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Astron. Astrophys. 351, 869-882 (1999)

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3. The NIR growth curve

The detailed 2D-fitting of the luminosity profile of galaxies (de Jong & van der Kruit 1994) is certainly the best way to compute their total magnitudes, but surface photometry in the NIR is available for too few of them to perform a statistical analysis. The largest such study is based on only 86 spiral galaxies of all types (de Jong 1996a , 1996b , 1996c), to compare to typically 100 galaxies per type in this paper. We therefore prefer to extrapolate aperture magnitudes with a growth curve. The computation of total (i.e. asymptotic) NIR magnitudes comparable to the optical ones determined by, e.g., de Vaucouleurs et al. (1991) or Prugniel & Héraudeau (1998) is however made difficult by the small apertures achieved at these wavelengths. Few galaxies have enough data from small to large apertures to constrain the shape of the growth curve and one has to use another method: combining observations of different galaxies having presumably the same curve (cf. Griersmith 1980). To this purpose, one needs to scale the apertures to a characteristic length [FORMULA] for each galaxy. The NIR growth curve [FORMULA] is then built by plotting [FORMULA] as a function of [FORMULA]. Usually (Gavazzi et al. 1996a; Gavazzi & Boselli 1996; Tormen & Burstein 1995; Frogel et al. 1978; Aaronson et al. 1979), the [FORMULA] diameter has been used as characteristic length. As noticed however by de Vaucouleurs et al. (1976), whereas the effective aperture [FORMULA] depends only on the shape of the profile, the [FORMULA] diameter is also related to the central surface brightness - i.e. the amplitude - and the ratio of [FORMULA] to [FORMULA] is therefore not constant. For this reason, we use [FORMULA] as characteristic length hereafter.

We adopt here the following procedure. We may expect some relation between the optical and the NIR profiles. For this reason, we decide to build a growth curve as a function of the B-photometric type [FORMULA] taken from Hypercat and of [FORMULA]. The infrared magnitude [FORMULA] in the B-effective aperture is computed by interpolation or by a small extrapolation in [FORMULA]. Rather than a straight line, we have used the functions proposed to compute H magnitudes at [FORMULA] by Gavazzi et al. (1996a):


where [FORMULA], and fitted a and b to the observations. This takes into account the curvature of the growth curve near [FORMULA] and improves the determination of [FORMULA]. Because they are polynomials, these functions are however not suitable to extrapolate the magnitude to the infinity.

The J, H and K data have been combined to build the growth curve. This is justified by the fact that only small [FORMULA] and [FORMULA] color gradients are observed (Aaronson 1977; Frogel et al. 1978). The growth curves are plotted in Fig. 1 for 7 bins of photometric type. As evidenced by this graph, the NIR growth curve is flatter than the optical one, especially for [FORMULA] corresponding to intermediate spirals: the NIR emission of galaxies is more concentrated than in the optical. This behavior is expected because the bulge is redder than the disk and is therefore more prominent in the NIR than in the optical. The scatter is also higher for intermediate types, which might be due to an inclination dependency of the growth curve (Christensen 1990; Kodaira et al. 1990). We have therefore distinguished in Fig. 1 between galaxies with [FORMULA] (rather face-on for disk galaxies) and [FORMULA], but no obvious trend is observed and we will neglect any inclination dependency in the following.

[FIGURE] Fig. 1. a -g : Growth curve of the NIR magnitude as a function of the aperture for the different photometric types. Hollow and filled triangles correspond respectively to galaxies with [FORMULA] and [FORMULA]. The solid and dashed lines are the mean optical and NIR growth curves. They are normalized to the effective aperture in the B-band and to the corresponding magnitude. h : The circles and vertical segments are the mean value [FORMULA] and the intrinsic scatter [FORMULA] of s as a function of the median value of [FORMULA] in each bin. The broken line is the 3-slope fit to [FORMULA] given in the text.

Because of the scatter and the lack of data at high aperture, where the flattening of the growth curve puts constraints on the curvature, attempts to fit growth curves similar to those of Prugniel & Héraudeau (1998) with 3 parameters ([FORMULA], [FORMULA] and [FORMULA]) did not prove successful. Plotting the NIR magnitudes versus the B magnitudes however reveals a nearly linear - though scattered - relation, between these quantities, suggesting to adopt a NIR growth curve of this form:


This ensures that the extrapolation at infinite A converges since [FORMULA]. Such relation has been fitted for each photometric type bin (Fig. 1, dashed lines) at [FORMULA].

The dispersion is due both to the uncertainties in the individual data and to the intrinsic scatter in the shape of the NIR growth curves for a given B-photometric type. The following convention is adopted hereafter: [FORMULA] means that xis distributed according to (or the density probability ofxis) a Gaussian with mean µ and variance [FORMULA] . Let us assume that, for each galaxy, the distribution of individual data around the best-fitting NIR growth curve [FORMULA] is [FORMULA] and that the distribution of the parameter s characterizing the growth curve is [FORMULA]. At any aperture,


A maximum likelihood estimation of these parameters yields [FORMULA], nearly independent of [FORMULA], [FORMULA] for early types ([FORMULA]) and [FORMULA] at later types. Note that the [FORMULA]-uncertainty on [FORMULA] is negligible when compared to the intrinsic scatter [FORMULA] in s. The value of [FORMULA] we obtained is plotted as a function of the median [FORMULA] of each bin in Fig. 1 and may be approximated with the following formulae:


The mean value [FORMULA] is less than one for all types, corresponding as expected to a blue-outwards gradient. This gradient is low for early-types, increases for spirals, peaking at [FORMULA] ([FORMULA] Sb) in good agreement with what has been obtained at optical wavelengths by de Vaucouleurs & Corwin (1977), and remains constant or slightly decreases for late types. The typical blueing of the [FORMULA] color of spirals from the effective aperture to the infinity is [FORMULA], close to the median value (-0.19) in [FORMULA] and [FORMULA] we have computed from the profiles published by de Jong (1996a).

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© European Southern Observatory (ESO) 1999

Online publication: November 16, 1999