The KBSS-KCWI Survey: The connection between extended Ly$\alpha$ halos and galaxy azimuthal angle at $z\sim 2-3$.

We present the first statistical analysis of kinematically-resolved, spatially-extended Ly$\alpha$ emission around $z = 2-3$ galaxies in the Keck Baryonic Structure Survey (KBSS) using the Keck Cosmic Web Imager (KCWI). Our sample of 59 star-forming galaxies ($z_\mathrm{med} = 2.29$) comprises the subset with typical KCWI integration times of $\sim 5$ hours and with existing imaging data from the Hubble Space Telescope and/or adaptive optics-assisted integral field spectroscopy. The high-resolution images were used to evaluate the azimuthal dependence of the intensity distribution and kinematics of diffuse Ly$\alpha$ emission with respect to the stellar continuum within projected galactocentric distances of $\lesssim 30$ proper kpc. We introduce cylindrically-projected 2D spectra (CP2D) that map the averaged Ly$\alpha$ spectral profile over a specified range of azimuthal angle, as a function of impact parameter around galaxies. The averaged CP2D spectrum of all galaxies shows clear signatures of Ly$\alpha$ resonant scattering by outflowing gas. When the CP2D spectra are binned using ranges of azimuthal angle corresponding to the projected major and minor axes, the spectra in two bins are almost consistent with only minor residual that comprises $\le 2\%$ ($\sim 2 \sigma$) of the integrated Ly$\alpha$ emission. The symmetry implies that the Ly$\alpha$ scattering medium is dominated by outflows in all directions within 30 kpc. Meanwhile, we find that the blueshifted component of Ly$\alpha$ emission is marginally stronger along galaxy minor axes for galaxies with relatively weak Ly$\alpha$ emission. We speculate that this weak directional dependence of Ly$\alpha$ emission becomes discernible only when the Ly$\alpha$ escape fraction is low. These discoveries highlight the need for similar analyses in simulations with Ly$\alpha$ radiative transfer modeling.