Up: Star formation history of environments
Subsections
The spectrum of a galaxy is produced by the sum of the spectral
characteristics of its stellar content.
The relative contribution given by each stellar type strongly
depends on the wavelength considered. Buzzoni (1989, 1995)
and Worthey (1992, 1994) have given estimates about the sensitivity of several indices to the
metallicity or to the age of a stellar population. From these studies it is
possible to infer that most of the line-strength indices in the Lick-IDS System
are sensible to the galaxy metallicity and that only the H
line-strength index is
connected in a significant way to the galaxy age. Since we are investigating
the effect of interaction on the stellar components of our sample galaxies, we
decided to measure and calibrate a set of line-strength indices sensible to
recent star Formation (SF), to which we refer as "blue'' indices,
in addition to those in the
standard Lick-IDS system ("red indices''). The details of the line-strength
indices are described in the sections below.
Table 4:
Observing parameters
|
Table 5:
Journal of galaxies observations
 |
Table 6:
Definition of the Lick-IDS indices
![\begin{tabular}
{rrccr}
\noalign{\hrule\medskip}
Index & Spectral & $\lambda_{\r...
...$5387.500 & Atomic \\ & & & 5415.000$-$5425.000 & [\AA] \\ \hline \end{tabular}](/articles/aas/full/1998/11/ds1429/tab6.gif) |
We indicate as red 16 line-strength indices defined in the
wavelength range between 4200 Å and 5500 Å. Atomic,
, and
molecular,
, indices are defined by the following formulas
(G93):
and
|  |
(1) |
The
function represents the spectral continuum
obtained by interpolating fluxes in two windows chosen near the two sides
of the feature:
|  |
(2) |



The adopted spectral bandpasses of the red indices are taken from
Burstein et al. (1984) and G93 and are detailed in Table 6.
Spectral ranges involved by the indices measurements are shown in the
Figs. 2a,b (shaded areas) superimposed on a set of stellar spectra.
Different spectral types are selected in order to emphasize the
variations of the line-strength indices as a function of the stellar
surface temperatures.
![\begin{figure*}
\includegraphics [width=8.5cm,clip=]{ds1429f2a.eps}
\includegraphics [width=8.5cm,clip=]{ds1429f2b.eps}
a)\hspace{8cm} b)\end{figure*}](/articles/aas/full/1998/11/ds1429/Timg34.gif) |
Figure 2:
Wavelength range (shaded area) of line-strength spectral indices
superimposed onto different stellar spectra.
The shaded areas are intended to highlight the variations
of the spectral features as a function of spectral types |
Almost all these indices are good metallicity indicators, while
they are only slightly sensitive to stellar age variations.
The only relevant exception is the H
index, that
is the most widely adopted optical age indicator.
Like all the Balmer absorptions, the H
line appears
very weak in the cold stellar types (M, K), while its
intensity grows with temperature, reaching its maximum value
in the spectra of A type stars. In Paper III, we will show some evidences
that suggest that the H
index is not very sensitive
to the ages of stellar populations younger than 1 Gyr.
We indicate as blue three indices, not present in the Lick set,
in the wavelength range
4200 Å, namely,
H+K(CaII) and H
/FeI indices, defined by Rose (1984, 1985),
and
the
(4000 Å) index defined by Hamilton (1985).
The "blue'' part of a galaxy spectrum is much more
sensitive to the stellar population age than the "red'' one (see Paper IV).
The H+K(CaII) index represents the ratio between the central
intensity of the H(CaII)+H
line (a blend of the
H(CaII)3968.5 Å with the Balmer H
) and that of
K(CaII)3933.7 Å line. In the same way, the definition of H
/FeI
index is the ratio of the central intensity of the Balmer H
line with the average value obtained from the central intensities of
two FeI lines, Fe4045 and Fe4063. The spectral windows adopted to identify
the centre of each of these lines are reported in Table 7.
These two indices are Balmer lines measures, and they are then
good age indicators (just like H
); H
/FeI is
sensitive also to the metallicity parameter
for its dependence from the FeI lines.
Table 7:
Definition of the "blue'' indices
|
The
(4000 Å) index maps the 4000 Å break. It is defined as
the ratio of the average fluxes (for frequency unit) measured in the
spectral ranges [4050 Å-4250 Å] and [3750 Å-3950 Å]:
| ![\begin{displaymath}
\Delta(4000~\mbox{\AA}) =\displaystyle\displaystyle\frac{F_{...
...x{\AA}]}
{F_{\nu}\left[3750~\mbox{\AA}-3950~\mbox{\AA}\right]}.\end{displaymath}](/articles/aas/full/1998/11/ds1429/img38.gif) |
(3) |
The definition of this index needs a measure of fluxes per
frequency units [Hz-1], while data are calibrated in counts per
wavelength units [Å-1]. So, we need to multiply the ratio
between fluxes/Å by the correction factor:
where
and
represent the central
wavelength of the two spectral bandpasses adopted for the
(4000 Å) measure.
Note that this index gives
information about the stellar parameters of the turn off stars
(and consequently about the mean age of the stellar population)
(W92).
Spectral bandpasses of the indices have been corrected for the
galaxy redshift z:


where
stands for a generic bound of the spectral
windows and
for its corresponding corrected value,
and
indicate respectively the
original and the corrected spectral width. The redshift value, z = v/c,
is directly estimated from the spectra lines.
The Lick Group (Burstein et al. 1984;
Faber et al. 1985; Burstein et al. 1986;
Gorgas et al. 1993; W92; Worthey et al. 1994)
has built
fitting functions for 21 indices, based on a stellar spectral library
of more than 400 stars. Their observations have been performed at the
3 m Shane Telescope (Lick Observatory) equipped with an Image Dissector
Scanner, characterized by a resolution of 8.2 Å (FWHM). The present
work is based on the measure of 16 red indices common to those studied
by the Lick Group, for which we will use their standard fitting
functions (Longhetti et al. 1997b, Paper III). In this context we need
to transform our data into the "standard'' Lick-IDS system. For this
purpose, we have observed a sample of 19 stars of different spectral
types (Table 8),
Table 8:
Stars from Lick Library
|
common to the Lick library. On their spectra, once
degraded to the IDS resolution, we measured the 16 red indices. The
comparison between our results with those of the Lick group
(Faber et al. 1985; Gorgas et al. 1993; W92)
shows an acceptable agreement
between the two measurement systems for some indices (H
, Mgb,
Fe5335, Ca4227, G4300, Fe5270), while systematic differences are
observed for the others. Table 9 reports the average
values of the differences found on the stellar sample between the two
measurement systems.
G93 has already pointed out that residual differences are connected to
the fact that while calibration of CCD data are really relative flux (i.e.
corrected for the CCD response function constructed from
observations of standard stars),
IDS data are calibrated with a tungsten lamp as a
reference source. As a consequence, IDS measurements contain the lamp
contribution to the corresponding spectral features. Following G93 we
have applied a shift to some indices measures in order to fully
transform them in the Lick-IDS system. The adopted shifts for each
index are listed in the Col. 4 of Table 9. The shifts have
been applied only to the indices for which the (IDS-CCD) values have a
systematic trend. G93 reports 8 "red'' indices (among the 21 of the
Lick set) measured on a sample of 35 stars common to the Lick library.
The average differences reported by G93 are compatible with ours within
errors. For comparison, in Table 9 we report also the shifts
adopted by G93. A remarkable exception is represented by
Fe5406, which shows a systematic scatter
between our and Lick data,
unlike G93 data. Figures 3a,b show the
comparison between our fully transformed data of the sample of 19 stars
and the Lick-IDS data.
![\begin{figure*}
\includegraphics [width=8.5cm,clip=]{ds1429f3a.eps}
\includegraphics [width=8.5cm,clip=]{ds1429f3b.eps}
a)\hspace{8cm} b)\end{figure*}](/articles/aas/full/1998/11/ds1429/Timg49.gif) |
Figure 3:
Comparison between our CCD measure (after the complete
transformation to the Lick system) and W92 IDS data on the common
sample of 19 stars. In each diagram, the error bar refers to the
average value obtained on the whole sample. The dimension of the error bar
along the abscissa is of the same order as the symbols |
The observed spectrum of a galaxy can be regarded as a stellar spectrum
(reflecting the global spectral characteristics of the galaxy)
convolved with the radial velocities distribution of its stellar
population.
Therefore the spectral features in a galaxy spectrum
are not the simple sum of
the corresponding stellar features, because of the motions of the stars
composing the galaxy. If we want to explain the measure of the
indices in terms of the stellar composition of the galaxies, we need to correct
them for the effects of the velocity dispersion. We
have estimated the correction studying the behaviour of all the
indices on a sample of about 80 stars. Stellar spectra (after they
have been degraded to the Lick-IDS resolution) have been convolved
with gaussian curves of various width in order to simulate different
galactic velocity dispersions. We have considered
velocity dispersions in the range
.
The results of these convolutions
are reported in Table 10. Corrections for the velocity field
were finally applied to the indices for which the correction
itself shows a monotonic variation as a function of the velocity
dispersion. This was the case for H+K(CaII), H
, Mg2, Mgb, G4300,
Fe5270, Ca4227, CN, CN2, Ca4427, Fe4531, Fe4668, Fe5015, Fe5335,
H
/FeI indices. The
(4000 Å) behaviour is not reported
in Table 10 because this index is insensitive to the spectral
broadening caused by velocity dispersion, since it refers to quite
large bandpasses. Mg1, Fe4383 and Fe5406 indices have not been
corrected since they show a fluctuating behaviour as a function of
and any tentative correction can introduce a further error.
Corrections are calculated as a linear interpolation of the data in
Table 10 corresponding to the actual velocity dispersion of each
galaxy. Since the spectral indices refer to the nuclear region
the correction is
derived assuming a value of the velocity dispersion in the same region.
Kinematical data adopted for the whole sample are reported in
Paper II.
Formally, the definition of an index is a ratio between fluxes integrated over
particular bandpasses. The estimate of the error is then the propagation of the
relative uncertainties in the fluxes used to calculate its value. If
uncertainties of relative fluxes in different bandpasses are independent,
the error is:
|  |
(4) |
where I = I(f1, f2, f3) indicates the dependence of the index on the fi
flux measured in the three bandpasses.
The derivatives of the formulas (1) and (2) give the expected
uncertainty for atomic (
) and for molecular indices
(
):
| ![\begin{displaymath}
\sigma^2(I_{\rm a})={F_{\rm I1,I2} \overwithdelims () C_{\rm...
... \overwithdelims () \lambda_{\rm r}-\lambda_{\rm b}}^2
\Biggl] \end{displaymath}](/articles/aas/full/1998/11/ds1429/img54.gif) |
(5) |
|  |
(6) |







where
is the spectral flux and
the
flux variance as a function of wavelength. The flux variance is
calculated from the wavelength calibrated frames, transforming the ADU
counts into the corresponding photons counts. In the present work, the
transformation is given by:
![\begin{displaymath}
I{\rm (col,row)[photons]} = {\rm ADU} \dot
( I{\rm (col,row)[counts]}) \end{displaymath}](/articles/aas/full/1998/11/ds1429/img65.gif)
with
. Summing the Read Out
Noise (RON) characterizing the CCD, we calculate the variance frame:
![\begin{displaymath}
\sigma^2({\rm col,row})=I{\rm (col,row)[photons]}+\sigma^2_{\rm RON}\end{displaymath}](/articles/aas/full/1998/11/ds1429/img67.gif)
where
. From this frame we extracted a 1D
spectrum with the same parameters adopted to extract the fully
calibrated spectrum of the corresponding object. This represents the
in the previous formulas. In fact, this variance
describes the uncertainty that characterizes the measurements of flux
for each spectrum, i.e. it represents the statistical error of the flux
measurement pixel by pixel, which is present even if the photometric
system is perfectly reproducible.
![\begin{figure}
\centering
\includegraphics [width=8.5cm,clip=]{ds1429f4.eps}\end{figure}](/articles/aas/full/1998/11/ds1429/Timg69.gif) |
Figure 4:
Comparison between our measures (indicated as "(our)'')
and those of G93 (indicated as "(Gonzalez)'') on a common sample of
5 template galaxies (Legenda: asterisk= NGC 7626, open square= NGC 7562,
full square= NGC 7785, open circle= NGC 7619 and full circle=NGC 584).
In both systems, data are not corrected for velocity dispersions |
Figure 4
shows the comparison between our and G93 data, on a
subset of 6 red indices, including the H
and Mg and Fe
indices which will be used to reconstruct the star formation history of
the galaxies. Our line-strength indices are in agreement, within the
errors, with those of G93.
Actually the measurement of a line-strength index
does not need an absolute flux calibrated spectrum, since only flux
ratios enter in its definition. The estimate of the error
calculated adopting (6) and (7) then corresponds to an upper
limit of the real uncertainty that characterizes our index measurement.
In fact, it does not take into account the consequences of the gaussian filter
applied to our data before measurements of the index since the data quality is
enhanced by this treatment to the spectral resolution cost. A more
realistic way to calculate the uncertainty that affects our indices
measures could then be to refer to a quantity that represents how the
corresponding spectral feature is visible within a noisy continuum.
We substitute Eqs. (1) and (2) with their approximations obtained
using constant average values of the fluxes in the integrals:
|  |
(7) |
|  |
(8) |
where
is the
flux average value in the central bandpass (indicated by
and
), and
is the average continuum flux calculated
with (3) at
.
In this way, Eqs. (6) and (7) become:
| ![\begin{displaymath}
\sigma^2(I_{\rm a}) = (\lambda_2 - \lambda_1)^2 {f_{\rm I}
...
...\overwithdelims ()
\lambda_{\rm r} - \lambda_{\rm b}}
\Biggl ]\end{displaymath}](/articles/aas/full/1998/11/ds1429/img75.gif) |
(9) |
| ![\begin{displaymath}
\sigma^2(I_{\rm m}) = (1.0875)^2 \Biggl [ {\sigma(f_{\rm I})...
...overwithdelims ()
\lambda_{\rm r} - \lambda_{\rm b}}\Biggl ]. \end{displaymath}](/articles/aas/full/1998/11/ds1429/img76.gif) |
(10) |
We then need to know only the average value of flux uncertainties,
,
and
, substituting the
variance function
. These average values can be
calculated as the dispersion of the flux around its average value in
the corresponding bandpass. Errors computed following the
procedure outlined above are reported in Tables 11, 12 and 13.
A remarkable exception is the error estimate for the H+K(CaII) and H
/FeI
indices. Their definitions are based on the flux values corresponding
to specific single pixels, and so their uncertainties are calculated
propagating the measure of the errors on the flux extracted
from the variance spectra
(referred before to
) at those pixels, decreased by
a factor of about 2.8 (which corresponds to the square root of the number
of the pixels involved in the gaussian filter windows).
Table 11 reports our nuclear line-strength indices on the 5 "template''
galaxies belonging to the G93 sample. The Table lists also the differences
between our results and those achieved by Worthey (1996, private
communication), on the common subset of 16 "red'' indices. Worthey IDS
data are of poorer quality than our CCD ones, and than they are
characterized by greater uncertainties (see also G93).
The comparison is made using line-strength indices before the correction
for the velocity dispersion, since this latter has been obtained by G93
with a procedure different from that described in Sect. 4.3. Our
corrections for velocity dispersion are nearly identical to those of G93 for
H
and Mg indices, but our procedure led to corrections which are of a few
percent smaller than in G93 for the Fe lines-strength indices. In
Paper II we show that our estimate of velocity dispersions for template
galaxies are in very good agreement with G93:
. These differences will
be taken into account during the comparison of the two set of data in
Paper III.
Data reported in Tables 12 and 13, relative to the indices
measurements in our sample galaxies, have not been corrected for a
possible contamination from the emission components.
Paper II will address the issue of
an analysis of these emission lines and a forthcoming paper that of a study of
the absorption lines that takes into account their contamination due to
filling.
Up: Star formation history of environments
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