Open Astron. 2021; 30: 1–11 Research Article Golden Gadzirayi Nyambuya* On the plausible origins of the spiral character of galaxies https://doi.org/10.1515/astro-2021-0001 Received Apr 19, 2020; accepted Aug 16, 2020 Abstract: We here-in demonstrate that the proposed hitherto unknown gravitomagnetic dark-force that hypothetically explains the Flat Rotation Curves of Spiral Galaxies — this same force, explains very well, the logarithmic and as-well, the barred spiral shapes of spiral galaxies. That is, much in line with Edward Arthur Milne (1896-1950)’s 1946 ideas — albeit, on a radically and asymptotically different philosophical train of thought, the galactic disk is here assumed to be in a state of free-fall around the central bulge with the hypothetical gravitomagnetic dark-force being the dominant force determining all gravity-related dynamics of the disk, thus leading to logarithmic and barred spiral orbits, hence the shape of spiral galaxies. Keywords: darkmatter, gravitatomagnetism, Tully-Fisher relation, galaxy rotation curves 1 Introduction 1970; Rubin and Ford 1970; Forman et al. 1970). It is in these spiral galaxies where this phenomenon manifests itself in the form of the flat rotation curves for test bodies lieing in This reading is the fourth in our four part series where we the galactic disk. Some of the finest and most important demonstrate that the Flat Rotation Curve Problem of Spiral questions that naturally visit the seeking mind are: Galaxies — commonly known as the Darkmatter Problem — does have a solution within the frame of gravitomagnetism 1. Why is this flat rotation curve phenomenon more (presented in the reading Nyambuya 2015b). In the second prominent in spiral galaxies and not any other type part (i.e., Nyambuya 2019b, and here-after Paper II) of the of galaxy? four part series — the proposed theory to explain the flat 2. Is there a relationship between the shape of spiral rotation curve problem of spiral galaxies was setup, and it galaxies and the flat rotation curve phenomenon? was shown (demonstrated) therein (Nyambuya 2019b) how These are some of the questions that this reading makes one can harness from this theory, the Tully and Fisher (1977) the temerarious endeavour to provide some answers — or 4 Relation (Mgal / VDisk) relating the mass of the galaxy and at the very least, set a base or basis from which these type the flat rotational speed in the material laying in the disk. of questions maybe answered. We here-in demonstrate (show) how one can explain the For example, it is known that the shape of the spiral shape of spiral galaxies from this same law that was able galaxies can be described by spiral equation of the form¹: to explain the flat rotation curves of spiral galaxies, and ±λSL φ r = RDe (see e.g., Puerari et al. 2014; Savchenko and as-well as the Tully and Fisher (1977) Relation. Reshetnikov 2013; Savchenko 2012; Savchenko and Reshet- When it comes to this issue of the flat rotation curve nikov 2011). If the stars in the galactic disk of spirals are problem of spiral galaxies, nowhere is this mysterious phe- on spiral trajectories, the question is ‘What force law would nomenon of ‘dark-matter’ more clearly evident than in spi- give rise to such trajectories?’ This is the key question that ral galaxies (see e.g., Swaters et al. 2012; Broeils 1992a,b; this work seeks a most perdurable answer. Begeman et al. 1991; Begeman 1987; Rubin et al. 1985, 1978, To that end — we here-in — against prevalent and con- ventional wisdom, hold that stars, star clusters and molecu- lar clouds (etc) resident in galactic disks around the galactic Corresponding Author: Golden Gadzirayi Nyambuya: National Uni- bulge of spiral galaxies — are in a state of free-fall on spiral versity of Science & Technology, Faculty of Applied Sciences — Depart- trajectories in much the same way that planets in the Solar ment of Applied Physics, Fundamental Theoretical and Astro-physics Group, P. O. Box AC 939, Ascot, Bulawayo, Republic of Zimbabwe; ±λ φ Email: [email protected] 1 This equation, r = RDe SL , will be explained at the instance of Eq. ORCID: https://orcid.org/0000-0002-3228-6467 (29). Open Access. © 2021 G. G. Nyambuya, published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 License 2 Ë G. G. Nyambuya, On the plausible origins of the spiral character of galaxies system are in a state of free-fall around the Sun on elliptical central region of the galaxy and in the case where there trajectories. Consequently, the shape of these galaxies must is a visible bulge, this mass can readily be assumed to be be determined by the equation of motion that emerges from the mass of the central bulge itself. In the case where there the consideration of the motion of test bodies orbiting the is no appreciable bulge (see e.g., Fisher and Drory 2011; central bulge. Current wisdom holds that test bodies in the Kormendy et al. 2010), the mass should be concentrated galactic disks of spiral galaxies are on elliptical trajectories in the assumed central massive black-hole of the galaxy in with the shape of these galaxies being a result of a density question. In both cases of bulge and bulge-less galaxy, the wave sweeping the galaxy (Lin and Shu 1964). mass of the galaxy Mgal shall here be denoted by MB, and Despite the general lack of agreement on the exact this is through the assumed relationship: Mgal ∼ MB. mechanism leading to the shape of spiral galaxies (e.g., Davis et al. 2015), the prevalent view is that the density waves (Lin and Shu 1964) propagating through the disk of 2.2 Idealised Rotation Curve of Spiral the galaxy are the responsible agent. For example, accord- Galaxies ing to Shu (2016), over the past six decades, Lin and Shu (1964)’s density wave theory has been the most cited as the As depicted in Figure 2, we assume a rotation curve that main agent for the ‘grand design spiral genesis in disk galax- has two major components, the Bulge Component and the ies’. Lin and Shu (1964)’s density wave theory introduces Disk Component, i.e.: the idea of long-lived quasi-static density waves that sweep 1. Bulge Component: In this region, the orbital speed across the galactic disk in which ensuring process the spi- of test bodies is assumed to increase in direct propor- ral structure emerges. Apart from explaining the structure tion with the radial distance from the galactic centre, of spiral galaxies, this theory has been cited in the litera- i.e. (VB / r). In the bulge region, the Newtonian grav- ture as having been very successful in explaining Saturn’s itational component is the predominate gravitational rings (see e.g., Hedman and Nicholson 2016; Tiscareno et al. force determining the dynamics of this region. This 2007, 2006; Phillipps 2005; Carroll and Ostlie 1995; Shu assumption that: VB / r, coupled with the assump- 1984; Goldreich and Tremaine 1982, 1978). tion that the Newtonian gravitational component Now, in-closing this introduction, we shall give a syn- (FN) is the predominate (jFNj o jFDj) gravitational opsis of the reading — it is organised as follows: in §(2), force determining the dynamics of the bulge region we lay bare our (simplistic) working assumptions. In §(3), directly implies that the density [ϱB(r)] profile of the we define the dark-force. In §(4), we present our proposed bulge must be a constant i.e.: ϱB(r) = ϱB = constant, theory as to why spiral galaxies have the shape that they for: 0 ≤ r ≤ RB, and VB is such that: have. In §(5), we give a general discussion and lastly, in §(6), the conclusion drawn thereof. (︂4πGϱ )︂1/2 V (r) = B r, for [0 ≤ r ≤ R ]. (1) B 3 B 2 Working Assumptions We herein make the following idealised assumptions about the mass and rotation curves of spiral galaxies: 2.1 Mass of a Spiral Galaxy As depicted in Figure 1, the total mass of a spiral galaxy Mgal, can be split into two parts, i.e.: Figure 1. Assumed Model of Spiral Galaxies: The bulk of the gravi- tating material of a spiral galaxy is here assumed to be contained 1. The mass of the galactic bulge, MB. in the galactic bulge. The material contained in the disk is insignif- 2. The mass of the galactic disk, MDisk. icant in comparison to the material in the bulge so that such that the stars, star clusters, molecular clouds etc, can be considered to That is to say: M = M + M . In our model, we assume gal B Disk be test bodies moving under the influence of the gravitational field that the bulk of the mass of the galaxy is contained in the setup by the gravitating material in the galactic bulge. bulge i.e.: MB o MDisk, so much so that: Mgal ∼ MB. That is to say, the bulk of the mass is concentrated in the G. G. Nyambuya, On the plausible origins of the spiral character of galaxies Ë 3 2. Disk Component: In this region: RB < r ≤ Rgal, for a given galaxy, RD is defined as follows: the orbital speed VDisk, of test bodies is assumed to (︂ )︂aD RM Mgal be a constant throughout the disk. The galactic disk RD = aD Rkpc, (4) M⊙ contains insignificant amounts of matter when com- where² a is a constant to be determined by demanding pared to the galactic bulge, hence this region con- D that the dark-force [defined in Eq.