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 $M_{\mathrm{UV,obs}} \gtrsim -18.9$.'
author:
- 'Satoshi <span style="font-variant:small-caps;">Yamanaka</span>'
- 'Toru <span style="font-variant:small-caps;">Yamada</span>,'
title: 'The UV spectral slope beta and stellar population of most active star-forming galaxies at z$\sim$4'
---

Introduction {#S1Intr}
============

The ultraviolet (UV) continuum spectrum of star-forming galaxies is characterized by the spectral index $\beta$ in the form of $f_{\lambda} \propto \lambda^{\beta}$ [@Calz94]. The $\beta$ values are related with physical quantities such as age, metallicity, and dust extinction of the galaxies. In the case of less dust attenuation, younger age, and lower metallicity, the galaxy has the larger negative $\beta$ value (e.g., [@Bouw10]; [@Stan16]). Since it is relatively simple to measure $\beta$ values even if objects are at high redshift, the $\beta$ index is a useful tool to probe their physical quantities.

The typical value of $\beta$ found in the previous works is $\sim -1.7$ at $z \sim 4$ for $\sim L_{*}$ galaxies with $M_{\mathrm{UV}} \sim -21.0$ ([@Bouw12]; [@Fink12]), and it is bluer at higher redshift up to $z \sim 7$ ($\beta$–*z* relation: e.g., [@Wil11]). At the fainter magnitude (e.g. $M_{\mathrm{UV}} \sim -19.0$), the observed $\beta$ value has still uncertainties 