We study vortex spin torque oscillators based on magnetic point contacts that operate in zero applied magnetic field. Static and dynamic vortex modes are shown to exist and have distinct electrical signatures. For the oscillatory mode, a spectrally pure slightly asymmetric voltage waveform is observed. It is subject to phase noise as sole fluctuations. The waveforms observed indicate that the vortex orbits outside the point contact region, with a pinned layer magnetization that is static but spatially nonuniform as a result of the current. This nonuniformity results in a reduction in the dc to rf power transduction yield.