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 $i' \leq 26.0$ in the Subaru/XMM-Newton Deep Survey field by using the SED fitting analysis. We find that the apparently redder ($\beta_{\mathrm{obs}} > -1.73$) LBGs tend to be dusty ($\mathrm{Av} > 1.0$), have the young stellar population ($\beta_{\mathrm{int}} < -2.42$), and the intrinsically active star-forming galaxies (SFR $\gtrsim$ a few $\times 10^{2}$ $\mathrm{M_{\odot}} \mathrm{yr^{-1}}$). 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 $z = 4$. We also find that an extrapolation of the $\beta_{\mathrm{int}}$-$M_{\mathrm{UV,int}}$ relation toward the fainter magnitude range below our sample magnitude limit intersects the $\beta_{\mathrm{obs}}$-$M_{\mathrm{UV,obs}}$ relation previously obtained in the deeper narrow-area observations at $M_{\mathrm{UV}} = -18.9$ and $\beta = -1.94$, which coincides with the break point of $\beta_{\mathrm{obs}}$-$M_{\mathrm{UV,obs}}$ relation observed so far. The coincidence suggest that we see the almost dust-free population at $M_{\mathrm{UV,obs}} \gtrsim -18.9$.