  Constraints on the original Cardassian model and the modified polytropic
Cardassian model are examined from the latest derived 397 Type Ia supernova
(SNe Ia) data, the size of baryonic acoustic oscillation peak from the Sloan
Digital Sky Survey (SDSS), the position of first acoustic peak of the Cosmic
Microwave Background radiation (CMB) from the five years Wilkinson Microwave
Anisotropy Probe (WMAP), the x-ray gas mass fractions in clusters of galaxies,
and the observational H(z) data. In the original Cardassian model with these
combined data set, we find $\Omega_{m0}=0.271^{+0.014}_{-0.014},
n=0.035^{+0.049}_{-0.049}$ at $1 \sigma$ confidence level. And in the modified
polytropic Cardassian model, we find that
$\Omega_{m0}=0.271^{+0.014}_{-0.015}$, $n=-0.091^{+0.331}_{-1.908}$ and
$\beta=0.824^{+0.750}_{-0.622}$ within $1\sigma$ confidence level. According to
these observations, the acceleration of the universe begins at
$z_T=0.55^{+0.05}_{-0.05} (1\sigma)$ for the original Cardassian model, and at
$z_T=0.58^{+0.12}_{-0.12} (1\sigma)$ for the modified polytropic Cardassian
model. Evolution of the effective equation of state $w_{eff}$ for the modified
polytropic Cardassian model is also examined here and results show that an
evolutionary quintessence dark energy model is favored.

Cosmology and Nongalactic Astrophysics