## 2. Data analysis## 2.1. Surface photometry and structural decompositionThe techniques used to reduce and analyze the photometric data are
detailed in Paper I. Briefly, we decomposed the surface brightness
distributions of each sample galaxy into the two components of bulge
and disk. Two independent methods were used: a) a parametric fit
assuming a generalized exponential bulge plus an exponential thin
disk; and b) an iterative non-parametric (np) decomposition algorithm.
We emphasize that both procedures decompose the entire two-dimensional
brightness distribution, rather than the brightness profiles, and take
into account the effects of seeing. The bulge is assumed to be an
oblate rotation ellipsoid coaxial with the disk. In addition to the
NIR images, ## 2.2. Observed rotation curvesRotation curves (RC's) exist for all the galaxies in our sample; the references for them are shown in Table 1, together with general information regarding the sample. More information about the sample objects (coordinates, etc.) can be found in Paper I. HI data are available for six objects; for the remainder, RC's were obtained from optical emission lines. We discarded absorption data since they are likely to yield a lower limit rather than a true estimate of the rotational velocity, due to the effect of velocity dispersion and projection along the line of sight. All distances were scaled to match our values, and circular speeds were corrected when estimated from inclinations differing from ours, with the exception of extended HI RC's derived from interferometric maps.
## 2.3. Model rotation curvesTo determine the shape of the RC for our galaxies we assumed: a) optical transparency (which was also assumed for the surface brightness decompositions); and b) the M/L ratio of bulge and disk to be constant within each component. The circular velocity in the equatorial plane of an axisymmetric mass distribution is given by where is the gravitational energy at radius
## 2.3.1. The bulgeThe circular speed of an axisimmetric ellipsoidal distribution of matter is given by (Binney & Tremaine 1987): where is the bulge M/L ratio,
the luminosity density at distance it is straightforward to determine (and hence the rotation speed from Eq. 2) once has been evaluated from the brightness distribution. Eq. 3, in turn, can be expressed either in terms of a parametric or np profile respectively, depending on the kind of decomposition considered. ## 2.3.2. The diskIn the case of an infinitely thin exponential disk, the rotation speed is given by (Freeman 1970): where , and are the modified Bessel functions of first and second kind, respectively; is the central disk surface density, and the disk scale length. For the np disk we have adopted the following expression for the circular speed (Toomre 1963; Kent 1986): where is again the disk surface density, and Here and are the complete elliptic integrals of first and second kind, respectively. Equation 5 can be rewritten in the more condensed form which we have used in our computations. ## 2.3.3. The dark haloWe have considered two different spherical distributions of matter to model the dark component. The first is a pseudo-isothermal sphere (Kent 1986) with density profile: where , the asymptotic circular speed, and , the scale length, are parameters of the distribution. The second is a sphere of constant density , with where is the only parameter of the
distribution. This distribution, with linearly
increasing with ## 2.4. Modified Newtonian dynamicsTo test the predictions of modified Newtonian dynamics (MOND: Milgrom 1983; Sanders 1990; Begeman et al. 1988 - hereafter BBS), we have altered our model RC's according to the prescriptions given by BBS. In particular, the relation between Newtonian () and modified () acceleration with can be used to derive the modified expression for the circular velocity. Although in most cases the available RC's are not very extended, in
six cases (namely NGC 1024, NGC 2841, NGC 3593, NGC 4698, NGC 5879,
and IC 724), the critical acceleration
( cm s © European Southern Observatory (ESO) 1998 Online publication: October 21, 1998 |