Atomizing liquids by injecting them into crossflows is a common approach in gas turbines and augmentors. Much of our current understanding of the processes resulting in atomization of the jets, the resulting jet penetration and spray drop size distribution have been obtained by performing laboratory experiments at ambient conditions. Yet, operating conditions under which jets in crossflows atomize can be far different from ambient. Hence, several dimensionless groups have been identified that are believed to determine jet penetration and resulting drop size distribution. These are usually the jet and crossflow Weber and Reynolds numbers and the momentum flux ratio. In this paper we aim to answer the question of whether an additional dimensionless group, the liquid to gas density ratio must be matched. To answer this question, we perform detailed simulations of the primary atomization region using the Refined Level Set Grid (RLSG) method to track the motion of the liquid/gas phase interface. We employ a balanced force, interface projected curvature method to ensure high accuracy of the surface tension forces, use a multi-scale approach to transfer broken off, small scale nearly spherical drops into a Lagrangian point particle description allowing for full two-way coupling and continued secondary atomization, and employ a dynamic Smagorinsky large eddy simulation (LES) approach in the single phase regions of the flow to describe turbulence. We present simulation results for a turbulent liquid jet (q=6.6, We=330, Re=14,000) injected into a gaseous crossflow (Re=740,000) analyzed under ambient conditions (density ratio 816) experimentally by Brown and Mc-Donnel (2006). We compare simulation results obtained using a liquid to gas density ratio of 10 to those obtained using a density ratio of 100, a value typical for gas turbine combustors. The results show that the increase in density ratio results in a noticeable increase in liquid core penetration with reduced bending in the crossflow and spreading in the transverse directions. The post-primary atomization spray, however, penetrates further in both the jet and transverse direction. Results further show that penetration correlations for the windward side trajectory commonly reported in the literature strongly depend on the value of threshold probability used to identify the leading edge. Correlations based on the penetration of the jet's liquid core center of mass, on the other hand, can provide a less ambiguous measure of jet penetration. Finally, the increase in density ratio results in a decrease in wavelength of the most dominant feature associated with a traveling wave along the jet as determined by proper orthogonal decomposition.