  Tropical cyclones (TC) are often generated from pre-existing ``seed"
vortices. Seeds with higher persistence might have a higher chance to undergo
TC genesis. What controls seed persistence remains unclear. This study proposes
that planetary Rossby wave drag is a key factor that affects seed persistence.
Using recently developed theory for the response of a vortex to the planetary
vorticity gradient, a new parameter given by the ratio of the maximum wind
speed ($V_{max}$) to the Rhines speed at the radius of maximum wind
($R_{max}$), here termed ``vortex compactness" ($C_v$), is introduced to
characterize the vortex weakening by planetary Rossby wave drag. The
relationship between vortex compactness and weakening rate is tested via
barotropic $\beta$-plane experiments. The vortex's initial $C_v$ is varied by
systematically varying their initial $V_{max}$ and $R_{max}$ in idealized wind
profile models. Experiments using vorticity distributions from real-world seeds
possessing are also taken from reanalysis. The weakening rate depends strongly
on the vortex's initial $C_v$ across both idealized and real-world experiments,
and the asymmetry introduces minor differences. Experiments doubling the size
of seed vortices cause them to weaken more rapidly in line with other
experiment sets. The dependence of the weakening rate on initial compactness
can be predicted from a simple theory, which is more robust for more compact
vortices. Our results suggest that a seed's structure strongly modulates how
long it can persist in the presence of a planetary vorticity gradient.
Connections to real seeds on Earth are discussed.
