The very small braking index of PSR J1734-3333, $n=0.9pm0.2$, challenges the current theories of braking mechanisms in pulsars. We present a possible interpretation that this pulsar is surrounded by a fall-back disk and braked by it. A modified braki
ng torque is proposed based on the competition between the magnetic energy density of a pulsar and the kinetic energy density of a fall-back disk. With this torque, a self-similar disk can fit all the observed parameters of PSR J1734-3333 with natural initial parameters. In this regime, the star will evolve to the region having anomalous X-ray pulsars and soft gamma repeaters in the $P-dot{P}$ diagram in about 20000 years and stay there for a very long time. The mass of the disk around PSR J1734-3333 in our model is about $10M_{oplus}$, similar to the observed mass of the disk around AXP 4U 0142+61.
The origin of the 6.67 hr period X-ray source, 1E161348-5055, in the young supernova remnant RCW 103 is puzzling. We propose that it may be the descendant of a Thorne-Zytkow Object (TZO). A TZO may at its formation have a rapidly spinning neutron sta
r as a core, and a slowly rotating envelope. We found that the core could be braked quickly to an extremely long spin period by the coupling between its magnetic field and the envelope, and that the envelope could be disrupted by some powerful bursts or exhausted via stellar wind. If the envelope is disrupted after the core has spun down, the core will become an extremely long-period compact object, with a slow proper motion speed, surrounded by a supernova-remnant-like shell. These features all agree with the observations of 1E161348-5055. TZOs are expected to have produced extraordinary high abundances of lithium and rapid proton process elements that would remain in the remnants and could be used to test this scenario.
To investigate the missing compact star of Supernova 1987A, we analyzed both the cooling and the heating processes of a possible compact star based on the upper limit of observational X-ray luminosity. From the cooling process we found that a solid q
uark-cluster star, which has a stiffer equation of state than that of conventional liquid quark star, has a heat capacity much smaller than a neutron star. It can cool down quickly, which can naturally explain the non-detection of a point source (neutron star or quark star) in X-ray band. On the other hand, we consider the heating process from magnetospheric activity and possible accretion, and obtain some constraints to the parameters of a possible pulsar. We conclude that a solid quark-cluster star can be fine with the observational limit in a large and acceptable parameter space. A pulsar with a short period and a strong magnetic field (or with a long period and a weak field) would has luminosity higher than the luminosity limit if the optical depth is not large enough to hide the compact star. The constraints of the pulsar parameters can be tested if the central compact object in 1987A is discovered by advanced facilities in the future.
We analyze the emission plateaus in the X-ray afterglow lightcurves of gamma-ray bursts (GRBs) and in the optical lightcurves of Type II superpernovae (SNe IIP) in order to study whether they have similar late energy injection behaviors. We show that
correlations of bolometric energies (or luminosities) between the prompt explosions and the plateaus for the two phenomena are similar. The Type II SNe are in the low energy end of the GRBs. The bolometric energies (or luminosities) in prompt phase E_{rm expl} (or L_{rm expl}) and in plateau phase E_{rm plateau} (or L_{rm plateau}) share relations of E_{rm expl} propto E_{rm plateau}^{0.73pm 0.14} and L_{rm expl} propto L_{rm plateau}^{sim 0.70}. These results may indicate a similar late energy injection behavior to reproduce the observed plateaus of the plateaus in the two phenomena.
