power at the thresholds.

The periodogram analysis in Figure \[fig:2M1425\_full\_lc\] confirms that does not exhibit significant variability in either channel. The sensitivity of our *Spitzer* observations and our knowledge of the maximum period for this target (5.6 hr, Section \[sec:rotvel\]) allow us to place strong constraints on the upper limit of the variability amplitude at each wavelength. To determine these upper limits we create a sensitivity plot, which shows the variability amplitudes and rotation periods detectable by each observation. We inject sinusoidal curves into light curves with Gaussian-distributed noise similar to that of . The simulated light curves have amplitudes of $0.05 - 0.5\%$, rotation periods of $0.5-6$ hr and random phase shifts. We analyse these simulated light curves using the periodogram analysis discussed above and calculate the detection probability as the percentage of light curves with a given variability amplitude and period that produces a periodogram power above the significance threshold. We show these sensitivity plots in Figure \[fig:sensitivity\]. Adopting a detection probability of $90
\%$ as our threshold, we place upper limits of $0.16\%$ and $0.18\%$ on the $3.6~\mu$m and $4.5~\mu$m variability amplitudes respectively.

[Estimating significance of variability using periodogram analysis assumes that the noise properties of the 