Where NGC 1275 Ends: A Two-Component Decomposition of the Perseus Cluster Core Light

In the Perseus cluster the light of the central galaxy NGC 1275 and the light belonging to the cluster as a whole overlap on the sky, and where one ends and the other begins is a modelling decision with quantitative consequences. This paper adopts a de Vaucouleurs profile for the galaxy, effective radius 12 kpc and effective surface brightness 22.3 magnitudes per square arcsecond in V, and an exponential for the intracluster component, central brightness 25.2 magnitudes per square arcsecond and scale length 58 kpc, then integrates both. The two profiles cross at 57 kpc, at a surface brightness of 26.27 magnitudes per square arcsecond; inside that radius the galaxy dominates, outside it the cluster component does, reaching 27.07 magnitudes per square arcsecond at 100 kpc against the galaxy's 28.12. Integrated to 400 kpc the galaxy contributes 1.42e+11 solar luminosities and the diffuse component 6.34e+10, so the intracluster fraction of the combined central system is 0.308. Within the inner 50 kpc, by contrast, the diffuse share is only 0.101. A single Perseus diffuse fraction is therefore meaningless without its aperture, and this paper supplies the aperture dependence explicitly.