ar X iv : 0 70 9 . 45 47 v 2 [ as tr o - ph ] 8 J an 2 00 8 Probe into the interior of compact stars

The interior of neutron stars contains nuclear matter at very high density for numerous subatomic particles compete with each other. Therefore, confirming the components and properties there is our significant task. Here we summarize the possible methods especial the way of r-mode instability to probe into the neutron star and show our some results. The KHz pulsar in XTE J1739-285 may give a significant implication. Since the idea of neutron star was proposed and then the concept that pulsars are rotating neutron star was accepted, the components and properties of interiors in neutron stars have attracted much attention. Neutron stars can actually be constituted of a large variety of particles other than just neutrons and protons, therefore, the equations of state (EOSs) are still an indeterminacy in investigation just due to the uncertainties of nuclear physics theories. Many investigators spontaneously expect to probe the matter under these conditions through astrophysical observations. Up to now, constraints of inferred masses and radii for pulsars with sufficient precision on EOSs cannot uniquely examine and distinguish the compositions inside neutron stars(Pan and Zheng (2007)) . Although Özel had ever claimed that the existence of condensates and unconfined quarks may be ruled out by the mass M and radius R of the neutron star EXO 0748-676(Özel (2006)), Alford et al. immediately disproved it(Alford (2007)). Along with the abundance of data about the spin frequency for pulsars, researchers begin to pay much attention to the constraints put by limit rotation. For a uniform compact star with M and R, its rotation frequency has an absolute mass-shedding limit νK = 1.042 (M/MJ)1/2 (R/10km)3/2 , (1) above which the star is unstable. It is foreign to the properties of the matter inside. After giving the frequency of observed pulsar and assuming it to be the Keplerian limit, we can easily obtain a M-R relation to constrain the EOSs and get an upper limit for the R of the compact stars (CSs). But unfortunately, past works have showed that CSs containing exotic particles are indistinguishable from traditional neutron stars (NSs) only by this method. Actually, gravitational waves instabilities may occur just before the rotation of CS could reach the Keplerian limit. There exists various oscillation modes in the CSs, while Andersson, Friedman and Morsink discovered that only the r-mode is the most important. It could cause the strongest instabilities of gravitational waves and plays a key role in determining whether rotating CSs are stable or not. The limiting rotation arises out of