This paper reports the results derived from an asteroseismological study of the cool ZZ Ceti star HL Tau 76. A grid of models has been computed in a parameter space covering the range of log g and Teff, formerly determined by spectroscopy, and a large range of hydrogen mass fraction. The adiabatic non-radial oscillations for all the models have been computed for the modes of degrees l=1 and l=2. An algorithm based on a χ2 test was applied to evaluate the quality of the fit between observed and theoretical periods. This method resulted in selecting a best fitting model for which the average relative matching of the periods is 0.7%. Then, a detailed comparison between the observed and the computed periods for the l=1 and l=2 modes of the best fitting model was achieved in order to identify as many observed modes as possible. To perform this identification we used the calculated periods for which we applied the rotational splitting as deduced from the observations. Through this process we identify the 36 independent modes observed in HL Tau 76. The best fitting model for HL Tau 76 is well constrained due to the large number of oscillations detected in this ZZ Ceti star. The main stellar parameters of HL Tau 76 derived from this analysis are: the total mass M*=0.575±0.005M☉, the hydrogen mass fraction qH, estimated as thick as 2.35±0.10x10–4. The helium mass fraction consistent with qH must be qHe=1x10–2. The method is not sensitive to Teff variations in the narrow domain of temperature derived from spectroscopy for HL Tau 76. The best adjustment is found however for Teff=11375K. The other derived stellar parameters are the luminosity (L/L☉=0.00389) and the radius (R/R☉=0.0162). We note some trends in the fit of the observed periods with the computed ones which suggest that the rotational splitting could be non-uniform and that the large amplitude modes might contain information on the convection-driven excitation mechanism.
stars: fundamental parameters - stars: white dwarfs - stars: oscillations - stars: individual: ZZ Ceti, HL Tau 76