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This article is intended for undergraduate students with the aim to provide apedagogical introduction to the physics of stellar tidal deformations. Thespherically symmetric shape of any star is deformed via rotation around anarbitrary axis or by the presence of an external tidal field. We compute theellipticity of such a stellar object and show that rotation can be treatedanalogously to tidal effects caused by an external field, which induces aquadrupole moment. The detection of gravitational waves from a binary neutronstar merger in 2017 set constraints on the tidal deformability parameter and onequations of state for compact stars. We derive the corresponding formalismclassically and show that the Newtonian limit taken via general relativity isjustified. The compressibility and the compactness of matter are discussedclassically and compared to the relativistic approach. We find thatrelativistically the main influence on tidal deformability is related to thestar's compactness.

Gravitational quadrupole deformation and the tidal deformability for stellar systems: (The number of) Love for undergraduates