1	Astro 1050 Fri. Oct. 25, 2002 Today: Astronomy Articles Homework #7 review Chapter 10: The Deaths of Stars Review for Exam
2	Homework #7 Q1. We see the Crab Nebula is about 1.35 parsecs in radius and is expanding at a rate of 1400 km/s. Extrapolate backwards in time and estimate about when would the supernova creating the Crab Nebula have exploded? Distance/rate/time problem so… 1.35 pc = 1400 km/s x time Convert pc to km: 1pc = 3.09 x 10¹³ km Time = (4.2x10¹³km)/(1400 km/s) = 3 x 10¹⁰ s Convert to years: 31.5 million seconds in a year Time = 950 years (if you don’t round get 920)
3	Homework #7 Q2. If the stars turning off the main sequence in the H-R diagram of a star cluster have masses of about 15 times solar, how old is the cluster? The cluster will be about as old as the main sequence lifetime. Can use lifetime (as fraction of solar lifetime) = 1/M^2.5and get 1/1000 of the solar lifetime or look up in the table in the slides. 15 solar masses is about a B star which have lifetimes of around 10 million years.
4	Homework #7 Q3. The Ring Nebula has an angular diameter of 72 arcsec, and we estimate it is 5000 light years away. What is its linear diameter? Linear diameter = 5000 ly x 72/206265 Linear diameter = 1.7 light years An aside. Exansion rate is 15 km/s, so the age is approximately 34,000 years old.
5	Homework #7 Q4. If a type G star like the sun expands to become a giant star with a radius 20 times larger, by what factor will its density decrease? Density is mass/volume. Volume of a sphere is 4/3πr³. If r increase by a factor of 20, volume increases by a factor of 20 cubed, or 8000. Mass remains the same, so density decreases by 8000 times.
6	Chandrasekhar Limit for White Dwarfs Add mass to an existing white dwarf Pressure (P) must increase to balance stronger gravity For degenerate matter, P depends only on density (r), not temperature, so must have higher density P vs. r rule such that higher mass star must actually have smaller radius to provide enough P As M_star ® 1.4 M_Sun v_electron ® c Requires much higher r to provide high enough P, so star must be much smaller. Strong gravity which goes with higher r makes this a losing game. For M ³ 1.4 M_Sun no increase in r can provide enough increase in P – star collapses
7	Implications for Stars Stars less massive than 1.4 M_Sun can end as white dwarfs Stars more massive than 1.4 M_Sun can end as white dwarfs, if they lose enough of their mass (during PN stage) that they end up with less than 1.4 M_Sun Stars whose degenerate cores grow more massive than 1.4 M_Sun will undergo a catastrophic core collapse: Neutron stars Supernova
8	Supernova When the degenerate core of a star exceeds 1.4 M_Sun it collapses Type II: Massive star where it runs out of fuel after converting core to Fe Type I: White dwarf in binary, which receives mass from its companion. Events: Star’s core begins to collapse Huge amounts of gravitational energy liberated Extreme densities allows weak force to convert matter to neutrons p⁺ + e^-® n + n Neutrinos (n) escape, carrying away much of energy, aiding collapse Collapsing outer part is heated, “bounces” off core, is ejected into space Light from very hot ejected matter makes supernova very bright Ejected matter contains heavy elements from fusion and neutron capture Core collapses into either: Neutron stars or Black Holes (Chapter 11)
9	Supernova in Another Galaxy Supernova 1994D in NGC 4526
10	Tycho’s Supernova of 1572 Now seen by the Chandra X-ray Observatory as an expanding cloud.
11	The Crab Nebula – Supernova from 1050 AD Can see expansion between 1973 and 2001 Kitt Peak National Observatory Images
12	What happens to the collapsing core? Neutron star (more in next chapter) Quantum rules also resist neutron packing Densities much higher than white dwarfs allowed R ~ 5 km r ~ 10¹⁴ gm/cm³ (similar to nucleus) M limit uncertain, ~2 or ~3 M_Sun before it collapses Spins very fast (by conservation of angular momentum) Trapped spinning magnetic field makes it: Act like a “lighthouse” beaming out E-M radiation (radio, light) pulsars Accelerates nearby charged particles
13	Spinning pulsar powers the Crab nebula Red: Ha Blue: “Synchrotron” emission from high speed electrons trapped in magnetic field
14	Review Chapters 7-10 Chapter 7: The Sun Atmospheric Structure Temperature, density, etc., with radius Sunspots/Magnetic Phenomena What are they? Why do they exist? Nuclear Fusion – proton-proton chain What is it? How does it produce energy? Solar Neutrino “Problem” What is it? Is it still a problem?
15	Review Chapters 7-10 Chapter 7: The Sun – example questions Q. The fusion process in the sun, the "proton-proton" chain, requires high temperatures because: c of the ground-state energy of the Hydrogen atom. c of the presence of Helium atoms. c the colliding protons need high energy to overcome the Coulomb barrier. c of the need for low density. c the neutrinos carry more energy away than the reaction produces.
16	Review Chapters 7-10 Chapter 8: The Properties of Stars Distances to Stars Parallax and Parsecs Spectroscopic Parallax Intrinsic Brightness: Luminosity Absolute Magnitude Luminosity, Radius, and Temperature Hertzsprung-Russell (H-R) Diagram Luminosity Classes (e.g., Main Sequence, giant) Masses of Stars Binary Stars and Kepler’s Law Mass-Luminosity Relationship
17	Review Chapters 7-10 Chapter 8: Properties of Stars--examples True/False: The main determinant of the lifetimes of stars is their mass. Q. A star’s luminosity depends only on the star’s: c distance and diameter. c temperature and distance. c distance. c temperature and diameter. c apparent magnitude Another version of the question\ can be made for apparent magnitude . Short answer: What are two methods for determining the distance to a star? Another version of the question can be made for masses.
18	Review Chapters 7-10 Ch. 9: The Formation & Structure of Stars Interstellar Medium Types of Nebulae (emission, reflection, dark) Interstellar Reddening from dust Star formation Protostar Evolution on H-R Diagram Fusion (CNO cycle, etc.) Pressure-Temperature “Thermostat” Stellar Structure (hydrostatic equilibrium, etc.) Convection, radiation, and opacity Stellar Lifetimes
19	Review Chapters 7-10 Ch. 9: The Formation & Structure of Stars Example questions True/false: The sun makes most of its energy via the CNO cycle. Short answer question: Explain what keeps the nuclear reactions in a star under control.
20	Review Chapters 7-10 Ch. 10: The Deaths of Stars Evolution off the main sequence (=> giant) Star Cluster Evolution on H-R Diagram Degenerate Matter Planetary Nebulae and White Dwarfs Binary Star Evolution (Disks, Novae, etc.) Massive Star Evolution and Supernovae
21	Review Chapters 7-10 Ch. 10: The Deaths of Stars—examples Short answer: Describe the ultimate fate of stars as a function of their initial mass. Q. Massive stars cannot generate energy through iron fusion because: c iron fusion requires very high densities. c stars contain very little iron. c no star can get high enough for iron fusion. c iron is the most tightly bound of all nuclei. c massive stars go supernova before they create an iron core.