Hertzsprung-Russell diagram and Stellar Evolution

One of the hotly debated issues in the early 1900’s was the interpretation of the Hertzsprung-Russell diagram. When the energy output of a star (Luminosity) was plotted against the surface temperature (essentially its observed color), it was found that as the temperature increased, so did the energy output. Somewhere between 80 to 90 percent of all stars are plotted in a path across the diagram that has become called the Main Sequence. It was initially thought that the diagram, for the most part, represented the evolutionary process of typical stars. Stars would start off as intensely bright burning, and as they consumed their fuel, they would end up as red dwarf stars. This evolutionary interpretation was abandoned when it was determined that the rate of mass loss was not enough to account for the reduced rate of energy loss. (For an example of the Hertzsprung-Russell diagram Link to http://ast.star.rl.ac.uk/hr.html )

(As another example of Astronomers confusing way to present data, they draw the Hertzsprung-Russell diagram partially “backwards”. The Y-axis is usually associated with the energy output, and as one reads vertically up the y-axis, luminosity increases. This is great. The X-axis on the other hand has decreasing temperature measures as one reads further out horizontally.)

If the expansion of space is truly uniform, as proposed by the uniform expansion theory (www.uniformexpansion.com ) then matter itself expands with the expansion of space. This means that objects in the past were denser. If this were the case then the effect of gravity would be greater in the past. For example, if our Earth, with the present amount of mass were to be reduced to half it’s size; the surface gravity would be increased 4 times. If the effect of gravity were greater in the past, the rate of energy production within stars would dramatically increase. This would reestablish, in part, some of the original arguments for interpreting the Hertzsprung-Russell relationship as illustrating an evolutionary process. (This is going to upset a lot of physicists who think they have the evolutionary process of stars like our sun figured out, actually let me take back that statement, they will just ignore me.)

Energy production from stars.

As a gas is compressed, energy is imparted to the gas, raising the temperature of the gas. Within stars the temperature increase is enough to fuse nuclei together, producing nuclear energy. The impact of the fusing nuclei must be great enough to overcome the forces maintaining the individual structure of the individual nuclei. The average temperature within a star is not enough to cause fusion but since the velocity of the nuclei are statistically distributed, there will be a few with enough momentum to allow fusion.

The velocity distribution of the nuclei in a star is a bell like curve with trailing tips. If we imagine two such curves, representing the probable velocities of two colliding nuclei, and we expand them more and more, starting with only the thin tips touching. Now we can visualize how the rate of energy production dramatically increases as the temperature increases and the bell shape curves expand. The area found within the overlap would indicate the number of nuclei involved in fusion. As the two curves overlap more and more, the intersecting area increases in a non-linear fashion.

It is this nonlinear relationship that primarily describes why the energy production of massive stars is so much greater than less massive stars. A very bright star with a mass equivalent to 60 of our suns represents something close to the maximum mass a star can have. Any more mass and the rate of energy production is so intense the star rips apart or explodes. A red dwarf star with a mass of about .05 solar masses is about the minimum size. (All these ranges of size are subject to variation by a magnitude of two or three). The ratio of masses for a bright star (type O5) and a small red dwarf (M0) is about 1,000 to 2,000 times. The difference in energy production is from about 10^6 of our suns energy output for a “Large Blue star” to about by 5 x 10^-4 of the energy production from our sun for a Red dwarf, a ratio range of 50,000,000 times.

The rate of energy production of a star is also influence by a number of other factors, particularly age and type of nuclear fuel used but this is beyond the point being made about the importance of the mass of a star to its energy output. If the effect of gravity varies as proposed, this in essence would be like increasing the mass of a star. This would mean that stars burned much brighter in the past. This would be in accordance with the original interpretation of the meaning of the Hertzsprung-Russell diagram.

It was illustrated earlier that in an 8 billion year old universe the effect of gravity when the universe was 2 billion years old would be 16 times greater. This would mean that our sun, 6 billion years ago, in an 8 billion year old universe, would behave as if it were 16 times more massive. This is a very bright star. This theory is in marked contrast to the accepted evolutionary model for our sun. Our sun started off not as a typical yellow star, but a bright burning star.

While it is unlikely anyone who was an advocate of the Hertzsprung-Russell / evolution theory is reading this, some of you may know some retired Astronomer who did. They might like to see a theory that bolstered their original ideas.

Snowflake.

No, it doesn't. The self-gravity of planets, stars, galaxies, and even clusters prevent them from expanding as space does. Only intercluster space (well, maybe intergalactic space, to a smaller degree) expands via the Hubble law.

But it measures increasing wavelength of peak energy output as you move from left to right, so it depends upon which factor you're talking about. At any rate, if you look at the original plots of Henry Norris Russell, you'll see that what he plotted was spectral class on the X-axis going from B on the left to M on the right. (There actually was a spot for an "N" class on the one I'm staring at but no stars were plotted.) It so happens that B stars are hotter than M stars. Russell was aware of this. One of the things his graph showed was that there were cool M-class stars with very large absolute magnitudes. In the luminosity formula, temperature and radius are your variables which meant that the only way to have a really high absolute magnitude star of a cool temperature was if the star had a large radius.

The H-R diagram does offer astronomers a method of interpreting the evolutionary history of stars and star clusters. Open and Globular star clusters can be age dated from the "main sequence turnoff". Since O-class stars last very short amount of time they're the first ones to evolve off the main sequence - and then the stars in the cluster continue to peel off from the top down as the cluster ages.

Snowflake is talking about snowflake's own theory with that statement.

Hey, how am I supposed to debunk him if I've got others going against me, too? :wink:

Hi Dgruss23

Thank you for the well thought out response.

I looked up the Original Russell’s plot, (I think we have the same resource (An Introduction to Modern Astrophysics by Bradley W. Carroll and Dale A Ostlie). You are right, there is an N classification.

This graph illustrates my problem with how Astronomers graph stuff. The average layman looking at the x-axis of the graph sees a series of letters that are not even in alphabetical order. I know that this is the result of historical sorting and cataloging of stars, but it makes it very hard for the layman to know what the heck is going on. It is like the scribes of Egypt writing in a language only they could know; it helped keep them in charge.

I have no complaint with Russell’s work, it represents a wonderful way to visualize that the stars are, for the most part, starting to conform to a kind of order. My complaint is that the theoreticians seem to drop the ball and let the existing order last. If you do have the mentioned reference, you will note that Figure 8.12 which is supposed to be the “theorist’s Hertzsprung-Russell diagram” is drawn with Temperature (not wave length) as decreasing as one moves along the x axis. This adherence to historical observation can lead to confusion. (This is particularly true when it comes to the proper description of the rate by which the universe is observed to be expanding.)

Again thank you for the well thought out response. I hope you are not too offended by my complaint about astronomers graphing techniques. But honestly, if you were drawing the graph to explain the relationships to someone else, wouldn’t you draw it differently? Increased temperature results in increase luminosity, a nice direct correlation. It then makes the exception for red giant stars more understandable.

Again, thanks

Snowflake.

Hi Tobin Dax

You mentioned that “ The self-gravity of planets, stars, galaxies, and even clusters prevent them from expanding as space does. Only intercluster space (well, maybe intergalactic space, to a smaller degree) expands via the Hubble law.”

Why stop the expansion of space at the boundary of galaxies? Why assume that self-gravity prevents stars and galaxies from expanding? Why not have the expansion of space-time be a unifying property of the universe? There is a lot of space with in galaxies, why not expand them. There is a lot of space within an atom, why not expand the atom?

So long as I provide a model for expansion that preserves celestial and atomic stability, what is the problem?

Snowflake

Alright, I won't argue with that last point. However, I doubt that it is assumed by those who know this that gravity prevents expansion. However, it is commonly taught, and so must be commonly accepted. It would only be commonly accepted if there was significant evidence for it, in which case it must be true. Since there is evidence that expansion is more significant in lesser gravitational fields, your theory should account for that.

I will admit that I am by no means an expert on this topic, but commonly accepted theory just can't be thrown out on a whim. I hope that you would respect others' theories as much as you would like yours to be respected.

Hi Tobin Dax

Fair enough and thank you.

Snowflake

I agree with you about the graphing. OBAFGKM is not a particularly easy way of looking at a graph, when it would theoretically make more sense to do it alphabetically.

The reason its not alphabetical is a matter of historical development of spectral classifications. James Kaler does a nice job of describing it in his book "The Stars and their Spectra".

Basically, stellar spectra were initially classified and had many more letters than the current sequence. Annie Jump Cannon is due a lot of credit for the current spectral sequence. The original ordering was based upon the strength of the hydrogen lines with A the strongest and O the weakest. Then it was realized that some spectral classes needed to be dropped (such as the original E and H). The result is OBAFGKM.

The reason O and B end up before A is that they have stronger helium lines but weaker hydrogen lines than A so they fit before A. The rest of the spectral classes actually do increase with the alphabet - and show corresponding changes in spectral lines - weakening hydrogen lines, increasing strength of metal lines and even molecule lines in the M-class stars.

Perhaps not pretty, but there are cute ways of remembering it:

"Oh Be A Fine Girl/Guy Kiss Me" and so on.

I understand and agree. I'm just saying that it would theoretically be easier alphabetically. The mneumonic works just as well though

I'll tell you why. Because we don't observe that sort of expansion. What is observed is this:
v_rec (km/s) = H_o x d(Mpc), where distance is measured in units of megaparsecs (3.26 million light years).

H_o is measured to be 70 km/s/Mpc. On the scale of the galaxy (100,000 light years = 0.03 Mpc), the Hubble flow has a value of 2 km/s. Well, the virial (gravitationally induced) motions of stars around the galaxy are FAR larger (local gravity is far stronger than the tendancy of space-time to expand). On the scale of the solar system (d ~ 1 AU = 4.8e-12 Mpc), the Hubble flow has a value of a grand total of 3 x 10^-10 km/s. The local gravitational field of the solar system is FAR, FAR stronger than the tendancy of space-time to expand. Likewise, the electromagnetic forces (and quantum mechanical effects) that hold together and give structure to atoms and molecules are gargantuan in comparison.

Now IF the expansion of space-time is indeed accelerating due to some energy density with the property of negative pressure, and if this acceleration tends toward an exponential growth in Hubble's parameter, then it is in principle possible that at some future time the Hubble flow could exceed the local forces of gravity in a galaxy or perhaps even the forces holding together atoms. This scenario is called the "Big Rip", and is described in this speculative paper
Phantom Energy and Cosmic Doomsday

and contested in papers such as this one:
Phantom scalar fields result in inflation rather than Big Rip

The objection of the stars alphabetical labeling is an non-issue. Astronomers remember it and like other "arbitrary" labeling schemas have mnemonics to help remember.
Oh Be A Fine Girl Kiss Me Right Now Smack
and for the academically challenged:
Oh Boy! Another Failing Grade Keeps Me Reconsidering Night School.


For absorption of light in water ( for scuba people)
Roy g. Biv Remember his name - red,orange,yellow,green,blue,indigo,violet

I won't tell you the mnemonic for the resistor color code since I've recently sworn off of uh swear words.
BBROYGBVGW

It's not an assumption, it's a derived result. Aside from the papers suggested by Spiff, see Future Island Universes in a Background Universe Accelerated by Cosmological Constant and by Quintessence, Tzihong Chiueh & Xiao-Gang He, Physical Review D, 65, paper no. 123518. The authors conclude, as stated in the abstract, ..."However, we find that many local regions in the universe can in fact be protected by their own gravity to form mini-universes, provided that their present matter densities exceed some critical value. Furthermore, they conclude in the paper that our own Local Group of galaxies will be one of their "absolutely stable" mini-universes.

This is a result derived from the physics of cosmology, and is not an assumption. If general relativity, and our understanding of the physics of an accelerated universe, are correct, then it will be so.

Hi Spaceman Spiff

I really appreciate your response. The questions and concerns you express are important to me. I will try to resolve the two issues you expressed. Both issues centered on my assertion that the expansion is continuous, which means that galaxies are included in the expansion. The standard accepted model is that galaxies do not expand since they are argued to be gravitationally bound. One of the issues was the lack of evidence of the expansion of galaxies, and the other was that the effect of the expansion is so insignificant that gravity prohibits the expansion.

I will address these concerns. First I will show that the proposed expansion predicted by my model will not be obviously detected. You seem to think that if galaxies did expand than we would be able to observe the expansion. Secondly I will contend that the proportional magnitude of a field relationship does not negate its existence or effect.

First issue, detection of expansion within galaxies.

You gave an excellent calculation of the expected expansion of a galaxy if the galaxy were included in the expansion. You said “On the scale of the galaxy (100,000 light years = 0.03 Mpc), the Hubble flow has a value of 2 km/s.” . I think you are suggesting that since It appears this proposed cosmological expansion is not observed, galaxies cannot be expanding.


Reply A Proportional measures are inherently undetected with proportional rulers.

Continuing with your example of a galaxy expanding at 2km/sec, how long would it take for the galaxy to be twice it’s size? Assuming the Ho is constant, (Which it is not in my model) it would take about 14 billion years for the galaxy to be twice as big. How big would we now measure the galaxy to be? Since our rulers are included in the expansion, no observed change is detected.

Reply B The “Doppler red shift” or cosmological red shifting of stars in a galaxy would not be detected.

I think this is the main concern expressed by you, if stars are moving away from each other due to a cosmological expansion, there should be an observed red shifting of the stars in our galaxy.

My response to this is that the variation in relative motion between stars masks the cosmological expansion. Stars in a galaxy are not fixed to a perfect orbit. Stars orbits are elliptical. The orbits of stars have been altered by past interaction with surrounding stars. There is even evidence that the motion of stars is different in regards to their evolutionary development in relation to the evolution of the galaxy itself.

Let’s see what is going on by doing the math and correlating it to observation.

Our sun is moving with the rotation of the galaxy, at about 220 kilometers per second. This is not directly relevant to the question at hand other than it helps give a sense of scale and proportion. It is standard practice to estimate the relative motion of our sun relative to its neighbors using a radius of 80 light years (Britannica). The result of this investigation reveals that our sun is moving towards the star Vega at 19.5 to 19.7 km/sec. (This is based on the standard reference frame, the basic reference frame, gives the speed as 16.5 km/sec).

How much cosmological red shifting would be detected for stars located 80 light years away?

The cosmological red shift associated with stars 80 light years away would be essentially 0. (80/100,000 x 2 km/s = .002 km/s ) The variation associated with the actual motion per my alleged cosmological motion is 1,000 times more important. The effect would be lost in the wash. Stars approaching us would actually have a slightly higher speed than we thought, and those moving away would actually have a slightly slower speed. The cosmological expansion would not be detected.

If we looked further away, the effect of the cosmological expansion would be greater, could we then measure it?

Looking across an entire galaxy presents a problem, there is a lot of dust interfering with our view. Finding stars similar to ours on the other side of the galaxy is not an option. Also the velocity dispersion or relative variation in speed between stars is dependant on the evolutionary development of the star and its location on the evolutionary development of the galaxy. The variational speed varies 10 to 20 km/sec between stars through out the galaxy, (Britannica). If we look towards the core of the galaxy a distance equal to about 1/2 the size of a galaxy, and then look away from the core the same distance but this time towards the outer most stars in the rim, any variation in red shift indicating a 1km/s cosmological expansion is going to be assumed to be the result of dynamic factors that do not include cosmological expansion.

There is a way to possibly to detect the expansion of our galaxy, but it would require a detailed analysis of the motion of hundreds of thousands of stars and categorizing them by there type, evolutionary status and evolutionary location in the galaxy. A statistical analysis of various groups of stars of similar stars at various distances should reveal a statistically significant evidence of this expansion. Since the expansion has been assumed to stop at the boundary of galaxies, no one has bothered to spend the time trying to extract the information.

(A fair amount of papers have been written on our galaxy expanding, but they all fall into two categories. One is the outflow of stars from the center of our galaxy being faster than those at the edge, most of which was done in the mid 1980’s. In the mid 70’s there were some studies looking for observed outflows of stars due to a variation of gravity. This was done after Dirac published his conjecture that the effect of gravity varied linearly with cosmic time. Dirac proposed that to preserve celestial stability mass increased. Since the mass in galaxies is not evenly distributed, certain predictions as to the motion of galaxies should be detected, they were not. None of the 20 studies I found considered statistical sampling to check for cosmological expansion of galaxies)

Reply C The expansion is so weak, it can not effect gravitational relationships.

The second argument you posed as an attempt to invalidate my theory was that this expansion is negated by the far stronger effects of gravity. Specifically you said, “local gravity is far stronger than the tendency of space-time to expand”.

My model requires that the expansion of space-time is a uniform field like expression affecting the entire universe exactly the same way. (Technically my theory falls partially under scalar field theories, but I do not like this term since the geometric structure is not expressed). The expansion of space-time is just like all other field type relationships, (except it forms the basic structural foundation for the other field relationships). Just like all other field expressions, effects are interrelated. For example, electrons are confined to an atom, yet the orbital pattern is shaped slightly by gravity. Electromagnetic fields interact with gravitational fields. Granted the effect is essentially negligible, but you could figure how much the deflection of the orbital patterns should be for each orbital arrangement. I am proposing that the expansion of space-time is also a true field like relationship.

Also thank you for the links to what others have proposed. I have reviewed them and they are fundamentally flawed. The mistake they make is that they are trying to describe our universe without a necessary dimension. There are two dimensions of time, Relative time, which is the time interval between points, and there is Cosmic time, which describes a point’s location historically. Any theory that does not include historical measures is going to become unbelievably complex.

Snowflake

Hi TillEulenspiegel

Thanks for the post.
WDYTOT? DTU!

Snowflake

Hi Tim Thompson

When I stated ... Why assume that self-gravity prevents stars and galaxies from expanding?

You said “It's not an assumption, it's a derived result.”

I checked out your reference and while interesting it has a number of flaws. Besides the lack of an extra dimension of time, there are a number of conceptual flaws. One is that the dark energy which is driving the “acceleration” is from somewhere else. The energy is extracted from our own universe. All systems loose energy with the expansion of space.

Quintessence has not garnered much support, just look at how complex the relationships are. Compare them to my proposed relationships

Ratios of Time
D2/D1 = (T2 /T1) ^ (2/3)
V2/ V1 = (T1/T2) ^(1/3)
E2/ E1 = (T1/T2) ^(2/3)
"G2/G1" = (T1/T2) ^(4/3)


It is possible to describe the basic idea of my proposed theoretical model in just one or two sentences. The uniform expansion of space conforms to a specific geometric structure of space and time; matter itself is part of the expansion.

Try to do that with Quintessence in terms an ordinary person is going to understand.

If one is going to try and describe reality, the most accurate and the simplest is usually correct.

Please also bear in mind that the proposed theory also corresponds to observation. When I say that the uniform expansion of space includes matter, the relationships are theoretically verified and experimentally confirmed, as I will be systematically proving in the course of the next few months.

I will be posting a series of papers validating the relationships and resolving some unsolved problems. I will be posting one soon on Iron plasma in the sun. The iron in the sun issue will probably not garner too much support right now since it conflicts with the mainstream view. Fortunately I am presenting this theory and making predictions at a time where increasing resolution of the interior of the sun will eventually affirm the assertion. Another issue I will be resolving is the image size problems of quasars. (They tend to appear to vary in image size only by a factor of two despite a wide range of red shift determined distances.)

Eventually someone is going to start to agree with me. I already have one graduate student with a PhD in physics agreeing that the model is mathematically consistent. (But he still will not accept the model, no reason given. I think it will take a particularly courageous physicist to be the first to support the ideas)

snowflake

Hi Spaceman Spiff and Tim Thompson


I thought that perhaps I should include a link that should give pause to any idea that the field effect associated with uniform expansion is stopped at the boundary of galaxies due to the force of gravity. The reason you and others adhere to this assertion is that the effect of gravity would be so much more powerful that no effect on stars in a galaxy would be possible.

http://www.aip.org/enews/physnews/2002/573.html


Electrons are deflected in their orbits around an atom due to the effect of gravity, even though the difference in their field effects are great. You can calculate how much the orbital pattern is deflected due to the force of gravity. The effect is there, minuscule but there. Field effects are interdependent.

The field effect associated with the expansion of space is interdependent with the field effect associated with gravity. (This is actually theoretically derived in my www.uniformexpansion.com site).

Snowflake

I look forward to your upcoming Nobel Prize in Physics. Good luck...