Comparison between Different Absorption Features

For the majority of the early-type galaxies, two different spectral bands could be used for the derivation ofσ. However, for some clusters with a mean cluster redshift around hzClusi ≈ 0.231 the Mg_b absorption line is impractical due to strong sky lines in this wavelength region.

Therefore, an additional second region around the G4300 index band was analysed in the case of A 2390, Cl 0849 and Cl 1702. Moreover, for A 2390 a third wavelength range around Hβ was used as a further verification. For thefield galax-ies the situation changed for each object because different absorption passbands get affected due to sky lines. Nevertheless, at least one σ mea-surement around the Mg_b or G-band was possi-ble. In four WHDF field galaxy spectra, both features were free of telluric emission lines and two independent σ results could be derived.

For each galaxy, the fiducial value of the veloc-ity dispersion is based on the comparisons of the broadened template star spectra with the galaxy spectrum, the line-of-sight-velocity-distribution with the Gauss-Hermite (GH) polynomial fit and the Fourier output results with the correlation function (cf. section 5.3.1). As a further con-sistency check, it is worthwhile to compare the velocity dispersion measured from different ab-sorption feature passbands. For the following tests, the aperture corrected velocity dispersions of distant samples are used.

The reference velocity dispersion measurements are indicated as σ₁, whereas velocity dispersions derived from other features are denoted with the corresponding absorption line. As for the refer-ence σ values, the σ determinations of the com-parison feature were verified with the tests as outlined in section5.3.1. Based on these verifica-tions, velocity dispersions were classified accord-ing to a scheme from 1 to 5 based on their over-all quality and accuracy. Galaxies with a quality parameter Q_σ = 1 are very good measurements without artifacts or variations in their LOSVD and GH fit and free from any contamination by night sky emission lines. Q_σ = 2 are good mea-surements with slight variations in LOSVD and GH fit and Qσ = 3 corresponds to intermediate quality with some variations in LOSVD and/or slight influences of residual sky lines near the fea-ture of interest. Qσ = 4 represent bad σ deter-minations with strong variations in LOSVD and clear signs of sky lines which deplete and affect parts or the whole absorption line. In cases of Q_σ = 5, no measurement was possible.

As very closely to the mean redshift of the A 2390 cluster (z = 0.231) the Mg_b line is strongly af-fected by a telluric emission line (λ = 6367 ˚A), it has to be verified how strong the effect re-flects on the velocity dispersion determinations based on the Mg_b feature. In Fig. 5.9 the ve-locity dispersions based on the Mgb feature are shown as a function of theσ reference values for the A 2390 galaxies. A total of 36 member

gal-Figure 5.9: Comparison of velocity dispersion mea-surements derived from different absorption features.

The values taken as reference are displayed on the x-axis, velocity dispersions based on the Mgb feature are shown on the y-axis. Filled symbols denote high quality σmeasurements, open symbols the low qual-ity σdeterminations.

axies, splitted into 28 galaxies with Qσ = 1 and Q_σ = 2 and 8 objects with Q_σ = 3 are com-pared to each other. 11 galaxies with a qual-ity parameter of Qσ = 4 were discarded and for one object (# 2106) no σ based on the Mg_b feature could be derived. On average, the 28 galaxies with 1 ≤ Qσ ≤ 2 show a difference of

∆(σ₁−σ_mg) = −6±17 km s⁻¹ with a median h∆(σ₁−σ_mg)i=−2 km s⁻¹. Both numbers are less than the typical internal uncertainty of the velocity dispersions, which is δσ > 6 km s⁻¹. The 8 galaxies with Q_σ = 3 have an average difference of ∆(σ1 −σmg) = −43±39 km s⁻¹ and a median of h∆(σ1−σmg)i =−41 km s⁻¹. Although a careful analysis of the σ determina-tions was performed, the secondary σ determi-nations based on the Mg_b absorption line yield on average to 1% and to 27% higher σ values than the reference values for Qσ = 1,2 and for Qσ = 3, respectively. A possible dependence on the mask setup for the galaxies with quality

par-Figure 5.10: Comparison of velocity dispersion mea-surements derived from different absorption features.

Upper panel: relative uncertainty of velocity disper-sions with the Mg_b values as a function of velocity dispersionsσ₁. Lower panel: ∆σ/σ₁ versus theS/N per ˚A. Symbol notations as in Fig.5.9.

ameter of 1 and 2 was not detected, all three sub–samples feature the similar scatter and un-certainties. The velocity dispersions for galaxies with intermediate quality (Q_σ = 3), are clearly offset. A probably reason is that a weak residual sky lines in the spectra close to the absorption line are present which affect strongly the final velocity dispersion measurement. In particular, all velocity dispersions withQσ ≥3 show higher σ values in comparison to their reference value, which gives support to the assumption that a contamination by residual sky lines in the spec-tra is even existent for the intermediate quality determinations. From this comparison it seems already clearly evident that the telluric emission line around the Mg_b has dramatic effect on the derived velocity dispersions. Before the conclu-sions are drawn from this test, the influence of the signal–to–noise ratio on the accuracy of the velocity dispersion determinations is discussed.

Chapter 5: Kinematic Analysis 109

The quality of the velocity dispersion measure-ment and therefore its formal uncertainty de-pends on the S/N in the spectrum, the compari-son of the galaxy velocity dispersion with the in-strumental resolution and to a lesser extent the chosen wavelength interval used for the deter-mination. Fig. 5.10 displays the formal relative uncertainty ∆σ/σ₁ as a function of velocity dis-persion (upper panel) and as a function of the S/N (lower panel) per ˚A. ∆σ/σ1 was derived as the relative difference in velocity dispersion val-ues of the G-band with the Mgb line, normalised to the reference velocity dispersions σ1. As ex-pected, the deviations of velocity dispersions in-crease with decreasing S/N ratios. The relative uncertainty for galaxies with Qσ = 3 falls into the range 0.14≤∆σ/σ₁≤0.56 with a median of h∆σ/σ₁i= 0.31. For galaxies with high quality measurements (Qσ = 1), the relative errors cover the range 0.02≤∆σ/σ₁≤0.21 with a median of h∆σ/σ₁i= 0.06. Two effects of the uncertainties can be seen in Fig. 5.10. First, the errors of ve-locity dispersions with intermediate quality are large even for high S/N. This means that the σ determination for theQσ = 3 is not reliable and a different absorption line should be used. Sec-ond, the uncertainties of the high quality mea-surements depend only weak on the S/N, which suggests that the σ values are in fairly good agreement. However, as even for the high qual-ityσ Mgbdeterminations a slight offset to higher σ values is found and a possible (not visual de-tectable) interference due to sky line residuals can not completely be excluded, for the major-ity of cluster galaxies in A 2390 and the two poor clusters the G-band was used for the derivation of velocity dispersions. For this reason, 45 out of 47σ1 values for the A 2390 galaxies are based on the G4300 feature, which showed in all cases no contamination of any residual sky lines. More-over, the G-band was appropriate feature for the poor clusters and was solely used for theσ mea-surements of 15 and 7 cluster members in Cl 0849 and Cl 1702, respectively.

Figure 5.11: Comparison of velocity dispersion mea-surements derived from different absorption features.

Upper panel: relative uncertainty of velocity disper-sions with the G–band values as a function of veloc-ity dispersions σ₁ of the WHDF field galaxies. All galaxies are high quality σ measurements. Lower panel: ∆σ/σ₁ versus the S/N per ˚A. Measurements are splitted according to theS/N of the feature (Mg_b circles, G–band triangles) to visualise possible sys-tematic errors of low S/N on σ. For S/N >∼ 15, effects of systematic uncertainties become negligible.

To test if the Mg_b absorption lines yield accu-rate velocity dispersion measurements and not any bias is introduced with the restriction to the G-band absorption feature, Mg_b σ determi-nations for four WHDF field early-type galaxies are compared to the σ values derived based on the G-band feature. Fig 5.11 shows the formal relative uncertainty ∆σ/σ1 as a function of ve-locity dispersion (upper panel) and as a function of the S/N (lower panel) per ˚A for the WHDF early–type galaxies where both measurements are available. The lower panel is divided accord-ing to the S/N of the feature of interest, S/N values from the Mgb lines are denoted as circles, whereas the S/N based on the G–band is indi-cated as triangles. Again, ∆σ/σ₁ was computed

Figure 5.12: Comparison of velocity dispersion mea-surements derived from different absorption features.

The values taken as reference are displayed on the x-axis, velocity dispersions based on the Hβfeature are shown on the y-axis. Symbol notations as in Fig.5.9.

as the relative difference in velocity dispersion values of the Mg_b with the G-band line, nor-malised to the reference velocity dispersions σ1. Both features were free from any contamination due to sky lines. The relative uncertainties cover the range 0.03 ≤ ∆σ/σ1 ≤ 0.06 with a median of h∆σ/σ₁i = 0.05. The σ determinations are in very good agreement and show similar abso-lute errors between 8 to 18 km s⁻¹. Even for the lowest S/N ratios the formal uncertainty of 5% is less than the typical individual error in the σ measurement. This limit is also the smallest formal uncertainty that can be reached with the instrumental resolution and the template stars.

Although this comparison is based on a small number, no trend of increasing systematic errors on the σ values with low S/N can be found. In addition, velocity dispersions derived for galaxies in the other clusters and field samples show sim-ilar results and a good agreement between σ_Mgb and σG−band. For all galaxy samples in this the-sis, regardless of their environment loci, the S/N was at least 13 per ˚A. Results from the

simula-Figure 5.13: Comparison of velocity dispersion mea-surements derived from different absorption features.

Upper panel: relative uncertainty of velocity disper-sions with the Hβ values as a function of velocity dispersionsσ₁. Lower panel: ∆σ/σ₁ versus theS/N per ˚A. Symbol notations as in Fig.5.9.

tions yielded that the effects of systematic errors on σ become important at S/N <∼ 10 (cf. sec-tion5.3). As this limit is lower than the average S/N in the spectra of low–velocity dispersion gal-axies, the formal uncertainty therefore becomes negligible even for the lowest derived velocity dis-persions in the galaxy samples. A comparison of the absolute velocity dispersions for the WHDF ellipticals is presented in Fig5.14.

A third comparison of velocity dispersions was performed for a sub–sample of 23 galaxies in A 2390 by analysing a wavelength range around the Hβ feature. In contrast to metallicity-sensitive indices, the Hβ index (commonly re-ferred as an age-sensitive index) varies consider-ably among elliptical galaxies (Gonz´alez 1993).

In most local early-type galaxies nebular emis-sion is present at a measurable level, which read-ily can fill in the Hβ absorption, thus making the accurate measurement of the true absorption

Chapter 5: Kinematic Analysis 111

a difficult business. As particularly lower order Balmer lines (Hα and Hβ) are stronger affected by emission from ionised gas (Osterbrock 1989), higher-order Balmer lines (Hγ and Hδ) are pre-ferred for the age determinations of galaxies at higher redshift, because lower order Balmer lines possibly get contaminated by night sky emission lines. In addition, for galaxies at higher redshift a possible weak nebular emission might not be clearly detectable and overlayed onto the absorp-tion feature. For this reason, the agreement be-tween the reference velocity dispersions and the measurements of velocity dispersions based on the Hβ index are less confident and theσ values derived from the Hβ feature are only regarded as an additional consistency check.

In a first step, the spectra of the template stars and the galaxies were inspected if the Hβ indices might be subjected to weak emission. Neither for the stars nor for the galaxies any Hβ emis-sion was detected. However, as just mentioned above, one must be aware of possible variations of the Hβ index. In Fig. 5.12 the σ reference values for the A 2390 galaxies are compared to the velocity dispersions derived via the Hβ ab-sorption line. Again, spectra were divided with respect to their quality. 18 early–type spectra were classified with a Q_σ parameter of 1 and 2, five galaxies have Q_σ = 3. On average, simi-lar results are found as for the velocity disper-sions based on the Mg_b line, although with a larger scatter. Galaxies with quality parameter Qσ = 1,2 are shown as filled circles, objects of lower reliability with Qσ = 3 are indicated as open circles. in Fig. 5.12. Again, the deviations of velocity dispersions decrease with increasing S/N ratios. With respect to the reference values, the 18 galaxies with 1≤Q_σ ≤2 have a difference of ∆(σ1−σHβ) =−22±20 km s⁻¹with a median of h∆(σ1−σ_Hβ)i =−17 km s⁻¹, corresponding to 8% higherσ values than the G-band. This re-sult is in fair agreement to theσreference values.

The 5 galaxies of lower quality withQσ = 3 have a difference of ∆(σ₁−σ_Hβ) =−34±41 km s⁻¹

and a median of h∆(σ1−σ_Hβ)i =−51 km s⁻¹, which are higher in σ by ∼30%. Both σ mea-surements based on the Hβ line are larger than the typical internal uncertainty of the velocity dispersions.

Fig. 5.13 shows the relative difference in veloc-ity dispersions derived from the Hβ feature plot-ted against the reference velocity dispersions σ1. The lower panel displays δσ/σ₁ as a function of the S/N per ˚A. The relative uncertainties for the 18 galaxies with Qσ = 1,2 cover the range 0.02 ≤ ∆σ/σ₁ ≤ 0.30 with a median of h∆σ/σ₁i = 0.11. For galaxies with low quality velocity dispersions (Qσ = 3) the relative errors fall in the range 0.15 ≤ ∆σ/σ₁ ≤ 0.52 with a median of h∆σ/σ₁i= 0.34.

The agreement between the Hβ and the G-band measurements is less confident because of the fol-lowing two reasons. Besides the presence of weak Hβ emission superimposed over the spectrum, another effect may be small variations of the Hβ line itself. The strength of the Hβabsorption line is assumed to be sensible due to changes in the (mean) age of the underlying stellar population.

Both effects can modify the shape of the absorp-tion line which has influence on the derived mea-sure of the velocity dispersion. A combination of both effects is therefore most likely.

5.3.4 Comparison between Repeat