  We examine the complete landscape of parameters which affect secondary
breakup of a Newtonian droplet under impulsive acceleration. A Buckingham-Pi
analysis reveals that the critical Weber number $\mathit{We}_\mathit{cr}$ for a
non-vibrational breakup depends on the density ratio $(\rho)$, the drop
$(\mathit{Oh}_d)$ and the ambient $(\mathit{Oh}_o)$ Ohnesorge numbers. Volume
of fluid (VOF) multiphase flow simulations are performed using Basilisk to
conduct a reasonably complete parametric sweep of the non-dimensional
parameters involved. It is found that, contrary to current consensus, even for
$\mathit{Oh}_d \leq 0.1$, a decrease in $\mathit{Oh}_d$ has a substantial
impact on the breakup morphology, motivating plume formation. In addition to
$\rho$, $\mathit{Oh}_o$ also affects the balance between pressure differences
between a droplet's pole and its periphery, and the shear stresses on its
upstream surface, which ultimately dictates the flow inside the droplet. This
behavior manifests in simulations through the observed pancake shapes and
ultimately the breakup morphology (forward or backward bag). All these factors
affecting droplet deformation process are specified and theories explaining the
observed results are provided. A $\mathit{We}_\mathit{cr}-\mathit{Oh}_d$ plot
is provided to summarize all variations in $\mathit{We}_\mathit{cr}$ observed
due to changes in the involved non-dimensional parameters. All observed
critical pancake and breakup morphologies are summarized using a phase diagram
illustrating all deformation paths a droplet might take under impulsive
acceleration. Finally, based on the understanding of process of bag breakup
gained from this work, a non-dimensional parameter to predict droplet breakup
threshold is derived and tested on all simulation data obtained from this work
and all experimental data gathered from existing literature.
