Rotation Curve

As confirmed by tests performed in the solar system, General Relativity (GR) presently represents the best description of gravitation. It is however challenged by observations at very large length scales, and already at the solar system scale, tracking of the Pioneer 10/11 probes has failed to confirm their expected behavior according to GR. Metric extensions of GR, which are presented here, have the quality of preserving the fundamental properties of GR while introducing scale dependent modifications. We show that they moreover represent an appropriate family of gravitation theories to be compared with observations when analysing gravity tests. We also discuss different tests which could allow one to determine the metric extension of GR prevailing in the solar system.

As confirmed by tests performed in the solar system, General Relativity (GR) presently represents the best description of gravitation. It is however challenged by observations at very large length scales, and already at the solar system scale, tracking of the Pioneer 10/11 probes has failed to confirm their expected behavior according to GR. Metric extensions of GR, which are presented here, have the quality of preserving the fundamental properties of GR while introducing scale dependent modifications. We show that they moreover represent an appropriate family of gravitation theories to be compared with observations when analysing gravity tests. We also discuss different tests which could allow one to determine the metric extension of GR prevailing in the solar system.

Despite its remarkable agreement with gravity tests in the solar system, general relativity is challenged at larger scales. Large scale tests performed in the solar system by the Pioneer 10/11 probes have failed to confirm the expected gravity laws. We discuss here extensions of general relativity which preserve its geometrical nature while showing an ability to conciliate the Pioneer anomalies with other gravity tests. Further testable phenomenological consequences are also briefly discussed.

Vibrational Theory (VT) models gravity as an emergent property of standing wave dynamics in the Dynamic Matter (DM) field, offering an alternative to the ΛCDM framework. In this work, we apply a modified gravitational potential, Φᵥ(r) =-GM(r)/r [1 + β sin(2πr/λ)], to derive orbital velocities of stars within galaxies. The resulting expression, v(r)² = GM/r [1 + β sin(2πr/λ) + β (2πr/λ) cos(2πr/λ)], reduces to Newtonian predictions for inner stellar orbits while producing flattened velocity curves for outer stars. Averaging over the vibrational correction terms yields the constant orbital speeds observed in galaxies, eliminating the need to invoke dark matter. This treatment extends VT's gravitational framework, already successful in modeling Solar System anomalies such as Mercury's orbit, to galactic scales. VT thus provides a unified explanation for redshift, orbital dynamics, and rotation curves through resonance in the DM field

This study presents a comprehensive analysis of galaxy rotation curves from the SPARC database, aimed at uncovering systematic patterns in their shape and oscillations. We show that the observed oscillations are not random noise. Instead, they are statistically significant, reproducible features exhibiting clear spatial localization and correlation with morphological type. Three robust dynamical regimes—rising, flat, and declining—are identified. These regimes show weak correlation with internal galaxy parameters, suggesting a dominant role of the large-scale environment. Analysis of the radial acceleration profile $g_{\rm obs}(r)$ reveals systematic oscillations, especially in central regions. This challenges the interpretation of scatter in the Radial Acceleration Relation (RAR) as a purely baryonic effect. Our results establish an \textbf{empirical fact}: any complete theory of galactic dynamics must explain not only the average shape of the rotation curve but also its oscillatory structure. We propose that the shape of the rotation curve be viewed as a \textbf{dynamic imprint} of a galaxy’s position within the hierarchical structure of the Universe.

We investigate the influence of the Hubble parameter H(z) on galactic dynamics and morphology. By introducing the cosmic expansion as an effective limit on Newtonian gravitation, we obtain a redshift-dependent critical radius that constrains both spiral structure and rotation curves. Galactic bars are interpreted as frozen spirals of high-z epochs nested inside extended low-z spirals. This framework naturally explains the coexistence of bulges, bars, disks and halos as the outcome of metric inflow and bulge reset events. The resulting morphology and kinematics provide a direct and testable connection between galactic structure and the cosmic expansion. We argue that this approach opens a new possibility to empirically derive H(z) from galaxy morphology and rotation curves and allows reconstructing the expansion history of the universe on galactic scales.

We propose a novel model where gravity emerges from tension fields driven by spatial gradients of a quantum foam density field ρ k (x µ). The effective potential Φ(ρ k) = c 2 g ln(ρ k /ρ 0) reproduces Newtonian gravity in high-acceleration regimes (e.g., Solar System) and MOND-like behavior in low-acceleration regimes (e.g., galactic rotation curves). Fitting 175 SPARC galaxies, the model achieves an average RMS error of 4.2 km s-1 and R 2 ≈ 0.987-0.996 with a universal a 0 ≈ 1.2 × 10-10 m s-2 , naturally yielding the Tully-Fisher relation without dark matter. Testable predictions include Planck-scale Casimir effect corrections, atom interferometry phase shifts, and TeVscale soliton resonances at the LHC. Deviations in a 0 across galaxies would falsify the model, ensuring robust testability.

This paper explores how the dynamics of quantum foam can explain galactic rotation curves and cluster lensing without invoking the dark matter hypothesis. The developed ∆Q model integrates density fluctuations at the Planck scale, morphology-dependent angular frequencies, and relaxation mechanisms at cosmic scales. This work presents the model's theoretical formulation, utilized datasets, methodology, results, and supporting tables and figures in detail.

Spiral galaxies exhibit flat or even rising rotation curves at large radii, a phenomenon widely attributed to massive halos of unseen dark matter. In this paper we show that such behavior arises naturally from flux attenuation in a transport-based revival of the Fatio-Le Sage process. Using the Beer-Lambert law of exponential attenuation applied to an isotropic momentum flux, the effective gravitational coupling becomes path-and geometry-dependent. In extended thin-disk systems such as spiral galaxies, cumulative in-plane attenuation suppresses the expected 1/r2 decline and produces flat rotation curves without recourse to dark matter. Numerical simulations with both structured and randomized stellar distributions reproduce measured profiles, including the upward "flip-up" observed in M33 and the averaged galaxy curves reported by NASA, with correlation coefficients exceeding 0.98. Because flux transport occurs at finite velocity c, the light-crossing time of large galactic disks (~10^5 years) introduces a rotational smearing of flux shadows, offering a causal explanation for velocity banding and spiral arm coherence. This analysis demonstrates one of the unique provisions of the transport model: spiral galaxy dynamics follow directly from the Fatio-Le Sage functional process when recast in modern radiation transport theory. The result highlights how causal substrate mechanics can replace ad hoc constructs, providing a testable alternative to dark matter in galactic dynamics.

A new algorithm for illustrating symmetric structure in galaxies was recently applied to a sample of 18 spirals ). The results were analyzed in terms of spiral-wave resonances using observed or generic rotation curves (scaled with absolute magnitude), and shown to provide some foundation to the expectation that spiral features with m-fold symmetry in azimuth lie primarily between the m: 1 Lindblad resonances. Here we say a bit more about this method.

Several models have been proposed to explain the cosmological constant as a consequence of alterations in the distance-redshift relation caused by the universe's inhomogeneities. We modelled the universe as a spherical galactic mass with a Gaussian radial profile, repeated at the nodes of a periodic 3D-lattice. The Einstein field density equation was solved to the first-order for the scalar field perturbation of the FLRW metric in the Newtonian gauge. The resulting metric solution is free of singularities. The diagonal Einstein spatial field equations exhibit only the subtraction of a constant second-order term. This term corresponds to the cosmological constant in the reference frame comoving with the galaxy positions. This geometrically derived cosmological constant accurately predicts the observed value using a realistic standard galaxy density profile and lattice periodicity, without introducing any additional adjustable parameters. Its value decreases exponentially as the galaxy size approaches the intergalactic distance. When the universe becomes homogeneous, the expansion rate equation reduces to that of the standard FLRW model. The model is Copernican in the sense that all galaxies share similar observational features. This approach opens a track of research to explain the origin of the cosmological constant within the framework of pure general relativity.

Previous attempts at disturbing the galactic disk by the Magellanic Clouds relied on direct tidal forcing. However, by allowing the halo to actively respond rather than remain a rigid contributor to the rotation curve, the Clouds may produce a wake in the halo which then distorts the disk. Recent work reported here suggests that the Magellanic Clouds use this mechanism to produce disk distortions su cient to account for both the radial location, position angle and sign of the HI warp and observed anomalies in stellar kinematics towards the galactic anticenter and LSR motion.

The Quantum Reflection Model (QRM) proposes a unified framework connecting quantum
mechanics and general relativity via a single principle of quantum reflection. Evolving from the
initial Big Hop hypothesis, the present revision provides a minimal, calculable, and falsifiable
formulation: a conformal effective metric, explicit field equations for two scalar sectors, and a
two-parameter core model that yields quantitative predictions at the 10−3 level. We clarify the
ontological status of the pre-observable |Φ⟩ space (operational vs physical readings), motivate
and generalize the anti-unitary selection R (beyond toy models), present an anomaly-induced
origin for the masking field M with discriminating tests, give explicit potentials consistent with
energy conditions (ghost-free, NEC/SEC) and linear stability, and supply an implementable
cosmological pipeline linking lab-scale δ0 to large-scale {μ, Σ}.

NSI Revisited: What this version fixes and why it supersedes the original

Short summary.
This release provides a complete, reproducible, and methodologically consistent re-evaluation of the Negentropic Stabilization Index (NSI) on SPARC galaxy rotation curves. Contrary to the original paper’s strong claims, we report negative results for “pure” NSI and introduce a pragmatic NFW+NSI-core hybrid tested side-by-side with NFW and MOND under a unified pipeline. All figures, tables, and appendices needed for full replication are included and compile out of the box.

What’s new and what we fixed vs. the original

Physical consistency of NSI.
We replace ad-hoc velocity additions with the force derived from the NSI potential
Φ
n
e
g
Φ
neg
​

, i.e. we add the acceleration
𝑔
N
S
I
=
∣
d
Φ
/
d
𝑟
∣
g
NSI
​

=∣dΦ/dr∣ to the budget. This resolves prior dimensional and conceptual inconsistencies.

Baryon-coupled NSI variant.
We implement a
𝜌
𝑞
ρ
q
aggregation with
𝑞
=
(
2
+
𝛽
)
/
(
1
+
𝛽
)
q=(2+β)/(1+β) and a radial taper
[
1
+
(
𝑟
/
𝑟
0
)
𝛽
]
−
1
[1+(r/r
0
​

)
β
]
−1
, i.e. an explicit coupling to the baryonic components instead of a free “dark” term.

Hybrid model (NFW + NSI-core).
We test NSI as a core-forming prior within a halo (not a dark-matter replacement). This clarifies where NSI can help (inner profiles) and where it cannot (outer flat parts in low surface-density disks).

Unified fitting across models.
NFW, MOND, and the Hybrid share the same baryonic scaling factor
𝑠
s and are fitted with the same coarse grid search, using the published velocity uncertainties and consistent units. No manual tuning.

Fair model selection with information criteria.
We report AIC and BIC for every galaxy and interpret
Δ
ΔAIC/
Δ
ΔBIC with standard thresholds (
>
10
>10 = decisive). We do not rely on hand-picked “nice” curves.

Full results and reproducibility.
The package contains all rotation curves (SPARC subset),
Δ
ΔAIC/
Δ
ΔBIC histograms, the RAR plot, a full per-galaxy parameter table, and an appendix. The LaTeX source is Overleaf-ready with no hidden dependencies.

Sober conclusions (self-correction).
On the tested LSB/dwarf-heavy subset (≈20 galaxies), NSI does not replace dark matter. The NFW+NSI-core hybrid can be locally competitive, but does not win in aggregate against NFW/MOND according to AIC/BIC.

Why this version supersedes the original

It fixes conceptual/units issues in how NSI was injected into the dynamics (we now add the derived acceleration, not an arbitrary term in
𝑣
2
v
2
).

It replaces incomplete evidence with a complete and reproducible bundle (all RC figures, RAR, histograms, tables, appendix).

It introduces transparent statistics (AIC & BIC) and a common fitting protocol with a shared
𝑠
s across models.

It revises conclusions: “pure” NSI is not a robust alternative to dark matter on this sample; NSI may be useful only as a baryon-tied core prior within halo modeling.

Contents of this Zenodo record

LaTeX source (REVTeX 4-2): NSI Revisited: Negative Results on SPARC Rotation Curves and a Pragmatic Hybrid with Dark Halos (Author: Karel Hrubec, no affiliation).

Figures/: all rotation-curve plots (one PNG per galaxy), RAR, and
Δ
ΔAIC/
Δ
ΔBIC histograms.

Tables/: longtable with AIC/BIC and their differences.

Appendix/: per-galaxy best-fit parameters (NFW/MOND/Hybrid).

references.bib: core bibliography (SPARC, NFW, MOND).

(Optional) Accompanying CSVs/scripts if included in this release; otherwise see linked repository.

Recommended citation

Hrubec, K. (2025). NSI Revisited: Negative Results on SPARC Rotation Curves and a Pragmatic Hybrid with Dark Halos. Zenodo. DOI: (to be added after this record is published).

Keywords: galaxy rotation curves; dark matter halos; MOND; NSI; baryon–DM coupling; AIC; BIC; SPARC; core–cusp; reproducibility
License: CC-BY 4.0 recommended (adjust if you prefer a different license).

Version notes (changelog)

Replaced ad-hoc NSI term with force-consistent
𝑔
N
S
I
g
NSI
​

.

Added baryon-coupled
𝜌
𝑞
ρ
q
NSI and an NFW+NSI-core hybrid.

Unified coarse-grid fitting with shared
𝑠
s; consistent error model.

Reported both AIC and BIC; added
Δ
ΔAIC/
Δ
ΔBIC histograms.

Included all figures, tables, and appendix for full reproducibility.

Revised conclusions: negative results for “pure” NSI; limited utility as a core prior.

This model reframes dark matter not as a particle, but as the gravitational memory of past mass — a persistent inertial field generated by early stellar populations. Derived from Newtonian gravity and mass history, it explains flat rotation curves without exotic physics. The coupling constant k is tuned to match observed halo density, confirming the model’s validity.

The interstellar object 3I/ATLAS (also C/2025 N1 (ATLAS), henceforth, 3I), discovered by the ATLAS Chile telescope on 2025 July 1, was rapidly revealed to be the third known interstellar object (ISO) transiting the solar system, with an incoming velocity at infinity of 57.9763 ± 0.0044 km s-1. An examination of 3I's pre-encounter kinematics shows that it is likely to be an object from the galactic thick disk, and thus a remnant of the Galaxy's "cosmic noon" period of intense star formation ∼9-13 gigayears ago. This kinematic assignment of 3I to the thick disk can be tested observationally in the transit of 3I through the solar system; if confirmed, 3I will provide a means to explore the stellar and planetesimal formation process, and its astrobiological implications, in an early period of galactic history. Unfortunately for terrestrial observers, the 3I perihelion will happen when it is on the other side of the Sun as seen from Earth, at a solar elongation of 12.80 • , rendering observation from Earth (or near-Earth space telescopes) hard or impossible. With a retrograde orbit inclined 175.114 • (only 4.886 • from the ecliptic plane), and a trajectory passing inside the orbit of Mars, 3I will pass relatively close to a number of already launched interplanetary spacecraft. We examined the observational opportunities of 15 spacecraft, both those on heliocentric orbits and also the spacecraft grouping at the planet Mars, and find a strong science case for observations in the periods of the close approaches of the Psyche spacecraft on 2025 September 4, at 0.302 AU, the martian spacecraft array on 2025 October 3, and the Juice spacecraft on 2025 November 4. In addition, the Europa Clipper, Hera and even the more distant Lucy spacecraft may pass through 3I's cometary tail in the period after its perihelion passage, potentially directly observing the conditions and composition there. Finally, three heliophysics space observatories (SOHO, Solar Orbiter and the Parker Solar Probe) will have 3I pass through their instrument's fields of view (FOV) in this period; the Parker Solar Probe and even the solar coronagraphs may be able to monitor 3I at intervals in the period from late September through mid November in 2025. Spacecraft observations could, to the extent they are possible, provide the only source of spectral and imaging data during the 3I perihelion passage, constrain the phase angle dependence of 3I coma dust, and test the 3I thick disk origin hypothesis.

Motion of test particles along rotating curved trajectories is considered. The problem is studied both in the laboratory and the rotating frames of reference. It is assumed that the system rotates with the constant angular velocity ω = const. The solutions are found and analyzed for the case when the form of the trajectory is given by an Archimedes spiral. It is found that particles can reach infinity while they move along these trajectories and the physical interpretation of their behaviour is given. The analogy of this idealized study with the motion of particles along the curved rotating magnetic field lines in the pulsar magnetosphere is pointed out. We discuss further physical development (the conserved total energy case, when ω = const) and astrophysical applications (the acceleration of particles in active galactic nuclei) of this theory.

The behaviour of composite connections has been widely investigated in last years within the international scientific community following the introduction in Eurocode 4 of the extension to composite connections of the Component Method, already suggested by Eurocode 3 for bare steel connections. With respect to bare steel joints, Eurocode 4 requires only the definition of two new components: the concrete slab in tension or in compression and the shear connectors. In last years, a lot of works have been carried out dealing with the application of this methodology to connections subjected to hogging moment, but there is still limited knowledge with reference to composite connections subjected to sagging moment as it can occur under seismic horizontal forces. Therefore, aiming to introduce the connection modelling in seismic structural analyses, this work deals with the application of the component approach to different typologies of semirigid composite connections subjected to both hogging and sagging moment. In particular, with reference to joints subjected to hogging moment, the need of properly predicting the extension of the compressed zone is pointed out. Starting from this observation, an alternative procedure with respect to the codified one is proposed. The main feature of the proposed procedure is the missing of any preliminary assumption regarding the location of the centre of compression in both the analysed cases (sagging moment and hogging moment). In addition, the prediction of the whole momentrotation curve is obtained by means of an appropriate modelling of the joint components. Finally, the comparison with available experimental results shows the improvements obtained by means of the proposed approach with respect to that suggested by Eurocode.

We present a novel method for estimating the cosmic expansion rate $H_z$ at high redshift ($z \approx 2$--$10$) using the internal dynamics and morphology of nearby galaxies—without relying on direct redshift–distance measurements. The approach models rotation curves of systems showing a clear structural transition between a central bar (interpreted as a fossil spiral) and an outer spiral disk. Within a dual-Lagrangian framework, these nested structures are assigned separate dynamical regimes, enabling $H_z$ to be extracted from the mass $M$ and \emph{critical radius} $r_c$ of the proto-bar region. The critical radius is defined locally by the condition $v_H(r_c) = v_{\rm esc}(r_c)$, which yields a \emph{local critical density} $\rho_c \propto H_z^2$. When this purely local relation is mapped onto cosmic time using the $\Lambda$CDM matter-era scaling $H(t) \propto t^{-1}$, it reproduces the universal $\rho_c \propto t^{-2}$ law. Applying the method to seventeen galaxies, and scanning early bulge mass fractions from $0.2\%$ to $20\%$ of today’s $M_{\rm bulge}$, we find that the $0.5\%$–$5\%$ range best matches the $\Lambda$CDM timeline for disk–spiral onset. A refined backward-time minimization, incorporating a power-law bulge growth model, further narrows the plausible onset window to $0.4$–$1.8$~Gyr after the Big Bang. This technique complements high-redshift probes such as \emph{JWST} imaging and CMB extrapolations, offering a new class of local, dynamical constraints on the early universe. If validated and applied to large rotation-curve samples, it could yield hundreds to thousands of independent $H_z$ determinations, refining both the cosmic expansion history and the baryonic structure formation timeline.

We identify the rich carbon star population of the Magellanic-type dwarf irregular galaxy WLM (Wolf-Lundmark-Melotte) and study its photometric properties from deep near-IR observations. The galaxy also exhibits a clear presence of oxygen-rich population. We derive a carbon to M-star ratio of C/M = 0.56 ± 0.12, relatively high in comparison with many galaxies. The spatial distribution of the AGB stars in WLM hints at the presence of two stellar complexes with a size of a few hundred parsecs. Using the H i map of WLM and the derived gas-to-dust ratio for this galaxy N(H i)/E(B -V) = 60 ± 10 [10 21 at. cm -2 mag -1 ] we re-determined the distance modulus of WLM from the IR photometry of four known Cepheids, obtaining (m -M) 0 = 24.84 ± 0.14 mag. In addition, we determine the scale length of 0.75 ± 0.14 kpc of WLM disk in the J-band.

This work presents RMB IV: Extension of the Space–Matter–Motion Theory, which builds on RMB I–III by integrating Hannah Mira Cairo’s 2025 counterexample to the Mizohata–Takeuchi conjecture. The inclusion of fractal and non-smooth Fourier structures closes a key mathematical gap, allowing for resonance modeling beyond smooth functions.

By incorporating fractal resonance functions into the RMB framework, the theory achieves precise agreement with observed galactic rotation curves (Gaia DR3) and external galaxies (NGC 3198), without invoking dark matter. Residual analyses demonstrate that the RMB correction significantly reduces systematic discrepancies compared to Newtonian predictions.

Beyond astrophysics, RMB IV provides a unified explanation for quantum entanglement as a resonance phenomenon within a shared frequency domain. This positions the theory as a bridge between galactic dynamics and quantum physics, laying the foundation for experimental validation through Casimir effect measurements, 21 cm line surveys, and precision spacecraft flybys.

In the brane world scenario the four-dimensional effective Einstein equation has extra source terms, which arise from the embedding of the three-brane in the bulk. These non-local effects, generated by the free gravitational field of the bulk, may provide an explanation for the dynamics of the neutral hydrogen clouds at large distances from the galactic centre, which is usually explained by postulating the existence of the dark matter. In the present paper we consider the asymptotic behaviour of the galactic rotation curves in the brane world models, and compare the theoretical results with observations of both high surface brightness and low surface brightness galaxies. For the chosen sample of galaxies we determine first the baryonic parameters by fitting the photometric data to the adopted galaxy model; then we test the hypothesis of the Weyl fluid acting as dark matter on the chosen sample of spiral galaxies by fitting the tangential velocity equation of the combined baryonic-Weyl model to the rotation curves. We give an analytical expression for the rotational velocity of a test particle on a stable circular orbit in the exterior region to a galaxy, with Weyl fluid contributions included. The model parameter ranges for which the χ 2 test provides agreement (within 1σ confidence level) with observations on the velocity fields of the chosen galaxy sample are then determined. There is a good agreement between the theoretical predictions and observations, showing that extra-dimensional models can be effectively used as a viable alternative to the standard dark matter paradigm.

Longslit spectroscopy is entering an era of increased spatial and spectral resolution and increased sample size. Improved instruments reveal complex velocity structure that cannot be described with a one-dimensional rotation curve, yet samples are too numerous to examine each galaxy in detail. Therefore, one goal of rotation curve measurement techniques is to flag cases in which the kinematic structure of the galaxy is more complex than a single-valued curve. We examine cross-correlation as a technique that is easily automated and works for low signal-to-noise spectra. We show that the technique yields well-defined errors which increase when the simple spectral model (template) is a poor match to the data, flagging those cases for later inspection. We compare the technique to the more traditional, parametric technique of simultaneous emission line fitting. When the line profile at a single slit position is non-Gaussian, the techniques disagree. For our model spectra with two well-separated velocity components, assigned velocities from the two techniques differ by up to ∼52 % of the velocity separation of the model components. However, careful use of the error statistics for either technique allows one to flag these non-Gaussian spectra.

Longslit spectroscopy is entering an era of increased spatial and spectral resolution and increased sample size. Improved instruments reveal complex velocity structure that cannot be described with a one-dimensional rotation curve, yet samples are too numerous to examine each galaxy in detail. Therefore, one goal of rotation curve measurement techniques is to flag cases in which the kinematic structure of the galaxy is more complex than a single-valued curve. We examine cross-correlation as a technique that is easily automated and works for low signal-to-noise spectra. We show that the technique yields well-defined errors which increase when the simple spectral model (template) is a poor match to the data, flagging those cases for later inspection. We compare the technique to the more traditional, parametric technique of simultaneous emission line fitting. When the line profile at a single slit position is non-Gaussian, the techniques disagree. For our model spectra with two well-separated velocity components, assigned velocities from the two techniques differ by up to ∼52 % of the velocity separation of the model components. However, careful use of the error statistics for either technique allows one to flag these non-Gaussian spectra.

We present a fit of the rotation curve of galaxy UGC 1281 using a model based on metric inflow velocities, without invoking dark matter. The model relies on a minimal set of physical parameters: bulge radius R, baryonic bulge mass M, and the cosmological Hubble parameter H(z). We evaluate the performance of the model using two fixed values for H(z) based on the Planck and SH0ES determinations of H 0. The ability of the model to differentiate between these cosmological values is discussed.

In this work we introduced a new proposal to study the gravitational lensing theory by spherical lenses, starting from its surface mass density Σ(x) written in terms of a decreasing function f of a dimensionless coordinate x on the lens plane. The main result is the use of the function f (x) to find directly the lens properties, at the same time that the lens problem is described by a first order differential equation which encodes all information about the lens. SIS and NIS profiles are used as examples to find their functions f (x). Using the Poisson equation we find that the deflection angle is directly proportional to f (x), and therefore the lens equation can be written in terms of the function and the parameters of the lens. The critical and caustic curves, as well as image formation and magnification generated by the lens are analyzed. As an example of this method, the properties of a lens modeled by a NFW profile are determined. Altough the puntual mass is spherically symmetric, its mass density is not continuous so that its f (x) function is discussed in the Appendix A.

This research presents an experimental investigation and finite element model on the performance of composite beam-to-column flush end plate connections utilising blind bolts. Previous research recommended improvements to the design of these connections if they are required to withstand a low probability high consequence earthquake of a 1-in-2500 years return period. Therefore, two full-scale sub-assemblages of cruciform composite joints were tested under static and cyclic loading. The test results were used to establish the loaddisplacement characteristics of the connection. The experimental results demonstrated improved stiffness and strength when compared with a previous study. Two finite element models were developed and validated with the experimental data. Parametric studies were performed to investigate the influence of the thickness of equal angles, end plate thickness, shear connection ratio, reinforcement ratio and slab thickness on the connection behaviour.

The present paper is devoted to a study of the equilibrium configurations of slowly rotating anisotropic stars in the framework of general relativity. For that purpose, we provide the equations of structure where the rotation is treated to second order in the angular velocity. These equations extend those first derived by Hartle for slowly rotating isotropic stars. As an application of the new formalism, we study the rotational properties of Bowers-Liang fluid spheres. A result of particular interest is that the ellipticity and mass quadrupole moment are negative for certain highly anisotropic configurations; thus, such systems are prolate rather than oblate. Furthermore, for configurations with high anisotropy and compactness close to their critical value, quantities like the moment of inertia, change of mass, and mass quadrupole moment approach to the corresponding Kerr black hole values, similar to other ultracompact systems like sub-Buchdahl Schwarzschild stars and analytic rotating gravastars.

We present high resolution Hα rotation curves of 4 late-type dwarf galaxies and 2 low surface brightness galaxies (LSB) for which accurate HI rotation curves are available from the literature. Observations are carried out at Telescopio Nazionale Galileo (TNG). For LSB F583-1 an innovative dispersing element was used, the Volume Phase Holographic (VPH) with a dispersion of about 0.35 Åpxl -1 .

We have obtained interferometer observations of the central region of the Sb galaxy NGC 4527 in the CO (J = 1-0) line emission using the Nobeyama Millimeter Array. We also obtained optical (Ha, [Nil]) spectroscopy using the Okayama 188-cm reflector along the major axis. The kinematical structure and the distribution of HII regions show symmetry around the nucleus, while the distribution of molecular gas is asymmetric. The molecular-gas mass shares only 10% of the dynamical mass in the central 1 kpc radius region. Using position-velocity diagrams, we have derived a center-to-disk rotation curve. It rises steeply in the central region, attaining a maximum of about 250 km s _1 at 400 pc radius, and then decreases to a minimum at 2 kpc radius, followed by a disk and outer flat part. The rotation curve may provide us with the most similar case to that of the Milky Way Galaxy.

We have obtained optical CCD spectroscopy along the major axes of 22 nearby spiral galaxies of Sb and Sc types in order to analyze their rotation curves. By subtracting the stellar continuum emission, we have obtained position-velocity (PV) diagrams of the Ha and [Nil] lines. We point out that the Ha line is often superposed by a broad stellar absorption feature (Balmer wing) in the nuclear regions, and, therefore, the [Nil] line is a better tracer of kinematics in the central few hundred parsec regions. By applying the envelope-tracing technique to the Ha and [Nil] PV diagrams, we have derived nucleus-to-disk rotation curves of the observed galaxies. The rotation curves rise steeply within the central few hundred parsecs, indicating a rapidly rotating nuclear disk and mass concentration near the nucleus.

This report derives the rest energy of a quantum gravitational soliton using entropy, temperature, and acceleration relationships rooted in the Mo framework. Thermodynamic and quantum expressions converge to confirm that the rest energy E = M o c 2 can emerge from entropy-gradient and quantum-field dynamics.

We consider static and cylindrically symmetric interior string type solutions in the scalar-tensor representation of the hybrid metric-Palatini modified theory of gravity. As a first step in our study, we obtain the gravitational field equations and further simplify the analysis by imposing Lorentz invariance along the t and z axes, which reduces the number of unknown metric tensor components to a single function W 2 (r). In this case, the general solution of the field equations can be obtained, for an arbitrary form of the scalar field potential, in an exact closed parametric form, with the scalar field φ taken as a parameter. We consider in detail several exact solutions of the field equations, corresponding to a null and constant potential, and to a power-law potential of the form V (φ) = V0φ 3/4 , in which the behaviors of the scalar field, of the metric tensor components and of the string tension can be described in a simple mathematical form. We also investigate the string models with exponential and Higgs type scalar field potentials by using numerical methods. In this way we obtain a large class of novel stable string-like solutions in the context of hybrid metric-Palatini gravity, in which the basic parameters, such as the scalar field, metric tensor components, and string tension, depend essentially on the initial values of the scalar field, and of its derivative, on the r = 0 circular axis.

We consider the mass-radius bounds for spherically symmetric static compact objects in the de Rham-Gabadadze-Tolley (dRGT) Massive Gravity theories, free of ghosts. In this type of gravitational theories the graviton, the quantum of gravity, may have a small, but non-vanishing mass. We derive the hydrostatic equilibrium and mass continuity equations in the Lorentz-violating Massive gravity in the presence of a cosmological constant and for a non-zero graviton mass. The case of the constant density stars is also investigated by numerically solving the equilibrium equations. The influence of the graviton mass on the global parameters (mass and radius) of these stellar configurations is also considered. The generalized Buchdahl relations, giving the upper and lower bounds of the mass-radius ratio are obtained, and discussed in detail. As an application of our results we obtain gravitational redshift bounds for compact stellar type objects in the Lorentz-violating dRGT Massive Gravity, which may (at least in principle) be used for observationally testing this theory in an astrophysical context.

We consider global and gravitational lensing properties of the recently suggested Einstein clusters of WIMPs as galactic dark matter halos. Being tangential pressure dominated, Einstein clusters are strongly anisotropic systems which can describe any galactic rotation curve by specifying the anisotropy. Due to this property, Einstein clusters may be considered as dark matter candidates. We analyse the stability of the Einstein clusters against both radial and non-radial pulsations, and we show that the Einstein clusters are dynamically stable. With the use of the Buchdahl type inequalities for anisotropic bodies, we derive upper limits on the velocity of the particles defining the cluster. These limits are consistent with those obtained from stability considerations. The study of light deflection shows that the gravitational lensing effect is slightly smaller for the Einstein clusters, as compared to the singular isothermal density sphere model for dark matter. Therefore lensing observations may discriminate, at least in principle, between Einstein cluster and other dark matter models.

We consider the possibility that the dark matter, which is required to explain the dynamics of the neutral hydrogen clouds at large distances from the galactic center, could be in the form of a Bose-Einstein condensate. To study the condensate we use the non-relativistic Gross-Pitaevskii equation. By introducing the Madelung representation of the wave function, we formulate the dynamics of the system in terms of the continuity equation and of the hydrodynamic Euler equations. Hence dark matter can be described as a non-relativistic, Newtonian Bose-Einstein gravitational condensate gas, whose density and pressure are related by a barotropic equation of state. In the case of a condensate with quartic non-linearity, the equation of state is polytropic with index n = 1. In the framework of the Thomas-Fermi approximation the structure of the Newtonian gravitational condensate is described by the Lane-Emden equation, which can be exactly solved. General relativistic configurations with quartic non-linearity are studied, by numerically integrating the structure equations. The basic parameters (mass and radius) of the Bose-Einstein condensate dark matter halos sensitively depend on the mass of the condensed particle and of the scattering length. To test the validity of the model we fit the Newtonian tangential velocity equation of the model with a sample of rotation curves of low surface brightness and dwarf galaxies, respectively. We find a very good agreement between the theoretical rotation curves and the observational data for the low surface brightness galaxies. The deflection of photons passing through the dark matter halos is also analyzed, and the bending angle of light is computed. The bending angle obtained for the Bose-Einstein condensate is larger than that predicted by standard general relativistic and dark matter models. The angular radii of the Einstein rings are obtained in the small angles approximation. Therefore the study of the light deflection by galaxies and the gravitational lensing could discriminate between the Bose-Einstein condensate dark matter model and other dark matter models.

In both Newtonian gravity and Einstein gravity there is no force on a test particle located inside a spherical cavity cut out of a static, spherically symmetric mass distribution. Inside the cavity exterior matter is decoupled and there is no external field effect that could act on the test particle. However, for potentials other than the Newtonian potential or for geometries other than Ricci flat ones this is no longer the case, and there then is an external field effect. We explore this possibility in various alternate gravity scenarios, and suggest that such (Machian) external field effects can serve as a diagnostic for gravitational theory.

A series of numerical dynamical models for the LMC are constructed in order to fit the observed rotational velocities and stellar velocity dispersions at various galactocentric distances. The models include a three-dimensional spherical disk and nonevolving spherical components with various relative masses. The two LMC rotation curves presented by and Sofue (2000), which differ strongly in the inner region of the galaxy, are compared. The latter curve requires the presence of a massive dark bulge. Models based on the rotation curve of Sofue ( ) cannot account for the observed velocity dispersion or the presence of a long-lived bar in the galaxy. A model with no dark bulge is in good agreement with the observations if we assume that the disk dominates over the halo in terms of the mass within the optical radius (about 7 kpc). c 2002 MAIK "Nauka/Interperiodica".

This paper concludes a series of three papers presenting ROSAT High-Resolution Imager (HRI) observations of unidentified Einstein and serendipitous ROSAT X-ray sources in the direction of the Magellanic Clouds. Accurate positions and fluxes have been measured for these sources. Optical photometry and spectroscopy were obtained to search for identifications in order to determine the physical nature of these sources. The present paper includes new data for 24 objects; identifications are given or confirmed for 30 sources. For six sources optical finding charts showing the X-ray positions are provided. The results from this program are summarized, showing the populations of luminous X-ray sources in the Magellanic Clouds are quite different from those in the Galaxy

Bipolar planetary nebulae (BPNe) offer a unique opportunity to test models that aim to reproduce the PNe morphologies. In particular, kinematic studies of BPNe allow a reconstruction of the 3D structure of the nebula, otherwise hidden in imaging studies. With this aim in mind we have obtained long-slit echelle spectra of a sample of PNe which cover the full range of observed bipolar morphologies, from elliptical to highly collimated. The analysis of our kinematical data reveals equatorial expansion velocities in the low to medium range (3 to 16 km s -1 ), while the polar expansion velocities range from 18 to 100 km s -1 . We find that the kinematics of the PN K 3-46 can only be explained by a decrease in the expansion velocity with time. The kinematical ages, calculated by using distances estimated from Galactic rotation curves, when available, or by using statistical values, show that the BPNe in our sample -even those which show non-extreme collimation -appear to be young. We have compared our results with the latest theoretical models of BPN formation, and find good agreement between the observed expansion velocities and the numerical models that use magnetic fields coupled with stellar rotation as the collimation mechanism.

We investigate the variation of bar strength with central velocity dispersion in a sample of barred spiral galaxies. The bar strength is characterized by Q g , the maximal tangential perturbation associated with the bar, normalized by the mean axisymmetric force. It is derived from the galaxy potentials which are obtained using near-infrared images of the galaxies. However, Q g is sensitive to bulge mass. Hence we also estimated bar strengths from the relative Fourier intensity amplitude (A 2 ) of bars in near-infrared images. The central velocity dispersions were obtained from integral field spectroscopy observations of the velocity fields in the centers of these galaxies; it was normalized by the rotation curve amplitude obtained from HI line width for each galaxy. We found a correlation between bar strengths (both Q g and A 2 ) and the normalized central velocity dispersions in our sample. This suggests that bars weaken as their central components become kinematically hotter. This may have important implications for the secular evolution of barred galaxies.