Doppler imaging and differential rotation of $\sigma^{2}$ Coronae Borealis using SONG
We present new Doppler images of both components of the double-lined binary $\sigma^{2}$ CrB, based on the high-resolution spectroscopic data collected during 11 nights in 2015 March--April. The observed spectra form two independent data sets with sufficient phase coverage. We apply the least-squares deconvolution to all observed spectra to obtain high signal-to-noise mean profiles, from which we derive the Doppler images of both components of $\sigma^{2}$ CrB simultaneously. The surfaces of both F9 and G0 components are dominated by pronounced polar spots. The F9 component exhibits a weak spot at latitude 30$^{\circ}$ and its mid-to-low latitudes are relatively featureless. The G0 star shows an extended spot structure at latitude 30$^{\circ}$, and its surface spot coverage is larger than that of the F9 star, which suggests a higher level of magnetic activity. With the cross-correlation method, we derive a solar-like surface differential rotation on the G0 star of $\sigma^{2}$ CrB for the first time, and the surface shear rate is $\Delta \Omega = 0.180 \pm 0.004$ rad d$^{-1}$ and $\alpha = \Delta \Omega / \Omega_{eq} = 0.032 \pm 0.001$. We do not obtain a clear surface shear law for the F9 star due to the lack of mid-to-low latitude features, but detect a systematic longitude shift of high-latitude spots, which indicates a slower rotation with respect to the co-rotating frame.