The UV spectral slope beta and stellar population of most active star-forming galaxies at z~4

We investigate the stellar population of star-forming galaxies at $z\sim 4$ by focusing on their slope of rest-frame ultraviolet (UV) continuum, $\beta$ where $f_{\lambda }\propto {\lambda }^{\beta }$. We investigate the sample of bright Lyman Break Galaxies (LBGs) with $i^{\mathrm{\prime }}\le 26.0$ in the Subaru/XMM-Newton Deep Survey field by using the SED fitting analysis. We find that the apparently redder (${\beta }_{\mathrm{o}\mathrm{b}\mathrm{s}}>-1.73$) LBGs tend to be dusty ($\mathrm{A}\mathrm{v}>1.0$), have the young stellar population ($\beta_{$\mathrm{i}\mathrm{n}\mathrm{t}$} < -2.42$),andtheintrinsicallyactivestar-forminggalaxies(SFR$\gtrsim$ a few $\times {10}^2$ ${\mathrm{M}}_{\odot }\mathrm{y}{\mathrm{r}}^{-1}$). It means that a significant fraction of the UV-selected LBGs at $z\sim 4$ is on-going active and dust obscured star-forming galaxies. We compare the IR to UV luminosity ratio assuming the dust attenuation laws with the sub-millimeter observations from previous works. The result suggests that the Calzetti-like dust attenuation law is preferable for the active and dusty star-forming LBGs at $z = 4$\mathrm{.}Wealsofindthatanextrapolationofthe$\beta_{$\mathrm{i}\mathrm{n}\mathrm{t}$}$-$M_{$\mathrm{U}\mathrm{V},\mathrm{i}\mathrm{n}\mathrm{t}$}$ relation toward the fainter magnitude range below our sample magnitude limit intersects the ${\beta }_{\mathrm{o}\mathrm{b}\mathrm{s}}$-$M_{\mathrm{U}\mathrm{V},\mathrm{o}\mathrm{b}\mathrm{s}}$ relation previously obtained in the deeper narrow-area observations at $M_{\mathrm{U}\mathrm{V}}=-18.9$ and $\beta = -1.94$,whichcoincideswiththebreakpointof$\beta_{$\mathrm{o}\mathrm{b}\mathrm{s}$}$-$M_{$\mathrm{U}\mathrm{V},\mathrm{o}\mathrm{b}\mathrm{s}$}$ relation observed so far. The coincidence suggest that we see the almost dust-free population at $M_{\mathrm{U}\mathrm{V},\mathrm{o}\mathrm{b}\mathrm{s}}\gtrsim -18.9$.