The Highly Flattened Dark Matter Halo of NGC 4244

In a previous paper (Olling 1995, \aj, 110, 591; astro-ph/9505002) a method was developed to determine the shapes of dark matter halos of spiral galaxies from an accurate determination of the rotation curve, the flaring of the gas layer and the velocity dispersion in the HI. Here this method is applied to the almost edge-on Scd galaxy NGC 4244 for which the necessary parameters are determined in the accompanying paper (AJ, Aug. 1996; astro-ph/9605110). The observed flaring of the HI beyond the optical disk puts significant constraints on the shape of the dark matter halo, which are almost independent of the stellar mass-to-light ratio. NGC 4244's dark matter halo is found to be highly flattened with a shortest-to-longest axis ratio of 0.2 (-0.1)(+0.3). If the dark matter is disk-like, the data presented in this paper imply that the vertical velocity dispersion of the dark matter must be 10% - 30% larger than the measured tangential dispersion in the HI. Alternatively, the measured flaring curve is consistent with a round halo if the gaseous velocity dispersion ellipsoid is anisotropic. In that case the vertical dispersion of the gas is 50 - 70% of the measured tangential velocity dispersion.Comment: 16 pages LaTeX, uses aaspptwo style (357kByte). Includes 3 figures. Complete paper, is also available at http://www.astro.soton.ac.uk/~olling/PrePrints/Paper_03/ or via anonymous ftp at ftp.astro.soton.ac.uk, cd pub/olling/Paper_03 To be published in the Aug. 1996 issue of the Astronomical Journa

The effects of flaring in H1 on the observed velocity field of spirals

This work is part of a larger project in which we want to determine the shapes of dark halos around spiral galaxies. Rotation curves 'probe' the halos in the radial direction. The derived halo mass distributions are badly constrained. The local halo densities fully determine the width of the gas distribution once the gaseous velocity dispersion is known. There where the dark halo dominates, the Full Width at Half Maximum (FWHM) of the gas layer is proportional to (rho(sub halo))(exp -0.5). Therefore, measuring the width of the gas layer probes the halo density directly. In a dark halo dominated potential, the FWHM of the gas layer increases linearly with radius. This increase of the thickness of the gas layer is known as 'flaring'. Flaring has been found inside the stellar disk. Beyond the edge of the stellar disk, the analysis is hampered by the onset of the warp. Since the galaxy we are studying, NGC 4244, has no significant warp we hope to extend Rupen's analysis into the halo dominated regime. The usual method to derive a rotation curve from an observed 2-dimensional velocity field is to assume that the hydrogen is distributed in infinitely thin rings. For a flaring disk, any line of sight samples many different parts of the galaxy, all having different densities and projected velocities. In order to fully exploit the information contained in the gas distribution, we have to understand the effects of flaring on the observables (the spectrum for each point of the galaxy). We have investigated the effects of a flaring disk on the observed velocity field. It is obvious that the largest (kinematical) effects are to be expected for low density dark halos at large inclinations. For low mass galaxies we expect that the flaring of the H1 layer will have a major effect on the observed kinematics. For galaxy with intermediate V(sub max,halo) seen at intermediate inclinations, one overestimates Vsin(i) typically by a few percent. For more massive galaxies, any effects arising from the flaring H1 layer are minuscule unless the inclination is not too far from 90 deg

Luminous and Dark Matter in the Milky Way

(Abridged) Axisymmetric models of the Milky Way exhibit strong interrelations between the Galactic constants (R_0 and T_0), the stellar columndensity (S_*) and the shape of the dark matter (DM) halo. Here we present analytical relations that can be used to investigate the effects of the uncertain gaseous velocity dispersion on the HI flaring constraints. The contribution of cosmic rays and magnetic fields to the pressure gradients is small. A significantly flattened dark matter halo is only possible if R_0 <~ 6.8 kpc. If R_0 is larger than ~7 kpc, or T_0 >~ 170 km/s, we can rule out two DM candidates that require a highly flattened DM halo: 1) decaying massive neutrinos; and 2) a disk of cold molecular hydrogen. It is only possible to construct self-consistent models of the Galaxy based on the IAU-recommended values for the Galactic constants in the unlikely case that the the stellar columndensity is smaller than ~18 M_sun/pc^2. If we assume that the halo is oblate and S_* = 35 +/- 5 M_sun/pc^2, R_0 <~ 8 kpc and T_0 <~ 200 km/s. Combining the best kinematical and star-count estimates of S_*, we conclude that: 25 <~ S_* <~ 45 M_sun/pc^2. Kuijken & Gilmore's (1991) determination of the columndensity of matter with |z|<=1.1 kpc is robust and valid over a wide range of Galactic constants. Our mass models show that the DM density in the Galactic centre is uncertain by a factor 1000. In the Solar neighbourhood we find: rho_DM ~0.42 GeV/c^2/cm^3 or (11 +/- 5) mM_sun/pc^3 -- roughly 15% of rho_tot.Comment: Accepted for publication in MNRA

On the usage of Flaring Gas Layers to determine the Shape of Dark Matter Halos

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. The potential arising from the {\em 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. I approximate the radial force due to the gaseous disk, and iteratively determine the vertical force due to the global distribution of the gas. The thickness of the gaseous disk is sensitive to both the flattening of the DM-halo and the self-gravity of the gas, but not 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.Comment: 40 pages including 14 Postscript figures (2MByet) also available via anonymous ftp at ftp://parsifal.phys.columbia.edu/pub/olling/ as files Halo-Shape.ps(.Z) (2360 kb, uncompressed), Halo-Shape-txt.ps.Z (the text, 362 kb, uncompressed) Halo-Shape-F##.ps.Z (the figures, 1173 kb, uncompressed