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.

Unusual glitch behaviours of two young pulsars

In this paper we report unusual glitches in two young pulsars, PSR J1825-0935 (B1822-09) and PSR J1835-1106. For PSR J1825-0935, a slow glitch characterised by a temporary decrease in the slowdown rate occurred between 2000 December 31 to 2001 December 6. This event resulted in a permanent increase in frequency with fractional size $\Delta\nu/\nu\sim31.2(2)\times10^{-9}$, however little effect remained in slowdown rate. The glitch in PSR J1835-1106 occurred abruptly in November 2001 (MJD 52220\pm3) with $\Delta\nu/\nu\sim14.6(4)\times10^{-9}$ and little or no change in the slow-down rate. A significant change in $\ddot\nu$ apparently occurred at the glitch with $\ddot\nu$ having opposite sign for the pre- and post-glitch data.Comment: Latex format, six files, 5 pages with 4 figues. accepted for MNRA

Color Superconductivity in Compact Stars

After a brief review of the phenomena expected in cold dense quark matter, color superconductivity and color-flavor locking, we sketch some implications of recent developments in our understanding of cold dense quark matter for the physics of compact stars. We give a more detailed summary of our recent work on crystalline color superconductivity and the consequent realization that (some) pulsar glitches may originate in quark matter.Comment: 19 pages. 2 figures. To appear in the proceedings of the ECT Workshop on Neutron Star Interiors, Trento, Italy, June 2000. Shorter versions contributed to the proceedings of Strong and Electroweak Matter 2000, Marseille, France, June 2000 and to the proceedings of Strangeness 2000, Berkeley, CA, July 2000. KR was the speaker at all three meeting

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

First hours of the GRB 030329 optical afterglow

We present the first results of the observations of the extremely bright optical afterglow of gamma-ray burst (GRB) 030329 with the 1.5m Russian-Turkish telescope RTT150 (TUBITAK National Observatory, Bakyrlytepe, Turkey). RTT150 was one of the first 1.5m-class telescopes pointed to the afterglow. Observations were started approximately 6 hours after the burst. During the first 5 hours of our observations the afterglow faded exactly as a power law with index -1.19+-0.01 in each of the BVRI Bessel filters. After that, in all BVRI filters simultaneously we observe a steepening of the power law light curve. The power law decay index smoothly approaches the value ~= -1.9, observed by other observatories later. This power law break occurs at t-t_0 =0.57 days and lasts for +-0.1 days. We observe no variability above the gradual fading with the upper limits 10--1% on time scales 0.1--1000s. Spectral flux distribution in four BVRI filters corresponds to the power law spectrum with spectral index \alpha=0.66+-0.01. The change of the power law decay index in the end of our observations can be interpreted as a signature of collimated ultrarelativistic jet. The afterglow flux distribution in radio, optical and x-rays is consistent with synchrotron spectrum. We continue our observations of this unique object with RTT150.Comment: Astronomy Letters, Vol. 29, No. 9, p. 573; 6 pages, 5 figures; pagination corrected; the original Russian version can be found at http://hea.iki.rssi.ru/~br/030329/pfh030329.pd

Timing of the 2008 Outburst of SAX J1808.4-3658 with XMM-Newton: A Stable Orbital Period Derivative over Ten Years

We report on a timing analysis performed on a 62-ks long XMM-Newton observation of the accreting millisecond pulsar SAX J1808.4-3658 during the latest X-ray outburst that started on September 21, 2008. By connecting the time of arrivals of the pulses observed during the XMM observation, we derived the best-fit orbital solution and a best-fit value of the spin period for the 2008 outburst. Comparing this new set of orbital parameters and, in particular, the value of the time of ascending-node passage with the orbital parameters derived for the previous four X-ray outbursts of SAX J1808.4-3658 observed by the PCA on board RXTE, we find an updated value of the orbital period derivative, which turns out to be $\dot P_{\rm orb} = (3.89 \pm 0.15) \times 10^{-12}$ s/s. This new value of the orbital period derivative agrees with the previously reported value, demonstrating that the orbital period derivative in this source has remained stable over the past ten years. Although this timespan is not sufficient yet for confirming the secular evolution of the system, we again propose an explanation of this behavior in terms of a highly non-conservative mass transfer in this system, where the accreted mass (as derived from the X-ray luminosity during outbursts) accounts for a mere 1% of the mass lost by the companion.Comment: 4 pages, 3 figures. Final version, including editing corrections, to appear on A&A Letter

Stability of the Magnetopause of Disk-Accreting Rotating Stars

We discuss three modes of oscillation of accretion disks around rotating magnetized neutron stars which may explain the separations of the kilo-Hertz quasi periodic oscillations (QPO) seen in low mass X-ray binaries. The existence of these compressible, non-barotropic magnetohydrodynamic (MHD) modes requires that there be a maximum in the angular velocity $\Omega_\phi(r)$ of the accreting material larger than the angular velocity of the star $\Omega_*$, and that the fluid is in approximately circular motion near this maximum rather than moving rapidly towards the star or out of the disk plane into funnel flows. Our MHD simulations show this type of flow and $\Omega_\phi(r)$ profile. The first mode is a Rossby wave instability (RWI) mode which is radially trapped in the vicinity of the maximum of a key function $g(r){\cal F}(r)$ at $r_{R}$. The real part of the angular frequency of the mode is $\omega_r=m\Omega_\phi(r_{R})$, where $m=1,2...$ is the azimuthal mode number. The second mode, is a mode driven by the rotating, non-axisymmetric component of the star's magnetic field. It has an angular frequency equal to the star's angular rotation rate $\Omega_*$. This mode is strongly excited near the radius of the Lindblad resonance which is slightly outside of $r_R$. The third mode arises naturally from the interaction of flow perturbation with the rotating non-axisymmetric component of the star's magnetic field. It has an angular frequency $\Omega_*/2$. We suggest that the first mode with $m=1$ is associated with the upper QPO frequency, $\nu_u$; that the nonlinear interaction of the first and second modes gives the lower QPO frequency, $\nu_\ell =\nu_u-\nu_*$; and that the nonlinear interaction of the first and third modes gives the lower QPO frequency $\nu_\ell=\nu_u-\nu_*/2$, where $\nu_*=\Omega_*/2\pi$.Comment: 10 pages, 7 figure

Future X-ray timing missions

Thanks to the Rossi X-ray Timing Explorer (RXTE), it is now widely recognized that fast X-ray timing can be used to probe strong gravity fields around collapsed objects and constrain the equation of state of dense matter in neutron stars. We first discuss some of the outstanding issues which could be solved with an X-ray timing mission building on the great successes of RXTE and providing an order of magnitude better sensitivity. Then we briefly describe the 'Experiment for X-ray timing and Relativistic Astrophysics' (EXTRA) recently proposed to the European Space Agency as a follow-up to RXTE and the related US mission 'Relativistic Astrophysics Explorer' (RAE).Comment: To be published in `Proceedings of the Third Microquasar Workshop: Granada Workshop on galactic relativistic jet sources', Eds A. J. Castro-Tirado, J. Greiner and J. M. Paredes, Astrophysics and Space Science, in press. More about EXTRA can be found at: http://www.cesr.fr/~barret/extra.htm

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

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