Galaxy Images
amateur astronomerJason Ware上有很多Galaxy圖片
http://www.astronomynotes.com/ismnotes/s8.htm winding problem http://www-astro.physics.uiowa.edu/~ri/modern_spr01/lect28/lect28.html Density Jam Knot http://www.astronomynotes.com/ismnotes/s8.htm http://www.nrao.edu/pr/2004/m51co/ http://www-astronomy.mps.ohio-state.edu/~pogge/Ast162/Unit4/spirals.html http://www.science.gmu.edu/~tle/Classes/Csi_801/Project/Discussion/node3.html http://encyclopedia.laborlawtalk.com/Galaxy http://encyclopedia.laborlawtalk.com/Hubble_sequence spiral 分類 http://cosmos.swin.edu.au/entries/hiiregion/hiiregion.html H-II Region http://casa.colorado.edu/~danforth/science/spiral/ http://ircamera.as.arizona.edu/astr_250/Lectures/Lecture_23.htm --- 寫得很好的文章 http://bustard.phys.nd.edu/PH308/galaxies/spiral.html winding dilemma
Spiral Arms Formation
http://home.cc.umanitoba.ca/~umcoll14/minorproject.html
http://casa.colorado.edu/~danforth/science/spiral/
Arm Formation in Spiral and Barred Spiral Galaxies
By Robert Collister
Spiral and barred spiral galaxies can be loosely classified into two types based on how distinct their arms are. Galaxies with thin, well-defined spiral arms are referred to as Grand Design sprials while those with fuzzy, loosely-defined spirals are described as flocculent. Ever since Edwin Hubble first began classifying galaxies based on the appearance of their spiral arms, there has been the problem of explaining the existence of these structures.
M51 - A Grand Design Spiral NGC 7339 - A flocculent galaxy
M51 - A Grand Design Spiral NGC 7793 - A Flocculent Spiral
Early Ideas
The very first idea about how spirals arms came to be was that they simply formed like that along with the galaxy. However, this model soon was proven false due to what is called the "winding problem". Since the disk of the galaxy rotates differentially, that is all different radii have the same speed but different length paths, a radial arm would quicky curve as the galaxy rotates. As time contiues to pass this "spoke" becomes more and more tightly wound, eventually obliterating the spirals. This model for spiral arms would last only a couple rotations of the galaxy, and thus better models were needed.
winding problem diagram
The "winding problem"
winding2
Tighter winding over time
The other model that proved untenable suggested that magnetic fields were responsible for the formation of spiral arms. This idea was never very well developed and soon was shown to be false. The strength of the fields that were needed to accomplish this feat were about five times stronger than what was being observed. Nevertheless, some good came out of the analysis of this model. It was discovered that while magnetic fields were not responsible for the arms, they do follow along the arms themselves.
Current Models
Spiral galaxies come in many, many different forms. The vast differences in the shape of one spiral galaxy to the next lead to the idea that there is more than one process involved in the formation of their spiral arms. There currently are three widely accepeted mechanisms for this. They are the Density Waves model first put forth by American astronomers Chia Chiao Lin and Frank Shu in the 1960s, self-propagating star formation put forth by M. W. Mueller and W. David Arnett in 1976. The third way is that the arms are a product of the collision between two galaxies.
First I will examine the collision model for spiral arms. When two galaxies approach one another they exert incredible tidal forces upon each other. The matter in each galaxy is pull together by these forces producing a bulge along the disk and even the formation of a star bridge between the two galaxies. As the collision progresses, the motion of the galaxies is changed and after the merging or brush-by, new spiral arms remain. It is very difficult to explain but I have found a supercomputer simulation of such an interaction between two galaxies. In it, you can see the leading bridges and trailing tails of the galaxies before collision.
Galaxy Collision Simulation
During the interaction those structures aquire the rotation that develops the spiral arms. Afterwards you can clearly see the two arms rotating about the center nucleus of the merged galaxies. This process works fine for explaining how the arms are formed, but does little to explain why they continue to exist.
This brings us to the self-propagating star formation model. When the first large, hot stars formed in the galaxy, their radiation and stellar winds push against and compress nearby gas and dust, causing more star formation. When those same stars go supernova, the resulting shockwaves produce the same process. Together, these two events contribute to a continuing cycle of star formation.
Propagation
Self-Propagating Star Formation
Stars do not form behind the front as in the diagram because the gas and dust is too hot to be packed tight enough for fusion to start. Now, since the all parts of the galaxy have the same angular speed around the nucleus but the inner areas have a shorter circumference to travel, the inner edge of the star forming region advances faster than the outer edge. The result is a spiral arm formed by the bright OB stars and their nearby emission nebulae. However, due to the already described motion around the galaxy, the spiral arm quickly becomes spread out and indistinct. Furthermore, these arms come and go seemingly at random. Also of note is that there is no explanation of how there could be two or more of these self-propagating waves moving around a galaxy. Hence it is believed this model is accurate for the more irregular spirals, such as the LMC, and the more filamentary aspects of other galaxies. This model does not explain Grand Design sprials very well.
LMC
Large Magellanic Cloud
Thirdly, the Density Wave model will be discussed. The initial idea is credited to Swedish astronomer Bertil Lindblad who in the 1940s proposed that spiral arms were a pattern that moved through a galaxy like waves on a pond. Lin and Shu expanded upon this idea to produce the Density Wave model. In this, the arms are a pattern of density waves moving around the galaxy in a steady-state. While this is probably not the exact case, I will discuss the modification later.
One important aspect of the Density Wave theory is that the wave itself moves more slowly than the galaxy itself rotates; the stars and interstellar gas and dust are moving through the wave, not the wave moving through the stars, gas and dust. As the gas and dust are compressed, they form nebulae which in turn become stars. All of the OBAFGKM classes of stars are formed. However, the O and B stars have very short lifetimes and after about 3-15 million years move off the main sequence and become red giants. This means that they only travel a short distance off of the spiral arm before they pass on and explains why the regions between spiral arms are much darker than the arms themselves. The luminous OB stars and any ionized hydrogen emission nebulae near them have become extinct leaving only the much fainter stars behind that will orbit around the galactic disk.
Density Wave
Density Wave Model
This model also explains why the stars in the disk of a galaxy are largely population I stars, that is they are composed of a small amount of metals, while the galatic nucleus is formed exclusively of population II stars, that is composed solely of hydrogen and helium. The model explains this because it shows that the OB stars that have died and gone nova have scattered metals in their general area. Once this part of the galaxy that contains these metals passes through the next density wave, the metals get combined with hydrogen and helium to form new population I stars. The nuclues where the density wave is absent, does not have the level of star formation that the disk has, hence new population I stars are lacking leaving only older population II stars. Furthemore, this explains why galactic nuclei appear more red and yellow than the disk, since the stars in the nucleus are cooler stars with longer lifetimes.
Current Research
The density wave model is still undergoing development. The single largest problem with the model is that it is unlikely the density waves are a steady-state on their own. Currently research is focused on finding a driving mechanism for the density waves that keeps them moving around the galaxy. Since it requires a great deal of energy to compress such a large amount of matter, it would be expected that the density wave would eventually die out, just like the wave on a pond. So far three of these mechanisms have been suggested. One proposed mechanism involves interactions from nearby companion galaxies (such as dwarfs) that again provide the required tidal forces. Another idea is that assymetrical distribution of globular clusters and other star formations in the halo of the galaxy provide the same differing tidal forces. A third idea suggests that a barred nucleus provides enough differing tidal forces to keep the wave going. Recent high resolution observations have detected barred structures in the majority of Grand Design spirals, lending much credence to this idea.
References
Toomre, A. (1981), in The Structure and Evolution of Normal Galaxies, eds. Fall, S.M. and Lynden-Bell, D. (Cambridge University Press, London). 111-136.
Danforth, Charles. (1998) The Origins of Spiral Arms. http://www.pha.jhu.edu/~danforth/index.html
Freedman, Roger A. and Kaufmann, William J. III. (2002) Universe, 6th ed. (Library of Congress Cataloging-in-Publication Data)
Dynamic approach of spiral density waves
Spiral Density Waves
Many different kinds of spiral structure are seen in disk galaxies. Most photogenic are the grand-design two-armed spiral galaxies such as M51, but far more common are ragged or flocculent spirals made up of many short arms. The diversity of spiral galaxies is paralleled by the diversity of theories of spiral structure. Grand-design spirals are often discussed in terms of the Lin-Shu theory discussed here (after Chia-Chiao Lin and Frank H. Shu), which views the spirals as slowly turning wave patterns maintaining their form for many rotation periods. However, classic grand-design spirals like M51 often have close companions, and it is possible that such spirals are actually excited by tidal interactions. Flocculent spirals, on the other hand, are generally thought to evolve over time, with individual spiral arms constantly forming and dissolving.
It seems clear now that the spiral structure of galaxies is a complex problem without any unique and tidy answer. Differential rotation clearly plays a central role. However, we know that the logical paths diverge soon and deservedly toward such separate themes as global instabilities, stochastic spirals, and also the shocks patterns that can arise in shearing gas disks when forced by bars.
Figure: In inner regions of the spiral galaxy M51 observed by HST. Several components of the spiral structure are clearly delineated: massive, hot, young stars in HII regions; narrow dust lanes; and the underlying, smoother old stellar population. \begin{figure}\epsfig{figure=m51HST.ps,width=2.0in,angle=0}\end{figure}
We approach the study of spiral galaxies by considering the dynamics of a thin, flat, rotating sheet of self-gravitating gas. Although disk galaxies contains interstellar gas, they is composed primarily of stars. Consequently, it would be more correct to treat the disk as stellar dynamics problem, and to study the Boltzmann equation for the stellar distribution function. A fluid model simplifies the analysis, and can be partially justified. A continnum description is valid if we are interested only in phenomena with length scales large enough that relevant regions of our fluid will contain large numbers of stars. However, we will also assume that our stellar fluid exerts pressure. This assumption is suspicious because the mean free path for a star is large compared to the dimensions of the system. A self-gravitating pressureless gas is unstable and so has limited usefulness as a model for a galaxy. A disk with pressure can overcome these instabilities in much the same way that a stellar system with random velocity components can, so that the acoustic speed a of the gaseous disk should be regarded as mimicking such a random stellar velocity.
The theoretical explanation of spiral structure in disks has been an active field since Lin & Shu's (1964) seminal paper, which introduced the fluid model. Although stellar dynamical models have subsequently been studied, fluid dynamical models have continued to prove useful. The problem of spiral structure has yet to be fully resolved. Fluid models are relatively simple, they are still relevant and, moreover, they are still not fully understood.
Dynamics Explaination
11.1. Bar Formation
The bar instability was discovered in early N-body simulations of rotating stellar disks (Miller & Prendergast 1968; Hockney & Hohl 1969). Because of these results, Kalnajs (1971, 1972) studied the stability of disks with respect to bar modes through a linear analysis, and made predictions about the eigenvalues and growth rates of the normal modes for a given density and velocity distribution. These have been verified by simulations in the linear regime (e.g. Sellwood and Athanassoula 1986).
Bars can be considered as long-lived modes, made by the superposition of leading and trailing waves, i.e. forming a standing wave. As such, the bar mode can grow through swing amplification, as outlined by Toomre (1981) for spiral density waves. The amplification of waves relies on the corotation region (CR), which separates the galaxy into two regions where the waves have opposite signs of energy and angular momentum (negative inside and positive outside CR). At CR a wave will be partially reflected and transmitted; the transmitted wave will carry energy of opposite sign as the incident wave, so that the reflected wave must have an increased amplitude to ensure conservation. The corotation amplifier, coupled with a feedback cycle that reflects the waves back to CR, can explain the growth of modes. Several feedback cycles were proposed, such as the WASER (Mark 1974b) based on long-trailing waves, while the swing involves the feedback of short leading waves. In the WKB theory, waves are, however, evanescent around CR, and tunnel through a forbidden zone (Lin & Shu 1964); the exponential decrease of wave amplitude in this region kills the amplifier, and the gain of the feedback cycles proposed is of the order of unity. Actual amplitude gain over a cycle relies on another kind of amplification, a positive feedback first identified by Goldreich & Lynden-Bell (1965) and Julian & Toomre (1966), and detailed by Toomre (1981), with the help of numerical simulations.
The amplification is due to a conspiracy between differential rotation, epicyclic oscillation, and self-gravity. Trailing density waves propagate radially towards the center, while leading waves propagate outwards. The leading wave packet becomes more and more open while traveling, due to differential shear, until it turns into a trailing wave. During this swing from leading to trailing, particles running on their epicyclic motion closely follow the wave, and strongly interact with it. Self-gravity contributes to gather particles, and amplify their density contrast. The wave energy is amplified at the expense of the rotational energy.
The trailing waves traveling inwards can be reflected in the center, while the leading waves give rise to trailing reflected waves, and transmitted waves at corotation. The reflection in the center occurs only if a wave can travel there without being damped at the inner Lindblad resonance. The problem of a possible Landau damping of waves at the inner resonance has long suggested that bars can only develop without this resonance. The pattern speed should then be high enough to prevent the resonance. This appears to be verified in N-body simulations in the linear regime, at the beginning of bar formation. But it does not seem to be the rule in the non-linear regime in N-body simulations, nor in the observations, when some hint can be gained of the bar pattern speed.
Another point of view to better understand the N-body problem is in terms of stellar orbits, and families of periodic orbits as will be described in the next section. Periodic orbits are closed orbits in the frame rotating with the bar. The stable ones trap regular orbits around them. They are thus the skeleton of the orbital structure of the disk. Periodic orbits are the fixed points that depend essentially on the symmetry of the potential, and not on the detailed mass distribution. In the potential of a rotating bar, the main family of orbits is elongated along the bar, supporting it, and we can understand under which conditions a self-gravitating system will become barred. When the mass concentration towards the center is strong enough, the elongated orbits will be replaced by periodic orbits perpendicular to the bar, and we can predict the dissolution of the bar. This approach can help to determine the pattern speed of realistic self-consistent bars. Such an approach has been developed by Contopoulos and collaborators (e.g. Contopoulos & Papayannopoulos 1980).
The consideration of near-resonant orbits aligned with the bar led Lynden-Bell (1979) to propose that bar instability could come from a kind of Jeans instability, trapping all elongated orbits and aligning their major axes. He studied the conditions under which an elongated closed orbit in the bar rotating frame will be forced to align with the bar, and therefore reinforce it, because of gravitational torques. He concluded that for this to occur, the precession rate of elongated orbits (Omega - kappa / 2) must increase with specific angular momentum, a condition that is fulfilled only in the central parts of galaxies where the velocity curve is rising. The pattern speed of the bar in this scenario must be lower than the peak of the Omega - kappa / 2 axisymmetric curve, which is not the case at the beginning of the bar instability in N-body simulations.
The development of the instability has now been followed through a wide series of N-body simulations (e.g. Sellwood 1981; Combes & Sanders 1981; Sellwood & Wilkinson 1993). In an initially axisymmetric stellar disk, first a transient two-armed spiral wave develops; since it is trailing, it transfers angular momentum outwards (Lynden-Bell & Kalnajs 1972). The bar then forms in two steps: first a short and weak bar forms, rotating with a high pattern speed which is always higher than the maximum of the precession rate Omega - kappa / 2. The bar, as a wave inside its corotation, has a negative angular momentum, and is amplified through the outwards transfer provided by the spiral arms. Then, the bar slows down, with a growing intensity, trapping more and more particles in its potential well. This can be understood in the frame of density wave theory as well as in stellar orbit theory. At the beginning, the perturbation is linear; for the swing amplifier to work, there should be no inner Lindblad resonance. This is fulfilled if the bar pattern speed is well over the Omega - kappa / 2 curve, justifying the fast rotation at the start.
In parallel, we can consider that the bar traps more particles in extending its length. Those particles, at larger radii, have lower precession rates, and it is likely that the global equalized rate, i.e. the pattern speed, will be lowered by the adjunction of these particles. As the pattern speed decreases, the bar loses angular momentum through the spiral wave.
Figure 57. Example of bar formation in an N-body simulation, with stars only. The galaxy is plotted every 200 Myr. t = 200 Myr
Figure 57 t = 400 Myr
Figure 57 t = 600 Myr
Figure 57
t = 800 Myr
Figure 57 t = 1 Gyr
Figure 57 t = 1.2 Gyr
Figure 57
Periodic orbits are parallel to the bar only inside corotation, as we shall see below. As Omega b decreases, corotation propagates outwards, and the bar extension could be higher. Bar formation by trapping of orbits is illustrated in the N-body simulation of Figure 57.
11. DYNAMICS OF BARS
spiral galaxies，大約其中的2/3是distored oval或是叫作non-axisymmetric bar，只有1/3才是擁有strong bar. Barred galaxies是由於cold gas component所組成，所以只能由red or infrared光譜來觀測。
About two-thirds of spiral galaxies possess a non-axisymmetric distortion or a bar in their stellar component, although only one-third possess a really strong bar, of SB type (e.g. de Vaucouleurs 1963). Red or near-infrared photometry has revealed many bars and oval distortions in the old stellar component that were not visible on a blue photograph of the same galaxy, because of dust and star-formation regions (Zaritsky & Lo 1986; Rix & Rieke 1993). A bar can be detected also by the cold gas component, which is a good tracer of faint perturbations in the potential (e.g. CO observations of IC 342, Ishizuki et al. 1990; NGC 6946, Ball et al. 1985; see also Turner 1996). It can therefore be concluded that a bar exists in the great majority of galaxies, and is not a peculiar structure, as was considered before the 1970's. Our own Galaxy appears barred from its kinematics and elliptical streamlines (e.g. Peters 1975; Mulder & Liem 1986), and also from its boxy and asymmetric near-infrared contours (Blitz & Spergel 1991), and its micro-lensing efficiency (Paczynski et al. 1994). Our nearby companions are also barred (M31, Large and Small Magellanic Clouds, etc.).
Observed and dynamical properties of bars have recently been nicely reviewed by Sellwood & Wilkinson (1993). As far as rings are concerned, it is interesting here to note that barred galaxies might be the only objects where a long-lived, quasi-stationary, normal mode can be recognized. Bars are essentially composed of an old population, and the spiral waves in a barred galaxy are strongly influenced (maybe driven?) by the bar. In strong bars, the spiral arms appear always in the continuation of the bar, suggesting that they rotate with the same pattern speed. The presence of a grand-design spiral is about twice as frequent in barred galaxies than in nonbarred ones, as determined by Elmegreen & Elmegreen (1983). While nonbarred galaxies can be multi-armed or stochastic, most barred galaxies possess a two-armed regular density wave. Barred galaxies are therefore ideal for studying resonance phenomena.
Dynamics of the spiral arms
11. DYNAMICS OF BARS
About two-thirds of spiral galaxies possess a non-axisymmetric distortion or a bar in their stellar component, although only one-third possess a really strong bar, of SB type (e.g. de Vaucouleurs 1963). Red or near-infrared photometry has revealed many bars and oval distortions in the old stellar component that were not visible on a blue photograph of the same galaxy, because of dust and star-formation regions (Zaritsky & Lo 1986; Rix & Rieke 1993). A bar can be detected also by the cold gas component, which is a good tracer of faint perturbations in the potential (e.g. CO observations of IC 342, Ishizuki et al. 1990; NGC 6946, Ball et al. 1985; see also Turner 1996). It can therefore be concluded that a bar exists in the great majority of galaxies, and is not a peculiar structure, as was considered before the 1970's. Our own Galaxy appears barred from its kinematics and elliptical streamlines (e.g. Peters 1975; Mulder & Liem 1986), and also from its boxy and asymmetric near-infrared contours (Blitz & Spergel 1991), and its micro-lensing efficiency (Paczynski et al. 1994). Our nearby companions are also barred (M31, Large and Small Magellanic Clouds, etc.).
Observed and dynamical properties of bars have recently been nicely reviewed by Sellwood & Wilkinson (1993). As far as rings are concerned, it is interesting here to note that barred galaxies might be the only objects where a long-lived, quasi-stationary, normal mode can be recognized. Bars are essentially composed of an old population, and the spiral waves in a barred galaxy are strongly influenced (maybe driven?) by the bar. In strong bars, the spiral arms appear always in the continuation of the bar, suggesting that they rotate with the same pattern speed. The presence of a grand-design spiral is about twice as frequent in barred galaxies than in nonbarred ones, as determined by Elmegreen & Elmegreen (1983). While nonbarred galaxies can be multi-armed or stochastic, most barred galaxies possess a two-armed regular density wave. Barred galaxies are therefore ideal for studying resonance phenomena.
密度波的由來
spiral arms 只在 flattened 或是 disks 的星系中發現。
differential rotation: the time to complete a full rotation increases with distance from the center.
所以 inner/outer 此2者的速度差造成了 winding(纏繞) 的現象，consequently 纏繞的結果會造成纏繞很多圈 (many turns) 的現象，與所觀測的結果不符合。
因為現在的星系大約年齡為 10 billions，但是星系中，環繞一次所花的時間為 .1 billion，所以可以知道應該星系己經繞了約 100 次，但是現在所觀測的 spiral arms，大約只有 1-2 turns，所以differentai rotation的預測與觀測結果，此2者並不吻合。
The second important piece of physics for understanding spiral structure is that the stars and gas in the disk of the galaxy exert an appreciable gravitational force, which helps maintain the spiral structure form against the tendency to wind up.
其實星系本身因為重力吸引的緣故，傾向於 winding up tightly，但由於 spiral arms 的結構提供了 appreciable gravitaional force，來對抗彼此重力的吸引。
that gravitational systems act to increase their central binding energy. Spiral arms remove angular momentum from the center of the galaxy, allowing it to achieve a state of higher binding energy. There are two main versions of the theory of spiraling: one in which the waves are steady and long-lived, the other in which spirals are transient features that come and go. The natural, but not very easy, test is to observe spiral galaxies for a few hundred million years and see what happens.
星系本身因為重力的吸引，就會傾向於binding，亦即會increase binding energy，而由於spiral arms會從galaxy中心移走角動量，造成binding energy的增加，也就造成winding的困難。有2種模型來解釋spiral arms結構的成因:
- spiral arms本身是wave, 但此wave是steady and long-lived
- spiral arms結構只是過渡(transient)性結構
藉由觀測一些年輕星系(只有數百萬年)的 spiral structure ，來推論 spiral 的穩定性，及其 spiral structure的理論，何者為正確的。
"Most spiral arms in galaxies are density waves, which are compression waves (like sound) that travel through the disk and cause a piling-up of stars and gas at the crest. The wave is temporarily sustained by the force of its own gravity, but it eventually wraps up or gets absorbed at orbital resonances, places where random stellar oscillations have the same period as the local wave. "In some galaxies, a large central bulge can prevent the wave from reaching a resonance; the wave then reflects off the bulge, giving rise to a giant standing spiral wave with a uniform rotation rate and a lifetime of perhaps 5 to 10 disk rotations (roughly one to two billion years). In all cases, the stars and gas rotate around the galaxy's center faster than the wave in the inner parts of the disk, and slower than the wave in the outer parts. This differential rotation forces gas to enter the wave at a high speed in the inner regions, causing it to shock and form long, thin dust lanes in each spiral arm.
spiral arms 的形成是由於密度波造成的，密度波可以想像類似音波的概念，密集的波峰部份，就是星球聚集產生的地方。
