We present an efficient, robust computational method for modeling the Newtonian dynamics for rotation curve analysis of thin-disk galaxies. For a disk galaxy with a typical flat rotation curve, our modeling results show that the surface mass density monotonically decreases from the galactic center toward periphery, according to Newtonian dynamics. In a large portion of the galaxy, the surface mass density follows an approximately exponential law of decay with respect to the galactic radial coordinate. Yet the radial scale length for the surface mass density seems to be generally larger than that of the measured brightness distribution, suggesting an increasing mass-to-light ratio with the radial distance in a disk galaxy. In a nondimensionalized form, our mathematical system contains a dimensionless parameter which we call the "galactic rotation number" that represents the gross ratio of centrifugal force and gravitational force. The value of this galactic rotation number is determined as part of the numerical solution. Through a systematic computational analysis, we have illustrated that this galactic rotation number remains within $\pm 10%$ of 1.70 for a wide variety of rotation curves. This implies that the total mass in a disk galaxy is proportional to $V_0^2\,R_g$, with $V_0$ denoting the characteristic rotation velocity and $R_g$ the radius of the galactic disk. The predicted total galactic mass of the Milky Way is in good agreement with the star-count data.
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…
We continue our analysis of Newtonian Fractional-Dimension Gravity, an extension of the standard laws of Newtonian gravity to lower dimensional spaces including those with fractional (i.e., non-integer) dimension. We apply our model to three rotationally supported galaxies: NGC 7814 (Bulge-Dominated Spiral), NGC 6503 (Disk-Dominated Spiral), and NGC 3741 (Gas-Dominated Dwarf). As was done in the general cases of spherically-symmetric and axially-symmetric structures, which were studied in previous work on the subject, we examine a possible connection between our model and Modified Newtonian Dy…
Recent statistical deconvolution methods have produced extended kinematical maps in a range of heliocentric distances that are a factor of two to three larger than those analysed in the Gaia Collaboration based on the same data. In this paper, we use such maps to derive the rotation curve both in the Galactic plane and in off-plane regions and to analyse the density distribution. By assuming stationary equilibrium and axisymmetry, we used the Jeans equation to derive the rotation curve. Then we fit it with density models that include both dark matter and predictions of the MOND (Modified Newto…
Astronomers use to derive MOdified Newtonian Dynamics (MOND) rotation curves using the simple algebraic rule of calculating the acceleration as equal to the Newtonian acceleration ($a$) divided by some factor $μ(a)$. However, there are velocity differences between this simple rule and the calculation derived from more sophisticated MOND versions such as AQUAL or QMOND, created to expand MOND heuristic law and preserve the conservation of momentum, angular momentum, and energy, and follow the weak equivalence principle. Here we provide recipes based on Milgrom's proposal to calculate semianalyt…
The Case Against Dark Matter and Modified Gravity: Flat Rotation Curves Are a Rigorous Requirement in Rotating Self-Gravitating Newtonian Gaseous Disks
We expand our analysis of Newtonian Fractional-Dimension Gravity (NFDG), an extension of the classical laws of Newtonian gravity to lower dimensional spaces, including those with fractional (i.e., non-integer) dimension. We apply our model to four rotationally supported galaxies (NGC 5033, NGC 6674, NGC 5055, NGC 1090), in addition to other three galaxies (NGC 7814, NGC 6503, NGC 3741) which were analyzed in previous studies. NFDG is able to fit the rotation curves of all these galaxies without any dark matter component. We also investigate the possible violation of the strong equivalence prin…
Recently, it has been suggested that the phenomenology of flat rotation curves observed at large radii in the equatorial plane of disk galaxies can be explained as a manifestation of General Relativity instead of the effect of Dark Matter halos. In this paper, by using the well known weak field, low velocity gravitomagnetic formulation of GR, the expected rotation curves in GR are rigorously obtained for purely baryonic disk models with realistic density profiles, and compared with the predictions of newtonian gravity for the same disks in absence of Dark Matter. As expected, the resulting rot…
Modified Newtonian dynamics by Milgrom is a paradigm for explaining the rotation curves of spiral galaxies and various other large scale structures. This paradigm includes several different theories. Here we present Milgrom's modified inertia (MI) theory in terms of a simple and tractable non-conservative Newtonian dynamics, which is useful in obtaining observable predictions of MI. It is found that: 1) Modified inertia theory is equivalent to a Newtonian theory, with a non-conservative gravitational field, and dark matter density; 2) The tidal force in the equivalent Newtonian dynamics is non…
