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Astron. Astrophys. 331, 894-900 (1998)

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4. Model fitting

A more careful examination of the galaxy image, especially in the B-band (Fig. 1), shows an asymmetry between the left (northern) and the right (southern) halves. This asymmetry appears in the dust lane, with the left half being brighter than the right one. This extra brightness of the left part is believed to be due to the presence of young OB stars. As already mentioned by van der Kruit & Searle (1981; see also Wainscoat et al. 1987), what seems to happen is that the spiral arm in the left half is approaching, with the dust trailing the arms. The young stars form [FORMULA] regions in front of the dust, thus resulting in an excess of light. Exactly the opposite happens in the right half of the galaxy, where the spiral arm is now receding, with the young stars hidden behind the dust and as a result the light of these stars is absorbed. This is evident in the B and V bands. FIR and radio continuum data also support the idea of the existence of star forming regions in the galaxy. This is shown in Fig. 2 (courtesy of Alton et al. 1997) where average surface brightness profiles along the major axis of the galaxy for 60 µ m (solid line) and 20 cm continuum (dotted line) are plotted. The dashed line traces the surface brightness of the IRAS beam. From this plot it is seen that there is an excess of FIR and radio emission which is very obvious in the left (northern) part of the galaxy while it is less evident in the right (southern) part. The region where we see this extra emission coinsides with the part of the galaxy which is brighter in the optical (see Fig. 1) and believed to be due to the existence of young stars. Because our model is not yet able to take into account any azimuthal structure, we folded the image so that the fitted galaxy is an average of the left and right halves of the galaxy. This method worked quite well for UGC 2048 (see Paper I) where "average" stellar and dust components were calculated.

[FIGURE] Fig. 2. Average surface brightness profiles for the [FORMULA] (solid line) and the 20 cm radio continuum emission (dotted line) along the major axis of NGC 891. The dashed line traces the surface brightness of the IRAS beam.

Our first attempt to fit the data with the distributions described above was successful for the I, J, K bands. In these bands we had excellent agreement between the real galaxy image and the model image that we created. For the B and V bands though, the fit was poor, giving high residuals between model and data. Furthermore, the stellar scalelength took values three or four times larger than those derived from the I, J and K bands. All these effects were the result of the young stars in the galactic plane, which contribute to the surface brightness along the major axis of the galaxy and make the exponential disk insufficient to describe both the main stellar population in the disk and the young stars. To overcome this problem (at least temporarily) we were led to model only the right half of the galaxy in the B and V bands which is "well behaved" (i.e. the dust lane is not perturbed by any clump of young stars, but instead it is clearly detected throughout the galaxy's major axis). In a later stage however (see end of this section), we did model the folded B and V images of the galaxy by introducing an additional stellar disk to describe the young stellar population.

As we did in Paper I, a global least squares fit of the model to the observed data is performed. For the fit, the Levenberg-Marquardt algorithm is used and the inverse Student's t distribution function is used to calculate the [FORMULA] confidence interval on the regression parameters. Both of these algorithms are embedded in the IMSL MATH/LIBRARY.

The full set of the parameters that are directly derived from the fit and are needed to describe the model galaxy are a) the central edge-on surface brightness [FORMULA] of the disk with the scaleheight [FORMULA] and scalelength [FORMULA], b) the central edge-on surface brightness of the bulge [FORMULA], with the effective radius [FORMULA] and the ellipticity b/a, c) the central face-on optical depth [FORMULA] with scaleheight [FORMULA] and scalelength [FORMULA] for the dust and finally d) the inclination angle [FORMULA]. As we described in Paper I, some preliminary values for the parameters are first derived by partial fitting techniques. The final values derived from the global fit are given in Table 1. In this table, the central edge-on surface brightness [FORMULA] of the main disk and of the bulge [FORMULA] are given in units of mags/arcsec2, while all lengths are given in kpc.


[TABLE]

Table 1. Global model fit parameters for NGC 891.


As mentioned before, our difficulties in modelling the B and V folded images of the galaxy had to do with the presence of the young stars. In order to solve this problem, we had to introduce the distribution of the young stars as a separate component in the model. Our first guess was to use a second exponential (in both R and z directions) disk. It turned out that the radial scalelength of this second disk was huge. Thus we approximated the second disk (hereafter young stellar disk) as being constant in the radial directions. The emissivity this disk is distributed exponentially in the vertical direction and is constant in the radial direction, truncated at the visual end of the galaxy, namely

[EQUATION]

with [FORMULA] being the emissivity of this disk at the center of the galaxy and [FORMULA] the scaleheight of this disk. Here [FORMULA] is the truncation radius of this disk which was taken to be approximately equal to the visual radius of the galaxy ([FORMULA] kpc). The central surface brightness for this model disk, if it is seen edge-on, is

[EQUATION]

Although the young stars seem to be distributed in a more clumpy and non-symmetric way, which probably has to do with the spiral structure, this disk approximately takes account of the extra light coming from the young stars and gives reasonable fits to the observed data (see below). Adding the new disk, the total stellar emissivity becomes

[EQUATION]

With the new distributions we run the model again in all five bands (B, V, I, J, K). Besides the parameters of the fit that were used before, two more parameters have been added ([FORMULA] and [FORMULA]). The young stellar disk that we included in the model was only detected in the V and B bands. In the other bands (I, J, K) this disk was not detected, in the sense that the values derived for the central luminosity density were very small positive or negative values with errors much larger than the values themselves and with all the other parameters taking values very similar to those presented in Table 1. This suggests that in these bands the contribution of the young stars is not important compared to the stars in the main disk of the galaxy. This is also evident just by visual inspection of the galaxy image in all bands. The values derived from the fit for the B and V bands are given in Table 2. Comparing the values for the common parameters given in Tables 1 and 2 for the B and V models, we see that all of them are very similar. This means that the young stellar disk that was included in the model, appears able to account for the light coming from the young stars, so that the rest of the galaxy can be very well described by the ten parameter model, the results of which are given in Table 1.


[TABLE]

Table 2. Global model fit parameters for NGC 891 in V and B bands using a second stellar disk.


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© European Southern Observatory (ESO) 1998

Online publication: March 3, 1998
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