Dav Lev said: "Therefore, the shape of spiral galaxy can't be used as a prove for the dark matter." Also, see further below, the definition of Milgromian dynamics, which seeks to replace the ideas of dark matter and Newtonian mechanics in galactic rotation.
However, the OCTOBER 22, 2016 Blog from Harvard states: Galactic Rotation Curves Revisited: A Surprise for Dark Matter
Historically, galactic rotation curves have suggested that galaxies are surrounded by a vast amount of invisible matter, otherwise known as a dark matter halo. A few weeks ago, a team of astrophysicists published a result that completely contradicts these halo models and could even change the popular understanding of dark matter. The team found that galactic rotation curves can be calculated explicitly from a simple equation that only depends on the amount of visible matter in the galaxy. The exact implications of this finding are still unclear, but the authors do suggest a few possibilities.
A galactic rotation curve is the radial velocity of the stars, dust, and gas that make up a galaxy plotted as a function of their distance from the galaxy’s center. Based on visible matter alone, one would expect that stars closest to the center of the galaxy would move faster than the stars near the galaxy’s outer edge (dashed line). However, in most galaxies inner and outer stars move at roughly the same velocity (solid line). There is some additional gravitational pull on the outer stars that isn’t fully described by the amount of visible matter in a galaxy. Most scientists have interpreted these rotation curves to mean that galaxies are surrounded by a halo of invisible dark matter. Image obtained under Creative Commons License. Credit: Gemini Observatory
At first glance, the group’s result suggests one could successfully develop a model of galactic rotation curves by modifying gravity, rather than adding in dark matter. However, astrophysicists have made several other observations of the universe that imply modifying gravity isn’t the best way to successfully describe nature. Alternatively, this result could imply a surprising coupling between regular and dark matter, making the two types of matter more correlated than expected. If this scenario were the case, the next step would be to try and probe this coupling in other dark matter experiments.There is a great deal of excitement surrounding the announcement. It is rare in science to find such a simple equation, with no adjustable parameters that describe observed data. The finding also appears to apply to all spiral and irregular galaxies, regardless of shape or size. Such an elegant and universal relationship suggests a new discovery could be just around the corner.
Acknowledgements: Many thanks to Emma Tolley, a PhD graduate student in Physics. Emma is a member of the Harvard ATLAS group, and is currently searching for dark matter signatures at the LHC.
Managing Correspondent: Karri DiPetrillo
"
Galactic rotation curves, the baryon-to-dark-halo-mass relation and space-time scale invariance"
by
Xufen Wu,
Pavel Kroupa
Low-acceleration space-time scale invariant dynamics (SID, Milgrom 2009a) predicts two fundamental correlations known from observational galactic dynamics: the baryonic Tully-Fisher relation (BTFR) and a correlation between the observed mass discrepancy and acceleration (MDA) in the low acceleration regime for disc galaxies. SID corresponds to the deep MOdified Newtonian Dynamics (MOND) limit. The MDA data emerging in cold/warm dark matter (C/WDM) cosmological simulations disagree significantly with the tight MDA correlation of the observed galaxies. Therefore, the most modern simulated disc galaxies, which are delicately selected to have a quiet merging history in a standard dark-matter-cosmological model, still do not represent the correct rotation curves. Also, the observed tight correlation contradicts the postulated stochastic formation of galaxies in low-mass DM halos. Moreover, we find that SID predicts a baryonic to apparent virial halo (dark matter) mass relation which agrees well with the correlation deduced observationally assuming Newtonian dynamics to be valid, while the baryonic to halo mass relation predicted from CDM models does not. The distribution of the observed ratios of dark-matter halo masses to baryonic masses may be empirical evidence for the external field effect, which is predicted in SID as a consequence of the forces acting between two galaxies depending on the position and mass of a third galaxy. Applying the external field effect, we predict the masses of galaxies in the proximity of the dwarf galaxies in the Miller et al. sample. Classical non-relativistic gravitational dynamics is thus best described as being Milgromian*, rather than Newtonian.
Milgromian dynamics MOND - Since its first formulation in 1983, Milgromian dynamics (MOND) has been very successful in predicting the gravitational potential of galaxies from the distribution of baryons alone, including general scaling relations and detailed rotation curves of large statistical samples of individual galaxies covering a large range of masses and sizes. Most predictions however rely on static models, and only a handful of N-body codes have been developed over the years to investigate the consequences of the Milgromian framework for the dynamics of complex evolving dynamical systems.
MOND is an alternative paradigm of
dynamics, seeking to replace Newtonian dynamics and general relativity. It aims to account for the ubiquitous mass discrepancies in the Universe, without invoking the dark matter that is required if one adheres to standard dynamics.
MOND departs from standard dynamics at accelerations smaller than a0: a new constant with the dimensions of acceleration that MOND introduces into physics. Such accelerations characterize galactic systems and the Universe at large. The other central tenet of MOND is space-time scale-invariance of this low-acceleration limit. MOND has predicted many clear-cut laws of
galactic dynamics (analogous to, and extending Kepler’s laws), most of which involve a0in different roles. In this way, MOND has unearthed a number of unsuspected laws of galactic dynamics, predicting them a priori, and leading to their subsequent tests and verification with data of ever increasing quality. One of these phenomenological laws is the baryonic
Tully-Fisher relation, which is underlaid by the MOND mass-asymptotic-speed relation (MASR). This is a relation between the asymptotic rotational speed around a galaxy, V∞ (predicted by MOND to be constant), and the total (baryonic) mass, M, of the galaxy: V4∞=MGa0. Another prediction of MOND is a tight correlation between the observed mass discrepancy in galactic systems, and the accelerations in them. This predicted mass-discrepancy-acceleration relation (MDAR), aka radial acceleration relation (RAR), has also been confirmed by many subsequent analyses.
For galaxy clusters, MOND reduces greatly the observed mass discrepancy: from a factor of ∼10, required by standard dynamics, to a factor of about 2. But, this systematically remnant discrepancy is yet to be accounted for. It could be due to, e.g., the presence of some small fraction of the yet undetected, “missing baryons”, which are known to exist (unlike the bulk of the putative “dark matter”, which cannot be made of baryons).
MOND, as a set of new laws, affords new tools for astronomical measurements–such as of masses and distances of far away objects–in ways not afforded by standard dynamics.
For galaxy clusters, MOND reduces greatly the observed mass discrepancy: from a factor of ∼10, required by standard dynamics, to a factor of about 2. But, this systematically remnant discrepancy is yet to be accounted for. It could be due to, e.g., the presence of some small fraction of the yet undetected, “missing baryons”, which are known to exist (unlike the bulk of the putative “dark matter”, which cannot be made of baryons).
See:
http://scholarpedia.org/article/The_MOND_paradigm_of_modified_dynamics
See:
https://arxiv.org/abs/1410.2256
The Milky Way is our home galaxy, one of billions of known galaxies in the Universe. In addition to our Sun, the Milky Way contains around 400 billion other stars - that's about 57 stars for every human being alive on Earth today! Even though that sounds big, the Milky Way is actually thought to be an average-sized galaxy.
The Milky Way is currently understood to be a barred spiral galaxy (Hubble type SBbc) that is 100,000 light-years across - that is, it takes 100,000 years for light (the fastest thing known to exist) to travel from one end of the Milky Way to the other. For comparison, light takes 8 minutes to get from the Sun to the Earth. While the light-year is a physically useful unit, astronomers tend to use "parsecs" when measuring distances. A parsec (short for "parallax-second") is 3.26 light-years, and is related to one of the most precise methods of determining distances to other stars ("parallax"). In Galactic astronomy, we work with truly astronomical distances, as so we use "kiloparsecs" (kpc), or thousands of parsecs, as our distance units. The radius of the Milky Way, then, is 15 kpc, with our Sun being 8 kpc from the center of the galaxy.
The modern view of the Milky Way galaxy contains four major components: The disk, bulge, stellar halo, and dark matter halo:
The disk is the most obvious component of the galaxy, and is considered to consist of two parts: the thin disk and the thick disk. The thin disk is about 0.3 kpc thick and contains almost all of the dust, gas, and young stars (including the Sun) in our Galaxy. The thick disk is about 1 kpc thick, and marks the thickness where star densities drop dramatically.
The bulge lies at the center of the disk, has a radius of only a few kpc, and contains both old and young stars. Recently, it was determined that the bulge contains a prominent bar. Additionally, a super massive black hole resides at the center of the galaxy - with a mass equal to that of 4 million Suns!
The stellar halo is a nearly spherical spheroid of stars that surrounds the entire galaxy. The density of stars in the halo is very low compared to densities found in the disk, and the majority of halo stars are found within 30 kpc of the galactic center. The stellar halo is the focus of Milkyway@home.
The dark matter halo is the most mysterious of all the galactic components. Information from galactic rotation curves, galaxy collisions, and dark matter simulations all strongly indicate that there is a large amount of invisible mass surrounding every galaxy. Modern astronomers hope to gain clues about the shape and composition of the dark matter halo from structures in the disk and stellar halo.
Dark Matter is the mass that is needed to make up for the unseen mass in physical observations. Although other solutions to these discrepancies have been proposed, such as modifications to Newton's and/or Einstein's theories of gravitation, dark matter is the only solution that describes all of the observed scientific anomalies simultaneously. Therefore, understanding dark matter is currently one of the major goals of science.
To understand what "dark" matter is, we need to understand "light" matter (the stuff we are used to). "Light" matter is made of baryons, which are particles that are made of quarks. The most important consequence of baryons being built of quarks is that they
interact electromagnetically. This means that light, which is an electromagnetic wave, can interact with baryons. Light waves have a large variety of wavelengths that make up the
electromagnetic spectrum (See Figure, from
Wikipedia). Depending on how the baryons are arranged, baryonic matter will absorb, reflect, or emit certain wavelengths of light. In fact, all baryonic matter will emit some wavelengths of light based on its temperature - stars, for example, are very hot, and so they can emit visible light. The higher an object's temperature, the shorter the wavelengths that can be emitted. Therefore, all baryonic matter "glows" at certain wavelengths (including humans! We glow in the infrared).
Dark matter is different. Dark matter does not emit light at
any wavelength. Dark matter does not absorb light, and it doesn't reflect it, either. Dark matter, then, does not interact electromagnetically
at all. This is why it is "dark:" light waves can never even know it's there.
Since dark matter doesn't interact with light, the only way that we can currently study it is through gravity. By studying the distribution of baryonic matter (stars and gas) in the Milky Way, we will gain insight into the arrangement and composition of dark matter. Milkyway@home furthers this goal by studying stars in the stellar halo, using data from the Sloan Digital Sky Survey.
Astronomers seek to understand the
Galactic potential of the Milky Way, which is a measure of how the Milky Way's gravity affects other objects, and therefore, a measure of the distribution of mass (matter) in the galaxy. If we can compare the galactic potential to the potential of the known (baryonic) matter, we can then determine the potential of the dark matter - which will tell us how dark matter is distributed in the Milky Way.
Astronomers use the physics of gravity to determine the potential of the Galaxy. In a simple analogy, let's look at how someone would go about investigating the potential of our sun. The Sun is massive and spherical, and so its potential will be simple - 'spherically symmetric,' in physics lingo. The measured strength of this spherically symmetric potential depends only on the mass of the Sun, and the distance that you are away from it.
The spherically symmetric gravitational potential of the Sun leads to
Kepler's Law. If we plot the velocity (or orbital speed) of planets orbiting the Sun versus their radius (or orbital distance) from the Sun, we get the
rotation curve of the Solar System. For a system obeying Kepler's Law, such as the Solar System, a clearly "falling" (decreasing with distance) rotation curve is observed:
Source: Matthew Newby, Milkyway@home
A Galaxy is a bit more complicated. Since there's not just one big mass at the center, the rotation curve should look different then that of the Solar System. When astronomers add up all of the light from stars in a Galaxy (even other Galaxies), we find that most of the light comes from near the center, with the amount of light decreasing with distance from the center. From this "light curve," we can calculate the distribution of light matter, which lets us calculate what the rotation curve of a Galaxy
should look like. What we find is that the curve should fall with distance - but when astronomers actually measure the rotation curve of the Milky Way (and other Galaxies), we find that it is almost
flat, and not falling much at all!
Source: Matthew Newby, Milkyway@home
The rotation problem actually goes back to the 1930's, with an astronomer named
Fritz Zwicky. Zwicky measured the velocities of galaxies rotating around a galaxy cluster, and concluded that there was "missing mass" that wasn't being seen in the cluster. In the 1970's, astronomer
Vera Rubin measured the rotation curves of other Galaxies, and showed definitively that there is, indeed, more mass in each galaxy than can be seen.
So, how do we find this dark matter? Our best bet seems to be gravity. Using
gravitational lensing, or the fact that dense pockets of matter can cause the path of light to warp around them, astronomers can actually map dark matter within very dense galaxy clusters, such as the Abell Cluster:
Abell galaxy cluster, Hubble ST
See:
https://sitn.hms.harvard.edu/flash/2016/galactic-rotation-curves-revisited-surprise-dark-matter/
G.O. Ludwig, in his 23 February 2021 paper "Galactic rotation curve and dark matter according to gravitomagnetism", explains:
The existence of dark matter has been postulated to resolve discrepancies between astrophysical observations and accepted theories of gravity. In particular, the measured rotation curve of galaxies provided much experimental support to the dark matter concept. However, most theories used to explain the rotation curve have been restricted to the Newtonian potential framework, disregarding the general relativistic corrections associated with mass currents.
On the other hand, the gravitomagnetic field produced by the currents modifies the galactic rotation curve, notably at large distances. The coupling between the Newtonian potential and the gravitomagnetic flux function results in a nonlinear differential equation that relates the rotation velocity to the mass density. The solution of this equation reproduces the galactic rotation curve without recourse to obscure dark matter components, as exemplified by three characteristic cases. A bi-dimensional model is developed that allows to estimate the total mass, the central mass density, and the overall shape of the galaxies, while fitting the measured luminosity and rotation curves. The effects attributed to dark matter can be simply explained by the gravitomagnetic field produced by the mass currents.
Using different assumptions for the mass distribution and possible combinations of spheroids and disks, the above theoretical models failed to convincingly reproduce the observed flat rotation curves. The discrepancy between models and observations was more evident in the measurements of the rotation curve using the Doppler shifted 21 cm neutral hydrogen line (HI) outside the galactic central portion. Most of the visible mass is located in this central region. The only way to eliminate the discrepancy using the existent models was by the introduction of a halo of non-observable matter (dark matter) concentrated in the outer region of spiral galaxies. The role of this dark matter component was detailed by van Albada et al. using improved HI data obtained by Begeman for the extended rotation curve of NGC 3198. The main conclusion was that “the amount of dark matter inside the last point of the rotation curve, at 30 kpc, is at least 4 times larger than the amount of visible matter”. Subsequently, the methods of analysis became more sophisticated, but invariably introducing the dark matter component as detailed, for example, by Sofue et al. , Eadie and Harris, Sofue and so many others. A detailed presentation of gravitational potential theory applied to several geometrical configurations of a large collection of stars, including the dark halo contribution, can be found in the book by Binney and Tremaine. More recent models were advanced by Cooperstock and Tieu, Balasin and Grumiller, and Crosta et al., considering general relativistic effects to describe the galactic dynamics. The relation between these papers and the present one is discussed later in this Introduction.
The motion of either stars or dust particles in a galaxy is determined by the gravitational interaction between masses only. The galactic system formed by a very large number of stars plus the surrounding gas can be approximated by a continuous mass distribution. This continuous fluid is essentially collisionless since binary encounters between stars are very rare (although long range encounters between passing stars determine the evolution of the system towards thermodynamic equilibrium on a very long time scale). Without binary encounters the interaction is described by collective Vlasov fields. Assuming steady-state the basic assumptions are established to describe the distributions of matter and of fluid velocity in a typical galaxy.
The balance between gravitoelectric, centrifugal, and gravitomagnetic forces in the moving fluid defines the mass distribution and affects the shape of the galactic disk. The actual shape is determined by the boundary condition matching the gravitoelectric potential and its gradient at the fluid-vacuum interface. Inside the dust equilibrium the gravitomagnetic field provides rotational flow in the absence of viscous forces. The Cauchy invariant demonstrates how the flow vorticity, gravitomagnetic field and mass density should distribute inside the galactic dust configuration during the time evolution.
The coupling between the gravitoelectric Newtonian potential and the gravitomagnetic flux function leads to a nonlinear relation between the rotation velocity and the mass density. The rotation velocity along the equatorial plane is governed by an Abel equation of the second kind, which reproduces the observations. Near the origin, where the gravitational field did not build up yet, the rotation curve shows a linear rise. Farther away from the origin the rotation speed shows a transition to a nearly constant value. At large distances the gravitomagnetic field is sufficiently intense to balance the decaying gravitational and centrifugal forces. Although the relativistic effects are weak (with a beta ratio of the order of 1/2000), the nonlinear coupling provides the mechanism that drives the transition in the rotation profile. This is similar to a soft phase transition, driven by weak perturbations, between asymptotic states. This transition between states should occur during the initial stages of formation of the galaxy, when the density rises at the origin and the potential well deepens. Near equilibrium the galaxy has been squeezed to its nearly disk-like shape bulging at the origin. This time evolution is a complex problem that requires much further study.
The galactic rotation curves were reproduced simply including the relativistic effects described by the gravitomagnetic field, without obscure dark matter components. The widely used one-dimensional circular-velocity thin disk model is clearly inadequate to find the galactic mass distribution. Possibly all calculations performed up-to-date using the thin disk circular velocity model must be reexamined, and the dark matter concept questioned, at least concerning the galactic rotation curves.
See:
https://link.springer.com/article/10.1140/epjc/s10052-021-08967-3
It is interesting to view Newtonian mechanics, dark matter theories, and Milgomian dynamics as they explain the velocity of stars at given distances from the galactic center. The work of Vera Rubin first began to show the inability of Newtonian mechanics to explain the discrepancy between them and the actually observed stellar veloceties, which gave rise to dark matter theories. Of late, Prof. Mordehai Milgrom of the Weizmann Institute of Science in Israel has postulated a new set of gravitomagnetics to explain Rubin's work rather than dark matter.
Hartmann352