Observed UV continuum slopes ($\beta$) of galaxies at $z=0.40-0.75$ in the GOODS-north field

We estimate the UV continuum slope ($\beta$) of 465 galaxies (with luminosities of 0.028 $-$ 3.3 $L_{z=0.5}^{\ast }$) in the Great Observatories Origins Survey (GOODS) Northern field in the redshift range $z=0.40-0.75$. We use two AstroSat/UVIT (N242W, N245M), two HST (F275W, F336W), and a KPNO (U) bands to sample the UV continuum slope of selected galaxies between 1215 and 2600 angstrom. The mean (median) and 1$\sigma$ scatter in the observed $\beta$ are found to be $-1.33\pm 0.07(-1.32)$ and 0.60 within the considered redshift range. We do not find any significant evolution in the mean $\beta$ within our redshift window. Our measurements add new data points to the global $\beta$ - $z$ relation in the least-explored redshift regime, further reinforcing the gradual reddening of galaxy UV continuum with cosmic time. We notice no strong consistent trend between $\beta$ and M${}_{1500}$ for the entire luminosity range $-21$ $<M_{1500}<-15$ mag. Although, the majority of the most luminous galaxies (M${}_{1500}<-19$ mag) are found to have relatively redder slopes. Using UVIT, we detect galaxies as faint as M${}_{1500}=-15.6$ mag (i.e., 0.028 $L_{z=0.5}^{\ast }$). The faintest galaxies (M${}_{1500}>-16$ mag) tend to be redder, which indicates they were less actively forming stars during this cosmic time interval. Our study highlights the unique capability of UVIT near-UV imaging to characterize the rest-frame far-UV properties of galaxies at redshift $z\sim 0.5$.