# Posts Tagged rotation curves

## Recent Postings from rotation curves

### Existence of wormholes with a barotropic equation of state

This paper examines the effect of the linear barotropic equation of state $p=\omega\rho$ on the existence or theoretical construction of traversable wormholes. If either the energy density or the closely related shape function is known, then the resulting redshift function $\Phi$ will almost always lead to an event horizon. Specifying the redshift function avoids this problem but only by relinquishing some of the control over the physics. Moving to a cosmological setting, we assume that $\Phi$ is such that $e^{2\Phi}=[(r+a)/b_0]^l$, $a\ge 0$, based on the existence of galactic rotation curves. Here the wormhole structure can only be maintained if $\omega<-1$. This condition is independent of $l$. The scope of this model can therefore be extended to zero and negative $l$ by taking $l$ to be a convenient parameter that is not necessarily related to the tangential velocity. The main reason is that if $a=0$, then the two special cases $l=0$ and $l<0$ correspond to the only exactly solvable models for wormholes supported by phantom energy, while simultaneously avoiding an event horizon, thereby providing an additional motivation for the form of the redshift function. A final topic is a possible unification of these cases by means of teleparallel gravity.

### The Luminous Convolution Model as an alternative to dark matter in spiral galaxies

The Luminous Convolution Model (LCM) demonstrates that it is possible to predict the rotation curves of spiral galaxies directly from estimates of the luminous matter. We consider two frame-dependent effects on the light observed from other galaxies: relative velocity and relative curvature. With one free parameter, we predict the rotation curves of twenty-three (23) galaxies represented in forty-two (42) data sets. Relative curvature effects rely upon knowledge of both the gravitational potential from luminous mass of the emitting galaxy and the receiving galaxy, and so each emitter galaxy is compared to four (4) different Milky Way luminous mass models. On average in this sample, the LCM is more successful than either dark matter or modified gravity models in fitting the observed rotation curve data. Implications of LCM constraints on populations synthesis modeling are discussed in this paper. This paper substantially expands the results in arXiv:1309.7370.

### Scalar Field Dark Matter mass model and evolution of rotation curves for Lsb galaxies

We study the evolution of gas rotation curves within the scalar field dark matter (SFDM) model. In this model the galactic haloes are astronomical Bose-Einstein Condensate drops of scalar field. These haloes are characterized by a constant-density core and are consistent with observed rotation curves of dark matter dominated galaxies, a missing feature in CDM haloes resulting from DM-only simulations. We add the baryonic component to the SFDM haloes and simulate the evolution of the dark matter tracer in a set of grid-based hydrodynamic simulations aimed to analyse the evolution of the rotation curves and the gas density distribution in the case of dark matter dominated galaxies. Previous works had found that when considering an exact analytic solution for a static SF configuration, the free parameters of the model allows for good fits to the rotation curves, we confirm that in our simulations but now taking into account the evolution of the baryonic component in a static dark matter and stellar disk potential. Including live gas is a step forward from the previous work using SFDM, as for example, the rotation velocity of the gas is not always exactly equal to the circular velocity of a test particle on a circular orbit. Contrasting with the data the cored mass model presented here is preferred instead of a cuspy one.

### Astrophysical Tests of Modified Gravity: Stellar and Gaseous Rotation Curves in Dwarf Galaxies

Chameleon theories of gravity predict that the gaseous component of isolated dwarf galaxies rotates with a faster velocity than the stellar component. In this paper, we exploit this effect to obtain new constraints on the model parameters using the measured rotation curves of six low surface brightness galaxies. For $f(R)$ theories, we rule out values of $f_{R0}>10^{-6}$. For more general theories, we find that the constraints from Cepheid variable stars are currently more competitive than the bounds we obtain here but we are able to rule out self-screening parameters $\chi_c>10^{-6}$ for fifth-force strengths (coupling of the scalar to matter) as low as $0.05$ the Newtonian force. This region of parameter space has hitherto been inaccessible to astrophysical probes. We discuss the future prospects for improving these bounds.

### Generalized curvature-matter couplings in modified gravity [Replacement]

In this work, we review a plethora of modified theories of gravity with generalized curvature-matter couplings. The explicit nonminimal couplings, for instance, between an arbitrary function of the scalar curvature $R$ and the Lagrangian density of matter, induces a non-vanishing covariant derivative of the energy-momentum tensor, implying non-geodesic motion and consequently leads to the appearance of an extra force. Applied to the cosmological context, these curvature-matter couplings lead to interesting phenomenology, where one can obtain a unified description of the cosmological epochs. We also consider the possibility that the behavior of the galactic flat rotation curves can be explained in the framework of the curvature-matter coupling models, where the extra-terms in the gravitational field equations modify the equations of motion of test particles, and induce a supplementary gravitational interaction. In addition to this, these models are extremely useful for describing dark energy-dark matter interactions, and for explaining the late-time cosmic acceleration.

### Generalized curvature-matter couplings in modified gravity [Replacement]

In this work, we review a plethora of modified theories of gravity with generalized curvature-matter couplings. The explicit nonminimal couplings, for instance, between an arbitrary function of the scalar curvature $R$ and the Lagrangian density of matter, induces a non-vanishing covariant derivative of the energy-momentum tensor, implying non-geodesic motion and consequently leads to the appearance of an extra force. Applied to the cosmological context, these curvature-matter couplings lead to interesting phenomenology, where one can obtain a unified description of the cosmological epochs. We also consider the possibility that the behavior of the galactic flat rotation curves can be explained in the framework of the curvature-matter coupling models, where the extra-terms in the gravitational field equations modify the equations of motion of test particles, and induce a supplementary gravitational interaction. In addition to this, these models are extremely useful for describing dark energy-dark matter interactions, and for explaining the late-time cosmic acceleration.

### Generalized curvature-matter couplings in modified gravity [Cross-Listing]

In this work, we review a plethora of modified theories of gravity with generalized curvature-matter couplings. The explicit nonminimal couplings, for instance, between an arbitrary function of the scalar curvature $R$ and the Lagrangian density of matter, induces a non-vanishing covariant derivative of the energy-momentum tensor, implying non-geodesic motion and consequently leads to the appearance of an extra force. Applied to the cosmological context, these curvature-matter couplings lead to interesting phenomenology, where one can obtain a unified description of the cosmological epochs. We also consider the possibility that the behavior of the galactic flat rotation curves can be explained in the framework of the curvature-matter coupling models, where the extra-terms in the gravitational field equations modify the equations of motion of test particles, and induce a supplementary gravitational interaction. In addition to this, these models are extremely useful for describing dark energy-dark matter interactions, and for explaining the late-time cosmic acceleration.

### Generalized curvature-matter couplings in modified gravity [Cross-Listing]

In this work, we review a plethora of modified theories of gravity with generalized curvature-matter couplings. The explicit nonminimal couplings, for instance, between an arbitrary function of the scalar curvature $R$ and the Lagrangian density of matter, induces a non-vanishing covariant derivative of the energy-momentum tensor, implying non-geodesic motion and consequently leads to the appearance of an extra force. Applied to the cosmological context, these curvature-matter couplings lead to interesting phenomenology, where one can obtain a unified description of the cosmological epochs. We also consider the possibility that the behavior of the galactic flat rotation curves can be explained in the framework of the curvature-matter coupling models, where the extra-terms in the gravitational field equations modify the equations of motion of test particles, and induce a supplementary gravitational interaction. In addition to this, these models are extremely useful for describing dark energy-dark matter interactions, and for explaining the late-time cosmic acceleration.

### Galactic space-times in modified theories of gravity [Cross-Listing]

We study Bertrand space-times (BSTs), which have been proposed as viable models of space-times seeded by galactic dark matter, in modified theories of gravity. We first critically examine the issue of galactic rotation curves in General Relativity, and establish the usefulness of BSTs to fit experimental data in this context. We then study BSTs in metric $f(R)$ gravity and in Brans-Dicke theories. For the former, the nature of the Newtonian potential is established, and we also compute the effective equation of state and show that it can provide good fits to some recent experimental results. For the latter, we calculate the Brans-Dicke scalar analytically in some limits and numerically in general, and find interesting constraints on the parameters of the theory. Our results provide evidence for the physical nature of Bertrand space-times in modified theories of gravity.

### Galactic space-times in modified theories of gravity [Cross-Listing]

We study Bertrand space-times (BSTs), which have been proposed as viable models of space-times seeded by galactic dark matter, in modified theories of gravity. We first critically examine the issue of galactic rotation curves in General Relativity, and establish the usefulness of BSTs to fit experimental data in this context. We then study BSTs in metric $f(R)$ gravity and in Brans-Dicke theories. For the former, the nature of the Newtonian potential is established, and we also compute the effective equation of state and show that it can provide good fits to some recent experimental results. For the latter, we calculate the Brans-Dicke scalar analytically in some limits and numerically in general, and find interesting constraints on the parameters of the theory. Our results provide evidence for the physical nature of Bertrand space-times in modified theories of gravity.

### On the rotation curves for axially symmetric disk solutions of the Vlasov-Poisson system

A large class of flat axially symmetric solutions to the Vlasov-Poisson system is constructed with the property that the corresponding rotation curves are approximately flat, slightly decreasing or slightly increasing. The rotation curves are compared with measurements from real galaxies and satisfactory agreement is obtained. These facts raise the question whether the observed rotation curves for disk galaxies may be explained without introducing dark matter. Furthermore, it is shown that for the ansatz we consider stars on circular orbits do not exist in the neighborhood of the boundary of the steady state.

### VADER: A Flexible, Robust, Open-Source Code for Simulating Viscous Thin Accretion Disks

The evolution of thin axisymmetric viscous accretion disks is a classic problem in astrophysics. While such models provide only approximations to the true processes of instability-driven mass and angular momentum transport, their simplicity makes them invaluable tools for both semi-analytic modeling and simulations of long-term evolution where two- or three-dimensional calculations are too computationally costly. Despite the utility of these models, there is no publicly-available framework for simulating them. Here we describe a highly flexible, general numerical method for simulating viscous thin disks with arbitrary rotation curves, viscosities, boundary conditions, grid spacings, equations of state, and rates of gain or loss of mass (e.g., through winds) and energy (e.g., through radiation). Our method is based on a conservative, finite-volume, second-order accurate discretization of the equations, which we solve using an unconditionally-stable implicit scheme. We implement Anderson acceleration to speed convergence of the scheme, and show that this leads to factor of ~5 speed gains over non-accelerated methods in realistic problems. We have implemented our method in the new code Viscous Accretion Disk Evolution Resource (VADER), which is freely available for download from https://bitbucket.org/krumholz/vader/ under the terms of the GNU General Public License.

### Spiral Galaxies - classical description of spiral arms and rotational velocity pattern - toy model

We propose an explanation of features of spiral galaxies: spiral arms and observed flat rotation curves, without the presence of an exotic form of matter. The formalism is based on Boltzmanns transport equation for the collisional matter and the very-low-velocity post-Newtonian approximation of the general relativity equations expressed in the Maxwell-like form. The Maxwell-like formulation provides the base for the explanation of the above phenomena in the language of dynamically created gravitoelectromagnetic fields by the movement of mass streams in the plane of the galaxy disc. In the model we use radical simplifications expressed as neglect of the gravitational interaction between neighbors and approximation of the incompressible mass flow. In this frame we show that if the galaxy is fuelled constantly by mass from an external gas reservoir, then the amplification of the gravitomagnetic field can be large enough to create the rotational velocity pattern and spiral arms without the necessity of introducing exotic matter or any other new phenomena. In this framework the collisional part of the mass gas in the galaxy disc plane, i.e. molecules and atoms, is responsible for the creation of the gravitomagnetic field. According to the model the spiral pattern of arms is static and determines the mass flow, identified by the galaxy spiral structure, which moves towards the galaxy center from the peripheries of the galaxy disc. The model reproduces qualitatively the observed spiral arms and reproduces well the shape of the rotational velocity pattern. Prediction for the radial velocity is below 10 $km\mbox{ }s^{-1}$, in agreement with observations. As an example of the usability of the proposed mechanism, we reproduce qualitatively the above features for the IC 342 and NGC 4321 galaxies.

### Extremely Flat Haloes and the Shape of the Galaxy

We present a set of highly flattened galaxy models with asymptotically constant rotation curves. The mass density in the equatorial plane falls like (distance)$^{-1}$ at large radii. Although the inner equidensity contours may be spherical, oblate or prolate, the outer parts are always severely flattened. The elongated shape is supported by rotation or tangential velocity anisotropy. The models are thickened Mestel discs, and form a previously undiscovered part of the Miyamoto & Nagai sequence of flattened galaxies. The properties of the models — axis ratios, velocity dispersions, streaming velocities and distribution functions — are all discussed in some detail. We pose the question: are extremely flattened or disk-like haloes possible for the Milky Way galaxy? This has never been examined before, as very flattened halo models were not available. We fit the rotation curve and the vertical kinematics of disc stars in the solar neighbourhood to constrain the overall shape of the Galaxy. Denoting the ratio of polar axis to major axis by $q$, we show that models with $q\lesssim 0.57$ cannot simultaneously reproduce the in-plane and out-of-plane constraints. The kinematics of the Sagittarius galaxy also strongly disfavour models with high flattening, as the orbital plane precession is too great and the height reached above the Galactic plane is too small. At least for our Galaxy, the dark halo cannot be flatter than E4 (or axis ratio $q \sim 0.57$) at the Solar circle. Models in which the dark matter is accounted for by a massive baryonic disc or by decaying neutrinos are therefore ruled out by constraints from the rotation curve and the vertical kinematics.

### Newtonian explanation of galaxy rotation curves based on distribution of baryonic matter

Circular velocities of stars and gas in galaxies generally do not decline in accordance with widely expected Keplerian fall-off in velocities further from the galactic nucleus. Two main groups of theories were proposed to explain the supposed discrepancy–first, the most commonly accepted, is the suggestion of the existence of large non-baryonic dark matter halo, and, second are theories advocating some modification to the law of gravity. So far however, there is no empirical evidence for either dark matter or modified gravity. Here we show that a broad range of galaxy rotation curves can be explained solely in accordance with Newton’s law of gravity by modeling the distribution of baryonic matter in a galaxy. We demonstrate that the expectation of Keplerian fall-off is incorrect, and that a large number of likely galaxy mass distribution profiles should in fact produce flat or accelerating rotation curves similar to those observed in reality. We further support our theoretical findings with the model fit of 47 rotation curves of real galaxies, representing a broad range of galactic types and sizes, and achieving correlation of expected and observed velocities of over 0.995 for all cases. Our results make theories of exotic dark matter or modified gravity unnecessary for the explanation of galaxy rotation curves.

### Constraints on Bose-Einstein-condensed Axion Dark Matter from The HI Nearby Galaxy Survey data [Replacement]

One of the leading candidates for dark matter is axion or axion-like particle in a form of Bose-Einstein condensate (BEC). In this paper, we present an analysis of 17 high-resolution galactic rotation curves from "The H{\footnotesize I} Nearby Galaxy Survey (THINGS)" data [F. Walter et al., Astron. J. 136, 2563 (2008)] in the context of the axionic Bose-Einstein condensed dark matter model. Assuming a repulsive two-body interaction, we solve the non-relativistic Gross-Pitaevskii equation for $N$ gravitationally trapped bosons in the Thomas-Fermi approximation. We obtain the maximum possible radius $R$ and the mass profile $M(r)$ of a dilute axionic Bose-Einstein condensed gas cloud. A standard least-$\chi^2$ method is employed to find the best-fit values of the total mass $M$ of the axion BEC and its radius $R$. The local mass density of BEC axion dark-matter is $\rho_{a}\simeq 0.02~{\rm GeV/cm}^3$, which agrees with that presented by Beck [C. Beck, Phys. Rev. Lett. 111, 231801 (2013)]. The axion mass $m_a$ we obtain depends not only on the best-fit value of $R$ but also on the $s$-wave scattering length $a$ ($m_a \propto a^{1/3}$). The transition temperature $T_a$ of axion BEC on galactic scales is also estimated. Comparing the calculated $T_a$ with the ambient temperature of galaxies and galaxy clusters implies that $a\sim 10^{-3}$ fm. The corresponding axion mass is $m_a\simeq 0.58$ meV. We compare our results with others.

### Constraints on Bose-Einstein-condensed Axion Dark Matter from The HI Nearby Galaxy Survey data

One of the leading candidates for dark matter is axion or axion-like particle in a form of Bose-Einstein condensate (BEC). In this paper, we present an analysis of 17 high-resolution galactic rotation curves from "The H{\footnotesize I} Nearby Galaxy Survey (THINGS)" data [F. Walter et al., Astron. J. 136, 2563 (2008)] in the context of the axionic Bose-Einstein condensed dark matter model. Assuming a repulsive two-body interaction, we solve the non-relativistic Gross-Pitaevskii equation for $N$ gravitationally trapped bosons in the Thomas-Fermi approximation. We obtain the maximum possible radius $R$ and the mass profile $M(r)$ of a dilute axionic Bose-Einstein condensed gas cloud. A standard least-$\chi^2$ method is employed to find the best-fit values of the total mass $M$ of the axion BEC and its radius $R$. The local mass density of BEC axion dark-matter is $\rho_{a}\simeq 0.02~{\rm GeV/cm}^3$, which agrees with that presented by Beck [C. Beck, Phys. Rev. Lett. 111, 231801 (2013)]. The axion mass $m_a$ we obtain depends not only on the best-fit value of $R$ but also on the $s$-wave scattering length $a$ ($m_a \propto a^{1/3}$). The transition temperature $T_a$ of axion BEC on galactic scales is also estimated. Comparing the calculated $T_a$ with the ambient temperature of galaxies and galaxy clusters implies that $a\sim 10^{-3}$ fm. The corresponding axion mass is $m_a\simeq 0.58$ meV. We compare our results with others.

### The H$\alpha$ kinematics of interacting galaxies in 12 compact groups

We present new Fabry-Perot observations for a sample of 42 galaxies located in twelve compact groups of galaxies: HCG 1, HCG 14, HCG 25, HCG 44, HCG 53, HCG 57, HCG 61, HCG 69, HCG 93, VV 304, LGG 455 and Arp 314. From the 42 observed galaxies, a total of 26 objects are spiral galaxies, which range from Sa to Im morphological types. The remaining 16 objects are E, S0 and S0a galaxies. Using these observations, we have derived velocity maps, monochromatic and velocity dispersion maps for 24 galaxies, where 18 are spiral, three are S0a, two are S0 and one is an Im galaxy. From the 24 velocity fields obtained, we could derive rotation curves for 15 galaxies; only two of them exhibit rotation curves without any clear signature of interactions. Based on kinematic information, we have evaluated the evolutionary stage of the different groups of the current sample. We identify groups that range from having no H$\alpha$ emission to displaying an extremely complex kinematics, where their members display strongly perturbed velocity fields and rotation curves. In the case of galaxies with no H$\alpha$ emission, we suggest that past galaxy interactions removed their gaseous components, thereby quenching their star formation. However, we can not discard that the lack of H$\alpha$ emission is linked with the detection limit for some of our observations.

### Bose-Einstein Condensate Dark Matter Halos confronted with galactic observations

We present a comparative confrontation of both the Bose-Einstein Condensate (BEC) and the Navarro-Frenk-White (NFW) dark halo models with galactic rotation curves and velocity dispersion data. We conclude that the BEC model fits better the dwarf galaxy dark matter distribution, but suffers from sharp cut-off in larger galaxies, where the NFW model performs better. In more detail, we employ 6 High Surface Brightness (HSB), 6 Low Surface Brightness (LSB) and 7 dwarf galaxies with rotation curves falling into two classes, based on their shapes. In the first class the rotational velocities increase with radius over the whole observed range, the BEC and NFW models giving comparable fits for both HSB and LSB galaxies, while significantly improving over the NFW fit for dwarf galaxies. This improvement is due to the central density cusp avoidance property of the BEC model. The rotational velocity of HSB and LSB galaxies falling into the second class exhibit long flat plateaus, resulting in a better fit of the NFW model for HSB galaxies, and comparable fits for LSB galaxies. The weaker performance of the BEC model for the HSB type II galaxies is due to the BEC density profiles dropping rapidly to zero outside a nearly constant density core. Finally we confront both models with the projected velocity dispersion profiles of 6 Virgo cluster galaxies, which after a steep rising, remain flat over the sampled region. The two models gave comparable combined $\tilde{\chi}_{\min}^{2}$ values for these galaxies but both model fits remained outside the 3$\sigma$ confidence level, pointing out the need for a better modelling of the velocity dispersion of galaxies that both the BEC and NFW models could provide.

### $R^n$ gravity is kicking and alive: the cases of Orion and NGC 3198

We analyzed the Rotation Curves of two crucial objects, the Dwarf galaxy Orion and the low luminosity Spiral NGC 3198, in the framework of $R^n$ gravity. We surprisingly found that the no DM power-law f(R) case fits them well, performing much better than $\Lambda$CDM Dark Matter halo models. The level of this unexpected success can be a boost for $R^n$ gravity.

### Phantom of RAMSES (POR): A new Milgromian dynamics N-body code

Since its first formulation in 1983, Milgromian dynamics (MOND) has been very successful in predicting the gravitational potential of galaxies from the distribution of baryons alone, including general scaling relations and detailed rotation curves of large statistical samples of individual galaxies covering a large range of masses and sizes. Most predictions however rely on static models, and only a handful of N-body codes have been developed over the years to investigate the consequences of the Milgromian framework for the dynamics of complex evolving dynamical systems. In this work, we present a new Milgromian N-body code, which is a customized version of the RAMSES code (Teyssier 2002) and thus comes with all its features: it includes particles and gas dynamics, and importantly allows for high spatial resolution of complex systems due to the adaptive mesh refinement (AMR) technique. It further allows the direct comparison between Milgromian simulations and standard Newtonian simulations with dark matter particles. We provide basic tests of this customized code and demonstrate its performance by presenting N-body computations of dark-matter-free spherical equilibrium models as well as dark-matter-free disk galaxies in Milgromian dynamics.

### Dark Matter In Disk Galaxies II: Density Profiles as Constraints on Feedback Scenarios

The disparity between the density profiles of galactic dark matter haloes predicted by dark matter only cosmological simulations and those inferred from rotation curve decomposition, the so-called cusp-core problem, suggests that baryonic physics has an impact on dark matter density in the central regions of galaxies. Feedback from black holes, supernovae and massive stars may each play a role by removing matter from the centre of the galaxy on shorter timescales than the dynamical time of the dark matter halo. Our goal in this paper is to determine constraints on such feedback scenarios based on the observed properties of a set of nearby galaxies. Using a Markov Chain Monte Carlo (MCMC) analysis of galactic rotation curves, via a method developed in a previous paper, we constrain density profiles and an estimated minimum radius for baryon influence, $r_1$, which we couple with a feedback model to give an estimate of the fraction of matter within that radius that must be expelled to produce the presently observed halo profile. We show that in the case of the gas rich dwarf irregular galaxy DDO 154, an outflow from a central source (e.g. a black hole or star forming region) could produce sufficient feedback on the halo without removing the disk gas. We examine the rotation curves of 8 galaxies taken from the THINGS data set and determine constraints on the radial density profiles of their dark matter haloes. For some of the galaxies, both cored haloes and cosmological $\rho \propto r^{-1}$ cusps are excluded. These intermediate central slopes require baryonic feedback to be finely tuned. We also find for galaxies which exhibit extended cores in their haloes (e.g. NGC 925), the use of a split power-law halo profile yields models without the unphysical, sharp features seen in models based on the Einasto profile.

### An f(R) model for dark matter: rotation curves and gravitational lensing

There should be two ways to describe the flat rotation curves of galaxies and cluster of galaxies. Either one can introduce a dark matter component for the matter filling the halo, or by modifying the gravity theory and give the flat rotation curve a geometrical nature. Here we adopt an f(R) model suitable for describing the effect. After matching the solution with the exterior solution, the effective density, radial and tangential pressures are obtained. Then the energy conditions and lensing effect is investigated.

### Strong lensing as a test for Conformal Weyl Gravity

Conformal Weyl Gravity (CWG) predicts galactic rotation curves without invoking dark matter. This makes CWG an interesting candidate theory as an alternative to GR. This removal of the necessity of dark matter arises because the exact exterior solution in CWG for a static, spherically symmetric source provides a linear potential $\gamma r$, which can explain the observed galactic rotation curves with a value for $\gamma$ given by $\sim + 10^{-26} \mathrm{m}^{-1}$. Previous work has also shown that CWG can explain lensing observations, but with $\gamma\sim – 10^{-26} \mathrm{m}^{-1}$ in order to ensure converging rays of light rather than diverging ones. Even though different expressions for the angle of deflection have been derived in CWG in order to remove this inconsistency, this paper shows that the $\gamma$ required to fit the lensing data is several orders of magnitude higher than that required to fit the galactic rotation curves.

### Phenomenology of MOND and gravitational polarization [Cross-Listing]

The phenomenology of MOND (flat rotation curves of galaxies, baryonic Tully-Fisher relation, etc.) is a basic set of phenomena relevant to galaxy dynamics and dark matter distribution at galaxy scales. Still unexplained today, it enjoys a remarkable property, known as the dielectric analogy, which could have far-reaching implications. In the present paper we discuss this analogy in the framework of simple non-relativistic models. We show how a specific form of dark matter, made of two different species of particles coupled to different Newtonian gravitational potentials, could permit to interpret in the most natural way the dielectric analogy of MOND by a mechanism of gravitational polarization.

### Phenomenology of MOND and gravitational polarization

The phenomenology of MOND (flat rotation curves of galaxies, baryonic Tully-Fisher relation, etc.) is a basic set of phenomena relevant to galaxy dynamics and dark matter distribution at galaxy scales. Still unexplained today, it enjoys a remarkable property, known as the dielectric analogy, which could have far-reaching implications. In the present paper we discuss this analogy in the framework of simple non-relativistic models. We show how a specific form of dark matter, made of two different species of particles coupled to different Newtonian gravitational potentials, could permit to interpret in the most natural way the dielectric analogy of MOND by a mechanism of gravitational polarization.

### A new approach to understanding dark matter

We consider a modification of General Relativity motivated by the treatment of anisotropies in Continuum Mechanics. The Newtonian limit of the theory is formulated and applied to galactic rotation curves. By assuming that the additional structure of spacetime behaves like a Newtonian gravitational potential for small deviations from isotropy, we are able to recover the Nevarro-Frenk-White profile of dark matter halos by a suitable identification of constants.

### Galaxy luminosity function and Tully-Fisher relation: reconciled through rotation-curve studies

The relation between galaxy luminosity L and halo virial velocity v_vir required to fit the galaxy luminosity function differs from the observed Tully-Fisher relation between L and disc speed v_rot. Hence the problem of reproducing the galaxy luminosity function and the Tully-Fisher relation simultaneously has plagued semianalytic models since their inception. Here we study the relation between v_rot and v_vir by fitting observational average rotation curves of disc galaxies binned in luminosity. We show that the v_rot – v_vir relation that we obtain in this way can fully account for this seeming inconsistency. Therefore, the reconciliation of the luminosity function with the Tully-Fisher relation rests on the complex dependence of v_rot on v_vir, which arises because the ratio of stellar mass to dark matter mass is a strong function of halo mass.

### Dark Matter Massive Fermions and Einasto Profiles in Galactic Haloes

On the basis of a fermionic dark matter model we fit rotation curves of The HI Nearby Galaxy Survey THINGS sample and compare our 3-parametric model to other models widely used in the literature: 2-parametric Navarro–Frenk–White, pseudoisothermal sphere, Burkhert models, and 3-parametric Einasto model, suggested as the new "standard dark matter profile" model in the paper by Chemin et. al., AJ 142 (2011) 109. The results from the fitting procedure provides evidence for an underlying fermionic nature of the dark matter candidate, with rest mass above the keV regime.

### Scalar graviton as dark matter [Cross-Listing]

In the report, the theory of unimodular bimode gravity built on principles of unimodular gauge invariance/relativity and general covariance is exposed. Besides the massless tensor graviton of General Relativity, the theory includes an (almost) massless scalar graviton treated as the gravitational dark matter. A spherically symmetric vacuum solution, describing the coherent scalar-graviton field for the soft-core dark halos with the asymptotically flat rotation curves, is demonstrated.

### Scalar graviton as dark matter

In the report, the theory of unimodular bimode gravity built on principles of unimodular gauge invariance/relativity and general covariance is exposed. Besides the massless tensor graviton of General Relativity, the theory includes an (almost) massless scalar graviton treated as the gravitational dark matter. A spherically symmetric vacuum solution, describing the coherent scalar-graviton field for the soft-core dark halos with the asymptotically flat rotation curves, is demonstrated.

### Scalar graviton as dark matter [Cross-Listing]

In the report, the theory of unimodular bimode gravity built on principles of unimodular gauge invariance/relativity and general covariance is exposed. Besides the massless tensor graviton of General Relativity, the theory includes an (almost) massless scalar graviton treated as the gravitational dark matter. A spherically symmetric vacuum solution, describing the coherent scalar-graviton field for the soft-core dark halos with the asymptotically flat rotation curves, is demonstrated.

### Compact nuclear objects and properties of their parent galaxies

We consider the relationship between the masses of the compact nuclear objects in the centers of disky galaxies — supermassive black holes (SMBHs) or nuclear star clusters (NCs) — and such parameters as the maximal velocity of rotation $V_{\textrm{max}}$, obtained from the rotation curves, indicative dynamical mass $M_{25}$, and the color index ($B{-}V$) of their parent galaxies. It was found that the mass of nuclear clusters $M_{\rm nc}$ correlates more closely with the velocity of rotation and total mass of galaxies than the mass of supermassive black holes $M_{\rm bh}$. The dependence of masses of the central objects on the color index is bimodal: galaxies of the red group (red-sequence), which have ($B{-}V) > 0.6{-}0.7$, differ from bluer galaxies, by higher values of $M_{\rm bh}$ for similar host-galaxy parameters. In contrast, in the diagrams for nuclear clusters the "blue" and "red" galaxies form unified sequences. It agrees with scenarios in which most red-group galaxies form as a result of loss of interstellar gas in a stage of high nuclear activity in galaxies whose central black-hole masses are high, exceeding $10^6 {-} 10^7 M_{\odot}$ (depending on the total mass of the galaxy). The active growth of nuclear star clusters possibly begun after the violent AGN activity.

### Rotation curves in Bose-Einstein Condensate Dark Matter Halos [Cross-Listing]

The study of the rotation curves of spiral galaxies reveals a nearly constant cored density distribution of Cold Dark Matter. N-body simulations however lead to a cuspy distribution on the galactic scale, with a central peak. A Bose-Einstein condensate (BEC) of light particles naturally solves this problem by predicting a repulsive force, obstructing the formation of the peak. After succinctly presenting the BEC model, we test it against rotation curve data for a set of 3 High Surface Brightness (HSB), 3 Low Surface Brightness (LSB) and 3 dwarf galaxies. The BEC model gives a similar fit to the Navarro-Frenk-White (NFW) dark matter model for all HSB and LSB galaxies in the sample. For dark matter dominated dwarf galaxies the addition of the BEC component improved more upon the purely baryonic fit than the NFW component. Thus despite the sharp cut-off of the halo density, the BEC dark matter candidate is consistent with the rotation curve data of all types of galaxies.

### Rotation curves in Bose-Einstein Condensate Dark Matter Halos

The study of the rotation curves of spiral galaxies reveals a nearly constant cored density distribution of Cold Dark Matter. N-body simulations however lead to a cuspy distribution on the galactic scale, with a central peak. A Bose-Einstein condensate (BEC) of light particles naturally solves this problem by predicting a repulsive force, obstructing the formation of the peak. After succinctly presenting the BEC model, we test it against rotation curve data for a set of 3 High Surface Brightness (HSB), 3 Low Surface Brightness (LSB) and 3 dwarf galaxies. The BEC model gives a similar fit to the Navarro-Frenk-White (NFW) dark matter model for all HSB and LSB galaxies in the sample. For dark matter dominated dwarf galaxies the addition of the BEC component improved more upon the purely baryonic fit than the NFW component. Thus despite the sharp cut-off of the halo density, the BEC dark matter candidate is consistent with the rotation curve data of all types of galaxies.

### Testing Grumiller's modified gravity at galactic scales [Replacement]

Using galactic rotation curves, we test a -quantum motivated- gravity model that at large distances modifies the Newtonian potential when spherical symmetry is considered. In this model one adds a Rindler acceleration term to the rotation curves of disk galaxies. Here we consider a standard and a power-law generalization of the Rindler modified Newtonian potential that are hypothesized to play the role of dark matter in galaxies. The new, universal acceleration has to be -phenomenologically- determined. Our galactic model includes the mass of the integrated gas and stars for which we consider a free mass model. We test the model by fitting rotation curves of thirty galaxies that has been employed to test other alternative gravity models. We find that the Rindler parameters do not perform a suitable fit to the rotation curves in comparison to the Burkert dark matter profile, but the models achieve a similar fit as the NFW’s profile does. However, the computed parameters of the Rindler gravity show some spread, posing the model to be unable to consistently explain the observed rotation curves.

### Testing Grumiller's modified gravity at galactic scales

Using galactic rotation curves, we test a -quantum motivated- gravity model that at large distances modifies the Newtonian potential when spherical symmetry is considered. In this model one adds a Rindler acceleration term to the rotation curves of disk galaxies. Here we consider a standard and a power-law generalization of the Rindler modified Newtonian potential that are hypothesized to play the role of dark matter in galaxies. The new, universal acceleration has to be -phenomenologically- determined. Our galactic model includes the mass of the integrated gas and stars for which we consider a free mass model. We test the model by fitting rotation curves of thirty galaxies that has been employed to test other alternative gravity models. We find that the Rindler parameters do not perform a suitable fit to the rotation curves in comparison to the Burkert dark matter profile, but the models achieve a similar fit as the NFW’s profile does. However, the computed parameters of the Rindler gravity show some spread, posing the model to be unable to consistently explain the observed rotation curves.

### Testing Grumiller's modified gravity at galactic scales [Replacement]

Using galactic rotation curves, we test a -quantum motivated- gravity model that at large distances modifies the Newtonian potential when spherical symmetry is considered. In this model one adds a Rindler acceleration term to the rotation curves of disk galaxies. Here we consider a standard and a power-law generalization of the Rindler modified Newtonian potential that are hypothesized to play the role of dark matter in galaxies. The new, universal acceleration has to be -phenomenologically- determined. Our galactic model includes the mass of the integrated gas and stars for which we consider a free mass model. We test the model by fitting rotation curves of thirty galaxies that has been employed to test other alternative gravity models. We find that the Rindler parameters do not perform a suitable fit to the rotation curves in comparison to the Burkert dark matter profile, but the models achieve a similar fit as the NFW’s profile does. However, the computed parameters of the Rindler gravity show some spread, posing the model to be unable to consistently explain the observed rotation curves.

### Testing Grumiller's modified gravity at galactic scales [Cross-Listing]

Using galactic rotation curves, we test a -quantum motivated- gravity model that at large distances modifies the Newtonian potential when spherical symmetry is considered. In this model one adds a Rindler acceleration term to the rotation curves of disk galaxies. Here we consider a standard and a power-law generalization of the Rindler modified Newtonian potential that are hypothesized to play the role of dark matter in galaxies. The new, universal acceleration has to be -phenomenologically- determined. Our galactic model includes the mass of the integrated gas and stars for which we consider a free mass model. We test the model by fitting rotation curves of thirty galaxies that has been employed to test other alternative gravity models. We find that the Rindler parameters do not perform a suitable fit to the rotation curves in comparison to the Burkert dark matter profile, but the models achieve a similar fit as the NFW’s profile does. However, the computed parameters of the Rindler gravity show some spread, posing the model to be unable to consistently explain the observed rotation curves.

### Evolution of dwarf galaxies: a dynamical perspective

For a rotating galaxy, the inner circular-velocity gradient d_{R}V(0) provides a direct estimate of the central dynamical mass density, including gas, stars, and dark matter. We consider 60 low-mass galaxies with high-quality HI and/or stellar rotation curves (including starbursting dwarfs, irregulars, and spheroidals), and estimate d_{R}V(0) as V(R_d)/R_d, where R_d is the galaxy scale-length. For gas-rich dwarfs, we find that V(R_d)/R_d correlates with the central surface brightness mu(0), the mean atomic gas surface density Sigma_gas, and the star formation rate surface density Sigma_SFR. Starbursting galaxies, such as blue compact dwarfs (BCDs), generally have higher values of V(R_d)/R_d than dwarf irregulars, suggesting that the starburst is closely related to the inner shape of the potential well. There are, however, some "compact" irregulars with values of V(R_d)/R_d similar to BCDs. Unless a redistribution of mass takes place, BCDs must evolve into compact irregulars. Rotating spheroidals in the Virgo cluster follow the same correlation between V(R_d)/R_d and mu(0) as gas-rich dwarfs. They have values of V(R_d)/R_d comparable to those of BCDs and compact irregulars, pointing at evolutionary links between these types of dwarfs. Finally, we find that, similarly to spiral galaxies and massive starbursts, the star-formation activity in dwarfs can be parametrized as Sigma_SFR = epsilon*Sigma_gas/t_orb, where t_orb is the orbital time and epsilon = 0.02.

### Test of conformal gravity with astrophysical observations [Cross-Listing]

Since it can describe the rotation curves of galaxies without dark matter and can give rise to accelerated expansion, conformal gravity attracts much attention recently. As a theory of modified gravity, it is important to test conformal gravity with astrophysical observations. Here we constrain conformal gravity with SNIa and Hubble parameter data and investigate whether it suffers from an age problem with the age of APM~08279+5255. We find conformal gravity can accommodate the age of APM~08279+5255 at 3 $\sigma$ deviation, unlike most of dark energy models which suffer from an age problem.

### Test of conformal gravity with astrophysical observations

Since it can describe the rotation curves of galaxies without dark matter and can give rise to accelerated expansion, conformal gravity attracts much attention recently. As a theory of modified gravity, it is important to test conformal gravity with astrophysical observations. Here we constrain conformal gravity with SNIa and Hubble parameter data and investigate whether it suffers from an age problem with the age of APM~08279+5255. We find conformal gravity can accommodate the age of APM~08279+5255 at 3 $\sigma$ deviation, unlike most of dark energy models which suffer from an age problem.

### Gravitational lensing of wormholes in the galactic halo region

A recent study by Rahaman et al. has shown that the galactic halo possesses the necessary properties for supporting traversable wormholes, based on two observational results, the density profile due to Navarro et al. and the observed flat rotation curves of galaxies. Using a method for calculating the deflection angle pioneered by V. Bozza, it is shown that the deflection angle diverges at the throat of the wormhole. The resulting photon sphere has a radius of 0.40 ly. Given the dark-matter background, detection may be possible from past data using ordinary light.

### Gravitational lensing of wormholes in the galactic halo region [Replacement]

A recent study by Rahaman et al. has shown that the galactic halo possesses the necessary properties for supporting traversable wormholes, based on two observational results, the density profile due to Navarro et al. and the observed flat rotation curves of galaxies. Using a method for calculating the deflection angle pioneered by V. Bozza, it is shown that the deflection angle diverges at the throat of the wormhole. The resulting photon sphere has a radius of 0.40 ly. Given the dark-matter background, detection may be possible from past data using ordinary light.

### Gravitational lensing of wormholes in the galactic halo region [Replacement]

A recent study by Rahaman et al. has shown that the galactic halo possesses the necessary properties for supporting traversable wormholes, based on two observational results, the density profile due to Navarro et al. and the observed flat rotation curves of galaxies. Using a method for calculating the deflection angle pioneered by V. Bozza, it is shown that the deflection angle diverges at the throat of the wormhole. The resulting photon sphere has a radius of 0.40 ly. Given the dark-matter background, detection may be possible from past data using ordinary light.

### Gravitational lensing of wormholes in the galactic halo region [Replacement]

A recent study by Rahaman et al. has shown that the galactic halo possesses the necessary properties for supporting traversable wormholes, based on two observational results, the density profile due to Navarro et al. and the observed flat rotation curves of galaxies. Using a method for calculating the deflection angle pioneered by V. Bozza, it is shown that the deflection angle diverges at the throat of the wormhole. The resulting photon sphere has a radius of 0.40 ly. Given the dark-matter background, detection may be possible from past data using ordinary light.

### Gravitational lensing of wormholes in the galactic halo region [Replacement]

A recent study by Rahaman et al. has shown that the galactic halo possesses the necessary properties for supporting traversable wormholes, based on two observational results, the density profile due to Navarro et al. and the observed flat rotation curves of galaxies. Using a method for calculating the deflection angle pioneered by V. Bozza, it is shown that the deflection angle diverges at the throat of the wormhole. The resulting photon sphere has a radius of 0.40 ly. Given the dark-matter background, detection may be possible from past data using ordinary light.

### Constraining the range of Yukawa gravity interaction from S2 star orbits

We consider possible signatures for Yukawa gravity within the Galactic Central Parsec, based on our analysis of the S2 star orbital precession around the massive compact dark object at the Galactic Centre, and on the comparisons between the simulated orbits in Yukawa gravity and two independent sets of observations. Our simulations resulted in strong constraints on the range of Yukawa interaction $\Lambda$ and showed that its most probable value in the case of S2 star is around 5000 – 7000 AU. At the same time, we were not able to obtain reliable constrains on the universal constant $\delta$ of Yukawa gravity, because the current observations of S2 star indicated that it may be highly correlated with parameter $\Lambda$ in the range $(0 <\delta < 1)$. For $\delta > 2$ they are not correlated. However, the same universal constant which was successfully applied to clusters of galaxies and rotation curves of spiral galaxies ($\delta=1/3$) also gives a satisfactory agreement with the observed orbital precession of the S2 star, and in that case the most probable value for the scale parameter is $\Lambda \approx 3000 \pm 1500$ AU. Also, the Yukawa gravity potential induces precession of S2 star orbit in the same direction as General Relativity for $\delta > 0$ and for $\delta < -1$, and in the opposite direction for $-1 <\delta < 0$. The future observations with advanced facilities, such as GRAVITY or/and European Extremely Large Telescope, are needed in order to verify these claims.

### Constraining the range of Yukawa gravity interaction from S2 star orbits [Cross-Listing]

We consider possible signatures for Yukawa gravity within the Galactic Central Parsec, based on our analysis of the S2 star orbital precession around the massive compact dark object at the Galactic Centre, and on the comparisons between the simulated orbits in Yukawa gravity and two independent sets of observations. Our simulations resulted in strong constraints on the range of Yukawa interaction $\Lambda$ and showed that its most probable value in the case of S2 star is around 5000 – 7000 AU. At the same time, we were not able to obtain reliable constrains on the universal constant $\delta$ of Yukawa gravity, because the current observations of S2 star indicated that it may be highly correlated with parameter $\Lambda$ in the range $(0 <\delta < 1)$. For $\delta > 2$ they are not correlated. However, the same universal constant which was successfully applied to clusters of galaxies and rotation curves of spiral galaxies ($\delta=1/3$) also gives a satisfactory agreement with the observed orbital precession of the S2 star, and in that case the most probable value for the scale parameter is $\Lambda \approx 3000 \pm 1500$ AU. Also, the Yukawa gravity potential induces precession of S2 star orbit in the same direction as General Relativity for $\delta > 0$ and for $\delta < -1$, and in the opposite direction for $-1 <\delta < 0$. The future observations with advanced facilities, such as GRAVITY or/and European Extremely Large Telescope, are needed in order to verify these claims.

### Scalar perturbations in cosmological models with quark nuggets [Replacement]

In this paper we consider the Universe at the late stage of its evolution and deep inside the cell of uniformity. At these scales, the Universe is filled with inhomogeneously distributed discrete structures (galaxies, groups and clusters of galaxies). Supposing that a small fraction of colored objects escaped hadronization and survived up to now in the form of quark-gluon nuggets (QNs), and also taking into account radiation, we investigate scalar perturbations of the FRW metrics due to inhomogeneities of dustlike matter as well as fluctuations of QNs and radiation. In particular, we demonstrate that the nonrelativistic gravitational potential is defined by the distribution of inhomogeneities/fluctuations of both dustlike matter and QNs. Consequently, QNs can be distributed around the baryonic inhomogeneities (e.g., galaxies) in such a way that it can solve the problem of the flatness of the rotation curves. We also show that the fluctuations of radiation are caused by both the inhomogeneities in the form of galaxies and the fluctuations of quark-gluon nuggets. Therefore, if QNs exist, the CMB anisotropy should contain also the contributions from QNs. Additionally, the spatial distribution of the radiation fluctuations is defined by the gravitational potential. All these results look physically reasonable.