1. 1931: Chadwick --discovers neutrons. 2. 1934:Baade & Zwicky suggested neutron-stars, and postulated their formation in supernovae. References: 1.A.

References:

1. A. G. Lyne & F. Graham-Smith, Pulsar AstronomyCambridge University Press, 1998

2. Shapiro & Teukolsky, WD, NS & BHs, Chapters 9 & 10

3. Lorimer: astro-ph/0104388 & 0301327

4. Camilo: astro-ph/0210620

1967: Hewish, Bell et al. discover radio pulsars.

1974: Nobel prize to Ryle (aperture synthesis)

and Hewish (pulsars).

1968: Gold proposes rotating NS model for Pulsars

Why neutron stars?

Pulsation timescale for WD is: (R3/GM)1/2/2pi ~ 1 s(The period of the closest orbit is similar;

moreover, these timescales decrease with time - not increase as for pulsars).

Not possible to get highly stable periodic signal from BHs.

The break-up rotation period, pulsation or dynamicaltime for a NS is ~ milli-sec; rotation can explain theobserved period range and stability.

The break-up rotation period for WDs is also ~ 1 s.

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Observational Properties of Pulsars

Period range: 1.5 milli-sec --- 8 sec.

Radio luminosity distribution: N(L) dL L-1 dL(This holds over 3-decades in L. The total number

of active pulsars for L> 1 mJy kpc2 is ~ 150,000;pulsars we observe are more luminous than average for the Galaxy by a factor 10-100, the Typical flux is of order 100 mJy).

Luminosity in the radio band ~ 1025 -- 1028 erg/s

The spectrum index is ~ 1.5 I.e. f --1.5 for < 1 GHz.

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Period Derivative

Collapse of a star -- conserving angular momentum & magnetic flux -- to NS gives rise to msec P and B~1012 G

Some elementary considerations:

M R2 = M R2n n Pn = P (Rn/R)2

R2 B = R2n Bn Bn = B (R/Rn)2

Pn ~ 1 ms (P ~ 1 month; R/ Rn ~ 1010)

Bn ~ 1012 Gauss

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Pulsar Distance Determination

1. Parallax

3. Dispersion measure: (pulses at different arrive at different times)

2 = 2p + k2 c2

2p = 4 ne e 2 /me = 3x109 ne (rad/s)2

DM = dl ne

2. Neutral H absorption at 21 cm:The Doppler shift of the 21cm absorption line together with the dynamical model of the Galaxycan be used to identify the location of the H-cloudand determine the distance to the pulsar.

Pulse Dispersion(Lyne & Graham-Smith in “Pulsar Astronomy)

Lyne & Graham-Smith in “Pulsar Astronomy)

Magnetic dipole Radiation formula

Magnetic dipole rad. energy loss rate:

dE/dt = -2(d 2 m/dt 2)2 /3c3 ; m = Bn R3n/2

m: the magnetic moment of the NS

Or dE/dt = - Bn2 R6

n n4 sin2 /6c3

dE/dt ~ 1035 erg/s for Bn ~ 1012 & P=0.1s

Solution of this equation and breaking index

E = I n2 dn/dt = - K n

a; a: breaking index

For the dipole model a=3. Observations give a between 1.4 & 2.8

B determined from the dipole radiation formula(Lyne & Graham-Smith in “Pulsar Astronomy”; Cambridge U. press 1998)

Pulsar magnetosphere

Goldreich-Julian model (aligned rotator)

Charge density (pulled from the surface of NS)

Electric potential drop along open B-field lines

NS surrounding is completely dominated by Electro-dynamics.

The pressure scale height on a NS for 108 K plasma is ~ 100 cm. Thus, the number density 100 m above the NS surface < 10-5/cc

(provided that EM forces are unimportant).

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Poynting flux at the light-cylinder & NS slowdown rate•

Summary of Axisymmetric NS magnetosphere results

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E r(R) ≈ ΩBR2C ≈107 B12Ω Statvolt cm-1

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FE

FG≈ 4x107 B12Ω

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n± ≈1010 B12Ω cm-3

Poyinting flux:

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dE

dt≈

BR2 R6Ω4

8π c 4(same as the dipole radiation formula)

(Goldreich-Julian density)

Summary of last lecture

Crab nebula

Blue: x-rayRed: opticalGreen:radio

The Luminosity ~ 1038 erg/s(mostly x-ray & gamma)

Synchrotron radiation

e-s with energy > 1014 ev are accelerated by the electric field in the polar region; these e-s are neededfor emission at 10 kev.

(Plerion)The nebula is powered by poynting outflow from the pulsar.

Rotational energy of the NS Is the energy source for

Pulsar radio-emission must be coherent radiation

Pulsar radio luminosity, assuming conical geometry, is found to be in the range of 1025 -- 1028 erg/s.

The source area ~ (c t)2 ; where t is the pulse width(t ~ a few milli-sec)

The brightness temperature Tb ~ 1023 -- 1026 K!

This implies

This is clearly not possible --- as it will lead to enormous luminosity.

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ms pulsars

(Lyne & Graham-Smith in “Pulsar Astronomy”; Cambridge U. press 1998)Milli-sec pulsars have low magnetic field

Spin-up of a NS in a binary system(Spherical accretion)

Ram pressure of in-falling gas balances the magnetic pressure:

€

ρv 2 =˙ M v

4πr2=

˙ M

4πr2

2GM

r=

B2(r)

8π=

B*2

8π

R*

r

⎛

⎝ ⎜

⎞

⎠ ⎟6

Or

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Req ≈ 1(8G )1/7 B*

47 R*

127 M− 1

7 ˙ M −27 ≈1.25x108 B12

47 R6

127 m− 3

7 ˙ m −27 cm

where

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M = mMo,

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˙ M =1.39x1018 m ˙ m g s-1

(For disk accretion the viscous torque in the disk is equated to the magnetic torque in from the star; Req turns out to have the same form as above and the numerical coefficient is also similar.)

The accretion is nearly spherical in that the accreting gas falls onto the star roughly equally all around it, but the in falling gas is rotating at nearly theKeplerian speed and carries angular momentum with it.

Spin-up Equilibrium

€

eq = GMReq

3 or

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Peq = 2πΩ eq

≈ 2.2 B9

67 R6

187 m− 8

7 ˙ m −37 ms

Spin-up Line:

The fastest spin rate for a NS corresponds to dm/dt =1.

Substitute for B in terms of P & dP/dt in the above equation

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Pmin

47 ˙ P −15

− 37 ≈ 0.8 R6

187 m− 8

7

All binary radio pulsars lie below the spin-up line.

Many single ms pulsars are seen, and they too lie belowthis line. It is believed that these too were spun-up in abinary system, and either the companion was evaporatedby the pulsar or was lost in a binary collision.

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˙ Ω ∝ B2Ω3( )

Propeller effect: If the period of the NS is smaller than Peq then matter is not accreted onto the NS. Click here to find details.

Spin-up Time

A crude model describing the time evolution of NS spin is:

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IdΩ

dt= − ˙ M (Ω − Ωeq )Req

2

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(t) = Ωeq 1− e− ˙ M Req2 t / I

[ ]or

The spin-up time:

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tspinup = I˙ M Req

2 ≈ 3.6x106 B9− 8

7R6− 24

7 m− 17 ˙ m −

37I45

yr

Anomalous x-ray pulsars (AXPs)

References:1. Mereghetti et al., 2002, Astro-ph/02051222. Thompson, astro-ph/0010016 & 01106793. Pavlov et al., 2001, Astro-ph/01123224. Hurley, 1999, astro-ph/99120615. Gaensler, 2002, astro-ph/0212086

Summary of observational propertiesFive confirmed cases of AXPs as of 2004.Pulsation period: 5--12 s.

x-ray luminosity: Lx ~ 1034 --1036 erg s-1.

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˙ P

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˙ P measured gives P/ ~ 103.5 -- 105.5 yr.Black-body kT < 0.5 kev + steep power-law spectrumNo radio emission.

No binary companion detected.2 or 3 are associated with supernovae remnants.

P ~ 6s & ~ 1 s-1 EKE ~ 5x1044 erg (insufficient to explain Lx).

(So unlike normal pulsars the energy source is NOT rotational)

Accretion is also ruled out since AXPs are not in binary systems.

The most likely source is the dissipation of magnetic field

P & dP/dt give B ~ 1014 -- 1015 Gauss. (click here for the P-B diagram)

Energy in B-field ~ 1045 -- 1047 erg

This is sufficient to explain Lx as resulting from a steady decay of B-field inside NS!

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Energy source for AXPs?

Soft gamma-ray repeaters

References:

• Thompson, astro-ph/0010016 & 0110679• Kaspi, V., 2004, Astro-ph/0402175• Woods, P.M., 2003, astro-ph/0304372

Summary of observational properties

4-6 objects are known.•

(bursts are associated with young stellar population)

(associated with NS or a BH)

All but one SGRs are in the Galactic plane (one in LMC).•

The one in the LMC is in a supernova remnant.•

(Rare events)

(almost certainly SGRs are associated with NS)

Soft -ray and x-ray bursts with typical energy ~ 1041 erg.Rise time ~ 10 ms & duration ~ 100 ms. Occasionally energyGreater than 4x1044 erg. But no binary companion detected.

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Bursts repeat episodically; could be inactive for years andthen hundreds of bursts could appear in a week.

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Generally thermal Bremsstrahlung spectrum with kT ~ 20 - 50 kev.

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Three SGRs have been seen to pulse with period inthe range 5--8 s. Two of these 3 have pulsations inx-rays during quiescence as well & are spinning down.

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(Not accretion powered! KE of NS rotation too little as well)

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˙ P In 2 cases the measured P and gives B ~1015 Gauss. •(The energy in magnetic field ~ 1047 erg; sufficient to power these bursts).

Exploring the x-ray Universe -- Charles & Seward, 1995,Cambridge U. Press

Taken from:

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Manchester, 2000, astro-ph/0009405

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