  We demonstrate the strong impact of the oscillator agility on the line
broadening by studying spin transfer induced microwave emission in MgO-based
tunnel junctions with current. The linewidth is almost not affected by
decreasing the temperature. At very low currents, a strong enhancement of the
linewidth at low temperature is attributed to an increase of the non linearity,
probably due to the field-like torque. Finally we evidence that the noise is
not dominated by thermal fluctuations but rather by the chaotization of the
magnetization system induced by the spin transfer torque.
