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tokens: gravity brightening exponent for the radiative, primary component, determined through our models, is ∼1 (von Zeipel 1924 ). For the secondary component, the posterior distribution is a slightly skewed normal distribution. By considering the peak of the skewed distribution (not the Gaussian fit to the posterior distribution), we find the gravity brightening exponent to be β = 0.59 ± 0.08. While this is not in agreement with the value of β = 0.32, suggested by Lucy ( 1967 ), we find our value in close agreement (∼2σ) with that of Claret Bloemen ( 2011 ), who computed β = 0.48 for comparable models. This value was computed using ATLAS models (Castelli Kurucz 2004 ) and the Kepler bandpass, and taking into account local gravity and convection. It is also likely that the tidal distortion affects the gravity darkening exponent, as discussed by Espinosa Lara Rieutord ( 2012 ). In our binary models, we fixed the primary and secondary rotation rates to those obtained through spectral fitting, v sin i 1 = 29(2) km s −1 and v sin i 2 = 9(2) km s −1 . Combining these values with our model-determined orbital inclination (assuming that the orbital and stellar rotational axes are aligned) and radii, for the model with pulsations, we obtained F 1 = 7.1(2) and F 2 = 4.0(1), where F is the ratio of the stellar rotational to orbital period and the subscript denotes the primary and secondary components, respectively. For both models, the one with, and the one without pulsations, we obtained the same values with slightly different uncertainties (see Table 4 ). Interestingly, under the assumption that the stellar rotational and orbital axes are aligned, the primary component is rotating slightly faster than the predicted pseudo-synchronous rotation rate (Hut 1981 ), the stellar rotation synchronous with the orbital velocity at periastron, which was calculated to be F = 5.3(2) for both components; while the secondary component is rotating slightly slower. However, if we relax the assumption that the orbital axes are aligned, it is possible to find configurations where both stars are rotating pseudo-synchronously. 5 SUMMARY AND CONCLUSIONS We have modelled the heartbeat star binary system KIC 3749404 by combining a comprehensive assortment of tools including the binary modelling software, phoebe ; emcee , a python implementation of the affine invariant mcmc techniques; and our own software to fit pulsations and Doppler boosting. With these tools, we were able to obtain two successful fits to the heartbeat star light and radial velocity curves simultaneously: one without pulsations and one with all the tidally induced pulsations greater than 20 μmag (seven pulsations). From these fits, we obtained the fundamental parameters of the binary system (see Table 3 ). The difference between the results of these two models hinges on the different inclination values: 602(1) without pulsations and 62(1)° with pulsations. This 2σ difference subsequently produced a larger