Tidal Radii in Coma: Why a Cluster Strips Dark Matter First and Stars Only on Deep Plunges

Tidal stripping is usually invoked in words; this paper invokes it in numbers for a single well-defined case, an L* satellite orbiting in the Coma cluster. Modelling Coma's potential as a singular isothermal sphere of velocity dispersion 1000 kilometres per second, the enclosed cluster mass is 9.30e+13 solar masses at 200 kpc, 2.32e+14 at 500 kpc, and 4.65e+14 at 1000 kpc. For a satellite of total mass 3.0e11 solar masses, the tidal radius rt = r (M_sat/3 M_enc)^(1/3) is 20 kpc at 200 kpc from the centre, 38 at 500 kpc, and 60 at 1000 kpc. Against the satellite's own structure those radii are generous to its stars: only 0.055 of its stellar mass, in a Plummer profile of scale 4 kpc, lies outside the tidal radius even at 200 kpc, while 0.475 of its dark halo, of scale 15 kpc, lies outside. Stars are stripped directly only on plunges that carry the satellite within 49 kpc of the centre, where the tidal radius shrinks to its stellar extent; the orbital period at 500 kpc is 2.17 billion years. Stripping in a Coma-like cluster is therefore an outside-in process with a definite order: dark matter first, at almost every radius; stars later, after the halo's loss has loosened them, or suddenly, on the rare deep plunge.