Continuum and line emission from accretion shocks at T tauri stars - I. Correlations with shock parameters

Fourteen models are calculated with the shock velocity ranging from 200 to 330 km s$^{-1}$ and pre-shock hydrogen nucleon density ranging from $2.5\times 10^{12}$ to $4\times 10^{13}$ cm$^{-3}$. Among them the summed emergent flux of all spectral lines accounts for about 0.1-0.3 of the total veiling flux. The hydrogen Balmer continuum accounts for 0.17-0.1, while a nearly constant fraction close to 0.5 comes from emission produced by the stellar atmosphere. The main results derived from the veiling continuum energy distributions are two strong correlations: (1) the Balmer jump (BJ) increases as F_K, the shock kinetic energy flux, decreases; and (2) at a fixed fraction of surface coverage by accretion shocks $r_{\lambda }$, the ratio of veiling to photospheric continuum flux at wavelength λ decreases as F_K decreases. Using the BJ-F_K and $r_{4500\,\mathring{\rm A}}$-F_K relations, the observed excess continua of 10 T Tauri stars are modelled. For BP Tau and 3 Orion stars our accretion luminosities are higher than published values by a factor of a few. For the six Chamaeleon I stars, our observed accretion luminosities are about 27-78 per cent higher than corresponding published values. Comparison of model results on the He I λ5876 Å flux with observed data indicates that, while those stars with dominant λ5876 Å narrow components can be readily accounted for by the calculated models, those with much stronger broad components cannot, and suggests that for the latter objects the bulk of their excess continua at 5876 Å do not originate from accretion shocks.