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Transcript
th 4 lecture of “Compact Object and Accretion”, Master Programme at Leiden Observatory nd 2 Neutron Stars class study material: Chapter 10, ShapiroTeukolsky these slides at http://home.strw.leidenuniv.nl/~emr/COA/ Friday, October 16, 2015 Neutron star observations Friday, October 16, 2015 Gravitational time dilation Locally, an interval in proper time is related to the space-time metric by An observer at rest on NS surface measures an interval in proper time while an observer at infinity will measures Therefore, an intrinsic period signal of the source on time scale T0 will be observed with a period longer periods Friday, October 16, 2015 Einstein’s gravitational redshift A signal of wavelength λ0 ~ T0 will then be redshifted where the object compactness is Note, for White Dwarfs This measurement may be used in principle to constrain M/R, however, as mentione in the introduction it is difficult to detect the surface emission and therefore line emission. In non thermal X-ray flares is easier, e.g. Cottam et al. 2002 with XMM, z~0.35 ==> compactness of ~0.23 in agreement with typical expectations Friday, October 16, 2015 Neutron star cooling (just some facts) • • A NS is born very hot ~1011 K • When T~108 K photon cooling becomes dominant, which corresponds to a surface T~106 K • Detection of thermal emission hampered by small radius and peak emission in soft X-ray Friday, October 16, 2015 It cool by neutrino emission for the first ~1000 yr. Initial cooling is quite rapid: on a day timescale T ~109-1010K Mass measurements In binary systems, the pulsar signal is modulated by the orbital period. The parameter T (period) and a1sin (i) (the distance form the centre of mass of primary projected perp. to line of sight) allows to determines a combination of primary and secondary masses M1 and M1: Newtonian mass function from 3rd Kepler The Doppler effect measured with lines gives a1 sin(i). If the mass function can be also constructed for the secondary, both mass can be determined, otherwise not. Additional uncertainty in “i”. This is also true for WDs Friday, October 16, 2015 Mass measurements For binaries with two NSs, general relativistic effects help constraining mass precisely, since effects depend on mass. E.g. pericenter precession of orbital motion, that “advances” at a rate: if also other effects like, Einstein’s redshifts, period’s change due to gravitational wave etc... can be measured, then the mass and orbital parameter measurements become very precise, allowing for orbital evolution predictions (e.g. Hulse & Taylor’s work) Friday, October 16, 2015 NS + WD Double NSs smaller errors Kiziltan et al. (2013) Friday, October 16, 2015 Pulsars how does it work ? Friday, October 16, 2015 Description • pulse period P extremely stable • pulse shape averaged over ~100 or more stable • pulse shape different from pulsar to pulsar • two populations of pulsars + magnetars • • dP/dt >0 typically d2P/dt2 <0 typically. P increases slower in time “recycled” milli-pulsars.1-100ms Friday, October 16, 2015 Normal pulsars: 30 ms-3 s Glitches • • • • sometimes the period suddenly decreases typically, but can be up to ~4 10-6 ~1% for for After glitches, the period goes back to its original value Friday, October 16, 2015 Pulsar emission model we need to consider magnetic fields... Friday, October 16, 2015 Basic model assumes: 1. Solid rotation with angular frequency Ω (P = 2π/Ω). Justified by superfluidity 2. Dipolar magnetic field configuration, with magnetic dipole m at angle α with rotation axis, again good guess 3. In vacuum (not so good) Friday, October 16, 2015 Dipolar emission Power emitted by an accelerated magnetic dipole (remember Larmor formula ?) In a Cartesian coordinate system with z-axis = rotation axis Let’s express “m” as a function of the polar magnetic field at the NS surface Friday, October 16, 2015 Dipole magnetic field in spherical coordinates with axis ( ) equal to the magnetic axis: Polar Magnetic field at r=R ; Solving for “m” and inserting in power formula: radiation power emitted by a rotating magnetic dipole in vacuum Friday, October 16, 2015 law of deceleration • • • Energy is lost at the expenses of rotational energy (mass and gravitational energy do not change) Energy conservation, ignoring GW emission from deformation (this may not be valid for young < 100 yr pulsars) of NS reads : Solving it, assuming constant NS structure i.e. constant moment of inertia “I” Friday, October 16, 2015 Magnetic field Note the pulsar decelerates with time! With this formula it is possible to estimate Bp, once P and are measured Friday, October 16, 2015 P-Pdot diagram t n a t s n o c Line of deceleration timescale constant i.e. The higher B, the faster deceleration. The rotational energy power is similar for all 3 populations Friday, October 16, 2015 Magnetars deceleration index measured it is possible to infer the deceleration index “n” let’s understand where it comes from. If we assume for the model developed here n=3. See deceleration law expressed in terms of Ω Friday, October 16, 2015 deceleration index Note: “n” is typically a bit different from ~3, this tells us that this simple model is too simple. Note however, that if the energy loss was only for gravitational waves n~5, which differs even more from observations Friday, October 16, 2015 deceleration timescale = age of a pulsar n If we integrate n n with n n n n n n when n is not measured is assumed n=3. For Crabe t = 1200 yr and we know that t= 961 yr (happened in 1054). good agreement! Friday, October 16, 2015 deceleration timescale = age of a pulsar • Classical pulsars are younger than ~100 Myr • millisecond Pulsars are older than ~100 Myr Friday, October 16, 2015 Goldreich & Julian (1969) Assumption of vacuum faulty: the rotating dipole induce a strong electric field, orders of magnitude larger than gravity : charges are accelerated from the NS crust at the poles and fill the magnetosphere: the potential drop in vacuum is the charges from a “pulsar” wind that escape through open B lines (see next slide) The pulsar wind carries most of the extracted rotational energy Friday, October 16, 2015 Poynting flux Goldreich & Julian (1969) The magnetosphere structure is different: there is a corotating magnetosphere at the interior of the light cylinder RL= c/Ω. The magnetic lines that intercepts RL are open and particles and escape Pulsar’s magnetosphere are larger Poynting flux Friday, October 16, 2015 more realistic models Friday, October 16, 2015 • Modern hydromagnetic simulations showed that the G-J model does not work as you need to include pair-production • standard view: charges that escape along B line emit radio via “curvature” emission • standard view: charges that heat back the NS crust causes the crust to heat up and emit thermal X-ray Open issues • model/simulate pair production • where the radiation, especially ϒ-rays is generated ? • what is Friday, October 16, 2015 the mechanism that produce radio ? Radiation: observational facts • radiation is around/less than 10% of the extracted rotational energy (spin-down energy) • radio makes up only about extracted energy • most of the radiation energy is in emitted in ϒ-rays around ~GeV, fro most but some. E.g. the Crab nebula emits mostly in X-ray Friday, October 16, 2015 -4 ~10 of total