Newtonian mechanics & gravity fully model disk galaxy rotation curves without dark matter

旋涡星系的旋转曲线和非牛顿引力：唯象方法

Rotation curves for spiral galaxies and non-Newtonian gravity: A phenomenological approach

螺旋星系的旋转曲线是已知的，具有合理的精度，为大量的星系具有类似的形态。数据表明，非开普勒下降--关闭被视为。这意味着（i）在星系尺度上一定存在大量的暗物质，或者（ii）牛顿引力必须以某种方式得到修正。本文提出了一种反演基本引力定律（如牛顿定律）与具有指数密度的薄圆盘分布所产生的引力场之间积分关系的方法。这使我们能够识别，直接从观察，{ \it扩展}的牛顿引力与属性的拟合一大类的旋转曲线。修改是从所观察到的旋转曲线推断，并最终写入牛顿常数或有效的潜在的测试质量在由点状粒子产生的字段中移动。

Spiral Galaxies Rotation Curves with a Logarithmic Corrected Newtonian Gravitational Potential

We analyze the rotation curves of 10 spiral galaxies with a newtonian potential corrected with an extra logarithmic term, using a disc modelization for the spiral galaxies. There is a new constant associated with the extra term in the potential. The rotation curve of the chosen sample of spiral galaxies is well reproduced for a given range of the new constant. It is argued that this correction can have its origin from string configurations. The compatibility of this correction with local physics is discussed.

Exploring the relativistic regime with Newtonian hydrodynamics: II. An effective gravitational potential for rapid rotation

We present the generalization of a recently introduced modified gravitational potential for self-gravitating fluids. The use of this potential allows for an accurate approximation of general relativistic effects in an otherwise Newtonian hydrodynamics code also in cases of rapid rotation. We test this approach in numerical simulations of astrophysical scenarios related to compact stars, like supernova core collapse with both a simplified and detailed microphysical description of matter, and rotating neutron stars in equilibrium. We assess the quality of the new potential, and demonstrate that …

Rotation curves of UMa galaxies in the context of modified Newtonian dynamics

This is the third in a series of papers in which spiral galaxy rotation curves are considered in the context of Milgrom's modified dynamics (MOND). The present sample of 30 objects is drawn from a complete sample of galaxies in the Ursa Major cluster with photometric data by Tully et al. (1996) and 21 cm line data by Verheijen (1997). The galaxies are roughly all at the same distance (15 to 16 Mpc). The radio observations are made with the Westerbork Synthesis Array which means that the linear resolution of all rotation curves is comparable. The greatest advantage of this sample is the existan…

Possible relation between galactic flat rotational curves and the Pioneers' anomalous acceleration

We consider a generic minimal modification of the Newtonian potential, that is a modification that introduces only one additional dimensional parameter. The modified potential depends on a function whose behavior for large and small distances can be fixed in order to obtain respectively (i) galactic flat rotational curves and (ii) a universal constant acceleration independent of the masses of the interacting bodies (Pioneer anomaly). Then using a dimensional argument we show that the Tully-Fisher relation for the maximal rotational velocity of spiral galaxies follows without any further assump…

Galactic Rotation Described with Various Thin-Disk Gravitational Models

For mature spiral galaxies, the rotation velocities quickly increase from the galactic center and achieve a constant velocity from the core to the periphery. This dynamic behavior is described by models balancing Newtonian gravitational and centrifugal forces in rotating thin axisymmetric disks. Freeman's disk assumes a mass density decreasing exponentially with radius which correctly produces rotational velocities which increase from the galactic center to a maximum near the outer core, but then decreases out to the periphery contrary to measurements. Mestel's disk assumes a mass distribution…

Scalar potential model of spiral galaxy HI rotation curves and rotation curve asymmetry

A scalar potential model (SPM) was developed from considerations of galaxy clusters and of redshift. The SPM is applied to HI rotation curves (RCs) and RC asymmetry of spiral galaxies. The resulting model adds the force of a scalar potential of the host galaxy and of neighboring galaxies to the Newtonian rotation velocity equation. The RC is partitioned radially into regions. The form of the equation for each parameter of each region is the same with differing proportionality constants. Integer values of each equation are determined empirically for each galaxy. Among the sample galaxies, the g…

Newtonian Aspects of General Relativistic Galaxy Models

Many cosmological observations call for the existence of dark matter. The most direct evidence for dark matter is inferred from the measured flatness of galactic rotation curves. The latter is based on Newtonian gravity. Alternative approaches to the rotation curve problem by means of general relativity have recently been put forward. The class of models of interest is a subset of the axially symmetric and stationary solutions of Einstein's equations with rotating dust. As a step toward the understanding of general relativistic galaxy models, we analyse rigidly as well as non-rigidly rotating …

Time evolution of the linear perturbations of a rotating Newtonian polytrope

We present the results of numerical time evolutions of the linearised perturbations of rapidly and rigidly rotating Newtonian polytropes while making the Cowling approximation. The evolution code runs stably for hundreds of stellar rotations, allowing us to compare our results with previously published eigenmode calculations, for instance the f-mode calculations of Ipser & Lindblom, and the r-mode calculations of Karino et al. The mode frequencies were found to be in agreement within the expected accuracy. We have also examined the inertial modes recently computed by Lockitch & Friedman, and w…

Modified Newtonian Dynamics as an Alternative to Dark Matter

Modified Newtonian dynamics (MOND) is an empirically motivated modification of Newtonian gravity or inertia suggested by Milgrom as an alternative to cosmic dark matter. The basic idea is that at accelerations below a0 ~ 10^{-8} cm/s^2 ~ cH0/6 the effective gravitational attraction approaches sqrt{gN*a0} where gN is the usual Newtonian acceleration. This simple algorithm yields flat rotation curves for spiral galaxies and a mass-rotation velocity relation of the form M ~ V^4 that forms the basis for the observed luminosity-rotation velocity relation-- the Tully-Fisher law. We review the phenom…

Mass Distribution, Rotation Curves and Gravity Theories

{Comparison of mass density profiles of galaxies of varying sizes based on some gravity theories from observed galaxy rotation curves and assessing the need for dark matter.} We present an analysis of the rotation curves of five galaxies of varying galactic radii: NGC6822 (4.8 kpc), Large Magellanic Cloud (9 kpc), The Milky Way (17 kpc), NGC3198 (30 kpc) and UGC9133 (102.5 kpc). The mass and mass density profiles of these galaxies have been computed using the scientific computing s/w package MATLAB taking the already available velocity profiles of the galaxies as the input, and without conside…

R-mode oscillations of differentially and rapidly rotating Newtonian polytropic stars

For the analysis of the r-mode oscillation of hot young neutron stars, it is necessary to consider the effect of it differential rotation, because viscosity is not strong enough for differentially rotating young neutron stars to be lead to uniformly rotating configurations on a very short time scale after their birth. In this paper, we have developed a numerical scheme to solve r-mode oscillations of differentially rotating polytropic inviscid stars. This is the extended version of the method which was applied to compute r-mode oscillations of uniformly rotating Newtonian polytropic stars. By …

Torsional Oscillations of Slowly Rotating Relativistic Stars

We study the effects of rotation on the torsional modes of oscillating relativistic stars with a solid crust. Earlier works in Newtonian theory provided estimates of the rotational corrections for the torsional modes and suggested that they should become CFS unstable, even for quite low rotation rates. In this work, we study the effect of rotation in the context of general relativity using elasticity theory and in the slow-rotation approximation. We find that the Newtonian picture does not change considerably. The inclusion of relativistic effects leads only to quantitative corrections. The de…

Non-Newtonian behavior in weak field general relativity for extended rotating sources

Exact stationary axially symmetric solutions of the 4D Einstein equations with corotating pressureless perfect fluid sources are studied. A particular solution with approximately flat rotation curve is discussed in some detail. We find that simple Newtonian arguments overestimate the amount of matter needed to explain these curves by more than 30%. The crucial insight gained by this model is that the Newtonian approximation breaks down globally, even though it is valid locally everywhere. No conflict with solar system tests arises.

Solar System tests of some models of modified gravity proposed to explain galactic rotation curves without dark matter

We consider the recently estimated corrections Δ\dot\varpi to the Newtonian/Einsteinian secular precessions of the longitudes of perihelia \varpi of several planets of the Solar System in order to evaluate whether they are compatible with the predicted precessions due to models of long-range modified gravity put forth to account for certain features of the rotation curves of galaxies without resorting to dark matter. In particular, we consider a logarithmic-type correction and a f(R) inspired power-law modification of the Newtonian gravitational potential. The results obtained by taking the ra…