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?