: Chadwick --discovers neutrons :Baade & Zwicky suggested neutron-stars, and postulated their formation in supernovae. References: 1.A. G. Lyne & F. Graham-Smith, Pulsar Astronomy Cambridge University Press, Shapiro & Teukolsky, WD, NS & BHs, Chapters 9 & Lorimer: astro-ph/ & Camilo: astro-ph/

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: (R 3 /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 dynamical time for a NS is ~ milli-sec; rotation can explain the observed period range and stability. The break-up rotation period for WDs is also ~ 1 s. Derive the break-up rotation speed. Argue that the higher harmonics of WD cannot explain pulsars because of the very high stability of the pulsar clock and because mode periods decrease with age not increase as seen for pulsar period.

Observational Properties of Pulsars Period range: 1.5 milli-sec 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 kpc 2 is ~ 150,000; pulsars we observe are more luminous than average for the Galaxy by a factor , the Typical flux is of order 100 mJy). 1 Jy = 10^{-23} erg/cm^2/s/Hz Luminosity in the radio band ~ erg/s The spectrum index is ~ 1.5 I.e. f  for < 1 GHz.

Period Derivative

Collapse of a star -- conserving angular momentum & magnetic flux -- to NS gives rise to msec P and B~10 12 G Some elementary considerations: M R 2  = M R 2 n  n  P n = P (R n /R) 2 R 2 B = R 2 n B n  B n = B (R/R n ) 2 P n ~ 1 ms (P ~ 1 month; R/ R n ~ ) B n ~ Gauss

Pulsar Distance Determination 1. Parallax 3. Dispersion measure: (pulses at different arrive at different times)  2 =  2 p + k 2 c 2  2 p = 4  n e e 2 /m e = 3x10 9 n e (rad/s) 2 DM =  dl n e 2. Neutral H absorption at 21 cm: The Doppler shift of the 21cm absorption line together with the dynamical model of the Galaxy can be used to identify the location of the H-cloud and determine the distance to the pulsar. Lecture 4

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

Lyne & Graham-Smith in “Pulsar Astronomy) Note: The derived varies only by a factor of a few.

Magnetic dipole Radiation formula Magnetic dipole rad. energy loss rate: dE/dt = -2(d 2 m/dt 2 ) 2 /3c 3 ; m = B n R 3 n /2 m: the magnetic moment of the NS Or dE/dt = - B n 2 R 6 n  n 4 sin 2  /6c 3 Larmor formula for electric dipole radiation: dE/dt = -2e^2 a^2/c^3 = -2(d d/dt)^2/c^3 dE/dt ~ erg/s for B n ~ & P=0.1s Solution of this equation and breaking index E = I  n 2 d  n /dt = - K  n a ; a: breaking index For the dipole model a=3. Observations give a between 1.4 & 2.8 The deviation of the breaking index from 3 could probably be due to torque on the pulsar from outflow of particles.

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 10 8 K plasma is ~ 100 cm. Thus, the number density 100 m above the NS surface < /cc (provided that EM forces are unimportant). 1969: Goldreich & Julian model published. Poynting flux at the light-cylinder & NS slowdown rate Lecture 5 ( detailed derivation of Goldreich-Julian results )

Summary of Axisymmetric NS magnetosphere results Statvolt cm -1 cm -3 Poyinting flux: (same as the dipole radiation formula) (Goldreich-Julian density)

Lecture # 6 Summary of last lecture

Crab nebula Blue: x-ray Red: optical Green:radio The Luminosity ~ erg/s (mostly x-ray & gamma) Synchrotron radiation (linear polarization of 9% averaged over nebula). e - s with energy > ev are accelerated by the electric field in the polar region; these e - s are needed for emission at 10 kev. (Plerion) Plerion: is derived from the Greek word “pleres” which means “full”. Crab nebula is the remnant of Sne explosion (perhaps type II) observed by the chinease Astronomers in 1054 (July 4th). The pulsar at the center has a period of 33milli-sec. Crab shows pulsed emission from radio to optical to >50 Mev! And moreover The pulse shape is nearly the same over this entire EM spectrum, suggesting A common origin for the radition which is believed to be synchrotron (curvature radiation). The radio is produced not too far away from the Neutron star (within 5-10 radaii) and high energy pulsed radiation is Likely produced near the light cylinder. The bolometric luminosity is pulsed radiation is about a factor 100 smaller Than nebular radiation; pulsed radio is smaller than total pulsed radiation By a factor of 10^4. 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 erg/s. The source area ~ (c  t) 2 ; where  t is the pulse width (  t ~ a few milli-sec) The brightness temperature T b ~ K! This implies This is clearly not possible --- as it will lead to enormous luminosity. Laser pointers have power output in the optical Light of ~ a few milli-watts, the bandwidth is Less than an Angstrom, and the beamwidth is About 1/2 degree. This gives the brightness Temperature to be about 10 6 k!

ms pulsars

(Lyne & Graham-Smith in “Pulsar Astronomy”; Cambridge U. press 1998) Milli-sec pulsars have low magnetic field Make sure to point out: 1.Most of the ms pulsars are in binary system. 2.Magnetic field for ms pulsars is low. 3.Ms pulsars lie below the spin-up line which we will derive shortly. 4.ms pulsars are the most stable clock --- dP/dt ~ ; in other words it loses s in one year!

1. This is a low mass x-ray binary system (the companion star is low mass which Supplying gas to the compact star via Roche-lobe overflow). 2. Milli-sec pulsars have been spun-up by the accreted gas. 3. Magnetic field must be low for the NS to be spun-up to milli-sec period.

Spin-up of a NS in a binary system (Spherical accretion) Ram pressure of in-falling gas balances the magnetic pressure: Or cm where g s -1 (For disk accretion the viscous torque in the disk is equated to the magnetic torque in from the star; R eq 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 the Keplerian speed and carries angular momentum with it.

Spin-up Equilibrium or 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 All binary radio pulsars lie below the spin-up line. Many single ms pulsars are seen, and they too lie below this line. It is believed that these too were spun-up in a binary system, and either the companion was evaporated by the pulsar or was lost in a binary collision. Spin-up equilibrium: accretion causes NS spin to Keplerian rotation speed at R eq. Milli-sec pulsars are formed in low-mass x-ray binaries (LMXB) which have a NS with small magnetic field and a low-mass Companion star. Such systems are old (compared to HMXB) and the NS magnetic field might have decayed with time or burried by accretion. Example: SAX J is a LMXB with a 2.5ms x-ray pulsar with magnetic field of Gauss, and 2 hr orbital period. Other LMXBs also have weak field but only 1 or 2 have pulsation. Propeller effect: If the period of the NS is smaller than P eq then matter is not accreted onto the NS. Click here to find details.Click here to find details

Spin-up Time A crude model describing the time evolution of NS spin is: or The spin-up time: yr

Anomalous x-ray pulsars (AXPs) References: 1.Mereghetti et al., 2002, Astro-ph/ Thompson, astro-ph/ & Pavlov et al., 2001, Astro-ph/ Hurley, 1999, astro-ph/ Gaensler, 2002, astro-ph/ Summary of observational properties Five confirmed cases of AXPs as of Pulsation period: s. x-ray luminosity: L x ~ erg s -1. measured gives P/ ~ yr. Black-body kT < 0.5 kev + steep power-law spectrum No radio emission. No binary companion detected. 2 or 3 are associated with supernovae remnants.

P ~ 6s &  ~ 1 s -1  E KE ~ 5x10 44 erg (insufficient to explain L x ). (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 ~ Gauss. (click here for the P-B diagram)click here for the P-B diagram  Energy in B-field ~ erg This is sufficient to explain L x as resulting from a steady decay of B-field inside NS! Energy source for AXPs?

Soft gamma-ray repeaters References: Thompson, astro-ph/ & Kaspi, V., 2004, Astro-ph/ Woods, P.M., 2003, astro-ph/ 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 ~ erg. Rise time ~ 10 ms & duration ~ 100 ms. Occasionally energy Greater than 4x10 44 erg. But no binary companion detected. Bursts repeat episodically; could be inactive for years and then hundreds of bursts could appear in a week. Generally thermal Bremsstrahlung spectrum with kT ~ kev. Three SGRs have been seen to pulse with period in the range 5--8 s. Two of these 3 have pulsations in x-rays during quiescence as well & are spinning down. (Not accretion powered! KE of NS rotation too little as well) In 2 cases the measured P and gives B ~10 15 Gauss. (The energy in magnetic field ~ erg; sufficient to power these bursts).

Exploring the x-ray Universe -- Charles & Seward, 1995, Cambridge U. Press Taken from: Click here to go back

Manchester, 2000, astro-ph/ Click to return