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Home , Black dwarf, Chandrasekhar limit, Helium flash

Discovery of • Discovered by Jocelyn Bell and Tony Hewish in 1967. • The signal was extremely regular (at about 3 pulses per second). • Little Green Men? No. – While av. very constant, pulses individually irregular – no modulation – broad-band – no planetary motion

PSR 1919+21 as a rotating

• Neutron are the only type of objects known to be capable of such a rapid and strictly periodic signal (1 part in 1012 ). • Beamed radiation from is modulated by the rotation. • Isolated neutron stars radiate energy via slowing Period down of rapid spinning motion (P usually < 1 sec, dP/dt>0) pulse • For Crab pulsar: P = 0.033 s, dP/dt=3 x 10-11 s-1 ~P/10 interpulse Rotating neutron star

• Gravitational force > centrifugal force GMm/r2 > mv2/r where M=4/3πr3ρ and v= 2πr/P Æ ρ > 3π/(GP2) = 1.3 x 1011 g/cm3 for the Crab pulsar This is too high for a dwarf (which has a of ~ 106 g/cm3), so it must be a neutron star. • The energy lost by the pulsar dE/dt ~ ½ (2/5MR2)(2π/P)2 – Assuming M~1 solar, R = 10 km for the Crab pulsar dE/dt ~ 3 x 1038 ergs/s – Greater than that inferred from the observed emission (e.g., the 2-20keV range) ~ 1.5 x 1037 ergs/s – Thus, the pulsar can power the nebula. Neutron Star Magnetic Field

Magnetic field induction Æ high B of NS • A radius collapse from 7 x 105 km () to 10 km

4 2 Bns ~ (7 x 10 ) BSun 2 • For the general BSun ~ 10 G, 11 Bns ~ 5 x 10 G • The B force

FB~ eVB ~ 0.3 dyn is a factor of ~ 1013 larger than the gravitational 2 -14 force Fg = GmeM/r ~ 10 dyn.

Thus FB dominates the particle distribution near a NS. Neutron star magnetosphere

Light cylinder • Magnetic axis and rotation axis cannot be co-aligned for a pulsar. ω r=c/ω • Electric field induced Open immediately outside NS surface field 8 (E ~ 2 x 10 B12/P) accelerates particles to very high energy Æ Outer gap cosmic rays • This alters the plasma NS distribution and magnetic field configuration. • charged particles are "guided" and accelerated by magnetic field Æ radiation beams from poles and outer gaps. Radiation Mechanisms

Radio beam

r=c/ω cylinder

Closed magnetosphere

X-ray beam Irregularities in pulsar emission

• Short timescales - pulsar slow-down rate is remarkably uniform. • Longer timescales - irregularities apparent - in particular, ‘glitches’ - discontinuous changes of period. • Glitches are caused by sudden angular momentum transfer from the faster rotating superfluid core to the slowed-down “ normal” surface crust. •For example, ∆P/P ~ 10-10 is the typical observed value for the Crab pulsar. P

t PSR J0537-6910 (16 ms pulsar)

Timing residuals PSR B1913+16 Hulse & Taylor •The orbital period of the binary pulsar decreases with time • This proves the existence of gravitational waves and gave to Hulse & Taylor the Nobel price in 1993.

Taylor J.H. 1993, Pulsar Population

• τ ~ P/(dP/dt) is known as “characteristic age” of a pulsar (e.g., τ ~ 2000 years for Crab) • In reality, may be longer than the real age. • Pulsar characteristic lifetime ~ 107 years • Total # of observable pulsars ~ 5 x 104 • To sustain this population then, 1 pulsar must form every 50 years. cf SN rate of 1 every 50 years • only ~10 pulsars associated with visible SNRs (pulsar lifetime 1-10 x 107 yrs, SNRs 1-10 x 104 yrs ... so consistent) • But not all SN may produce pulsars! Pulsars: summary • Pulsar can be thought of as a non-aligned rotating magnet. • Electromagnetic forces dominate over gravitational in magnetosphere. • Field lines which extend beyond the light cylinder are open. • Particles escape along open field lines, accelerated by strong electric fields. • Even if a plasma is absent, a pulsar radiates as a rotating non-aligned magnet (e.g., magnetic dipole model). • The energy loss slows down the pulsar except for glitches. • binary companion => rising from the dead again ! Lab Assignment 2

• Suggested targets: – NGC 4594 (except for the nuclear source; Pellegrini et al. 2002) – NGC 4945 (except for the nuclear source; Schurch et al. 2002) – NGC 1068 (except for the nuclear source; Young et al. (2001) Compact Objects

• White Dwarfs, neutron stars, and black holes • White dwarfs are fairly common (~ 6 ×10-3 pc-3, or about 50 within 40 light years of the Sun). • The majority of the 100 brightest objects on the X-ray sky are accreting binaries with , neutron star, or primaries • Neutron stars in the form of rotation powered pulsars are among the most conspicuous objects on the radio sky. • They are extreme objects, with of the order of 106 gcm-3 (white dwarfs) and 4×1014 gcm-3 (neutron stars), respectively • They serve as a laboratory for physics under extreme conditions. White Dwarf (WD) WD: Formation

• End product of Sun-like stars. During their MS phase, ``ash'' builds up. • Nursed in low-mass stars. During shell burning, the helium core contracts and becomes fully degenerate • (exclusion) degeneracy opposes • pressure ∝ density, but NOT ∝ temperature (like for gas) • Normal, steady, not allowed in . Thus fusion occurs in a runaway (eg, ) WD: stage

Shedding the extended atmosphere => the ``planetary nebula'' stage WD: Mass

• An O-Ne-Mg degenerate core (leading to a ~ 1Msun WD)

• C-O core ( ~ 0.6 Msun WD) • or a He core (lower mass WD, but rare because universe is still too young).

•if M > 1.4 MSUN gravity wins () => collapse followed by explosion ()

No White Dwarfs with M > 1.4 MSUN ! WD: evolution

Young white dwarfs have plenty of internal thermal energy left from the nuclear fusion; they radiate it away and cool over the next billions of years. • initially very hot ~ 105 K (surface), rapidly cool to ~ 104 K (over millions of years) • finally, cool off (and dim) to become • If the mass of a white dwarf (in an accreting binary) increases beyond the Chandrasekhar limit, it will cause either: – Complete detonation of the white dwarf = . – Induced Collapse, forming a neutron star. WD: Structure Gas Properties at “low T”

• No two can occupy the same quantum mechanical states (=Pauli's exclusion principle). • Distribution function of ideal gas is: -1 • f(E) = [exp((E-EF)/kT)±1] – plus sign for Fermions – negative sign for Bosons. • For both types, at high enough temperature (kT >>

EF) and low enough pressure, the distribution becomes Maxwellian (f(E) ∝ exp((EF-E)/kT)). • Fermions at the low temperature limit fills all

states up to E = EF and none have higher energies (=complete degeneracy). of Number of quantum states in a phase space

dxdydzdpx dp y dpz dN = 2 3 (2πh) Total number of quantum states (or total number of particles of a Fermi gas at T = 0 K) pF 4πp 2dpV Vp 3 N = 2 = F ∫ 3 2 3 0 (2πh) 3π h 1 Total energy pF 4πp 2dpV E = ε 2 ε ∫ 3 F 0 (2πh) kT ε where ε is the particle energy p 2 DEGENERACY TEMPERATURE ε = for a non - relativistic case 2m kT ≈ ε =p 2/2m = cp for a relativistic case F F F Statistical Physics by Landau & Lifshitz Equation of state of Fermi gas (cont.) Pressure : 5/3 2E (3π 2 ) 2 / 3 2  N  P = = h   for a non - relativistic case 3V 5m  V  4/3 1E (3π 2 )1/ 3 c  N  = = h   for a relativistic case 3V 4  V  where N ρ = V µ Therefore,the equation of state P = κρ γ where γ = 5/3 (non - relativistic)or = 4 / 3 (relativistic), corresponding to polytropic index n = 3/2 and = 3, respectively. Chandrasekhar limit These equations allow for the calculation of the density as a dP GMρ function of radius r. = − dr r 2 For example (see Longair Vol 2, section 15.3), Mass consservation 2n/(1-n) ρc ∝ R dM M ∝ρR3 ∝ R(3-n)/(1-n) = 4πr 2 ρ c dr Thus M ∝ R-3, if n=3/2.

As M↑, R↓ and ρc↑, until a critical M is research, nÆ 3 (relativisitic), when M is independent of R. The critical

mass is the Chandrasekhar Mch = 1.46 . Basic properties of a neutron star

• radius ~ 10 km • mass ~ 1-3 MSUN (cannot be more or Black Hole) • density ~ billion tons/cm3 => solid => low (dim) • super strong magnetic field (rotation + squeezing) ~ 1012 times Earth • extremely rapid rotation P ~ 0.01 seconds Black Holes in General Relativity

• the spherically symmetric solution for a single mass (Schwarzschild metric in natural units; G = c = 1): ds2 = - (1-2M/r) dt2+ (1-2M/r)-1 dr2 + r2 dθ2+ r2 sin2 θdφ2 • The , 2 Rs = 2GM/c ∼ 3 [M/( M\odot )] km. defines the event horizon. – Once inside the event horizon, no light nor particle can escape to the outside: thus, J.C. Wheeler coined the term, black hole. – Objects just outside an event horizon are seen to experience severe time dilation by an observer at infinity. • A singularity at the center of a black hole -- a point of infinite density, where the known laws of physics break down. • Black holes can have only three measurable properties: mass, spin, and charge. • Real black holes are unlikely to accumulate a significant charge, but spinning black holes (described by the Kerr metric) are highly likely. • By definition, black holes emit no radiation, except for the probably tiny Hawking radiation due to a quantum process that converts some of their mass into radiation (splitting virtual particle- antiparticle pairs) • They may be inferred from gravitational waves from double compact stars, binary systems with missing companion, X-ray emission from hot gas (106 K) in