arXiv:1802.02734v2 [astro-ph.GA] 17 Feb 2018 1 t fteam hc smd po ra fgreater of areas of up made is stabil- which the arms Thus the further. of gravitational strengthened ity the be would then would which and stars field together, increases, the crowd density of to the velocity cause stars down the slowed make the would on hand, field; gravitational star other strengthened the the the the area of and because arm stars velocity the dense their form into down thus slow coming and would After materials shape spiral arm. a spiral in a are with density peaks the highest therefore, the radius, the along time same the a forms which motion, wave wave( a density stars in the vary of center density the and around speed rotation the that holds ory [email protected] ..Lnadohr a enakolde ymany by by acknowledged developed been has theory investiga- others people( wave and Among of density Lin lot out. the C.C. a carried works, been and have those people, verifications have many and mechanism tions by formation made the Conjec- of been hypothesis time. the and all ture attention people’s attracts galaxy h aetaesbt ln h etrcrl n at and circle center the along both travels wave The rpittpstuigL using 2018 typeset 20, Preprint February version Draft h euiu n nsa prlsrcueo spiral of structure spiral unusual and beautiful The i Shu & Lin aaishv ag-cl oain n ohtefrainadev and formation rotation. the background Keywords: both this tab and by back driven the the rotation, are on that large-scale galaxies coins concluded a spinning be have can a it like galaxies analysis, galaxy, the number the warped of arm Through the the structure movement. of of warped surface change the disc the th give the and between also arm relationship simulation the spiral three-dimensional also of but existence show shape, the spiral analysis both the numerical th is and The particle considered th is the introduced. wave model density is t galaxy the by background particle by driven rotational double proposed is simple evolution galaxies a isolated spiral galaxies, an the the of of result formation a the not that discussed is It Pasha 1. olg fPyisSineadTcnlg,Seyn Normal Shenyang Technology, and Science Physics of College ( 1964 aaywre tutr—Glx:prlarm Galaxy:spiral structure— Galaxy:warped INTRODUCTION ( aaybcgon oain—Glx:prlglx aayCroi fo Galaxy:Coriolis — galaxy Galaxy:spiral — rotation Galaxy:background A 2004 T E , tl ATX .1.0 v. AASTeX6 style X 1966 )). olg fSine hnagArsaeUiest,Shenya University, Aerospace Shenyang Science, of College ) h est aethe- wave density The )). STESIA AAYACSI HURRICANE? COSMIC A GALAXY SPIRAL THE IS I ig HN Tingting ZHENG Ling, LIU ABSTRACT A Zexin CAO iywv hoyfrtesia aaywt multi- struc- with warped galaxy ubiquitous galaxy( the the spiral there of for the ture and problems, den- for structure the above suf- on arms theory the not based illus- wave explanations is To to reasonable sity theory no addition high. wave still In are so density is but the galaxies ficient. structures, case, spiral this non-spiral theory the wave trate simu- of of density variety The ratio the the a random, to show is according should particles results the lating of phase ar- initial shapes( accumulation spiral the arms NGC ( show and obvious still M33 but no eas, as have such for which clearly galaxies, 7793, explain spiral to dif- flocculent theory is wave ex- it the density be However, the can theory. for M74, wave ficult density and the M81 by galaxy plained the as such galaxies, galaxies. to the of galaxies, structure of spiral equation the dynamical demonstrate gravitational quasi- and the the equations from theory, obtained wave field be density can the solutions of steady model Accord- the to self-consistently. ing maintained be would density 1992 1 h prlsrcueosre rmtesia disc spiral the from observed structure spiral The ); Kennicutt nvriy hnag103,China 110034, ShenYang University, htntol h rjcoyof trajectory the only not that s rudevrneto h spiral the of environment ground eoiyadterdu reveals radius the and velocity e g103,China 110136, ng nadto,terslso the of results the addition, In . oy oaayetemtosof motions the analyze To eory. prlglxe,adsosthat shows and galaxies, spiral ecsi akrudrotation, background cosmic he lto fhriaelk spiral hurricane-like of olution e xssawoeoverturning whole a exists le, oilsfrefre ythe by formed force Coriolis e eqe Papaloizou & Terquem ( 1981 ); Sellwood urr Dottori & Puerari ( 2011 c — rce ) o the For )). ( 2000 ); Kim 2

(2014); Elmegreen (1982); Grosbφl, Patsis & Pompei In the density wave theory, the formation of spiral arm (2004)). There are other theories, which do not is a combined results of particles doing elliptical motion yet explain the spiral structure very well(Toomre under the central potential, which actually considers the (1972); de Souza (2013); Sellwood & Carlberg (1984); galaxies as a relatively isolated system. Aiming at this Baba, Saitoh, & Wada (2013); Reshetnikov (2016); point, it is proposed that the spiral galaxy in cosmos Gamaleldin (1995)). is not a relatively isolated statistical system, and its The density wave theory is proposed mainly for the evolution is also driven with the motion of the back- formation of the spiral arm. However, the existence of ground. A non-inertial force evoked from the universal the spiral arm does not mean that the trajectory of the background motion participates in the evolution of the single moving particle will exhibit a spiral structure. It galaxies, which is the significant reason for the galac- is considered in density wave theory that the particle in tic spiral structure. Therefore, the inertial force should the spiral galaxies is doing the elliptical motion in the be taken into account when the structure and evolution central potential. Nevertheless, even if the spiral struc- of the galaxies are simulated. A galactic particle in its ture is formed, it is difficult for the galaxy to keep the movement is attracted by other particles with the force stability and sustainability of the spiral arm. Relatively, of gravitation. Because of the central symmetry, the net a spiral galaxy tends to be stable. Both the local damage force on every particle is centripetal. However, there is and the deformation of spiral structure are difficult to no enough huge mass in the center to provide this kind be observed(Dobbs & Baba (2014)). However, the ob- of gravitational force to make the particle moving in an servations show that the spiral structure of the galaxy elliptical orbit. Therefore, the galaxy is considered as a is very stable, and no damage phenomenon of the struc- many-body system in classical mechanics while analyz- ture is observed. Therefore, there must be other reasons ing its kinetic mechanism. for the formation of the spiral structure and the spiral a net viscous force is also provided from the arm. interactions between the galactic particles for a In this work, a new view for the general existence of single particle other than both the central net the spiral galaxies is proposed that it is due to the large force and the non-inertial force exerted by the scale rotation of the background, and then the spiral rotational background(Lynden-Bell & Pringle (1974); galaxy is not a relatively isolated system during its evo- Hofner & Sparke (1994); C. B. New, K., et al (1998); lution process. The rotation of its physical background Flebbe (1994)). This viscous force is actually produced makes the galaxies more like a cosmic hurricane. from the gravitational forces of other matters around the Based on this view point, a physical mechanism which particle, i.e., the viscous force is one component of the is very different from the density wave theory is proposed gravitational force. Up to now, there are no sufficient for the formation of the spiral structure in the spiral theoretical and experimental data to give the explicit ex- galaxy. the problem of the galactic evolution is reduced pressions for the viscous force of the galaxies. Therefore, to a viscous two-body problem in a non-inertial system. the viscous coefficient is taken as a free parameter, and The viscous two-body system is simulated for research- the viscous force is considered as proportional to the ve- ing the force upon the galactic particle and its influ- locity of the particle. The viscous force here is one kind ence to the galaxies. The trajectory of a single galactic of the inner gravitational force of the whole galaxies, so particle is calculated under the actions of the gravita- the total mechanical energy of the galactic system does tional force, the galaxy viscous force and the Coriolis not changed while a particle is under the viscous force. force. The results show that the trajectory of galactic And the lost energy of the single particle will make the particle under the background rotation is a spiral struc- change of the rotational velocity of the whole galaxy. It ture itself, not an elliptic orbit. And the origin of both is neglected in simulation cause its effect on the single the spiral arm and the warping structure can be demon- particle is very little. strated self-consistently. Under the effect of the rotation By doing so, the evolution of galactic system can be background, the transverse velocity of the galactic par- considered as a many-body problem under these three ticle rotating around the centre is mainly the result of forces now. The spiral structure of the galaxy can be the Coriolis force, rather than the effect of the rotat- given by many multi-body and fluid simulations com- ing velocity of the elliptical orbit under the action of ing from some galactic theory such as the density wave central gravitational force. And this transverse velocity theory. Nevertheless, the influence of an inertia force does not need to be explained with dark mater(Turner can not be clearly investigated by the more compli- (2000)). cated multi-body and fluid simulations, and the rela- tionship between the forces and the galactic evolution 2. THE PHYSICAL MECHANISM IN THE can not be comprehended intuitively. In this work, the MOTION OF GALAXIES kinetic properties of galaxy under those forces is ana- 3 lyzed with the simplest galactic system only consisting the self evolution of the galaxy. Therefore, the influence of two particles. The research on the evolution of the of the background in uniformly accelerated motion is re- overall galaxy in detail requires further simulations of gardless. And the inertia force provided by the cosmic a system with more particles. However, the simplified background in an uniform rotation is taken into account two-particle galaxy can not only give the explicit conclu- for the effect of the galaxy evolution. With respect to sion, but also make the relationship of the forces and the the large scale background rotation, the galactic scale D evolution of the galaxy comprehended more intuitively is far less than the radius of the background rotation R, and easier when the effect of those forces is investigated. i.e., D ≪ R. So the difference of centripetal force pro- Then the reduced galactic system consisted of two parti- duced by the rotational background on each particle is cles makes the conclusion more convincing. Therefore, it omitted. Thus the inertial force on each galactic particle is necessary to carry out such analysis before the many- produced by the uniform rotation of the background is body or Hydrodynamic simulations is given. only Coriolis force, which can be expressed as The main forces exerted on the galactic particle are F~ = −2m~ω × ~v (4) the gravitational force, viscous force and non-inertial c force, so the net force on one galactic particle can be where m is the mass of the galactic particle, and ~v is represented as the velocity of galactic particle relative to the galac- tic centroid in the background rotation frame, and ~ω is F~ = F~g + F~v + F~c (1) the angular velocity of the background rotation. In this Where F~g is the net gravitational force on the particle, case, the forces on the galactic particle under the large F~v is the viscous force, and F~c is the non-inertial force scale rotation of the background are one gravitational exerted by the rotational physical background. The force, one viscous force and one Coriolis force. The net force F~c is an important factor for the galactic evolution force can be expressed as here. Because of the rotational symmetry of a spiral m m F~ = −G 1 2 ~r − η~v − 2m ~ω × ~v (5) galaxy, the net gravitational force exerted on a galac- r3 1 tic particle by all the other galactic particles is a cen- Based on these reasonable assumption, a reduced galac- tripetal force. In this simplified two-particle galaxy, the tic system consisted of two particles is produced. Those net gravitational force is represented with the gravita- particles have the same mass because of the rotational tional force between two particles, so the gravitational symmetry of the galaxy, and the initial relative veloc- term in equation (1) can be written as ity of each particle is set as zero. The movement of the m1m2 galactic particle can be numerically simulated with the F~g = −G ~r (2) r3 net force in equation (5). where G is the gravitational constant,m1andm2 are the masses of the two particles respectively, ~r is the distance 3. SIMULATION AND ANALYSIS ABOUT vector between two particles. VISCOUS TWO-BODY PROBLEM When a particle moves in a galaxy, it is also pulled Because the main physical properties of the model is by a residual gravitational force from other particles, focused on here, the dimensionless unit is used in sim- which forms the viscous force exerted on this particle. ulating the equation (5), i.e., G = m1 = m2 = m = 1. The viscous force is introduced in our double particles The dynamical equations for particles of a two-particle galaxy model, and the viscous force is supposed to be galaxy can be represented as proportional to the velocity of the particle empirically, d2~r ~r i.e. 1 − 12 − − ×  2 = 3 η~v1 2~ω ~v1 ~ − dt r12 Fv = η~v (3)  (6)  2 d ~r2 ~r12 where η is the viscosity coefficient for the galactic par- = − η~v2 − 2~ω × ~v2  dt2 r3 ticles. According to the data from current galaxy re-  12 searches, there is not yet a convincing numerical value Where ~r12 is the displacement vector of particle 1 rel- for η, which is taken as a free parameter here. ative to particle 2, both ~v1 and ~v2 are the relative ve- As an assumption, it is not suitable to generate the locities of particle 1 and particle 2 in the non-inertial inertial force from the cosmic background in a compli- system, respectively, η and ~ω are the adjustable param- cated way. There are two simple ways to provide an eters. In the simulation, the trajectories of particles in inertia force, one is the uniformly accelerated motion, equation (6) can be calculated by setting the initial po- and another is the uniform rotation. The same iner- sition and the adjustable parameters, and the properties tia acceleration is provided to each particle in uniformly of galactic evolution are investigated. The important re- accelerated motion, which can not exert an influence on sults are given via the simulating calculation.The spiral 4 structure is conspicuous and stable in the trajectories of galaxy NGC 6814(or the Milk Way) and hurricane Al- particles. but also that the formation of the spiral arm berto(2000) shown in figure 3(Hurricane Alberto (2000); can be explained specifically through relation between NGC 6814 (2018)). the velocity and the radius. Moreover, the unusual phys- It is also showed that this spiral trajectory is very ical phenomenon, such as distinct warped structure, is in accord with that of a logarithmic spiral function in given by the three-dimensional simulation, which is con- the simulation calculation. One particle’s trajectory in sistent with the real warped galaxies. the double-particle galaxy with the initial position of ( ± 5, ∓5) is represented as that shown in figure . The 3.1. spiral structure trajectory can be fitted very well with the logarithmic In the case of plane motion, the direction of ~ω is set spiral function as Z axis, and the centroid location of the two particles r =2.015e0.531θ is taken as the original point. The line connecting two particles is perpendicular to ~ω, and the initial velocities Therefore, that the initially static particle looks likes of the particles are all zero, and then the motion of the rotating around the center of galaxy, is the result of system can be investigated. Coriolis force, rather than of be attracted by the galac- By setting without the viscous force, i.e., η = 0, and tic matter as an isolated system. Moreover, the previ- giving some initial conditions, there have no spiral struc- ous assumption of introducing dark matter to explain ture in the trajectory calculated from the equation (6), the particle’s motion as the effect of center gravitational and the result is shown in figure 1. The trajectories show force should be reevaluated. a petal-shaped structure with sharp end, which is simi- It is shown that the trajectory of the particle gener- lar to the trajectory of Foucault Pendulum with a zero ated from the equation (6) has a spiral structure consis- initial velocity(Somerville (1972)). The reason for ap- tent with that of a spiral galaxy in the above analysis. pearing this petal shape is that only the direction of the Unlike in the density wave theory, the particle’s trajec- particle velocity is changed by Coriolis force, while the tory is not an elliptical orbit, but is initially a spiral energy of the system can not be influenced. When the shape, which could explain why there exists a similar particle is attractive by another one and moves towards spiral structure in the flocculent galaxy without any ex- the center, the magnitude of the particle’s velocity is in- plicit spiral arms. The spiral structure of the galaxies creased, and the direction of the particle’s velocity also is so stable without any broken case, primarily because keeps changing under the action of Coriolis force. the trajectory of the particle is originally spiral, not an At the position where is the nearest neighborhood elliptical shape. from the center, the particle’s radial velocity decreases to zero, and its tangential velocity reaches the maxi- 3.2. The formation and evolution of spiral arm mum value. At this time, Coriolis force also reaches it’s It is impossible to simulate the formation of the spiral maximum value. At the tip position, the potential en- arm in a galaxy of two particles, because the number of ergy comes up to the maximum value, both the velocity particles is too small. Nevertheless, the velocity chang- and Coriolis force are zero. this process is repeated and ing with the radius is represented in figure 5, and it the particle’s moving direction is always changed by the can be seen that the velocity-radius curve of the par- Coriolis force. Then a petal-shaped structure around ticle have some turning-back. Considering the trajec- the center is formed in the trajectory of the particle. tories with η = 0 in figure 1, it can be observed that It can also be seen from this trajectory that Coriolis the turning-back area actually change from those end- force does not change the energy of the system. when point driven by both the Coriolis force and the viscous the viscosity coefficient does not equal zero, the galac- force. While the particles in a galactic disc move along tic particle surrounds and tends to the original point the trajectories of the spiral curve, the foregoing parti- because the particle’s energy loses continuously for the cle with the turning-back will gather together near the action of viscous force. Then a spiral structure appears orbit with the subsequent particle in the same trajec- in the trajectory of the particle, which is displayed in tory and those nearby. As a result, the higher density figure 1. area is generated, which then forms the galactic spiral Various shapes of the spiral structure can be given arm. The hurricane on the earth also has the similar by adjusting the viscosity coefficient and the angular spiral shape and the similar spiral arm under the action velocity of the galactic background, and these spiral of Coriolis force generated from the earth spin. Just structures are very similar to that in the spiral galaxies because of this turning-back of the velocity, the clouds observed at present and the tropical hurricanes. The area with different density is generated and forms the trajectory of the spiral structure in figure 2, for in- spiral arm-like structure of the hurricane. Furthermore, stance, is extremely consistent with that of the spiral the hurricane’s spiral arm can be explained only with 5

3 Particle 1 Particle 2

2

1

0 Y axis

−1

−2

−3 −3 −2 −1 0 1 2 3 X axis Figure 1. Moving trajectories of double particles with η = 0

2 Particle 1 Particle 2

1.5 ω=0.3 η=0.06 1

0.5

Y 0

−0.5

−1

−1.5

−2

−3 −2 −1 0 1 2 3 X

Figure 2. Trajectories of the double particles with η = 0.06

Coriolis force, while both the density wave theory and trajectories, which could explain the general existence the dark matter are needless. of the spiral arm and the time stability of the spiral If the large-scale background rotation existed, the spi- structure. the broken spiral arm caused by the moving ral arm of the galaxy should be formed by the turning- particle in an elliptical orbit supposed in density wave back driven by Coriolis force, and which is very different theory has never been observed in astronomy. from the explanation of the density wave theory. More- Further, the turning-back drives the formation of the over, all the particles move steadily along their spiral spiral arm, and along the circumference there have many 6

(a) Hurricane Alberto (b) NGC 6814

Figure 3. The similar spiral structure in Hurricane Alberto and NGC 6814

90

8 120 60

6

Particle 150 4 Fitting Curve 30

ω=0.11 η=0.11 2

180 0

210 330

240 300

270 Figure 4. The logarithmic spiral curve fitting for a particle’s trajectory turning-back location which can be seen in figure 1, duces slowly due to the turning-back evoked by Corio- so the arm number in the original galaxy might be lis forces. However, in the direction parallel to ~ω, there more than two. However, during the evolution of the have no turning back for the component of Coriolis force galaxy’s multi-arm structure, the nearby spiral arms get being zero, and this energy loss is more than the one together continuously due to the sustained impact of perpendicular to ~ω under the only viscous force at the those turning-back, and the number of arms is reduced same time. The velocity component parallel to ~ω de- to two. crease more rapidly. In this case, the particles in the direction parallel to 3.3. The origin of thin disc structure the ~ω accumulate in the thin disc plane soon. however, The thin disc structure is an significant feature of the the particles perpendicular to the ~ω direction are still spiral galaxies. By analysis the physical model in equa- doing spiral motion far from the center at the same time. tion 6, it is obtained that the formation of the disc struc- Therefore, a thin disc is formed before long during the ture is directly associated to the viscous force −η~v and evolution of the galaxy by this way. Coriolis force ~ω × ~v. During the particles falling to the 3.4. The formation of the warped structure center, the velocity component perpendicular to ~ω re- 7

2

1.8

1.6

1.4

1.2

1 Speed

0.8

0.6

0.4

0.2

0 0 0.5 1 1.5 2 2.5 3 Radius

Figure 5. the relationship between velocity and radius of particle motion

Through setting the direction of angular velocity of ponent is called as the leaving-plane force here. The par- the background rotation as the z-axis, and making the ticle will move away from the rotational plane along its straight line between the two particles no longer in the normal direction under the action of this leaving-plane same plane perpendicular to the Z-axis, the 3D trajec- force. tory of particles is simulated too. In addition to the case The leaving-plane force reaches the maximum value of plane motion, the three-dimensional simulation also when the particle’s velocity are vertical to ~ω⊥, and give some important conclusion, especially the warped it is zero when the particle’s velocity is parallel to structure which usually appears in the trajectories of the ~ω⊥. It can be seen that the leaving-plane force is two-particle galaxy. Therefore, the 3D trajectory is no anti-centrosymmetric in the disc. The direction of the longer a kind of plane distribution. leaving-plane force on one point is opposite to the one on The three-dimensional simulation of the equation (6) its centrosymmetric point. And the leaving-plane force can be proceeded by the following setting: the initial po- is changed with the particle’s velocity. In this way, the sitions of the two particles are located at ~r10 = (3, 5, 10) warped structure is formed by the action of this compo- and ~r20 = (5, 3, 10), respectively; the initial velocities nent of the Coriolis force. are all zero; and the angular velocity of the background It is always a tough task to explain rotation is set as the warped structure of the galaxies, and π π most of them need to employ dark matter ~ω = 0.36 cos( ), 0, 0.36 sin( )  6 6  (L´opez-Corredoira, Betancort-Rijo & Beckman (2002); Debattista & Sellwood (1999); Kerr (1957); Binney which is no longer set as z-axis; the viscosity coefficient (1978)). Different from the current theory on the warped is set as η = 0.16. The three-dimensional spatial tra- structure, the spatial warped structure is derived natu- jectory of the particles is shown in figure 6. It can be rally from the background rotation in this work, and no seen distinctly from the XY projection that a spatial additional assumption is required. The influence of the warped structure is in the particles’ 3D trajectory. And related parameters such as the background rotational the different shapes of the warped structure can be also frequency on the warped structure is also investigated simulated in the galactic particles’ trajectories by set- through the numerical simulations. It is shown in ting some different initial parameters. the simulating results that the warped structure is a When the angular velocity of the background rotation general phenomenon except the normal direction of is not parallel to the normal of the rotational galactic the disc completely parallel to the angular velocity of disc, there is a component ~ω⊥ parallel to the rotational the background rotation. This conclusion is consistent disc, which occurs a component of Coriolis force m~ω⊥×~v with the astronomical observations(Gamaleldin (1995); perpendicular to the rotational plane. This force com- 8

5 10.5 Particle 1 Particle 1 Particle 2 Particle 2

4.5 Z Y 4 10

3.5

3 9.5 3 3.5 4 4.5 5 3 3.5 4 4.5 5 X X

10.5 Particle 1 Particle 2 10.5 Particle 1 Particle 2

10 Z

Z 10

9.5 5 5 4 4.5 4 9.5 3.5 3 3.5 4 4.5 5 3 3 Y Y X

Figure 6. 3D trajectory and its projections of two particles’ motion

Sanchez-Saavedra, Battaner & Florido (1990)). served as usual. Those reference need more observed Due to the existence of the real galactic disc, it should evidence to prove. be noted that the warped structures is different notice- ably between the two-particle galaxy and the many- 4. CONCLUSIONS AND PROSPECTS particle galaxies. The more results approach to the real A model of the simplified galaxy for its evolution is galaxies need to be investigated through the N-body simulated and analyzed with the existence of the back- simulation. However, on the physical relationship be- ground rotation in this work. The research of the whole tween Coriolis force and the warped structure, the result galactic evolution still needs the further many-body sim- given in this work is more intuitive. If the background ulation or the hydrodynamic simulation. However, with were rotating, the warped structure should appear cer- regard to the properties of the forces and the resulting tainly in the real galaxies. spiral structures, spiral arms and warped structures and so on, the effects of forces can be demonstrated more 3.5. The whole turning of the galactic disc clearly here, and the conclusions are more convincing In addition to the formation of the warped structure, for the simplicity and intuition of the model. the whole turning of the thin galactic disc can be evoked In the density wave theory, the particle is doing an by a torque ~r×(m~ω⊥ ×~v) produced by the leaving-plane elliptical motion, and the particle’s velocity is periodic. force ~ω⊥. The sum torque vector is in the thin disc plane The spiral arm is made up of areas of greater density. and passes through the center of the thin disc, and is Furthermore, the assumption of dark matter is intro- perpendicular to ~ω⊥. The direction of the whole turning duced for explaining the huge centripetal gravitational of the disc, should be parellel to the torque vector. force for the rotation. However in this work, the trajec- It might be an important evidence of the overturn- tory of a single particle is itself spiral, and the high tan- ing of the disc that the jet-current from the center of gential velocity is associated to Coriolis force and viscous Centaurus A turns into a form with the s-shape through force, not contributed by the huge centripetal gravita- processional motion. And if there exists the background tional force. Therefore, the dark matter is not required rotation, the circumferential band formed by the histor- yet. If there is a large scale rotation of the galactic back- ical rudiments, i.e., a small amount of the material left ground indeed, the assumption of dark matter needs to during the galactic overturn process, and the other re- be reevaluated. lated phenomenons about the overturning could be ob- In addition, different from the explanation of the spi- 9 ral arm in density wave theory, the spiral arm is asso- scale rotation in the universe can basically be regarded ciated to turning-back of the particle’s velocity in this as a normal and general phenomenon. work. the turning-back makes the particles in the same In our previous work(Cao Zexin, Chen & Liu (2003)), spiral trajectory and the nearby areas aggregate, and the horizon problem of the rotation velocity within the impulses the form of spiral arm. Moreover, this model Galileo rotating framework had been solved in the spe- can also be applied to explain the spiral arm structures cial relativistic rotating frame. No horizon problem re- of the tropical hurricane on the earth, which can not stricts a large-scale rotation in the cosmos now. The be demonstrated by the density wave theory under the results in that paper showed that the large-scale rota- centripetal gravitational force obviously. tion of the galactic background can exist. Therefore, the A tropical hurricane on the earth is mainly a two- percentage that the transverse Doppler red shift formed dimensional structure as it keeps close to the ground. by the background rotation occupies in the Hubble red However, the three-dimensional galaxies in the back- shift is also a problem worthy of discussing. ground rotation also have some physical phenomena worthy of attention, such as warped spiral structure, spi- ral arm and the whole turning of the disc(Burns & Price (1983)). Although the background rotation need to be We appreciate the helpful comments from the anony- confirmed by further astronomical observations, if the mous referee. We thank the students CAI Yuanqiang, background rotation exists, it can be supposed suffi- GONG Jiguang, GUO Juanjuan and ZHANG Jingyu ciently that the spiral galaxy is exactly a cosmic hur- for their helpful work in computer, and we also thank ricane under the background rotation. According to the WANG Heng, JU Liping for their helpful discussions and widespread distribution of the spiral galaxies, the large- comments.

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