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Using cosmological dark matter only simulations of a $(1.6$ Gpc$/h)^3$ volumefrom the Legacy simulation project, we calculate Cosmic Mach Numbers (CMN) andperform a theoretical investigation of their relation with halo properties andfeatures of the density field to gauge their use as an measure of theenvironment.  CMNs calculated on individual spheres show correlations with both theoverdensity in a region and the density gradient in the direction of the bulkflow around that region. To reduce the scatter around the median of thesecorrelations, we introduce a new measure, the rank ordered Cosmic Mach number($\hat{\mathcal{M}}_g$), which shows a tight correlations with the overdensity$\delta=\frac{\rho-\bar{\rho}}{\bar{\rho}}$. Measures of the large scaledensity gradient as well as other average properties of the halo population ina region show tight correlations with $\hat{\mathcal{M}}_g$ as well. Ourresults in this first empirical study suggest that $\hat{\mathcal{M}}_g$ is anexcellent proxy for the underlying density field and hence environment that cancircumvent reliance on number density counts in a region. For scales between$10$ and $100 Mpc$/h, Mach numbers calculated using dark matter halos $(>10^{12}$ M$_{\odot})$ that would typically host massive galaxies are consistentwith theoretical predictions of the linear matter power spectrum at a level of$10\%$ due to non-linear effects of gravity. At redshifts $z\geq 3$, thesedeviations disappear. We also quantify errors due to missing large scale modesin simulations. Simulations of box size $\leq 1 $ Gpc/$h$ typically predictCMNs 10-30\% too small on scales of$\sim 100$ Mpc$/h$.

The Cosmic Mach Number as an Environment Measure for the Underlying Dark Matter Density Field