We calculate light curves produced by r modes with small azimuthal wavenumbers, m, propagating in the surface fluid ocean of rotating neutron stars. We include relativistic effects due to rapid rotation, and propagate photons from the stellar surface to a distant observer using the Schwarzschild metric. The wave motions of the surface r modes are confined to the equatorial region of the star, and the surface pattern of the temperature variation can be either symmetric (for even modes) or antisymmetric (for odd modes) with respect to the equator. Because for the surface r modes the oscillation frequency in the corotating frame of the star is much smaller than the rotation frequency, Ω, we employ the approximation in which the oscillation frequency in the inertial frame, σ, is given by σ = -mΩ. We find that the even, m = 1 r mode produces the largest light variations. The dominant Fourier component in the light curves of these modes is the fundamental having σ = -Ω, and the first harmonic component having σ = -2Ω is always negligible in comparison. The dominant Fourier component of the even, σ -2r modes is the first harmonic. Although the odd r modes produce smaller amplitude light variations compared with the even modes, the light curves of the former have a stronger first harmonic component. If both m = 1 and 2 r modes are excited simultaneously, a rich variety of light curves is possible, including those having an appreciable first harmonic component. We show that the phase difference, δ - δE, between the bolometric light curve and that at a particular photon energy can possibly be used as a probe of the stellar compactness, R/M, where R and M are the radius and mass of the star. We find that hard leads are expected in general rather than hard lags, although there exists a parameter space of R and the inclination angle i that produces hard lags for the odd modes.
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