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Astron. Astrophys. 327, 966-982 (1997)

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2. Approach

2.1. Sample selection, observations and data reduction

To study the structural parameters of edge-on spiral galaxies we selected a statistically complete sample taken from the Surface Photometry Catalogue of the ESO-Uppsala Galaxies (ESO-LV; Lauberts & Valentijn 1989) with the following properties:

  • their inclinations are greater than or equal to 87 [FORMULA] ;
  • the angular blue diameters ([FORMULA]) are larger than [FORMULA];
  • the galaxy types range from S0 to Sd, and
  • they should be non-interacting.

The inclinations were determined following Guthrie (1992), assuming a true axial ratio [FORMULA], corresponding to an intrinsic flattening [FORMULA] of 0.11. From this intrinsic flattening the inclinations i were derived by using Hubble's (1926) formula

[EQUATION]

where [FORMULA] is the observed axis ratio.

Of the total sample of 93 southern edge-ons, an arbitrary subsample of 24 galaxies was observed in the near-infrared [FORMULA] band in two observing runs of 4 and 3 nights, respectively. The selection of these 24 observed sample galaxies depended solely on the allocation of telescope time; the galaxies cover the southern sky rather uniformly.

By applying a [FORMULA] completeness test (e.g., Davies 1990; de Jong & van der Kruit 1994) we derived that the ESO-LV is statistically complete for diameter-limited samples with [FORMULA]. To check the completeness of our subsample, we calculated, based on a limiting diameter [FORMULA], that [FORMULA], which implies statistical completeness.

The near-infrared observations were obtained with the IRAC2B camera at the ESO/MPI 2.2m telescope of the European Southern Observatory (ESO) in Chile. The IRAC2B camera is equipped with a Rockwell 256 [FORMULA] 256 pixel NICMOS3 HgCdTe array. For both observing runs, in July 1994 and January 1995, we used the IRAC2B camera with Objective C, corresponding to a pixel size of [FORMULA] (40 [FORMULA] m) and a field of view of [FORMULA].

At both runs we used the [FORMULA] filter available at ESO (central wavelength [FORMULA] m, bandpass [FORMULA] m). We chose to observe in [FORMULA] rather than in K band (with [FORMULA] m, and [FORMULA] m), since the [FORMULA] band is almost as little affected by dust as the K band, but has a lower sky background (Wainscoat & Cowie 1992).

We took sky images and object frames alternately, both with equal integration times (in sequences of 12 [FORMULA] 10s), and spatially separated by [FORMULA].

Supplementary observations in the Thuan & Gunn (1976) I band were obtained during a number of observing runs at ESO. Most of the I -band observations were obtained with the Danish 1.54m telescope, equipped with a 1081 [FORMULA] 1040 pixel TEK CCD with a pixel size of 24 [FORMULA] m (0.36 [FORMULA] /pix). The field of view thus obtained is [FORMULA]. The TEK CCD was used in slow read-out mode in order to decrease the pixel-to-pixel noise. The Thuan & Gunn (1976) I -band characteristics match those of a Johnson I filter (Buser 1978). For all observed galaxies we determined the colour terms required for the calibration to the Cousins system using standard stars.

Gaps in the observed sample were filled in by service observations with the Dutch 0.92m telescope, equipped with a 512 [FORMULA] 512 pixel TEK CCD. It has a pixel size of 27 [FORMULA] m (0.44 [FORMULA] /pix), corresponding to a field of view of [FORMULA].

Both telescopes were used in direct imaging mode, at prime focus. Details of the specific observations can be found in Table  1.

[TABLE]

Table 1. Log of the I and [FORMULA] -band observations Columns: (1) Galaxy name (ESO-LV); (2) Telescope used (Dan 1.5 = Danish 1.54m; Dut 0.9 = Dutch 0.92m; ESO 2.2 = ESO/MPI 2.2m); (3) Date of observation (ddmmyy) (4) Passband observed in; (5) Exposure time in seconds; (in the [FORMULA] band the same integration time was spent to observe sky images) (6) Seeing FWHM in arcsec

During the reduction of the near-infrared observations, each sky frame was compared with the two sky frames taken nearest in time in order to detect stars in the sky frames. These stars were filtered out by using a median filter and thus the resulting cleaned sky images are very similar to the actual sky contributions.

To circumvent the effects of bad pixels and to obtain accurate flatfielding we moved the object across the array between subsequent exposures. Therefore, for most galaxies mosaicing of either 4 or 8 image frames was required to obtain complete galaxy images. The mosaicing was done by using common stars in the frames to determine the exact spatial offsets. In the rare case that no common stars could be determined, we used the telescope offsets as our mosaicing offsets. The overlapping area was used to determine the adjustment of sky levels needed by means of a least squares fit.

Bad pixels and bad areas on the array were masked out and not considered during the entire reduction process. Only after mosaicing was finished, the areas that still did not contain any valid observations were interpolated by a 2-dimensional linear plane fit (see Peletier [1993] for a detailed description of the reduction method used).

The calibration of the near-IR observations was done by using the SAAO/ESO/ISO Faint Standard Stars (Carter & Meadows 1995). We used the corrections published by Wainscoat & Cowie (1992) to transform the [FORMULA] measurements to the K band. The accuracy of the [FORMULA] -band zero-point offsets we could reach was [FORMULA] mag at both observing runs. The limiting factors here were flatfielding errors.

The I -band images were reduced following standard reduction procedures (see de Grijs & van der Kruit 1996); for the calibration of these observations Landolt fields were used (Landolt 1992). The I -band calibration could be done to an accuracy of [FORMULA] mag, depending on the telescope and observing run.

Both our I -band observations and the [FORMULA] -band data were taken at photometric (parts of) nights.

2.2. Vertical profiles

We extracted vertical luminosity profiles at a number of positions along the major axes of the sample galaxies. A semi-logarithmic binning algorithm was applied to the galaxies both radially and vertically, in order to retain an approximately constant overall signal-to-noise (S/N) ratio in the resulting vertical profiles. Since the most significant differences between our models become clear at small z, no vertical binning was applied close to the galaxy planes.

We rejected those profiles with low S/N ratios (generally the outermost profiles) and those that were clearly affected by artifacts in the data or foreground stars. For all galaxies we have been able to sample the vertical light distribution at various positions along the major axis outside the region where the bulge contribution dominates. For galaxies of types [FORMULA] we could determine these distributions for at least 4 of these independent positions.

The positions of the galaxy planes were determined by folding the vertical profiles and under the assumption of symmetrical light distributions with respect to the planes, in the near-infrared [FORMULA] -band observations.

In Fig. 1 we present the I-K colour maps of the galaxies discussed in this paper.

[FIGURE] Fig. 1. Calibrated I-K colour maps of our sample galaxies, displayed on the same scale. Each colour map has been inserted in a rectangular frame of size [FORMULA]. Galaxy images were rotated from their original sky orientations so that the major axes lie vertically. The corresponding calibrated I-K colours are indicated by the gray-scale bar at the bottom of the figure. a  ESO026G-06; b  ESO041G-09; c  ESO141G-27; d  ESO142G-24; e  ESO157G-18; f  ESO201G-22; g  ESO263G-15; h  ESO286G-18; i  ESO311G-12; j  ESO315G-20; k  ESO340G-09; l  ESO358G-29; m  ESO383G-05; n  ESO416G-25; o  ESO435G-14; p  ESO435G-25; q  ESO437G-62; r  ESO446G-18; s  ESO446G-44; t  ESO460G-31; u  ESO487G-02; v  ESO500G-24; w  ESO509G-19; x  ESO564G-27.

2.3. Comparison to published luminosity profiles

Surface brightness profiles of edge-on galaxies observed with modern detectors are scarcely available in the recent literature.

In the near-infrared K band we compared our observations of the large southern edge-on galaxy ESO 435G-25 with those of Wainscoat et al. (1989), obtained using a raster scan technique with an aperture of 5 [FORMULA]. Although our observations of ESO 435G-25 are of a much higher quality and were taken with a much higher resolution, we find remarkably good agreement between Wainscoat et al.'s (1989) and our K -band observations, as can be seen in Fig. 2. We have extracted vertical profiles from our calibrated K -band image at exactly the same positions and in the same way as was done by Wainscoat et al. (1989). The distinct drop in the difference profiles at the position of the galaxy plane is caused by the difference in resolution between both data sets.

[FIGURE] Fig. 2. Comparison of K -band vertical profiles obtained by Wainscoat et al. (1989) and our observations. To obtain these profiles we averaged strips of [FORMULA] wide.

A large and homogeneous set of I -band observations of southern Sb-Sc galaxies has recently been published by Mathewson et al. (1992) and Mathewson & Ford (1996).

Azimuthally averaged luminosity profiles were obtained by fitting ellipses to the galaxy isophotes, whose intensity, ellipticity and position angle were allowed to vary with each ellipse. Bad pixels, cosmic rays and foreground stars were masked out, so that these would not affect the results from the ellipse-fitting routine. Although this method works sufficiently well for low and moderately-inclined galaxies, when dealing with highly-inclined or edge-on galaxies the ellipse fitting is severely influenced by the presence of a central dust lane and the non-elliptical outer galaxy isophotes. Unfortunately, since Mathewson et al. (1922) and Mathewson & Ford (1996) did not tabulate the ellipticities nor the position angles used for the individual ellipses obtained for each galaxy, we can at best compare azimuthally averaged profiles which were obtained with the same free parameters. A comparison between the azimuthally averaged I -band luminosity profiles of Mathewson et al. (1992) and Mathewson & Ford (1996) and those obtained from our observations is shown in Fig. 3.

[FIGURE] Fig. 3. Comparison between azimuthally averaged I -band profiles published by Mathewson et al. (1992) and Mathewson & Ford (1996), and those obtained from fitting ellipses to our observations.

In general, we find that the differences between our and Mathewson's measurements are small, although clear deviations are appreciated in a number of cases. In particular for those galaxies for which the difference between our and Mathewson's profiles is relatively large (e.g., ESO 138G-14), we used observations obtained on different nights or with a different telescope to check our results. It was found that the features shown in Fig. 3 can be reproduced to within the observational errors. The main cause of deviations between Mathewson's and our profiles, in particular at small semi-major axis radii, is the unpredictable influence of dust, which greatly affects the ellipse fitting in the inner galaxy regions.

From this comparison to previously published surface brightness profiles, we conclude that our observations reproduce both the photometric zero points and the behaviour of the galaxy light as a function of position across the galaxy disk to within the observational errors.

2.4. Extinction correction

As was shown by Aoki et al. (1991), the inner contours of the K -band image of NGC 891 are asymmetric. This shows that absorption is not completely negligible, even at these near-infrared wavelengths.

To correct for this small absorption effect at K, we used the I-K colour index as an extinction indicator, following Knapen et al. (1995). We assumed that deviations from an average I-K colour are due to dust only and that the Galactic extinction law applies also in external galaxies (see, e.g., Jansen et al.gh the exact use of this law requires a detailed knowledge of the geometry of the mixture of dust and stars, any errors caused by our assumptions are of second order, since the K extinction due to dust is small.

As an example, in NGC 891, Aoki et al. (1991) pointed out that the southwest part of the K -band image is rather patchy along the major axis, compared to the northeast part. The most likely explanation for this patchiness is that it is due to dust associated with spiral arms, as can be deduced from colour images.

In our assumptions, we ignore two kinds of systematic errors, as was pointed out by Knapen et al. (1995): a contribution of smoothly distributed dust, which does not alter the galaxy's morphology, and effects due to population changes, which are believed to be small. In general I-K colours of stellar populations are very similar. For example stellar population models (e.g., Vazdekis et al. 1996) only show a small range for models of different ages and metallicities. Although population gradients probably are present, the errors made by not taking them into account are likely to be so small that it is better to apply this extinction correction than not to apply it.

Summarized, we corrected our profiles as follows:

[EQUATION]

where [FORMULA] and [FORMULA] are the corrected and observed profiles, [FORMULA] and [FORMULA] are the observed and mean [FORMULA] colours, and [FORMULA] and [FORMULA] are the extinction in I and K, respectively. We used [FORMULA] (Rieke & Lebofsky 1985). This extinction correction amounts to 0.55 mag in K at maximum, thus showing that we are dealing with optically thin regions in our galaxies. Therefore, by applying this correction, the errors that are caused by the incorrect underlying assumption that the dust is distributed in a foreground screen, are small.

2.5. A generalized family of density laws

By analyzing these [FORMULA] -band images of our sample of edge-on disk galaxies we should be able to distinguish statistically between the various models for the vertical luminosity and mass density distribution.

As it seems reasonable to take the isothermal and exponential distributions as the two extremes, van der Kruit (1988) proposed to use the family of density laws

[EQUATION]

where K(z) is the observed K -band vertical density profile, [FORMULA] is the extrapolated outer surface density in the galaxy plane, z is the distance from the plane, and [FORMULA] is the vertical scale parameter. The isothermal model is the extreme for n = 1, and the exponential is the other extreme for [FORMULA]. For comparison, for the isothermal sheet [FORMULA], where [FORMULA] is the exponential vertical scale height. Therefore, the sharpness of the peak in a luminosity profile is determined by the exponent 2/n of this family of density laws (6).

In Fig. 4 we plot a few model luminosity distributions, with the exponential and the isothermal functions as the two extremes. We have adopted identical central surface brightnesses and vertical scale heights for each of these models.

[FIGURE] Fig. 4. The family of density (luminosity) laws ( 6) with the isothermal (2/n = 2.0) and the exponential (2/n = 0.0) distributions as the two extremes. The difference in 2/n between two successive model distributions is 0.125; for clarity, the sech(z ) model distribution (2/n = 1.0) is shown as the dashed profile ([FORMULA] is the central surface brightness).
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© European Southern Observatory (ESO) 1997

Online publication: April 6, 1998
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