# Posts Tagged rotation curves

## Recent Postings from rotation curves

### On possible tachyonic state of neutrino dark matter [Cross-Listing]

We revive the historically first dark matter model based on neutrinos, but with an additional assumption that neutrinos might exist in tachyonic almost sterile states. To this end, we propose a group-theoretical algorithm for the description of tachyons. The key point is that we employ a distinct tachyon Lorentz group with new (superluminal) parametrization which does not lead to violation of causality and unitarity. Our dark matter model represents effectively scalar tachyonic neutrino-antineutrino conglomerate. Distributed all over the universe, such fluid behaves as stable isothermal/stiff medium which produces somewhat denser regions (halos') around galaxies and clusters. To avoid the central singularity inherent to the isothermal profile, we apply a special smoothing algorithm which yields density distributions and rotation curves consistent with observational data.

### On possible tachyonic state of neutrino dark matter [Cross-Listing]

We revive the historically first dark matter model based on neutrinos, but with an additional assumption that neutrinos might exist in tachyonic almost sterile states. To this end, we propose a group-theoretical algorithm for the description of tachyons. The key point is that we employ a distinct tachyon Lorentz group with new (superluminal) parametrization which does not lead to violation of causality and unitarity. Our dark matter model represents effectively scalar tachyonic neutrino-antineutrino conglomerate. Distributed all over the universe, such fluid behaves as stable isothermal/stiff medium which produces somewhat denser regions (halos') around galaxies and clusters. To avoid the central singularity inherent to the isothermal profile, we apply a special smoothing algorithm which yields density distributions and rotation curves consistent with observational data.

### Halpha Kinematics of S4G Spiral Galaxies - III. Inner rotation curves

We present a detailed study of the shape of the innermost part of the rotation curves of a sample of 29 nearby spiral galaxies, based on high angular and spectral resolution kinematic Halpha Fabry-Perot observations. In particular, we quantify the steepness of the rotation curve by measuring its slope dRvc(0). We explore the relationship between the inner slope and several galaxy parameters, such as stellar mass, maximum rotational velocity, central surface brightness ({\mu}0), bar strength and bulge-to-total ratio. Even with our limited dynamical range, we find a trend for low-mass galaxies to exhibit shallower rotation curve inner slopes than high-mass galaxies, whereas steep inner slopes are found exclusively in high-mass galaxies. This trend may arise from the relationship between the total stellar mass and the mass of the bulge, which are correlated among them. We find a correlation between the inner slope of the rotation curve and the morphological T-type, complementary to the scaling relation between dRvc(0) and {\mu}0 previously reported in the literature. Although we find that the inner slope increases with the Fourier amplitude A2 and decreases with the bar torque Qb, this may arise from the presence of the bulge implicit in both A2 and Qb. As previously noted in the literature, the more compact the mass in the central parts of a galaxy (more concretely, the presence of a bulge), the steeper the inner slopes. We conclude that the baryonic matter dominates the dynamics in the central parts of our sample galaxies.

### Dark matter as a condensate: Deduction of microscopic properties

In the present work we model dark matter as a Bose-Einstein condensate and the main goal is the deduction of the microscopic properties, namely, mass, number of particles, and scattering length, related to the particles comprised in the corresponding condensate. This task is done introducing in the corresponding model the effects of the thermal cloud of the system. Three physical conditions are imposed, i.e., mechanical equilibrium of the condensate, explanation of the rotation curves of stars belonging to dwarf galaxies, and, finally, the deflection of light due to the presence of dark matter. These three aforementioned expressions allow us to cast the features of the particles in terms of detectable astrophysical variables. Finally, the model is contrasted against observational data and in this manner we obtain values for the involved microscopic parameters of the condensate. The deduced results are compared with previous results in which dark matter has not been considered a condensate. The main conclusion is that they do not coincide.

### Modified Dark Matter [Cross-Listing]

Modified dark matter (MDM, formerly known as MoNDian dark matter) is a phenomenological model of dark matter, inspired by quantum gravity. We review the construction of MDM by generalizing entropic gravity to de-Sitter space as is appropriate for an accelerating universe (in accordance with the Lambda-CDM model). Unlike cold dark matter models, the MDM mass profile depends on the baryonic mass. We successfully fit the rotation curves to a sample of 30 local spiral galaxies with a single free parameter (viz., the mass-to-light ratio for each galaxy). We show that dynamical and observed masses agree in a sample of 93 galactic clusters. We also comment on strong gravitational lensing in the context of MDM.

### Modified Dark Matter [Cross-Listing]

Modified dark matter (MDM, formerly known as MoNDian dark matter) is a phenomenological model of dark matter, inspired by quantum gravity. We review the construction of MDM by generalizing entropic gravity to de-Sitter space as is appropriate for an accelerating universe (in accordance with the Lambda-CDM model). Unlike cold dark matter models, the MDM mass profile depends on the baryonic mass. We successfully fit the rotation curves to a sample of 30 local spiral galaxies with a single free parameter (viz., the mass-to-light ratio for each galaxy). We show that dynamical and observed masses agree in a sample of 93 galactic clusters. We also comment on strong gravitational lensing in the context of MDM.

### Modified Dark Matter

Modified dark matter (MDM, formerly known as MoNDian dark matter) is a phenomenological model of dark matter, inspired by quantum gravity. We review the construction of MDM by generalizing entropic gravity to de-Sitter space as is appropriate for an accelerating universe (in accordance with the Lambda-CDM model). Unlike cold dark matter models, the MDM mass profile depends on the baryonic mass. We successfully fit the rotation curves to a sample of 30 local spiral galaxies with a single free parameter (viz., the mass-to-light ratio for each galaxy). We show that dynamical and observed masses agree in a sample of 93 galactic clusters. We also comment on strong gravitational lensing in the context of MDM.

### Tachyonic models of dark matter

We consider a spherically symmetric stationary problem in General Relativity, including a black hole, inflow of normal and tachyonic matter and outflow of tachyonic matter. Computations in a weak field limit show that the resulting concentration of matter around the black hole leads to gravitational effects equivalent to those associated with dark matter halo. In particular, the model reproduces asymptotically constant galactic rotation curves, if the tachyonic flows of the central supermassive black hole in the galaxy are considered as a main contribution.

### Tachyonic models of dark matter [Cross-Listing]

We consider a spherically symmetric stationary problem in General Relativity, including a black hole, inflow of normal and tachyonic matter and outflow of tachyonic matter. Computations in a weak field limit show that the resulting concentration of matter around the black hole leads to gravitational effects equivalent to those associated with dark matter halo. In particular, the model reproduces asymptotically constant galactic rotation curves, if the tachyonic flows of the central supermassive black hole in the galaxy are considered as a main contribution.

### Asymmetric mass models of disk galaxies - I. Messier 99 [Replacement]

Mass models of galactic disks traditionally rely on axisymmetric density and rotation curves, paradoxically acting as if their most remarkable asymmetric features, such as lopsidedness or spiral arms, were not important. In this article, we relax the axisymmetry approximation and introduce a methodology that derives 3D gravitational potentials of disk-like objects and robustly estimates the impacts of asymmetries on circular velocities in the disk midplane. Mass distribution models can then be directly fitted to asymmetric line-of-sight velocity fields. Applied to the grand-design spiral M99, the new strategy shows that circular velocities are highly nonuniform, particularly in the inner disk of the galaxy, as a natural response to the perturbed gravitational potential of luminous matter. A cuspy inner density profile of dark matter is found in M99, in the usual case where luminous and dark matter share the same center. The impact of the velocity nonuniformity is to make the inner profile less steep, although the density remains cuspy. On another hand, a model where the halo is core dominated and shifted by 2.2-2.5 kpc from the luminous mass center is more appropriate to explain most of the kinematical lopsidedness evidenced in the velocity field of M99. However, the gravitational potential of luminous baryons is not asymmetric enough to explain the kinematical lopsidedness of the innermost regions, irrespective of the density shape of dark matter. This discrepancy points out the necessity of an additional dynamical process in these regions: possibly a lopsided distribution of dark matter.

### Asymmetric mass models of disk galaxies - I. Messier 99

Mass models of galactic disks traditionnally rely on axisymmetric density and rotation curves, paradoxically acting as if their most remarkable asymmetric features, like e.g. lopsidedness or spiral arms, were not important. In this article, we relax the axisymmetry approximation and introduce a methodology that derives 3D gravitational potentials of disk-like objects and robustly estimates the impacts of asymmetries on circular velocities in the disk mid-plane. Mass distribution models can then be directly fitted to asymmetric line-of-sight velocity fields. Applied to the grand-design spiral M99, the new strategy shows that circular velocities are highly non-uniform, particularly in the inner disk of the galaxy, as a natural response to the perturbed gravitational potential of luminous matter. A cuspy inner density profile of dark matter is found in M99, in the usual case where luminous and dark matter share the same centre. The impact of the velocity non-uniformity is to make the inner profile less steep, though the density remains cuspy. On another hand, a model where the halo is core-dominated and shifted by 2.2-2.5 kpc from the luminous mass centre is more appropriate to account for most of the kinematical lopsidedness evidenced in the velocity field of M99. However, the gravitational potential of luminous baryons is not asymmetric enough to explain the kinematical lopsidedness of the innermost regions, irrespective of the density shape of dark matter. This discrepancy points out the necessity of an additional dynamical process in these regions, maybe a lopsided distribution of dark matter.

### Scale dynamical origin of modification or addition of potential in mechanics. A possible framework for the MOND theory and the dark matter [Cross-Listing]

Using our mathematical framework developed in \cite{cresson-pierret_scale} called \emph{scale dynamics}, we propose in this paper a new way of interpreting the problem of adding or modifying potentials in mechanics and specifically in galactic dynamics. An application is done for the two-body problem with a Keplerian potential showing that the velocity of the orbiting body is constant. This would explain the observed phenomenon in the flat rotation curves of galaxies without adding \emph{dark matter} or modifying Newton's law of dynamics.

### The Impact of Molecular Gas on Mass Models of Nearby Galaxies

We present CO velocity fields and rotation curves for a sample of nearby galaxies, based on data from the HERACLES survey. We combine our data with literature THINGS, SINGS and KINGFISH results to provide a comprehensive sample of mass models of disk galaxies inclusive of molecular gas. We compare the kinematics of the molecular (CO from HERACLES) and atomic (${\rm H{\scriptstyle I}}$ from THINGS) gas distributions to determine the extent to which CO may be used to probe the dynamics in the inner part of galaxies. In general, we find good agreement between the CO and ${\rm H{\scriptstyle I}}$ kinematics with small differences in the inner part of some galaxies. We add the contribution of the molecular gas to the mass models in our galaxies by using two different conversion factors $\mathrm{\alpha_{CO}}$ to convert CO luminosity to molecular gas mass surface density - the constant Milky Way value and the radially varying profiles determined in recent work based on THINGS, HERACLES and KINGFISH data. We study the relative effect that the addition of the molecular gas has upon the halo rotation curves for Navarro-Frenk-White (NFW) and the observationally motivated pseudo-isothermal halos. The contribution of the molecular gas varies for galaxies in our sample - for those galaxies where there is a substantial molecular gas content, using different values of $\mathrm{\alpha_{CO}}$ can result in significant differences to the relative contribution of the molecular gas and, hence, the shape of the dark matter halo rotation curves in the central regions of galaxies.

### Three-Dimensional Distribution of the ISM in the Milky Way Galaxy: III. The Total Neutral Gas Disk

We present newly obtained three-dimensional gaseous maps of the Milky Way Galaxy; HI, H$_2$ and total-gas (HI plus H$_2$) maps, which were derived from the HI and $^{12}$CO($J=1$--0) survey data and rotation curves based on the kinematic distance. The HI and H$_2$ face-on maps show that the HI disk is extended to the radius of 15--20 kpc and its outskirt is asymmetric to the Galactic center, while most of the H$_2$ gas is distributed inside the solar circle. The total gas mass within radius 30 kpc amounts to $8.0\times 10^9$ M$_\odot$, 89\% and 11\% of which are HI and H$_2$, {respectively}. The vertical slices show that the outer HI disk is strongly warped and the inner HI and H$_2$ disks are corrugated. The total gas map is advantageous to trace spiral structure from the inner to outer disk. Spiral structures such as the Norma-Cygnus, the Perseus, the Sagittarius-Carina, the Scutum-Crux, and the Orion arms are more clearly traced in the total gas map than ever. All the spiral arms are well explained with logarithmic spiral arms with pitch angle of $11\degree$ -- $15\degree$. The molecular fraction to the total gas is high near the Galactic center and decreases with the Galactocentric distance. The molecular fraction also locally enhanced at the spiral arms compared with the inter-arm regions.

### Kinematics of dwarf galaxies in gas-rich groups, and the survival and detectability of tidal dwarf galaxies

We present DEIMOS multi-object spectroscopy (MOS) of 22 star-forming dwarf galaxies located in four gas-rich groups, including six newly-discovered dwarfs. Two of the galaxies are strong tidal dwarf galaxy (TDG) candidates based on our luminosity-metallicity relation definition. We model the rotation curves of these galaxies. Our sample shows low mass-to-light ratios (M/L=0.73$\pm0.39M_\odot/L_\odot$) as expected for young, star-forming dwarfs. One of the galaxies in our sample has an apparently strongly-falling rotation curve, reaching zero rotational velocity outside the turnover radius of $r_{turn}=1.2r_e$. This may be 1) a polar ring galaxy, with a tilted bar within a face-on disk; 2) a kinematic warp. These scenarios are indistinguishable with our current data due to limitations of slit alignment inherent to MOS-mode observations. We consider whether TDGs can be detected based on their tidal radius, beyond which tidal stripping removes kinematic tracers such as H$\alpha$ emission. When the tidal radius is less than about twice the turnover radius, the expected falling rotation curve cannot be reliably measured. This is problematic for as much as half of our sample, and indeed more generally, galaxies in groups like these. Further to this, the H$\alpha$ light that remains must be sufficiently bright to be detected; this is only the case for three (14%) galaxies in our sample. We conclude that the falling rotation curves expected of tidal dwarf galaxies are intrinsically difficult to detect.

### Rotation Curve Decomposition for Size-Mass Relations of Bulge, Disk, and Dark Halo in Spiral Galaxies

Rotation curves of more than one hundred spiral galaxies were compiled from the literature, and deconvolved into bulge, disk, and dark halo using $\chi^2$ fitting in order to determine their scale radii and masses. Correlation analyses were obtained of the fitting parameters for galaxies that satisfied selection and accuracy criteria. Size-mass relations indicate that the sizes and masses are positively correlated among different components in such a way that the larger or more massive is the dark halo, the larger or more massive are the disk and bulge. Empirical size-mass relations were obtained for bulge, disk and dark halo by the least-squares fitting. The disk-to-halo mass ratio was found to be systematically greater by a factor of three than that predicted by cosmological simulations combined with photometry. A preliminary mass function for dark halo was obtained, which is represented by the Schechter function followed by a power law.

### The Case Against Dark Matter and Modified Gravity: Flat Rotation Curves Are a Rigorous Requirement in Rotating Self-Gravitating Newtonian Gaseous Disks

By solving analytically the various types of Lane-Emden equations with rotation, we have discovered two new coupled fundamental properties of rotating, self-gravitating, gaseous disks in equilibrium: Isothermal disks must, on average, exhibit strict power-law density profiles in radius $x$ on their equatorial planes of the form $A x^{k-1}$, where $A$ and $k-1$ are the integration constants; and flat'' rotation curves precisely such as those observed in spiral galaxy disks. Polytropic disks must, on average, exhibit strict density profiles of the form $\left[\ln(A x^k)\right]^n$, where $n$ is the polytropic index; and flat'' rotation curves described by square roots of upper incomplete gamma functions. By on average,'' we mean that, irrespective of the chosen boundary conditions, the actual profiles must oscillate around and remain close to the strict mean profiles of the analytic singular equilibrium solutions. We call such singular solutions the intrinsic'' solutions of the differential equations because they are demanded by the second-order equations themselves with no regard to the Cauchy problem. The results are directly applicable to gaseous galaxy disks that have long been known to be isothermal and to protoplanetary disks during the extended isothermal and adiabatic phases of their evolution. In galactic gas dynamics, they have the potential to resolve the dark matter--modified gravity controversy in a sweeping manner, as they render both of these hypotheses unnecessary. In protoplanetary disk research, they provide observers with powerful new probing tool, as they predict a clear and simple connection between the radial density profiles and the rotation curves of self-gravitating disks in their very early (pre-Class 0 and perhaps the youngest Class Young Stellar Objects) phases of evolution.

### The Case Against Dark Matter and Modified Gravity: Flat Rotation Curves Are a Rigorous Requirement in Rotating Self-Gravitating Newtonian Gaseous Disks [Replacement]

By solving analytically the various types of Lane-Emden equations with rotation, we have discovered two new coupled fundamental properties of rotating, self-gravitating, gaseous disks in equilibrium: Isothermal disks must, on average, exhibit strict power-law density profiles in radius $x$ on their equatorial planes of the form $A x^{k-1}$, where $A$ and $k-1$ are the integration constants, and "flat" rotation curves precisely such as those observed in spiral galaxy disks. Polytropic disks must, on average, exhibit strict density profiles of the form $\left[\ln(A x^k)\right]^n$, where $n$ is the polytropic index, and "flat" rotation curves described by square roots of upper incomplete gamma functions. By "on average," we mean that, irrespective of the chosen boundary conditions, the actual profiles must oscillate around and remain close to the strict mean profiles of the analytic singular equilibrium solutions. We call such singular solutions the "intrinsic" solutions of the differential equations because they are demanded by the second-order equations themselves with no regard to the Cauchy problem. The results are directly applicable to gaseous galaxy disks that have long been known to be isothermal and to protoplanetary disks during the extended isothermal and adiabatic phases of their evolution. In galactic gas dynamics, they have the potential to resolve the dark matter--modified gravity controversy in a sweeping manner, as they render both of these hypotheses unnecessary. In protoplanetary disk research, they provide observers with powerful new probing tool, as they predict a clear and simple connection between the radial density profiles and the rotation curves of self-gravitating disks in their very early (pre-Class 0 and perhaps the youngest Class Young Stellar Objects) phases of evolution.

### Static spherically symmetric solutions in mimetic gravity: rotation curves & wormholes [Replacement]

In this work, we analyse static spherically symmetric solutions in the framework of mimetic gravity, an extension of general relativity where the conformal degree of freedom of gravity is isolated in a covariant fashion. Here we extend previous works by considering in addition a potential for the mimetic field. An appropriate choice of such potential allows for the reconstruction of a number of interesting cosmological and astrophysical scenarios. We explicitly show how to reconstruct such a potential for a general static spherically symmetric space-time. A number of applications and scenarios are then explored, among which traversable wormholes. Finally, we analytically reconstruct potentials which leads to solutions to the equations of motion featuring polynomial corrections to the Schwarzschild spacetime. Accurate choices for such corrections could provide an explanation for the inferred flat rotation curves of spiral galaxies within the mimetic gravity framework, without the need for particle dark matter.

### Static spherically symmetric solutions in mimetic gravity: rotation curves & wormholes [Replacement]

In this work, we analyse static spherically symmetric solutions in the framework of mimetic gravity, an extension of general relativity where the conformal degree of freedom of gravity is isolated in a covariant fashion. Here we extend previous works by considering in addition a potential for the mimetic field. An appropriate choice of such potential allows for the reconstruction of a number of interesting cosmological and astrophysical scenarios. We explicitly show how to reconstruct such a potential for a general static spherically symmetric space-time. A number of applications and scenarios are then explored, among which traversable wormholes. Finally, we analytically reconstruct potentials which leads to solutions to the equations of motion featuring polynomial corrections to the Schwarzschild spacetime. Accurate choices for such corrections could provide an explanation for the inferred flat rotation curves of spiral galaxies within the mimetic gravity framework, without the need for particle dark matter.

### Static spherically symmetric solutions in mimetic gravity: rotation curves & wormholes [Replacement]

In this work, we analyse static spherically symmetric solutions in the framework of mimetic gravity, an extension of general relativity where the conformal degree of freedom of gravity is isolated in a covariant fashion. Here we extend previous works by considering in addition a potential for the mimetic field. An appropriate choice of such potential allows for the reconstruction of a number of interesting cosmological and astrophysical scenarios. We explicitly show how to reconstruct such a potential for a general static spherically symmetric space-time. A number of applications and scenarios are then explored, among which traversable wormholes. Finally, we analytically reconstruct potentials which leads to solutions to the equations of motion featuring polynomial corrections to the Schwarzschild spacetime. Accurate choices for such corrections could provide an explanation for the inferred flat rotation curves of spiral galaxies within the mimetic gravity framework, without the need for particle dark matter.

### Combined Solar System and rotation curve constraints on MOND

The Modified Newtonian Dynamics (MOND) paradigm generically predicts that the external gravitational field in which a system is embedded can produce effects on its internal dynamics. In this communication, we first show that this External Field Effect can significantly improve some galactic rotation curves fits by decreasing the predicted velocities of the external part of the rotation curves. In modified gravity versions of MOND, this External Field Effect also appears in the Solar System and leads to a very good way to constrain the transition function of the theory. A combined analysis of the galactic rotation curves and Solar System constraints (provided by the Cassini spacecraft) rules out several classes of popular MOND transition functions, but leaves others viable. Moreover, we show that LISA Pathfinder will not be able to improve the current constraints on these still viable transition functions.

### Galactic mapping with general relativity and the observed rotation curves

Typically, stars in galaxies have higher velocities than predicted by Newtonian gravity in conjunction with observable galactic matter. To account for the phenomenon, some researchers modified Newtonian gravitation; others introduced dark matter in the context of Newtonian gravity. We employed general relativity successfully to describe the galactic velocity profiles of four galaxies: NGC 2403, NGC 2903, NGC 5055 and the Milky Way. Here we map the density contours of the galaxies, achieving good concordance with observational data. In our Solar neighbourhood, we found a mass density and density fall-off fitting observational data satisfactorily. From our GR results, using the threshold density related to the observed optical zone of a galaxy, we had found that the Milky Way was indicated to be considerably larger than had been believed to be the case. To our knowledge, this was the only such existing theoretical prediction ever presented. Very recent observational results by Xu et al. have confirmed our prediction. As in our previous studies, galactic masses are consistently seen to be higher than the baryonic mass determined from observations but still notably lower than those deduced from the approaches relying upon dark matter in a Newtonian context. In this work, we calculate the non-luminous fraction of matter for our sample of galaxies that is derived from applying general relativity to the dynamics of the galaxies. The evidence points to general relativity playing a key role in the explanation of the stars' high velocities in galaxies. Mapping galactic density contours directly from the dynamics opens a new window for predicting galactic structure.

### Nonlocal Gravity in the Solar System [Cross-Listing]

The implications of the recent classical nonlocal generalization of Einstein's theory of gravitation for gravitational physics in the Solar System are investigated. In this theory, the nonlocal character of gravity simulates dark matter. Nonlocal gravity in the Newtonian regime involves a reciprocal kernel with three spatial parameters, of which two have already been determined from the rotation curves of spiral galaxies and the internal dynamics of clusters of galaxies. However, the short-range parameter a_0 remains to be determined. In this connection, the nonlocal contribution to the perihelion precession of a planetary orbit is estimated and a preliminary lower limit on a_0 is determined.

### Nonlocal Gravity in the Solar System

The implications of the recent classical nonlocal generalization of Einstein's theory of gravitation for gravitational physics in the Solar System are investigated. In this theory, the nonlocal character of gravity simulates dark matter. Nonlocal gravity in the Newtonian regime involves a reciprocal kernel with three spatial parameters, of which two have already been determined from the rotation curves of spiral galaxies and the internal dynamics of clusters of galaxies. However, the short-range parameter a_0 remains to be determined. In this connection, the nonlocal contribution to the perihelion precession of a planetary orbit is estimated and a preliminary lower limit on a_0 is determined.

### Nonlocal Gravity in the Solar System [Replacement]

The implications of the recent classical nonlocal generalization of Einstein's theory of gravitation for gravitational physics in the Solar System are investigated. In this theory, the nonlocal character of gravity appears to simulate dark matter. Nonlocal gravity in the Newtonian regime involves a reciprocal kernel with three spatial parameters, of which two have already been determined from the rotation curves of spiral galaxies and the internal dynamics of clusters of galaxies. However, the short-range parameter a_0 remains to be determined. In this connection, the nonlocal contribution to the perihelion precession of a planetary orbit is estimated and a preliminary lower limit on a_0 is determined.

### Nonlocal Gravity in the Solar System [Replacement]

The implications of the recent classical nonlocal generalization of Einstein's theory of gravitation for gravitational physics in the Solar System are investigated. In this theory, the nonlocal character of gravity appears to simulate dark matter. Nonlocal gravity in the Newtonian regime involves a reciprocal kernel with three spatial parameters, of which two have already been determined from the rotation curves of spiral galaxies and the internal dynamics of clusters of galaxies. However, the short-range parameter a_0 remains to be determined. In this connection, the nonlocal contribution to the perihelion precession of a planetary orbit is estimated and a preliminary lower limit on a_0 is determined.

### Disk galaxy scaling relations at intermediate redshifts - I. The Tully-Fisher and velocity-size relations

Galaxy scaling relations such as the Tully-Fisher relation (between maximum rotation velocity Vmax and luminosity) and the velocity-size relation (between Vmax and disk scale length) are powerful tools to quantify the evolution of disk galaxies with cosmic time. We took spatially resolved slit spectra of 261 field disk galaxies at redshifts up to z~1 using the FORS instruments of the ESO Very Large Telescope. The targets were selected from the FORS Deep Field and William Herschel Deep Field. Our spectroscopy was complemented with HST/ACS imaging in the F814W filter. We analyzed the ionized gas kinematics by extracting rotation curves from the 2-D spectra. Taking into account all geometrical, observational and instrumental effects, these rotation curves were used to derive the intrinsic Vmax. Neglecting galaxies with disturbed kinematics or insufficient spatial rotation curve extent, Vmax could be determined for 137 galaxies covering redshifts 0.05<z<0.97. This is one of the largest kinematic samples of distant disk galaxies to date. We compared this data set to the local B-band Tully-Fisher relation and the local velocity-size relation. The scatter in both scaling relations is a factor of ~2 larger at z~0.5 than at z~0. The deviations of individual distant galaxies from the local Tully-Fisher relation are systematic in the sense that the galaxies are increasingly overluminous towards higher redshifts, corresponding to an over-luminosity Delta_MB=-(1.1+-0.5) mag at z=1. This luminosity evolution at given Vmax is probably driven by younger stellar populations of distant galaxies with respect to their local counterparts. The analysis of the velocity-size relation reveals that disk galaxies of a given Vmax have grown in size by a factor of ~1.5 over the past ~8 Gyr, likely via accretion of cold gas and/or small satellites.

### Angular momentum of disc galaxies with a lognormal density distribution

Whilst most galaxy properties scale with galaxy mass, similar scaling relations for angular momentum are harder to demonstrate. A lognormal (LN) density distribution for disc mass provides a good overall fit to the observational data for disc rotation curves for a wide variety of galaxy types and luminosities. In this paper, the total angular momentum J and energy $\vert{}$E$\vert{}$ were computed for 38 disc galaxies from the published rotation curves and plotted against the derived disc masses, with best fit slopes of 1.683$\pm{}$0.018 and 1.643$\pm{}$0.038 respectively, using a theoretical model with a LN density profile. The derived mean disc spin parameter was $\lambda{}$=0.423$\pm{}$0.014. Using the rotation curve parameters V$_{max}$ and R$_{max}$ as surrogates for the virial velocity and radius, the virial mass estimator $M_{disc}\propto{}R_{max}V_{max}^2$ was also generated, with a log-log slope of 1.024$\pm{}$0.014 for the 38 galaxies, and a proportionality constant ${\lambda{}}^*=1.47\pm{}0.20\times{}{10}^5\ M_{sun\ }{kpc}^{-1}{km}^{-2}\ s^2$. This relationship was close to the theoretical slope of 1, and had less scatter than the corresponding Tully Fisher relation, $M\propto{}{\left(V_{rot}\right)}^{\alpha{}}$, suggesting that the virial mass estimator may provide an alternative method to determine disc masses.

### The Luminous Convolution Model for spiral galaxy rotation curves

The Luminous Convolution Model (LCM) is an empirical formula, based on a heuristic convolution of Relativistic transformations, which makes it possible to predict the observed rotation curves of a broad class of spiral galaxies from luminous matter alone. Since the LCM is independent of distance estimates or dark matter halo densities, it is the first model of its kind which constrains luminous matter modeling directly from the observed spectral shifts of characteristic photon emission/absorption lines. In this paper we present the LCM solution to a diverse sample of twenty-five (25) galaxies of varying morphologies and sizes. For the chosen sample, it is shown that the LCM is more accurate than either Modified Newtonian Dynamics or dark matter models and returns physically reasonable mass to light ratios and exponential scale lengths. Unlike either Modified Newtonian Dynamics or dark matter models, the LCM predicts something which is directly falsifiable through improvements in our observational capacity, the luminous mass profile. The question, while interesting, of if the LCM constrains the relation of the baryonic to dark matter is beyond the scope of the current work. The focus of this paper is to show that it is possible to describe a broad and diverse spectrum of galaxies efficiently with the LCM formula. Moreover, since the LCM free parameter predicts the ratio of the Milky Way galaxy baryonic mass density to that of the galaxy emitting the photon, if the Milky Way mass models can be trusted at face values, we then show that the LCM becomes a zero parameter model. This paper substantially expands the results in arXiv:1309.7370 and arXiv:1407:7583.

### A universal velocity dispersion profile for pressure supported systems: evidence for MONDian gravity across 12 orders of magnitude in mass

For any MONDian extended theory of gravity where the rotation curves of spiral galaxies are explained through a change in physics rather than the hypothesis of dark matter, a generic dynamical behaviour is expected for pressure supported systems: an outer flattening of the velocity dispersion profile occurring at a characteristic radius, where both the amplitude of this flat velocity dispersion and the radius at which it appears are predicted to show distinct scalings with the total mass of the system. By carefully analysing dynamics of globular clusters, elliptical galaxies and galaxy clusters, we are able to significantly extend the astronomical scales over which MONDian gravity has been tested, from those of spiral galaxies, to the much larger range covered by pressure supported systems. We show that a universal projected velocity dispersion profile accurately describes various classes of pressure supported systems, and further, that the expectations of extended gravity are met, across twelve orders of magnitude in mass. This observed scalings are not expected under dark matter cosmology, and would require particular explanations tuned at the scales of each distinct astrophysical system.

### Dissipative dark matter and the rotation curves of dwarf galaxies [Replacement]

There is ample evidence from rotation curves that dark matter halos around disk galaxies have nontrivial dynamics. Of particular significance are: a) the cored dark matter profile of disk galaxies, b) correlations of the shape of rotation curves with baryonic properties, and c) the Tully-Fisher relation. Dark matter halos around disk galaxies may have nontrivial dynamics if dark matter is strongly self interacting and dissipative. Multicomponent hidden sector dark matter featuring a massless dark photon' (from an unbroken dark $U(1)$ gauge interaction) which kinetically mixes with the ordinary photon provides a concrete example of such dark matter. The kinetic mixing interaction facilitates halo heating by enabling ordinary supernovae to be a source of these dark photons'. Dark matter halos can expand and contract in response to the heating and cooling processes, but for a sufficiently isolated halo could have evolved to a steady state or equilibrium' configuration where heating and cooling rates locally balance. This dynamics allows the dark matter density profile to be related to the distribution of ordinary supernovae in the disk of a given galaxy. In a previous paper a simple and predictive formula was derived encoding this relation. Here we improve on previous work by modelling the supernovae distribution via the measured UV and $H\alpha$ fluxes. The resulting dark matter halo profile is then tested against the rotation curve data of all 26 dwarf galaxies in the LITTLE THINGS sample. The dissipative dark matter concept is further developed and some conclusions drawn.

### Dissipative dark matter and the rotation curves of dwarf galaxies [Replacement]

There is ample evidence from rotation curves that dark matter halos around disk galaxies have nontrivial dynamics. Of particular significance are: a) the cored dark matter profile of disk galaxies, b) correlations of the shape of rotation curves with baryonic properties, and c) the Tully-Fisher relation. Dark matter halos around disk galaxies may have nontrivial dynamics if dark matter is strongly self interacting and dissipative. Multicomponent hidden sector dark matter featuring a massless dark photon' (from an unbroken dark $U(1)$ gauge interaction) which kinetically mixes with the ordinary photon provides a concrete example of such dark matter. The kinetic mixing interaction facilitates halo heating by enabling ordinary supernovae to be a source of these dark photons'. Dark matter halos can expand and contract in response to the heating and cooling processes, but for a sufficiently isolated halo could have evolved to a steady state or equilibrium' configuration where heating and cooling rates locally balance. This dynamics allows the dark matter density profile to be related to the distribution of ordinary supernovae in the disk of a given galaxy. In a previous paper a simple and predictive formula was derived encoding this relation. Here we improve on previous work by modelling the supernovae distribution via the measured UV and $H\alpha$ fluxes. The resulting dark matter halo profile is then tested against the rotation curve data of all 26 dwarf galaxies in the LITTLE THINGS sample. The dissipative dark matter concept is further developed and some conclusions drawn.

### Dissipative dark matter and the rotation curves of dwarf galaxies

There is ample evidence from rotation curves that dark matter halo's around disk galaxies have nontrivial dynamics. Of particular significance are: a) the cored dark matter profile of disk galaxies, b) correlations of the shape of rotation curves with baryonic properties, and c) the Tully-Fisher relation. Dark matter halo's around disk galaxies may have nontrivial dynamics if dark matter is strongly self interacting and dissipative. Multicomponent hidden sector dark matter featuring a massless dark photon' (from an unbroken dark $U(1)$ gauge interaction) which kinetically mixes with the ordinary photon provides a concrete example of such dark matter. The kinetic mixing interaction facilitates halo heating by enabling ordinary supernovae to be a source of these dark photons'. Dark matter halo's can expand and contract in response to the heating and cooling processes, but for a sufficiently isolated halo should have evolved to a steady state or `equilibrium' configuration where heating and cooling rates locally balance. This dynamics allows the dark matter density profile to be related to the distribution of ordinary supernovae in the disk of a given galaxy. In a previous paper a simple and predictive formula was derived encoding this relation. Here we improve on previous work by modelling the supernovae distribution via the measured UV and $H\alpha$ fluxes. The resulting dark matter halo profile is then tested against the rotation curve data of all 26 dwarf galaxies in the LITTLE THINGS sample. The dissipative dark matter concept is further developed and some conclusions drawn.

### A matter of measurement: rotation velocities and the velocity function of dwarf galaxies

The velocity function derived from large scale surveys can be compared with the predictions of LCDM cosmology, by matching the measured rotation velocities Vrot of galaxies to the maximum circular velocity of dark matter (DM) halos Vmax. For Vrot<50km/s, a major discrepancy arises between the observed and LCDM velocity functions. However, the manner in which different observational measures of Vrot are associated with Vmax is not straight forward in dwarf galaxies. We instead relate galaxies to DM halos using the empirical baryon- mass to halo-mass relation, and show that different observational measures of Vrot result in very different velocity functions. We show how the W50 velocity function, i.e. using the HI profile line width at 50% of peak HI flux to measure Vrot, can be reconciled with a LCDM cosmology. Our semi-empirical methodology allows us to determine the region of rotation curves that are probed by HI measurements (RHI), and shows that the Vrot of dwarfs are generally measured at a fraction of Rmax, explaining their tendency to have rising rotation curves. We provide fitting formulae for relating RHI and Reff (the effective radius) to the virial radius of DM halos. To continue to use velocity functions as a probe of LCDM cosmology, it is necessary to be precise about how the different measures of rotation velocity are probing the mass of the DM halos, dropping the assumption that any measure of rotational velocity can be equally used as a proxy for Vmax.

### The Variation of Rotation Curve Shapes as a Signature of the Effects of Baryons on Dark Matter Density Profiles

Rotation curves of galaxies show a wide range of shapes, which can be paramaterized as scatter in Vrot(1kpc)/Vmax i.e.the ratio of the rotation velocity measured at 1kpc and the maximum measured rotation velocity. We examine whether the observed scatter can be accounted for by combining scatters in disc scale-lengths, the concentration-halo mass relation, and the Mstar-Mhalo relation. We use these scatters to create model galaxy populations; when housed within dark matter halos that have universal, NFW density profiles, the model does not match the lowest observed values of Vrot(1kpc)/Vmax and has too little scatter in Vrot(1kpc)/Vmax compared to observations. By contrast, a model using a mass dependant dark matter profile, where the inner slope is determined by the ratio of Mstar/Mhalo, produces galaxies with low values of Vrot(1kpc)/Vmax and a much larger scatter, both in agreement with observation. We conclude that the large observed scatter in Vrot(1kpc)/Vmax favours density profiles that are significantly affected by baryonic processes. Alternative dark matter core formation models are also disfavoured by the large scatter in Vrot(1kpc)/Vmax, implying that baryonic physics would be required to affect density profiles in such models, which defeats a large part of their motivation without ruling them out.

### The Variation of Rotation Curve Shapes as a Signature of the Effects of Baryons on Dark Matter Density Profiles [Replacement]

Rotation curves of galaxies show a wide range of shapes, which can be paramaterized as scatter in Vrot(1kpc)/Vmax i.e.the ratio of the rotation velocity measured at 1kpc and the maximum measured rotation velocity. We examine whether the observed scatter can be accounted for by combining scatters in disc scale-lengths, the concentration-halo mass relation, and the M*-Mhalo relation. We use these scatters to create model galaxy populations; when housed within dark matter halos that have universal, NFW density profiles, the model does not match the lowest observed values of Vrot(1kpc)/Vmax and has too little scatter in Vrot(1kpc)/Vmax compared to observations. By contrast, a model using a mass dependent dark matter profile, where the inner slope is determined by the ratio of M*/Mhalo, produces galaxies with low values of Vrot(1kpc)/Vmax and a much larger scatter, both in agreement with observation. We conclude that the large observed scatter in Vrot(1kpc)/Vmax favours density profiles that are significantly affected by baryonic processes. Alternative dark matter core formation models such as SIDM may also account for the observed variation in rotation curve shapes, but these observations may provide important constraints in terms of core sizes, and whether they vary with halo mass and/or merger history.

### 3D-Barolo: a new 3D algorithm to derive rotation curves of galaxies

We present 3D-Barolo, a new code that derives rotation curves of galaxies from emission-line observations. This software fits 3D tilted-ring models to spectroscopic data-cubes and can be used with a variety of observations: from HI and molecular lines to optical/IR recombination lines. We describe the structure of the main algorithm and show that it performs much better than the standard 2D approach on velocity fields. A number of successful applications, from high to very low spatial resolution data are presented and discussed. 3D-Barolo can recover the true rotation curve and estimate the intrinsic velocity dispersion even in barely resolved galaxies (about 2 resolution elements) provided that the signal to noise of the data is larger that 2-3. It can also be run automatically thanks to its source-detection and first-estimate modules, which make it suitable for the analysis of large 3D datasets. These features make 3D-Barolo a uniquely useful tool to derive reliable kinematics for both local and high-redshift galaxies from a variety of different instruments including the new-generation IFUs, ALMA and the SKA pathfinders.

### Cosmological Galaxy Evolution with Superbubble Feedback I: Realistic Galaxies with Moderate Feedback

We present the first cosmological galaxy evolved using the modern smoothed particle hydrodynamics (SPH) code GASOLINE2 with superbubble feedback. We show that superbubble-driven galactic outflows powered by Type II supernovae alone can produce $\rm{L^*}$ galaxies with flat rotation curves with circular velocities $\sim 200\; \rm{km/s}$, low bulge-to-disc ratios, and stellar mass fractions that match observed values from high redshift to the present. These features are made possible by the high mass loadings generated by the evaporative growth of superbubbles. Outflows are driven extremely effectively at high redshift, expelling gas at early times and preventing overproduction of stars before $z=2$. Centrally concentrated gas in previous simulations has often lead to unrealistically high bulge to total ratios and strongly peaked rotation curves. We show that supernova-powered superbubbles alone can produce galaxies that agree well with observed properties without the need for additional feedback mechanisms or increased feedback energy. We present additional results arising from properly modelled hot feedback.

### Cosmological Galaxy Evolution with Superbubble Feedback I: Realistic Galaxies with Moderate Feedback [Replacement]

We present the first cosmological galaxy evolved using the modern smoothed particle hydrodynamics (SPH) code GASOLINE2 with superbubble feedback. We show that superbubble-driven galactic outflows powered by Type II supernovae alone can produce $\rm{L^*}$ galaxies with flat rotation curves with circular velocities $\sim 200\; \rm{km/s}$, low bulge-to-disc ratios, and stellar mass fractions that match observed values from high redshift to the present. These features are made possible by the high mass loadings generated by the evaporative growth of superbubbles. Outflows are driven extremely effectively at high redshift, expelling gas at early times and preventing overproduction of stars before $z=2$. Centrally concentrated gas in previous simulations has often lead to unrealistically high bulge to total ratios and strongly peaked rotation curves. We show that supernova-powered superbubbles alone can produce galaxies that agree well with observed properties without the need for additional feedback mechanisms or increased feedback energy. We present additional results arising from properly modelled hot feedback.

### Cosmological Galaxy Evolution with Superbubble Feedback I: Realistic Galaxies with Moderate Feedback [Replacement]

We present the first cosmological galaxy evolved using the modern smoothed particle hydrodynamics (SPH) code GASOLINE2 with superbubble feedback. We show that superbubble-driven galactic outflows powered by Type II supernovae alone can produce $\rm{L^*}$ galaxies with flat rotation curves with circular velocities $\sim 200\; \rm{km/s}$, low bulge-to-disc ratios, and stellar mass fractions that match observed values from high redshift to the present. These features are made possible by the high mass loadings generated by the evaporative growth of superbubbles. Outflows are driven extremely effectively at high redshift, expelling gas at early times and preventing overproduction of stars before $z=2$. Centrally concentrated gas in previous simulations has often lead to unrealistically high bulge to total ratios and strongly peaked rotation curves. We show that supernova-powered superbubbles alone can produce galaxies that agree well with observed properties without the need for additional feedback mechanisms or increased feedback energy. We present additional results arising from properly modelled hot feedback.

### Mass models of disk galaxies from the DiskMass Survey in MOND

This article explores the agreement between the predictions of Modified Newtonian Dynamics (MOND) and the rotation curves and stellar velocity dispersion profiles measured by the DiskMass Survey. A bulge-disk decomposition was made for each of the thirty published galaxies, and a MOND Poisson solver was used to simultaneously compute, from the baryonic mass distributions, model rotation curves and vertical velocity dispersion profiles, which were compared to the measured values. The two main free parameters, the stellar disk's mass-to-light ratio ($M/L$) and its exponential scale-height ($h_z$), were estimated by Markov Chain Monte Carlo modelling. The average best-fit K-band stellar mass-to-light ratio was $M/L \simeq 0.55 \pm 0.15$. However, to match the DiskMass Survey data, the vertical scale-heights would have to be in the range $h_z=200$ to $400$ pc which is a factor of two lower than those derived from observations of edge-on galaxies with a similar scale-length. The reason is that modified gravity versions of MOND characteristically require a larger $M/L$ to fit the rotation curve in the absence of dark matter and therefore predict a stronger vertical gravitational field than Newtonian models. It was found that changing the MOND acceleration parameter, the shape of the velocity dispersion ellipsoid, the adopted vertical distribution of stars, as well as the galaxy inclination, within any realistic range, all had little impact on these results.

### Testing modified Newtonian dynamics in the Milky Way [Replacement]

Modified Newtonian dynamics (MOND) is an empirical theory originally proposed to explain the rotation curves of spiral galaxies by modifying the gravitational acceleration, rather than by invoking dark matter. Here,we set constraints on MOND using an up-to-date compilation of kinematic tracers of the Milky Way and a comprehensive collection of morphologies of the baryonic component in the Galaxy. In particular, we find that the so-called "standard" interpolating function cannot explain at the same time the rotation curve of the Milky Way and that of external galaxies for any of the baryonic models studied, while the so-called "simple" interpolating function can for a subset of models. Upcoming astronomical observations will refine our knowledge on the morphology of baryons and will ultimately confirm or rule out the validity of MOND in the Milky Way. We also present constraints on MOND-like theories without making any assumptions on the interpolating function.

### Testing modified Newtonian dynamics in the Milky Way

Modified Newtonian dynamics (MoND) is an empirical theory originally proposed to explain the rotation curves of spiral galaxies by modifying the gravitational acceleration, rather than by invoking dark matter. Here, we set constraints on MoND using an up-to-date compilation of kinematic tracers of the Milky Way and a comprehensive collection of morphologies of the baryonic component in the Galaxy. In particular, we find that the so-called "standard" interpolating function cannot explain at the same time the rotation curve of the Milky Way and that of external galaxies for any of the baryonic models studied, while the so-called "simple" interpolating function remains viable for a subset of models. Upcoming astronomical observations will refine our knowledge on the morphology of baryons and will ultimately confirm or rule out the validity of MoND in the Milky Way. We also present constraints on MoND-like theories without making any assumptions on the interpolating function.

### Gravitational, lensing, and stability properties of Bose-Einstein condensate dark matter halos

The possibility that dark matter, whose existence is inferred from the study of the galactic rotation curves and from the mass deficit in galaxy clusters, can be in a form of a Bose-Einstein condensate has recently been extensively investigated. In the present work, we consider a detailed analysis of the astrophysical properties of the Bose-Einstein condensate dark matter halos that could provide clear observational signatures and help discriminate between different dark matter models. In the Bose-Einstein condensation model dark matter can be described as a non-relativistic, gravitationally confined Newtonian gas, whose density and pressure are related by a polytropic equation of state with index $n=1$. The mass and the gravitational properties of the condensate halos are obtained in a systematic form, including the mean logarithmic slopes of the density and of the tangential velocity. Furthermore, the lensing properties of the condensate dark matter are also investigated in detail. In particular, a general analytical formula for the surface density, an important quantity that defines the lensing properties of a dark matter halos, is obtained in the form of series expansions. This enables arbitrary-precision calculations of the surface mass density, deflection angle, deflection potential, and of the magnification factor, thus providing the possibility of comparing the predicted lensing properties of the condensate dark matter halos with observations. The stability properties of the condensate halos are also investigated by using the scalar and the tensor virial theorems, respectively, and the virial perturbation equation for condensate dark matter halos is derived.

### Gravitational, lensing, and stability properties of Bose-Einstein condensate dark matter halos [Replacement]

The possibility that dark matter, whose existence is inferred from the study of the galactic rotation curves, and from the mass deficit in galaxy clusters, can be in a form of a Bose-Einstein Condensate, has been extensively investigated lately. In the present work, we consider a detailed analysis of the astrophysical properties of the Bose-Einstein Condensate dark matter halos that could provide clear observational signatures that help discriminate between different dark matter models. In the Bose-Einstein condensation model dark matter can be described as a non-relativistic, gravitationally confined Newtonian gas, whose density and pressure are related by a polytropic equation of state with index $n=1$. The mass and gravitational properties of the condensate halos are obtained in a systematic form, including the mean logarithmic slopes of the density and of the tangential velocity. The lensing properties of the condensate dark matter are investigated in detail. In particular, a general analytical formula for the surface density, an important quantity that defines the lensing properties of a dark matter halos, is obtained in the form of series expansions. This enables arbitrary-precision calculations of the surface mass density, deflection angle, deflection potential, and of the magnification factor, thus giving the possibility of the comparison of the predicted lensing properties of the condensate dark matter halos with observations. The stability properties of the condensate halos are also investigated by using the scalar and the tensor virial theorems, respectively, and the virial perturbation equation for condensate dark matter halos is derived.

### Gravitational, lensing, and stability properties of Bose-Einstein condensate dark matter halos [Cross-Listing]

The possibility that dark matter, whose existence is inferred from the study of the galactic rotation curves and from the mass deficit in galaxy clusters, can be in a form of a Bose-Einstein condensate has recently been extensively investigated. In the present work, we consider a detailed analysis of the astrophysical properties of the Bose-Einstein condensate dark matter halos that could provide clear observational signatures and help discriminate between different dark matter models. In the Bose-Einstein condensation model dark matter can be described as a non-relativistic, gravitationally confined Newtonian gas, whose density and pressure are related by a polytropic equation of state with index $n=1$. The mass and the gravitational properties of the condensate halos are obtained in a systematic form, including the mean logarithmic slopes of the density and of the tangential velocity. Furthermore, the lensing properties of the condensate dark matter are also investigated in detail. In particular, a general analytical formula for the surface density, an important quantity that defines the lensing properties of a dark matter halos, is obtained in the form of series expansions. This enables arbitrary-precision calculations of the surface mass density, deflection angle, deflection potential, and of the magnification factor, thus providing the possibility of comparing the predicted lensing properties of the condensate dark matter halos with observations. The stability properties of the condensate halos are also investigated by using the scalar and the tensor virial theorems, respectively, and the virial perturbation equation for condensate dark matter halos is derived.

### Gravitational, lensing, and stability properties of Bose-Einstein condensate dark matter halos [Replacement]

The possibility that dark matter, whose existence is inferred from the study of the galactic rotation curves, and from the mass deficit in galaxy clusters, can be in a form of a Bose-Einstein Condensate, has been extensively investigated lately. In the present work, we consider a detailed analysis of the astrophysical properties of the Bose-Einstein Condensate dark matter halos that could provide clear observational signatures that help discriminate between different dark matter models. In the Bose-Einstein condensation model dark matter can be described as a non-relativistic, gravitationally confined Newtonian gas, whose density and pressure are related by a polytropic equation of state with index $n=1$. The mass and gravitational properties of the condensate halos are obtained in a systematic form, including the mean logarithmic slopes of the density and of the tangential velocity. The lensing properties of the condensate dark matter are investigated in detail. In particular, a general analytical formula for the surface density, an important quantity that defines the lensing properties of a dark matter halos, is obtained in the form of series expansions. This enables arbitrary-precision calculations of the surface mass density, deflection angle, deflection potential, and of the magnification factor, thus giving the possibility of the comparison of the predicted lensing properties of the condensate dark matter halos with observations. The stability properties of the condensate halos are also investigated by using the scalar and the tensor virial theorems, respectively, and the virial perturbation equation for condensate dark matter halos is derived.

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