  In this paper a class of higher order finite element methods for the
discretization of surface Stokes equations is studied. These methods are based
on an unfitted finite element approach in which standard Taylor-Hood spaces on
an underlying bulk mesh are used. For treating the constraint that the velocity
must be tangential to the surface a penalty method is applied. Higher order
geometry approximation is obtained by using a parametric trace finite element
technique, known from the literature on trace finite element methods for scalar
surface partial differential equations. Based on theoretical analyses for
related problems, specific choices for the parameters in the method are
proposed. Results of a systematic numerical study are included in which
different variants are compared and convergence properties are illustrated.
