stars in the accreting systems (such as the compact objects in X-ray binaries) or the systems that clearly have strong accretion history (such as the “recycled” millisecond pulsars).

### Rapid rotation

A rapidly rotating newborn strange star can prevent accretion from happening. [*Only when a strange star rotates slowly enough, could the accretion onto the surface be possible*]{}. There are three characteristic scale lengthes in describing the accretion scenarios of magnetized compact stars. The magnetospheric radius (or Alfven radius), defined by equating the kinematic energy density of free-fall particles with the magnetic energy density, is $
r_{\rm m}= ({R^6B^2\over \dot M \sqrt{2GM}})^{2/7}
\sim 3.2\times 10^{10} B_{12}^{4/7} R_6^{12/7}
M_1^{-1/7} \dot M_{10}^{-2/7}
$ cm, where $B=10^{12}B_{12}$ G is the surface magnetic field of the star, $R=10^6R_6$ cm is the stellar radius, $\dot M=10^{10}\dot M_{10}({\rm ~g~s^{-1}})$ is the accretion rate, and $M_1=M/M_\odot$ is the stellar mass in unit of solar mass. The co-rotating radius, defined by the balance of gravitational force and the centrifugal force, is $r_{\rm c}=({GM\over 4\pi^2})^{1/3}P^{2/3} = 1.5\times 10^8
M_1^{1/3}P^{2/3}$ cm, where the rotation period $P$ is in unit of second. The third scale length is the radius of light cylinder, which reads $r_{\rm l}={cP\over 2\pi} = 4.8\times 10^9 P$ 