1	Astro 1050 Mon. Mar. 8, 2004 Today: End Ch. 10: The Deaths of Stars Start Ch. 11: Neutron Stars, Black Holes
2	Is a star stable against catastrophic collapse? Imagine compressing a star slightly (without removing energy) Pressure goes up (trying to make star expand) Gravity also goes up (trying to make star collapse) Does pressure go up faster than gravity? If Yes: star is stable – it bounces back to original size If No: star is unstable – gravity makes it collapses Ordinary gas: P does go up fast – stable Non-relativistic degenerate gas: P does go up fast – stable Relativistic degenerate gas: P does not go up fast – unstable Relativistic: Mean are the electrons moving at close to the speed of light Non-relativistic degenerate gas: increasing r means not only more electrons, but faster electrons, which raises pressure a lot. Relativistic degenerate gas: increasing r can’t increase electron velocity (they are already going close to speed of light) so pressure doesn’t go up as much
3	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
4	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
5	Supernova When the degenerate core of a star exceeds 1.4 M_Sun it collapses Type II: Massive star runs out of fuel after converting core to Fe Type I: White dwarf in binary, which receives mass from its companion (collapse ignites carbon burning). 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)
6	Supernova in Another Galaxy Supernova 1994D in NGC 4526
7	Tycho’s Supernova of 1572 Now seen by the Chandra X-ray Observatory as an expanding cloud.
8	The Crab Nebula – Supernova from 1050 AD Can see expansion between 1973 and 2001 Kitt Peak National Observatory Images
9	Chapter 11: Neutron Stars and Black Holes What happens to the collapsing core? Neutron star 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
10	Spinning pulsar powers the Crab nebula Red: Ha Blue: “Synchrotron” emission from high speed electrons trapped in magnetic field
11	Another pic of the Crab, Pulsar
12	Why a “pulsar?”
13	“Lighthouse” Model for Pulsars
14	Another Neutron Star in a SNR
15	Other cool stuff about Neutron Stars Novel Dragon’s Egg by Robert L. Forward Short Story “Neutron Star” by Larry Niven Binary Pulsars Gamma Ray Bursts? Pulsar Planets
16	Black Holes -- basics Nothing can stop collapse after neutron pressure fails Escape velocity from a surface at radius R: As R shrinks (but M is fixed), V_escape gets larger and larger At some point V_Escape= c (speed of light) Happens at Schwarzschild radius: Not even light can escape from within this radius
17	Examples: The Schwarzschild Radius: Mass in solar masses R_s (km) 10 3 2 1 0.000003 (Earth)
18	Examples: The Schwarzschild Radius: Mass in solar masses R_s (km) 10 30 3 9 2 6 1 3 0.000003 (Earth) 0.9 cm
19	Black Holes -- details Remember – gravity is same as before, away from mass Black holes do NOT necessarily pull all nearby material in A planet orbiting a new black hole would just keep on orbiting as before (assuming the ejected material or radiated energy didn’t have an effect) Any mass can potentially be made into a black hole – if you can compress it to a size smaller than R_S = 2GM/c² 1 M_Sun: 3.0 km 10⁶ M_Sun 3´10⁶ km 1 M_Earth 8.9 mm
20	Black Holes -- details If you do make material fall into a black hole, material will be falling at close to the speed of light when it reaches R_S If that falling gas collides with and heats other gas before it reaches R_S, then light from that hot material (outside R_S) can escape (important in quasars!).
21	Black Holes – detection By definition – can’t see light from black hole itself Can see large amounts of energy released by falling material just before it crosses R_S Can see motion of nearby objects caused by gravity of black hole
22	Black Holes – detection Example: Like White Dwarf accretion disk but w/ black hole instead Gas from red giant companion spills over towards black hole Gas spirals in toward black hole, through accretion disk Gas will be much hotter because it falls further, to very small R_S Gas will be moving at very high velocity Much faster than with white dwarf since much closer (P² µ a³) Signature of black hole: Very high energy release, very high velocity We find MASSIVE black holes in centers of most galaxies
23	Cygnus X-1
24	More Cool Stuff About Black Holes Time Dilation – originally “Frozen Stars” Gravitational Redshift Wicked Tidal Forces Hawking Radiation