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Astron. Astrophys. 352, L36-L39 (1999)

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2. Quantitative surface brightness photometry

We use the methods of two-dimensional image fitting as developed by MAG to model the surface brightness of NGC 1288 in a quantitative way. In Fig. 1 an I-band image is reproduced. The disk is fitted by an exponential density law,

[EQUATION]

where R denotes the galactocentric radius in the plane of the disk. The bulge is modelled by a spherical density distribution of the form

[EQUATION]

The surface brightness profile follows a similar law with the exponent [FORMULA] lowered by 0.5. The resulting parameters are listed in Table 1. According to the radial velocity [FORMULA] = 4405 km s-1 (RC3, de Vaucouleurs et al. 1991) of NGC 1288 we assume a distance of 60 Mpc. Thus 1" corresponds to 290 pc or 1 kpc to 3.44". Although we use a different bulge model than MAG, the quality of the fit is comparable to that of MAG.

[FIGURE] Fig. 1. I-band image of NGC 1288. North is up, east to the left, the size is [FORMULA] corresponding to 41 kpc[FORMULA]41 kpc.


[TABLE]

Table 1. Photometric parameters of NGC 1288


As can be seen in Fig. 2 the residuals [FORMULA] of the data with respect to the axisymmetric fit model show the positive and negative brightness modulation due to the spiral arms. These have been Fourier analyzed with respect to the azimuthal angle [FORMULA] along galactocentric annuli,

[EQUATION]

The Fourier coefficients [FORMULA] to [FORMULA] are shown in Fig. 3 as function of galactocentric radius for each filter band as a two-dimensional contour plot. These allow a quantitative measurement of the multiplicity of the spiral arms.

[FIGURE] Fig. 2. Grey scale representation of the residuals of the surface brightness with respect to the axisymmetric model. The residuals have been normalized by the axisymmetric model. Same size and orientation as in Fig. 1.

[FIGURE] Fig. 3. Coefficients of the Fourier decomposition of the residuals of the surface brightness with respect to the axisymmetric model as function of galactocentric radius shown as a two-dimensional contour plot for each filter band. The orders of the Fourier coefficients are marked on the vertical axes of the diagrams. The Fourier coefficients have been normalized by the axisymmetric brightness component. Full contour lines correspond to the values 0.1, 0.2, 0.3, 0.4; dotted lines to 0.05, 0.15, 0.25, 0.35, respectively.

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© European Southern Observatory (ESO) 1999

Online publication: November 23, 1999
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