INT - Neutron Star Crust and Surface

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Monday, June 25: Isolated Neutron Stars and Pulsars

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Dong Lai - Surfaces of magnetic neutron stars

  • Cohesive energy of neutron star surfaces; strong magnetic field yields a condensed surface for iron and carbon
  • Could imagine that hot magnetars can fill the gap; while cold magnetars would leave a vacuum gap, so have high-B field radio pulsars
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Eric Gotthelf - CCO pulsars as anti-magnetars

  • Evidence for neutron stars weakly magnetized at birth
  • new results: steady pulsations without detected spin-dow in two CCOs (PSR J1210-5209, PSR J1852+0040)
  • A new interpretation for the nature of CCOs
  • X-ray bright unresolved point sources located near the centre of a SNR; no evidence for non X-ray emission, steady flux in thermal blackbody (0.4 keV like the AXPs - small emission area)
  • Two with periods have 105ms and 424ms (bold in next line)
  • Cas A, Pup A, G266.1-1.2, Kes 79, PKS 1209-51, G347.3-0.5
  • CCO: 1E 1207.4-5209; 0.424s period, deep absorption features, pulse period is steady, deep radio and optical limits, spin-down age exceeds the age of the remnant by three orders of magnitude
  • Kes 79 - 105ms pulsar detected with XMM, no significant change in pulse period; spin down again exceed age by three orders of magnitude
  • The x-ray luminosity exceeds the spin down luminosity; but comparable to the cooling luminosity
  • The B-field is less than 1011 G, remnant
  • Look at Kes 79 for absorption features
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H.J. Schulze - Pairing gaps in neutron star matter

  • Goal is to calculate the pairing gaps from fundamental interaction (bare potential)
  • Electron systems
  • T=1, nn, pp pairing (isospin=1):
    • Pairing force in finite (halo) nuclei
    • Superfluidity in neutron stars: glitches, cooling
  • T=0, np pairing:
    • Relevance for finite nuclei (N\approx Z)
    • Deuteron corrleations and productions
  • Pairing in trapped atomic gases
  • Colour superconductivitiy
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General Theory

  • General framework: single particle propagator is related to self-energy; Dyson equation
  • Gap is analogoue to the self-energy (kin=kout for self-energy and kin=-kout
  • The BCS approximation assumes that the interaction is through the bare nucleon-nucleon potential.
  • Can expand the gap in terms of partial waves, e.g. interaction through the 1S0 channel
  • BCS at low density (weak-coupling approximation)
  • Get

\frac{\Delta(k_F)}{\epsilon_f} = \frac{8}{e^2} \exp \left [ \frac{\pi}{2k_f a_{nn}} \right ] where ann is the scattering length.

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nn Pairing Gaps

  • The pairing gap (s-wave) peaks at 3MeV around kF of an inverse ferm disappears for higher densitiesi; various fits to nucleon-nucleon interaction give similar results at the BCS level
  • BCS results with bare nn potentials for p-wave interaction are not well-constrained above 2 inverse fermi because this regime is not constrained by observations of phase shifts in the nuclear scattering
  • At high density you should also include 3-body interaction
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In-Medium Interaction

  • BUT when the first-order diagram is included the gap is typically smaller and much more uncertain due to uncertainties in how to include the polarization
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Gaps in beta-stable matter

  • Get pairing between n-n, p-p and n-p in beta stable matter as in neutron stars (both p-wave and s-wave)
  • Different pairing gaps with hyperons
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A. Schwenk - Superfluidity in neutron stars

  • impact on cooling: suppresses ν emission, but thermal quasiparticles can emit neutrino-anti-neutrino bremsstrahlung
  • similar to the Li-11 halo nuclei that decay via a weak interaction in the core not the paired halo neutrons
  • neutron-neutron scattering length is a_{nn} = -18.5 \pm 0.3{\rm fm}, low density neutrons can be constrained by experiments with cold atoms (T_c\sim 0.2-0.3T_F; gaps are smaller than the BCS approximations
  • neutron matter in stars is less dilute - effective range of neutron-neutron interaction is 2.7 fm, important for momenta greater than 0.3 inverse fermi or so
  • inverse interactions beyond BCS change the prefactor of the gap equation even for low density (a factor of three)
  • sum over the planar diagrams using renormalization group flow
  • build a difermion effective field theory to use at lower densities
  • induced interactions strongly affect the p-wave results, must include spin-orbit, spin-spin and tensor interactions
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E. Vigezzi - Pairing calculations beyond MF in the inner crust

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Mean-field Approximation

  • Looking at the properties of free neutrons traveling through a field of nuclei; assume that one can look at a single Wigner-Seitz cell
  • What is the pairing in this system?
    • Near the centre of the nucleus, high Fermi momentum, small gap
    • Near the edge of the nucleus, medium Fermi momentum, big gap
    • Outside, low Fermi momentum, small gap
    • In total expect to lower the gap; calculations indicate that the gap is reduce by about 10%
  • The decrease in the gap increases the specific heat (by an order of magnitude perhaps) but the electron specific heat is much larger unless the neutron matter is not superfluid
  • The difference in the effective mass leads to important consequences in vortex pinning (see talk by Barranco)
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Beyond the mean-field approximation

  • medium effects increase the gap (exchange of vibration of the system with or without spin)
  • surface nature of the modes causes a big difference with bulk neutron matter (where the spin interaction decreases the gap)
  • pinning of vortices occurs at the surface of the nuclei so keeping track of this effect is crucial
  • Could this affect the transition with neutron drip? Could you get a discontinuous jump in the neutron fraction with increasing density?
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F. Barranco - Microscopic calculation of vortex-nucleus interaction

  • motivated by the observations of glitches which are caused by the sudden unpinning of vortex lines
  • similar theoretical framework to Vigezzi
  • Inner crust nuclei rotates as a rigid body with the outer crust, Magnus force pushes the superfluid vortices outwards
  • Compare the energy of a vortex in an interstitial configuration to a vortex stuck onto a nucleus
  • Find that the vortex is pinned at low and high densities (kF 0.45 or above 1.2 inverse fermi)
  • The pairing gap is strongly suppressed in the nucleus; the pairing is destroyed near the edge of the nucleus
  • Vortex core radius is much larger when the vortex is pinning (much larger increase than found in semiclassical calculations)
  • The vortex is not so well excluded from the core of the nucleus for larger effective mass in the effective interaction
  • No pinning except for a small region in the crust (low density); bad for glitches -- move glitches into the core (different modes of turbulence in the core)
  • How do medium effects change these results?
  • What are the consequences for vortex dynamics?
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J. Carlson: Pairing gaps in low-density neutron matter and cold atoms

  • S-wave pairing in neutron stars and cold atoms
  • Transition from weak (BCS) to strong (BEC) pairing and 'exotic' states of matter
  • Interaction strength adjustable, range essentially zero
  • At infinite scattering length, all energies are a universal constant times the Fermi energy
    • ground state = 0.25, pairing gap = 0.5, superfluid transition = 0.25
  • Away from the infinite scattering length, these ratios are a function of the Fermi energy
  • Equation of state: neutrons vs cold atoms, good agreement up to 0.5 inverse Fermi
  • Diffusion (Green's function) Monte Carlo; use a variation wavefunction and vary the locations of the nodes of the wf to minimize the energy
  • Energy of the gas compared to the Fermi gas energy is 0.42(2) calculation agrees with observations of cold atoms
  • Radial modes in a trap can be calculated too with good agreement
  • Big depletion of particles just below the Fermi surface and excess particles above the Fermi surface; up and up are correlated as in a free Fermi gas but up and down are highly correlated
  • RF response gives 0.2 EF for the gap from RF response but the final flipped particle is highly correlated with particles of the same spin (not like other particles with the same spin which are not highly correlated)
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Tuesday, June 26: Isolated Neutron Stars and Pulsars

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C. Horowitz: Neutron rich matter and neutron star crusts

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Neutrinosphere in supernovae and the viral expansion

  • Temperature is 4 MeV, ρ about 1011 g cm-3
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Neutrino pressure

  • Virial expansion:
  1. System is the gas phase
  2. Fugacity is small (z=eμ/T)
  • Expand pressure in powers of z;

P=2T/\lambda^3 \left [ z + b_2 z^2 + b_3 z^3 \right ]

  • b2 is the second virial coefficient which can be calculated from the two point phase shifts.
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Nuclear pressure

  • Neutrons, protons and alpha particles; again expand in fugacity
  • Formation of clusters (alphas) tends to mess up microscopic calculations, but the virial expansion works well
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Neutrino response

  • Vector response is given by the derivative of the equation of state more or less
  • Stronger response that used customarily in SN calculations.
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Crust properties and the density dependence of the symmetry energy

  • Update of Pb radius (PREX)
  • Symmetry energy S describes how E of nuclear matter rises as one goes away from equal numbers of neutrons and proton
  • Pressure depends on derivative of E with respect desntiy. P of nuclear matter small and largely known so the pressure of neutron matter depends on the density dependence of the symmetry energy.
  • Heavy nucleus has neutron rich skin; thickness of skin depends on the pressure of neutron matter as n are pushed out against surface tensions
  • The weak charge of the neutron is much higher than that of a proton so the parity violating portion of the scattering depends on the thickness of the neutron skin
  • Crust of neutron star is at similar densities as the neutron-rich skin
  • The symmetry energy is also related to the electron chemical potential and therefore the charge density of neutron matter - direct Urca process can work if the proton fraction is large enough.
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Nuclear pasta phases and MD simulations

  • Frustration between comparable attractive nuclear and repulsive Coulomb interactions
  • n and p interact via a 2 body phenomenological potential
  • Need structure factor of nucleons (essentially Fourier transform of two-point correlation) to determine neutrino scattering, but the wavelength of the neutrino is about 120fm, so need a large simulation (105 nucleons)
  • Expect a very large S(0) in two-phase coexistence region of liquid-solid transition, but in the end this doesn't happen because the transition is gradual.
  • Dynamical response of pasta may be important for transport properties (time dependent correlation function)
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Chemical separation in the crust of accreting neutron stars

  • rp process ash from x-ray bursts is very proton-rich. As it get pushed down, it moves toward neutron drip and get a range of nuclei
  • Liquid ocean is enriched in the low Z elements whereas the solid is enriched with high Z elements
  • Single component system 3456 ions where each ion has the same charge gives a melting point of Γ = 176 compared with Γ = 177 as expected for a one component plasma
  • For example 16O is greatly depleted in the solid phase compared with the liquid
  • Impurities lower the melting temperature by about 30%
  • Ocean of the accreting star will be greatly enriched by a factor of ten; if carbon survives to the bottom of the ocean, it would be greatly enriched -- superbursts
  • As accretion rate decreases even the low-Z stuff can freeze so get layers with various compositions.
  • Shape of the neutron star, shear modulus, breaking strength of the crust
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J. Piekarewicz: The Impact of Terrestrial Facilities on the Structure of the Neutron Star Crust

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Nuclear Physics 101

  • Bethe-Weiszacker mass formula: nuclear forces saturates so there is a equilibrium density; surface tension, Coulomb force and symmetry energy
  • Mixture of heavy clusters (nuclei) and nucleons (gas)
  • Slope of the energy per nucleon with respect to density is not constrained by nuclear ground state properties, so the pressure is not constrained.
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The Jefferson Lab

  • electroweak (clean) meusurement of the neutron radius in lead.
  • constrain - crust-to-core transition radius, electron fraction and Urca cooling, neutron-star mass-radius relation
  • softer symmetry energy reaches drip lines first; softer EOS for neutron stars
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The Overridding Questions

  • What characterizes the crust-to-core transition and what are the phases between the Fermi liquid and the Wigner crystal?
  • Steve Kivelson with Reza Jamei and Boris Spivak theorem: In the presence of long range interactions r-x, no first order phase transition is possible for d-1<x<d. Rather you get a gradual transition through mixtures between two phases.
  • Density functional theory to calculate the EOS from the outer crust to the inner core.
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J. Lattimer: Observational Constraints on the Neutron Star Crust and Their Implications for the Dense Matter Equation of State

  • The neutron star crust: inner edge transition between phases with nuclei and uniform matter
  • Transition density and pressure; crustal extent in radius, moment of inertia and mass (radial extent depends on enthalpy at transition, moment of inertia depends on pressure at the transition)
  • Phenomenological model where the Coulomb and surface energies depend on the dimension of the pasta phase
  • Fission instability and clustering instability
  • Lower limit of a pasta phase is insensitive to nuclear parameters but the upper limit does depend sensitively on the density dependence on the symmetry energy (if the symmetry pressure is too large, there is no pasta phase)
  • Composition is also symmetry dependent
  • Maximum mass around 4 Msolar, mimimum period is around 1ms, maximum density is around 4e15
  • Neutron star pressure is approximately proportional to the density squared -- so the radius is approximately independent of the mass; radius measurement gives the pressure around saturation density
  • Estimates of radiation radii from 1856 and globular clusters
  • Torsional mode frequencies
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K. Sato: Nuclear "pasta" phases by Quantum Molecular Dynamics

  • Use Hamiltonian with symmetry and surface energy and integrate the particles forward in time with Hamilton's equations with viscous term.
  • Smooth nucleons -- the nucleons are not strictly localized
  • An extra energy to account for the Pauli exclusion principle
  • Phase diagram, spongy mixed phases
  • As the temperature increases the edge of the slab becomes diffuse, neutron drip, bridges between slabs
  • At higher temperature get more regions with mixed phases
  • Amplification of neutrino opacities from the disorder introduced by the pasta phases
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B. Link: The Dynamics of Vortex Pinning in the Neutron Star Crust

Vortices are attracted to nuclei in the crust, but do they pin? Probably they cannot.

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Why worry about vortex pinning?

  • spin jumps (glitches)
  • precession ("wobble", nutation); constrains pairing states of the outer core
  • Stochastic spin variations (timing noise)
  • Crust shear modes: difficult to explain with a strange star
  • Pinning/unpinning might be responsible for spin jumps
  • Problem: pinning in the crust is inconsistent with observations of long-period NS precession
  • Macroscopic distribution of vortices determines the angular momentum of the fluid; their mobility determines the transfer of angular momentum (this is dissipative so this must occur in the normal core of the vortex)
  • Straight vortices have on average zero force with nuclei; bend the vortex to intersect many nuclei then the force per unit length is the pinning force for a single nuclei divided by the distance between the nuclei
  • However, the vortex carries a tension of 10 MeV/fm, so it doesn't bend easily. The vortex will bend to come close to the neighboring nuclei and strike a compromise. Bending length is much greater than the internuclear separation.
  • To get to the pinned state, the vortex must lose some energy (energy dissipation by exciting phonons in the lattice). Need for there to be vortex-nucleus interaction, need to propagate phonons and bend the vortex.
  • The final state has the vortex offset relative to the nucleus; closer but not on top because of the string tension
  • Calculations of the pinning time indicate that we are in the low drag regime
  • Pinning of a vortex with net translational motion; it must move slowly enough so that v tt is less than the internuclear distance -- about 10 cm/s
  • Pinning is marginal as best; probably impossible in a spinning-down NS; low-drag motion allows long-period precession
  • But how to explain glitches.
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S. Price: Time-correlated Structure in Spin Fluctuations of an Isolated Neutron Star

Goal: To identify evidence of non-rigid body rotation

  • Timing noise: response of the crust to stochastic torque
  • All the modes are excited, but previous studies using Fourier techniques have found no evidence of non-rigid body rotation
  • Two component model of a neutron star

I_c \dot \Omega_c = N(t) - \frac{I_r}{\tau} \left ( \Omega_c - \Omega_s \right ), I_s \dot \Omega_s = \frac{I_r}{\tau} \left ( \Omega_c - \Omega_s \right )

  • The frequency response of the two-component star has a knee at frequencies 1/τ whose height depends on the ratio of the two components. Analysis in the frequency domain has not yet discovered any frequency structure
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PSR 1133+16

  • Period of about 1s, good data on timing residuals with amplitude of about 1ms.
  • The distribution is the residuals is not well fit by a Gaussian, lots of events far away from the mean
  • Calculation the auto-correlation function generalized for unevenly sampled data;
  • Find a correlation over a period of about ten days
  • Perform Monte Carlo simulations by shuffling the times of the residuals, don't find such a strong correlation in 104 trials.
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A. Turbiner: One-two electrons atomic-molecular systems in a strong magnetic field

  • One and two electron Coulomb systems made out of several protons and/or alpha particles
  • Variation method; choose good trial functions
    • physical relevance
    • don't worry about mathematical simplicity
    • resulting perturbation theory should be convergent
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One-Electron Systems

  • Linear configurations, binding energy of systems grows while size shrinks
  • Binding energy of strongest bound helium species is about twice that of strongest bound hydrogen
  • Above the Schwinger field, many more exotic systems begin to exisit
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Two-Electron Systems

  • As magnetic field grows a change in quantum numbers of the ground state should occur (true level crossing)
  • ml = 0,ms = 0 to ml = 0,ms = − 1 and finally for strongest field ml = − 1,ms = − 1.
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M. Baldo: Microscopic theory of the neutron star inner crust

  • Above the neutron drip line the chemical potential of neutrons exceeds zero; this separates the inner crust from the outer crust
  • The last bound nucleus was 114Kr.
  • Systematic analysis about the neutron drip point found a similar drip point with a variety of nuclei
  • Models separate from each other at high mass density
  • Energy density functional: mean field with effective interaction (the parameters of the effective interaction are fit to the properties of normal nuclei)
  • Includes neutron and proton pairing, modern functional, study of the boundary conditions in the WS method
  • Changing the boundary conditions can change the value of Z for the nucleus -- internal uncertainty of the WS method
  • Two competing drip regions -- depending on the details of the DFT
  • Direct solution of the gap versus the LDA suppresses the gap by a factor of 2
  • Outlook:
  1. Different accurate functionals for the structure
  2. The EOS seems to be less sensitive (oscilattions, ... )
  3. Excitations/finite temperature
  4. Include deformations
  5. Structure from band theory
  6. inter-band Cooper pairs
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J. Margueron: Equation of state in the inner crust of neutron matter: discussion of the shell effects

  • "bare" calculations of the EoS
  • discussion of shell effects
  • equation of state in the inner crust with partial removal of continuum shell effects
  • deformation of the nuclear cluster
  • shell effects, band theory
  • nuclear force at low densities and large asymmetries
  • zero range effect pairing force; smooth or sharp cut-off
  • Outlook
  1. Perform the same analysis with pairing and finite temperature
  2. The model provides the basic ingredients of macroscopic models
  3. Link between gap in homogenous matter and non-hom matter
  4. Application: cooling process (specific heat)
  5. Explore the sensitivity of the macroscopic variables on nuclear interaction, symmetry energy, pairing interaction
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C. Fryer: After the Shock, Magnetic Fields and Fallback on Newly Formed Neutron Stars

  • Fallback invoked since the early 1970s; Arnett argued that the innermost material would not agree with the nucleosynthetic yields; Colgate said that this material would fallback
  • Explanations for fallback:
  1. Material pushing against outer layers slows until its velocity falls below the escape velocity -- early fallback (few seconds)
  2. As the shock decelerates as it moves through the shallow density gradients of the star, its velocity drops below the escape velocity and send a reverse shock back -- late-time fallback (few hours)
  • Modern simulations of fallback
  1. Fallback seen in nearly all modern (energy injection explosion models) simulations
  2. For 1-2 foe explosions the accretion rate for stars more massive than 15 solar masses is 0.1-1.5 solar masses in the first few seconds.
  3. Colgate fallback scenario correct - occurs in both II and Ib/c supernovae.
  • SN 2005bf had a late-time maximum; lots of excess Ni that later disappears or maybe a magnetar
  • If the fallback is too rapid, it drives super-Eddington accretion that ejects much of the matter (seen in one and two dimensional simulations)
  • During fallback lots of energy that would have ended up in neutrinos going to ejecting the infalling material -- changes neutrino luminosities -- also affects nucleosynthetic yields.
  • The kinetic energy of the outflowing matter in the simulation quickly rises to a few 1048erg/s stopping further fallback.
  • Rapid n+p capture rp-process, so you don't get stuck at the waiting points for neutron capture (just get a proton)
  • Conclusions
  1. Fallback happens
  2. Fallback accretion is at least as turbulent as the explosion mechanism itself
  3. Could probe the fallback using yields and explosion effects
  4. Expect much more work on this in the near future!!!
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A. Hungerford: Neutrino Scattering in Proto-Neutron Stars

  • Motivation for this project; angular effects in neutrino transport
  • Differential scattering kernel
  • Post-process Monte Carlo neutrino transport
  • Neutrino heating plays an important role in core-collapse SnE
    • affects explosion energy and timing
    • core-collapse theorists have argued that high-order transport is necessary for treating neutrinos (asymmetries in the explosion and anisotropic scattering but is there shadowing)
  • Radiation-hydrodynamics
  • Multi-angle transport methods are memory and cpu-intensive but multi-energy is more tractable
  • Include correlations between the direction of the incoming and outgoing neutrinos, changes in its energy and their dependence on Ye, ρ etc.; sample this distribution using a Monte Carlo realization of the radiation field
  • Energy exchange is important in determining the spectrum of neutrinos at a given time but they don't agree with the inline gray, flux diffusion transport scheme.
  • The opacity model must be consistent with the simulation
  • Smaller scattering opacity allows neutrinos to escape more readily and do not help support the collapsing material, so the bounce is stronger
  • Summary
  1. Rejection sampling technique seems affordable for investigating effects of detailed scattering kinematics
  2. Time independent transport studies can be used to look at trends between numerical techniques
  3. Multi-energy more important than multi-angle.
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Wednesday, June 27: Magnetars - Pulsars

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V. Kaspi: Magnetars

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SGRs

  • sources of rate, brief, intense and repeating soft gamma ray and

x-ray bursts.

  • 5 known, 4 in Galaxy anf one in LMC.
  • March 5, 1979 : E > 5 1044 erg, from N49 SNR in LMC
  • December 27, 2004: SGR 1806-20
  • Could be relevant to a fraction of GRBs
  • Much more common are small bursts, tend to occur in bunches that

last weeks and recur on timescales of years; 100ms duration

  • X-ray pulsations in quiescence at the same periods as in the giant

flares with steady spin down.

  • Emission is much bigger than spin down power
  • Need magnetar field to confine the energy in the tails of giant

bursts; light curve

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AXPs

  • 8, possibly 9, sources
  • X-ray emission cannot be powered by spin-down
  • No evidence for a companion
  • Fall-back disk but no bursts possible
  • Magnetars: "quieter" form of SGR, but with slightly lower magnetic

fields.

  • AXPs exhibit SGR-like x-ray bursts (now seen in 5 AXPs).
  • AXPs are generally rotationally stable but do exhibit timing noise
  • Renders accretion models unlikely, makes glitch detection easy
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AXP Glitches

  • Glitches seen in a couple of AXPs, some of them completely heal
  • No large flux changes in these objects.
  • June 2004: burst from 1E 1048-5937
  • June 2002 : 1E 2259+586 had 80 bursts detected over a few weeks,

large increase in pulsed flux and profile changes and glitch. First glitch with radiative changes (19% recovery over two weeks, requiring double the spin down rate during the recovery period)

  • Some glitches are radiatively loud, others are quiet as in radio

pulsars (8 glitches in total)

  • Fractional amplitude of glitches is large for AXPs relative to radio

PSRs, but the absolute amplitude is not remarkable.

  • Calculate the G parameter from Link, Epstein and Lattimer

G=\frac{\nu}{\dot \nu} A_g.

  • The angular momentum resevoir but have

G\leq \frac{I_{\rm res}}{I}.

  • AXP 1E 2259 stands out with G of about 25%.
  • Large and fast glitch recoveries require extremely big increases in the spin

down rate relative radio pulsars

  • For 1E 2259, 8/9 of I must be decoupled, for 1708/1841 about 40% of

moment of inertia decoupled.

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Connection to EOS

  • Could the glitches be in the core superfluid?
  • Possibly, the superfluid ends up rotating slower than the crust

after the glitch (the glitch overshoots!)

  • How is high B related? Ruderman et al 1998 consider vortex line

interaction with magnetic flux tubes (could high B enhance this interaction?)

  • A new magnetar model: pion condensate produces a strong screened

magnetic field, as the screening currents decay generating heat. SGRs would be older than AXPs which is consistent with SNR associations.

  • Naturally explains the cessation of magnetar activity for P>12s, the

field eventually reaches a dipole configuration.

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Transient Magnetars and Birthrate

  • AXP discovered in "outburst": XTE J1810-197. Quiescent luminosity

is 10-100 lower than in outburst but no bursts detected.

  • AXP candidate J1845-0258 seen in 1993 only; now it is at least 100

times fainter.

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AXPs and Radio Pulsars

  • Is the B distribution is bi-modal? There is overlap in the spin 
 properties (P/Pdot, timing noise and glitches).
  • XTE J1810-197 (transcient AXP) had radio pulsations (brightest 
 radio pulsar at 22 GHz).
  • Only one high B-field radio pulsar has been detected in x-ray. 
 Consistent with initial cooling but spectrum and flux consistent
 with transient AXP in quiescence.
  • PSR J1119-6127: high pulsed fraction in soft x-rays, consistent with 
 initial cooling.
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A. Watts: Magnetar seismology

  • Duncan argued that the giant flares could excited torsional modes of the neutron star.
  • Found seismic activity in the giant flare of 27 Dec 2004 (SGR 1806-20) in RXTE and RHESSI and also in 27 Aug 1998 (SGR 1900+14).
  • In 1900 get a bunch of modes that line up with n=0 modes with different radial dependence.
  • In 1806 get a bunch of n=0 modes plus some that might be n=1, n=3 and 'core Alfven modes'
  • Widths of about 2 Hz, Q values from 10-1000, no viable non-seismic mechanism.
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QPO Properties

  • The oscillations only occur in the secondary peak of the rotational pulse.
  • 150Hz is active throughout the flare
  • 92Hz and 29Hz - during a short time
  • The Q-values would indicate that the modes should decay over a few seconds but they persist for tens of seconds (phase jumps)
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Magnetic connection with the core

  • A strong field should couple the crust to the fluid core so free slip is inappropriate.
  • Magnetized core will have its own natural vibration frequencies - possibly the lowest frequency QPOs.
  • In the core there is a continuous spectra of waves (apparently). Unusual oscillations when kicked (initial value simulations). Star behaves as a coupled oscillator but with drifting and amplification at the natural crust frequencies.
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Magneto-seismology

What can the mode frequencies tell us about the properties of the crust?

  1. Disfavours a hard EOS.
  2. The 625 Hz QPO seen in SGR 1806-20 is thought to be the first radial

overtone of the crust shear modes. Frequency of this mode is highly dependent on crust thickness. 626 Hz and 30Hz implies a thick crust and low mass.

  1. Thin nuclear crust model and strange nuggest crust cannot yield the

observed frequency over a wide range of mass, radius and models of the outer crust.

  1. Clear distinction in predictions for neutron star and strange star

crusts. Cannot fit the data without reducing the magnetic field by an order of magnitude.

  1. Limits from LIGO on a future giant flare will be physically

interesting.

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Smaller flares, smaller quakes?

  • Giant flares are rare and unpredictable.
  • Look at the regular intermediate and the normal flares for QPOs but

nothing found yet.

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Crust and surface issues

  • Why do we see the oscillations? Critical if we are to use X-ray 
 amplitudes to deduce the physical amplitudes.
  • Crust fracture: how does it work?
  • Pasta phase.
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S. Zane: SGRs long term spectral variability

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R. Turolla: X-ray Spectra from Magnetar Candidates

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D. Eichler: What Can We Learn about Magnetar Crusts from the QPO Component of their Flare Emission?

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Thursday, June 28: Accreting Neutron Stars

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E. Cackett: Crustal cooling in accretion heated neutron stars

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A. Steiner: Symmetry energy, crust thicknesses, and KS 1731

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N. Sandulescu: Nuclear Superfluidity and Cooling Time of Neutron-Star Crust

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C. Heinke: Constraints on Neutron Star Physics from Transiently Accreting Neutron Stars in Quiescence

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K. Levenfish: Thermal steady-states of neutron stars in SXTs vs deep crustal heating

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E. Brown: Crust electron captures: Implications for superbursts and transient lightcurves

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S. Reddy: Weak interactions in superfluids and cooling rates in the inner crust

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Glossary of Neutron Star Classes

These are <5 sentence definitions of the different observed classes of neutron stars.

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Low Mass X-ray Binaries (LMXBs)

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High Mass X-ray Binaires (HMXBs)

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Radio Pulsars

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Millisecond Radio Pulsars (MSPs)

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X-ray Dim Isolated Neutron Stars

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Magnetars

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Anomalous X-ray Pulsars (AXPs)

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Soft Gamma-Ray Repeaters (SGRs)

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Compact Central Objects (CCOs)

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