6.3 Determination of Line Indices

The Lick/IDS system (Faber et al. 1985, Worthey et al. 1994) contains twenty-one optical absorption feature indices. All indices measure the strength of a spectral feature (either molecular or atomic) relative to a pseudocontinuum on each side of the feature.

Here only the indices ${ {\rm Mg}_2}$, Mgb, Fe5270 and Fe5335 will be considered. Their wavelength definitions are listed in Table . In the Lick/IDS system, molecular indices (e.g. ${ {\rm Mg}_2}$) are expressed in magnitudes, and atomic indices (e.g. Mgb) are expressed in angstroms of equivalent width. We do not use Fe5270 and Fe5335 individually, but only their mean, ${ <{\rm Fe}>}\equiv ({\rm Fe5270} + {\rm Fe5335})/2$.

 

Table: Wavelength Definitions for the used Line Indices

Index	Units	Blue continuum	Index passband	Red continuum	Measures
${ {\rm Mg}_2}$	mag	4895.125-4957.625	5154.125-5196.625	5301.125-5366.125	MgH, Mgb, FeI
Mgb	Å	5142.625-5161.375	5160.125-5192.625	5191.375-5206.375	Mgb
Fe5270	Å	5233.150-5248.150	5245.650-5285.650	5285.650-5318.150	FeI, CaI
Fe5335	Å	5304.625-5315.875	5312.125-5352.125	5353.375-5363.375	FeI

 

Notes: The definitions are from Worthey et al. (1994). The passbands are given in Å.

1-dimensional galaxy spectra were extracted from the 2-dimensional spectra as the central 13 rows. These 1-dimensional spectra were convolved to the Lick/IDS instrumental dispersion of 200 km/s (Gonzáles 1993) and then binned linearly in wavelength. The spectra were flux-calibrated using two spectra of the two spectrophotometric stars LTT7379 and LTT7987. Since not all the spectra had been obtained in photometric weather, the flux-calibration was only relative. Then the line indices ${ {\rm Mg}_2}$, Mgb, Fe5270 and Fe5335 were calculated according to the prescription in Worthey et al. (1994).

The indices were corrected to an aperture of metric diameter 1.19 h^-1 kpc. This was done for ${ {\rm Mg}_2}$ following JFK95b as

$${ {\rm Mg}_2}_{\rm norm} = { {\rm Mg}_2}_{\rm aperture} + 0.... ...( \frac{{r_{\rm aperture}}}{{r_{\rm norm}}} \right) \enspace ,$$ (6.5)

and for Mgb and the iron indices following J97 as

$$\log {\rm (index)_{norm}} = \log {\rm (index)_{aperture}} + ... ...( \frac{{r_{\rm aperture}}}{{r_{\rm norm}}} \right) \enspace .$$ (6.6)

All the line indices were corrected for the effect of the velocity dispersion. We used the corrections from JFK95b for ${ {\rm Mg}_2}$ and from J97 for ${ <{\rm Fe}>}$. The principles in establishing this correction are as follows: The spectra of K giant template stars are first convolved to the Lick/IDS instrumental dispersion and then convolved with Gaussian broadening functions having dispersions in the range 50 to 350 km/s. From these spectra, the various indices at various velocity dispersions are determined. For ${ {\rm Mg}_2}$, the difference between the index derived from the unconvolved ($\sigma$ = 0 km/s) and convolved ( $\sigma = 50,\ldots,350$ km/s) spectra is fitted with a low-order polynomial, giving the amount to add to the index to correct to zero velocity dispersion. For the other indices, the quotient is used, giving the correction to multiply the given index with. At $\sigma$ = 200 km/s, the additive correction for ${ {\rm Mg}_2}$ is 0.002, and the multiplicative correction for ${ <{\rm Fe}>}$ is 1.15.