  We develop a theory for the coaxial configuration of a N\'eel-type skyrmion
and a Pearl vortex in thin superconductor-chiral ferromagnetic
heterostructures. Using direct numerical solution of the Euler-Lagrange
equation and micromagnetic simulations we demonstrate that the inhomogeneous
magnetic field of the Pearl vortex significantly modifies the skyrmion profile
with respect to the one in the absence of the vortex. We discover drastic
enlargement of the skyrmion's radius and inversion of the skyrmion's chirality.
To unravel physics behind these effects we invent novel two-parameter ansatz
for the magnetization profile of the skyrmion in the presence of the vortex.
Chirality inversion and radius blow-up are controlled not only by the material
parameters of the heterostructure but also by the thickness of the
superconductor. Our findings can have implications for Majorana modes localized
at skyrmion-vortex pairs.
