  We present significantly improved measurements of turbulent velocities in the
hot gaseous halos of nearby giant elliptical galaxies. Using deep XMM-Newton
Reflection Grating Spectrometer (RGS ) observations and a combination of
resonance scattering and direct line broadening methods, we obtain well bounded
constraints for 13 galaxies. Assuming that the turbulence is isotropic, we
obtain a best fit mean 1D turbulent velocity of ~110 km/s. This implies a
typical 3D Mach number ~0.45 and a typical non-thermal pressure contribution of
~6 per cent in the cores of nearby massive galaxies. The intrinsic scatter
around these values is modest - consistent with zero, albeit with large
statistical uncertainty - hinting at a common and quasi-continuous mechanism
sourcing the velocity structure in these objects. Using conservative estimates
of the spatial scales associated with the observed turbulent motions, we find
that turbulent heating can be sufficient to offset radiative cooling in the
inner regions of these galaxies (<10 kpc, typically 2-3 kpc). The full
potential of our analysis methods will be enabled by future X-ray
microcalorimeter observations.
