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Astron. Astrophys. 332, 459-478 (1998)

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5. PCA applied to the ESS sample

In this section we apply the PCA to the ESS sample of 347 flux-calibrated spectra described is Sect. 2. As the input spectra for the PCA must have identical wavelength intervals and number of bins, each spectrum is rebinned to rest frame wavelength with a step of 5 Å/pix which is small enough for not destroying spectral features and large enough for not introducing non-existent patterns in the signal. This step is slightly larger than the typical steps obtained with the 3.6m and the NTT, which are [FORMULA] 3.4 and 2.3 Å/pix, respectively (see Sect. 2). Because the spectra were obtained with multi-object spectroscopy, the wavelength coverage is not the same for all the spectra in the catalogue and is a function of the position of the slit along the dispersion direction on the aperture mask. In order to maximize the number of spectra to be analyzed, one must carefully select the wavelength domain. Sample 1 defined in Table 3 provides a good compromise between a wide wavelength interval and a large number of spectra (80% of the total number of spectra analyzed). The wavelength interval contains major emission and absorption features usually present in galaxy spectra: [OII] (3727 Å), the H & K CaII lines (3933 and 3968 Å), CaI line (4227 Å), H [FORMULA] (4101 Å), the G band (4304 Å), H [FORMULA] (4863 Å), [OIII] (4958 Å and 5007 Å), and MgI (5175 Å). Samples 2 and 3, contain the "blue" and "red" spectra caused by extreme positions on the aperture masks (near the edges) sometimes combined accidentally with high or low redshift. The PCA is applied separately to samples 1, 2 and 3. For the 10 objects which do not belong to any of samples 1, 2 or 3, we only apply the [FORMULA] method described in Sect. 3. For application of the PCA to the 3 samples defined in Table 3, we normalize each spectrum by its norm as defined in Eq. (1) and we use the sum of squares and cross product matrix method for the PCA, described in Sect. 3.


[TABLE]

Table 3. Minimum and maximum rest wavelengths defining samples 1, 2 and 3. Also shown is the number of galaxies in each sample.


The main PCA analysis of the ESS data is performed on sample 1. The redshift distribution for this sample has the same shape as for the full sample of 347 objects (a Kolmogorov-Smirnov test shows that the two distributions have a 78.2% probability to originate from the same parent distribution, with a confidence level of 87.7%). We are therefore not introducing a redshift bias when using sample 1. Fig. 5a shows the projections of the 277 spectra of sample 1 onto the first 2 PC's derived from that sample. The galaxy marked with an arrow is an extremely blue galaxy. Fig. 5b shows the projections after normalizing to the first 3 projections ([FORMULA]). Although the normalization to the first 3 PC's artificially decreases the scatter in the ([FORMULA], [FORMULA]) sequence, this normalization changes the position of the points in the ([FORMULA], [FORMULA]) plane by a very small amount: [FORMULA] and [FORMULA] (see Fig. 5c).

[FIGURE] Fig. 5a-c. Uppermost two panels: a projections onto the first 2 eigenvectors for the spectra of sample 1 of the ESS (see text and Table 3). b same as upper panel, with normalization to the first 3 projections: [FORMULA]. The arrow indicates an extremely blue galaxy. Bottom panel c: the 277 galaxies of sample 1 in the classification space ([FORMULA], [FORMULA]) with normalization to the first 3 projections (open triangles) and without normalization(filled circles). Open circles map the projections of the 27 Kennicutt templates of Table 2 onto the first 3 PC's obtained from sample 1 and with the [FORMULA] normalization.

Justification for adopting the [FORMULA] normalization comes from the high reconstruction level reached using the first 3 PC's, with [FORMULA] 98% for sample 1. The distribution of errors we make with this approximation for sample 1 is shown in Fig. 6, where we plot the [FORMULA] value between the original and reconstructed spectra (using 3 PCs) and the error in the reconstruction defined as

[EQUATION]

It can be shown analytically that the following relation exists:

[EQUATION]

with A, B constants [FORMULA]. The label n denotes the spectrum n. The linear relation between [FORMULA] and [FORMULA] is clearly visible in Fig.  6. This result also confirms the reliability of the PCA reconstruction and associated error [FORMULA].


[FIGURE] Fig. 6. The relationship between the error in the PCA [defined by Eq. (7)] and the [FORMULA] value between the input spectrum and its reconstruction using the first 3 PC's.

Figs. 5a, b show that the spectral sequence for the ESS galaxies is similar to the sequence found by Connolly et al. (1995) for the 10 Kinney nearby galaxies. The spectral sequence of Fig. 5c is also similar to that shown in Fig. 3 (left), for the Kennicutt spectra (see Table 2). Note that we verified (as in Sect. 4) that the inclusion or rejection of the emission lines mainly affects the [FORMULA] parameter, and therefore the presence of emission lines does not significantly affect the results of the spectral classification.

To compare the ([FORMULA], [FORMULA]) sequence for sample 1 with that for the Kennicutt templates, we project the spectra of Table 2 onto the PC's obtained by the application of the PCA to sample 1 of the ESS (open circles in Fig. 5c). The normal Kennicutt galaxies lie along the sequence for sample 1, which shows that the ESS data describes the full Hubble sequence. We also notice in the ESS sample the existence of galaxies redder and bluer than the earliest and latest normal Kennicutt Hubble types, respectively. These and other cases will be discussed in Sect. 6. Application of the PCA to samples 2 and 3 yields a fairly well defined sequence in the ([FORMULA], [FORMULA]) plane, similar to that for sample 1. However, the absence of the 4000 Å break within the wavelength interval for sample 3 yields a larger scatter in ([FORMULA], [FORMULA]).

Fig. 7 shows the first 4 PC's obtained for sample 1 (bold lines). The first PC of sample 1 is characterized by the CaII K and H absorption lines near 4000 Å, a pronounced continuum break and by the other absorption features typical of early-type galaxies. The first 4 PC's also contain [OII], H [FORMULA] and both [OIII] emission lines. The projections onto the first 4 PC's for sample 1 satisfy [FORMULA], [FORMULA], [FORMULA], [FORMULA]. In addition, [FORMULA] and PC's of higher order contribute less than 1% of the total flux. Fig. 7 also shows the PC's derived by application of the PCA onto the Kennicutt spectra (thin lines), using a wavelength interval restricted to the same spectral range as for sample 1 (from 3700 [FORMULA] 5250 Å). The resemblance of the first 4 PC's for both samples is striking, which shows that the galaxy population in sample 1 has similar spectral properties to the sample of normal, local galaxies selected by Kennicutt. One must however be careful in comparing both samples, because the number of objects differ by a factor of [FORMULA] and properties such as the blue and red continuum and the strength of emission lines in the first PC's depend on the frequency of the particular Hubble types. In this respect, although the selected Kennicutt spectra are representative of the spectral features observed in normal galaxies, the population fractions are not representative of the local universe. This could be responsible for the slight differences in the PC's between sample 1 and the Kennicutt sample: the [FORMULA] and the [FORMULA] PC of the sample 1 are redder and bluer than the [FORMULA] and the [FORMULA] PC's of the Kennicutt sample, respectively; and the strengths of the emission lines for the 4 PC's differ.

In conclusion, according to the PCA technique, the ESS galaxies with [FORMULA] have similar spectral properties in the range [FORMULA] Å to the Kennicutt sample of galaxies with [FORMULA], which supports a close resemblance of the fractions of stellar populations between the two samples.


[FIGURE] Fig. 7a-d. First four eigenvectors for the PCA applied to sample 1 of the ESS (bold lines) and for the selected galaxy sample from Kennicutt (thin lines). The spectral range for both samples, when applying the PCA, is [FORMULA] Å.

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© European Southern Observatory (ESO) 1998

Online publication: March 23, 1998
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