The significance of anisotropic signals hiding in the type Ia supernovae
  We use two different methods, i.e., dipole-fitting (DF) and hemisphere
comparison (HC), to search for the anisotropic signals hiding in the Union2.1
data set. We find that the directions of maximum matter density derived using
these two methods are about $114^{\circ}$ away from each other. We construct
four Union2.1-like mock samples to test the statistical significance of these
two methods. It is shown that DF method is statistically significant, while HC
method is strongly biased by the distribution of data points in the sky. Then
we assume that the anisotropy of distance modulus is mainly induced by the
anisotropy of matter density, which is modeled to be the dipole form
$\Omega_M=\Omega_{M0}(1-\cos\theta)$. We fit our model to Union2.1, and find
that the direction of maximum matter density is well consistent with the
direction derived using DF method, but it is very different from the direction
previously claimed. Monte Carlo simulations show that our method is
statistically more significant than HC method, although it is not as
significant as DF method. The statistical significance can be further improved
if the data points are homogeneously distributed in the sky. Due to the low
quality of present supernovae data, however, it is still premature to claim
that the Universe has any preferred direction.
