  Starting with the polarization dependent Wigner function of vector mesons, we
derive an expression for the 00-component ($\rho_{00}$) of spin density matrix
in terms of the second order gradients of the vector meson distribution
functions. We further apply a thermal model to analyze the transverse momentum
and the azimuthal angle dependence of $\rho_{00}$ for $\phi$ and $K^{*0}$
mesons resulting from distribution gradients in Au-Au collisions with
$\sqrt{s_{NN}}=130$ GeV at mid-rapidity. Our results for the transverse
momentum dependence indicate that the deviations of $\rho_{00}$ from $1/3$ as
the signal for spin alignment are greatly enhanced at large transverse momenta
and have a strong centrality dependence while analysis of the azimuthal angle
($\phi_q$) dependence suggest that such deviations have a $\cos(2\phi_q)$
structure with opposite sign for $\phi$ and $K^{*0}$. Our finding may be
considered as a baseline for probing spin-alignment mechanisms beyond
hydrodynamic gradients.
