We present observations and analysis of an unusual [ C II ] emission line in the very luminous QSO SDSS J155426.16+193703.0 at z \sim 4.6 .
The line is extremely broad ( FWHM 735 km s ^ { -1 } ) and seems to have a flat-topped or double-peaked line profile .
A velocity map of the line shows a gradient across the source that indicates large-scale rotation of star-forming gas .
Together , the velocity map and line profile suggest the presence of a massive rotating disc with a dynamical mass M _ { \mathrm { dyn } } \ga 5 \times 10 ^ { 10 } ~ { } M _ { \odot } .
Using the assumption of a rotating disc origin , we employ an empirical relation between galaxy disc circular velocity and bulge velocity dispersion ( \sigma ) to estimate that \sigma > 310 km s ^ { -1 } , subject to a correction for the unknown disc inclination .
This result implies that this source is consistent with the local M – \sigma relation , or offset at most by an order of magnitude in black hole mass .
In contrast , the assumption of a bulge origin for the [ C II ] emission line would lead to a conclusion that the black hole is nearly two orders of magnitude more massive than predicted by the M – \sigma relation , similar to previous findings for other high-redshift QSOs .
As disc rotation may be a common origin for [ C II ] emission at high redshifts , these results stress that careful consideration of dynamical origins is required when using observations of this line to derive properties of high-redshift galaxies .