The photometric parameters R_e and mu_e of 74 early-type (E+S0+S0a) galaxies in the Coma cluster are derived for the first time in the near IR H band. These are used, coupled with measurements of the central velocity dispersion found in the literature, to determine the H band Fundamental Plane (FP) relation of this cluster. The same procedure is applied to previously available photometric data in the B, V, r, I, and K bands, to perform a multi-wavelength study of the FP. Because systematic uncertainties in the value of the FP parameters are introduced both by the choice of the fitting algorithm, and by the presence of statistical biases connected with the sample selection procedure, we emphasize the importance of deriving the FP parameters in the six photometric bands using an identical fitting algorithm, and appropriate corrections to eliminate the effects of sample incompleteness. We find that the FP mu_e coefficient is stable with wavelength, while the sigma coefficient increases significantly with increasing wavelength, in agreement with an earlier result presented by Pahre & Djorgovski. The slope of the FP relation, although changing with wavelength, never approaches the virial theorem expectation. We also find that the magnitude of the slope change can be entirely explained by the presence of the well known relation between color and magnitude among early-type galaxies. We conclude that the tilt of the Fundamental Plane is significant, and must be due to some form of broken homology among early-type galaxies, while its wavelength dependence derives from whatever mechanism (currently the preferred one is the existence of a mass-metal content sequence) produces the color-magnitude relation in those galaxies.
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