Extended Data Fig. 4: Rotational properties of the target haloes.
From: Formation of massive black holes in rapidly growing pre-galactic gas clouds
a, Radially averaged profiles of circular velocity \({v}_{{\rm{Kep}}}=\sqrt{GM/r}\) (red lines) and rotational velocity vrot (blue lines) around the largest principal axis of the MMH (dashed lines) and the LWH (solid lines) at the end of the simulation. b, Radially averaged profiles of the fractional rotational support; a ratio greater than one indicates that rotational velocities are sufficient to prevent gravitational collapse. The shaded regions show where the systems are rotationally supported: 2 × 103Mʘ–3.3 × 105Mʘ for the MMH (light shading) and 7 × 103Mʘ–6 × 104Mʘ for the LWH (dark shading). Rotation works in tandem with thermal and turbulent pressures to marginally slow the collapse, seen in the lower infall speeds at these mass scales in Extended Data Fig. 3. Inside 100Mʘ, this rotational measure becomes ill-defined because the rotation centre and centre-of-mass are not co-located; thus, we do not conclude that the inner portions are rotationally supported even though vrot/vKep > 1.
