Spectral index of the Galactic foreground emission in the 50-87 MHz range

Total-power radiometry with individual meter-wave antennas is a potentially effective way to study the Cosmic Dawn ($z\sim20$) through measurement of sky brightness arising from the $21$~cm transition of neutral hydrogen, provided this can be disentangled from much stronger Galactic and extra-galactic foregrounds. In the process, measured spectra of integrated sky brightness temperature can be used to quantify the foreground emission properties. In this work, we analyze a subset of data from the Large-aperture Experiment to Detect the Dark Age (LEDA) in the range $50-87$~MHz and constrain the foreground spectral index $β$ in the northern sky visible from mid-latitudes. We focus on two zenith-directed LEDA radiometers and study how estimates of $β$ vary with local sidereal time (LST). We correct for the effect of gain pattern chromaticity and compare estimated absolute temperatures with simulations. We develop a reference dataset consisting of 14 days of optimal condition observations. Using this dataset we estimate, for one radiometer, that $β$ varies from $-2.55$ at LST~$<6$~h to a steeper $-2.58$ at LST~$\sim13$~h, consistently with sky models and previous southern sky measurements. In the LST~$=13-24$~h range, however, we find that $β$ fluctuates between $-2.55$ and $-2.61$ (data scatter $\sim0.01$). We observe a similar $β$ vs. LST trend for the second radiometer, although with slightly smaller $|β|$, in the $-2.46<β<-2.43$ range, over $24$~h of LST (data scatter $\sim0.02$). Combining all data gathered during the extended campaign between mid-2018 to mid-2019, and focusing on the LST~$=9-12.5$~h range, we infer good instrument stability and find $-2.56<β<-2.50$ with $0.09<Δβ<0.12$.