Is the effective aperture of an antenna a constant?

When finding the effective aperture of an antenna we use:
[tex]A_{eff}\;=\;D_0\frac{\lambda^2}{4\pi}\;\hbox{ where }\;\frac{\lambda^2}{4\pi}\;\hbox { is the effective aperture of a isotropic antenna.}[/tex]

I read from Wikipedia and other sources that in order to use this equation, you assume the polarization of the incident wave matches the receiving antenna. AND the output impedance of the receiving antenna is conjugate match to the load for maximum power transfer.

But in the Antenna Theory book by Balanis:
[tex]A_{eff}\;=\;e_0|\hat{\rho_w}\cdot\hat{\rho_a}|^2 D_0\frac{\lambda^2}{4\pi}\;\hbox { where }\; e_0=e_{cd}(1-|\Gamma|^2)[/tex]

##e_{cd}## is the ohmic loss, ##(1-|\Gamma|^2)## is the load matching loss, and ##|\hat{\rho_w}\cdot\hat{\rho_a}|^2## is the polarization loss factor.

Balanis includes all the loss factors to calculate the effective area. This implies the effective area of the receiving antenna depends on the polarization of the incident TEM wave AND the load matching. This means the effective area varies with other outside parameters. I don't think that is correct. Please give me your thoughts.

Thanks