Efrain J. Ferrer Paramagnetism in Compact Stars Western Illinois University IRGAC 2006, Barcelona, Spain

OUTLINE Gluons in Magnetized Color Superconductors Gluon Vortices and Magnetic Antiscreening Chromomagnetic Instabilities in Color Superconductivity and Magnetic Field Induction Conclusions and Future Directions Ferrer and de la Incera, hep-ph/0604136 IRGAC 2006.

CFL Pairing & Magnetic Field Penetration u d u u d s s s IRGAC 2006.

Effects on the Gluons Ferrer & de la Incera hep-ph/0604136 Because of the modified electromagnetism, gluons are charged in the color superconductor 1 -1 Effective action for the charged gluons within CFL at asymptotic densities where IRGAC 2006.

with corresponding eigenvector: Assuming that there is an external magnetic field in the z-direction, one mode becomes unstable when with corresponding eigenvector: “Zero-mode problem” for spin-1 non-Abelian gauge fields whose solution is the formation of a vortex condensate of charged gluons Skalozub, Sov.JNP23 (1978); Nielsen & Olesen NPB 144 (1978) Skalozub, Sov.JNP243 (1986); Ambjorn & Olesen, NPB315 (1989) Ferrara & Porrati, MPLA8 (1993); Ferrer& de la Incera, IJMPA 11 (1996) IRGAC 2006.

We can use the Gibbs free-energy To obtain the equations for the gluon condensate and the induced magnetic field due to the G condensate’s backreaction on the electromagnetic field Look alike Ginzburg-Landau equations for conventional superconductivity, except for the sign of the anomalous magnetic moment term which leads to antiscreening of the applied magnetic field thus the system behaves as a paramagnet. IRGAC 2006.

Surface Energy Density and Vortex Nucleation CFL Normal Phase Condensed Phase Since we have that which is the required condition for vortex nucleation.

Penetration Length λ and Coherence Length ξ in Type I Superconductors IRGAC 2006.

Variation of internal magnetic field (B) with applied external magnetic field (H) for Type I, Type II, and Color Superconductors B Hc H IRGAC 2006.

One can linearize the equations around the critical field where to find the solution IRGAC 2006.

The vortex lattice induces a magnetic field that forms a fluxoid along the z-direction. The first pictures of a vortex lattice were taken in 1967 by U. Essmann and H. Trauble who sprinkled their sample surfaces with a ferromagnetic powder that arranges itself in a pattern reflecting the magnetic flux line structure. First image of Vortex lattice, 1967 IRGAC 2006.

Meissner Screening Masses & Chromomagnetic Instabilities in Neutral Dense Two-Flavor Quark Matter Huang/Shovkovy, PRD 70 (2004) 051501 IRGAC 2006.

Meissner Screening Masses & Chromomagnetic Instabilities in Gapless Three-Flavor Quark Matter Fukushima, PRD 72 (2005) 074002; Casalbouni et al, PLB 605 (2005) 362; Alford/Wang JPG 31 (2005) 719. IRGAC 2006.

We can use the Gibbs free-energy To obtain the equations for the gluon condensate and the induced magnetic field due to the G condensate’s backreaction on the electromagnetic field Look alike Ginzburg-Landau equations for conventional superconductivity, except for the sign of the anomalous magnetic moment term which leads to antiscreening of the applied magnetic field thus the system behaves as a paramagnet. IRGAC 2006.

Origin of the Galactic Magnetic Field IRGAC 2006.

Some reasons and some implications… Same gluon effective action, but with imaginary Meissner mass and zero external magnetic field. Same nonlinear equations will produce SSB of rotational symmetry. Because of the anomalous magnetic moment the gluon vortices would provide a source of magnetic fields in the star. Inhomogeneous gluon condensate would imply an inhomogeneous gap. IRGAC 2006.

Conclusions and Future Tasks Exploring color superconductivity in a magnetic field can help to understand CS in realistic systems as compact stars. Investigate the consequences of the gluon vortices on the gap, as well as the field strengths at which this is relevant. Determine whether the paramagnetic phase of gluon vortices corresponds to the stable ground state in gapless CS. IRGAC 2006.