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Parameters

The parameters $a_i$, $b_i$ and $GM_i$ have been chosen to provide a typical rotation curve, increasing linearly below $3\, \rm kpc$ and staying flat up to $40\, \rm kpc$, beyond which it decreases smoothly. For the bulge, $a_b=0$, $b_b=1.5$ and $GM_b=0.066$, which is equivalent to a Plummer sphere. The parameters for the visible and gas disks are respectively : $a_d=6.5$, $b_d=0.5$, $GM_d=0.171$, $a_g=25$, $b_g=0.5$, $GM_g=0.763$. For convenience the length unit is chosen to be the kpc and time unit the Myr. Fixing the gravitational constant $G$ to a value of 1, the mass unit corresponds to $2.2 \cdot 10^{11} \textrm{M}_\odot$. With this set, the velocity unit is about $1000\, \textrm{km} \cdot \textrm{s}^{-1}$. Fig. 1 shows the isodensity curves corresponding to the model. Well above the galaxy disk, negative density regions do exist, however our results are not spoiled by negative densities as long as orbits do not cross such regions.

Figure 1: 3D isodensity surface of the warped model at $5\cdot 10^{-4}$ and $5\cdot 10^{-5}\textrm {M}_{\odot }\cdot \textrm {kpc}^{-3}$ ($w=0.005$ kpc$^{-1}$). The surface is sliced with respect to the $y=0$ plane.
\resizebox{\hsize}{!}{\includegraphics[angle=-90]{isodensite5.ps}}

The amplitude of the deformation $w$ is chosen to be equal to $0.005\,\textrm{kpc}^{-1}$, developing a warp of the same order as the one of the Galaxy. For example, see the values indicated by Burton ([1992]) or Smart et al. ([1998]). Hence, the results obtained are applicable in typical cases of observed warped galaxies.


next up previous
Next: Hamiltonian Up: Model Previous: Warped disk model
2002-03-16