine of the body. For Earth the escape velocity from it is about 11 km/s. 2 It can be shown that escape velocity = 2 Gravitational Constant Mas/Radius. For given mass (M) V escincreases with decreasing R. Schwarzschild radius R issthe radius of the event horizon. R =3M s Example: For M=10M. R =30ks For M=20M. R =60 km s Nothing including light, can escape the region within the event horizon! Hence the name “Black Hole.” How is one to detect a black hole? -Look for a binary system consisting of a regular star -And an invisible object with a mass of at least 3 solar masses (3M.) Third Kepler’s Law as formulated by Newton A /p = M + m (2) -From (1) to (2) one can find M and m. -Also the invisible companion needs to be an intense source of x-rays. Stellar wind particles produced by the regular star in the binary system are accelerated by the strong gravitational pull near the event horizon and as a result produce x-ray radiation. First discovered in 1971 by Tom Bolton using 1.9m reflector at David Dunlap observatory in Richmond Hill (Toronto). M=15M. m=27M. (Cygnus X-1) (Cygnus) To describe the black holes one needs Einstein’s general theory of relativity. February 1, 2013 Einstein’s General Theory of Relativity (1915)-Theory of gravity: A mass bends space (and time, so called space-time) and other bodies and light move in this curved space along the paths of the shortest distance (geodesics). This predicted deflection of starlight by massive objects such as the Sun. In 1919 A.S. Eddington went on expedition to look for this during a total solar eclipse. The observations confirmed the prediction of the general theory of relativity. Further predictions of the general theory of relativity: -The stronger the force of gravity on a clock, the slower it runs and vice versa. This is important for proper functioning of GPS (Global Positioning System). The clocks on the satellites experience smaller gravitational pull compared to those on exactly, and thus run faster- over perios of one day they would be 45 ns=45 x 7 10 c ahead because the satellites are moving (at 14,000 km/hour) their clocks are running slower (the effect of special theory of relativity)- they would be 7 ns = 7 x 10 c behind. The net effect is: (45-7) ns/day =35 ns/day (TOO FAST) The speed of light is about 1.44/1ns, 1ns=10 s, 1ns= 1000ns So the clocks on the satellite has to run slower (by 35ns/day) compared to those on Earth- otherwise the error in determining the distance would have been tens of km each day! -The larger is the force of gravity on a source of light, the largest is the increase in wavelength that an observer detects (this is so-called gravitational remnant). February 4, 2013 The Milky Way Galaxy A diffuse band of light across the sky. Greeks called it galaxies Kuklos (Milky Circle) Romaus called it via Lactea (milky way) Galileo used his telescope in 1609 to find that it consists of many faint (because they are very distant) stars. th In the 18 century Thomas Wright and Immanuel Kant proposed that we observe this band of light because we live in one disk of stars. Size of the Milky Way and our location in it: After WW1 Harlow Shapley measured our distance from globular clusters (clusters of 100,000 to 1,000,000 stars). He noticed that they are located on one side of the sky near the constellation of Sagittarius. Shapley Assumed that they are distributed in a spherical manner around the centre of our galaxy by measuring the distances to them he could deduce how far away we are from the centre. Using the similar method the astronomers have determined the size and the shape of the Milky Way Side View: He used the Cepheid variables to measure the distances to the globular clusters. The method was established by Henrietta Swan Leavitt (1912) Cepheid variables are variable yellow giant. L=const. R T4 R=radius T=surface temperature L=Luminosity Their luminosity will change with their radius in a periodic way. Leavitt Found Peak Luminosity – period of luminosity variation correlation Once we know the luminosity L, we measure the
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