Modified Newtonian Dynamics (MOND) vs Newtonian Dynamics: The Simple Test to Solve the Constant Speed of Galaxy Rotation

Huda Nasrulloh


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.

DOI: 10.17977/um024v7i12022p001


Modified Newtonian Dynamics (MOND); Newtonian Dynamics (ND); galaxy rotation curve.

Full Text:



J. A. Sellwood, “Secular evolution in disk galaxies,” Rev. Mod. Phys., vol. 86, no. 1, p. 1, 2014, doi: 10.1103/RevModPhys.86.1.

T. Naab and J. P. Ostriker, “Theoretical challenges in galaxy formation,” Annu. Rev. Astron. Astrophys., vol. 55, pp. 59–109, 2017, doi: 10.1146/annurev-astro-081913-040019.

P. Galianni, M. Feix, H. Zhao, and K. Horne, “Testing quasilinear modified newtonian dynamics in the solar system,” Phys. Rev. D, vol. 86, no. 4, p. 044002, 2012, doi: 10.1103/PhysRevD.86.044002.

B. Joachimi et al., “Galaxy alignments: An overview,” Space Sci. Rev., vol. 193, no. 1, pp. 1–65, 2015, doi: 10.1007/s11214-015-0177-4.

R. Zaregonbadi, M. Farhoudi, and N. Riazi, “Dark matter from f (R, T) gravity,” Phys. Rev. D, vol. 94, no. 8, p. 084052, 2016, doi: 10.1103/PhysRevD.94.084052.

J. I. Read, “The local dark matter density,” J. Phys. G: Nucl. Part. Phys., vol. 41, no. 6, p. 063101, 2014, doi: 10.1088/0954-3899/41/6/063101.

G. Bertone and T. M. Tait, “A new era in the search for dark matter,” Nature, vol. 562, no. 7725, pp. 51–56, 2018, doi: 10.1038/s41586-018-0542-z.

G. Hinshaw et al., “Nine-year wilkinson microwave anisotropy probe (WMAP) observations: Cosmological parameter results,” Astrophys. J. Suppl. Ser., vol. 208, no. 2, p. 19, 2013, doi: 10.1088/0067-0049/208/2/19.

D. Baumann and L. McAllister, Inflation and String Theory. Cambridge, United Kingdom: Cambridge University Press, 2015.

A. Joyce, B. Jain, J. Khoury, and M. Trodden, “Beyond the cosmological standard model,” Phys. Rep., vol. 568, pp. 1–98, 2015, doi: 10.1016/j.physrep.2014.12.002.

G. Leon and E. N. Saridakis, “Dynamical behavior in mimetic F (R) gravity,” J. Cosmol. Astropart. Phys., vol. 2015, no. 04, p. 031, 2015, doi: 10.1088/1475-7516/2015/04/031.

K. Koyama, “Cosmological tests of modified gravity,” Rep. Prog. Phys., vol. 79, no. 4, p. 046902, 2016, doi: 10.1088/0034-4885/79/4/046902.

R. Myrzakulov, L. Sebastiani, S. Vagnozzi, and S. Zerbini, “Static spherically symmetric solutions in mimetic gravity: Rotation curves and wormholes,” Class. Quantum Gravity, vol. 33, no. 12, p. 125005, 2016, doi: 10.1088/0264-9381/33/12/125005.

X. Wu and P. Kroupa, “Galactic rotation curves, the baryon-to-dark-halo-mass relation and space–time scale invariance,” Mon. Notices Royal Astron. Soc., vol. 446, no. 1, pp. 330–344, 2015, doi: 10.1093/mnras/stu2099.

M. Milgrom, “MOND theory,” Can. J. Phys., vol. 93, no. 2, pp. 107–118, 2014, doi: 10.1139/cjp-2014-0211.

A. O. Hodson and H. Zhao, “Generalizing MOND to explain the missing mass in galaxy clusters,” Astron. Astrophys., vol. 598, p. A127, 2017, doi: 10.1051/0004-6361/201629358.

S. Mendoza, “MOND as the basis for an extended theory of gravity,” Can. J. Phys., vol. 93, no. 2, pp. 217–231, 2015, doi: 10.1139/cjp-2014-0208.

E. Barrientos and S. Mendoza, “A relativistic description of MOND using the Palatini formalism in an extended metric theory of gravity,” Eur. Phys. J. Plus, vol. 131, no. 10, pp. 1–10, 2016, doi: 10.1140/epjp/i2016-16367-0.

A. Karam, L. Marzola, T. Pappas, A. Racioppi, and K. Tamvakis, “Constant-roll (quasi-) linear inflation,” J. Cosmol. Astropart. Phys., vol. 2018, no. 05, p. 011, 2018, doi: 10.1088/1475-7516/2018/05/011.

Y. Sofue, “Rotation and mass in the Milky Way and spiral galaxies,” Publ. Astron. Soc. Jpn., vol. 69, no. 1, p. R1, 2017, doi: 10.1093/pasj/psw103.

Y. Sofue, “Rotation curve of the Milky Way and the dark matter density,” Galaxies, vol. 8, no. 2, p. 37, 2020, doi: 10.3390/galaxies8020037.

M. Cappellari, “Structure and kinematics of early-type galaxies from integral field spectroscopy,” Annu. Rev. Astron. Astrophys., vol. 54, pp. 597–665, 2016, doi: 10.1146/annurev-astro-082214-122432.

P. Bull et al., “Beyond ΛCDM: Problems, solutions, and the road ahead,” Phys. Dark Universe, vol. 12, pp. 56–99, 2016, doi: 10.1016/j.dark.2016.02.001.

J. Schee, Z. Stuchlík, and M. Petrásek, “Influence of the cosmic repulsion on the MOND model of the Magellanic Cloud motion in the field of Milky Way,” J. Cosmol. Astropart. Phys., vol. 2013, no. 12, p. 026, 2013, doi: 10.1088/1475-7516/2013/12/026.

B. Famaey and S. S. McGaugh, “Modified newtonian dynamics (MOND): Observational phenomenology and relativistic extensions,” Living Rev. Relativ., vol. 15, no. 1, pp. 1–159, 2012, doi: 10.12942/lrr-2012-10.

M. Milgrom, “Testing MOND over a wide acceleration range in x-ray ellipticals,” Phys. Rev. Lett., vol. 109, no. 13, p. 131101, 2012, doi: 10.1103/PhysRevLett.109.131101.

M. Milgrom, “The MOND paradigm of modified dynamics,” Scholarpedia, vol. 9, no. 6, p. 31410, 2014, doi: 10.4249/scholarpedia.31410.

M. Milgrom, “Universal modified newtonian dynamics relation between the baryonic and “dynamical” central surface densities of disc galaxies,” Phys. Rev. Lett., vol. 117, no. 14, p. 141101, 2016, doi: 10.1103/PhysRevLett.117.141101.

G. N. Candlish, R. Smith, and M. Fellhauer, “Numerical simulations of modified newtonian dynamics,” J. Phys.: Conf. Ser., vol. 720, no. 1, p. 012012, 2016, doi: 10.1088/1742-6596/720/1/012012.

B. Famaey, S. McGaugh, and M. Milgrom, “MOND and the dynamics of NGC 1052− DF2,” Mon. Notices Royal Astron. Soc., vol. 480, no. 1, pp. 473–476, 2018, doi: 10.1093/mnras/sty1884.

B. A. Ahmed, L. K. Abood, and M. A. Salih, “Simulation on rotation curve of spiral galaxies,” J. Phys.: Conf. Ser., vol. 1234, no. 1, p. 012031, 2019, doi: 10.1088/1742-6596/1234/1/012031.

A. McDaniel, T. Jeltema, and S. Profumo, “X-ray shapes of elliptical galaxies and implications for self-interacting dark matter,” J. Cosmol. Astropart. Phys., vol. 2021, no. 05, p. 020, 2021, doi: 10.1088/1475-7516/2021/05/020.

I. Banik et al., “The global stability of M33 in MOND,” The Astrophys. J., vol. 905, no. 2, p. 135, 2020, doi: 10.3847/1538-4357/abc623.

G. Pezzulli, F. Fraternali, and J. Binney, “The angular momentum of cosmological coronae and the inside-out growth of spiral galaxies,” Mon. Notices Royal Astron. Soc., vol. 467, no. 1, pp. 311–329, 2017, doi: 10.1093/mnras/stx029.

P. E. M. Piña et al., “Robust H I kinematics of gas-rich ultra-diffuse galaxies: Hints of a weak-feedback formation scenario,” Mon. Notices Royal Astron. Soc., vol. 495, no. 4, pp. 3636–3655, 2020, doi: 10.1093/mnras/staa1256.

Copyright (c) 2022 Huda Nasrulloh

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License