Disc galaxy evolution models in a hierarchical formation scenario: structure and dynamics
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We predict the internal structure and dynamics of present-day disc galaxies using galaxy evolution models within a hierarchical formation scenario. The halo mass aggregation histories, for a flat cold dark matter model with cosmological constant, were generated and used to calculate the virialization of dark matter haloes. A diversity of halo density profiles were obtained, the most typical one being close to that suggested by Navarro, Frenk & White. We modelled the way in which discs in centrifugal equilibrium are built within the evolving dark haloes, using gas accretion rates proportional to the halo mass aggregation rates, and assuming detailed angular momentum conservation. We calculated the gravitational interactions between halo and disc — including the adiabatic contraction of the halo due to disc formation — and the hydrodynamics, star formation and evolution of the galaxy discs. We find that the slope and zero-point of the Tully-Fisher (TF) relation in the infrared bands may be explained as a direct consequence of the cosmological initial conditions. This relation is almost independent of the assumed disc mass fraction, when the disc component in the rotation curve decomposition is non-negligible. Thus, the power spectrum of fluctuations can be normalized at galaxy scales through the TF relation independently of the disc mass fraction assumed. The rms scatter of the model TF relation originates mainly from the scatter in the dark halo structure and, to a minor extension, from the dispersion of the primordial spin parameter λ. The scatter obtained from our models does not disagree with the observational estimates. Our models allow us to understand why the residuals of the TF relation do not correlate significantly with disc size or surface brightness. We can also explain why low and high surface brightness galaxies have the same TF relation; the key point is the dependence of the star formation efficiency on the disc surface density. The correlations between gas fraction and surface brightness, and between scalelength and Vmax obtained with our models agree with those observed. Discs formed within the growing haloes, where λ is assumed to be time independent, have nearly exponential surface density distributions. The shape of the rotation curves changes with disc surface brightness and is nearly flat for most cases. The rotation curve decompositions show a dominance of dark matter down to very small radii, in conflict with some observational inferences. The introduction of shallow cores in the dark halo attenuates this difficulty and produces haloes with slightly smaller rotation velocities. Other features of our galaxy models are not strongly influenced by the shallow core.Keywords:
Structure formation
Abstract Nowadays, the scientific community has generally accepted the existence of dark matter. Astrophysicists investigate this assumption by astronomical observation. The galaxy rotation curve is one of the pieces of evidence for dark matter’s existence. The TLM18 telescope detects a 21 cm radio wave from the Milky Way to measure the rotation curve of the Milky Way. This article analyzes the frequency-power data to find out the rotation curve of the galaxy. The rotation curve is compared to existing theories, including the Kepler model, the exponential disk model, and the isothermal dark matter halo. Combining the exponential disk model with the isothermal dark matter halo, the calculation fits well with observation.
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I provide a model rotation curve for the Milky Way that matches the details of the terminal velocity curve normalized to the Galactocentric distance $R_0 = 8.122$ kpc obtained by the GRAVITY collaboration and the corresponding circular speed of the LSR $\Theta_0 = 233.3$ km/s. The model provides a numerical representation of the azimuthally averaged radial run of the gravitational potential of each mass component of the Galaxy (bulge-bar, stellar disk, gas disk, and dark matter) as represented by the rotation curve of each. It provides precise estimates of quantities like the stellar mass of the Galaxy ($6.16 \pm 0.31 \times 10^{10}\;\mathrm{M}_{\odot}$) and the local density of dark matter ($\rho_{DM}(R_0) = 6.76^{+0.08}_{-0.14} \times 10^{-3}\; \mathrm{M}_{\odot}\,\mathrm{pc}^{-3} = 0.257^{+0.003}_{-0.005}\; \mathrm{GeV}\,\mathrm{cm}^{-3}$). The dark matter density implied by the radial force is less than that found in many studies of the vertical force, perhaps indicating that the usual assumption of a spherical dark matter halo is no longer adequate.
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We predict the internal structure and dynamics of present-day disc galaxies using galaxy evolution models within a hierarchical formation scenario. The halo mass aggregation histories, for a flat cold dark matter model with cosmological constant, were generated and used to calculate the virialization of dark matter haloes. A diversity of halo density profiles were obtained, the most typical one being close to that suggested by Navarro, Frenk & White. We modelled the way in which discs in centrifugal equilibrium are built within the evolving dark haloes, using gas accretion rates proportional to the halo mass aggregation rates, and assuming detailed angular momentum conservation. We calculated the gravitational interactions between halo and disc — including the adiabatic contraction of the halo due to disc formation — and the hydrodynamics, star formation and evolution of the galaxy discs. We find that the slope and zero-point of the Tully-Fisher (TF) relation in the infrared bands may be explained as a direct consequence of the cosmological initial conditions. This relation is almost independent of the assumed disc mass fraction, when the disc component in the rotation curve decomposition is non-negligible. Thus, the power spectrum of fluctuations can be normalized at galaxy scales through the TF relation independently of the disc mass fraction assumed. The rms scatter of the model TF relation originates mainly from the scatter in the dark halo structure and, to a minor extension, from the dispersion of the primordial spin parameter λ. The scatter obtained from our models does not disagree with the observational estimates. Our models allow us to understand why the residuals of the TF relation do not correlate significantly with disc size or surface brightness. We can also explain why low and high surface brightness galaxies have the same TF relation; the key point is the dependence of the star formation efficiency on the disc surface density. The correlations between gas fraction and surface brightness, and between scalelength and Vmax obtained with our models agree with those observed. Discs formed within the growing haloes, where λ is assumed to be time independent, have nearly exponential surface density distributions. The shape of the rotation curves changes with disc surface brightness and is nearly flat for most cases. The rotation curve decompositions show a dominance of dark matter down to very small radii, in conflict with some observational inferences. The introduction of shallow cores in the dark halo attenuates this difficulty and produces haloes with slightly smaller rotation velocities. Other features of our galaxy models are not strongly influenced by the shallow core.
Structure formation
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The formation of galactic discs and the efficiency of star formation within them are issues central to our understanding of galaxy formation. We have developed a detailed and versatile model of disc formation which combines the strengths of previous studies of isolated discs with those of hierarchical galaxy formation models. Disc structure is inferred from the distribution of angular momentum in hot halo gas and the hierarchical build-up of dark matter, leading to theoretically generated systems where the evolution of surface density, rotation, velocity dispersion, stability and metallicity is predicted for annular regions of width 20-100 pc. The model will be used to establish whether the accepted theory of large-scale structure formation in the universe is consistent with observed trends in the properties of disc galaxies. This first paper explicitly examines the importance of embedding such calculations within a merging hierarchy of dark matter haloes, finding that this leads to dramatically different formation histories compared to models in which discs grow in isolation. Different models of star formation are explored, and are found to have only a secondary influence on the properties of the resulting galaxy discs, the main governing factor being the infalling gas supply from the hot halo.
Structure formation
Protogalaxy
Dark galaxy
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Strict criteria are applied to the sample of spiral galaxies with measured rotation curves in order to select those objects for which the observed rotation curve is an accurate tracer of the radial force law. The resulting sub-sample of 10 galaxies is then considered in view of two suggested explanations for the discrepancy between the luminous mass and the conventional dynamical mass of galaxies: dark haloes and the modified Newtonian dynamics (MOND). This is done by means of least-squares fits to the rotation curves. Three-parameter dark-halo models (M/L for the visible disc, the core radius and the asymptotic circular velocity of the halo) work well in reproducing the observed rotation curves, and it is found that, for the higher luminosity galaxies, the visible matter dominates the mass distribution within the optically bright disc. However, in the low-luminosity gas-rich dwarfs the dark component is everywhere dominant. MOND, with one free parameter, (M/L for the visible disc) generally works well in predicting the form of the rotation curves, in some cases better than multi-parameter dark-halo fits. If the distance to the galaxy is also taken as a free parameter, then the MOND fits are as good as three parameter dark-halo models and, with one exception, the implied distances are consistent with the adopted distances within the probable uncertainty in the distance estimates. Restricting the number of parameter in dark-halo models by making use of the disc-halo coupling does not produce satisfactory fits to the rotation curves. The overall conclusion is that MOND is currently the best phenomenological description of the systematics of the discrepancy in galaxies.
Modified Newtonian dynamics
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We show that the Tully-Fisher relation observed for spiral galaxies can be explained in the current scenario of galaxy formation without invoking subtle assumptions, provided that galactic-sized dark haloes have shallow, core-like central profiles, with a core radius proportional to halo circular velocity. In such a system, both disk and halo contribute significantly to the maximum rotation of the disk, and the interaction between the disk and halo components acts to reduce the scatter in the Tully-Fisher relation. With model parameters chosen in plausible ranges, the model can well accommodate the zero-point, slope, scatter of the observed Tully-Fisher relation, as well as the large range of disk sizes. The model predicts that LSB disks obey a Tully-Fisher relation similar to that of normal disks, if disk mass-to-light ratio is properly taken into account. The halo profile required by the Tully-Fisher relation is as shallow as that required by the rotation curves of faint disks, but much shallower than that predicted by conventional CDM models. Our results cannot be explained by some of the recent proposals for resolving the conflict between conventional CDM models and the rotation-curve shapes of faint galaxies. If dark matter self-interaction (either scattering or annihilation) is responsible for the shallow profile, the observed Tully-Fisher relation requires the interaction cross section \sigma_X to satisfy <\sigma_{X}|v|>/m_{X}~10^{-16} cm^3/s/GeV.
Tully–Fisher relation
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In this work, to investigate the dynamical nature of the kinematic asymmetry in the isolated gas-rich dwarf irregular galaxy W LM in the Local Group, we consider that the dark matter halo and the disk do not have the same center of mass (i.e., the disk lies off-center in the potential of the extended dark matter halo), which is one of the possible physical explanations for the kinematic lopsidedness. To do so, we generate a lopsided halo potential by considering two dark matter mass density models, ISO and Burkert, and we add up the contribution to the rotation curve of a perturbation term [Formula: see text] in the gravitational potential, which arises from the offset between the disk and the dark matter halo. We show that such an m = 1 perturbation improves the rotation curve modeling when compared to a non-perturbed potential and the shape of the HI gas rotation curves is fitted better in the approaching side if the perturbation term in the halo potential is taken into account for this galaxy dynamics. In fact, displacing the disk center by 0.1 kpc from the halo center is sufficient to provide such an improvement in modeling the rotation curve.
Gravitational potential
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We present the 21-cm rotation curve of the nearby galaxy M33 out to a galactocentric distance of 16 kpc (13 disc scalelengths). The rotation curve keeps rising out to the last measured point and implies a dark halo mass ≳5×1010 M⊙. The stellar and gaseous discs provide virtually equal contributions to the galaxy gravitational potential at large galactocentric radii, but no obvious correlation is found between the radial distribution of dark matter and the distribution of stars or gas. Results of the best fit to the mass distribution in M33 picture a dark halo which controls the gravitational potential from 3 kpc outward, with a matter density which decreases radially as R−1.3. The density profile is consistent with the theoretical predictions for structure formation in hierarchical clustering cold dark matter (CDM) models, and favours lower mass concentrations than those expected in the standard cosmogony.
Gravitational potential
Mass distribution
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I provide a model rotation curve for the Milky Way that matches the details of the terminal velocity curve normalized to the Galactocentric distance $R_0 = 8.122$ kpc obtained by the GRAVITY collaboration and the corresponding circular speed of the LSR $\Theta_0 = 233.3$ km/s. The model provides a numerical representation of the azimuthally averaged radial run of the gravitational potential of each mass component of the Galaxy (bulge-bar, stellar disk, gas disk, and dark matter) as represented by the rotation curve of each. It provides precise estimates of quantities like the stellar mass of the Galaxy ($6.16 \pm 0.31 \times 10^{10}\;\mathrm{M}_{\odot}$) and the local density of dark matter ($\rho_{DM}(R_0) = 6.76^{+0.08}_{-0.14} \times 10^{-3}\; \mathrm{M}_{\odot}\,\mathrm{pc}^{-3} = 0.257^{+0.003}_{-0.005}\; \mathrm{GeV}\,\mathrm{cm}^{-3}$). The dark matter density implied by the radial force is less than that found in many studies of the vertical force, perhaps indicating that the usual assumption of a spherical dark matter halo is no longer adequate.
Gravitational potential
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In this paper, the effect of halo substructures on galaxy rotation curves is investigated using a simple model of dark matter clustering. A dark matter halo density profile is developed based only on the scale-free nature of clustering that leads to a statistically self-similar distribution of the substructures at the galactic scale. A semi-analytical method is used to derive rotation curves for such a clumpy dark matter density profile. It is found that the halo substructures significantly affect the galaxy velocity field. Based on the fractal geometry of the halo, this self-consistent model predicts a Navarro–Frenk–White-like rotation curve and a scale-free power spectrum of the rotation velocity fluctuations.
Cuspy halo problem
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