WIMP Annihilation and Cooling of Neutron Stars

We study the effect of WIMP annihilation on the temperature of a neutron star. We shall argue that the released energy due to WIMP annihilation inside the neutron stars, might affect the temperature of stars older than 10 million years, flattening out the temperature at $\sim 10^4$ K for a typical neutron star.Comment: 20 pages, 2 figure

Damping of differential rotation in neutron stars

We derive the transport relaxation times for quasiparticle-vortex scattering processes via nuclear force, relevant for the damping of differential rotation of superfluids in the quantum liquid core of a neutron star. The proton scattering off the neutron vortices provides the dominant resistive force on the vortex lattice at all relevant temperatures in the phase where neutrons only are in the paired state. If protons are superconducting, a small fraction of hyperons and resonances in the normal state would be the dominant source of friction on neutron and proton vortex lattices at the core temperatures $T\ge 10^{7}$ K.Comment: 5 pages, Revtex, Phys. Rev. D 58, Rapid Communication, in pres

The rigidity of crystalline color superconducting quark matter

We calculate the shear modulus of crystalline color superconducting quark matter, showing that this phase of dense, but not asymptotically dense, three-flavor quark matter responds to shear stress like a very rigid solid. To evaluate the shear modulus, we derive the low energy effective Lagrangian that describes the phonons that originate from the spontaneous breaking of translation invariance by the spatial modulation of the gap parameter $\Delta$. These massless bosons describe space- and time-dependent fluctuations of the crystal structure and are analogous to the phonons in ordinary crystals. The coefficients of the spatial derivative terms of the phonon effective Lagrangian are related to the elastic moduli of the crystal; the coefficients that encode the linear response of the crystal to a shearing stress define the shear modulus. We analyze the two particular crystal structures which are energetically favored over a wide range of densities, in each case evaluating the phonon effective action and the shear modulus up to order $\Delta^2$ in a Ginzburg-Landau expansion, finding shear moduli which are 20 to 1000 times larger than those of neutron star crusts. The crystalline color superconducting phase has long been known to be a superfluid -- by picking a phase its order parameter breaks the quark-number $U(1)_B$ symmetry spontaneously. Our results demonstrate that this superfluid phase of matter is at the same time a rigid solid. We close with a rough estimate of the pinning force on the rotational vortices which would be formed embedded within this rigid superfluid upon rotation. Our results raise the possibility that (some) pulsar glitches could originate within a quark matter core deep within a neutron star.Comment: 38 pages, 5 figures. v3. Two new paragraphs in Section V (Conclusion); some additional small changes. A paragraph discussing supercurrents added in Section I (Introduction). Version to appear in Phys. Rev.

Superfluid Friction and Late-time Thermal Evolution of Neutron Stars

The recent temperature measurements of the two older isolated neutron stars PSR 1929+10 and PSR 0950+08 (ages of $3\times 10^6$ and $2\times 10^7$ yr, respectively) indicate that these objects are heated. A promising candidate heat source is friction between the neutron star crust and the superfluid it is thought to contain. We study the effects of superfluid friction on the long-term thermal and rotational evolution of a neutron star. Differential rotation velocities between the superfluid and the crust (averaged over the inner crust moment of inertia) of $\bar\omega\sim 0.6$ rad s$^{-1}$ for PSR 1929+10 and $\sim 0.02$ rad s$^{-1}$ for PSR 0950+08 would account for their observed temperatures. These differential velocities could be sustained by pinning of superfluid vortices to the inner crust lattice with strengths of $\sim$ 1 MeV per nucleus. Pinned vortices can creep outward through thermal fluctuations or quantum tunneling. For thermally-activated creep, the coupling between the superfluid and crust is highly sensitive to temperature. If pinning maintains large differential rotation ($\sim 10$ rad s$^{-1}$), a feedback instability could occur in stars younger than $\sim 10^5$ yr causing oscillations of the temperature and spin-down rate over a period of $\sim 0.3 t_{\rm age}$. For stars older than $\sim 10^6$ yr, however, vortex creep occurs through quantum tunneling, and the creep velocity is too insensitive to temperature for a thermal-rotational instability to occur. These older stars could be heated through a steady process of superfluid friction.Comment: 26 pages, 1 figure, submitted to Ap

Tkachenko waves, glitches and precession in neutron star

Here I discuss possible relations between free precession of neutron stars, Tkachenko waves inside them and glitches. I note that the proposed precession period of the isolated neutron star RX J0720.4-3125 (Haberl et al. 2006) is consistent with the period of Tkachenko waves for the spin period 8.4s. Based on a possible observation of a glitch in RX J0720.4-3125 (van Kerkwijk et al. 2007), I propose a simple model, in which long period precession is powered by Tkachenko waves generated by a glitch. The period of free precession, determined by a NS oblateness, should be equal to the standing Tkachenko wave period for effective energy transfer from the standing wave to the precession motion. A similar scenario can be applicable also in the case of the PSR B1828-11.Comment: 6 pages, no figures, accepted to Ap&S

Microscopic structure of a vortex line in superfluid neutron star matter

The microscopic structure of an isolated vortex line in superfluid neutron star matter is studied by solving the Bogoliubov-de Gennes equations. Our calculation, which is the starting point for a microscopic calculation of pinning forces in neutron stars, shows that the size of the vortex core varies differently with density, and is in general smaller than assumed in some earlier calculations of vortex pinning in neutron star crusts. The implications of this result are discussedComment: 5 pages, 2 figure

Pulsar Constraints on Neutron Star Structure and Equation of State

With the aim of constraining the structural properties of neutron stars and the equation of state of dense matter, we study sudden spin-ups, glitches, occurring in the Vela pulsar and in six other pulsars. We present evidence that glitches represent a self-regulating instability for which the star prepares over a waiting time. The angular momentum requirements of glitches in Vela indicate that at least 1.4% of the star's moment of inertia drives these events. If glitches originate in the liquid of the inner crust, Vela's `radiation radius' must exceed ~12 km for a mass of 1.4 solar masses. Observational tests of whether other neutron stars obey this constraint will be possible in the near future.Comment: 5 pages, including figures. To appear in Physical Review Letter

Crystalline Color Superconductivity

In any context in which color superconductivity arises in nature, it is likely to involve pairing between species of quarks with differing chemical potentials. For suitable values of the differences between chemical potentials, Cooper pairs with nonzero total momentum are favored, as was first realized by Larkin, Ovchinnikov, Fulde and Ferrell (LOFF). Condensates of this sort spontaneously break translational and rotational invariance, leading to gaps which vary periodically in a crystalline pattern. Unlike the original LOFF state, these crystalline quark matter condensates include both spin zero and spin one Cooper pairs. We explore the range of parameters for which crystalline color superconductivity arises in the QCD phase diagram. If in some shell within the quark matter core of a neutron star (or within a strange quark star) the quark number densities are such that crystalline color superconductivity arises, rotational vortices may be pinned in this shell, making it a locus for glitch phenomena.Comment: 40 pages, LaTeX with eps figs. v2: New paragraph on Ginzburg-Landau treatment of LOFF phase in section 5. References added. v3: Small changes only. Version to appear in Phys. Rev.