Posts Tagged rotation curves

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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

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

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 [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.

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.

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.

The MOND phenomenology [Cross-Listing]

The Lambda-CDM cosmological model is succesful at reproducing various independent sets of observations concerning the large-scale Universe. This model is however currently, and actually in principle, unable to predict the gravitational field of a galaxy from it observed baryons alone. Indeed the gravitational field should depend on the relative contribution of the particle dark matter distribution to the baryonic one, itself depending on the individual assembly history and environment of the galaxy, including a lot of complex feedback mechanisms. However, for the last thirty years, Milgrom’s formula, at the heart of the MOND paradigm, has been consistently succesful at predicting rotation curves from baryons alone, and has been resilient to all sorts of observational tests on galaxy scales. We show that the few individual galaxy rotation curves that have been claimed to be highly problematic for the predictions of Milgrom’s formula, such as Holmberg II or NGC 3109, are actually false alarms. We argue that the fact that it is actually possible to predict the gravitational field of galaxies from baryons alone presents a challenge to the current Lambda-CDM model, and may indicate a breakdown of our understanding of gravitation and dynamics, and/or that the actual lagrangian of the dark sector is very different and richer than currently assumed. On the other hand, it is obvious that any alternative must also, in fine, reproduce the successes of the Lambda-CDM model on large scales, where this model is so well-tested that it presents by itself a challenge to any such alternative.

The MOND phenomenology

The Lambda-CDM cosmological model is succesful at reproducing various independent sets of observations concerning the large-scale Universe. This model is however currently, and actually in principle, unable to predict the gravitational field of a galaxy from it observed baryons alone. Indeed the gravitational field should depend on the relative contribution of the particle dark matter distribution to the baryonic one, itself depending on the individual assembly history and environment of the galaxy, including a lot of complex feedback mechanisms. However, for the last thirty years, Milgrom’s formula, at the heart of the MOND paradigm, has been consistently succesful at predicting rotation curves from baryons alone, and has been resilient to all sorts of observational tests on galaxy scales. We show that the few individual galaxy rotation curves that have been claimed to be highly problematic for the predictions of Milgrom’s formula, such as Holmberg II or NGC 3109, are actually false alarms. We argue that the fact that it is actually possible to predict the gravitational field of galaxies from baryons alone presents a challenge to the current Lambda-CDM model, and may indicate a breakdown of our understanding of gravitation and dynamics, and/or that the actual lagrangian of the dark sector is very different and richer than currently assumed. On the other hand, it is obvious that any alternative must also, in fine, reproduce the successes of the Lambda-CDM model on large scales, where this model is so well-tested that it presents by itself a challenge to any such alternative.

Rotation curves of rotating galactic BEC dark matter halos [Cross-Listing]

We present the dynamics of rotating Bose Condensate galactic dark matter halos, made of an ultralight spinless boson. We restrict to the case of adding axisymmetric rigid rotation to initially spherically symmetric structures and show there are three regimes: i) small angular momentum, that basically retains the drawbacks of spherically symmetric halos related to compactness and failure at explaining galactic RCs, ii) an intermediate range of values of angular momentum that allow the existence of long-lived structures with acceptable RC profiles, and iii) high angular momentum, in which the structure is dispersed away by rotation. We also present in detail the new code used to solve the Gross-Pitaevskii Poisson system of equations in three dimensions.

Rotation curves of rotating galactic BEC dark matter halos

We present the dynamics of rotating Bose Condensate galactic dark matter halos, made of an ultralight spinless boson. We restrict to the case of adding axisymmetric rigid rotation to initially spherically symmetric structures and show there are three regimes: i) small angular momentum, that basically retains the drawbacks of spherically symmetric halos related to compactness and failure at explaining galactic RCs, ii) an intermediate range of values of angular momentum that allow the existence of long-lived structures with acceptable RC profiles, and iii) high angular momentum, in which the structure is dispersed away by rotation. We also present in detail the new code used to solve the Gross-Pitaevskii Poisson system of equations in three dimensions.

Astrophysics of Bertrand Space-times

We construct a model for galactic dark matter that arises as a solution of Einstein gravity, and is a Bertrand space-time matched with an external Schwarzschild metric. This model can explain galactic rotation curves. Further, we study gravitational lensing in these space-times, and in particular we consider Einstein rings, using the strong lensing formalism of Virbhadra and Ellis. Our results are in good agreement with observational data, and indicate that under certain conditions, gravitational lensing effects from galactic dark matter may be similar to that from Schwarzschild backgrounds.

Astrophysics of Bertrand Space-times [Cross-Listing]

We construct a model for galactic dark matter that arises as a solution of Einstein gravity, and is a Bertrand space-time matched with an external Schwarzschild metric. This model can explain galactic rotation curves. Further, we study gravitational lensing in these space-times, and in particular we consider Einstein rings, using the strong lensing formalism of Virbhadra and Ellis. Our results are in good agreement with observational data, and indicate that under certain conditions, gravitational lensing effects from galactic dark matter may be similar to that from Schwarzschild backgrounds.

The Luminous Convolution Model

We present a heuristic model for predicting the rotation curves of spiral galaxies. The Luminous Convolution Model (LCM) utilizes Lorentz-type transformations of very small changes in photon frequencies from curved space-times to construct a model predictive of galaxy rotation profile observations. These frequency changes are derived from the Schwarzschild red-shift result or the analogous result from a Kerr wave equation. The LCM maps the small curvatures of the emitter galactic frame onto those of the receiver galactic frame, and then returns the map to the associated flat frames where measurements are made. This treatment rests upon estimates of the luminous matter in both the emitter and receiver galaxies to determine these small curvatures. The LCM is tested on a sample of 23 galaxies, represented in 35 different data sets. LCM fits are compared to those of the Navarro, Frenk and White (NFW) Dark Matter Model, and/or to the Modified Newtonian Dynamics (MOND) model when possible. The high degree of sensitivity of the LCM to the initial assumption of a luminous mass-to-light ratio ($M_L/L$) is shown. We demonstrate that the LCM is successful across a wide range of spiral galaxies for predicting the observed rotation curves.

Refining the M_BH-V_c scaling relation with HI rotation curves of water megamaser galaxies

Black hole – galaxy scaling relations provide information about the coevolution of supermassive black holes and their host galaxies. We compare the black hole mass – circular velocity (MBH – Vc) relation with the black hole mass – bulge stellar velocity dispersion (MBH – sigma) relation, to see whether the scaling relations can passively emerge from a large number of mergers, or require a physical mechanism, such as feedback from an active nucleus. We present VLA H I observations of five galaxies, including three water megamaser galaxies, to measure the circular velocity. Using twenty-two galaxies with dynamical MBH measurements and Vc measurements extending to large radius, our best-fit MBH – Vc relation, log MBH = alpha + beta log(Vc /200 km s^-1), yields alpha = 7.43+/-0.13, beta = 3.68+1.23/-1.20, and intrinsic scatter epsilon_int = 0.51+0.11/-0.09. The intrinsic scatter may well be higher than 0.51, as we take great care to ascribe conservatively large observational errors. We find comparable scatter in the MBH – sigma relations, epsilon_int = 0.48+0.10/-0.08, while pure merging scenarios would likely result in a tighter scaling with the dark halo (as traced by Vc) than baryonic (sigma) properties. Instead, feedback from the active nucleus may act on bulge scales to tighten the MBH – sigma relation with respect to the MBH – Vc relation, as observed.

MOG Weak Field Approximation: A Modified Gravity Compatible with Chandra X-ray Clusters

We use the covariant Scalar-Vector-Tensor theory of gravity (so-called MOG), in the weak field approximation limit to study the dynamics of clusters of galaxies. The ionized gas density and the temperature profile of the clusters are our observables, which have been measured by the Chandra telescope for the nearby clusters. The MOG effective gravitational potential in the weak field approximation is composed of attractive Newtonian and repulsive Yukawa terms. Two parameters $\alpha$ and $\mu$ in the effective potential determine the asymptotic gravitational constant and the mass of the vector field, respectively. These parameters have been fixed by fitting MOG dynamics to the rotation curves of galaxies. Our analysis shows that the internal dynamics of clusters can be well explained within $1\sigma$ with a virial theorem in the framework of MOG, such that the best fit for the ratio of the dynamical mass to the baryonic mass is: $M_{\rm dyn}/M_{\rm b} = 0.98^{+0.02}_{-0.02}$. This result means that MOG is a theory of modified gravity that describes the dynamics of structures from the solar system to Mega parsec scales without the need for dark matter.

A scan of f(R) models admitting Rindler type acceleration [Replacement]

As a manifestation of large distance effect Grumiller modified Schwarzschild metric with an extraneous term reminiscent of Rindler acceleration. Such a term has the potential to explain the observed flat rotation curves in general relativity. The same idea has been extended herein to the larger arena of $f\left( R\right)$ theory. With particular emphasis on weak energy conditions (WECs) for a fluid we present various classes of $f\left( R\right)$ theories admitting a Rindler-type acceleration in the metric.

The WDM particle mass from Thomas-Fermi galaxy structure theory and rotation curves data

The Thomas-Fermi approach to galaxy structure determines selfconsistently the fermionic warm dark matter (WDM) gravitational potential given the distribution function f(E). This framework is appropriate for macroscopic quantum systems: neutron stars, white dwarfs and WDM galaxies. Compact dwarf galaxies follow from the quantum degenerate regime, while dilute and large galaxies from the classical Boltzmann regime. We find analytic scaling relations for the main galaxy magnitudes as halo radius r_h, mass M_h and phase space density. The observational data for a large variety of galaxies are all well reproduced by these theoretical scaling relations. For the compact dwarfs, our results show small deviations from the scaling due to quantum macroscopic effects. We contrast the theoretical curves for the circular velocities and density profiles with the observational ones. The best fit determines the only free parameter here, the WDM particle mass: m = 2.42 \pm 0.18 keV for the rotation curves and m = 2.31 \pm 0.05 keV for the density profiles. All these results are independent of any WDM particle physics model, they only follow from the gravity interaction of the WDM particles and their fermionic nature. These m values satisfy the known lower bounds on m. The theory rotation and density curves reproduce very well for r < r_h the observations of 10 different and independent sets of data for galaxy masses from 5×10^9 Msun till 5×10^{11} Msun. Our normalized circular velocity curves turn to be universal functions of r/r_h for all galaxies and coincide with the observational curves for r < r_h. Conclusion: the Thomas-Fermi approach correctly describe the galaxy structures (Abridged).

Observational rotation curves and density profiles vs. the Thomas-Fermi galaxy structure theory [Replacement]

The Thomas-Fermi approach to galaxy structure determines selfconsistently the fermionic warm dark matter (WDM) gravitational potential given the distribution function f(E). This framework is appropriate for macroscopic quantum systems: neutron stars, white dwarfs and WDM galaxies. Compact dwarf galaxies follow from the quantum degenerate regime, while dilute and large galaxies from the classical Boltzmann regime. We find analytic scaling relations for the main galaxy magnitudes as halo radius r_h, mass M_h and phase space density. The observational data for a large variety of galaxies are all well reproduced by these theoretical scaling relations. For the compact dwarfs, our results show small deviations from the scaling due to quantum macroscopic effects. We contrast the theoretical curves for the circular velocities and density profiles with the observational ones. All these results are independent of any WDM particle physics model, they only follow from the gravity interaction of the WDM particles and their fermionic nature. The theory rotation and density curves reproduce very well for r < r_h the observations of 10 different and independent sets of data for galaxy masses from 5×10^9 Msun till 5×10^{11} Msun. Our normalized circular velocity curves turn to be universal functions of r/r_h for all galaxies and reproduce very well the observational curves for r < r_h. Conclusion: the Thomas-Fermi approach correctly describes the galaxy structures (Abridged).

Observational rotation curves and density profiles vs. the Thomas-Fermi galaxy structure theory [Replacement]

The Thomas-Fermi approach to galaxy structure determines selfconsistently the fermionic warm dark matter (WDM) gravitational potential given the distribution function f(E). This framework is appropriate for macroscopic quantum systems: neutron stars, white dwarfs and WDM galaxies. Compact dwarf galaxies follow from the quantum degenerate regime, while dilute and large galaxies from the classical Boltzmann regime. We find analytic scaling relations for the main galaxy magnitudes as halo radius r_h, mass M_h and phase space density. The observational data for a large variety of galaxies are all well reproduced by these theoretical scaling relations. For the compact dwarfs, our results show small deviations from the scaling due to quantum macroscopic effects. We contrast the theoretical curves for the circular velocities and density profiles with the observational ones. All these results are independent of any WDM particle physics model, they only follow from the gravity interaction of the WDM particles and their fermionic nature. The theory rotation and density curves reproduce very well for r < r_h the observations of 10 different and independent sets of data for galaxy masses from 5×10^9 Msun till 5×10^{11} Msun. Our normalized circular velocity curves turn to be universal functions of r/r_h for all galaxies and reproduce very well the observational curves for r < r_h. Conclusion: the Thomas-Fermi approach correctly describes the galaxy structures (Abridged).

Exponential Galaxy Disks from Stellar Scattering

Stellar scattering off of orbiting or transient clumps is shown to lead to the formation of exponential profiles in both surface density and velocity dispersion in a two-dimensional non-self gravitating stellar disk with a fixed halo potential. The exponential forms for both nearly-flat rotation curves and near-solid body rotation curves. The exponential does not depend on initial conditions, spiral arms, bars, viscosity, star formation, or strong shear. After a rapid initial development, the exponential saturates to an approximately fixed scale length. The inner exponential in a two-component profile has a break radius comparable to the initial disk radius; the outer exponential is primarily scattered stars.

The DiskMass Survey. VII. The distribution of luminous and dark matter in spiral galaxies

We present dynamically-determined rotation-curve mass decompositions of 30 spiral galaxies, which were carried out to test the maximum-disk hypothesis and to quantify properties of their dark-matter (DM) halos. We used measured vertical velocity dispersions of the disk stars to calculate dynamical mass surface densities. Together with our atomic and molecular gas mass surface densities, we derived the stellar mass surface densities, and thus have absolute measurements of all dominant baryonic components. Using K-band surface brightness profiles, we calculated the K-band mass-to-light ratio of the stellar disks (M/L). Our result is consistent with all galaxies in the sample having equal M/L, with a sample average and scatter of <M/L>=0.31+/-0.07. Rotation-curves of the baryonic components were calculated from their mass surface densities, and used with circular-speed measurements to derive the structural parameters of the DM halos, modeled as either a pseudo-isothermal sphere (pISO) or an NFW halo. All galaxies in our sample are submaximal, such that at 2.2 disk scale lengths (hR) the ratios between the baryonic and total rotation-curves (Fb^{2.2hR}) are less than 0.75. We find this ratio to be nearly constant between 1-6 hR within individual galaxies. We find a sample average and scatter of <Fb^{2.2hR}>=0.57+/-0.07, with trends of larger Fb^{2.2hR} for more luminous and higher-surface-brightness galaxies. To enforce these being maximal, we need to scale M/L by a factor 3.6 on average. The DM rotation curves are marginally better fit by a pISO than by an NFW halo. For the nominal-M/L (submaximal) case, the derived NFW-halo parameters have values consistent with LCDM N-body simulations, suggesting that the baryonic matter has only had a minor effect on the DM distribution. In contrast, maximum-M/L decompositions yield halo concentrations that are too low compared to the LCDM simulations.

The Mass Distribution and Rotation Curve in the Galaxy

The mass distribution in the Galaxy is determined by dynamical and photometric methods. Rotation curves are the major tool for determining the dynamical mass distribution in the Milky Way and spiral galaxies. The photometric (statistical) method utilizes luminosity profiles from optical and infrared observations, and assumes empirical values of the mass-to-luminosity (M/L) ratio to convert the luminosity to mass. In this chapter the dynamical method is described in detail, and rotation curves and mass distribution in the Milky Way and nearby spiral galaxies are presented. The dynamical method is categorized into two methods: the decomposition method and direct method. The former fits the rotation curve by calculated curve assuming several mass components such as a bulge, disk and halo, and adjust the dynamical parameters of each component. Explanations are given of the mass profiles as the de Vaucouleurs law, exponential disk, and dark halo profiles inferred from numerical simulations. Another method is the direct method, with which the mass distribution can be directly calculated from the data of rotation velocities without employing any mass models. Some results from both methods are presented, and the Galactic structure is discussed in terms of the mass. Rotation curves and mass distributions in external galaxies are also discussed, and the fundamental mass structures are shown to be universal.

The DiskMass Survey. VI. Gas and stellar kinematics in spiral galaxies from PPak integral-field spectroscopy

We present ionized-gas (OIII) and stellar kinematics (velocities and velocity dispersions) for 30 nearly face-on spiral galaxies out to as much as three disk scale lengths (h_R). These data have been derived from PPak IFU spectroscopy (4980-5370A), observed at a mean resolution of R=7700 (sigma_inst=17km/s). These data are a fundamental product of our survey and will be used in companion papers to, e.g., derive the detailed (baryonic+dark) mass budget of each galaxy in our sample. Our presentation provides a comprehensive description of the observing strategy, data reduction, and analysis. Along with a clear presentation of the data, we demonstrate: (1) The OIII and stellar rotation curves exhibit a clear signature of asymmetric drift with a rotation difference that is 11% of the maximum rotation speed of the galaxy disk, comparable to measurements in the solar neighborhood in the Milky Way. (2) The e-folding length of the stellar velocity dispersion is two times h_R on average, as expected for a disk with a constant scale height and mass-to-light ratio, with a scatter that is notably smaller for massive, high-surface-brightness disks in the most luminous galaxies. (3) At radii larger than 1.5 h_R, the stellar velocity dispersion tends to decline slower than the best-fitting exponential function, which may be due to an increase in the disk mass-to-light ratio, disk flaring, or disk heating by the dark-matter halo. (4) A strong correlation exists between the central vertical stellar velocity dispersion of the disks and their circular rotational speed at 2.2 h_R, with a zero point indicating that galaxy disks are submaximal. Moreover, weak but consistent correlations exist such that disks with a fainter central surface brightness in bluer and less luminous galaxies of later morphological types are kinematically colder with respect to their rotational velocities.

Feebly Self-Interacting Cold Dark Matter: New theory for the Core-Halo structure in GLSB Galaxies

We explore the low energy cosmological dynamics of feebly self-interacting cold dark matter and propose a new simple explanation for the rotation curves of the core-halo model in massive LSB (Low Surface brightness)galaxies. We argue in favor of the truly collisionless nature of cold dark matter,which is feebly,self-interacting at small scales between epochs of equality and recombination.For this, we assume a model, wherein strongly coupled baryon-radiation plasma ejects out of small regions of concentrated cold dark matter without losing its equilibrium. We use the Merscerskii equation i.e. the variable mass formalism of classical dynamics.We obtain new results relating the oscillations in the CMB anisotropy to the ejection velocity of the baryon-radiation plasma,which can be useful tool for numerical work for exploring the second peak of CMB. Based on this model, we discuss the growth of perturbations in such a feebly self-interacting,cold dark matter both in the Jeans theory and in the expanding universe using Newton’s theory.We obtain an expression for the growth of fractional perturbations in cold dark matter,which reduce to the standard result of perturbation theory for late recombination epochs. We see the effect of the average of the perturbations in the cold dark matter potential on the cosmic microwave background temperature anisotropy that originated at redshifts between equality and recombination i.e. 1100 < z < z_{eq}. Also we obtain an expression for the Sachs-Wolfe effect,i.e. the CMB temperature anisotropy at decoupling in terms of the average of the perturbations in cold dark matter potential.

Feebly Self-Interacting Cold Dark Matter: New theory for the Core-Halo structure in GLSB Galaxies [Replacement]

We explore the low energy cosmological dynamics of feebly self-interacting cold dark matter and propose a new simple explanation for the rotation curves of the core-halo model in massive LSB (Low Surface brightness)galaxies. We argue in favor of the truly collisionless nature of cold dark matter,which is feebly,self-interacting at small scales between epochs of equality and recombination.For this, we assume a model, wherein strongly coupled baryon-radiation plasma ejects out of small regions of concentrated cold dark matter without losing its equilibrium. We use the Merscerskii equation i.e. the variable mass formalism of classical dynamics.We obtain new results relating the oscillations in the CMB anisotropy to the ejection velocity of the baryon-radiation plasma,which can be useful tool for numerical work for exploring the second peak of CMB. Based on this model, we discuss the growth of perturbations in such a feebly self-interacting,cold dark matter both in the Jeans theory and in the expanding universe using Newton’s theory.We obtain an expression for the growth of fractional perturbations in cold dark matter,which reduce to the standard result of perturbation theory for late recombination epochs. We see the effect of the average of the perturbations in the cold dark matter potential on the cosmic microwave background temperature anisotropy that originated at redshifts between equality and recombination i.e. 1100 < z < z_{eq}. Also we obtain an expression for the Sachs-Wolfe effect,i.e. the CMB temperature anisotropy at decoupling in terms of the average of the perturbations in cold dark matter potential.

Gravitational theoretical development supporting MOND [Cross-Listing]

Conformal geometry is considered within a general relativistic framework. An invariant distant for proper time is defined and a parallel displacement is applied in the distorted space-time, modifying Einstein’s equation appropriately. A particular solution is introduced for the covariant acceleration potential that matches the observed velocity distribution at large distances from the galactic centre, i.e. Modified Newtonian Dynamics (MOND). This explicit solution, of a general framework that allows both curvature and explicit local expansion of space-time, thus reproduces the observed flattening of galaxys’ rotation curves without the need to assume the existence of dark matter. The large distance expansion rate is found to match the speed of a spherical shock wave.

Possible existence of wormholes in the galactic halo region [Replacement]

Two observational results, the density profile from simulations performed in the $\Lambda$CDM scenario and the observed flat galactic rotation curves, are taken as input with the aim of showing that the galactic halo possesses some of the characteristics needed to support traversable wormholes. This result should be sufficient to provide an incentive for scientists to seek observational evidence for wormholes in the galactic halo region.

Possible existence of wormholes in the galactic halo region [Replacement]

Two observational results, the density profile from simulations performed in the $\Lambda$CDM scenario and the observed flat galactic rotation curves, are taken as input with the aim of showing that the galactic halo possesses some of the characteristics needed to support traversable wormholes. This result should be sufficient to provide an incentive for scientists to seek observational evidence for wormholes in the galactic halo region.

Possible existence of wormholes in the galactic halo region [Replacement]

Two observational results, the density profile from simulations performed in the $\Lambda$CDM scenario and the observed flat galactic rotation curves, are taken as input with the aim of showing that the galactic halo possesses some of the characteristics needed to support traversable wormholes. This result should be sufficient to provide an incentive for scientists to seek observational evidence for wormholes in the galactic halo region.

Possible existence of wormholes in the galactic halo region [Replacement]

Two observational results, the density profile from simulations performed in the $\Lambda$CDM scenario and the observed flat galactic rotation curves, are taken as input with the aim of showing that the galactic halo possesses some of the characteristics needed to support traversable wormholes. This result should be sufficient to provide an incentive for scientists to seek observational evidence for wormholes in the galactic halo region.

An empirical formula for the distribution function of a thin exponential disc

An empirical formula for a Shu distribution function that reproduces a thin disc with exponential surface density to good accuracy is presented. The formula has two free parameters that specify the functional form of the velocity dispersion. Conventionally, this requires the use of an iterative algorithm to produce the correct solution, which is computationally taxing for applications like Markov Chain Monte Carlo (MCMC) model fitting. The formula has been shown to work for flat, rising and falling rotation curves. Application of this methodology to one of the Dehnen distribution functions is also shown. Finally, an extension of this formula to reproduce velocity dispersion profiles that are an exponential function of radius is also presented. Our empirical formula should greatly aid the efficient comparison of disc models with large stellar surveys or N-body simulations.

The MOG weak field approximation and observational test of galaxy rotation curves [Replacement]

As an alternative to dark matter models, MOdified Gravity (MOG) theory can compensate for dark matter by a covariant modification of Einstein gravity. The theory introduces two additional scalar fields and one vector field. The aim is to explain the dynamics of astronomical systems based only on their baryonic matter. The effect of the vector field in the theory resembles a Lorentz force where each mass has a charge proportional to the inertial mass. In this work, we obtain the weak field approximation of MOG by perturbing the metric and the fields around Minkowski space-time. We derive an effective gravitational potential which yields the Newtonian attractive force plus a repulsive Yukawa force. This potential, in addition to the Newtonian gravitational constant, $G_N$, has two additional constant parameters $\alpha$ and $\mu$. We use the THINGS catalog of galaxies and fix the two parameters $\alpha$ and $\mu$ of the theory to be $\alpha =8.89 \pm 0.34$ and $\mu =0.04 \pm 0.004 {\rm kpc}^{-1}$. We then apply the effective potential with the fixed universal parameters to the Ursa-Major catalog of galaxies and obtain good fits to galaxy rotation curve data with an average value of $\bar{\chi^2} = 1.07$. In the fitting process, only the stellar mass-to-light ratio $(M/L)$ of the galaxies is a free parameter. As predictions of MOG, our derived $M/L$ is shown to be correlated with the color of galaxies, and we fit the Tully-Fisher relation for galaxies. As an alternative to dark matter, introducing an effective weak field potential for MOG opens a new window to the astrophysical applications of the theory.

The MOG weak field approximation and observational test of galaxy rotation curves [Replacement]

As an alternative to dark matter models, MOdified Gravity (MOG) theory can compensate for dark matter by a covariant modification of Einstein gravity. The theory introduces two additional scalar fields and one vector field. The aim is to explain the dynamics of astronomical systems based only on their baryonic matter. The effect of the vector field in the theory resembles a Lorentz force where each mass has a charge proportional to the inertial mass. In this work, we obtain the weak field approximation of MOG by perturbing the metric and the fields around Minkowski space-time. We derive an effective gravitational potential which yields the Newtonian attractive force plus a repulsive Yukawa force. This potential, in addition to the Newtonian gravitational constant, $G_N$, has two additional constant parameters $\alpha$ and $\mu$. We use the THINGS catalog of galaxies and fix the two parameters $\alpha$ and $\mu$ of the theory to be $\alpha =8.89 \pm 0.34$ and $\mu =0.04 \pm 0.004 {\rm kpc}^{-1}$. We then apply the effective potential with the fixed universal parameters to the Ursa-Major catalog of galaxies and obtain good fits to galaxy rotation curve data with an average value of $\bar{\chi^2} = 1.07$. In the fitting process, only the stellar mass-to-light ratio $(M/L)$ of the galaxies is a free parameter. As predictions of MOG, our derived $M/L$ is shown to be correlated with the color of galaxies, and we fit the Tully-Fisher relation for galaxies. As an alternative to dark matter, introducing an effective weak field potential for MOG opens a new window to the astrophysical applications of the theory.

The MOG weak field approximation and observational test of galaxy rotation curves

As an alternative to dark matter models, MOdified Gravity (MOG) theory can compensate for dark matter by a covariant modification of Einstein gravity. The theory introduces two additional scalar fields and one vector field. The aim is to explain the dynamics of astronomical systems based only on their baryonic matter. The effect of the vector field in the theory resembles a Lorentz force where each mass has a charge proportional to the inertial mass. In this work, we obtain the weak field approximation of MOG by perturbing the metric and the fields around Minkowski space-time. We derive an effective gravitational potential which yields the Newtonian attractive force plus a repulsive Yukawa force. This potential, in addition to the Newtonian gravitational constant, $G_N$, has two additional constant parameters $\alpha$ and $\mu$. We use the THINGS catalog of galaxies and fix the two parameters $\alpha$ and $\mu$ of the theory to be $\alpha =8.89 \pm 0.34$ and $\mu =0.04 \pm 0.004 {\rm kpc}^{-1}$. We then apply the effective potential with the fixed universal parameters to the Ursa-Major catalog of galaxies and obtain good fits to galaxy rotation curve data with an average value of $\bar{\chi^2} = 1.07$. In the fitting process, only the stellar mass-to-light ratio $(M/L)$ of the galaxies is a free parameter. As predictions of MOG, our derived $M/L$ is shown to be correlated with the color of galaxies, and we fit the Tully-Fisher relation for galaxies. As an alternative to dark matter, introducing an effective weak field potential for MOG opens a new window to the astrophysical applications of the theory.

The MOG weak field approximation and observational test of galaxy rotation curves [Replacement]

As an alternative to dark matter models, MOdified Gravity (MOG) theory can compensate for dark matter by a covariant modification of Einstein gravity. The theory introduces two additional scalar fields and one vector field. The aim is to explain the dynamics of astronomical systems based only on their baryonic matter. The effect of the vector field in the theory resembles a Lorentz force where each mass has a charge proportional to the inertial mass. In this work, we obtain the weak field approximation of MOG by perturbing the metric and the fields around Minkowski space-time. We derive an effective gravitational potential which yields the Newtonian attractive force plus a repulsive Yukawa force. This potential, in addition to the Newtonian gravitational constant, $G_N$, has two additional constant parameters $\alpha$ and $\mu$. We use the THINGS catalog of galaxies and fix the two parameters $\alpha$ and $\mu$ of the theory to be $\alpha =8.89 \pm 0.34$ and $\mu =0.04 \pm 0.004 {\rm kpc}^{-1}$. We then apply the effective potential with the fixed universal parameters to the Ursa-Major catalog of galaxies and obtain good fits to galaxy rotation curve data with an average value of $\bar{\chi^2} = 1.07$. In the fitting process, only the stellar mass-to-light ratio $(M/L)$ of the galaxies is a free parameter. As predictions of MOG, our derived $M/L$ is shown to be correlated with the color of galaxies, and we fit the Tully-Fisher relation for galaxies. As an alternative to dark matter, introducing an effective weak field potential for MOG opens a new window to the astrophysical applications of the theory.

Evolution of the gas kinematics of galaxies in cosmological simulations

We studied the evolution of the gas kinematics of galaxies by performing hydrodynamical simulations in a cosmological scenario. We paid special attention to the origin of the scatter of the Tully-Fisher relation and the features which could be associated with mergers and interactions. We extended the study by De Rossi et al. (2010) and analysed their whole simulated sample which includes both, gas disc-dominated and spheroid-dominated systems. We found that mergers and interactions can affect the rotation curves directly or indirectly inducing a scatter in the Tully-Fisher Relation larger than the simulated evolution since z=3. In agreement with previous works, kinematical indicators which combine the rotation velocity and dispersion velocity in their definitions lead to a tighter relation. In addition, when we estimated the rotation velocity at the maximum of the rotation curve, we obtained the best proxy for the potential well regardless of morphology.

Towards the Chalonge Meudon Workshop 2013. Highlights and Conclusions of the Chalonge Meudon workshop 2012: warm dark matter galaxy formation in agreement with observations

Warm Dark Matter(WDM), considerably clarifies and simplifies galaxies and galaxy formation in agreement with observations. WDM essentially works, naturally reproducing the astronomical observations over all scales, small (galactic) as well as large and cosmological scales.Evidence that CDM, CDM+baryons and proposed tailored cures do not work in galaxies is staggering, The Chalonge Meudon Workshop 2012 approached DM in a fourfold coherent way: astronomical observations (galaxy and cluster properties, haloes, rotation curves, density profiles, surface density), LambdaWDM N-body simulations, WDM theory (Boltzmann-Vlasov evolution, halo mass functions, halo models, improved perturbative approachs), quantum WDM fermions forming the observed cores, WDM particle and nuclear physics (sterile neutrinos) and its experimental search. N Amorisco, P Biermann, S Das, H J de Vega, A Kamada, E Ferri(MARE),I D Karanchetsev, W Liao, M Lovell, M Papastergis, N G Sanchez, P Valageas,C Watson, J Zavala,He Zhang present their Highlights.Inside galaxy cores, N-body classical physics simulations are incorrect for WDM because of important quantum effects at such scales.Quantum WDM calculations (Thomas-Fermi) provide galaxy cores, galaxy masses, velocity dispersions and density profiles in agreement with observations.Baryons (16% of DM) are expected to give a correction to pure WDM results. The summary and conclusions by H. J. de Vega and N. G. Sanchez stress that all evidences point to a DM particle mass around 2 keV. Peter Biermann in his live minutes concludes that a few keV sterile neutrino is the most serious DM candidate. MARE -and hopefully KATRIN- could provide a sterile neutrino signal.There is a formidable WDM work to perform ahead of us, these highlights point research directions worthwhile to pursue.Photos of the Workshop are included (Abridged).

Towards the Chalonge Meudon Workshop 2013. Highlights and Conclusions of the Chalonge Meudon workshop 2012: warm dark matter galaxy formation in agreement with observations [Replacement]

Warm Dark Matter(WDM), considerably clarifies and simplifies galaxies and galaxy formation in agreement with observations. WDM essentially works, naturally reproducing the astronomical observations over all scales, small (galactic) as well as large and cosmological scales.Evidence that CDM, CDM+baryons and proposed tailored cures do not work in galaxies is staggering, The Chalonge Meudon Workshop 2012 approached DM in a fourfold coherent way: astronomical observations (galaxy and cluster properties, haloes, rotation curves, density profiles, surface density), LambdaWDM N-body simulations, WDM theory (Boltzmann-Vlasov evolution, halo mass functions, halo models, improved perturbative approachs), quantum WDM fermions forming the observed cores, WDM particle and nuclear physics (sterile neutrinos) and its experimental search. N Amorisco, P Biermann, S Das, H J de Vega, A Kamada, E Ferri(MARE),I D Karanchetsev, W Liao, M Lovell, M Papastergis, N G Sanchez, P Valageas,C Watson, J Zavala,He Zhang present their Highlights.Inside galaxy cores, N-body classical physics simulations are incorrect for WDM because of important quantum effects at such scales.Quantum WDM calculations (Thomas-Fermi) provide galaxy cores, galaxy masses, velocity dispersions and density profiles in agreement with observations.Baryons (16% of DM) are expected to give a correction to pure WDM results. The summary and conclusions by H. J. de Vega and N. G. Sanchez stress that all evidences point to a DM particle mass around 2 keV. Peter Biermann in his live minutes concludes that a few keV sterile neutrino is the most serious DM candidate. MARE -and hopefully KATRIN- could provide a sterile neutrino signal.There is a formidable WDM work to perform ahead of us, these highlights point research directions worthwhile to pursue.Photos of the Workshop are included (Abridged).

Gas rotation in galaxy clusters: signatures and detectability in X-rays [Replacement]

We study simple models of massive galaxy clusters in which the intracluster medium (ICM) rotates differentially in equilibrium in the cluster gravitational potential. We obtain the X-ray surface brightness maps, evaluating the isophote flattening due to the gas rotation. Using a set of different rotation laws, we put constraint on the amplitude of the rotation velocity, finding that rotation curves with peak velocity up to \sim 600 km s^-1 are consistent with the ellipticity profiles of observed clusters. We convolve each of our models with the instrument response of the X-ray Calorimeter Spectrometer on board the ASTRO-H to calculate the simulated X-ray spectra at different distance from the X-ray centre. We demonstrate that such an instrument will allow us to measure rotation of the ICM in massive clusters, even with rotation velocities as low as \sim 100 km s^-1

Gas rotation in galaxy clusters: signatures and detectability in X-rays

We study simple models of massive galaxy clusters in which the intracluster medium (ICM) rotates differentially in equilibrium in the cluster gravitational potential. We obtain the X-ray surface brightness maps, evaluating the isophote flattening due to the gas rotation. Using a set of different rotation laws, we put constraint on the amplitude of the rotation velocity, finding that rotation curves with peak velocity up to \sim 600 km s^-1 are consistent with the ellipticity profiles of observed clusters. We convolve each of our models with the instrument response of the X-ray Calorimeter Spectrometer on board the ASTRO-H to calculate the simulated X-ray spectra at different distance from the X-ray centre. We demonstrate that such an instrument will allow us to measure rotation of the ICM in massive clusters, even with rotation velocities as low as \sim 100 km s^-1

Gas rotation in galaxy clusters: signatures and detectability in X-rays [Replacement]

We study simple models of massive galaxy clusters in which the intracluster medium (ICM) rotates differentially in equilibrium in the cluster gravitational potential. We obtain the X-ray surface brightness maps, evaluating the isophote flattening due to the gas rotation. Using a set of different rotation laws, we put constraint on the amplitude of the rotation velocity, finding that rotation curves with peak velocity up to \sim 600 km s^-1 are consistent with the ellipticity profiles of observed clusters. We convolve each of our models with the instrument response of the X-ray Calorimeter Spectrometer on board the ASTRO-H to calculate the simulated X-ray spectra at different distance from the X-ray centre. We demonstrate that such an instrument will allow us to measure rotation of the ICM in massive clusters, even with rotation velocities as low as \sim 100 km s^-1

The formation of disc galaxies in high resolution moving-mesh cosmological simulations

We present cosmological hydrodynamical simulations of eight Milky Way-sized haloes that have been previously studied with dark matter only in the Aquarius project. For the first time, we employ the moving-mesh code AREPO in zoom simulations combined with a new comprehensive model for galaxy formation physics designed for large cosmological simulations. Our simulations form in most of the eight haloes strongly disc-dominated systems with realistic rotation curves, close to exponential surface density profiles, a stellar-mass to halo-mass ratio that matches expectations from abundance matching techniques, and galaxy sizes and ages consistent with expectations from large galaxy surveys in the local Universe. There is no evidence for any dark matter core formation in our simulations, even so they include repeated baryonic outflows by supernova-driven winds and black hole quasar feedback. The simulations significantly improve upon the results obtained for the same objects in some of the earlier work based on the SPH technique, and also on the results obtained in the recent `Aquila’ code comparison project which focused on one of the haloes from our set. For this Aquila object, we carried out a resolution study with our techniques, covering a dynamic range of 64 in mass resolution. Without any change in our feedback parameters, the final galaxy properties are reassuringly similar, in contrast to other modeling techniques used in the field that are inherently resolution dependent. This success in producing realistic disc galaxies is reached without resorting to a high density threshold for star formation, a low star formation efficiency, or early stellar feedback, factors deemed crucial for disc formation by other recent numerical studies.

WSRT observations and surface photometry of two unusual spiral galaxies

We discuss the results of a mass decomposition of two spiral galaxies, NGC 6824 and UGC 11919. In a previous analysis of the Hyperleda catalog, the galaxies were identified as having a peculiar dynamical $M/L$. The aim of this study is to confirm or disprove the preliminary findings, indicating a non-standard stellar initial mass function (IMF) for the galaxies. The surface photometry in B, V, and R bands was carried out with the Apache Point 0.5-m telescope and the \ion{H}{I} data cubes were obtained with the Westerbork Synthesis Radio Telescope (WSRT). Photometric profiles were decomposed into bulge and exponential disk components. Using the obtained \ion{H}{I} data cubes, rotation curves of both galaxies were constructed. Employing the photometric profiles, the mass distribution of the galaxies was decomposed into mass components: bulge, stellar disk, gas, and pseudo-isothermal dark halo. We conclude that NGC 6824 possesses a stellar disk with mass-to-light ratio $(M/L_B)_{\rm disk} = 2.5$, in agreement with its color $(B-V)_0$. On the contrary, UGC 11919 appears to have a very lightweight disk. Its dynamically estimated mass corresponds to a low stellar disk mass-to-light ratio $(M/L_B)_{\rm disk} \approx 0.5$. Under standard assumptions, this ratio does not agree with the relatively red color of the disk, while a bottom light stellar initial mass function is needed to explain the observations.

Kinematic classification of non-interacting spiral galaxies

Using neutral hydrogen (HI) rotation curves of 79 galaxies, culled from the literature, as well as measured from HI data, we present a method for classifying disk galaxies by their kinematics. In order to investigate fundamental kinematic properties we concentrate on non-interacting spiral galaxies. We employ a simple parameterized form for the rotation curve in order to derive the three parameters: the maximum rotational velocity, the turnover radius and a measure of the slope of the rotation curve beyond the turnover radius. Our approach uses the statistical Hierarchical Clustering method to guide our division of the resultant 3D distribution of galaxies into five classes. Comparing the kinematic classes in this preliminary classification scheme to a number of galaxy properties we find that our class containing galaxies with the largest rotational velocities has a mean morphological type of Sb/Sbc while the other classes tend to later types. Other trends also generally agree with those described by previous researchers. In particular we confirm correlations between increasing maximum rotational velocity and the following observed properties: increasing brightness in B-band, increasing size of the optical disk (D_25) and increasing star formation rate (as derived using radio continuum data). Our analysis also suggests that lower velocities are associated with a higher ratio of the HI mass over the dynamical mass. Additionally, three galaxies exhibit a drop in rotational velocity amplitude of >~ 20% after the turnover radius. However recent investigations suggest that they have interacted with minor companions which is a common cause for declining rotation curves. (Figures 12, 14, 16 and 17 are interactive in the electronic pdf version of this paper.)

Effects of spacetime anisotropy on the galaxy rotation curves [Replacement]

The observations on galaxy rotation curves show significant discrepancies from the Newtonian theory. This issue could be explained by the effect of the anisotropy of the spacetime. Conversely, the spacetime anisotropy could also be constrained by the galaxy rotation curves. Finsler geometry is a kind of intrinsically anisotropic geometry. In this paper, we study the effect of the spacetime anisotropy at the galactic scales in the Finsler spacetime. It is found that the Finslerian model has close relations with the Milgrom’s MOND. By performing the best-fit procedure to the galaxy rotation curves, we find that the anisotropic effects of the spacetime become significant when the Newtonian acceleration $GM/r^2$ is smaller than the critical acceleration $a_0$. Interestingly, the critical acceleration $a_0$, although varies between different galaxies, is in the order of magnitude $cH_0/2\pi\sim 10^{-10} \rm{m\,\, s^{-2}}$.

Effects of spacetime anisotropy on the galaxy rotation curves

The observations on galaxy rotation curves show significant discrepancies from the Newtonian theory. This issue could be explained by the effect of the anisotropy of the spacetime. Conversely, the spacetime anisotropy could also be constrained by the galaxy rotation curves. Finsler geometry is a kind of intrinsically anisotropic geometry. In this paper, we study the effect of the spacetime anisotropy at the galactic scales in the Finsler spacetime. It is found that the Finslerian model has close relations with the Milgrom’s MOND. By performing the best-fit procedure to the galaxy rotation curves, we find that the anisotropic effects of the spacetime become significant when the Newtonian acceleration $GM/r^2$ is smaller than the critical acceleration $a_0$. Interestingly, the critical acceleration $a_0$, although varies between different galaxies, is in the order of magnitude $cH_0/2\pi\sim 10^{-10} \rm{m\,\, s^{-2}}$.