Pulsars ASTR2110 Sarazin. Crab Pulsar in X-rays

Pulsars ASTR2110 Sarazin Crab Pulsar in X-rays

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

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.)

Material: Test #2 (Cont.) Chapters 5, 7, 13.5-13.7, 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

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

Pulsars ASTR2110 Sarazin Crab Pulsar in X-rays

Pulse Profile: Radio

Pulsars: Properties mid 1968 Periods: P = 0.2 2 seconds d P / dt < 10-13 sec/sec, very good clock dp/dt > 0, pulses slowing very slightly Pulse duration >~ 20 ms

Pulsars = Rotating Neutron Stars

Crab Pulsar

Crab Pulsar 1968 P = 0.033 sec dp/dt = 4 x 10-13 t slow ~ P/(dP/dt) ~ 2000 years ~ time since supernova Decrease in rotational kinetic energy = energy from Crab Nebula

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 10 38 erg/s ~ energy from Crab Nebula Energy for pulsar, nebula due to rotational kinetic energy of neutron star 1.4 M 8 10 km

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 ~ 0.001 sec Magnetic field frozen-in Magnetic field increases to ~10 12 G = pulsar ~10 14 G = magnetar New NSs rotate rapidly, highly magnetized

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 ~ 0.001 sec, B ~ 10 12 G generates 10 20 V!! Pull particles [electrons, positrons, protons(?)] from NS Beams of particles shoot out along field lines, radiate Rotating beams of emission, lighthouse

Pulsar Model

Fermi Gamma-Only Pulsars

How Does Pulsar Power Crab Nebula? Pulsar Wind Nebulae red = optical blue = X-ray

Crab Chandra Xray Pulsar Wind Nebulae

Pulsar Wind Nebulae

Pulsar Wind Nebulae Vela Pulsar Chandra Xray

Related Neutron Stars

P-Pdot diagram Related Neutron Stars

P-Pdot diagram Age (dash) Magnetic field (dashdot) Spin-down luminosity (dash-dot) Line of Death (solid) Related Neutron Stars

Young radio pulsars Crab, Vela Often still in supernova remnants (stars) Related Neutron Stars

Young radio pulsars Crab, Vela Often still in supernova remnants (stars) Related Neutron Stars Crab pulsar

Young radio pulsars Crab, Vela Often still in supernova remnants (stars) Related Neutron Stars Vela pulsar

Young radio pulsars Crab, Vela Often still in supernova remnants (stars) Related Neutron Stars

Young radio pulsars Crab, Vela Often still in supernova remnants (stars) Normal, middle aged radio pulsars Related Neutron Stars

Life history of normal radio pulsar Born fast, strong magnetic field Slow down, B gets weaker Stops emitting pulses Related Neutron Stars

Millisecond Radio Pulsars Very fast rotation Very weak magnetic field Very Accurate Clocks Many in globular clusters Most are binaries (circles) Related Neutron Stars

Millisecond Pulsars in Globular Cluster

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

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

Anti-Magnetars Weak Magnetic Field Fast rotation? NOT RADIO PULSARS X-ray Sources Central source in Cas-A SNR Related Neutron Stars

End of Material for Test 2

Compact Binaries ASTR2110 Sarazin

Neat Dead Stars White Dwarf (WD) Neutron Star (NS) Black Hole (BH) But, dead, so no energy = no light?

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

Stellar Evolution in Close Binaries Close a radius of giant star ~ AU, P year Tidal Evolution Close strong tidal distortion of stars

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

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

Roche Potential PE = Potential Energy orbital plane

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

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

Roche Potential PE = Potential Energy orbital plane

Roche Potential Project equipotentials onto orbital plane

Shapes of Stars in Binaries Small stars = spheres Larger stars distorted, egg-shaped Equipotentials in orbital plane

Shapes of Stars in Binaries Small stars = spheres Larger stars distorted, egg-shaped

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)

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

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

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?