Context. The bipolar outflows associated with low-mass protostars create cavities in the infalling envelope. These cavities are illuminated by the central protostar and inner disk, creating a bipolar scattered light nebula at near-infrared and mid-infrared wavelengths. The variability of the scattered light nebula in both total intensity and intensity as a function of position in the scattered light nebula can provide important insights into the structure of the inner disk that cannot be spatially resolved. Aims. We aim to determine the likelihood that a warped inner disk is the origin of the surface brightness variability in the bipolar scattered light nebula associated with L1527 IRS. Methods. We present results from near-IR imaging conducted over the course of seven years, with periods of monthly cadence monitoring. We used Monte Carlo radiative transfer models to interpret the observations. Results. We find a time varying, asymmetrical brightness in the scattered light nebulae within the outflow cavities of the protostar. Starting in 2007, the surface brightnesses of the eastern and western outflow cavities were roughly symmetric. Then, in 2009, the surface brightnesses of the cavities were found to be asymmetric, with a substantial increase in surface brightness and a larger increase in the eastern outflow cavity. More regular monitoring was conducted from 2011 to 2014, revealing a rotating pattern of surface brightness variability in addition to a slow change of the eastern and western outflow cavities toward symmetry, but still not as symmetric as observed in 2007. We find that an inner disk warp is a feasible mechanism to produce the rotating pattern of surface brightness variability.
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