LIGHTS. A robust technique to identify galaxy edges

The LIGHTS survey is imaging galaxies at a depth and spatial resolution comparable to what the Legacy Survey of Space and Time (LSST) will produce in 10 years (i.e., $\sim$31 mag/arcsec$^2$; 3$σ$ in areas equivalent to 10$^{\prime\prime}$$\times$ 10$^{\prime\prime}$). This opens up the possibility of probing the edge of galaxies, as the farthest location of in-situ star formation, with a precision that we have been unable to achieve in the past. Traditionally, galaxy edges have been analyzed in one-dimension through ellipse averaging or visual inspection. Our approach allows for a two-dimensional exploration of galaxy edges, which is crucial for understanding deviations from disc symmetry and the environmental effects on galaxy growth. In this paper, we propose a novel method using the second derivative of the surface mass density map of a galaxy to determine its edges. This offers a robust quantitative alternative to traditional edge-detection methods when deep imaging is available. Our technique incorporates Wiener-Hunt deconvolution to remove the effect of the Point Spread Function (PSF) by the galaxy itself. By applying our methodology to the LIGHTS galaxy NGC 3486, we identify the edge at 205$^{\prime\prime}$ $\pm$ 5$^{\prime\prime}$. At this radius, the stellar surface mass density is $\sim$1 M$_\odot$/pc$^2$, supporting a potential connection between galaxy edges and a threshold for in-situ star formation. Our two-dimensional analysis on NGC 3486 reveals an edge asymmetry of $\sim$5$\%$. These techniques will be of paramount importance for a physically motivated determination of the sizes of galaxies in ultra-deep surveys such as LSST, Euclid and Roman.