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The Lives of Stars

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The Lives of Stars 9: The Lives of Stars Physics 17: Black Holes and Extreme Astrophysics 2 places we find black holes X-ray image from NuSTAR shows X-ray binaries • Stellar mass (~10�⨀) throughout galaxy black holes formed at the ends of the lives of massive stars — seen in X-ray binaries throughout galaxy when they accrete from a companion star Andromeda Galaxy • Supermassive black " # holes (10 ~10 �⨀) in galactic nuclei • Orbits of stars in the center of the Milky Way • Active galactic nuclei — powerful sources of radiation and jets when supermassive black holes accrete from their surrounding Orbits of stars in the Galactic center NGC 1365 Goals • We ultimately aim to discover how massive stars become black holes over the next 2 lectures • Understand how stars shine • Find out how stars are formed, how they evolve and how they die • See the roles that stars play in our Universe Reading Begelman & Rees • Chapter 2: Stars (p24-41) The Sun • Main sequence star "# • Mass �⨀ = 2×10 kg (mid-size) • Luminosity �⨀ = 3.8×10$% W • ~5 billion years old (middle- aged) • Will remain on main sequence for another ~5 billion years BigI In a black body, electromagnetic radiation is in equilibrium with the matter Black Body Radiation • Completely opaque, absorbs all incoming radiation (no reflection) • Emits energy in radiation at the same energy it Flux (power emitted per unit absorbs energy so the radiation has the same surface area): ‘temperature’ as the matter � = ��! • Emitted radiation has a specific spectrum � = 5.7×10!" W m!# K!$ (power at different wavelengths) – energy divided equally among wavelength “modes” Peak wavelength • Requires quantum mechanics – light can only 2.9×10&' be emitted by atoms at specific steps in � = m "#$% �⁄� wavelength, not at any wavelength – it is quantized WILtY Start by assuming that a star emits radiation like a black body From its color (distribution of emitted wavelengths), can estimate its surface temperature In quantum mechanics, atoms can only emit and absorb light at specific wavelengths What’s it made of? (corresponding to the differences between energy levels of electrons in the atoms) Sun WILtY (absorption on top of black Different atoms, with arrangements of electrons, body emission) and different numbers of protons in the nucleus, emit and absorb light at different, specific colors Hydrogen On top of the continuous black body spectrum, see bright/dark bands of emission/absorption at specific colors. Exact positions of the bands Helium identifies different chemical elements in a star If the atoms are moving, the light is Doppler shifted, shifting the bands to bluer or redder Mercuty colors. We can measure the velocity of a star or the motion of its surface. Spectroscopy: splitting light into its Mercury constituent wavelengths (prism, grating), and measuring the intensity at each wavelength Q1: Q2: Let’s assume that the Sun was formed when a cloud The nucleus of a hydrogen atom consists of just one &$' of gas collapsed under the force of gravity. proton with mass �% = 1.67×10 kg or 1.007826u (a ‘u’ is an atomic mass unit) The Sun is seen to emit total power �⨀ = 3.8×10$" W In a nuclear fusion reaction, 4 hydrogen nuclei can be combined to form one helium nucleus. The spectrum of light emitted from the Sun peaks at 500nm (1nm = 10-9 m) A helium nucleus has a mass of 4.002602u. a. Estimate the temperature and radius of the What happens to the ‘lost’ mass in a nuclear fusion Sun. reaction? b. What happens to the gravitational energy when the cloud collapses? c. How much energy is available from the collapse of the cloud when the Sun formed? d. How long would the Sun be able to shine for? e. Is this long enough? $.#×./!" d. If energy is being radiated at rate �, the a. Using � = m with � = 500nm, ()*+ 1⁄2 ()*+ luminosity, we can estimate the time taken to � = 5800K radiate the stored energy, � 3 Power �� is emitted per unit area, so �⨀ = � 3 $ �~ = 10.4s = 3×10' yr ��� and the surface area of the sun � = 4�� . � 4 �⨀ = 7×10 km (the Kelvin-Helmholtz timescale) b. As a could of gas collapses to form a star, e. Radioactive dating of rocks on the Earth shows gravitational energy is converted to kinetic their ages to be ~700 million years. The Sun energy. As the gas is compressed, this becomes must therefore be older and requires another thermal energy, heating the gas. The hot gas energy source. then radiates this energy as light. c. The change in gravitational energy when a The mass of four protons (hydrogen nuclei) is particle, mass m, falls from infinity to radius � 4.0313u. 1� = 1.66×10&$'kg 567 around the gravitating mass � is � = 8 Four hydrogen nuclei fuse to form a helium nucleus, In this case, the cloud is self-gravitating – it is the with mass 4.002602u. 0.028702u = 0.028702� = mutual attraction of the gas that causes it to 5×10&$#kgis lost. � = �. collapse, so we assume $ ��$ � = �� : the lost mass is equivalent to energy, �~ = 4×103. J 5×10&.$J. This is the energy released during nuclear � fusion. BigI The first step p-p chain requires a nuclear Nuclear Fusion in the Sun beta decay (a �( decay), which converts one of the protons into a neutron. ( � → � + � + �) • The Sun is powered by nuclear fusion in the core • Nuclei are positively charged (protons + neutrons), so repel each other To conserve charge, a positively charged • Nuclear fusion requires high densities, temperatures and pressures to positron (antimatter equivalent of the overcome this repulsion. This is possible in the core of a star where gravity electron) is emitted. is compressing the gas. WILtY • Nuclear fusion proceeds via the p-p chain reaction, fusing hydrogen Also emitted is a neutrino (an electron # nuclei (single protons) into helium ( He , 2 protons + 2 neutrons) neutrino). Neutrinos are low mass (less than $ % -7 � + � → H + � + �& 10 electron mass), weakly interacting $H + � → 'He + γ particles. They easily escape from the core of the Sun and we can detect (some) them on 'He + 'He → #He + 2� Earth • The total mass of the helium nucleus is less than the summed mass of its constituents, and it is in a lower energy, more stable state. � = ��$ Neutrino flux on the surface of the Earth is — the lost mass is the energy output of the fusion reaction which ~10*+ cm&,s&*, but most pass through powers starlight without interacting! BigI 30 Mass (�⨀) 2 x 10 kg 5 The Sun: The big picture Radius (�⨀) 7 x 10 km 26 Luminosity (�⨀) 3.8 x 10 W Core Density: 10- kg m&' . Temperature: 10 K Energy transport by Nuclear fusion reactions radiation in inner regions H → He Due to high density in the center, photons travel Surface ~1mm before they are Density: 10&! kg m&' absorbed, then re-emitted Temperature: 5800 K Can only see light from the top ~100km (the photosphere) Energy transport by convection in outer layers Neutrinos from fusion reactions in core can escape The Solar Corona • Magnetic fields are generated inside the Sun • As the Sun rotates, magnetic field gets twisted WILtY • Causes Solar prominences and darker spots (sunspots) to appear on surface • The field lines ‘snap’ releasing large amounts of energy in Solar flares • Magnetic fields store a large amount of energy and can exert a large force BigI BigI (A very simple view) of Star Formation A cloud of gas is Angular momentum is disturbed, causing small conserved as the cloud clumps to from. Gravity collapses, forming an pulls more material in accretion disc onto the towards clump and it growing protostar starts to collapse into a Protostar is powered by protostar gravitational energy released during infall Density & pressure get Clumps in disc also high enough in protostar attract surrounding to start nuclear fusion material through reactions, converting gravitational force — hydrogen into helium these form protoplanets Nuclear fusion will power Excess material driven the star on the main away sequence Infrared radiation can pass through the dust. We see young stars inside the clouds The Eagle Nebula The Pillars of Creation Measure the luminosity (magnitude) of a star High Mass Stars and its color (difference in magnitude at two • Bright and hot wavelengths) — plotting these against each • High pressure in core other forms a Hertzsprung-Russell (HR) leads to rapid nuclear diagram fusion reactions • Live fast and die Color measures surface temperature of the young (1-100Myr) star (assuming the star radiate like a black body – slide 6) Stars divide into populations BigI • The main sequence, from hot, bright stars, to dimmer, cool stars • Giant stars, at the top of the main sequence (the blue giants – hottest, brightest stars) and the giant branch (red giants) • Low Mass Stars The white dwarfs – small, dim, hot (blue) • Cooler and dimmer stars (Lecture 10) • Live for 100Myr-1Tyr • On the main sequence, thermal pressure from the gas, heated by nuclear fusion in the core, The End of the Main Sequence balances the gravitational force pulling the gas together (which would collapse the star) • Once the hydrogen runs out in the fuel, there is no longer fuel for the nuclear fusion reaction 2. Heat from collapsing core that heats the gas (fusing helium would take causes outer envelope to more energy) expand, then cool • Thermal pressure drops and the core starts to 1. When fusion stops, core collapses under gravity collapse under gravity • As core collapses, gravitational energy is converted to thermal energy in the gas (Lecture 3. Fusion of hydrogen 7) — the core heats up happens in heated • shell outside the core The heat from the core causes the outer envelope of the star to expand — as it expands, 4.
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