We present observations of the double-peaked broad H$alpha$ profile emitted by the active nucleus of NGC 7213 using the the Gemini South Telescope in 13 epochs between 2011 September 27 and 2013 July 23. This is the first time that the double-peaked line profile of this nucleus -- typical of gas emission from the outer parts of an accretion disk surrounding a supermassive black hole (SMBH) -- is reported to vary. From the analysis of the line profiles we find two variability timescales: (1) the shortest one, between 7 and 28 days, is consistent with the light travel time between the ionizing source and the part of the disk emitting the line; and (2) a longer one of $gtrsim 3$ months corresponding to variations in the relative intensity of the blue and red sides of the profile, which can be identified with the dynamical timescale of this outer part of the the accretion disk. We modeled the line profiles as due to emission from a region between $approx$ 300 and 3000 gravitational radii of a relativistic, Keplerian accretion disk surrounding the SMBH. Superposed on the disk emissivity, the model includes an asymmetric feature in the shape of a spiral arm with a rotation period of $approx$ 21 months, which reproduces the variations in the relative intensity of the blue and red sides of the profile. Besides these variations, the $rms$ variation profile reveals the presence of another variable component in the broad line, with smaller velocity width W$_{68}$ (the width of the profile corresponding to 68$%$ of the flux) of $sim 2100$ km s$^{-1}$.
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