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4. Discussion

We have obtained NIR surface photometry of a complete volume-limited sample of late-type galaxies in the Virgo cluster. Some obvious features of this sample can be briefly discussed here. Total B and K' magnitudes, taken from Table 3, will be used in the following analysis.
The relation between the optical diameters tex2html_wrap_inline2300 determined at the 25.5 mag arcsectex2html_wrap_inline2302  isophote by Binggeli et al. (1985) and the K' diameters determined in this work is shown in Fig. 4 (click here). Near infrared diameters at the 22.0 mag arcsectex2html_wrap_inline2306  isophote are systematically smaller than the optical ones at the 25.5 mag arcsectex2html_wrap_inline2308  isophote.

The linear regression analysis gives the following relations:
which imply that the present NIR observations cover a substantial fraction of the optical size of the galaxies.

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Figure 3: a): Left hand panels: Grey-level/contour representations of the K' band brightness distributions of galaxies measured with the 2.2 m telescope in both H and K' bands. N is up, E to the left. The faintest contour level shown is 20.5 mag arcsectex2html_wrap_inline2316 with a step of 0.5 mag arcsectex2html_wrap_inline2318; the grey scale is arbitrary. The scale given in the image is in pixels. The angular scale of the images can be determined using the pixel size given in Table 5. Right hand panels: Differential H and K' band radial surface brightness and colour profiles obtained by azimuthal integration along elliptical annuli. The horizontal scale gives the radius in arcsec as measured from the galaxy centre along the major axis of the ellipse. b): as for a) but for galaxies with only one band image available. c): as for b) but for galaxies observed with the 3.5 m telescope; (if both the observations are available the combined image is given). The faintest contour level shown is 21.0 mag arcsectex2html_wrap_inline2324 with a step of 0.5 mag arcsectex2html_wrap_inline2326

Figure 5 (click here) shows that the ratio between the optical (tex2html_wrap_inline2328) to NIR (tex2html_wrap_inline2330) diameters correlates with the B-K' colour index, (bluer galaxies have larger optical-to-NIR ratios) (given the uncertainty on the B photographic magnitudes, the estimated error on the B-K' colour index is tex2html_wrap_inline2338). Since the ratio of the optical to NIR surface brightness is not constant in galaxies of different luminosity and colour (Gavazzi et al. 1996c), the trend observed in Fig. 4 (click here) is not entirely due to the non-linearity between the optical and NIR diameters.

Figure 4: Relation between K' band diameters at the 22 mag arcsectex2html_wrap_inline2342 isophote determined in this work and the optical B diameters from Binggeli et al. (1985)

Figure 5: The relation between the optical (tex2html_wrap_inline2346) to NIR (tex2html_wrap_inline2348) diameter ratio versus the B-K' colour index

This result indicates that in the red galaxies, which are generally bright spirals (see Sect. 4.2), the old and young stellar components are distributed on discs of comparable dimensions. In the bluest objects, which are generally dwarfs, young stars are characterized by an higher surface density, thus by a larger isophotal diameter, than the old stellar component.

Figure 6: Relation between the ellipticity (1-b/a) in the K' band determined in this work and the corresponding ellipticity derived in the visible. Galaxies with tex2html_wrap_inline2356 are marked with filled dots, open dots indicate objects with tex2html_wrap_inline2358

The relation between the ellipticity determined in the K' band and the one determined in the B band by Binggeli et al. (1985) is given in Fig. 6 (click here). Two different symbols are used for bright (tex2html_wrap_inline2364) and weak (tex2html_wrap_inline2366) objects. As expected, there is a better agreement for bright galaxies, while a large scatter is observed for dwarf irregulars and blue compact objects, for which ellipses are just a crude representation of their shape. Part of the scatter is probably due to the different techniques used to determine the ellipticity by Binggeli et al. (1985) and by us: while in the B band the ellipticity is calculated from the ratio of the minor to the major diameter at 25.5 mag arcsectex2html_wrap_inline2370  isophote, in the NIR it is given by the ellipse which best fits the tex2html_wrap_inline2372 mag arcsectex2html_wrap_inline2374  isophote of the galaxy.

Figure 7: Relation between the uncorrected colour B-K' and the morphological type

Figure 8: Relation between the concentration index (at the 22.0 mag arcsectex2html_wrap_inline2378 isophote) and the morphological type

The relation between the uncorrected colour index B-K' and the morphological type is given in Fig. 7 (click here), while Fig. 8 (click here) shows the relation between the concentration index (at the 22.0 mag arcsectex2html_wrap_inline2382) and the morphological type.

Galaxies of earliest morphological classes have in general redder B-K' colours and higher concentration indices than dwarfs and late type systems, indicating that they are generally dominated by old stars mainly distributed in the bulge and/or in steep discs. The scatter in both relations is however large. Pure exponential discs (tex2html_wrap_inline2386; Gavazzi et al. 1996c) are found generally in late-type systems, with some exceptions in early spirals.

This result is in agreement with that found by Gavazzi et al. (1996a,b). It is interesting to note that, although BCD galaxies have B-K' colours similar to Sm and Im galaxies, they have higher K' concentration indices. This indicates that in BCD galaxies the stars emitting in the NIR bands have a centrally concentrated distribution, as for the blue component.

Figure 9: Relation between the B-K' colour and the K' magnitude

The relation between the B-K' colour and the K' magnitude is given in Fig. 9 (click here). Since the galaxies are at the same distance, this relation corresponds to a colour - absolute magnitude relation. Furthermore, as shown by Gavazzi (1993) and Gavazzi et al. (1996c), the NIR absolute magnitude is a good indicator of the total mass of galaxies. Figure 9 (click here) thus indicates that brighter and more massive galaxies have redder colours than low mass objects. The scatter in this relation is significantly lower than in the colour - morphological type relation, indicating that the history of star formation, as traced by the B-K' colour, is probably more closely related to the mass of the galaxies than to the morphological class. No systematic differences are observed between cluster core and periphery objects. Given the low scatter, many authors (Wyse 1982; Tully et al. 1982; Bothun 1984) suggested to use the NIR colour-magnitude relation as a distance indicator. Figure 9 (click here) shows however that the dispersion in the B-K' versus K' relation is tex2html_wrap_inline2406, thus significantly higher than the one obtained with other distance indicators such as the Tully-Fisher relation (Bothun 1984; Jacoby et al. 1992).

Figure 10: Relation between the concentration index (at the 22.0 mag arcsectex2html_wrap_inline2408 isophote) and the K' magnitude

All galaxies with tex2html_wrap_inline2412 have a concentration index tex2html_wrap_inline2414, which is consistent with an exponential disc (Gavazzi et al. 1996c), independent of their morphological type (see Fig. 10 (click here)). Stars are more concentrated in bulges and/or in discs only in luminous spirals (tex2html_wrap_inline2416). The presence of bulges and of steep discs in galaxies is thus better discriminated by the NIR luminosity (or by the mass) than by the morphological type. An accurate analysis of the colour-magnitude relation and of the concentration index-magnitude relation extended to a complete sample including dwarf and giant galaxies is addressed in Gavazzi et al. (1996c).

4.1. The NIR morphology of galaxies

Inspection of Fig. 3 (click here) clearly shows that the majority of the surveyed galaxies can be represented with exponential light profiles, typical of disks. Only a minority - generally bright early type spirals - show the characteristic signature of the bulge. Other features which characterize the morphology in the visible bands are also present in the NIR. Spiral arms, bars and rings are evident in spiral galaxies (see for example VCC 1615) albeit more diffuse and less clumpy. Many of the morphological differences observed between B and K' images are due to the more drastic effect of dust obscuration at optical wavelengths. A typical case is the edge-on VCC 92 (NGC 4192), which is one of the largest galaxies in the Virgo cluster. In the B band (Boselli et al., in preparation) a prominent dust lane is observable across the nucleus, and two spiral arms are clearly visible in the outer parts. The K' image shows a bright boxy-shaped central region and the two spiral arms close to the centre of the galaxy, not observable in the B band because of dust extinction.

Figure 11: a) The B luminosity function of the complete volume-limited sample of 88 late-type galaxies (tex2html_wrap_inline2582 Sa) with tex2html_wrap_inline2584 observed in this work. The dashed line indicates the 62 spirals (Sa tex2html_wrap_inline2586 type tex2html_wrap_inline2588 Sm), while the full line shows the 26 dwarfs (Im, BCD). b) as for a) but in the K' band

In some spiral galaxies, however, giant HII regions can occasionally be seen in the NIR images. An example is VCC 66 (NGC 4178), where two giant HII regions are observable in the S-W part of the disc, about tex2html_wrap_inline2592 from the nucleus. At these wavelengths, the emission of the HII regions is dominated by relatively young (tex2html_wrap_inline2594) red supergiant stars (Mas-Hesse & Kunth 1991), while in the B band and in particular in tex2html_wrap_inline2598 the emission is dominated by young and massive OB stars (tex2html_wrap_inline2600) (Kennicutt 1990). Low surface brightness galaxies are faint and diffuse in the NIR. Compact structures in the NIR are more common in BCD galaxies and contribute significantly to the integrated emission. As for giant spirals, these clumpy structures are HII regions, and in the NIR their emission is probably dominated by relatively young red supergiants. On the other hand, HII regions visible in tex2html_wrap_inline2602 and in B band are sometimes not seen in the NIR; in this case the HII regions are probably too young (tex2html_wrap_inline2606) to have produced red supergiants. The comparison of NIR with optical and tex2html_wrap_inline2608 images could be a useful tool to evaluate the age of HII regions within galaxies; some preliminary comparisons between tex2html_wrap_inline2610 and K' images are given by Boselli et al. (1995b). We plan to use the available NIR images in conjunction with new tex2html_wrap_inline2614 (Hippelein et al. 1996) images to study the recent star formation history of these objects and to investigate dependencies on morphological type and environment.

4.2. The NIR luminosity function of spirals

The subsample of spiral galaxies with available K' data constitutes a complete, volume-limited sample suitable for statistical studies. At present all galaxies in the sample with tex2html_wrap_inline2622 and of morphological type S0a or later have been imaged (94 objects). In Fig. 11 (click here)a we compare the B luminosity function of the 62 spiral galaxies (Sa to Sm; dashed line) with the one of the 26 dwarfs (Im, BCD, Im/BCD, Sm/BCD; continuum line) observed in this work (using B magnitudes from Binggeli et al. 1985). Given the limiting magnitude of the VCC catalogue of tex2html_wrap_inline2628, the bell-shaped distribution centered at tex2html_wrap_inline2630 represents the intrinsic luminosity function of spiral galaxies in Virgo and, as emphasised by Sandage et al. (1985) is not due to an observational cut-off. On the other hand, the distribution of the dwarfs represents the bright tail (B > 13.0) of their luminosity function (see Fig. 19 of Sandage et al. 1985); the cut-off at tex2html_wrap_inline2634 corresponds to the magnitude limit of the present observations. Figure 11 (click here)b shows the K' luminosity function of spirals and dwarfs (notice however that this is an ``hybrid" K' luminosity function since galaxies were selected in the B band, thus the sample is not magnitude limited in the K' band). Two features are worth mentioning: 1) the average B-K' of spirals is tex2html_wrap_inline2646 4.0 mag, while that of dwarfs is tex2html_wrap_inline2648 2.0 mag; 2) the K' band spiral distribution is significantely broader than the corresponding B band distribution. The difference between the two distributions is in accordance with the B-K' versus K' relation shown in Fig. 9 (click here) (see also Gavazzi et al. 1995b). Galaxies at the faint end (11< K' <14) populate the 14<B<16 bins, thus they have <B-K'> tex2html_wrap_inline2664 2.0, bluer than average.

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