  Transit and radial velocity observations continuously discover an increasing
number of exoplanets. However, when it comes to the composition of the observed
planets the data are compatible with several interior structure models. Thus, a
planetary parameter sensitive to the planet's density distribution could help
constrain this large number of possible models even further. We aim to
investigate to what extent an exoplanet's interior can be constrained in terms
of core mass and envelope metallicity by taking the tidal Love number k_2 into
account as an additional possibly observable parameter. Because it is the only
planet with an observationally determined k_2, we constructed interior models
for the Hot Jupiter exoplanet HAT-P-13b by solving the equations of hydrostatic
equilibrium and mass conservation for different boundary conditions. In
particular, we varied the surface temperature and the outer temperature
profile, as well as the envelope metallicity within the widest possible
parameter range. We also considered atmospheric conditions that are consistent
with nongray atmosphere models. For all these models we calculated the Love
number k_2 and compared it to the allowed range of k_2 values that could be
obtained from eccentricity measurements of HAT-P-13b. We use the example of
HAT-P-13b to show the general relationships between the quantities temperature,
envelope metallicity, core mass, and Love number of a planet. For any given k_2
value a maximum possible core mass can be determined. For HAT-P-13b we find
Mcore < 27 ME, based on the latest eccentricity measurement. We are able to
constrain both the envelope and bulk metallicity of HAT-P-13b to 1 -- 11 times
stellar metallicity and the extension of the isothermal layer in the planet's
atmosphere to 3 -- 44 bar. Assuming equilibrium tidal theory, we find lower
limits on the tidal Q consistent with 10^3 - 10^5.
