Pulsars ASTR2110 Sarazin. Crab Pulsar in X-rays
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1 Pulsars ASTR2110 Sarazin Crab Pulsar in X-rays
2 Test #2 Monday, November 13, 11-11:50 am Ruffner G006 (classroom) Bring pencils, paper, calculator You may not consult the text, your notes, or any other materials or any person You may bring a 3x5 card with equations ~2/3 Quantitative Problems (like homework problems) ~1/3 Qualitative Questions Multiple Choice, Short Answer, Fill In the Blank questions No essay questions
3 Test #1 (Cont.) Equation/Formula Card: You may bring one 3x5 inch index card with equations and formulae written on both sides. DO NOT LIST pc, AU, M, L, R DO NOT INCLUDE ANY QUALITATIVE MATERIAL (text, etc.)
4 Material: Test #2 (Cont.) Chapters 5, 7, , 14, 15, 17, 18, 23.3 Binary Stars, the Sun, Atomic Physics, Stellar Spectra and Atmospheres, Stellar Interiors, Nuclear Energy, Stellar Evolution, Stellar Remnants, General Relativity, Black Holes, Stellar Deaths, Neutron Stars and Pulsars (Quantitative problems only) (Qualitative problems only) Homeworks 6-9 Know pc, AU, M, L, R
5 Material: Test #2 (Cont.) Chapters 5, 7, , 14, 15, 17, 18, 23.3 Binary Stars, the Sun, Atomic Physics, Stellar Spectra and Atmospheres, Stellar Interiors, Nuclear Energy, Stellar Evolution, Stellar Remnants, General Relativity, Black Holes, Stellar Deaths, Neutron Stars and Pulsars (Quantitative problems only) Homeworks 6-9 Know pc, AU, M, L, R
6 Test #2 (Cont.) No problem set week of November 6 13 to allow study for test Review Session: Discussion session Friday, November 10, 3-4 pm
7 Pulsars ASTR2110 Sarazin Crab Pulsar in X-rays
8 Pulse Profile: Radio
9 Pulsars: Properties mid 1968 Periods: P = seconds d P / dt < sec/sec, very good clock dp/dt > 0, pulses slowing very slightly Pulse duration >~ 20 ms
10 Pulsars = Rotating Neutron Stars
11 Crab Pulsar
12 Crab Pulsar 1968 P = sec dp/dt = 4 x t slow ~ P/(dP/dt) ~ 2000 years ~ time since supernova Decrease in rotational kinetic energy = energy from Crab Nebula
13 Crab Pulsar Rotational kinetic energy = (1/2) I Ω 2 = (1/2) I (2π/P) 2 I = moment of inertia ~ M R 2 ~10 45 gm cm 2 Decrease in rotational kinetic energy ~ 2 x erg/s ~ energy from Crab Nebula Energy for pulsar, nebula due to rotational kinetic energy of neutron star 1.4 M 8 10 km
14 Pulsar Model Neutron stars formed by collapse of core of star to ~10 km Core rotating, magnetic field Angular Momentum Conservation Core rotation speeds up to P ~ sec Magnetic field frozen-in Magnetic field increases to ~10 12 G = pulsar ~10 14 G = magnetar New NSs rotate rapidly, highly magnetized
15 Pulsar Model (Cont.) Most astrophysical objects have magnetic fields which are (at least) slightly miss-aligned with their rotation axis. Earth, Sun, other planets, most stars Rotating magnets = changing B field = generator NS with P ~ sec, B ~ G generates V!! Pull particles [electrons, positrons, protons(?)] from NS Beams of particles shoot out along field lines, radiate Rotating beams of emission, lighthouse
16 Pulsar Model
17 Pulsar Model
18 Pulsar Model
19 Fermi Gamma-Only Pulsars
20 How Does Pulsar Power Crab Nebula? Pulsar Wind Nebulae red = optical blue = X-ray
21 Crab Chandra Xray Pulsar Wind Nebulae
22 Pulsar Wind Nebulae
23 Pulsar Wind Nebulae Vela Pulsar Chandra Xray
24 Related Neutron Stars
25 P-Pdot diagram Related Neutron Stars
26 P-Pdot diagram Age (dash) Magnetic field (dashdot) Spin-down luminosity (dash-dot) Line of Death (solid) Related Neutron Stars
27 Young radio pulsars Crab, Vela Often still in supernova remnants (stars) Related Neutron Stars
28 Young radio pulsars Crab, Vela Often still in supernova remnants (stars) Related Neutron Stars Crab pulsar
29 Young radio pulsars Crab, Vela Often still in supernova remnants (stars) Related Neutron Stars Vela pulsar
30 Young radio pulsars Crab, Vela Often still in supernova remnants (stars) Related Neutron Stars
31 Young radio pulsars Crab, Vela Often still in supernova remnants (stars) Normal, middle aged radio pulsars Related Neutron Stars
32 Life history of normal radio pulsar Born fast, strong magnetic field Slow down, B gets weaker Stops emitting pulses Related Neutron Stars
33 Millisecond Radio Pulsars Very fast rotation Very weak magnetic field Very Accurate Clocks Many in globular clusters Most are binaries (circles) Related Neutron Stars
34 Millisecond Pulsars in Globular Cluster
35 Millisecond Radio Pulsars Very fast rotation Very weak magnetic field Very Accurate Clocks Many in globular clusters Most are binaries (circles) Not on life track of normal radio pulsars How are they made? Related Neutron Stars
36 Magnetars Very Strong Magnetic Field Slow rotation NOT RADIO PULSARS X-ray Sources Soft Gamma Repeaters Powered by magnetic energy, not rotation Related Neutron Stars
37 Magnetars Very Strong Magnetic Field Slow rotation NOT RADIO PULSARS X-ray Sources Soft Gamma Repeaters Powered by magnetic energy, not rotation Related Neutron Stars
38 Magnetars Very Strong Magnetic Field Slow rotation NOT RADIO PULSARS X-ray Sources Soft Gamma Repeaters Powered by magnetic energy, not rotation Related Neutron Stars
39 Magnetars Very Strong Magnetic Field Slow rotation NOT RADIO PULSARS X-ray Sources Soft Gamma Repeaters Powered by magnetic energy, not rotation Related Neutron Stars
40 Anti-Magnetars Weak Magnetic Field Fast rotation? NOT RADIO PULSARS X-ray Sources Central source in Cas-A SNR Related Neutron Stars
41 Anti-Magnetars Weak Magnetic Field Fast rotation? NOT RADIO PULSARS X-ray Sources Central source in Cas-A SNR Related Neutron Stars
42 End of Material for Test 2
43 Compact Binaries ASTR2110 Sarazin
44 Neat Dead Stars White Dwarf (WD) Neutron Star (NS) Black Hole (BH) But, dead, so no energy = no light?
45 Binary Stars! 1/2 of stars are in binaries More massive star will die first Second star will become a giant, dump gas onto stellar corpse Accreting WDs = Cataclysmic Variables = CVs Accreting NSs or BHs = X-ray Binaries
46 Stellar Evolution in Close Binaries Close a radius of giant star ~ AU, P year Tidal Evolution Close strong tidal distortion of stars
47 Stellar Evolution in Close Binaries Close a radius of giant star ~ AU, P year Tidal Evolution Close strong tidal distortion of stars Tidal Friction Synchronize rotation, orbit Circular orbit Rotation axes aligned Rotation axes = orbital axis P rot = P orb Lowest energy state Moon is an example, many others in the Solar System
48 Roche Geometry Go to rotating frame on CM, P = P rot = P orb everything is stationary Need to include centrifugal acceleration, Coriolis effect Define effective potential energy as gravity of two stars plus centrifugal acceleration
49 Roche Potential PE = Potential Energy orbital plane
50 Shapes of Stars in Binaries Single non-rotating star = sphere What is shape of star with rotation, and/or in binary? At surface, P = 0 no pressure forces along surface No gravitational + centrifugal force parallel to surface or material would move F
51 Shapes of Stars in Binaries No gravitational + centrifugal force parallel to surface ΔPE = F ds along surface = 0 PE = constant on stellar surface, including all gravity and centrifugal forces Stellar surfaces are equipotentials
52 Roche Potential PE = Potential Energy orbital plane
53 Roche Potential Project equipotentials onto orbital plane
54 Shapes of Stars in Binaries Small stars = spheres Larger stars distorted, egg-shaped Equipotentials in orbital plane
55 Shapes of Stars in Binaries Small stars = spheres Larger stars distorted, egg-shaped
56 Shapes of Stars in Binaries Small stars = spheres Larger stars distorted, egg-shaped Roche lobe = separate regions for two stars Roche lobes meet at Inner Lagrangian Point L1 Equipotentials in orbital plane (5 Lagrangian points, where force = 0)
57 Mass Transfer in Binaries Higher mass star bigger Roche lobe If a star expands, material will first pass through L1 to other star Mass Transfer If M tot = M 1 + M 2 = constant and angular momentum is conserved, mass transfer decreases size of Roche lobe of losing star R 1 minimum when M 1 /M tot = 0.4 Mass transfer continues until more massive star becomes least massive
58 Stellar Evolution in Binaries 1. Two stars form in a close binary a R 1 (giant), M 1 M 2 2. Tidal Friction Synchronize rotation, orbit 3. Star 1 evolves first, becomes giant, overflows Roche lobe, mass transfer to star 2 4. Mass transfer continues until M 1 < (2/3) M 2 More massive star (initially) becomes least massive
59 Algol Paradox In many close binary star systems, there is a lower mass evolved star and a higher mass main sequence star. Algol: eclipsing binary with lower mass K giant star and higher mass B main sequence star Mystery (originally): why didn t the more massive star become a giant first?
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