A&A Supplement series, Vol. 127, February I 1998, 597-605

Received April 24; accepted June 17, 1997

Reliable random error estimation in the measurement of line-strength indices

N. Cardiel, J. Gorgas, J. Cenarro, and J.J. González

Departamento de Astrofısica, Facultad de Fısicas, Universidad Complutense, 28040 Madrid, Spain
Instituto de Astronomıa, U.N.A.M., Apdo. Postal 70-264, 04510 México D.F., México

Abstract:

We present a new set of accurate formulae for the computation of random errors in the measurement of atomic and molecular line-strength indices. The new expressions are in excellent agreement with numerical simulations. We have found that, in some cases, the use of approximated equations can give misleading line-strength index errors. It is important to note that accurate errors can only be achieved after a full control of the error propagation throughout the data reduction with a parallel processing of data and error images. Finally, simple recipes for the estimation of the required signal-to-noise ratio to achieve a fixed index error are presented.

keywords: methods: data analysis -- methods:
analytical -- methods: statistical

• 1. Introduction
• 2. Definitions
• 3. Propagation of errors throughout data reduction
• 4. Numerical simulations
• 5. Analytical formulae: Previous works
• 6. The new formulae
• 7. Estimation of S/N ratios
• 8. Summary
• References