Aims. Despite photometry and spectroscopy of its oscillations obtained over the past 25 years, the pulsation frequency spectrum of the rapidly oscillating Ap (roAp) star gamma Equ has remained poorly understood. Better time-series photometry, combined with recent advances to incorporate interior magnetic field geometry into pulsational models, enable us to perform improved asteroseismology of this roAp star. Methods. We obtained 19 days of continuous high-precision photometry of gamma Equ with the MOST (Microvariability & Oscillations of STars) satellite. The data were reduced with two different reduction techniques and significant frequencies were identified. Those frequencies were fitted by interpolating a grid of pulsation models that include dipole magnetic fields of various polar strengths. Results. We identify 7 frequencies in gamma Equ that we associate with 5 high-overtone p-modes and 1st and 2nd harmonics of the dominant p-mode. One of the modes and both harmonics are new discoveries for this star. Our best model solution (1.8 M_sun, log T_eff ~ 3.882; polar field strength ~8.1 kG) leads to unique mode identifications for these frequencies (ell = 0, 1, 2 and 4). This is the first purely asteroseismic fit to a grid of magnetic models. We measure amplitude and phase modulation of the primary frequency due to beating with a closely spaced frequency which had never been resolved. This casts doubts on theories that such modulation - unrelated to the rotation of the star - is due to a stochastic excitation mechanism.
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