Luminosity of a quark - star undergoing torsional oscillations and the problem of γ - ray bursts

Aims. We discuss whether the process of winding-up the magnetic field by differential rotation in a newborn quark-star can cause an energy emission rate high enough and lasting sufficiently long to explain long gamma ray bursts. Methods. Within the magneto-hydrodynamics, we study the torsional oscillations and the extraction of energy from a newborn , hot, differentially rotating quark-star. Results. The newborn compact star is a fast rotator which blows a relativistic leptonic wind. The star's torsional oscillation considerably modulates this wind emission when it is odd and of a sufficient amplitude, which is relatively easy to reach. Odd oscillations may occur just after the formation of a quark-star. Other asymmetries can cause similar effects. The buoyancy of wound-up magnetic fields is inhibited, or its effects are limited, by a variety of different mechanisms described in the paper. Direct electromagnetic emission by the torsional oscillation in an outside vacuum or in the leptonic wind surrounding the compact object is found to be insignificant. On the contrary, the twist given to the outer magnetic field by an odd torsional oscillation is generally sufficient to break the star's magnetosphere open. The Poynting emission of the star in its leptonic environment is then radiated from all its surface and is considerably enhanced during these open episodes, tapping at the bulk rotational energy of the star. This results in intense energy shedding in the first tens of minutes after the collapse for magnetized quark-stars with an initial poloidal field of order of 10 14 Gauss, sufficient to explain long gamma-ray bursts. Key words. gamma-ray bursts – quark-stars – magnetic field – plasma – stars