A Derivation of Flat Rotation Curve of Spiral Galaxies and Baryonic Tully-Fisher Relation
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Fundamentally for the extended disc region of a spiral galaxy, an alternative solution to Laplace equation has been presented for a potential that is radially symmetric on the disc plane. This potential, unlike newtonian one, is shown to be logarithmic in distance from the centre, which allows for the rotation velocity to be constant along the disc radius.It is also shown that this potential easily manifests into a relationship between inner mass of the galaxy and terminal rotation velocity, which has been empirically observed and known as Baryonic Tully-Fisher relations.Keywords:
Tully–Fisher relation
Modified Newtonian dynamics
Abstract The problem of dark matter in galaxies is still one of the most important unsolved problems in the contemporary extragalactic astronomy and cosmology. The existence of a significant dynamic difference between the visible mass and the conventional mass of galaxies firmly establishes observational result. In this paper an unconventional explanation will be tested as an alternative to the cold dark matter hypothesis; which is called the modified Newtonian dynamics (MOND). In this paper covers the simulation of galactic evolutions; where the two hypotheses are tested via the rotation curves. N-body simulation was carried adopting different configuration like a hot disk, elliptical (with arms and without arms) with a different parameter that covers the objects distribution, masses and velocities. It is shown from the simulation results that the MOND hypothesis has generated better rotation curves than the Newtonian theorem. Moreover, the appropriate configuration and parameters for spiral galaxy are investigated. It is shown that this assignment has not been easy; because the problem is very delicate and unstable.
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In this paper we study consistent solutions of spherically symmetric space in metric ) (R f gravity theory. Here we inversely obtain a generic action from metric solutions that describe flat rotation curves in spiral galaxies without dark matter. Then we show that obtained solutions are in conformity with Tully-Fisher relation and modified Newtonian dynamics, which are two strong constraints in justification of flat rotation curves in spiral galaxies.
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We carry out an objective classification of four samples of spiral galaxies having extended rotation curves beyond the optical radius. A multivariate statistical analysis (viz., principal component analysis [PCA]) shows that about 96% of the total variation is due to two components, one being the combination of absolute blue magnitude and maximum rotational velocity beyond the optical region and the other being the central density of the halo. On the basis of PCA a fundamental plane has been constructed that reduces the scatter in the Tully-Fisher relation up to a maximum of 16%. A multiple stepwise regression analysis of the variation of the overall shape of the rotation curves shows that it is mainly determined by the central surface brightness, while the shape purely in the outer part of the galaxy (beyond the optical radius) is mainly determined by the size of the galactic disk.
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The rotation curve of galaxies for M33 in 1959 by Louise Volders gave the new hypothetical about the invisible matter that contributes inside of the galaxy, which later we call dark matter (DM). However, recently the theory about DM is still incomplete to understand this matter. This situation makes some scientists look for alternative ways such as f(R) gravity and conformal gravity theory. We have studied Modified Newtonian Dynamics (MOND) and Newtonian Dynamics (ND). We try to show the simple model that aims to give an analysis that MOND can correct to solve the constant speed of galaxy rotation. For simplicity, we consider the value of α = 1. The graph shows that the MOND model has a constant speed of 100 kilometres per second. While for the ND model, the speed will decrease for radius goes to infinity because the speed is dependent on r. Based on this result, we obtain that MOND can show the constant speed of galaxy rotation than ND. This result can conclude that MOND can solve the rotation curve of the galaxy.
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view Abstract Citations (62) References (16) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS On the Use of Galaxy Rotation Curves to Test the Modified Dynamics Milgrom, Mordehai Abstract I expound various aspects of the testing of the predictions of the modified Newtonian dynamics (MOND) on galaxy rotation curves. This is done with particular reference to the extensive study of rotation curves, in light of MOND, published recently by Kent. The general properties of MOND rotation curves are discussed. In particular, it is shown how the various galaxy parameters (distance, inclination, stellar M/L, etc.) and the acceleration constant of MOND enter the comparison of calculated with observed curves. This exposition, it is hoped, will help optimize the efficacy of tests of MOND that are based on rotation curves, as it shows what sort of information can be extracted from various types of galaxies. I emphasize the crucial role played by low-surface-density galaxies (somewhat neglected by Kent) in assaying the modified dynamics. Kent points out two possible difficulties for MOND that are brought to light by his analysis. They concern the spread of the values he gets for the acceleration constant, and the behavior of some rotation curves at large radii. Examining Kent's procedure, I find that both these potentially deleterious conclusions may be imputed in part to the omission of the observed H I mass from the mass models he uses. The gas contributes to the mass substantially in some cases (more than half the stellar contribution) and is distributed differently from the light. In one other consequential case (which gave the smallest value for a_0_), Kent uses the two-side-average rotation curve of a galaxy (NGC 3031) that has a highly asymmetrical curve. Some revised results provided by Kent are given, viz., new best-fit values of a_0_ for mass models that include hydrogen, and the MOND rotation curves with a_0_ fixed for all the galaxies. I also comment on the possible significance of secondary features on the rotation curve. Publication: The Astrophysical Journal Pub Date: October 1988 DOI: 10.1086/166777 Bibcode: 1988ApJ...333..689M Keywords: Dark Matter; Dynamic Characteristics; Galactic Rotation; H I Regions; Mass To Light Ratios; Stellar Mass; Angular Velocity; Galactic Nuclei; Mass Distribution; Astrophysics; GALAXIES: INTERNAL MOTIONS; STARS: STELLAR DYNAMICS full text sources ADS | data products SIMBAD (11) NED (11)
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We present modified Newtonian dynamics (MOND) fits to 15 rotation curves of low surface brightness (LSB) galaxies. Good fits are readily found, although for a few galaxies minor adjustments to the inclination are needed. Reasonable values for the stellar mass-to-light ratios are found, as well as an approximately constant value for the total (gas and stars) mass-to-light ratio. We show that the LSB galaxies investigated here lie on the one, unique Tully-Fisher relation, as predicted by MOND. The scatter on the Tully-Fisher relation can be completely explained by the observed scatter in the total mass-to-light ratio. We address the question of whether MOND can fit any arbitrary rotation curve by constructing a plausible fake model galaxy. While MOND is unable to fit this hypothetical galaxy, a normal dark-halo fit is readily found, showing that dark matter fits are much less selective in producing fits. The good fits to rotation curves of LSB galaxies support MOND, especially because these are galaxies with large mass discrepancies deep in the MOND regime.
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The log-normal distribution represents the probability of finding randomly distributed particles in a micro canonical ensemble with high entropy. To a first approximation, a modified form of this distribution with a truncated termination may represent an isolated galactic disk, and this disk density distribution model was therefore run to give the best fit to the observational rotation curves for 37 representative galaxies. The resultant curves closely matched the observational data for a wide range of velocity profiles and galaxy types with rising, flat or descending curves in agreement with Verheijen's classification of 'R', 'F' and 'D' type curves, and the corresponding theoretical total disk masses could be fitted to a baryonic Tully Fisher relation (bTFR). Nine of the galaxies were matched to galaxies with previously published masses, suggesting a mean excess dynamic disk mass of dex0.61+/-0.26 over the baryonic masses. Although questionable with regard to other measurements of the shape of disk galaxy gravitational potentials, this model can accommodate a scenario in which the gravitational mass distribution, as measured via the rotation curve, is confined to a thin plane without requiring a dark-matter halo or the use of MOND.
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A sample of 22 spiral galaxy rotation curves, measured in the 21 cm line of neutral hydrogen, is considered in the context of Milgrom's modified dynamics (MOND). Combined with the previous, highly selected sample of Begeman et al., this constitutes the current total sample of galaxies with published (or available) extended rotation curves and photometric observations of the light distribution. This is the observational basis of present quantitative understanding of the discrepancy between the visible mass and classical dynamical mass in galaxies. It is found that the gravitational force calculated from the observed distribution of luminous material and gas by use of the simple MOND formula can account for the overall shape and amplitude of these 22 rotation curves, and in some cases, the predicted curve agrees with the observed rotation curve in detail. The fitted rotation curves have, in 13 cases, only one free parameter, which is the mass-to-light ratio of the luminous disk; in nine cases, there is an additional free parameter, which is M/L of a central bulge or light concentration. The values of the global M/L (bulge plus disk) are reasonable and, when the gas mass is also included, show a scatter consistent with that in the Tully-Fisher relation. The success of the MOND prescription in predicting the rotation curves in this larger, less stringently selected sample lends further support to the idea that dynamics or gravity is non-Newtonian in the limit of low acceleration and that it is unnecessary to invoke the presence of large quantities of unseen matter.
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