ar X iv : a st ro - p h / 95 05 00 2 v 1 2 M ay 1 99 5 On the usage of Flaring Gas Layers to determine the Shape of Dark Matter

I present a new method of deriving the shape of the dark matter (DM) halos of spiral galaxies. The method relies on the comparison of model predictions with high spectral and spatial resolution HI observations of the gas layer. So far, determinations of the flaring of the gas layer (i.e. the increase of the thickness with galactocentric radius) have been used to determine the mass-to-light ratio, M/L , of the stellar disk of several edge-on galaxies. In this paper I describe a method which can be used to determine the shape of DM-halos. This technique will be applied in a forthcoming paper. I show that the model predictions of the gas layer width are best calculated using a global approach, in which the potential arising from the total mass distribution of the galaxy is used in the calculation of the vertical distribution of the gas. I developed a new algorithm to calculate the force field of an arbitrary, azimuthally symmetric, density distribution. This algorithm is used to calculate the forces due to the radially truncated stellar disk as well as of the flaring gas layer. I use a simple two-parameter family of disk-halo models which have essentially the same observed equatorial rotation curve but different vertical forces. This mass model is composed of a stellar disk with constant M/L , and a DM-halo with a given axial ratio (Sackett & Sparke [ApJ, 1990, 361, 408]). I approximate the radial force due to the gaseous disk, and iteratively determine the vertical force due to the global distribution of the gas. In agreement with Maloney [ApJ, 414, 41, 1993] I find that beyond the Holmberg radius, the thickness of the gaseous disk is sensitive to both the flattening of the DMhalo and the self-gravity of the gas. I also show that the inferred DM-halo flattening is not sensitive to the particular choice of disk-halo decomposition. I show that the determination of the thickness of the gas layer is not restricted to edge-on galaxies, but can be measured for moderately inclined systems as well. Thus, in combination with detailed modeling, high resolution HI imaging of nearby galaxies with extended HI envelopes will enable us to determine the shape of the DM halo of these galaxies.