On the origin of the correlations between the accretion luminosity and emission line luminosities in pre-main sequence stars

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Correlations between the accretion luminosity and emission line luminosities (Lₐcc and Lₗine) of pre-main sequence (PMS) stars have been published for many different spectral lines, which are used to estimate accretion rates. Despite the origin of those correlations is unknown, this could be attributed to direct or indirect physical relations between the emission line formation and the accretion mechanism. This work shows that all (near-UV/optical/near-IR) Lₐcc-Lₗine correlations are the result of the fact that the accretion luminosity and the stellar luminosity (Lₛtar) are correlated, and are not necessarily related with the physical origin of the line. Synthetic and observational data are used to illustrate how the Lₐcc-Lₗine correlations depend on the Lₐcc-Lₛtar relationship. We conclude that because PMS stars show the Lₐcc-Lₛtar correlation immediately implies that Lₐcc also correlates with the luminosity of all emission lines, for which the Lₐcc-Lₗine correlations alone do not prove any physical connection with accretion but can only be used with practical purposes to roughly estimate accretion rates. When looking for correlations with possible physical meaning, we suggest that Lₐcc/Lₛtar and Lₗine/Lₛtar should be used instead of Lₐcc and Lₗine. Finally, the finding that Lₐcc has a steeper dependence on Lₛtar for T-Tauri stars than for intermediate-mass Herbig Ae/Be stars is also discussed. That is explained from the magnetospheric accretion scenario and the different photospheric properties in the near-UV.