What is the relationship between modulation index and carrier-suppressed condition in FM.
What should the modulation index be when the carrier is suppressed in FM?
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The answer to this fills whole chapters of some large textbooks[1], but to summarize a lengthy discussion involving Bessel functions of the first kind, the carrier component vanishes for M=2.405, 5.520, 8.653, 11.79, 14.93, ... Mathematically, these are the zeros of J0(M).
[1]: Cook & Liff, Frequency Modulation Receivers, Prentice Hall, 1968, Fig 1-19, but you will find the same diagram in numerous texts.
