Line-strength indices have proven to be excellent tools for the study of absorption features in the spectra of astronomical objects. In particular, since the pioneering work of Faber (1973), the behaviour of indices in composite stellar systems has supplied fundamental clues for understanding the history of their stellar populations (e.g. Burstein et al. 1984; Bica et al. 1990; Gorgas et al. 1990; Worthey et al. 1992; Bender et al. 1993; Jones & Worthey 1995; Davies 1996). At the light of up-to-date stellar population models, line-strength indices can provide constrains about important parameters such as mean age, metallicity, or abundance ratios (e.g. Worthey 1994; Vazdekis et al. 1996; Bressan et al. 1996). In addition, line-strength indices have been widely employed to determine basic stellar atmospheric parameters (Rich 1988; Zhou 1991; Terndrup et al. 1995) and star cluster abundances (Brodie & Hanes 1986; Mould et al. 1990; Gregg 1994; Minniti 1995; Huchra et al. 1996), as well as to confront cosmological issues by providing new distance indicators (Dressler et al. 1987) and a powerful tool to investigate the redshift evolution of galaxies (Hamilton 1985; Charlot & Silk 1994; Bender et al. 1996).
Obviously, the suitability of line-strength indices to investigate the above
items relies on a proper determination of the associated index errors. For
illustration, it is interesting to note how errors in the measurement of
absorption features translate into uncertainties in the derived mean age and
metallicity of an old stellar population. Taking the predictions of the
single-burst stellar population models of Worthey (1994) as a reference,
typical errors of 0.20 Å in the Lick indices Fe5270 and H
(see
below) translate into 
dex and 
Gyr respectively (for a composite population of 10 Gyr and
metallicity around [Fe/H] = 0.3). Another example in which it is extremely
important to obtain reliable index errors is the analysis of the intrinsic
scatter of relations such as that of Mg2 with velocity dispersion in
elliptical galaxies (Schweizer et al. 1990;
Bender et al. 1993).
An accurate error determination is therefore needed in order to draw confident interpretations from observed data. Although this requires the estimation of both random and systematic errors, in this paper we will concentrate in the former. Whereas random errors can be readily derived by applying statistical methods, systematic errors do not always allow such a straight approach. Several authors have dealt with the most common sources of systematic errors in the measurement of line-strength indices. These include: flux calibration effects (González 1993; Davies et al. 1993; Cardiel et al. 1995), spectral resolution and velocity dispersion corrections (Gorgas et al. 1990; González 1993; Carollo et al. 1993; Davies et al. 1993; Fisher et al. 1996; Vazdekis et al. 1997), sky subtraction uncertainties (Saglia et al. 1993; Davies et al. 1993; Cardiel et al. 1995; Fisher et al. 1995), scatter light effects (González 1993), wavelength calibration and radial velocity errors (Cardiel et al. 1995; Vazdekis et al. 1997), seeing and focus corrections (Thomsen & Baum 1987; González 1993; Fisher et al. 1995), deviations from linearity response of the detectors (Gorgas et al. 1990; Cardiel et al. 1995), and contamination by nebular emission lines (González 1993; Goudfrooij & Emsellem 1996).
Although it is always possible to obtain estimates of index errors by performing multiple observations of the same object, analytical formulae to avoid such an observing time effort are clearly needed. In this paper we present a set of analytical expressions to derive reliable errors in the measurement of line-strength indices (hereafter we use error to quote random errors exclusively). General index definitions are given in Sect. 2 (click here). Section 3 (click here) describes how a proper treatment of error propagation throughout data reduction is a prerequisite to compute confident index errors. Random errors can be obtained through numerical simulations, presented in Sect. 4 (click here), or analytically. Previous works are briefly reviewed in Sect. 5 (click here), with special emphasis to the approach followed by González (1993). Our final set of formulae is presented in Sect. 6 (click here). Section 7 (click here) gives some recipes to estimate the required signal-to-noise ratios to achieve a fixed index error.