PHY688, Neutron Stars and Pulsars

James Lattimer

Department of Physics & Astronomy 449 ESS Bldg. Stony Brook University

March 7, 2017

James Lattimer PHY688, Neutron Stars and Pulsars Pulsars: The Early History

1932 Landau suggests the existence of giant nucleus stars. 1932 Chadwick discovers the neutron. 1934 Baade & Zwicky predicts the existence of neutron stars as the end products of supernovae. 1939 Oppenheimer and Volkoff predict the upper mass limit of neutron star. 1964 Hoyle, Narlikar and Wheeler predict neutron stars rapidly rotate. 1964 Prediction that neutron stars have intense magnetic fields. 1966 Colgate and White incorporate neutrinos into supernova hydrodynamics. 1966 Wheeler predicts the Crab nebula is powered by a rotating neutron star. 1967 Pacini makes the first magnetic pulsar model. 1967 C. Schisler discovers a dozen pulsing radio sources, including one in the Crab pulsar, using secret military radar in Alaska. 1967 Hewish et al. discover the pulsar PSR 1919+21, Aug 6. 1968 Discovery of a pulsar in the Crab Nebula which was slowing down, ruling out binary models. Also clinched the connection with core-collapse supernovae. 1968 T. Gold identifies pulsars with rotating magnetized neutron stars. 1968 The term “pulsar” first appears in print, in the Daily Telegraph. 1969 Vela pulsar glitches observed; evidence for superfluidity in neutron stars. 1971 Accretion powered X-ray pulsar discovered by Uhuru (not the Lt.). 1974 Hewish awarded Nobel Prize (but Jocelyn Bell Burnell was not).

James Lattimer PHY688, Neutron Stars and Pulsars Pulsars: Later Discoveries 1974 Lattimer & Schramm suggest neutron star mergers make the r-process. 1974 First binary pulsar, PSR 1913+16, discovered by Hulse and Taylor. 1979 Taylor et al. observe orbital decay due to gravitational radiation in the PSR 1913+16 system, leading to their Nobel Prize in 1993. 1979 Chart recording of PSR 1919+21 used as album cover for Unknown Pleasures by Joy Division (#19/100 greatest British albums ever). 1982 First millisecond pulsar, PSR B1937+21, discovered by Backer et al. 1992 Wolszczan and Frail discover the first extra-solar planets, orbiting PSR B1257+12. 1988 First black widow pulsar, PSR 1957+20, discovered by Fruchter et al. 1992 Duncan & Thompson predict existence of magnetars. 1994 Discovery of PSR J0108-1431 which has the lowest known dispersion measure and is possibly the closest known pulsar. 2004 Largest burst of energy in our Galaxy since Kepler’s SN 1604 is observed from magnetar SGR 1806-20. It was brighter than the full moon in gamma rays and radiated more energy in 0.1 second than the Sun does in 100,000 years. 2004 Hessels et al. discover the fastest (716 Hz) pulsar, PSR J1748-2446ad. 2005 Burgay et al. discover the first binary with two pulsars, PSR J0737-3039. 2013 Measurement of largest n.s. mass, 2.01 M , for PSR J0348+0432. 2013 Ransom et al. discover a pulsar in a triple system with 2 white dwarfs. 2014 Bachetti et al. discover the first ultraluminous pulsar, has L ∼ 100LEdd .

James Lattimer PHY688, Neutron Stars and Pulsars sleevage.com/joy-division-unknown-pleasures

James Lattimer PHY688, Neutron Stars and Pulsars Magnetic Dipole Model for Pulsars

A misaligned magnetic dipole (α > 0) emits low-frequency electromagnetic radiation. Larmor formula for electric dipoles (charge q, accelerationv ˙ ) is 2q2v˙ 2 2 2¨p2 P = = (q¨r sin α)2 = ⊥ rad 3c2 3c3 3c2

where p⊥ is the perpendicular component of the electric dipole moment. A uniformly magnetized sphere with radius R and surface ﬁeld B has a magnetic dipole moment |m| = BR3, and if rotating with period P = 2π/Ω, has m = |m|e−iΩt and |m¨ | = Ω2|m|. By analogy to an electric dipole, 2 m¨ 2 2 “ ”2 „ 2π «4 P = ⊥ = BR3 sin α rad 3 c3 3c2 P This radiation appears at the low frequency ν = P−1 < 1 kHz, too low to propagate throught the ionized ISM and be detected. The total rotational energy and spin-down power, using I = (2/5)MR2, are „ «„ «2 „ «2 1 2 50 M R 10 ms Erot = I Ω ' 1.6 · 10 erg, 2 M 10 km P „ «„ «2 „ «3 „ ˙ « ˙ 40 M R 10 ms −P −1 Prot = −I ΩΩ ' 1.6 · 10 −12 erg s . M 10 km P 10

James Lattimer PHY688, Neutron Stars and Pulsars Magnetic Fields and Ages

Setting Prad = −Prot , one ﬁnds s s 3 ˙ „ «2 ˙ 3c IPP 1 1 12 10 km M P P B = 2 3 2 ' 2.9 · 10 −12 G 8π R sin α R sin α M .01 s 10 which is a minimum value since sin α < 1. The characteristic age is estimated by assuming PP˙ ' constant, or Z P Z τ P2 − P2 PdP = PP˙ dt = PP˙ τ = 0 , 2 P0 0

giving, with P0 >> P, P P 10−12 τ = ' 158 yr. 2P˙ .01 s P˙ A death line exists when the voltage V ∝ BΩ2 near the polar cap drops below that needed to generate e+e− pairs: BR3Ω2 B „ 0.01 s «2 „ R «3 Φ = ' 6.6 · 1016 V. 2c2 1012 G P 10 km

−2 p −3 −2 12 −2 Note BP ∝ PP˙ ∝ Prot . Death line is where BP ∼ 0.2 · 10 G s . A log P˙ − log P diagram for pulsars is like an H-R diagram for stars. James Lattimer PHY688, Neutron Stars and Pulsars The P − P˙ Diagram

p B ∝ PP˙ τ ∝ P/P˙ −3 Prot ∝ P P˙

The “death line” is 30 −1 Prot ∼ 10 erg s

James Lattimer PHY688, Neutron Stars and Pulsars Distances to Pulsars

Pulsars can probe the ISM, which is a plasma with a refractive index

r 2 r 2 r “ ωp ” 4πe ne ne µ = 1 − , ωp = ' 8.97 −3 kHz 2πν me cm

where ωp is the plasma frequency. −3 Typically, ne ∼ 0.03 cm and ωp/(2π) ∼ 1.5 kHz.

When 2πν < ωp, µ is imaginary and photons cannot propagate.

The group velocity vg = µc < c. When 2πωp << ν,

„ 2π2ω2 « v ' c 1 − p , g ν2

an increasing function of frequency. Lorimer & Kramer This produces a dispersion delay Z d dx d e2DM Z d td = − ' 2 , DM ≡ ne dx is the disperson measure. 0 vg c 2πme cν 0

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James Lattimer PHY688, Neutron Stars and Pulsars Binary Mass Measurements X-ray timing Mass function 3 P(v2 sin i) f (M1) = 2πG 3 (M1 sin i) = 2 (M1+M2) > M1 3 P(v1 sin i) f (M2) = 2πG 3 (M2 sin i) = 2 (M1+M2) Optical spectroscopy > M2 In an X-ray binary, voptical has the largest uncertainties. In some cases sin i ∼ 1 if eclipses are observed. If no eclipses observed, limits to i can be made based on the estimated radius of the optical star.

James Lattimer PHY688, Neutron Stars and Pulsars Pulsar Mass Measurements Mass function for pulsar precisely obtained. It is also possible in some cases to obtain the rate of periastron advance and the combined

eﬀects of variations in the transverse ◦ −1 Doppler eﬀect and the gravitational 17 yr in PSR 0737 redshift around an elliptical orbit: 3 2π 5/3 GM 2/3 ω˙ =1−e2 P c2 2/3 P 1/3 G γ = 2π eM2(M + M2) M2c2 Gravitational radiation leads to orbit decay: 5/3 P˙ = −192π 2πG (1 − e2)−7/2 1 + 73 e2 + 37 e4 M1M2 5c5 P 24 96 M1/2 In edge-on systems, it’s possible to detect Shapiro time delay, with parameters r (imagnitude) and s = sin i (shape).

James Lattimer PHY688, Neutron Stars and Pulsars PSR J0737-3039

PSR J0737-3039 Kramer et al. (2007)

James Lattimer PHY688, Neutron Stars and Pulsars PSR J1614-2230

3.15 ms pulsar in 8.69d orbit with 0.5 M white dwarf companion. Shapiro delay tightly conﬁnes the edge-on inclination: sin i = 0.99984 Pulsar mass is 1.97 ± 0.04 M Distance > 1 kpc, B ' 1.8 × 108 G ) s µ ( t

∆ Demorest et al. 2010

James Lattimer PHY688, Neutron Stars and Pulsars Shapiro Time Delay

Shapiro delay produces a delay in pulse arrival times

δ (φ) » 1 + e cos φ – S = ln 2M2T 1 − sin(ω + φ) sin i with φ the true anomaly, the orbital angular parameter deﬁning the position of the pulsar relative to the periastron position ω. GM T = = 4.9255 µs c3

δS is a periodic function with approximate amplitude

˛ ˛ ˛ »„ 1 + e sin ω «„ 1 + sin i «–˛ ˛ ˛ ∆S ' 2M2T ˛ln ˛. ˛ 1 − e sin ω 1 − sin i ˛ This is large only if sin i ∼ 1 or if both e and sin ω are nearly unity.

James Lattimer PHY688, Neutron Stars and Pulsars van Kerkwijk 2010 Romani et al. 2012 Martinez et al. 2015

Although simple average mass of w.d. companions is 0.23 M larger, weighted average is only 0.07 M larger.

Demorest et al. 2010 Fonseca et al. 2016 Antoniadis et al. 2013 Barr et al. 2016

Champion et al. 2008

James Lattimer PHY688, Neutron Stars and Pulsars Black Widow Pulsar PSR B1957+20

A 1.6ms pulsar in circular 9.17h orbit with ∼ 0.03 M companion. The pulsar is eclipsed for 50-60 minutes each orbit; the eclipsing object has a volume much larger than the secondary or its Roche lobe. The pulsar is ablating the companion leading to mass loss and the eclipsing plasma cloud. The secondary may nearly ﬁll its Roche lobe. Ablation by the pulsar leads to secondary’s eventual disappearance. The optical light curve tracks the motion of the secondary’s irradiated hot spot rather than its center of mass motion. pulsar radial velocity

eclipse

NASA/CXC/M.Weiss James Lattimer PHY688, Neutron Stars and Pulsars Black Widow Pulsar PSR B1957+20

The peak radial velocity of the center of mass of component i is: ai sin i Ki = 2π P 0.045 MP a∗ K∗ obs q = = = K M a K = ∗ P P 2 0.040 K R∗ 0 K obs K∗ = Kobs 1 + = a∗ → K L1 0.035 ∗ ) Companion’s hot spot has ¡ R 1 L

a smaller orbit than its (M R

= ¢ center of mass. Comp 0.030 R ∗ M =45 3 i 2 P KP MP = q(1+q) 2πG sin i 0.025 £ i =60 Modeling of light curve ¤ i =75 shape suggests that 0.020 ◦ MP > 1.8M , sin i < 66 Most probable values: 1.0 1.5 2.0 2.5 3.0

MPSR (M ) 2.20M < MP < 2.55M van Kerkwijk 2010

James Lattimer PHY688, Neutron Stars and Pulsars Companion Light Curves and Radial Velocity

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20.5 0 -0.2 0 0.5 1 1.5 2 21 0 0.5 1 1.5 2 Phase James Lattimer PHY688, Neutron Stars and Pulsars System Masses Radial velocity amplitudes: Ki = 2πai sin i/P 0.045

◦ obs Light curve shape ⇒ i ' 65 ± 2 K XX = 2 X0.040X K XXX K1 = 5.093 km/s, Kobs = 324±3 km/s X K obs XX = 0 = X L1 XX ∗ K 0.035 X R ) ¡ XXz

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M =45 K∗ ' Kobs (1 + R∗/a∗) i = R ∗ G(M +M )P2 = (4π)2(a +a )3 0.025 £ P ∗ P ∗ i =60 ¤ van Kerkwijk 2010 2/3 i =75 RL1 = 0.46ap(1 + q) 0.020

3 2 P KP 1.0 1.5 2.0 2.5 3.0

M = q(1 + q) M (M ) P 2πG sin i PSR

2 3 3 2π (aP sin i) (M∗ sin i) −6 = 2 = 5.2×10 M P G (MP + M∗)

James Lattimer PHY688, Neutron Stars and Pulsars Another Black Widow Pulsar

PSR J1311-3430

Romani et al. 2012

James Lattimer PHY688, Neutron Stars and Pulsars Pulsars

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