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Register a new userTensorial solution of the Poisson equation and the dark matter amount and distribution of UGC 8490 and UGC 9753
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Authors
P. Repetto
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In the first part of this article we expand three fundamental aspects of the methodology connected to the determination of a relation among the spatial density and the gravitational potential that can be specialised to distinct mass density agglomerations. As a consequence, we obtain general relations for the diagonal entries of a square symmetric matrix without zeros, we provide an expression of the gravitational potential, suitable, to represent several different mass density configurations, and we determine relations for the semi-axes of a triaxial spheroidal mass distribution, as a function of the spheroid mass density, volume density and radius. In the second part of this manuscript, we employ the tools developed in the first part, to analyse the mass density content and the inner and global structure of the dark matter haloes of UGC 8490 and UGC 9753, through the fits to the dark matter rotation curves of the two galaxies, assuming a triaxial spheroidal dark matter mass configuration. We employ the Navarro Frenk and White, Burkert, DiCintio, Einasto and Stadel dark matter models, and we obtain that both a cored Burkert and cuspy DiCintio and Navarro Frenk and White inward dark matter distributions could represent equally well the observed data, furthermore we determine an oblate spheroidal dark matter mass density configuration for UGC 8490 and UGC 9753. The latter outcome is confirmed by the estimation of the gravitational torques exerted by the dark matter halo of each analysed galaxy, on the corresponding baryonic components.
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In this paper we derive a novel circular velocity relation for a test particle in a 3D gravitational potential applicable to every system of curvilinear coordinates, suitable to be reduced to orthogonal form. As an illustration of the potentiality of the determined circular velocity expression we perform the rotation curves analysis of UGC 8490 and UGC 9753 and we estimate the total and dark matter mass of these two galaxies under the assumption that their respective dark matter halos have spherical, prolate and oblate spheroidal mass distributions. We employ stellar population synthesis models and the total HI density map to obtain the stellar and HI+He+metals rotation curves of both galaxies. The subtraction of the stellar plus gas rotation curves from the observed rotation curves of UGC 8490 and UGC 9753 generates the dark matter circular velocity curves of both galaxies. We fit the dark matter rotation curves of UGC 8490 and UGC 9753 through the newly established circular velocity formula specialised to the spherical, prolate and oblate spheroidal mass distributions, considering the Navarro, Frenk and White, Burkert, Di Cintio, Einasto and Stadel dark matter halos. Our principal findings are the following: globally, cored dark matter profiles Burkert and Einasto prevail over cuspy Navarro, Frenk and White and Di Cintio. Also, spherical/oblate dark matter models fit better the dark matter rotation curves of both galaxies than prolate dark matter halos.
Our GMRT HI observations of the ultra diffuse galaxy (UDG) UGC 2162, projected $sim$ 300 kpc from the centre of the M77 group, reveal it to a have an extended HI disk (R$_{HI}$/R$_{25}$ $sim$ 3.3) with a moderate rotational velocity (V$_{rot} sim$ 31 km/s). This V$_{rot}$ is in line with that of dwarf galaxies with similar HI mass. We estimate an M$_{dyn}$ of $sim$ 1.14 $times$ 10$^{9}$ M$_odot$ within the galaxys R$_{HI}$ $sim$ 5.2 kpc. Additionally, our estimates of M$_{200}$ for the galaxy from NFW models are in the range of 5.0 to 8.8 $times$ 10$^{10}$ M$_odot$. Comparing UGC 2162 to samples of UDGs with HI detections show it to have amongst the smallest R$_e$ with its M$_{HI}$/M$_{star}$ being distinctly higher and g -- i colour slightly bluer than typical values in those samples. We also compared HI and dark matter (DM) halo properties of UGC 2162 with dwarf galaxies in the LITTLE THINGS sample and find its DM halo mass and profile are within the range expected for a dwarf galaxy. While we were unable to to determine the origin of the galaxys present day optical form from our study, its normal HI rotation velocity in relation to its HI mass, HI morphology, environment and dwarf mass DM halo ruled out some of the proposed ultra diffuse galaxy formation scenarios for this galaxy.
In this article we investigate the outer and inner mass distributions of the irregular galaxies UGC 4284 and UGC 11861, taking advantage of published HI and H{alpha} high resolution rotation curves and constraining the stellar disk of both galaxies throughout stellar population synthesis studies. In addition we take into account the gas content of both galaxies deriving the HI+He rotation curve. The deduced baryonic rotation curves (star+gas) are inadequate to account for the total mass of UGC 4284 and UGC 11861, for that reason we examine the possibility of dark matter to explain the incongruity between the observed HI and H{alpha} rotation curves of UGC 4284 and UGC 11861 and the derived baryonic rotation curves. We consider NFW, Burkert, DiCintio, Einasto, and the Stadel dark matter halos, to analyse the dark matter content of UGC 4284 and UGC 11861. The principal results of this work are that cored dark matter models better reproduce the dark matter H{alpha} and HI rotation curves of UGC 11861 and the dark matter HI rotation curve of UGC 4284, while, the H{alpha} rotation curve of UGC 4284 is better reproduced by a cuspy DiCintio DM model. In general, cored exponential two-parameters models Einasto and Stadel, give better fits than Burkert. This trend, as well as to confirm past results, presents for the first time a comparison between two different exponential dark matter models, Einasto and Stadel, in an attempt to better constrain the range of possible exponential dark matter models applied to real galaxies.
The low surface brightness (LSB) spiral UGC 8839 is nearly devoid of star formation aside from a large HII region complex located in the extreme outer disc. In order to understand the origin and nature of this complex, we compare new H{alpha} and archival broad-band images of UGC 8839 to similar data for four other spiral galaxies. We conclude that the extreme off-axis star formation in UGC 8839 is likely due to a hyper-stable disc that is dark matter dominated at all radii, with the Toomre parameter reaching a minimum only in the extreme outer disc. Using analysis strategies designed to be particularly insensitive to the pitfalls of low-surface brightness objects and small number statistics, we determine that the presence of this complex in UGC 8839 is not exceptional when the HII region luminosity function is modelled by a power law, suggesting that it is a native structure and not a merging satellite. However, we find that the entire population of HII regions in UGC 8839 shows a preference for larger galactocentric radii when compared to HII regions in the other galaxies in our sample. UGC 8839 dramatically highlights the relationship between the baryonic/dark matter ratio and disk stability. A three-body interaction, similar to a scaled-down version of the interaction suspected to be responsible for Malin 1, is consistent with the extreme outer disk star formation that we see in the extended disk of UGC 8839.
In this work we study the mass distribution of two irregular galaxies, UGC 6446 and UGC 7524, by means of HI rotation curves derived from high resolution HI velocity fields obtained through the Westerbork Synthesis Radio Telescope data archive. We constrain the stellar and gas content of both galaxies with stellar population synthesis models and by deriving the HI+He+metals rotation curves from the total HI surface density maps, respectively. The discrepancy between the circular velocity maxima of the stellar plus the HI+He+metals rotation curves and the observed HI rotation curves of both galaxies requires the inclusion of a substantial amount of dark matter. We explore the Navarro Frenk and White, Burkert, Di Cintio, Einasto and Stadel dark matter halo models. We obtain acceptable fits to the observed HI rotation curves of UGC 6446 and UGC 7524 with the cored Burkert, Einasto and Stadel dark matter halos. In particular, Einasto and Stadel models prove to be an appropriate alternative to the Burkert dark matter halo. This result should increase the empirical basis that justify the usage of dark matter exponential models to adjust the observed rotation curves of real galaxies.
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