3 The data

3.1 Observations

Longslit spectra were taken at the La Silla Observatory of the European Southern Observatory (ESO) during three observing runs from 12 to 19 of October 1995, 10 to 14 of April 1996 and 17 to 20 of October 1996. The Boller & Chivens spectrograph mounted on the 1.52-m telescope was used. A Ford aerospace 15-micron pixel CCD was used for the first run while a Loral/Lesser 15-micron pixel CCD was used in the other two subsequent runs. The slit width of 2 arcsec, in combination with all the other set-up parameters of the instrument, yielded a resolution of $\approx$100-120 km s^-1, sufficient to measure the velocity dispersions $\sigma$ for most of the early-type galaxies observed. This choice of slit width ensured at the same time enough light throughput for good signal-to-noise ratio spectra with exposure times of $\approx$30 min and enough spatial resolution (0.81 arcsec pix^-1) for a typical half-light radius of 30 arcsec. A sufficiently large part of the CCD was read out to allow accurate sky subtraction. No binning at read-out was applied to the data. The mean seeing was $\sim$1.3 $\pm$ 0.2 arcsec.

Figure 2: Histograms of the environmental densities for our sample galaxies, defined by means of the NGT parameter (see the text). For reference, values of the environmental density of galaxies in or near the centers of the Local Group (LG) and the Fornax and Virgo clusters of galaxies are indicated.

The observed wavelength covered the range from H${\beta}$ to TiO₂ for a zero redshift galaxy in all the runs.

Bias frames were taken throughout the night. During the day time dark frames as well as high signal-to-noise dome flatfields were also made. The dome flatfields were produced before and after each night for the purpose of mapping pixel to pixel variations and possible sensitivity changes for example due to dust particles during the night. The median of 9-11 dome flats resulted in a noise level of the order of 0.1 per cent. In addition, sky flatfields were taken at dusk and dawn to correct the deviating slit illumination of the dome flatfields compared to sky images. This procedure ensured that the night-sky spectrum could be subtracted correctly.

A number of G- and K-giants stars were observed from the list of Worthey et al. (1994), in order to calibrate our line-strength index measurements to the Lick system, Further stars from the Bright Star Catalogue (Hoffleit et al. 1982) and from González (1993) were added, for the purpose of kinematical analysis (Table 2).

 

 

Table 2: Observed stars. FAB: Faber et al. (1985), GON: González (1993) and BSC: bright star catalogue (Hoffleit 1982); Run ID's are reported in the last column.

Name	spectral	V	src	Run
	type	mag
HD 036003	K5 V	7.64	BSC	1a, 1b
HD 064606	G8 V	7.44	BSC	1a
HR 1015	K3 III	5.09	FAB	1a
HR 2389	K0 III	5.22	BSC	3
HR 2429	K1 III	3.95	FAB	3
HR 2574	K4 III	4.07	FAB	3
HR 2701	K0 III	4.92	FAB	2, 3
HR 2708	G8 III	5.46	BSC	3
HR 2778	G9 III	5.89	BSC	3
HR 2854	K3 III	4.32	FAB	2
HR 2970	K0 III	3.93	FAB	2
HR 3145	K2 III	4.39	FAB	2
HR 3242	K1 III	5.78	BSC	2
HR 3280	K1 III	5.07	BSC	2
HR 3392	G9 III	6.33	BSC	2
HR 3418	K2 III	4.44	FAB	1a
HR 3427	K0 III	6.39	FAB	1b
HR 3428	K0 III	6.44	FAB	1a
HR 3513	G8 III	5.87	BSC	2
HR 3728	G6 III	4.81	BSC	2
HR 3907	G9 III	6.35	BSC	2
HR 4287	K0 III	4.08	FAB	2
HR 6049?	K2 III	6.14	BSC	2
HR 6136	K4 IIIp	5.39	FAB	1a
HR 6159	K7 III	4.84	FAB	1a, 1b
HR 6501	K0 III	6.02	BSC	2
HR 6547	K0 III	5.93	BSC	2
HR 6590	G7 III	5.95	BSC	2
HR 6648	G8 III	5.84	BSC	2
HR 6651	K1 III	6.06	BSC	2
HR 6770	G8 III	4.64	FAB	1a, 1b, 2, 3
HR 6998	G4 V	5.86	GON	1a, 1b
HR 7051	A4 V	5.06	GON	1a
HR 7116	K2 I	4.83	GON	1a, 1b
HR 7149	K2 III	4.83	BSC	2, 3
HR 7264	F2 II	2.89	GON	1a
HR 7317	K3 III	6.06	BSC	3
HR 7429	K3 IIIb	4.45	FAB	1a, 1b, 3
HR 7430	G9 IIIa	5.12	FAB	1b, 2, 3
HR 7456	G0 Ib	5.98	GON	1a
HR 7965	G7 III	4.90	BSC	3
HR 7987	K2 III	5.35	BSC	3
HR 8229	K0 III	5.29	BSC	3
HR 8924	K3 IIIv	6.25	FAB	1a, 1b

The stars were moved perpendicular to the slit back and forth in order to obtain a uniform illumination of the slit and high signal-to-noise ratios.

Helium-argon spectra were used to wavelength calibrate the spectra.

Total exposure times for galaxies ranged between $\approx$720-6600 s. The spectra with longest exposure times usually resulted from two to three spectra with individual exposure times of about $\approx$1800-2400 s.

During Runs 2 and 3 the slit was aligned with the major axis of the galaxy. The position angles of the galaxies (see Table 5) either came from the unpublished data of Bender et al. (1989) or were derived from Digitized Sky Survey plates. During Run 1 no alignment was performed to save valuable exposure time. The CCD in this run had a low quantum efficiency and it was decided to use the time which would have been needed to rotate the instrument to enhance the signal-to-noise ratio of the galaxy spectra. However, signal-to-noise ratios of the spectra taken during Run 1 are still considerably lower than those of Runs 2 and 3.

3.2 Standard data reduction

The bias frames showed temporal variations in the mean level as well as spatial gradients which were constant with time. Therefore a high signal-to-noise bias frame was constructed and subtracted from the science frames. The dark current for both chips was measured to be $\la$1 e^- pix^-1 hr^-1. Since most exposure times for the individual science frames were well below one hour, a subtraction of the dark current was omitted for all the frames.

In order to flat field the frames the median dome flat frames were corrected for nonuniform illumination using twilight flats. With this technique it was possible to flatfield the sky to better than 1 per cent in all cases.

Cosmic rays were removed with the MIDAS task FILTER/COSMIC. Care was taken not to remove real features. Afterwards the images were checked and remaining cosmic rays were removed manually.

The wavelength calibration of the data was done using the 10-15 strongest lines of the Helium-argon lamp. A fourth order polynomial was used to model the transformation from pixel to wavelength scale. Typical residuals are of the order of $\la$0.05 Å, over the whole wavelength region covered. No significant deviation in the calibration was found when using the Helium-argon spectra taken before or after the galaxy exposure. The spectra were rebinned to a logarithmic wavelength scale to make the redshifting of lines independent of wavelength.

The subtraction of sky lines at the position of the galaxy spectrum was performed by linear interpolation using two windows of night sky not contaminated by spectra of neighbouring objects, one on each side of the galaxy spectrum. The windows were chosen to be as far away from the galaxy spectrum as possible in order not to subtract signal from the galaxy itself. This proved to remove most of the skylines in a sufficiently good manner. Remaining features for the strong skylines were removed manually.

The spectra were then rectified to lie exactly parallel to the dispersion direction. Afterwards, 1-dimensional spectra were extracted inside a range of $\pm$1/10 effective radius along the observed axis which corresponds to a typical aperture of 2.8 arcsec times 2.0 arcsec. The values for the effective radii were taken from unpublished photometry. The effective radii derived for galaxies in common with the 7 Samurai sample are compared with the data of Faber et al. (1989) in Beuing (1998). A very good agreement is found. The values for the effective radii are listed in Table 5. For 24 galaxies (16 per cent of the sample) photometry is not available. In these cases we assumed a typical value of $\approx$30 arcsec for the effective radius, which corresponds to the median effective radius of the sample (Beuing 1998). As index gradients in elliptical galaxies are shallow (Davies et al. 1993; Kuntschner 2000; Mehlert et al. 2000), the central values ( $r<1/10\ r_{\rm eff}$) measured in this paper are not significantly affected by this choice within the errors.

3.3 Velocity dispersions

The Fourier-correlation-coefficient method (FCQ) of Bender (1990) was used to measure velocity dispersions. The FCQ method is based on the unfolding of the maximum of the galaxy-template star-correlation function with the maximum of the autocorrelation function of the template star. It minimizes the effect of template mismatching onto the measured value of the galaxy velocity dispersion.

The continuum subtraction was performed by first fitting the continuum of the template stars and the galaxies by a polynomial. With the spectra produced in this way a first approximate value of the velocity dispersion was determined. Afterwards, the spectra of the template stars were broadened with this approximate velocity dispersion to make them matching the galaxy spectrum as good as possible. In a next step, the continuum shape of the broadened template star was fitted by the same polynomial as was used for the galaxy spectrum and subtracted from the unbroadened template star spectrum. This template star spectrum, after the second iteration for continuum subtraction, was then used to determine the final velocity dispersion of the galaxy via the FCQ method. In this way, errors due to continuum subtraction are minimized.

Monte Carlo simulations were performed to choose the best suited template stars and to find the best polynomial fit for continuum subtraction following the subsequent recipe for all the template stars individually. A synthetic galaxy spectrum was constructed from a template star spectrum using the input parameters velocity dispersion and deviations of the line shapes from a Gaussian in form of Gauss-Hermite coefficients (H₃ and H₄, see van der Marel & Franx 1993) at a certain noise level. Afterwards, the template stars from which the synthetic galaxy spectra were constructed, were used to recover the input parameters through FCQ using the same scheme for continuum subtraction as described above. All different combinations of template stars and synthetic galaxy spectra were tested. The input parameters were thereby varied systematically in a plausible range for early-type galaxies. Each combination of the input parameters was performed with 100 different noise patterns of a certain signal-to-noise ratio. Only stars for which the input parameters could be recovered with a precision of better than a few percent (using the mean values of the 100 simulations) were selected to be suitable to derive the velocity dispersions of our sample galaxies. Moreover, by realizing 100 noise patterns also the error estimates of FCQ were calibrated, which are derived from photon statistics and read out noise. The template stars chosen in this way yielded very consistent results when applied to the real galaxy spectra (see below).

The velocity dispersions of Run 1 were derived calculating the mean of the values determined with the stars HR 3428 (K0 III), HR 6770 (G8 III), HR 3427 (K0 III) and HR 7430 (G9 III). They proved best suited from the Monte-Carlo simulations. The wavelength region used to determine the velocity dispersion lies between 4900 Å and 5500 Å (Fe5015 to Fe5406). H${\beta}$ was not included to avoid additional template mismatching due to possible emission filling up ${\rm H}\beta$. For about 10% of the galaxies, additional observations were made for consistency check. In these cases, mean values weighted by the measurement errors were calculated. The mean FCQ error in the velocity dispersion in this run was $\sim$10 km s^-1. The measurements using the different template stars agreed very well with each other. The standard deviation around the mean value was $\approx$8.5 km s^-1. This value was of the same order as the mean FCQ error and thus indicates that the error estimate is correct and includes both the random errors as well as the systematic errors due the choice of the template star.

In Run 2 no significant difference of velocity dispersion measurements using all the different template stars was found. Hence mean values of all values were calculated. The mean FCQ error in velocity dispersion in this case was 6 km s^-1. The same value was found for the standard deviation around the mean value calculated from all the different template stars, again indicating the validity of the error estimates. The lower error was mostly a result of the improved signal-to-noise ratio due to the new Loral/Lesser chip inserted into the spectrograph.

In Run 3 the Monte-Carlo simulations selected the stars HR 2429 (K1 III), HR 2701 (K0 III), HR 2708 (G8 III), HR 6770 (G8 III) and HR 7430 (G9 III). The mean FCQ measurement error was even lower than in Run 2, yielding a value of only 4 km s^-1. The standard deviations around the mean values calculated from the different template stars mentioned above was 3 km s^-1, again consistent with the FCQ error estimates.

The velocity dispersions together with the error estimates and heliocentric velocities are summarized in Table 5. The heliocentric velocities were calculated applying two corrections. The non-zero redshift correction for each star was determined using the Fe5335 line feature at $\lambda = 5328.05$ Å, because this line was almost free of blends and strong enough. The correction to the heliocentric system was calculated according to Stumpff (1980). The typical 1$\sigma$error on the heliocentric radial velocity measurement is $\pm$20 km s^-1.

Figure 3: Comparison of the velocity dispersions derived here ( $\sigma _{{\rm own}}$) with the data given in the catalogue of Prugniel & Simien (1995, PS). Filled squares represent values averaged over at least two different studies, filled triangles show the data of the 7 Samurai, open squares indicate data from DFB and open triangles refer to CPWSM, DON+94, TD81, LC, BER+94 (for references see PS). The long dashed line is a bisector least-square fit to the data, the dotted lines are the individual least-square fits in X/Y and Y/X direction. The bottom panel shows the residuals.

Figure 3 shows the comparison of the velocity dispersions derived here with those from the catalogue of Prugniel & Simien (1995). Excellent agreement is found. The Bisector (BS) zero-point shift proves to be not significant (2.7 $\pm$ 10 km s^-1). Also the BS slope does not deviate from 1 significantly (0.99 $\pm$ 0.04 km s^-1). The scatter around the fitted line amounts to 23 km s^-1, close to what expected from the quadratically combined errors in both directions (22 km s^-1). This comparison sample however is biased to high $\sigma$ values.

Figure 4: Comparison of the velocity dispersions derived in this study ( $\sigma _{{\rm own}}$) with data given in the literature. Filled squares represent values of Jørgensen (1997), filled triangles stand for the values of Kuntschner (2000), open circles mark values of González (1993), and open triangles represent values from Faber et al. (1997). The lower panel shows the deviations from the line of correspondence shown as a solid line in the upper panel.

Figure 4 shows another comparison with more recent results from the literature. The velocity dispersions given by Faber et al. (1997) are in excellent agreement with our measurements. A BS fit yields an insignificant zero-point shift of 5 ($\pm$16) and a slope of 1.01 ($\pm$0.08), consistent with 1.

At $\sigma<200$ km ^-1 we derive systematically higher values by $\sim$25 km ^-1 than Jørgensen (1997) and Kuntschner (2000). As Jørgensen (1997) and Kuntschner (2000) use fixed apertures, they sample a larger portion of the galaxy in low-$\sigma$ objects, which leads to lower mean $\sigma$'s due to gradients.

All comparisons are summarized in Table 3.

 

 

Table 3: Comparison of $\sigma _{0}$. Bisector fits resulting from comparison of our measurement with the data of Prugniel & Simien (1995, PS 95), Faber et al. (1997, F97), Jørgensen (1997, J97) and Kuntschner (2000, K00). ZP and SL stand for zero-point and slope respectively, d(ZP) and d(SL) for their errors.

Source	ZP	d(ZP)	SL	d(SL)
	km s-1	km s-1
PS95	3	10	0.99	0.04
F97	-5	18	1.01	0.08
J97	41	21	0.91	0.09
K00	40	9	0.85	0.05

   
3.4 Line-strength indices

Line-strength indices were measured in the Lick/IDS system as introduced by Faber et al. (1985) and extended and redefined by Worthey et al. (1994). We refer to the latter for the index definitions. The step by step procedure adopted to measure the line-strength indices was the following. 1) All the spectra were matched to the Lick resolution. 2) The line-strength indices were measured using the definitions of Worthey et al. (1994). 3) These raw measurements were corrected for the effects of velocity dispersion. 4) Zero-point to the Lick/IDS system were removed. Steps 1, 3 and 4 are explained in more detail below.

Step 1: our spectra were taken at the resolution of 4 Å (corresponding to $\sigma\sim 100$ km s^-1 at 5100 Å) which is higher than that of the Lick spectra (8.6 Å corresponding to $\sigma_{\rm Lick}\sim$ 220 km s^-1 at 5100 Å). Therefore, our galaxy spectra and template star spectra were broadened to the typical resolution of the Lick data by convolving them with a Gaussian of dispersion $(\sigma_{{\rm Lick}}^2 -\sigma_{{\rm i}}^2)^{1/2}$.

Step 3: the velocity dispersion of the stars in galaxies broaden the galaxy spectral features (in addition to the instrumental broadening). As a result, line-strength indices decrease as their wings extend outside their index windows. In addition, other lines might reduce the continuum level by being broadened into the continuum windows. For this reason it is important to derive correction factors as a function of the velocity dispersion for each of the indices. These corrections are obtained adopting the standard procedure, as described e.g. in Davies et al. (1993).

In brief, template stars are broadened to simulate different velocity dispersions, ranging from 0 and 500 km s^-1. Lick line-strength indices are then measured on these templates allowing to determine the velocity dispersion dependence of each index.

The measurement errors of the line-strength indices were derived as follows. For each continuum window and absorption line window, the read noise of the detector and the rms error from the electron count statistics were added in quadrature. Sky noise was never significant, as the central parts of the objects have higher surface brightness than the sky. Using standard error propagation the errors of the fluxes in the continuum windows and the line windows were combined to determine the error for each line-strength index. The reliability of the error estimate was checked by comparing repeated measurements of the same object and found satisfactory.

Step 4: zero-point corrections were finally applied to remove the offsets to the Lick system. These offsets were determined by measuring the indices of 3-8 stars per observing run (Table 2).

The values for the line-strength indices derived in this work and in the literature (Worthey et al. 1994) are shown in Fig. 5. The offsets were obtained assuming slope 1 in each case. The offset is largest in case of Run 1. Except for Fe5709, the agreement between our measurements and the Lick values are good within the errors after zero-point corrections are applied. The adopted offsets are given in Table 4.

 

 

Table 4: Offsets applied to calibrate on the Lick system.

Index	Run 1	Run 2	Run 3
Mg1	0.082	0.014	0.016
Mg2	0.060	0.005	0.006
Mg b	0.290	0.145	0.102
H${\beta}$	0.123	0.012	0.008
Fe5015	0.135	-0.312	-0.257
Fe5270	0.034	-0.153	-0.079
Fe5335	0.138	0.029	0.009
Fe5406	-0.074	-0.092	-0.119
Fe5709	-0.197	-0.124	-0.323
Fe5782	-0.195	-0.120	-0.192
NaD	-0.062	-0.132	-0.278
TiO1	-0.011	-0.020	-0.020
TiO2	-0.004	-0.007	-0.008

Figure 5: Comparisons of the values for the line-strength indices derived in this work and in the literature (Worthey et al. 1994, W94). The offsets for the indices measured in each run were obtained assuming that the slope is 1. The crosses and the dotted lines correspond to the data and best fit to the data of Run 1, respectively. Open triangles and a long-dashed line correspond to Run 2 while filled circles and the dot-dashed lines correspond to Run 3. The line of correspondence is shown as a continuous line in each panel.

The galaxy database which has most objects in common with our sample is provided by Trager et al. (1998). Their NGC numbers are: 584, 596, 636, 1172, 1209, 1339, 1395, 1399, 1400, 1404, 1407, 2974, 3078, 3091, 3923, 5796, 5812, 6903, 7173, 7180. Figure 6 shows the comparison of the two data sets. In most cases the values compare well with each other within the error bars. The iron lines and the TiO₁ band do not match very well. The reason for this stems mainly from the large errors of these indices in the Lick sample, which stretch the data distributions along the x-axis. The consistency of the iron line-strength indices derived by us with other sources in the literature supports this interpretation (see below).

Figure 6: Comparisons of the line-strength index measurements in common between our data and the data of Trager et al. (1998). Crosses, open triangles and filled circles refer to Run 1, Run 2 and Run 3, respectively. The error bars in the upper left corner of each panel indicate the median measurement errors. It should be stressed that our line-strength index measurements were calibrated exclusively by comparison stars. No further calibrations incorporating the galaxies in common with Trager et al. (1998) were made.

The slightly larger scatter of our data taken in Run 1, which appears in Mg₁ and Fe5015, is likely to be attributed to worse observational conditions compared to Runs 2 and 3 (see Sect. 3.1).

In Fig. 7 we compare our measurements with González (1993), Jørgensen (1997), Longhetti et al. (2000), and Kuntschner (2000).

On average these comparisons show better agreement than that with Trager et al. (1998). Here the various line-strength index systems seem to be on consistent scales inside the errors, although some nonzero systematic errors and zero-point offsets might be present.

Figure 7: Comparisons of the line-strength index measurements in common between our data and those from González (1993) (circles), Jørgensen (1997) (triangles), Longhetti et al. (2000) (diamonds), and Kuntschner (2000) (squares). The error bars in the upper left corner of each panel indicate the median measurement errors. The average Fe index $<{\rm Fe}>$ = $({\rm Fe5270}+{\rm Fe5335})/2$ is added (bottom-left panel), because Fe5270 and Fe5335 are not given separately in Jørgensen (1997).

Sources of systematic errors are: aperture and seeing effects, spectral sensitivity curves and possible applied calibration. The latter effect leads to different continuum levels and therefore affects the measurement process, especially for the indices for which the integration extends over a large range in wavelength. Particularly the scatter in the plots for Mg₁ and Mg₂ in Figs. 6 and 7 are larger than the error bars on the data most probably because of systematic differences in the continuum subtraction.

As a last remark on aperture effects, it should be stressed that index gradients are known to be rather small (see González 1993; Mehlert et al. 2000; Kuntschner 2000) and the errors we make by comparing measurements at different apertures is probably smaller than the error bars on the data. This is particularly true for the comparison with the data from Trager et al. (1998) plotted in Fig. 6.

The line-strength index measurements are given in Table 6. To briefly summarize, the values were derived from non-fluxed-calibrated spectra, inside a range of 1/10 of the effective radius of the galaxy along the major axis (except Run 1) corresponding to a typical aperture of 2.8 arcsec times 2.0 arcsec. They are corrected for the effects of velocity dispersion and calibrated to the Lick/IDS system by means of comparison stars using the data published by Worthey et al. (1994). The errors are derived from photon statistics and read out noise.