  This paper reports detections of H$\alpha$ emission and stellar continuum out
to approximately 30 physical kpc, and H$\alpha$ directionality in the outskirts
of H$\alpha$-emitting galaxies (H$\alpha$ emitters) at $z=0.4$. This research
adopts narrow-band selected H$\alpha$ emitters at $z=0.4$ from the
emission-line object catalog by Hayashi et al. (2020), which is based on data
in the Deep and Ultradeep layers of the Hyper Suprime-Cam Subaru Strategic
Program. Deep narrow- and broad-band images of 8625 H$\alpha$ emitters across
16.8 deg$^2$ enable us to construct deep composite emission-line and continuum
images. The stacked images show diffuse H$\alpha$ emission (down to
$\sim5\times10^{-20}$ erg~s$^{-1}$cm$^{-2}$arcsec$^{-2}$) and stellar continuum
(down to $\sim5\times10^{-22}$ erg~s$^{-1}$cm$^{-2}$A$^{-1}$arcsec$^{-2}$),
extending beyond 10 kpc at stellar masses $>10^9$ M$_\odot$, parts of which may
originate from stellar halos. Those radial profiles are broadly consistent with
each other. In addition, we obtain a dependence of the H$\alpha$ emission on
the position angle because relatively higher H$\alpha$ equivalent width has
been detected along the minor-axis towards galaxy disks. While the H$\alpha$
directionality could be attributed to biconical outflows, further research with
hydrodynamic simulations is highly demanded to pin down the exact cause.
