Our Nearest Spiral Galaxy
As my first topic on my website, I wanted to tackle a subject that I believe hasn’t been given due attention elsewhere – why are there spiral galaxies and why do so many galaxies present themselves as spirals? This is the first of a series of posts intended to explain how it all works.
A Strange Attraction – M31 Andromeda Galaxy
Televue 127is; AP 1100GTO AE; QHY 600M, – Baader L,R,G,B & 6.5nm H,O Cmos Opt.
L: (97 x 120s 61 Bin 1, Gain 26R,G,B: (54,52,47 x 150s, Bin 1, Gain 26)H,O: (53,29 x 720s, Bin 1, Gain 26)
Total integration time = 26 hrs (Sep29,& Oct 1,2 , 2024) Maple Bay, BC
This image is of the Andromeda Galaxy, part of our local group of galaxies that also includes the Triangulum Galaxy,
(Click on image for full res, downloadable version at Victoria Centre’s RASC Zenfolio or Astrobin sites)
Two Physical Ingredients in Multiple Phases
To form a galaxy requires two physical ingredients – the first of which is a bunch of hydrogen atoms. As far as astrophotography is concerned, hydrogen in a gaseous, unexcited form is transparent and colourless. The only way we can see the hydrogen in a galaxy is either in the form of a star, or when it is in an excited state (Halpha or Hbeta emissions). Most of the hydrogen in a spiral galaxy is not within the stars, because as we shall see, a galaxy whose mass is predominantly stars, will cease to have a spiral structure. So this is worth bearing in mind, as most of the mass of the galaxy is our first ingredient…invisible hydrogen.
Before we get too far, I have to talk about a couple of properties of our hydrogen at the prevailing conditions of space. First off, the conditions (ultra-low pressures and temperatures) in space cannot easily be replicated in a lab. We have to surmise what we can from the properties that we can measure together with analogies to how other gases behave. Fundamentally, in most of volume of galactic hydrogen exists as individual atoms or ions- a proton and an electron that may be associated with one another. This basic state I will refer to as interstellar medium or ISM. The pressure and density is soooo low, that for our current purposes, you can think of this as a vacuum (at least for now).
It may happen, due to some gravitational force, that if this ISM is compressed from its ultra-extremely low pressure to one that is merely extremely low (by our standards), hydrogen atoms will encounter each other with enough frequency and pressure force that they will form H2 molecules and transform into what we will call a molecular cloud. This is simply a LeChetalier reaction to changing conditions from nearly a complete vacuum to a relatively speaking, higher density, pressure, and overcrowded locale. (Here, the drive to a lower energy state over-rides the drive for higher entropy associated with atoms. ) Since the pressure is now higher, this gas is much more dense and its properties become very different from ISM.
As it turns out, the galactic arms in a spiral galaxy are made (primarily) out of this, somewhat compressed, molecular cloud (MC), separated by lower pressure atomic ISM. In fact, most of the mass of hydrogen within the clouds is in this diatomic molecular form – despite it occupying a considerably smaller volume than the ISM. Both the MC and ISM, with only a few exceptions, are invisible in our images and we only know this from our images via the many products of hydrogen behavior (stars, dust, and narrowband emissions) created within the galaxy itself.
Stars, themselves are a forms of hydrogen that we can see in our images. They are in a yet another phase-state – mainly a liquid metallic state, surrounded by a gassy plasma – but stars are are mainly born from molecular clouds within galaxies, so somehow we have to put the galaxy together with only a very few stars at our disposal.
Gravity versus Pressure in a Spherical Form – Newton’s Shell
It is popular belief that a sufficiently large MC alone can create either a star or even a galaxy, and this misconception is propagated using Newton’s Shell Theorem (math below)…
Newton’s Shell Theory suggests that to any point at the outer edge of a spherical shell or cloud of material or farther away (points 1 and 2), the object will act as a point source gravitational attractor with a mass equal to that of the entire sphere or cloud. What is really cool, is that for any point within the cloud (point 3), the centre continue to behave as a point gravitational attractor, but with a reduced mass comprised of only the matter that exists closer to the central point. Perhaps the most important point of the theorem is that the material that exists outside of the sphere defined the distance from the central point to point3 exerts no net gravitational influence within it. It is as if (gravitationally at least) that it doesn’t even exist as far as point 3 is concerned.
As we can see, Newton’s Shell Theory says that the gravitational force towards the centre increases from 0 at the centre, and increases linearly with radius, at the outer edge as the cloud becomes larger. Total mass, gets larger with radius cubes, while distance to other particles only decreases with the inverse of radius squared. With each spherical shell of gas added to the cloud, the maximum pull of gravity that exists at the outmost radius, gets stronger and stronger. This is because the pull of gravity varies with the in James Jeans in a famous theorem, suggested that there was an critical mass (or size of cloud at a given homogeneous density) that would cause the whole cloud to collapse, at least to a smaller compact version.
As we will see in future parts of this post series, Newton’s Shell Theory is a useful concept in understanding the dynamics of material in outer space, but we will see that we have to be careful in its application. While the concept on the distribution of gravity within spherioidal bunch of gaseous molecules or atoms is helpful, stating that either spherical galaxies are formed by the spontaneous, adiabatic collapse of spheres of gas is oversimplistic and deeply misleading, It’s reliance to describe the spiral structure of galaxies in terms the distribution of the material and gravitational forces, either as ISM or MC or stars is unphysical. I liken it to the “raisin bun” model of the atom – post discovery of electrons but prior to the orbit theory. Ditto for the use of spontaneous adiabatic collapse of clouds into stars, or even for the spontaneous collapse of larger, disperse clouds into denser, higher pressure ones.
At one time, Newton’s Shell Theory was interpreted to mean that there was a critical radius of material, where even a gas would spontaneously collapse. This was known as Jean’s theorem.
Here is where it all falls apart for the following reasons.
- The theory goes that that the gravitational pull of the virtual “central attractor” will increase as we add material (gasses) on the outer edge (making the sphere more massive). Eventually, a critical cloud diameter will be reached where the cloud does collapse, due to this increased gravitational pull and the gas will condense to the centre (and form a star!). I refer to this kind of collapse as an outside-in one. The theory itself, in that any material added to the outside of the sphere cannot change or influence what is in the inside – and therefore, the inside of the sphere cannot collapse. The outside shell, will simply pass right through the next shell in and now become an inside shell. But now the material that was outside becomes inside – no longer influenced by the ones now outside. The now outside shell, cannot feel the influence until is passes by. The former outer shell will compress as it moves toward the centre. As it travels inward it is feeling less and less gravitational attraction toward the centre and yet needs to continually compress more an more to continue its journey on getting smaller and smaller. Eventually, this former outside shell will reach the centre, where the particles need to simulataneously stop. It should be at high pressure here, but because it is has no gravity it should have no pressure.
- An alternative suggestion is that some compression should take place simultaneously throughout the sphere, and this would increase the density of the sphere, as if were a balloon – keeping its homogeneity. This is fact, does happen quite readily as we add more mass to a cloud it will contract and compress until it’s pressure (which increases with density, which increases with radius cubed) offsets the additional gravitational force. However, as pressure increases, compressibility decreases too for real fluids, and there is a limit when additional gas added on the outside will have less and less an effect.
- A third alternative is an inside-out collapse of a cloud. This can be accomplished by placing a much more dense mass at the centre of the cloud, so that gravitational force decreases with the radius outward. This essentially describes our solar system and our local “cloud of planets” happily orbit it.
- What convinced detractors from Jeans’s cloud collapse theory was that if, the gas cloud was larger than the critical sphere, the placement of the sphere was rather arbitrary as long as it was contained within the cloud, so how would any gas particle know where to collapse to? The superposition of two spheres, each with a mass exceeding any critical value would see gravity some what oppose each other, cancelling out their potential. This fundamental reasoning conflict led the theory to be known as “Jeans swindle”.
- If the cloud is not spherically symmetric from its centre, then the superposed “centre of gravity” and gravity force magnitude would be different depending upon the particles position in the cloud. The same would be true of any density variations within the cloud. Some variable compression is to be expected under this scenario, but certainly not to a defined point in space
- Other forces including inertial, viscous drag, and electromagnetic forces have not been considered in the spontaneously collapse theorm, that act in various directions, and non-linearly as well. Clouds of gas need to be considered as non-linearly dynamic and chaotic, that undermines the proposed model of galaxy and star formation.
- What convinced me right away, however, it that the notion of spontaneous adiabatic collapse, even if it were perfectly spherical and consisted of just the right amount of mass dictated by Jeans’s theorem, and this relates to thermodynamics in general and the second law in particular. Thinking of the cloud as a continuous fluid, work needs to be done on the system to compress it. If one could build a steam engine large enough, one could take portions of the cloud, run a machine powered by the energy of expansion and then the spent energy would be returned by just letting the cloud spontaneously collapse again.
- The more massive a homogeneous cloud gets, the further away from every other point new particles are Be definition, the only way to change this is to place more particles on one side of the outside
- The equations shown have assumed a constant density, more reflective of a liquid or solid, than a gas. If one could create a spherical gas cloud, its pressure and density would be greatest at the outside of the cloud and almost nil in the middle. The density of gas in the sphere would adjust (according to isothermal conditions) such that outward pressure would counterbalance the gravitational force at all arbitrary radii. The centre of the cloud, would indeed have no gravitational forces, but also, no pressure or density. At the same time, additional material added to the outside of the cloud, would have to be added at increasing pressure, requiring work be done on the material outside of the cloud. To penetrate the outside shell and create a collapse, gas at a higher pressure would have to be added.
- To summarize, while Shell Theory is quite interesting and certainly applicable to condensed materials, it cannot and does not apply to real gases. Gases, by definition will always expand to fill their container – they will not be confined by an outer shell of high gravity, rather because pressure will defy containment at the spherical centre. Work has to be done, in one shape or form on the gas to compress it.
I don’t want to belabour the point here, but the concept of critical cloud radius, or Jeans instability (or more accurately, Jeans swindle) is one of those concepts that really should be laid to rest and given a decent burial. In fact, the only way to keep a molecular cloud contained and somewhat compressed is via a concentration of condensed matter at the cloud centre employing an inside out model. Nonetheless, we will make use of the Shell Theory when describing the balancing off of forces – and why it only holds for spherical geometry.
Gravity from within – Our second physical, (incompressible) ingredient
While Shell Theory cannot contain a gas cloud from the outside, a sufficiently large condensed point mass can contain the gas cloud from within. If we were to carefully place such a point mass right in the centre of our spherical cloud, without inducing any orbiting or angular momentum, the cloud can remain spherical. However, now the cloud will have the lowest potential energy right at the point mass, and not at it’s outer shell. The pressure / density would be highest at this new centre, with gas molecules held tightest against the point mass, where the potential energy becomes a minimum. The size of an individual gas cloud that can be contained by such a point mass is dependent upon the diameter/mass of the point condensed mass such that the derivative of pressure with respect to radius is always negative.
This brings us to the second ingredient for our galaxy – a point mass strong enough to hold all the gas together. As a pick of something small, but heavy enough, I would choose either a black hole or a neutron star – maybe even a very massive star? for a very small cloud. To give a sense of what I am talking about, we need it to be large so that when approaching our cloud, both the cloud and the mass can become gravitationally locked together. In the case of our Milky Way, the mass of the Sagittarius “A” black hole that forms our galactic gravitation attractor is very heavy (4.3E6 solar masses), but only 0.3% the mass of the whole galaxy (1.5E9 solar masses). Even with such a relatively small central attractor, the Shell model for our galaxy can be made stable as long as the angular momentum is low.
In a gas cloud with a point mass in the middle, the gravitational fields of both the “point mass” and the hydrogen particles (Shell model) must be superposed or superimposed upon one another. To analyse the galactic structure, we can still make use of Newton’s Shell Theory, we just have to add the gravitational force of the central mass to that of the cloud. Unlike Newton’s Shell, gravitational acceleration will be highest the closer one is to the centre of the cloud rather than the reverse. Ultimately, it is a point source at the galactic centre is what holds the MC together as a galaxy.
The solar system is full of examples where a central mass holds on to a gas cloud. On Earth, the mass of the planet contains our atmosphere. In Earth’s case, the highest pressure exists at the surface, and not at the outer edge as in our Newton’s shell. On Jupiter condensed material is sufficient to make its hydrogen and helium super-critical at its core. Even our sun, made out of liquid metallic hydrogen, has a gasous (or plasma) atmosphere. These examples hold on very tightly to their atmospheres, but in a galaxy, the gases are not such much an atmosphere on the mass, but more spread out – despite the centre actually being a black hole!
Nasa image
One final note, here that I do wish to point out, is that I did specify that the point mass had to be placed very carefully at the centre of the gas cloud so as to avoid any angular momentum between the gas molecules and the central gravitational attractor. In practice, this never occurs, and there is always some angular momentum of the gas cloud and rather than a sphere, a rotating gas cloud will become oblate or fatter in the middle. So, while I may have misled you into believing that there can be a spherical galactic gas cloud, I have yet to image one. Instead, I turned to AI to generate what such a cloud might look like. Please let me know if you happen to image something like this, because I might have to update this post.
We Need some other Forces
To understand why this is, in my next blog, I will introduce angular momentum (centrifugal force) and how this balances off the gravity to create a dynamic, but relatively stable galaxy. Angular momentum will transform our cloud into a more recognizable disc shape. In addition, the non-spherically-symmetric disc shape will force us to partially abandon Shell Theory too. It may not seem very gratifying to end up with a spherical cloud with a black hole or neutron star in the middle – looking nothing like a spiral galaxy yet, but things are about to get interesting….
