Rotation Curves Of Spiral Galaxies Research Articles

Galactic rotation curves of spiral galaxies and dark matter in f(ℛ,T) gravity theory

Galactic rotation curve is a powerful indicator of the state of the gravitational field within a galaxy. The flatness of these curves indicates the presence of dark matter (DM) in galaxies and their clusters. In this paper, we focus on the possibility of explaining the rotation curves of spiral galaxies without postulating the existence of DM in the framework of [Formula: see text] gravity, where the gravitational Lagrangian is written by an arbitrary function of [Formula: see text], the Ricci scalar and of [Formula: see text], the trace of energy–momentum tensor [Formula: see text]. We derive the gravitational field equations in this gravity theory for the static spherically symmetric spacetime and solve the equations for metric coefficients using a specific model that has minimal coupling between matter and geometry. The orbital motion of a massive test particle moving in a stable circular orbit is considered and the behavior of its tangential velocity with the help of the considered model is studied. We compare the theoretical result predicted by the model with observations of a sample of 19 galaxies by generating and fitting rotation curves for the test particle to check the viability of the model. It is observed that the model could almost successfully explain the galactic dynamics of these galaxies without the need of DM at large distances from the galactic center.

Internal kinematics of Gaia DR3 wide binaries: anomalous behaviour in the low acceleration regime

ABSTRACT The Gaia eDR3 catalogue has recently been used to study statistically the internal kinematics of wide binary populations using relative velocities of the two component stars, ΔV, total binary masses, mB, and separations, s. For s ≳ 0.01 pc, these binaries probe the low-acceleration a ≲ 2a0 regime where gravitational anomalies usually attributed to dark matter are observed in the flat rotation curves of spiral galaxies, where a0 ≈ 1.2 × 10−10 m s−2 is the acceleration scale of MOND. Such experiments test the degree of generality of these anomalies, by exploring the same acceleration regime using independent astronomical systems of vastly smaller mass and size. A signal above Newtonian expectations has been observed when a ≲ 2a0, alternatively interpreted as evidence of a modification of gravity, or as due to kinematic contaminants; undetected stellar components, unbound encounters, or spurious projection effects. Here I take advantage of the enhanced DR3 Gaia catalogue to perform a more rigorous study of the internal kinematics of wide binaries than what has previously been possible. Internally determined Gaia stellar masses and estimates of binary probabilities for each star using spectroscopic information, together with a larger sample of radial velocities, allow for a significant improvement in the analysis and careful exclusion of possible kinematic contaminants. Resulting ΔV scalings accurately tracing Newtonian expectations for the high acceleration regime, but markedly inconsistent with these expectations in the low acceleration one, are obtained. A non-Newtonian low acceleration phenomenology is thus confirmed.

Apparent dark matter as a non-local manifestation of emergent gravity

We disclose a close correspondence between Verlinde’s Emergent Gravity (VEG) theory and the non-local gravity theories. Such non-local effects can play crucial role at small distances as well as in large scale structures. In particular, we argue that the emergent gravity effectively is a manifestation of the entanglement entropy and can modify Newton’s law of gravity as well as address the flat rotation curves of spiral galaxies. In the cosmological setup, we have considered three different models for the apparent dark matter density. In the first model, we have found that Friedmann equations get modified due to the presence of the apparent dark matter (DM) in such a way that Newton’s constant of gravity shifts as G→G1+ζ, where ζ is a dimensionless small parameter. Using the flat rotating curves we estimate ζ∼10−7. For such a model, we find out that by rescaling the radial coordinate, r, the curvature space constant, k, and the scale factor of the universe, a, the effect of apparent DM can change the geometry of the universe and can shift the curvature space constant as k⋆=k(1−ζ). To this end, we study a more realistic model with evolving densities where we obtain the ΛCDM model in Verlinde’s gravity and comment on the Hubble tension problem with evolving densities.

Dark Matter in Fractional Gravity. I. Astrophysical Tests on Galactic Scales

We explore the possibility that the dark matter (DM) component in galaxies may originate fractional gravity. In such a framework, the standard law of inertia continues to hold, but the gravitational potential associated with a given DM density distribution is determined by a modified Poisson equation including fractional derivatives (i.e., derivatives of noninteger type) that are meant to describe nonlocal effects. We analytically derive the expression of the potential that in fractional gravity corresponds to various spherically symmetric density profiles, including the Navarro–Frenk–White (NFW) distribution that is usually exploited to describe virialized halos of collisionless DM as extracted from N-body cosmological simulations. We show that in fractional gravity, the dynamics of a test particle moving in a cuspy NFW density distribution is substantially altered with respect to the Newtonian case, mirroring what in Newtonian gravity would instead be sourced by a density profile with an inner core. We test the fractional gravity framework on galactic scales, showing that (i) it can provide accurate fits to the stacked rotation curves of spiral galaxies with different properties, including dwarfs; (ii) it can reproduce to reasonable accuracy the observed shape and scatter of the radial acceleration relation over an extended range of galaxy accelerations; and (iii) it can properly account for the universal surface density and the core radius versus disk scale length scaling relations. Finally, we discuss the possible origin of the fractional gravity behavior as a fundamental or emerging property of the elusive DM component.

Empirical Evidence of Nonminimally Coupled Dark Matter in the Dynamics of Local Spiral Galaxies?

Abstract We look for empirical evidence of a nonminimal coupling (NMC) between dark matter (DM) and gravity in the dynamics of local spiral galaxies. In particular, we consider a theoretically motivated NMC that may arise dynamically from the collective behavior of the coarse-grained DM field (e.g., via Bose–Einstein condensation) with averaging/coherence length L. In the Newtonian limit, this NMC amounts to modify the Poisson equation by a term L 2∇2 ρ proportional to the Laplacian of the DM density itself. We show that such a term, when acting as a perturbation over the standard Navarro–Frenk–White profile of cold DM particles, can substantially alter the dynamical properties of galaxies, in terms of their total radial acceleration within the disk and rotation velocity. Specifically, we find that this NMC model can properly fit the stacked rotation curves (RCs) of local spiral galaxies with different velocities at the optical radius, including dwarfs and low-surface-brightness systems, at a level of precision comparable to, and in some instances even better than, the phenomenological Burkert profile. Finally, we show that by extrapolating down to smaller masses the scaling of L versus halo mass found from the above RC analysis, the NMC model can adequately reproduce the radial acceleration relation in shape and normalization down to the dwarf spheroidal galaxy range, a task which constitutes a serious challenge for alternative DM models even inclusive of baryonic effects.

Mathematical Description of the Rotation of Spiral Galaxies Linearly Dependent on the Distance of Dark Energy

The article explains why astrophysicists had to enter a dark mass and dark energy. We just assumed that the amount of dark energy increases linearly with distance from the center of the galaxy. This assumption, apparently, makes best describe rotary rotation curves of spiral galaxies.

How the Redshift of Gravitons Explains Dark Matter and Dark Energy

The theory that gravitons lose energy by way of gravitational redshift while traveling in a gravitational field is applied to the expansion of the universe and to spiral and dwarf galaxy rotation curves using General Relativity. This is a graviton self interaction model which derives an expansion equation which is identical in form to the standard Lambda Cold Dark Matter model. In the domain of galaxies, spiral and dwarf galaxy rotation curves are matched using only baryonic mass. Thus, the requirement for dark matter and dark energy in the universe is replaced by this paradigm.

Measurement of the Dark Matter Velocity Dispersion with Dwarf Galaxy Rotation Curves

Warm dark matter has, by definition, a velocity dispersion. Let vhms(a)=vhms(1)/a be the root-mean-square velocity of non-relativistic warm dark matter particles in the early universe at expansion parameter a. vhms(1) is an adiabatic invariant. We obtain vhms(1) in the core of 11 dwarf galaxies dominated by dark matter, from their observed rotation curves, up to a rotation and relaxation correction. We obtain a mean 0.490 km/s and standard deviation 0.160 km/s, with a distribution peaked at the lower end. We apply a mild, data driven, rotation and relaxation correction that obtains the adiabatic invariant in the core of the galaxies: vhms(1)=0.406 ± 0.069 km/s. These two small relative standard deviations justify the prediction that the adiabatic invariant vhms(1) in the core of the galaxies is of cosmological origin if dark matter is warm. This result is in agreement with measurements of vhms(1) based on spiral galaxy rotation curves, galaxy ultra-violet luminosity distributions, galaxy stellar mass distributions, the formation of first galaxies, reionization, and the velocity dispersion cut-off mass.

Measurement of the Dark Matter Velocity Dispersion with Galaxy Stellar Masses, UV Luminosities, and Reionization

The root-mean-square of non-relativistic warm dark matter particle velocities scales as vhrms(a)=vhrms(1)/a , where a is the expansion parameter of the universe. This velocity dispersion results in a cut-off of the power spectrum of density fluctuations due to dark matter free-streaming. Let kfs (teq) be the free-streaming comoving cut-off wavenumber at the time of equal densities of radiation and matter. We obtain , and , at 68% confidence, from the observed distributions of galaxy stellar masses and rest frame ultra-violet luminosities. This result is consistent with reionization. From the velocity dispersion cut-off mass we obtain the limits vhrms(1)kfs (teq) >1.5 Mpc-1. These results are in agreement with previous measurements based on spiral galaxy rotation curves, and on the formation of first galaxies and reionization. These measured parameters determine the temperature-to-mass ratio of warm dark matter. This ratio happens to be in agreement with the no freeze-in and no freeze-out warm dark matter scenario of spin 0 dark matter particles decoupling early on from the standard model sector. Spin 1/2 and spin 1 dark matter are disfavored if nature has chosen the no freeze-in and no freeze-out scenario. An extension of the standard model of quarks and leptons, with scalar dark matter that couples to the Higgs boson that is in agreement with all current measurements, is briefly reviewed. Discrepancies with limits on dark matter particle mass that can be found in the literature are addressed.

Theory of Gravitons in Spiral and Dwarf Galaxy Rotation Curves

We hypothesize that gravitons contribute significantly to the process that flattens galaxy rotation curves. Gravitons travelling against a gravitational field experience an energy loss due to gravitational redshift identical to the effect on light. This energy loss requires an increased rotational velocity to stabilize a galaxy. We will show that this approach successfully explains the rotational properties of spiral and dwarf galaxies.

Comments on Warm Dark Matter Measurements and Limits

Observed spiral galaxy rotation curves allow a measurement of the warm dark matter particle velocity dispersion and mass. The measured thermal relic mass mh ≈ 100 eV is in disagreement with limits, typically in the range 1 to 4 keV. We review the measurements, update the no freeze-in and no freeze-out scenario of warm dark matter, and try to identify the cause of the discrepancies between measurements and limits.

The Phantom Dark Matter Halos of the Local Volume in the Context of Modified Newtonian Dynamics

Abstract We explore the predictions of Milgromian gravity (MOND) in the local universe by considering the distribution of the “phantom” dark matter (PDM) that would source the MOND gravitational field in Newtonian gravity, allowing an easy comparison with the dark matter framework. For this, we specifically deal with the quasi-linear version of MOND (QUMOND). We compute the “stellar-to-(phantom)halo mass relation” (SHMR), a monotonically increasing power law resembling the SHMR observationally deduced from spiral galaxy rotation curves in the Newtonian context. We show that the gas-to-(phantom)halo mass relation is flat. We generate a map of the Local Volume in QUMOND, highlighting the important influence of distant galaxy clusters, in particular Virgo. This allows us to explore the scatter of the SHMR and the average density of PDM around galaxies in the Local Volume, ΩPDM ≈ 0.1, below the average cold dark matter density in a ΛCDM universe. We provide a model of the Milky Way in its external field in the MOND context, which we compare to an observational estimate of the escape velocity curve. Finally, we highlight the peculiar features related to the external field effect in the form of negative PDM density zones in the outskirts of each galaxy, and test a new analytic formula for computing galaxy rotation curves in the presence of an external field in QUMOND. While we show that the negative PDM density zones would be difficult to detect dynamically, we quantify the weak-lensing signal they could produce for lenses at z ∼ 0.3.

Modified inertia as nonconservative Newtonian dynamics

Modified Newtonian dynamics by Milgrom is a paradigm for explaining the rotation curves of spiral galaxies and various other large scale structures. This paradigm includes several different theories. Here we present Milgrom's modifed inertia (MI) theory in terms of a simple and tractable nonconservative Newtonian dynamics, which is useful in obtaining observable predictions of MI. It is found that: 1) Modified inertia theory is equivalent to a Newtonian theory, with a nonconservative gravitational field, and dark matter density; 2) The tidal force in the equivalent Newtonian dynamics is nonconservative, and its effect on a binary system in free fall in the gravitational field of a spheroid is addressed. We also discuss attempts to restore conservations in MI.

Topological black holes in mimetic gravity

In this paper, we construct some new classes of topological black hole solutions in the context of mimetic gravity and investigate their properties. We study the uncharged and charged black holes, separately. We find the following novel results: (i) In the absence of a potential for the mimetic field, black hole solutions can address the flat rotation curves of spiral galaxies and alleviate the dark matter problem without invoking particle dark matter. Thus, mimetic gravity can provide a theoretical background for understanding flat galactic rotation curves through modifying Schwarzschild space–time. (ii) We also investigate the casual structure and physical properties of the solutions. We observe that in the absence of a potential, our solutions are not asymptotically flat, while in the presence of a negative constant potential for the mimetic field, the solutions are asymptotically anti-de Sitter (AdS). (iii) Finally, we explore the motion of massless and massive particles and give a list of the types of orbits. We study the differences of geodesic motion in the Einstein gravity and in mimetic gravity. In contrast to the Einstein gravity, massive particles always move on bound orbits and cannot escape the black hole in mimetic gravity. Furthermore, we find stable bound orbits for massless particles.

Elongated Gravity Sources as an Analytical Limit for Flat Galaxy Rotation Curves

The flattening of spiral-galaxy rotation curves is unnatural in view of the expectations from Kepler’s third law and a central mass. It is interesting, however, that the radius-independence velocity is what one expects in one less dimension. In our three-dimensional space, the rotation curve is natural if, outside the galaxy’s center, the gravitational potential corresponds to that of a very prolate ellipsoid, filament, string, or otherwise cylindrical structure perpendicular to the galactic plane. While there is observational evidence (and numerical simulations) for filamentary structure at large scales, this has not been discussed at scales commensurable with galactic sizes. If, nevertheless, the hypothesis is tentatively adopted, the scaling exponent of the baryonic Tully–Fisher relation due to accretion of visible matter by the halo comes out to reasonably be 4. At a minimum, this analytical limit would suggest that simulations yielding prolate haloes would provide a better overall fit to small-scale galaxy data.

Gravitoelectromagnetism and stellar orbits in galaxies

Beyond the Newtonian approximation, gravitational fields in general relativity can be described using a formalism known as gravitoelectromagnetism. In this formalism, a vector potential, the gravitomagnetic potential, arises as a result of moving masses, in strong analogy with the magnetic force due to moving charges in Maxwell’s theory. Gravitomagnetism can affect orbits in the gravitational field of a massive, rotating body. This raises the possibility that gravitomagnetism may serve as the dominant physics behind the anomalous rotation curves of spiral galaxies, eliminating the need for dark matter. In this essay, we methodically work out the magnitude of the gravitomagnetic equivalent of the Lorentz force and apply the result to the Milky Way. We find that the resulting contribution is too small to produce an observable effect on these orbits. We also investigate the impact of cosmological boundary conditions on the result and find that these, too, are negligible.

Stochastic modification of Newtonian dynamics and induced potential—Application to spiral galaxies and the dark potential

Using the formalism of stochastic embedding developed by Cresson and Darses [J. Math. Phys. 48, 072703 (2007)], we study how the dynamics of the classical Newton equation for a force deriving from a potential is deformed under the assumption that this equation can admit stochastic processes as solutions. We focus on two definitions of a stochastic Newton equation called differential and variational. We first prove a stochastic virial theorem that is a natural generalization of the classical case. The stochasticity modifies the virial relation by adding a potential term called the induced potential, which corresponds in quantum mechanics to the Bohm potential. Moreover, the differential stochastic Newton equation naturally provides an action functional that satisfies a stochastic Hamilton–Jacobi equation. The real part of this equation corresponds to the classical Hamilton–Jacobi equation with an extra potential term corresponding to the induced potential already observed in the stochastic virial theorem. The induced potential has an explicit form depending on the density of the stochastic process solutions of the stochastic Newton equation. It is proved that this density satisfies a nonlinear Schrödinger equation. Applying this formalism for the Kepler potential, one proves that the induced potential coincides with the ad hoc “dark potential” used to recover a flat rotation curve of spiral galaxies. We then discuss the application of the previous formalism in the context of spiral galaxies following the proposal and computations given by Da Rocha and Nottale [Chaos, Solitons Fractals, 16(4), 565–595 (2003)] where the emergence of the “dark potential” is seen as a consequence of the fractality of space in the context of the scale relativity theory.

On the plausible origins of the spiral character of galaxies

Abstract We here-in demonstrate that the proposed hitherto unknown gravitomagnetic dark-force that hypothetically explains the Flat Rotation Curves of Spiral Galaxies — this same force, explains very well, the logarithmic and as-well, the barred spiral shapes of spiral galaxies. That is, much in line with Edward Arthur Milne (1896-1950)’s 1946 ideas — albeit, on a radically and asymptotically different philosophical train of thought, the galactic disk is here assumed to be in a state of free-fall around the central bulge with the hypothetical gravitomagnetic dark-force being the dominant force determining all gravity-related dynamics of the disk, thus leading to logarithmic and barred spiral orbits, hence the shape of spiral galaxies.

The Principle of Equivalence: Periastron Precession, Light Deflection, Binary Star Decay, Graviton Temperature, Dark Matter, Dark Energy and Galaxy Rotation Curves

The nature of the principle of equivalence is explored. The path of gravitons is analyzed in an accelerating system equivalent to a gravitating system. The finite speed of the graviton results in a delay of the gravitational interaction with a particle mass. From the aberration found in the path of the graviton we derive the standard expression for the advancement of the periastron of the orbit of the mass around a star. In a similar way, by analysing the aberrations of the graviton and light paths in an accelerating reference frame, the expression for the deflection of light by a massive body is obtained identically to the standard result. We also examine the binary star system and calculate the decay in its orbital period. The decay is attributed to the redshift of the graviton frequency relative to the accelerating system. Here too, we obtain good agreement with experimental measurements. Also, hypothesizing that gravitons behave like photons, we determine the temperature of the gravitons in a binary star system and form the Bose-Einstein distribution. Finally, we show how the redshift of gravitons may be the source of dark matter, dark energy and flat line spiral galaxy rotation curves.

Thermodynamic Constraints on the Non-Baryonic Dark Matter Gas Composing Galactic Halos

To explain rotation curves of spiral galaxies through Newtonian orbital models, massive halos of non-baryonic dark matter (NBDM) are commonly invoked. The postulated properties are that NBDM interacts gravitationally with baryonic matter, yet negligibly interacts with photons. Since halos are large, low-density gaseous bodies, their postulated attributes can be tested against classical thermodynamics and the kinetic theory of gas. Macroscopic models are appropriate because these make few assumptions. NBDM–NBDM collisions must be elastic to avoid the generation of light, but this does not permit halo gas temperature to evolve. If no such collisions exist, then the impossible limit of absolute zero would be attainable since the other available energy source, radiation, does not provide energy to NBDM. The alternative possibility, an undefined temperature, is also inconsistent with basic thermodynamic principles. However, a definable temperature could be attained via collisions with baryons in the intergalactic medium since these deliver kinetic energy to NBDM. In this case, light would be produced since some proportion of baryon collisions are inelastic, thereby rendering the halo detectable. Collisions with baryons are unavoidable, even if NBDM particles are essentially point masses. Note that <0.0001 × the size of a proton is needed to avoid scattering with γ-rays, the shortest wavelength used to study halos. If only elastic collisions exist, NBDM gas would collapse to a tiny, dense volume (zero volume for point masses) during a disturbance—e.g., cosmic rays. NBDM gas should occupy central galactic regions, not halos, since self-gravitating objects are density stratified. In summary, properties of NBDM halos as postulated would result in violations of thermodynamic laws and in a universe unlike that observed.