PDF Chapters 16, 15: The Sun

Chapters 16, 15: The Sun Solar energy: The Sun’s spectrum is close to that of an idealized thermal emitter with a temperature of 5800 K. Luminosity = total energy output per second = 3.9 x 1026 Joules/s = 3.9 x 10 26 Watts = detonation of 100 billion 1-megaton nuclear bombs per sec...

Chapters 16, 15: The Sun Solar energy: The Sun’s spectrum is close to that of an idealized thermal emitter with a temperature of 5800 K. Luminosity = total energy output per second = 3.9 x 1026 Joules/s = 3.9 x 10 26 Watts = detonation of 100 billion 1-megaton nuclear bombs per sec 1 Joule is the amount of energy it takes to lift an apple up by 1 meter. 1 Calorie = 4184 Joules (this is the food Calorie we are familiar with) Energy is generated by thermonuclear fusion The proton-proton chain – what is it, what are its ingredients: Proton proton chain is the nuclear fusion in the core of the sun that gives the sun its energy. Three step process. ○ 1. Hydrogen is converted into Helium Step 1 (must happen twice): Two Protons (1H) collide. One proton decays and becomes a neutron and this forms a deuterium (2H; One proton, one nuerton). This step needs to occur twice. One Positron and One Neutrino are released. ○ 2. Energy is generated by thermonuclear fusion Step 2 (must occur twice): 1 Deuterium (2H) collides with a proton to form a nucleus of Helium-3 (3He; 2 proton, one neutron). Gamma Rays are released. ○ 3. The temperatures and pressures deep within the core of the Sun are so intense that hydrogen nuclei can combine (fuse) to produce helium nuclei. Step 3: Two Helium-3 (3He) collide to form Helium-4 (4He). 2 protons (1H) are released. ○ Note: The protons overcome their mutual repulsive force because the temperature in the core of the Sun is very high, 15 million K. This means that they move very fast in an extremely dense environment and overcome their (protons in first step) mutual electrical repulsion and merge. ○ Note: The energy generated as gamma rays leaves the Sun as visible light, but it takes a few hundred thousand years to make its way to the Sun’s surface. This is because it is absorbed and re-emitted many times as it bounces off matter in the Sun’s interior How does the Sun produce its energy? E=mc2 The sum of all the masses created in the proton proton chain reaction is less than the mass of the particles that were used up. The lost mass (0.7%) has been converted to energy. This is the energy that powers the Sun and that eventually radiates out into space. Neutrinos: Neutrinos generated in the core travel cleanly through the Sun because they have no charge, and they interact very weakly with matter. Neutrinos leave near the speed of light and escape into space a few seconds after being created Neutrino = v = weakly interacting neutral particles that travel at nearly the speed of light and have nearly no mass By studying neutrinos from the Sun we can investigate the conditions in the interior of the Sun Hydrostatic equilibrium – what is it? Equilibrium is maintained by a balance among forces. Hydrostatic equilibrium - inward gravitational force is balanced by outward gas and radiation pressure The higher the temperature, the higher the gas pressure Gas and radiation pressure get higher as you go deeper into the Sun The Sun has high gravity and does not collapse because the pressure of the gas inside the sun pushes against gravity and is balanced by the inward force of gravity. Within each point within the sun, the outward push due to pressure is balanced by the inward pull due to gravity. Deeper in the sun = more gravity and more pressure which means higher temperature. Structure of the Sun – regions from core to corona Core Radiation Zone Convection Zone Photosphere Chromosphere Corona Energy transport inside the Sun – radiation and convection Convection is the process of transferring heat through air or liquid currents. Radiation heat transfer occurs via electromagnetic waves 1. The core of the Sun is where its energy is generated. 2. Then the energy is transported by radiation through photons in the radiation zone. 3. Then the energy is transported by convection through mass motions of gas in the convection zone. 4. Then the energy is carried away from the Sun through radiation. Modeling the interior of the Sun Density, temperature, and pressure increase toward the center, thus creating the necessary conditions for nuclear fusion Helioseismology Oscillations (Longitudinal waves) of the Sun’s surface are measured by the Doppler shifts in the emitted light. Scientists can model the Sun’s interior based on the surface oscillations Sun is opaque Sun Stats: size, mass, core and surface temperatures, luminosity, composition Diameter = 1.4 x 106 km = 109 x diameter of earth Mass = 2.0 x 1030 kg = 332,000 x mass of earth Surface temperature = 5,800 K Core temperature = 15 x 106 K = 15,000,000 K The Sun is a ball of superheated plasma, a gas composed of charged particles – protons, electrons, and ions 2% H and 7.8% He by number of nuclei = 73.4% H and 25 % He by mas Luminosity = 3.846 × 1026 watts Solar atmosphere – photosphere, chromosphere, corona Photosphere - the apparent surface of the Sun is the point at which light can directly escape into space. 400 km thick layer. The Sun’s thermal spectrum, the light that we measure from the Sun, comes from the photosphere Layers are directly observed Granulation on the photosphere: High-resolution photographs of the Sun’s surface reveal a blotchy pattern called granulation Convection cells in the photosphere Rising hot gas produces granules Cooler gas sinks downward along the boundaries between granules; this gas glows less brightly, giving the boundaries their dark appearance. This convective motion transports heat from the Sun’s interior outward to the solar atmosphere Sunspots: temperature, how they form, sunspot cycle: Sunspot - a region in the photosphere where the temperature is relatively low, which makes it appear darker than its surroundings.  Occur because of changes in the Sun's magnetic field. Because the rotation period of the Sun is faster at the equator than towards the poles, a 'differential rotation' is created. The average number of sunspots on the Sun is not constant, but varies in a predictable sunspot cycle every 11 years At the beginning of a cycle, spots appear far from the equator; they appear closer to the equator as the cycle progresses. Solar rotation (what is differential rotation?) Differential rotation - the Sun rotates faster at its equator than at its poles The strong magnetic field gets distorted and twisted as it wraps around the equator. Convection causes the magnetized gas to leave the surface and loop through the atmosphere taking the magnetic field with it. It creates a sunspot pair linked by magnetic fields. Prominences, solar flares Prominences are arcs of magnetic field and solar plasma. ○ The plasma contains ionized atoms and free electrons. ○ These charged particles become trapped in the magnetic field of prominence. ○ Prominences can last a few hours or a few days Solar Flares - sudden increases in the brightness of a region of the Sun. ○ They are caused by the breaking and reconnecting of magnetic field lines. ○ Large amounts of energy (radiation) are released in this process. ○ Flares usually happen near the Sun’s surface and close to sunspots. Solar prominences are the plasma loops that connect two sunspots. Solar flares and coronal mass ejections are eruptions of highly energetic particles that can erupt from the Sun's surface and cause problems with power grids and communications on Earth. Chromosphere, Corona (very high temperature, why?) Chromosphere: above the photosphere ○ Reddish Emission line because its hot gasses emit light at certain wavelengths ○ Spicules are jets of chromospheric gas that surge upward into the Sun’s outer atmosphere. Corona - is the outer layer of the Sun’s atmosphere, extending out to a distance of several million kilometers ○ Is only about one-millionth as bright as the photosphere and can be viewed only when the light from the photosphere is blocked out ○ Looks like numerous streamers extending in different directions far above the solar surface, changing over days and weeks ○ Contains very little thermal energy with low atoms ○ Has temperatures far greater than the temperatures in the Chromosphere  It is not clear what heats the corona, but apparently the magnetic field of the Sun acts like a pump that increases the speed of particles in the corona. Solar wind Solar Wind is the outflow of coronal gasses, traveling at a million kilometers per hour escapes the Sun mostly through coronal holes, which can be seen in X-ray images The Sun’s reach of influence on its environment is the heliosphere Coronal mass ejections: Huge blasts of high energy particles are followed by vast amounts of solar plasma traveling outward at hundreds of km/s. In a day or two they reach the orbit of the Earth Aurorae Formed from electrically charged particles that are released by the Sun Chapter 16,17,18 Parallax and parsec Proper motion Proper motion is real motion of the star in space Luminosity and apparent brightness Luminosity, or intrinsic brightness, is a measure of the total energy radiated by a star – it has units of energy per second. Apparent brightness is how bright a star appears when viewed from Earth; it depends on the luminosity but also on the distance to the star. The farther away you are from a light source, the dimmer it looks. Inverse square law of radiation: The amount of light received by any given patch on the sphere gets diluted by the square of the distance from the source Star color and temperature – Wien’s Law red stars are cooler, blue stars are hotter Spectral classes OBAFGKM - what is this a sequence of? Temperature Surface temperature affects stellar spectra – why? Their absorption lines can occur only if these stars have surface temperatures above 25,000 K  For hydrogen lines to be prominent in a star’s spectrum, the star must be hot enough to excite the electrons out of the ground state but not so hot that all the hydrogen atoms become ionized. A stellar surface temperature of about 9000 K produces the strongest hydrogen lines; this is the case with A0 - A5 stars. Every other type of atom or molecule also has a characteristic temperature range in which it produces prominent absorption lines in the observable part of the spectrum Brown dwarfs Objects with masses less than about 7.5% of the mass of our Sun do not become hot enough for hydrogen fusion to take place. L,T,Y These objects are about the size of Jupiter, but denser. They burn deuterium in their cores Star sizes – direct measurement, indirect measurement Some stars are close enough and big enough that we can directly measure their sizes, for example, Betelgeuse. It is hundreds of time larger than the Sun Relationship between a Star’s Luminosity, Radius, and Surface Temperature. Equation is the indirect measurement ○ A cool star can be bright if it has a very large radius. ○ A very hot star can be dim if it has a very small radius. Relationship between L, R, T of a star The Luminosity of a star is proportional to its Effective Temperature to the 4th power and its Radius squared Binary stars useful for calculating masses of stars; concept of center of mass Same orbital period. Binary Stars Orbit each other. The star with a higher mass will be closer to the center of mass. Never collide since they are always on the opposite side of the center of mass. Period and size of the orbit and velocities of the two stars can sometimes be observed. Force of gravity and Kepler’s third law P² = a³, so the period of a planet's orbit (P) squared is equal to the size semi-major axis of the orbit (a) cubed when it is expressed in astronomical units = kepler's third law M1R1 = M2R2 Types of binary stars – visual, spectroscopic, eclipsing, astrometric 1. Visual Binary Stars - can be measured directly; through telescope Sirius.  2. Spectroscopic Stars - can be measured through their doppler shifts (radial velocity). Spectral lines move back and forth as the stars move toward and away from us in turn as they orbit around each other 3. Eclipsing Binary Stars - easiest to measure. 4. Astrometric Binary Stars - Some stars, if observed repeatedly over time, show a perturbation or "wobble" in their proper motion. If this is a periodic occurrence, we can infer that the perturbation occurs due to the gravitational influence of an unseen companion. We have a system in which a visible star and a dimmer companion orbit a common center of mass. Binary systems detected by such astrometric means are called astrometric binaries H-R diagram – what’s on the axes? What are the main regions? Where is the Sun on this diagram? Sun in the middle at 1 luminosity Luminosity on y-axis Surface Temperature on x-axis. Main sequence - red dwarfs - most common Red Giants Blue Giants Supergiants White dwarfs - hot, dense, not luminous What is the Main Sequence? Where most stars spend their lifetime Darkened curve Red dwarfs, white dwarfs, red giants, blue giants – where are they on the diagram? Mass determines a star’s position on the MS. What is the most common type of star? Red Dwarfs The Mass-Luminosity relation for stars on the main sequence Greater the mass, greater its luminosity, radius, luminosity, surface temperature What does stellar lifetime depend on? Mass. Most massive stars have the shortest lifetime Chapters 20: The Interstellar Medium Type of nebulae – dark, emission, reflection – what are their properties? Examples Dark - Glows, due to hot stars. Horsehead Nebula. Emission - Dust cloud. ROSETTE NEBULA. hot, thin gas. Reflection -Blue, due to light scattering by dust. Reflection nebulae have lower concentrations of dust than dark nebulae. Pleiades. Shines only because the dust within it scatters light from a nearby bright source What does dust do to light? extinction and reddening Extinction - dust blocks visible light from stars. Fainter. Redding - Ultraviolet and blue light waves are absorbed or scattered, while red and IR waves pass through. Dust blocks short wavelengths of light. Redder Dust emits infrared light What is the ISM made of? – gas and dust – properties Ninety-nine percent of the interstellar medium is gas and 1 percent is interstellar dust Dust is made up of silicates, carbon, and iron, as well as dirty ice – water ice contaminated with ammonia, methane, etc. Interstellar medium is the gas and dust between the stars. thin gas and thick clouds. Interstellar gas regions – ionized H, neutral H, ultra-hot, molecular Ionized H - emission - Ionized Hydrogen (HII) Regions – gas near hot stars. Made primarily of protons, or ionized H Neutral H - Cold interstellar gas. Lower temperature clouds have neutral hydrogen atoms. Electrons and protons have spin, which are in alignment or not. When spin states flip, the atom emits a radio wave at 𝜆 = 21 cm. This transition is rare. A hydrogen atom would undergo one transition every 11 million years. Ultra-hot - temperatures of millions of K. The edges of the remnant are colliding with the interstellar medium, heating the gas Molecular - are cold enough (10 K) for hydrogen to be in H 2 molecules. They are the coldest gas clouds in the interstellar medium. Dense and appear dark. Chapters 21, 22: Birth of Stars and Low Mass Star (Sun) Evolution large molecular cloud collapses and fragments: Star formation happens when part of molecular cloud (a cold, dense part of the ISM) begins to shrink under its own gravitational force As it collapses, the center becomes hotter and denser, eventually forming an opaque object – a protostar.  Only regions, where a lot of cold gas is concentrated together, will collapse due to gravity and form stars A molecular cloud starts to contract, probably triggered by a shock or pressure wave from a nearby star, or even a supernova. As it contracts, the cloud fragments into smaller pieces, eventually forming many tens or hundreds of individual stars. Stars form in clusters. As the core collapses, the self-gravity grows stronger. As gravity increases, collapse speeds up. The molecular-cloud core collapses from the inside out What are T-Tauri ‘stars’, bipolar jets? T-Tauri ‘stars = Low-mass protostars Herbig Ae/Be = higher-mass protostars Bipolar outflow = two continuous flows of gas from the poles of a star ○ Result of magnetic interactions between the protostar and the disk When these outflows are organized and move quickly, they make jets Observations of molecular clouds and protostars Material that falls inward in a collapsing molecular-cloud core accumulates in a flat, rotating accretion disk. The object at the center of the disk is a protostar. Conversion of gravitational potential energy to thermal energy heats the protostar. The core gradually reaches 1 million kelvin. The protostar is always in hydrostatic equilibrium. As it accumulates more material, the balance point between gravity and pressure changes. The added material causes the protostar to contract, raising the internal temperature. The core reaches a temperature of 10 million K, and nuclear fusion begins Protostar on Hayashi track in HR diagram 100 R of the sun The protostar’s luminosity decreases even as its temperature rises because it is becoming more compact Goes down to the left. Pre-main sequence evolution on the H-R diagram is called the Hayashi Track Protostar energy from gravity: How does the composition of a star change while it is on the Main Sequence? it means that its L and/or T change What happens to the Sun and low mass stars after hydrogen gets depleted in the core?  Hydrogen shell burning causes the star to expand into a red giant and hydrogen fuses to become helium. Core Contracts when the hydrogen fuel in the core is all used up. Star burns hotter and starts pushing outer layers out. Red giant, helium fusion, hydrogen shell burning: Red Giant goes right and up on the HR diagram Big star with a lower surface temperature because the outer layers are expanding and moving away from the core. Its luminosity increases enormously due to its large size. Triple-alpha process - He to C: When the core hits 100,000,000 K, helium in core fuses. 3 helium nuclei fuse to form carbon. Beryllium is produced – very briefly. Helium fuses into carbon. Outer layers grow and the core keeps shrinking. It does not produce any energy to support itself. Two shells of hydrogen and helium with a carbon core. Planetary nebula, white dwarf - what are these? How large and how much mass? Planetary nebula - There is no more outward radiation pressure due to fusion being generated in the core, and so the carbon core continues to contract. Outer layers are unstable and eject themselves. Envelope is called a planetary nebula and dissipates. White dwarf - Star loses 40% of its mass and exposes the core. Contraction of the core stops when pressure due to electron degeneracy (The density reaches a point where electrons cannot be squeezed any tighter. The electrons lock in place and prevent further contraction) kicks in. The electrons hold up the star. The core is now called a white dwarf. The star is dead. It doesn’t produce any energy anymore. It just simply cools of Electron degeneracy pressure cannot support a stellar core against its own gravity if the mass is greater than 1.4 solar masses. This is called the Chandrasekhar limit. A star with a core mass greater than 1.4 solar masses (about 8 solar masses for the whole star before the outer layers are blown off in the planetary nebula phase) cannot become a white dwarf. Approximate timeline of sun evolution Birth. Gradual warming 6-9 billion. Red giant 10 billion. Planetary Nebula 11 billion. White dwarf 12-14 CHAPTER 22,23: Stellar Explosions, Evolution of High Mass Stars, Star Clusters Novae (from white dwarfs): Mass transfer happens via Roche lobe overflow in binary stars that are close to each other. In a binary system, each star has a Roche lobe: the region around the star where its gravity is dominant over the gravity of the companion star. If the larger star expands  beyond its Roche lobe, the excess material can cascade across to the compact companion star Nova: Hydrogen can accumulate on the surface of the white dwarf. If enough builds up, it can re-experience the hydrogen shell burning phase. But there is no upper star to hold the fusion in. An explosive burning phase engulfs the surface, and there is a huge explosion as material is ejected. The body of the white dwarf barely cares and settles back down to receiving more hydrogen (so novae can re-occur many times) Chandrasekhar limit for white dwarfs (1.4 solar masses) Electron degeneracy pressure can only support a mass less than 1.4 MSun Type Ia Supernovae (from white dwarfs): thought to be the result of the explosion of a carbon-oxygen white dwarf in a binary system as it goes over the Chandrasekhar limit, either due to accretion from a donor or mergers. Main Sequence core temps > 20 million K – CNO cycle to get from H He Carbon burning at 600 million K Successive heavier element fusion – onion-like core structure What’s special about Iron (Fe)? Neutron core formation Type II Supernovae Nucleosynthesis during supernova created heavier elements Supernova remnants – e.g., Crab nebula Type Ia vs. Type II Supernovae – telling them apart