Asteroseismology of the <formula notation="TeX">$\beta$</formula> Cep star HD 129929

We perform a detailed seismic study of the <formula notation="TeX">$\beta$</formula> Cep star HD 129929. Our analysis is based on the recent derivation of six pulsation frequencies. These frequencies are unambiguously identified from the seismic modelling and the photometric amplitudes to be the radial fundamental, the <formula notation="TeX">$\ell=1$</formula>, <formula notation="TeX">$p_1$</formula> triplet, two consecutive components of the <formula notation="TeX">$\ell=2$</formula>, <formula notation="TeX">$g_1$</formula> quintuplet. A non-adiabatic analysis allows us to constrain the metallicity of the star to <formula notation="TeX">$Z \in [0.016, 0.022]$</formula>. In addition, the fitting of three independent frequencies, two of which correspond to axisymmetric (<formula notation="TeX">$m=0$</formula>) modes, allows us to constrain the core overshooting parameter to <formula notation="TeX">$\alpha_{\rm ov}=0.10\,\pm\,0.05$</formula>, as well as the other global parameters of the star. Finally, from the observation of the <formula notation="TeX">$\ell=1$</formula> triplet and part of the <formula notation="TeX">$\ell=2$</formula> quintuplet, we derive constraints on the internal rotation of this star.