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Pulsars

Pulsars. •. References:. •. A. G. Lyne & F. Graham-Smith , Pulsar Astronomy Cambridge University Press, 1998. •. 2. Shapiro & Teukolsky, WD, NS & BHs , Chapters 9 & 10. •. 3. Lorimer: astro-ph/0104388 & 0301327. 4. Camilo: astro-ph/0210620. •. •. •.

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Pulsars

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  1. Pulsars • References: • A. G. Lyne & F. Graham-Smith, Pulsar Astronomy Cambridge University Press, 1998 • 2.Shapiro & Teukolsky, WD, NS & BHs, Chapters 9 & 10 • 3.Lorimer: astro-ph/0104388 & 0301327 4.Camilo: astro-ph/0210620 • • • 1. 1931: Chadwick --discovers neutrons. 2. 1934:Baade & Zwicky suggested neutron-stars, and postulated their formation in supernovae.

  2. 1967: Hewish, Bell et al. discover radio pulsars. 1974: Nobel prize to Ryle (aperture synthesis) and Hewish (pulsars).

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

  4. Pulsar period distribution

  5. Observational Properties of Pulsars • Period range: 1.5 milli-sec --- 8 sec. • Luminosity in the radio band ~ 1025 -- 1028erg/s • 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). • The spectrum index is ~ 1.5 I.e. f  --1.5 for  < 1 GHz. 1 Jy = 10^{-23} erg/cm^2/s/Hz

  6. Period Derivative

  7. Some elementary considerations: Collapse of a star -- conserving angular momentum & magnetic flux -- to NS gives rise to msec P and B~1012 G • M R2 = M R2nn  Pn = P (Rn/R)2 Pn ~ 1 ms (P ~ 1 month; R/ Rn ~ 1010) • R2B = R2nBn  Bn = B (R/Rn)2 Bn ~ 1012 Gauss

  8. Lecture 4 Pulsar Distance Determination 1. Parallax 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. 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

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

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

  11. 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 R6n n4 sin2 /6c3 dE/dt ~ 1035 erg/s for Bn ~ 1012 & P=0.1s Solution of this equation and breaking index E = I n2 dn/dt = - Kna; a: breaking index For the dipole model a=3. Observations give a between 1.4 & 2.8 Larmor formula for electric dipole radiation: dE/dt = -2e^2 a^2/c^3 = -2(d d/dt)^2/c^3 The deviation of the breaking index from 3 could probably be due to torque on the pulsar from outflow of particles.

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

  13. Lecture 5 (detailed derivation of Goldreich-Julian results) • Pulsar magnetosphere • 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). • Goldreich-Julian model (aligned rotator) Charge density (pulled from the surface of NS) • Electric potential drop along open B-field lines • • Poynting flux at the light-cylinder & NS slowdown rate 1969: Goldreich & Julian model published.

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

  15. Lecture # 6 Summary of last lecture

  16. 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. Crab nebula (Plerion) The nebula is powered by poynting outflow from the pulsar. e-s with energy > 1014 ev are accelerated by the electric field in the polar region; these e-s are needed for emission at 10 kev. (linear polarization of 9% averaged over nebula). Rotational energy of the NS Is the energy source for The Luminosity ~ 1038 erg/s (mostly x-ray & gamma) Blue: x-ray Red: optical Synchrotron radiation Green:radio 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.

  17. 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) This implies The brightness temperatureTb ~ 1023 -- 1026 K! 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 106 k!

  18. milli-sec pulsars ms pulsars

  19. Milli-sec pulsars have low magnetic field (Lyne & Graham-Smith in “Pulsar Astronomy”; Cambridge U. press 1998) Make sure to point out: Most of the ms pulsars are in binary system. Magnetic field for ms pulsars is low. Ms pulsars lie below the spin-up line which we will derive shortly. ms pulsars are the most stable clock --- dP/dt ~ 10-20 ; in other words it loses 10-13 s in one year!

  20. 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.

  21. where g s-1 Spin-up of a NS in a binary system (Spherical accretion) Ram pressure of in-falling gas balances the magnetic pressure: Or cm (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 the Keplerian speed and carries angular momentum with it.

  22. Spin-up equilibrium: accretion causes NS spin to Keplerian rotation speed at Req. 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. Spin-up Equilibrium ms or 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 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. Example: SAX J1808.4-3658 is a LMXB with a 2.5ms x-ray pulsar with magnetic field of 108--9 Gauss, and 2 hr orbital period. Other LMXBs also have weak field but only 1 or 2 have pulsation.

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

  24. Anomalous x-ray pulsars (AXPs) measured gives P/ ~ 103.5 -- 105.5 yr. References: Mereghetti et al., 2002, Astro-ph/0205122 Thompson, astro-ph/0010016 & 0110679 Pavlov et al., 2001, Astro-ph/0112322 Hurley, 1999, astro-ph/9912061 Gaensler, 2002, astro-ph/0212086 Summary of observational properties Five confirmed cases of AXPs as of 2004. Pulsation period: 5--12 s. x-ray luminosity: Lx ~ 1034 --1036 erg s-1. 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.

  25. Energy source for AXPs? • • 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!

  26. • 4-6 objects are known. • All but one SGRs are in the Galactic plane (one in LMC). • The one in the LMC is in a supernova remnant. 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 (Rare events) (bursts are associated with young stellar population) (associated with NS or a BH)

  27. • 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. • Soft -ray and x-ray bursts with typical energy ~ 1041 erg. Rise time ~ 10 ms & duration ~ 100 ms. Occasionally energy Greater than 4x1044 erg. But no binary companion detected. In 2 cases the measured P and gives B ~1015 Gauss. • • Bursts repeat episodically; could be inactive for years and then hundreds of bursts could appear in a week. • Generally thermal Bremsstrahlung spectrum with kT ~ 20 - 50 kev. (almost certainly SGRs are associated with NS) (Not accretion powered! KE of NS rotation too little as well) (The energy in magnetic field ~ 1047 erg; sufficient to power these bursts).

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

  29. Manchester, 2000, astro-ph/0009405 Click to return

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