Is the anisotropy of the upper critical field of Sr$_2$RuO$_4$ consistent with a helical $p$-wave state?

We calculate the angular and temperature $T$ dependencies of the upper critical field $H_{c2}(\theta,\phi,T)$ for the $C_{4v}$ point group helical $p$-wave states, assuming a single uniaxial ellipsoidal Fermi surface, Pauli limiting, and strong spin-orbit coupling that locks the spin-triplet $\vec{\bf d}$-vectors onto the layers. Good fits to the Sr$_2$RuO$_4$ $H_{c2,a}(\theta,T)$ data of Kittaka et al. [2009 Phys. Rev. B 80, 174514] are obtained. Helical states with $\vec{\bf d}({\bf k})=\hat{\bf k}_x\hat{\bf x}-\hat{\bf k}_y\hat{\bf y}$ and $\hat{\bf k}_y\hat{\bf x}+\hat{\bf k}_x\hat{\bf y}$ (or $\hat{\bf k}_x\hat{\bf x}+\hat{\bf k}_y\hat{\bf y}$ and $\hat{\bf k}_y\hat{\bf x}-\hat{\bf k}_x\hat{\bf y}$) produce $H_{c2}(90^{\circ},\phi,T)$ that greatly exceed (or do not exhibit) the four-fold azimuthal anisotropy magnitudes observed in Sr$_2$RuO$_4$ by Kittaka et al. and by Mao et al. [2000 Phys. Rev. Lett. 84, 991], respectively.