We simulate the phase-space distribution of stellar mass in nine massive \Lambda CDM galaxy clusters by applying the semi-analytic particle tagging method of Cooper et al .
to the Phoenix suite of high-resolution N -body simulations ( M _ { 200 } \approx 7.5 – 33 \times 10 ^ { 14 } \mathrm { M _ { \sun } } ) .
The resulting surface brightness ( SB ) profiles of brightest cluster galaxies ( BCGs ) match well to observations .
On average , stars formed in galaxies accreted by the BCG account for \gtrsim 90 per cent of its total mass ( the remainder is formed in situ ) .
In circular BCG-centred apertures , the superposition of multiple debris clouds ( each \gtrsim 10 per cent of the total BCG mass ) from different progenitors can result in an extensive outer diffuse component , qualitatively similar to a ‘ cD envelope ’ .
These clouds typically originate from tidal stripping at z \lesssim 1 and comprise both streams and the extended envelopes of other massive galaxies in the cluster .
Stars at very low SB contribute a significant fraction of the total cluster stellar mass budget : in the central 1 \mathrm { Mpc } ^ { 2 } of a z \sim 0.15 cluster imaged at SDSS-like resolution , our fiducial model predicts 80–95 per cent of stellar mass below a SB of \mu _ { V } \sim 26.5 \mathrm { mag arcsec ^ { -2 } } is associated with accreted stars in the envelope of the BCG .
The ratio of BCG stellar mass ( including this diffuse component ) to total cluster stellar mass is \sim 30 per cent .