A study of spectral curvature in the radio relic in Abell 4038 using the uGMRT

The remnant radio galaxies in galaxy clusters are important sources of seed relativistic electron population in the intra-cluster medium (ICM). Their occurrence and spectral properties are poorly studied. In this work we present a broadband study of the radio relic in the galaxy cluster Abell 4038 using the Upgraded Giant Metrewave Radio Telescope (uGMRT). We present the uGMRT images in the bands 300 - 500 MHz and 1050 - 1450 MHz having rms noise $70\,\mu$Jy beam$^{-1}$ and $30\,\mu$Jy beam$^{-1}$, respectively, that are the deepest images of this field so far. A spectral analysis of the relic over 300 - 1450 MHz using images in sub-bands scaled to have constant fractional bandwidths to achieve a closely matched uv-coverage was carried out. The 100 kpc extent of the relic is divided into Loop, Arc, Bridge and North-end. The Loop has a steep spectral index of $\alpha=2.3\pm0.2$ ($S_{\nu}\propto\nu^{-\alpha}$). The North-end has ultra-steep spectra in the range $2.4 - 3.7$. The Arc is found to skirt a curved region seen in the \emph{Chandra} X-ray surface brightness image and the highest spectral curvature in it reaches $1.6\pm0.3$. We interpret the morphology and spectral properties of the relic in the scenario of an adiabatically compressed cocoon from the past activity of the Brightest Cluster Galaxy in the cluster. A comparison of the properties of the A4038 relic with a sample of 10 such relics is discussed.