An Exponential Profile for the Virgo Cluster Intracluster Light and the Light Beyond 100 Kiloparsecs

Deep wide-field imaging of the Virgo cluster shows diffuse starlight extending hundreds of kiloparsecs from the cluster core, but a profile quoted in magnitudes is awkward to plan with or to compare against mass budgets. This paper takes the published description of Virgo's intracluster light as an exponential of central surface brightness 25.9 magnitudes per square arcsecond in V and scale length 52 kpc, and works out its consequences. The central intensity is 1.59 solar luminosities per square parsec; the profile fades to 26.94 magnitudes per square arcsecond at 50 kpc, 27.99 at 100 kpc, 30.08 at 200 kpc, and 32.16 at 300 kpc. Integrated, the component carries 2.70e+10 solar luminosities and 7.55e+10 solar masses of stars. Only 1.55e+10 solar luminosities lie inside 100 kpc: a fraction 0.427 of the diffuse light sits beyond that radius, and 0.104 beyond 200 kpc, which is the arithmetic reason the component escaped detection for so long and why aperture choices dominate published comparisons. The scale length subtends 10.8 arcminutes at Virgo's distance, a reminder that in the nearest cluster the diffuse component is an enormous angular structure that happens to be extremely faint.