If the amplitude of a message signal is kept fixed, and the frequency is increased, then will the modulating index decrease?
According to thr Bessel function the side tones will be more spaced when the frequency increases, but if the modulating index decreases then the amplitude of the central tone frequency should increase (if the modulating index goes below 2). Then how is the Bessel 0 point achieved?
Narrow Band FM, spectrally, looks similar to AM, in that only a carrier and two sidebands carry most of the energy.
Have you defined the "data eye" your system requires, to have acceptable Bit Errors?
Once you have done so, the presence or absence of the further_out Bessel components will become easier to compute.
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I think the modulating index is also called "beta", and is the phase deviation.
