We consider three samples of O- and B-type stars from the solar neighborhood 0.6--4 kpc for which we have taken the distances, line-of-sight velocities, and proper motions from published sources. The first sample contains 120 massive spectroscopic binaries. O stars with spectroscopic distances from Patriarchi et al. constitute the second sample. The third sample consists of 168 OB3 stars whose distances have been determined from interstellar calcium lines. The angular velocity of Galactic rotation at the solar distance $Ω_0,$ its two derivatives $Ω'_0$ and $Ω"_0,$ and the peculiar velocity components of the Sun $(U,V,W)_\odot$ are shown to be well determined from all three samples of stars. They are determined with the smallest errors from the sample of spectroscopic binary stars and the sample of stars with the calcium distance scale. The fine structure of the velocity field associated with the influence of the Galactic spiral density wave clearly manifests itself in the radial velocities of spectroscopic binary stars and in the sample of stars with the calcium distance scale.
We propose a method to determine the galactic constants R_0 (distance to the Galactic Center) and V_0 (rotation velocity of the Sun) from measurements of distances, radial velocities and proper motions of objects near the solar circle. This is a modification of the solar-circle method to a more practical observational method. We apply the method to determine R_0 using data from the literature with known distances and radial velocities, and obtain R_0 = 7.54 +/- 0.77 kpc.
The fundamental 28SiH+ ion has been characterized in a collaborative work, utilizing a hollow-cathode-discharge laser-spectrometer and a cryogenic ion trap spectrometer. Twenty-three vibration-rotation transitions around 4.75 um have been detected with high accuracy. This has facilitated the first direct measurement of the pure rotational transition J=1<-0 at 453056.3632(4) MHz in the trap spectrometer. The measured and accurately predicted transitions enable the search for this ion in space with IR and sub-mm telescopes.
Here we statistically evaluate recent advances in determining the Sun-Galactic Center distance (Rsun) as well as recent measures of the orbital velocity around the Galactic Center (Vlsr), and the angular rotation parameters of various objects. Recent statistical results point to Rsun = 8.0 +- 0.2 kpc, Vlsr= 230 +- 3 km/s, and angular rotation at the Sun (ω) near 29 +- 1 km/s/kpc for the gas and stars at the Local Standard of Rest, and near 23 +- 2 km/s/kpc for the spiral pattern itself. This angular difference is similar to what had been predicted by density wave models, along with the observa…
The Exeter FCRAO CO Galactic Plane Survey consists of 12CO and 13CO (J=1-0) observations over the galactic plane covering 55 degrees <= l <= 102 degrees, |b| >= 1 degree and 141 degrees <= l <= 195 degrees, -3.5 degrees <= b <= 5.5 degrees with a spatial resolution of ~45" and a spectral resolution of ~0.15km/s. We will present the methodology of a threshold-based cloud and clump determination method which retains hierarchical information, then discuss associating sources with clouds in the catalogue. Once complete, this catalogue of clouds and clumps will encompass the majority of the Norther…
The rotation curve of a magnetized plasma cloud orbiting in the gravitational potential of a galaxy is calculated by statistical arguments. The working assumption is that a mild magnetic field, decreasing with distance from the galactic center, permeates space. It is shown that the resulting probability density is compatible with a flat rotation curve.
We revisit the methods to determine the Galactic rotation curve and kinematical distances from radial velocities and proper motions. We construct "accuracy diagrams" to show the distributions in the galactic plane of expected uncertainties in the derived quantities such as rotation velocities and kinematical distances. We discuss how to optimize the source selection for measurements of kinematical quantities based on the accuracy diagrams.
The rotation of the galactic objects has been seen by asymmetric Doppler shift in the CMB data. Molecular hydrogen clouds at virial temperature may contribute to the galactic halo dark matter and they might be the reason for the observed rotational asymmetry in the galactic halos. We present a method to constrain the parameters of these virial clouds given that they are composed of a single fluid. The method is such that it should be possible to extend it to more than one fluid.
I present an alternative explanation of flat rotational curves of galaxies that does not require dark matter but rather relies on classical Newtonian dynamics and an overlooked effect of quantum tunneling. I introduce a rotational drag force, which arises from subatomic particle tunneling through potential barriers caused by energy fluctuations in rotating gravitational field, and present a model for a galactic rotational curve based on Newtonian dynamics, rotational drag force and galactic mass-density distribution. To support the rotational drag force hypothesis I supply the results of analy…
We conducted the astrometry of H2O masers in the Galactic star-forming region Onsala 1 (ON1) with VLBI Exploration of Radio Astrometry (VERA). We measured a trigonometric parallax of 0.404+/-0.017 mas, corresponding to a distance of 2.47+/-0.11 kpc. ON1 is appeared to be located near the tangent point at the Galactic longitude of 69.54 deg. We estimate the angular velocity of the Galactic rotation at Sun, the ratio of the distance from Sun to the Galactic center and the Galactic rotation velocity at Sun, to be 28.7+/-1.3 km/s/kpc using the measured distance and proper motion of ON1. This value…
Faraday rotation provides a valuable tracer of magnetic fields in the interstellar medium; catalogs of Faraday rotation measures provide key observations for studies of the Galactic magnetic field. We present a new catalog of rotation measures derived from the Canadian Galactic Plane Survey, covering a large region of the Galactic plane spanning 52 deg < l < 192 deg, -3 deg < b < 5 deg, along with northern and southern latitude extensions around l ~ 105 deg. We have derived rotation measures for 2234 sources (4 of which are known pulsars), 75% of which have no previous measurements, over an ar…
Action-angle coordinates are an essential tool for understanding the properties of the six dimensional phase space involved in orbits of stars in galactic potentials. A new method, which does not require specific knowledge of a generating function, is described, implemented and tested that calculates the actions of an orbit in an arbitrary potential of an integrable Hamiltonian given a set of Cartesian phase space points. The method chooses between the simple harmonic oscillator and isochrone potentials to fit the data using a Levenberg-Marquardt routine. An average is taken over the angle coo…
In galactic disks, galactic rotation sets the bulk motion of gas, and its energy and momentum can be transferred toward small scales. Additionally, in the interstellar medium, random and noncircular motions arise from stellar feedback, cloud-cloud interactions, and instabilities, among other processes. Our aim is to comprehend to which extent small-scale gas dynamics is decoupled from galactic rotation. We study the relative contributions of galactic rotation and local noncircular motions to the circulation of gas, $Γ$, a macroscopic measure of local rotation, defined as the line integral of t…
We present the measurements of Faraday rotation for 477 pulsars observed by the Parkes 64-m radio telescope and the Green Bank 100-m radio telescope. Using these results along with previous measurements for pulsars and extra-galactic sources, we analyse the structure of the large-scale magnetic field in the Galactic disk. Comparison of rotation measures of pulsars in the disk at different distances as well as with rotation measures of background radio sources beyond the disk reveals large-scale reversals of the field directions between spiral arms and interarm regions. We develop a model for t…
We present new measurements of the centers for 65 Milky Way globular clusters. Centers were determined by fitting ellipses to the density distribution within the inner $2\arcmin$ of the cluster center, and averaging the centers of these ellipses. The symmetry of clusters was also analyzed by comparing cumulative radial distributions on opposite sides of the cluster across a grid of trial centers. All of the determinations were done with stellar positions derived from a combination of two single-orbit ACS images of the core of the cluster in $F606W$ and $F814W$. We find that the ellipse-fitting…
We have determined the Galactic rotation parameters and the solar Galactocentric distance R_0 by simultaneously solving Bottlinger's kinematic equations using data on masers with known line-of-sight velocities and highly accurate trigonometric parallaxes and proper motions measured by VLBI. Our sample includes 73 masers spanning the range of Galactocentric distances from 3 to 14 kpc. The solutions found are Omega_0 = 28.86 +/- 0.45 km/s/kpc, Omega'_0 = -3.96 +/- 0.09 km/s/kpc^2, Omega"_0 =0.790 +/- 0.027 km/s/kpc^3, and R_0=8.3 +/- 0.2 kpc.In this case, the linear rotation velocity at the sola…
In the past few decades, some studies pointed out that magnetic field might affect the rotation curves in galaxies. However, the impact is relatively small compared with the effects of dark matter and the baryonic components. In this letter, we revisit the impact of magnetic field on the rotation curve of our Galaxy. We show that the inner Galactic rotation curve could be affected significantly by the magnetic field. The addition of the inner bulge component, which has been proposed previously to account for the inner rotation curve data, is not necessary. The magnetic field contribution can f…
Interstellar magnetic fields play critical roles in many astrophysical processes. Yet despite their importance, our knowledge about magnetic fields in our Galaxy remains limited. For the field within the Milky Way, much of what we do know comes from observations of polarisation and Faraday rotation measures (RMs) of extragalactic sources and pulsars. A high angular density of RM measurements in several critical areas of the Galaxy is needed to clarify the Galactic magnetic field structure. Using observations made with the VLA, we have determined RMs for sources in regions of the Galactic plane…
We revisit the anomaly of rotation curve in the nearly face-on galaxy M51 that shows an apparently faster decrease of rotation velocity than the Keplerian law in the outer disk, further showing apparent counter rotation in the outermost HI disk. We interpret this anomaly as due to warping of the galactic disk, and determined the warping structure of M51's disk using the tilted-ring method, assuming that the intrinsic rotation curve is normal. It is shown that the disk is nearly flat in the inner disk at a constant inclination angle, but the disk suddenly bends at radius 7.5 kpc by about 27$°$.…
In this paper we present a brief discussion on the salient points of the computational analysis that are at the basis of the paper \cite{StSc}. The computational and data analysis have been made with the software Mathematica$^\circledR$ and presented at Mathematica Italia User Group Meeting 2011.
Based on data on Galactic masers with measured trigonometric parallaxes, we have tested a nonlinear model of Galactic rotation using generalized Oort formulas. This model is shown to yield pretty good results up to heliocentric distances of 3--4 kpc. The main feature of the method is the possibility of estimating the solar Galactocentric distance Ro. This distance has been found by analyzing approximately 60 masers to be Ro=8.3+/-0.4 kpc. Our study of the three-dimensional kinematics of more than 100 masers based on the Ogorodnikov--Milne model has shown that significant nonlinearities are pre…
We present a study of the vertical magnetic field of the Milky Way towards the Galactic poles, determined from observations of Faraday rotation toward more than 1000 polarized extragalactic radio sources at Galactic latitudes |b| > 77 degs, using the Westerbork Radio Synthesis Telescope and the Australia Telescope Compact Array. We find median rotation measures (RMs) of 0.0 +/- 0.5 rad/m^2 and +6.3 +/- 0.7 rad/m^2 toward the north and south Galactic poles, respectively, demonstrating that there is no coherent vertical magnetic field in the Milky Way at the Sun's position. If this is a global p…
Analyzing high-resolution longitude-velocity (LV) diagrams of the Galactic Center observed with the Nobeyama 45-m telescope in the CO and CS line emissions, we obtain a central rotation curve of the Milky Way. We combine it with the data for the outer disk, and construct a logarithmic rotation curve of the entire Galaxy. The new rotation curve covers a wide range of radius from r ~ 1 pc to several hundred kpc without a gap of data points. It links, for the first time, the kinematical characteristics of the Galaxy from the central black hole to the bulge, disk and dark halo. Using this grand ro…
We examine the constraints imposed by Faraday rotation measures of extragalactic point sources on the structure of the magnetic field in the halo of our Galaxy. Guided by radio polarization observations of external spiral galaxies, we look in particular into the possibility that field lines in the Galactic halo have an X shape. We employ the analytical models of spiraling, possibly X-shape magnetic fields derived in a previous paper to generate synthetic all-sky maps of the Galactic Faraday depth, which we fit to an observational reference map with the help of Markov Chain Monte Carlo simulati…
The determination of ages of central stars of planetary nebulae (CSPN) is a complex problem, and there is presently no single method that can be generally applied. We have developed several methods to estimate the ages of CSPN, based both on the observed nebular properties and in some properties of the stars themselves.Our aim is to estimate the ages and the age distribution of CSPN and to compare the derived results with mass and age determinations of CSPN and white dwarfs based on empirical determinations of these quantities. We discuss several methods to derive the age distribution of CSPN,…
We report on the detection of a small overdensity of stars in velocity space with systematically higher Galactocentric rotation velocity than the Sun by about 20 km s$^{-1}$ in the $Gaia$ Data Release 1 Tycho-Gaia astrometric solution (TGAS) data. We find these fast Galactic rotators more clearly outside of the Solar radius, compared to inside of the Solar radius. In addition, the velocity of the fast Galactic rotators is independent of the Galactocentric distance up to $R-R_{\odot}\sim0.6$ kpc. Comparing with numerical models, we qualitatively discuss that a possible cause of this feature is …
As galactic halos are not directly visible, there are many ambiguities regarding their composition and rotational velocity. Though most of the dark matter is non-baryonic, {\it some fraction is}, and it can be used to trace the halo rotation. Asymmetries in the CMB towards M31 had been seen in the Planck data and ascribed to the rotational Doppler shift of the M31 halo. Subsequently, the same methods were used in the direction of five other galaxies belonging to the Local Group, namely M33, M81, M82, NGC 5128, and NGC 4594. It had been proved that there could be stable clouds of gas and dust i…
We consider the problem of determining the geometric parameters of a Galactic spiral arm from its segment by including the distance to the spiral pole, i.e., the distance to the Galactic center ($R_0$). The question about the number of points belonging to one turn of a logarithmic spiral and defining this spiral as a geometric figure has been investigated numerically and analytically by assuming the direction to the spiral pole (to the Galactic center) to be known. Based on the results obtained, in an effort to test the new approach, we have constructed a simplified method of solving the probl…
Rotation measures of pulsars and extragalactic point sources have been known to reveal large-scale antisymmetries in the Faraday rotation sky with respect to the Galactic plane and halo that have been interpreted as signatures of the mean magnetic field in the Galactic halo. We describe Faraday rotation measurements of the diffuse Galactic polarized radio emission over a large region in the northern Galactic hemisphere. Through application of Rotation Measure Synthesis we achieve sensitive Faraday rotation maps with high angular resolution, capable of revealing fine-scale structures of about 1…
We present a study of the Milky Way disk and halo magnetic field, determined from observations of Faraday rotation measure (RM) towards 641 polarized extragalactic radio sources in the Galactic longitude range 100-117 degs, within 30 degs of the Galactic plane. For |b| < 15 degs, we observe a symmetric RM distribution about the Galactic plane. This is consistent with a disk field in the Perseus arm of even parity across the Galactic mid-plane. In the range 15<|b|<30 degs, we find median rotation measures of -15+/-4 rad/m^2 and -62+/-5 rad/m^2 in the northern and southern Galactic hemispheres, …
We discuss a model for the Milky Way obtained by fitting the observed terminal velocities with the radial acceleration relation. The resulting stellar surface density profile departs from a smooth exponential disk, having bumps and wiggles that correspond to massive spiral arms. These features are used to estimate the term for the logarithmic density gradient in the Jeans equation, which turn out to have exactly the right location and amplitude to reconcile the apparent discrepancy between the stellar rotation curve and that of the interstellar gas. This model also predicts a gradually declini…
The paper investigates the question of whether or not determinations of the distance between the Sun and the Galactic center R0 are affected by the so-called "bandwagon effect", leading to selection effects in published data that tend to be close to expected values, as was suggested by some authors. It is difficult to estimate numerically a systematic uncertainty in R0 due to the bandwagon effect; however, it is highly probable that, even if widely accepted values differ appreciably from the true value, the published results should eventually approach the true value despite the bandwagon effec…
Here we discuss impacts of distance determinations on the Galactic disk traced by relatively young objects. The Galactic disk, about 40 kpc in diameter, is a cross-road of studies on the methods of measuring distances, interstellar extinction, evolution of galaxies, and other subjects of interest in astronomy. A proper treatment of interstellar extinction is, for example, crucial for estimating distances to stars in the disk outside the small range of the solar neighborhood. We'll review the current status of relevant studies and discuss some new approaches to the extinction law. When the exti…
Helical randomization of magnetized Galactic and galaxy clusters plasmas: from magnetorotational disc dynamo to the Faraday rotation and synchrotron emission skies
We present an online catalog of distance determinations for $\rm 6036$ K giants, most of which are members of the Milky Way's stellar halo. Their medium-resolution spectra from SDSS/SEGUE are used to derive metallicities and rough gravity estimates, along with radial velocities. Distance moduli are derived from a comparison of each star's apparent magnitude with the absolute magnitude of empirically calibrated color-luminosity fiducials, at the observed $(g-r)_0$ color and spectroscopic [Fe/H]. We employ a probabilistic approach that makes it straightforward to properly propagate the errors in…
A unified parametrization of the circular velocity, which accurately fits 850 galaxy rotation curves without needing in advance the knowledge of the luminous matter components, nor a fixed dark matter halo model, is proposed. A notable feature is that the associated gravitational potential increases with the distance from the galaxy center, giving rise to a length scale indicating a finite size of a galaxy, and after, the Keplerian fall-off of the parametrized circular velocity is recovered according to Newtonian gravity, making possible the estimation of the total mass enclosed by the galaxy.
Dark matter has been a long-standing and important issue in physics, but direct evidence of its existence is lacking. This work aims to elucidate the mystery and show that the dark matter hypothesis is unnecessary. We can nicely reproduce the observed rotation curves using only conventional Newtonian dynamics based on experimental surface brightness profiles of several galaxies. Our success is based on realizing that the mass radial distribution follows a stretched exponential decay with a small exponent over a few hundred kiloparsecs. Our quantitative analysis indicates that for these four ex…
One of the key parameters that characterize spiral arms in disk galaxies is a pitch angle that measures the inclination of a spiral arm to the direction of galactic rotation. The pitch angle differs from galaxy to galaxy, which suggests that the rotation law of galactic disks determines it. In order to investigate the relation between the pitch angle of spiral arms and the shear rate of galactic differential rotation, we perform local $N$-body simulations of pure stellar disks. We find that the pitch angle increases with the epicycle frequency and decreases with the shear rate and obtain the f…
In this paper we derive a novel circular velocity relation for a test particle in a 3D gravitational potential applicable to every system of curvilinear coordinates, suitable to be reduced to orthogonal form. As an illustration of the potentiality of the determined circular velocity expression we perform the rotation curves analysis of UGC 8490 and UGC 9753 and we estimate the total and dark matter mass of these two galaxies under the assumption that their respective dark matter halos have spherical, prolate and oblate spheroidal mass distributions. We employ stellar population synthesis model…
We carried out global three-dimensional magneto-hydrodynamic simulations of dynamo activities in galactic gaseous disks without assuming equatorial symmetry. Numerical results indicate the growth of azimuthal magnetic fields non-symmetric to the equatorial plane. As magneto-rotational instability (MRI) grows, the mean strength of magnetic fields is amplified until the magnetic pressure becomes as large as 10% of the gas pressure. When the local plasma $β$ ($ = p_{\rm gas}/p_{\rm mag}$) becomes less than 5 near the disk surface, magnetic flux escapes from the disk by Parker instability within o…
I present three methods to determine the distance to the Galactic centre R0, the solar azimuthal velocity in the Galactic rest frame Vg,\odot and hence the local circular speed Vc at R0. These simple, model-independent strategies reduce the set of assumptions to near axisymmetry of the disc and are designed for kinematically hot stars, which are less affected by spiral arms and other effects. The first two methods use the position-dependent rotational streaming in the heliocentric radial velocities U. The resulting rotation estimate θ from U velocities does not depend on Vg,\odot. The first ap…
The recently formulated model of black holes coupled to the radial flows of dark matter (RDM-stars) is considered and the shape of the galactic rotation curves predicted by the model is evaluated. Under the assumption that the density of black holes is proportional to the density of luminous matter, the model perfectly fits the experimental data, both for the universal rotation curve, describing the spiral galaxies of a general form, and for the grand rotation curve, describing the orbital velocities of Milky Way galaxy in a wide range of distances. The modeling of the galactic gravitational f…
We present here a quantitative, accurate estimate of the impact of uncertainties of astrophysical nature on the determination of the dark matter distribution within our Galaxy, the Milky Way. Based on an update of a previous analysis, this work is motivated by recent new determinations of astrophysical quantities of relevance -- such as the Galactic parameters (R0,V0) -- from the GRAVITY collaboration and the GAIA satellite, respectively. We find that even with these state-of-the-art determination and a range of uncertainties -- both statistical and systematic -- much narrowed with respect to …
Here we review the efforts of a number of recent results that use old tracers to understand the build up of the Galaxy. Details that lead directly to using these old tracers to measure distances are discussed. We concentrate on the following: (1) the structure and evolution of the Galactic bulge and inner Galaxy constrained from the dynamics of individual stars residing therein; (2) the spatial structure of the old Galactic bulge through photometric observations of RR Lyrae-type stars; (3) the three\--dimensional structure, stellar density, mass, chemical composition, and age of the Milky Way …
Conformal gravity theory can explain observed flat rotation curves of galaxies without invoking hypothetical dark matter. Within this theory, we obtain a generic formula for the sizes of galaxies exploiting the stability criterion of circular orbits. It is found that different galaxies have different finite sizes uniquely caused by the assumed quadratic potential of cosmological origin. Observations on where circular orbits might actually terminate could thus be very instructive in relation to the galactic sizes predicted here.
We estimated the magnetic field strength at the event horizon for a sample of supermassive black holes (SMBHs) in active galactic nuclei (AGNs). Our estimates were made using the values of the inclination angles of the accretion disk to the line of sight, that we obtained previously from spectropolarimetric observations in the visible spectrum. We also used published values of full width at half maximum (FWHM) of spectral line $H_β$ from broad line region, masses of SMBHs and luminosity of AGNs at 5100 angstrom. In addition we used literature data on the spins of SMBHs obtained from their X-ra…
In this paper we present the discussion on the salient points of the computational analysis that are at the basis of the paper \emph{Rotation Curves of Galaxies by Fourth Order Gravity} \citep{StSc}. In fact in this paper any galactic component (bulge, disk and Dark matter component) required an onerous numerical computation since the Gauss theorem is not applicable in the Fourth Order Gravity. The computational and data analysis have been made with the software Mathematica$^\circledR$.
We investigate galactic rotation curves in $f(T)$ gravity, where $T$ represents a torsional quantity. Our study centers on the particular Lagrangian $f(T)=T+α{T^n}$, where $|n|\neq 1$ and $α$ is a small unknown constant. To do this we treat galactic rotation curves as being composed from two distinct features of galaxies, namely the disk and the bulge. This process is carried out for several values of the index $n$. The resulting curve is then compared with Milky Way profile data to constrain the value of the index $n$ while fitting for the parameter $α$. These values are then further tested o…
We study geometries of galactic rotation curves from Dark Matter (DM) and Modified Newtonian Dynamics (MOND) models in $(g_{\rm bar},g_{\rm tot})$-space ($g2$-space) where $g_{\rm tot}$ is the total centripetal acceleration of matter in the galaxies and $g_{\rm bar}$ is that due to the baryonic (visible) matter assuming Newtonian gravity. The $g2$-space geometries of the models and data from the SPARC database are classified and compared in a rescaled $\hat{g}2$-space that reduces systematic uncertainties on galaxy distance, inclination angle and variations in mass to light ratios. We find tha…
We show quantitatively that an exact solution of Einstein's conformal gravity can explain very well the galactic rotation curves for a sample of 104 galaxies without need for dark matter or other exotic modification of gravity. The metric is an overall rescaling of the Schwarzschild-de Sitter spacetime as required by Weyl conformal invariance, which has to be spontaneously broken, and the velocity of the stars depends only on two universal parameters determined on the base of the observational data.
Collider, space, and Earth based experiments are now able to probe several extensions of the Standard Model of particle physics which provide viable dark matter candidates. Direct and indirect dark matter searches rely on inputs of astrophysical nature, such as the local dark matter density or the shape of the dark matter profile in the target in object. The determination of these quantities is highly affected by astrophysical uncertainties. The latter, especially those for our own Galaxy, are ill-known, and often not fully accounted for when analyzing the phenomenology of particle physics mod…
We report results from an exploratory study implementing a new probe of Galactic evolution using archival Hubble Space Telescope imaging observations. Precise proper motions are combined with photometric relative metallicity and temperature indices, to produce the proper motion rotation curves of the Galactic bulge separately for metal-poor and metal-rich Main Sequence samples. This provides a "pencil-beam" complement to large-scale wide-field surveys, which to-date have focused on the more traditional bright Giant Branch tracers. We find strong evidence that the Galactic bulge rotation curves…
On the basis of the Poincare-Weyl gauge theory of gravitation, a new conformal Weyl-Dirac theory of gravitation is proposed, which is a gravitational theory in Cartan-Weyl spacetime with the Dirac scalar field representing the dark matter model. A static approximate axially symmetric solution of the field equations in vacuum is obtained. On the base of this solution in the Newtonian approximation one considers the problem of rotation velocities in spiral components of galaxies.
There are two observations of galaxies that can offer some insight into the nature of the dark matter (DM), namely the rotation curves and the gravitational lensing. While the first one can be studied using the Newtonian limit, the second one is completely relativistic. Each one separately can not determine the nature of DM, but both together give us key information about this open problem. In this work we use a static and spherically symmetric metric to model the DM halo in a galaxy or in a galaxy cluster. The metric contains two free functions, one associated with the distribution of mass an…
