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Glitches in Superfluid Neutron Stars

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Glitches in Superfluid Neutron Stars GLITCHES IN SUPERFLUID NEUTRON STARS Marco Antonelli [email protected] Centrum Astronomiczne im. Mikołaja Kopernika Polskiej Akademii Nauk Quantum Turbulence: Cold Atoms, Heavy Ions ans Neutron Stars INT, Seattle (WA) – April 16, 2019 Outline Summary: Why glitches (in radio pulsars) tell us something about rotating neutron stars? - A bit of hystory: why superfluidity is needed to explain glitches. Intrinsic difficulty: model the exchange of angular momentum that causes the glitch (mutual friction) - Many-scales (coherence length → stellar radius) - Possible memory effects (also observed in He-II experiments) Which microscopic input do we need? I will focus on two quantities: - Pinning forces (or better, the critical current for unpinning) - Entrainment Is it possible to use glitches to obtain “model-independent” statements about neutron stars interiors? SPOILER: yes, we have at the moment 2 models: 1 – Activity test → “entrainment” 2 – Largest glitch test → “pinning forces” Question: is it possible to go beyond these two tests? What can be done? Neutron stars – RPPs What we observe, since: What we think it is, since: Hewish, Bell et al., Observation of a rapidly pulsating Pacini, Energy emission from a neutron star (1967) radio source (1968) Gold, Rotating neutron stars as the origin of the pulsating radio sources (1968) Magnetic field lines Radiation beam Coordinated observations with three telescopes: 22-s data slice of the pulsed radiation at four different radio Open issue: precise description bands obtained of the 1.2 s pulsar B1113+16. of beamed emission mechanism Why? Coherent (i.e. non-thermal) emission + brightness + small period: only possible for very compact objects A vibrating WD or NS? excluded by pulsar-timing data: P increases with time. BH accretion? No regular pulses... SOLUTION: pulsars are strongly magnetized rotating neutrons stars. Neutron stars - structure Sketch of nuclear matter phase diagram What we can not observe: internal structure Main idea: compressing matter liberates degrees of freedom. Gravity, holds the star together Electromagnetism, makes pulsars pulse and magnetars flare Strong interaction, determines the internal composition and prevents gravitational collapse Weak interaction, determines the internal composition and affects reaction rates (chemical equilibrium and neutrino cooling) Neutron stars – M-R relation TOV equations: hydrostatic equilibrium in GR TOV inversion: Lindblom, ApJ 398, 569 (1992) EOS lines not intersecting the J1614-2230 band are ruled out. Rotation increases the maximum possible mass for each EOS: ≲2% correction for P~3 ms. Demorest et al. Nature 467 (2010) Shapiro delay forPSR J1614-2230 PB Demorest Residuals “with GR” Residuals “without GR” Shapiro delay functional form In In contrast withX-ray-based mass/radius measurements,Shapiro delay providesno information about the NS radius. et al. Nature 467 ,1081-1083 (2010) (0.500±0.006) M helium-carbon-oxygen WD Companion: andthe companion. infer the masses of both the neutron pulsar star systems, Shapiro delay For allows to nearly edge-on millisecond radio (1.97±0.04) M Millisecond pulsar ⊙ ⊙ Shapiro delay: high-mass MSP J0740-6620 Cromartie et al. arXiv:1904.06759 A very massive neutron star: relativistic Shapiro delay measurements of PSR J0740+6620 12-year data set yielded a pulsar mass of 2.17+/-0.10 MSun at 68.3% credibility. Modeling the thermal pulse profile of this MSP at X-ray energies will aid in constraining both M and R. Pulsartiming Period derivative ( s/s ) Infer red feld ma gnet Perio ic d d ( s ) derivative) are precisely determined. Period P and spin-down rate (period a very small glitch in a binary system). magnetars and millisecond pulsars and catalogue (including few glitches in objects reported in To date the ~500 Jodrell glitch Bank events irregularities (glitches). in ~170 down... except Stable clocks for with random predictable timing spin- the second derivative ofis P needed. Sanity check from the braking index, but B). regions (inferred age and magnetic field Different classes populate different Pulsar glitches “Lack” of radiative/pulse profile changes (in RPPs): → Evidence for internal origin Vela: almost no recovery Long recoveries: → Impossible to explain if viscosity is present Diverse phenomenology in RPPs: → probably due to different age (temperature), mass, rotational parameters... Crab: nearly complete recovery Key point: to describe glitches we need that a NS is comprised of (at least) two components that exchange angular momentum. Can we identify the (two?) components ? Which part of the NS provides the angular momentum needed to spin-up the “observable component” ? Starquake model Ruderman, Nature 223, 597 (1969) Liquid interior The quake causes a sudden rearrangement of the moment of inertia and ultimately a glitch. With this model it is possible to explain only the “jump”, not the subsequent relaxation. Further problem: according to this theory, glitches should be rare: Baym&Pines, Ann. Phys. 66 (1971) ( in the Vela every ~3 yrs, not enough time to develop stresses, Giliberti et al. arXiv:1902.06345 ) Glitch recovery The recovery from glitches in not uniform: - Sometimes an “exponential” relaxation is observed, sometimes a “step-like” increase of the frequency. - Both behaviours can be seen in the same object! The instantaneous jump may be described in terms of a sudden rearrangement of the star crust, but not the recover. We need another ingredient (the superfluid) to describe glitches. Two-component model Baym et al. “Spin Up in Neutron Stars : The Future of the Vela Pulsar”, Nature (1969) The long recovery time-scales (of order months) observed after the first Vela glitch were considered to be evidence for a weakly coupled superfluid component in the stellar interior. Superfluidity → “no viscosity” → long relaxation timescale “crust” “neutrons” bra tor ki qu ng e (“mu Intern tual f al to rictio rque n”) Neutron drip → Inner core? → Two-component model Two-component Superfluidity → “no viscosity” → long relaxation timescale the stellar interior. evidence for a weakly coupled superfluid component in observed after glitch the were first considered Vela to be The long recovery time-scales (of order months) Baym etal. “SpinPulsar”, Nature Up (1969)in Neutron FutureTheStars : ofthe Vela “c “n rust eutr ” ons” bra tor qu ki ng e (“mu Intern tual f al toal rictio rque n”) (too much oblateness and building stress rate needed) → → Coupling timescale: fitted from post-glitch relaxation. the “healing parameter” Q. the change in the moment of inertia sets the amplitude and Spin-up is given by the settling of the crust (starquake): Still problems with very large glitches Relaxation is always exponential -5 Angular velocity (~10 rad/s) # o s t - g l i t c $ s % i n - d o w n m o d e l !"servational # "lac windor w e - Time (~wee s) (~wee Time g l i t c $ s % i n - d o w n (1-Q) m o d e ΔΩ l gl ΔΩ gl (1-Q) Q ΔΩ gl ΔΩ gl Glitch mechanism (vortex mediated) Anderson & Itoh Pulsar glitches and restlessness as a hard superfluidity phenomenon (1975) - The charged component steadily looses angular momentum t x s e - Vortices are pinned the superfluid cannot spin-down a t p r o w v o l → vortex line carried by the charged component a F → a velocity lag builds up → neutron current in the frame of the normal component Magnus force - Magnus force ≃ pinning force: the vortex line unpins → analogy between unpinning lag and critical current in superconductors → vortices can move: mutual friction between the components Expulsion of vortex lines from bulk superfluid Local: vortex creep Global: vortex avalanche (thermally activated) (trigger?) Analogy: “noisiness” in superconductors velocity of flux-lines S. Field et al. Superconducting Vortex Avalanches (1995) velocity of flux-lines “Strong pinning regimes by spherical inclusions in anisotropic type-II superconductors” R. Willa et al. (2018) In the complete phase diagram of the dynamical phases also the variable J should be considered! Hydrodynamics in neutron stars The dynamics of vortices is hidden inside this term. Pinning modifies the mutual friction (when all vortices are perfectly pinned the mutual friction is zero) (x = n or p) Assumption: the charged component Widely used approximation: (and possibly the superfluid core) circular flow (no meridional circulation) rotates as a rigid body On the other hand, the superfluid in the crust can rotate non-uniformly. - - - - Entrainment coupling: crustand core In the core: the In In the crust: the In → Alpar et al. coupled to the crust on the timescale of a second. → - Local effect: m*<1 different mechanism: actually - Very idea similarmore toA&B the original - Entrainment is due to the strong interaction between protons and neutrons star core, Chamel N., Haensel P. for pulsar glitch theory. component: reduced mobility of free neutrons is a potential problem → - Bragg scattering by crustal lattice, non-local effect: m* > 1 the framework of the band theory of solids, Chamel N. Consequence #2: Dipole-dipole interaction with flux-tubes (core pinning?) Consequence #1: Scattering of electrons off vortex cores: the core is Consequence: the crustal superfluid is entrained by the normal Phys. Rev. C 73 (2006). Phys. Rev. Neutron conduction in the inner crust of a neutron star in Rapid postglitch spin-up of the superfluid core in pulsars(1984) Entrainment parameters in a cold superfluid neutron Phys Rev C 85 (2012) Core of the vortex line Attached magnetic field E Vortex n d t I r line n r a d a t i h g n u e g e c e d e n d d p e v r u e o e t l t r e l o o o c n n c t r s i t o f y l n a u f s n i d i d e l d i n Test #1: entrainment Entrainment parameters: Chamel, N.
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