| A lot of instabilities exist in the newly born neutron stars (NSs), one of the most important is r-mode instability. In a rotating, fluid star, the Chandrasekhar-Friedman-Schutz(CFS) instability driven by gravitational wave (GW) radiation can lead to a qusi-circlc perturbation, which is the r-mode perturbation. R-mode in-stability is essentially a rotation-related instability, which arises due to the effect of Coriolis force, with positive feedback enhancing the GW radiation. However, the growth of r-mode can be suppressed by some non-linear effects. Particularly, by expanding the r-mode up to the second order of its amplitude, the differential ro-tation can be found to determine the saturation amplitude of the mode. Moreover, differential rotation can also wind the primordial poloidal magnetic fields to form and amplify the toroidal magnetic fields. However, the ultra-strong toroidal fields are unstable. With the action of Tayler instability, the toroidal field could partially be transformed to the new poloidal fields, which extends to the stellar surface and connect with the enhanced dipole fields. By considering the the amplification of toroidal fields by r-modes and Tayler instability, we firstly suggest a new formation scenario for the millisecond magnetars harbored in gamma-ray bursts. The Alfven frequency will increase with the amplification of toroidal fields. Meanwhile, the NS will spin down due to the r-mode GW radiation, the condition for Tayler instability can eventually be satisfied. Our result shows that, for a newly born NS with a seed poloidal magnetic field of-1011G, it can evolve into a magnetar with surface dipole magnetic field of～1015G, and internal toroidal field of～1017G on timescale of～102-3s, the precondition is the NS should have a initial spin period≤1.7ms. With the amplification of the magnetic fields, the spin periods of the magnetars would increase to-5ms due to GW radiation of magnetic deformation and the r-mode at a few hundred to thousand seconds after their formation.The inner cores of neutron stars (NSs) may be made up of quark matter if the star is dense enough. More specially, strange stars (SSs), which are wholly constituted by strange quarks may also exit. However, what state the quark matter of SSs are in is still in dispute. As generally considered, when the density is relative low, quark matter are in normal phase, and if the density is extremely high, quark matter are in the color-flavor-locked (CFL) phase. However, in SSs whether the density is high enough that all quarks are in CFL phase? To probe whether SSs could be in the CFL phase, we have investigated the thermal evolution of NSSs (SSs in the normal phase) and CSSs (SSs in the CFL phase). Both the shear viscous heating of r-mode and deconfinement heating of SSs crusts are involved in the thermal evolution. It should be stressed that the mechanisms which determine the saturation amplitude of r-mode are very complicated, in our second work, only first order r-mode is considered and the saturation amplitude is inserted by hand. Moreover, in the second work, the magnetic fields evolution induced by r-modes are not considered as the formation of the fields formation could suppress r-modes. We find the thermal evolution of NSSs do not differ too much from the standard cooling. However, the cooling curves of CSSs show two very unusual features, a big bump exists during the first100yrs and a steep temperature decay (about7%per ten years) is present at104-6yrs. Actually, by now neither of the two features is confirmed by thermal observations of pulsars. As a result, by adopting this thermal test method, we have verified the CSSs model could indeed not survive, which is consistent with the conclusion suggested by Madsen through a rotational test method. |
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