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PulsarsASTR2110
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.)
Test #2 (Cont.) Material:
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.) Material:
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) 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
PulsarsASTR2110
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
tslow ~ 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 Ω2 = (1/2) I (2π/P)2
I = moment of inertia ~ M R2 ~1045 gm cm2
Decrease in rotational kinetic energy ~ 2 x 1038 erg/s ~ energy from Crab Nebula
Energy for pulsar, nebula due to rotational kinetic energy of neutron star
10 km
1.4 M8
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
~1012 G = pulsar ~1014 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 ~ 1012 G generates 1020 V !! Pull particles [electrons, positrons, protons(?)] from NS Beams of particles shoot out along field lines, radiate
Rotating beams of emission, lighthouse
Pulsar Model
Pulsar Model
Pulsar Model
Fermi Gamma-Only Pulsars
How Does Pulsar Power Crab Nebula?
Pulsar Wind Nebulae
red = optical
blue = X-ray
Pulsar Wind Nebulae
Crab
Chandra Xray
Pulsar Wind Nebulae
Pulsar Wind Nebulae – Vela Pulsar
Chandra Xray
Related Neutron Stars
Related Neutron Stars
P-Pdot diagram
Related Neutron Stars
P-Pdot diagram Age (dash) Magnetic field (dash-dot) 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)
Crab pulsar
Related Neutron Stars
Young radio pulsars Crab, Vela Often still in supernova remnants (stars)
Vela pulsar
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)
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)
Millisecond Pulsars in Globular Cluster
Related Neutron Stars
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
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
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
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
Anti-Magnetars Weak Magnetic Field Fast rotation? NOT RADIO PULSARS X-ray Sources Central source in Cas-A SNR
End of Material for Test 2
Compact BinariesASTR2110
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 • Prot = Porb • Lowest energy state • Moon is an example, many others in the Solar System
Roche Geometry • Go to rotating frame on CM, P = Prot = Porb →
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
Equipotentials in orbital plane
• Small stars = spheres
• Larger stars distorted, egg-shaped
Shapes of Stars in Binaries
• Small stars = spheres
• Larger stars distorted, egg-shaped
Shapes of Stars in Binaries
Equipotentials in orbital plane
• Small stars = spheres
• Larger stars distorted, egg-shaped
• “Roche lobe” = separate regions for two stars
• Roche lobes meet at “Inner Lagrangian Point” L1
• (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 Mtot = M1 + M2 = constant and angular momentum is conserved, mass transfer decreases size of Roche lobe of losing star
• R1 minimum when M1/Mtot = 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 ≲ R1 (giant), M1 ≥ M2
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 M1 < (2/3) M2
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?