We present a set of analytical formulae to compute random errors in the measurement of line-strength indices. The new expressions constitute an improvement compared with the approaches followed in previous works, providing a straight method to attain reliable random error estimates. In particular, the derived equations should be preferred to methods involving either numerical simulations (a computer time demanding method) or multiple observations (usually prohibitive at low light levels). As a useful tool for observation planning, we also provide simple recipes to estimate the required signal-to-noise ratio to achieve a desired index error.
We want to stress here that full benefit from these formulae can only be obtained after a proper treatment of the error propagation throughout the data reduction. Apart from this, the analytical method followed to derived the expressions given in Sect. 6 (click here) is exact, in the sense that it does not involve any approximation (exception made for the unavoidable data sampling).
Acknowledgements
We are grateful to the referee for useful comments. The JKT is operated on the island of La Palma by the Royal Greenwich Observatory at the Observatorio del Roque de los Muchachos of the Instituto de Astrofısica de Canarias. The Calar Alto Observatory is operated jointly by the Max-Planck-Institute für Astronomie, Heidelberg, and the Spanish Comisión Nacional de Astronomıa. This work was supported by the Spanish ``Programa Sectorial de Promoción General del Conocimiento'' under grant No. PB96-0610.