PHY688, Neutron Stars and Pulsars - Stony Brook UniversityPHY688, Neutron Stars and Pulsars James Lattimer Department of Physics & Astronomy 449 ESS Bldg. Stony Brook University March

PHY688, Neutron Stars and Pulsars

James Lattimer

Department of Physics & Astronomy449 ESS Bldg.

Stony Brook University

March 7, 2017

Nuclear Astrophysics [email protected]

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 endproducts 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 theCrab 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, rulingout 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).


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 thePSR 1913+16 system, leading to their Nobel Prize in 1993.1979 Chart recording of PSR 1919+21 used as album cover for UnknownPleasures 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 PSRB1257+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 dispersionmeasure and is possibly the closest known pulsar.2004 Largest burst of energy in our Galaxy since Kepler’s SN 1604 is observedfrom magnetar SGR 1806-20. It was brighter than the full moon in gamma raysand 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 .


sleevage.com/joy-division-unknown-pleasures


Magnetic Dipole Model for Pulsars

A misaligned magnetic dipole (α > 0) emits low-frequency electromagneticradiation. Larmor formula for electric dipoles (charge q, acceleration v) is

Prad =2q2v 2

3c2=

2

3c3(qr sinα)2 =

2p2⊥

3c2

where p⊥ is the perpendicular component of the electric dipole moment.

A uniformly magnetized sphere with radius R and surface field B has amagnetic 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,

Prad =2

3

m2⊥

c3=

2

3c2

“BR3 sinα

”2„

2π

P

«4

This radiation appears at the low frequency ν = P−1 < 1 kHz, too low topropagate throught the ionized ISM and be detected.

The total rotational energy and spin-down power, using I = (2/5)MR2, are

Erot =1

2IΩ2 ' 1.6 · 1050

„M

M

«„R

10 km

«2„10 ms

P

«2

erg,

Prot = −IΩΩ ' 1.6 · 1040

„M

M

«„R

10 km

«2„10 ms

P

«3„ −P

10−12

«erg s−1.


Magnetic Fields and Ages

Setting Prad = −Prot , one finds

B =

s3c3IPP

8π2

1

R3

1

sin2 α' 2.9 · 1012

„10 km

R sinα

«2s

M

M

P

.01 s

P

10−12G

which is a minimum value since sinα < 1.

The characteristic age is estimated by assuming PP ' constant, orZ P

P0

PdP = PP

Z τ

0

dt = PPτ =P2 − P2

0

2,

giving, with P0 >> P,

τ =P

2P' 158

P

.01 s

10−12

Pyr.

A death line exists when the voltage V ∝ BΩ2 near the polar cap drops belowthat needed to generate e+e− pairs:

Φ =BR3Ω2

2c2' 6.6 · 1016 B

1012 G

„0.01 s

P

«2„R

10 km

«3

V.

Note BP−2 ∝p

PP−3 ∝ Prot . Death line is where BP−2 ∼ 0.2 · 1012 G s−2.

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

B ∝√

PPτ ∝ P/PProt ∝ P−3P

The “death line” isProt ∼ 1030 erg s−1


Distances to Pulsars

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

µ =

r1−

“ ωp

2πν

”2

, ωp =

r4πe2ne

me' 8.97

rne

cm−3kHz

where ωp is the plasma frequency.

Typically, ne ∼ 0.03 cm−3 andωp/(2π) ∼ 1.5 kHz.

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

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

vg ' c

„1−

2π2ω2p

ν2

«,

an increasing function of frequency.

This produces a dispersion delay

Lorimer & Kramer

td =

Z d

0

dx

vg− d

c' e2DM

2πmecν2, DM ≡

Z d

0

nedx is the disperson measure.


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Zhang & Xie


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Binary Mass Measurements

Mass function

f (M1) =P(v2 sin i)3

2πG

=(M1 sin i)3

(M1+M2)2

> M1

f (M2) =P(v1 sin i)3

2πG

=(M2 sin i)3

(M1+M2)2

> M2

In an X-ray binary, voptical has thelargest uncertainties. In somecases sin i ∼ 1 if eclipses areobserved. If no eclipses observed,limits to i can be made based onthe estimated radius of theoptical star.

X-ray timing

Optical spectroscopy


Pulsar Mass Measurements

Mass function for pulsar precisely obtained.It is also possible in some cases to obtain the rate ofperiastron advance and the combinedeffects of variations in the transverseDoppler effect and the gravitationalredshift around an elliptical orbit:

ω = 31−e2

(2πP

)5/3 (GMc2

)2/3

γ =(

P2π

)1/3eM2(M + M2)

(G

M2c2

)2/3

Gravitational radiation leads to orbitdecay:

P = −192π5c5

(2πGP

)5/3(1− e2)−7/2

(1 + 73

24e2 + 37

96e4) M1M2

M1/2

In edge-on systems, it’s possible to detect Shapiro time delay,with parameters r (imagnitude) and s = sin i (shape).

17 yr−1 in PSR 0737


PSR J0737-3039

PSR J0737-3039

Kramer et al. (2007)


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 = 0.99984Pulsar mass is 1.97± 0.04 MDistance > 1 kpc, B ' 1.8× 108 G

Demorest et al. 2010∆t(µs)


Shapiro Time Delay

Shapiro delay produces a delayin pulse arrival times

δS(φ)

2M2T= ln

»1 + e cosφ

1− sin(ω + φ) sin i

–with φ the true anomaly, theorbital angular parameterdefining the position of thepulsar relative to the periastronposition ω.

T =GMc3

= 4.9255 µs

δS is a periodic function with

approximate amplitude

∆S ' 2M2T

˛˛ln»„

1 + e sinω

1− e sinω

«„1 + sin i

1− sin i

«–˛˛.

This is large only if sin i ∼ 1 or if both e and sinω are nearly unity.


Although simpleaverage mass ofw.d. companionsis 0.23 M larger,weighted average isonly 0.07 M larger.

Champion et al. 2008

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

Romani et al. 2012

van Kerkwijk 2010

Martinez et al. 2015


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 objecthas a volume much larger than the secondary or its Roche lobe.The pulsar is ablating the companion leading to mass loss and theeclipsing 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 irradiatedhot spot rather than its center of mass motion.

pulsar radial velocity

NASA/CXC/M.Weiss

eclipse


Black Widow Pulsar PSR B1957+20

The peak radial velocity of the center of mass of component i is:

Ki = 2πai sin i

P

q =MP

M∗=

a∗aP

=K∗KP

K∗ = Kobs

(1 +

R∗a∗

)Companion’s hot spot hasa smaller orbit than itscenter of mass.

MP = q(1+q)2 P

2πG

(KP

sin i

)3

Modeling of light curveshape suggests that

MP > 1.8M, sin i < 66

Most probable values:

2.20M < MP < 2.55M

1.0 1.5 2.0 2.5 3.0MPSR (M)

0.020

0.025

0.030

0.035

0.040

0.045

MComp(M

)i=45

i=60

i=75

K 2=K ob

s

K L1=K ob

s

van Kerkwijk 2010

R ∗→

0

R ∗=

R L1


Companion Light Curves and Radial Velocity

18

19

20

21

22

23

24

25

26

27 0 0.5 1 1.5 2

Mag

nitu

de

Phase

18

19

20

21

22

23

24

25

26

27 0 0.5 1 1.5 2

Mag

nitu

de

Phase

-0.4 0

0.4

0 0.5 1 1.5 2

17

17.5

18

18.5

19

19.5

20

20.5

21 0 0.5 1 1.5 2

Mag

nitu

de

Phase

17

17.5

18

18.5

19

19.5

20

20.5

21 0 0.5 1 1.5 2

Mag

nitu

de

Phase

-0.2

0

0.2

0 0.5 1 1.5 2

Reynolds et al. 2007

R-band

U-band


System Masses

Radial velocity amplitudes:Ki = 2πai sin i/P

Light curve shape ⇒ i ' 65± 2

K1 = 5.093 km/s, Kobs = 324±3 km/s

q = Mp/M∗ = K∗/Kp = a∗/aP

K∗ ' Kobs(1 + R∗/a∗)

G (MP +M∗)P2 = (4π)2(aP +a∗)3

RL1 = 0.46ap(1 + q)2/3

MP = q(1 + q)2 P

2πG

(KP

sin i

)3

(2π

P

)2(aP sin i)3

G=

(M∗ sin i)3

(MP + M∗)2= 5.2×10−6M

1.0 1.5 2.0 2.5 3.0MPSR (M)

0.020

0.025

0.030

0.035

0.040

0.045

MComp(M

)i=45

i=60

i=75

K 2=K ob

s

K L1=K ob

s

R ∗=

0

R ∗=

R L1

XXXXXXXXXXXXXXXXz

van Kerkwijk 2010


Another Black Widow Pulsar

Romani et al. 2012

PSR J1311-3430


Pulsars


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Documents

PHY688, Neutron Stars and Pulsars - Stony Brook UniversityPHY688, Neutron Stars and Pulsars James Lattimer Department of Physics & Astronomy 449 ESS Bldg. Stony Brook University March