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Magnetism in Neutron stars, pulsars and magnetars. N.J.Stone, Oxford and Tennessee Russbach, March 2016 Outline Magnetism is the cinderella interaction – it’s time she came to the party - very general survey talk at an introductory level - to take any topic further consult references and move on Magnetism in cosmic bodies Planets and the sun Field configurations in rotating, conductive bodies Neutron stars (NS) Internal and external structure How large are NS magnetic fields? Possible mechanisms for generation of sufficient fields Is stellar magnetism significant? strong; coulomb: gravity … ? Start with the earth Surface field weak non-axial wandering axis with infrequent reversals understood(?) Environmental field: magnetosphere ionosphere rotating charges deflection of solar wind importance Other planets Mercury Earth-like field 1% of H(E) Venus No magnetic field Mars No inner core field Jupiter Field ~ 2000 H(E), 10o off axis. Moon Ganymede has its own field Saturn Field ~ 600 H(E) on axis Uranus Field ~ 50 H(E), 60o off axis Neptune Field ~ 25 H(E), 47o off axis General reference Space Science Review vol 152 (2010) The Sun (C. A. Jones et al., Space Sci Rev 152 591 (2010)) Global field mainly quasi -axial, dipolar poliodal. Internal fields more complex. Regions Solid body core rotation with outer convection zone where there is differential rotation, faster at equator and slower at poles. Medium of convection zone is plasma – conductive fluid Convection leads - through Coriolis effect – to spiral motion about polar field lines– induction - and toroidal fields which penetrate surface as Sunspots. Resulting field configuration has coupled poloidal and toroidal components – the aW dynamo – complex theory! The direction of the poloidal field reverses every ~ 11 years Poloidal field deflects galactic cosmic rays which produce isotopes such as 14C and 10B in the Earth’s atmosphere. These in trees and polar ice caps reveal the persistence of the sun spot cycle over hundreds of years. How different are neutron stars compared to the Earth? Earth Neutron star Mass 6 x 10^24 Kg ~ 1.5 x solar … 3 x 10^30 Kg Radius 6400 km 10 km Surface gravity g ~ 10 m/s^2 1.6 x 10^11 m/s^2 Volume 1.1 x 10^21 m^3 4.2 x 10^12 m^3 Mean density 5.5 x 10^3 Kg/m^3 7.1 x 10^17 Kg/m^3 Expect application of the laws of physics in a very different regime No practical possibility of terrestrial experimentation Dependent upon observation (all aspects: spectrum. timing, deduced location ….) and theory, pushed to extreme limits The Challenge: magnetism in neutron stars Neutron stars Products of cataclysmic explosions of stars at the end of their burning cycle when gravity causes collapse and disruption with loss of > 70% of material Properties: Position Motion Mass ~ 1.5 M(s), Radius ~ 10 km, Energy ~ 10^51 erg Temp initially ~ 10^10, cooling to ~ 10^8 K In the vicinity of supernova remnants Can be travelling at > 10,000 km/s wrt surroundings Pulsars Subgroup (~10%) of neutron stars which exhibit ‘lighthouse’ like emission of EM radiation over a wide wavelength range. Directed emission thought to be result of magnetic dipole field rotating at an angle to the axis of rotation of the star. Fields in the region of 10^11 – 10^12 G [10^7 – 10^8 T]. Properties: Slow down of period. Glitches (abrupt small changes) Magnetars Further subgroup (~3%) with even higher fields ~ 10^14- 10^16 G Neutron star structure Atmosphere - thin Outer crust Inner crust Core beta equilibrium requires presence of protons, electrons and (great majority) neutrons. Inner core Likely to contain hyperons and heavier mesons Conductivity By highly relativistic electrons in all regions and (superconductive) protons until mesons appear. Beyond the stellar surface. Magnetosphere standard model considers this divided into regions of open and closed field lines. Magnetosphere rotates with the NS out to where this would imply velocities > vel. of light.. Closed field region filled by charged particles such that their electric field, in the rotating reference frame, cancels that from rotation of the star. Open field region has strong electric field which accelerates charged particles to close to speed of light. Particle motion in magnetic field causes emission of cyclotron radiation. Pulsars also emit gamma, x-ray and thermal radiation. Role of magnetosphere in radiation propagation: detailed analysis of radiative propagation in plasma is complex . Observable radiation varies with B field and temperature, which are not uniform across the star surface. Composition of thin atmosphere ions (H, He) affects spectrum. Such questions of great importance in attempts to extract neutron star radii. A. Y. Potehkin - Physics Uspekhi 57 735 (2014) and arXiv:1403.007v5 5 Jan 2016. Evidence for magnitude of magnetic field in pulsars Some spectra (in pulsars accreting material from a binary partner) show lines which have been associated with electron cyclotron resonance involving radiation from electrons orbiting the poloidal field lines. Frequencies correspond to fields of up to ~ 1.4 x 10^12 G. For isolated pulsars use is made of the relation between the period of rotation and its slowing, assuming magnetic dipole radiation and star parameters: Radius R, MoI I, angular velocity W and angle between field and rotation axes a. dW/dt = - 2 R6B2W3sin2a/3I The results again show B ~ 10^12 G. Magnetic fields beyond and within the star. General remarks. Simple dipolar magnetic fields are unstable in systems which can support currents such as NS interiors. In these there is a more stable configuration involving a dipolar component ( a poloidal field) and a toroidal field. The latter may not be ‘visible’ at the star surface – same idea as sun spots. Conduction is by highly relativistic electrons and superconductive protons. Superconductive currents are considered to flow at the core – inner crust interface Fujisawa and Kisaka MNRAS 445 2777 (2014) More elaborate field profiles combining poloidal and toroidal fields Fujisawa and Kisaka MNRAS 445 2777 (2014) Origin of magnetic fields in N S: circulating currents or intrinsic magnetization of constituents Spruit H. C. AIP Conf Proc 983 391 (2008) 1. Fossil fields Hansson and Ponga ISRN Astr Astro 2011 article 378493 Inherited from precursor star by flux conservation through reduced surface area. How is problematic. 2. Dynamo processes circulating currents (see references to a-W dynamo) Rossby Number: Ratio of inertial to convective forces. Governs Coriolis as opposed to convective contribution to dynamo magnetic field amplification in stars. Reynolds Number: ratio of inertial to viscous forces. Low value – streamline flow: High value – turbulent flow with eddies. Dynamo action requires R above a specified value to be sustained. In neutron star matter R >> 1 (Thompson and Duncan 1993) 3. Constituent magnetisation Polarisation of electrons, protons, neutrons. All have intrinsic magnetic moments and VERY HIGH DENSITY Fossil fields For the first years after the discovery of pulsars the thinking was that these remnants of precursor main sequence stars could ‘inherit’ their huge magnetic fields, either direct from the progenitor or even from the primordial pre-stellar medium. Some stars have fields in the 10^4 G range and radii of (few x10^6) km. If magnetic structure were somehow maintained during the supernova process then, with radius reduced to ~ 10 km, fields (flux/area) could reach 10^4 x [(4 10^6/10)]^2 ~ 10^15 G. Later thinking realised that such flux conservation is unlikely (Spruit ). Mass loss during the explosion and the smaller initial area of the remnant as part of the precursor core brings the maximum below that observed in magnetars, even for an initial 10^4 G precursor. Furthermore only very few precursors have fields ~ 10^4 G. These and other technical arguments have led to the dropping of this idea as the source of neutron star fields. Dynamo effect and field amplification (no detail - ref NOVA What drives the earth’s Magnetic Field ?) When a conducting medium moves through a magnetic field it constitutes a current, which, in turn, produces a second field. This field adds to the first and produces a field which is larger. This ‘amplification’ requires energy input to sustain the fields and currents, and there are losses through viscous and other resistive forces. In the earth, energy is derived from slow ‘freezing’ of the inner surface of the molten outer core onto the inner solid core, the heat so generated driving convective action which keeps the molten, conductive, outer core moving through the field. Coriolis effects also contribute by imparting a spiraling motion to the moving liquid (just as in the bath or so they say!) and such spirals generate additional magnetic field sources, which are roughly aligned and add to the total field. This may contribute to the SN explosion (Obergaulinger, Janka, Aloy MNRAS 445 3169 (2014) Convective motion of a conducting medium is a typical feature of many types of star structure: seen as the principal means of generation of magnetic fields. The convection may be driven by any type of entropy gradient: T ….. Composition, …. Requirements for dynamo existence and persistence. N.B. Field is not static or ‘permanent’ but must be continuously generated. Existence 1. An electrically conductive, fluid medium – exists in NS central regions. 2. Kinetic energy – provided by planetary rotation. 3. Internal energy source to drive convective motions in the fluid – this is often provided by Coriolis forces associated with rotation. In the earth thermal convection in the liquid iron outer core drives the motion. Persistence There will be losses associated with the field generation, largely from viscous forces. If these are too large the field will die away. The ratio of the generating power to the resistive losses must exceed unity for the field to grow and this limits the maximum field through Lorentz forces if nothing else acts first. Collective magnetism in (neutron) stars History: Brownell and Callaway 1969, Rice (1969) Silverstein (1969) see Heansel and Bonazzola (Astron Astro 314 1017 (1996)) First ideas : Neutron pair interaction favours triplet state (S = 1) at high density which avoids short range strongly repulsive n-n interaction in singlet (S = 0) state by Pauli Principle. This would lead to ‘ferromagnetic’ (F) transition above some critical density and below a critical temperature T(c). Estimated T(c) ~ 10^10 K. Later: Detailed calculations showed dense pure n matter would not undergo F transition. However the addition of a small proton density was shown to predict a stable polarised system (Kutschera and Wojcik P Lett B 223 11 (1989). Full polarisation produces far too HIGH a magnetisation density (10^16 G) for the observed normal pulsar fields, but high enough to produce magnetars (~ 10^15 G). Details existence of Domains as in Ferromag materials reduce effective magnetisation Screening of core field by inner crust proton superconductivity (Type I would give total screening, Type II partial screening) Non-coaxiality: result of complex domain structure? Magnetisation in NS produced during initial cooling phase since ordering temp ~ 10^10 K. - some memory of precursor star field direction (?). a Angle a between rotation and magnetic field axes Inspiration… Toy model of two dipoles α 1950’s 2000 ? Assumptions: 1. Fixed moment of inertia 2. Fixed magnitude M1, M2, θ1 and r 3. M1 and M2 co-planar M1 – dynamo M2 - polarized matter Coexistence of dynamo and collective magnetism Possible evidence General: Wide range of observed magnetisations in N stars and white dwarfs Specific: Angle a between resultant magnetic dipole field and rotation axis is slowly changing. (Lyne et al., Science 342 598 (2013) Crab pulsar pulse analysis) Data: Pulsar pulses have structure. Separation in time of different components is found to change over the 22 years of observation of this pulsar in a way consistent with change in angle a at rate of 0.62 degree per century towards orthogonality of the two axes. Mechanism for a change. Two non-coaxial dipoles exert couple tending either to perpendicular or parallel configuration dependent upon initial configuration. Conclusions Two possible mechanisms (dynamo, magnetization) for origin of NS magnetism. Both claim to produce fields as observed in both regular pulsars and in magnetars. There seems no clear reason why they cannot co-exist. Both are consistent/compatible with other aspects of NS structure including Superconductivity and Superfluidity. Pulsars also show rapid small step changes in period. Origin not fully determined. Glitches: Possibly related to adjustment as superfluid component shares angular momentum with the normal component after this has lost energy and slowed. Stellar Magnetism. A wonderfully open field for new ideas which demand new observations and sophisticated analysis. Thank you Source: presentation by C. Auer ‘ABC of Magnetars’ 2008 Alternative to dynamo polarised Neutromagnets [Hansson and Ponga] Polarised neutrons (major constituent – others too few to be important) NS born at temp ~ 10^10 K. Estimated bound neutron spin triplet energy in presence of strong gravity ~ 0.5 MeV – predicts ordering transition also with T(c) ~ 10^10 K . Thus as neutron star is made and cools it falls below neutron ordering temperature – Curie Temperature – and forms an ordered system comparable to a ferromagnet If all neutrons align in NS of mass ~ 1.4 solar masses, combined neutron moments would generate field ~ 10^12 T that is 10^16 G – comparable to highest estimates for magnetar fields. Positive feature of this mechanism – existence of domain structure allows partial magnetisation having axis independent of the pulsar rotation axis – as observed. Other - dynamo - mechanism associated with circulation of superfluid, superconducting protons have difficulty providing fields with non-axial symmetry.