Phase-modulated Noise
The classic analog spectrum analyzer cannot detect phase variations of the carrier, unless sidebands are created.

Given the modulation Factor is deltaFreq/Fmodulation, and the modulation factor is expressed in radians, wee can see the simply fact of "some phase modulation" might not cause sidebands to exist.

By the way, on a spectrum-analyzer you cannot tell the difference between PM sidebands and AM sidebands. You need to examine the sidebands as PHASORS; PM have oppositely rotating phases, so the carrier energy remains constant; AM phasors rotate in the same direction and cause variation in the carrier energy.