We consider $f(R,T)$ modified theories of gravity, where the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar $R$ and of the trace of the stress-energy tensor $T$. We obtain the gravitational field equations in the metric formalism, as well as the equations of motion for test particles, which follow from the covariant divergence of the stress-energy tensor. Generally, the gravitational field equations depend on the nature of the matter source. The field equations of several particular models, corresponding to some explicit forms of the function $f(R,T)$, are also presented. An important case, which is analyzed in detail, is represented by scalar field models. We write down the action and briefly consider the cosmological implications of the $f(R,{T}^{\ensuremath{\phi}})$ models, where ${T}^{\ensuremath{\phi}}$ is the trace of the stress-energy tensor of a self-interacting scalar field. The equations of motion of the test particles are also obtained from a variational principle. The motion of massive test particles is nongeodesic, and takes place in the presence of an extra-force orthogonal to the four velocity. The Newtonian limit of the equation of motion is further analyzed. Finally, we provide a constraint on the magnitude of the extra acceleration by analyzing the perihelion precession of the planet Mercury in the framework of the present model.

$f(R,T)$ gravity

http://staff.ustc.edu.cn/~wzhao7/c_index_files/main.files/lss.pdf

Large scale structure of the universe and cosmological perturbation theory

We present Keck DEIMOS spectroscopy of stars in eight of the newly discovered ultra-faint dwarf galaxies around the Milky Way. We measure the velocity dispersions of Canes Venatici I, Canes Venatici II, Coma Berenices, Hercules, Leo IV, Leo T, Ursa Major I, and Ursa Major II from the velocities of 18-214 stars in each galaxy and find dispersions ranging from 3.3 to 7.6 km s^(-1). The six galaxies with absolute magnitudes M_V < -4 are highly dark matter dominated, with mass-to-light ratios approaching 1000 M_☉/L_(☉,V). For the fainter galaxies we find tentative evidence for tidal disruption. The measured velocity dispersions of the ultra-faint dwarfs are correlated with their luminosities, indicating that a minimum mass for luminous galactic systems may not yet have been reached. We also measure the metallicities of the observed stars and find that the new dwarfs have mean metallicities of [Fe/H] = -2.0 to -2.3; these galaxies represent some of the most metal-poor stellar systems known. The six brightest of the ultra-faint dwarfs extend the luminosity-metallicity relationship followed by more luminous dwarfs by a factor of ~30 in luminosity. We detect metallicity spreads of up to 0.5 dex in several objects, suggesting multiple star formation epochs. UMa II and Com, despite their exceptionally low luminosities, have higher metallicities that suggest they may once have been much more massive. Having established the masses of the ultra-faint dwarfs, we re-examine the missing satellite problem. After correcting for the sky coverage of the Sloan Digital Sky Survey, we find that the ultra-faint dwarfs substantially alleviate the discrepancy between the predicted and observed numbers of satellites around the Milky Way, but there are still a factor of ~4 too few dwarf galaxies over a significant range of masses. We show that if galaxy formation in low-mass dark matter halos is strongly suppressed after reionization, the simulated circular velocity function of CDM subhalos can be brought into approximate agreement with the observed circular velocity function of Milky Way satellite galaxies.

/pdf/the-kinematics-of-the-ultra-faint-milky-way-satellites-2nupjde7s9.pdf

The Kinematics of the Ultra-faint Milky Way Satellites: Solving the Missing Satellite Problem

The cooling of gas in the centers of dark matter halos is expected to lead to a more concentrated dark matter distribution. The response of dark matter to the condensation of baryons is usually calculated using the model of adiabatic contraction, which assumes spherical symmetry and circular orbits. In contrast, halos in the hierarchical structure formation scenarios grow via multiple violent mergers and accretion along filaments, and particle orbits in the halos are highly eccentric. We study the effects of the cooling of gas in the inner regions of halos using high-resolution cosmological simulations that include gas dynamics, radiative cooling, and star formation. We find that the dissipation of gas indeed increases the density of dark matter and steepens its radial profile in the inner regions of halos compared to the case without cooling. For the first time, we test the adiabatic contraction model in cosmological simulations and find that the standard model systematically overpredicts the increase of dark matter density in the inner 5% of the virial radius. We show that the model can be improved by a simple modification of the assumed invariant from M(r)r to M()r, where r and are the current and orbit-averaged particle positions. This modification approximately accounts for orbital eccentricities of particles and reproduces simulation profiles to within 10%-20%. We present analytical fitting functions that accurately describe the transformation of the dark matter profile in the modified model and can be used for interpretation of observations.

http://iopscience.iop.org/article/10.1086/424914/pdf

Response of Dark Matter Halos to Condensation of Baryons: Cosmological Simulations and Improved Adiabatic Contraction Model

▪ Abstract Modified Newtonian dynamics (MOND) is an empirically motivated modification of Newtonian gravity or inertia suggested by Milgrom as an alternative to cosmic dark matter. The basic idea is that at accelerations below ao ≈ 10−8 cm/s2 ≈ cHo/6 the effective gravitational attraction approaches , where gn is the usual Newtonian acceleration. This simple algorithm yields flat rotation curves for spiral galaxies and a mass-rotation velocity relation of the form M ∝ V4 that forms the basis for the observed luminosity–rotation velocity relation—the Tully-Fisher law. We review the phenomenological success of MOND on scales ranging from dwarf spheroidal galaxies to superclusters and demonstrate that the evidence for dark matter can be equally well interpreted as evidence for MOND. We discuss the possible physical basis for an acceleration-based modification of Newtonian dynamics as well as the extention of MOND to cosmology and structure formation.

/pdf/modified-newtonian-dynamics-as-an-alternative-to-dark-matter-4dgh2n87xt.pdf

Modified Newtonian dynamics as an alternative to dark matter

Using the standard dynamical theory of spherical systems, we calculate the properties of spherical galaxies and clusters whose density profiles obey the universal form first obtained in high resolution cosmological N-body simulations by Navarro, Frenk & White. We adopt three models for the internal kinematics: isotropic velocities, constant anisotropy and increasingly radial Osipkov-Merritt anisotropy. Analytical solutions are found for the radial dependence of the mass, gravitational potential, velocity dispersion, energy and virial ratio and we test their variability with the concentration parameter describing the density profile and amount of velocity anisotropy. We also compute structural parameters, such as half-mass radius, effective radius and various measures of concentration. Finally, we derive projected quantities, the surface mass density and line-of-sight as well as aperture velocity dispersion, all of which can be directly applied in observational tests of current scenarios of structure formation. On the mass scales of galaxies, if constant mass-to-light is assumed, the NFW surface density profile is found to fit well Hubble-Reynolds laws. It is also well fitted by Sersic R^(1/m) laws, for m ~ 3, but in a much narrower range of m and with much larger effective radii than are observed. Assuming in turn reasonable values of the effective radius, the mass density profiles imply a mass-to-light ratio that increases outwards at all radii.

Properties of spherical galaxies and clusters with an NFW density profile

We study velocity moments of elliptical galaxies in the Coma cluster using Jeans equations. The dark matter distribution in the cluster is modelled by a generalised formula based upon the results of cosmological N-body simulations. Its inner slope (cuspy or flat), concentration, and mass within the virial radius are kept as free parameters, as well as the velocity anisotropy, assumed independent of position. We show that the study of line-of-sight velocity dispersion alone does not allow to constrain the parameters. By a joint analysis of the observed profiles of velocity dispersion and kurtosis we are able to break the degeneracy between the mass distribution and velocity anisotropy. We determine the dark matter distribution at radial distances larger than 3% of the virial radius and we find that the galaxy orbits are close to isotropic. Due to limited resolution, different inner slopes are found to be consistent with the data and we observe a strong degeneracy between the inner slope $\alpha$ and concentration $c$: the best-fitting profiles have the two parameters related with $c=19 - 9.6 \alpha$. Our best-fitting NFW profile has concentration $c=9$, which is 50% higher than standard values found in cosmological simulations for objects of similar mass. The total mass within the virial radius of $2.9 h_{70}^{-1}$ Mpc is $1.4 \times 10^{15} h_{70}^{-1} M_{\sun}$ (with 30% accuracy), 85% of which is dark. At this distance from the cluster centre, the mass-to-light ratio in the blue band is $351 h_{70}$ solar units. The total mass within the virial radius leads to estimates of the density parameter of the Universe, assuming that clusters trace the mass-to-light ratio and baryonic fraction of the Universe, with $\Omega_0=0.29 \pm 0.1$.

Dark matter distribution in the Coma cluster from galaxy kinematics: breaking the mass-anisotropy degeneracy

Elliptical galaxies are modelled with a a 4-component model: Sersic stars, LCDM dark matter (DM), hot gas and central black hole. DM is negligible in the inner regions, which are dominated by stars and the central black hole. This prevents any kinematical estimate (using a Jeans analysis) of the inner slope of the DM density profile. The gas fraction rises, but the baryon fraction decreases with radius, at least out to 10 effective radii (R_e). Even with line-of-sight velocity dispersion (VD) measurements at 4 to 6 R_e with 20 km/s accuracy and perfectly known velocity anisotropy, the total mass within the virial radius (r_v) is uncertain by a factor over 3. The DM distributions found in LCDM simulations are consistent with the stellar VD profiles, but appear inconsistent with the low VDs measured by Romanowsky et al. (2003) of planetary nebulae between 2 and 5 R_e, which imply such low M/Ls that the baryon fraction within r_v must be greater than the universal value. Replacing the NFW DM model by the new model of Navarro et al. (2004) decreases slightly the VD at a given radius. So, given the observed VD measured at 5 R_e, the inferred M/L within r_v is 40% larger than predicted with the NFW model. Folding in the slight (strong) radial anisotropy found in LCDM (merger) simulations, which is well modelled (much better than with the Osipkov-Merritt formula) with beta(r) = 1/2 r/(r+a), the inferred M/L within r_v is another 1.6 (2.4) times higher than for the isotropic NFW model. Thus, the DM model and radial anisotropy can partly explain the low PN VDs, but not in full. In an appendix, single integral expressions are derived for the VDs in terms of the tracer density and total mass profiles, for 3 anisotropic models: radial, Osipkov-Merritt, and the model above, for general radial profiles of luminosity density and mass.

https://arxiv.org/pdf/astro-ph/0405491.pdf

Dark matter in elliptical galaxies: II. Estimating the mass within the virial radius

Using high resolution N-body simulations we address the problem of emptiness of giant 20 Mpc/h diameter voids found in the distribution of bright galaxies. Are the voids filled by dwarf galaxies? Do cosmological models predict too many small dark matter haloes inside the voids? Can the problems of cosmological models on small scales be addressed by studying the abundance of dwarf galaxies inside voids? We find that voids in the distribution of 10^12 Msun/h haloes (expected galactic magnitudes ~ M_*) are almost the same as the voids in 10^11 Msun/h haloes. Yet, much smaller haloes with masses 10^9 Msun/h and circular velocities v_circ about 20 km/s readily fill the voids: there should be almost 1000 of these haloes in a 20 Mpc/h void. A typical void of diameter 20 Mpc/h contains about 50 haloes with v_circ > 50 km/s. The haloes are arranged in a pattern, which looks like a miniature Universe: it has the same structural elements as the large-scale structure of the galactic distribution of the Universe. There are filaments and voids; larger haloes are at the intersections of filaments. The only difference is that all masses are four orders of magnitude smaller. There is severe (anti)bias in the distribution of haloes, which depends on halo mass and on the distance from the centre of the void. Large haloes are more antibiased and have a tendency to form close to void boundaries. The mass function of haloes in voids is different from the ``normal'' mass function. It is much steeper for high masses resulting in very few M33-type galaxies (v_circ about 100 km/s). We present an analytical approximation for the mass function of haloes in voids.

The structure of voids

(Abridged) The tidal stirring model posits the formation of dSph galaxies via the tidal interactions between rotationally-supported dwarfs and MW-sized host galaxies. Using a set of collisionless N-body simulations, we investigate the efficiency of the tidal stirring mechanism. We explore a wide variety of dwarf orbital configurations and initial structures and demonstrate that in most cases the disky dwarfs experience significant mass loss and their stellar components undergo a dramatic morphological and dynamical transformation: from disks to bars and finally to pressure-supported spheroidal systems with kinematic and structural properties akin to those of the classic dSphs in the Local Group (LG). Our results suggest that such tidal transformations should be common occurrences within the currently favored cosmological paradigm and highlight the key factor responsible for an effective metamorphosis to be the strength of the tidal shocks at the pericenters of the orbit. We demonstrate that the combination of short orbital times and small pericenters, characteristic of dwarfs being accreted at high redshift, induces the strongest transformations. Our models also indicate that the transformation efficiency is affected significantly by the structure of the progenitor disky dwarfs. Lastly, we find that the dwarf remnants satisfy the relation Vmax = \sqrt{3} * sigma, where sigma is the 1D, central stellar velocity dispersion and Vmax is the maximum halo circular velocity, with intriguing implications for the missing satellites problem. Overall, we conclude that the action of tidal forces from the hosts constitutes a crucial evolutionary mechanism for shaping the nature of dwarf galaxies in environments such as that of the LG. Environmental processes of this type should thus be included as ingredients in models of dwarf galaxy formation and evolution.

/pdf/on-the-efficiency-of-the-tidal-stirring-mechanism-for-the-2aeb1grugk.pdf

On the Efficiency of the Tidal Stirring Mechanism for the Origin of Dwarf Spheroidals: Dependence on the Orbital and Structural Parameters of the Progenitor Disky Dwarfs

Ewa L. Lokas

Papers

Properties of spherical galaxies and clusters with an NFW density profile

Dark matter distribution in the Coma cluster from galaxy kinematics: breaking the mass-anisotropy degeneracy

Dark matter in elliptical galaxies: II. Estimating the mass within the virial radius

The structure of voids

On the Efficiency of the Tidal Stirring Mechanism for the Origin of Dwarf Spheroidals: Dependence on the Orbital and Structural Parameters of the Progenitor Disky Dwarfs