The linewidth-size relationship in the dense ISM of the Central
  Molecular Zone
  The linewidth (sigma) - size (R) relationship has been extensively measured
and analysed, in both the local ISM and in nearby normal galaxies. Generally, a
power-law describes the relationship well with an index ranging from 0.2-0.6,
now referred to as one of "Larson's Relationships." The nature of turbulence
and star formation is considered to be intimately related to these
relationships, so evaluating the sigma-R correlations in various environments
is important for developing a comprehensive understanding of the ISM. We
measure the sigma-R relationship in the Central Molecular Zone (CMZ) of the
Galactic Centre using spectral line observations of the high density tracers
N2H+, HCN, H13CN, and HCO+. We use dendrograms, which map the hierarchical
nature of the position-position-velocity (PPV) data, to compute sigma and R of
contiguous structures. The dispersions range from ~2-30 km/s in structures
spanning sizes 2-40 pc, respectively. By performing Bayesian inference, we show
that a power-law with exponent 0.3-1.1 can reasonably describe the sigma-R
trend. We demonstrate that the derived sigma-R relationship is independent of
the locations in the PPV dataset where sigma and R are measured. The uniformity
in the sigma-R relationship suggests turbulence in the CMZ is driven on the
large scales beyond >30 pc. We compare the CMZ sigma-R relationship to that
measured in the Galactic molecular cloud Perseus. The exponents between the two
systems are similar, suggestive of a connection between the turbulent
properties within a cloud to its ambient medium. Yet, the velocity dispersion
in the CMZ is systematically higher, resulting in a coefficient that is nearly
five times larger. The systematic enhancement of turbulent velocities may be
due to the combined effects of increased star formation activity, larger
densities, and higher pressures relative to the local ISM.
