How is molecular hydrogen detected?

[JDoolin]

My textbook seems to give conflicting information on whether molecular hydrogen can or cannot be detected. On the one hand it says (p393) "Dark matter is not hydrogen gas (atomic or molecular), nor is it made up of ordinary stars. Given the amount of matter that must be accounted for, we would have been able to detect it with present-day equipment if it were in either of those forms."

However, it also says (p302) "Molecular hydrogen...does not emit or absorb radio radiation, so it cannot easily be used as a probe of cloud structure...Instead, astronomers use radio observations of other molecules, such as carbon monoxide, hydrogen cyanide, ammonia, water, and formaldehyde, to study the dark interiors of these dusty regions", i.e. they never actually see the hydrogen--they see the other molecules in the area, and assume the molecular hydrogen must also be there.

So on the one hand, they say "We'd be able to H₂ if it were there" and on the other hand they are saying "we can't see H₂ directly--we can only see the other molecules in its presence."

If they can't detect any radio emissions of molecular hydrogen, what spectrum ARE they using to locate it?

(Source- Astronomy-A Beginner's Guide to the Universe-Sixth Edition)

 

[cepheid]

It's true that most H2 is too cold for any of its radiative transitions to be excited, therefore we can't see it (I'm pretty sure that there are exceptions -- places where we can see warmer H2). For the most part, we need to use CO as a tracer for it. Certain empirical rules are used to determine the total amount of molecular gas (which is almost all H2) that is present based on the amount of CO emission. The accuracy of these techniques is debated, but I always got the impression that it was sort of a "factor of 2" type of problem. So the point is, when it comes to dark matter, even if you take into account that most H2 is unseen (at least in emission), anywhere where it's cold enough for there to be H2, it's also cold enough for there to be other molecules, and indeed, for there to be solid matter condensed out in the form of tiny microscopic grains, which astronomers call "dust". We can see the other molecules, and we can see dust. So, if H2 were to account for the missing mass attributed to dark matter, we would have see a LOT more emission from its visible tracers than we do see. We'd also have to explain why dynamical considerations require the DM to be everywhere in a spheroidal halo surrounding the galaxy, whereas molecular gas clearly cannot exist everywhere.

Besides all that, there are a host of other good observational reasons why DM has be non-baryonic (ie not made of ordinary atoms), not the least of which is that it doesn't interact with visible matter through any means other than the gravitational force, and it certainly doesn't absorb or emit light.

 

[JDoolin]

Well, I can see how the presence of Carbon Monoxide implies the presence of molecular hydrogen, but I don't see how the presence of molecular hydrogen implies Carbon Monoxide.

If I understand right, Carbon can only occur as a result of nuclear fission inside a star. So if you see carbon monoxide, you're seeing the emissions of a star, a red-giant or supernova explosion. But the hydrogen was there before the star formed, and it would have existed without any Carbon or heavier atoms.

 

[cepheid]

A couple of other points. I never answered your question of how H2 is detected in cases where it can be seen in emission. The intro to this paper talked about how the molecule's rotational transitions lead to emission in the mid-infrared (tens of microns):

http://arxiv.org/abs/1109.2544

The second point is that even if you can't see molecular hydrogen in emission, I'm pretty sure there are cases where you can see it in absorption (sillouhetted against luminous emission from nearby stars, and even seeing absorption line features from it in the spectra of other objects e.g. in the UV portion of stellar spectra). Granted, this may only allow you to see the densest clouds that happen to be in warmer surroundings (and haven't been fully dissociated by ionizing radiation), but at least it is an indication that it is there.

 

[cepheid]

Well, I can see how the presence of Carbon Monoxide implies the presence of molecular hydrogen, but I don't see how the presence of molecular hydrogen implies Carbon Monoxide.

If I understand right, Carbon can only occur as a result of nuclear fission inside a star. So if you see carbon monoxide, you're seeing the emissions of a star, a red-giant or supernova explosion. But the hydrogen was there before the star formed, and it would have existed without any Carbon or heavier atoms.

The ISM has been enriched with "metals" (elements heavier than helium) through billions of years (several generations) of star formation in our galaxy. So it's no longer true that these elements are localized only to supernova remnants or planetary nebulae (relics of dead stars). They've had time to spread out somewhat homogeneously. In fact, the molecular gas in the galaxy is spread out over a fairly wide area. It exists in a large ring between 3.5 kpc - 7.5 kpc from the galactic centre, in the galactic plane (although I understand that there is also some diffuse stuff at high galactic latitudes i.e. off the plane). We know this from tracing CO emission ;)

 

[JDoolin]

(Note: I have not read post 4 and 5 yet--criss-crossed communication.)

My real question here is whether it really is that clear that molecular hydrogen gas "cannot exist everywhere." Is it really 100% transparent to the radio waves? Precisely how much light-blocking power does it have, and at what frequencies? At what densities would it be possible to see through a billion light-years of the stuff as though it weren't even there?

The thing is, yeah, clearly, you'd think it was unlikely that a substance could be that transparent, but on the other hand, when you think about star formation, when you look at the lobes of a radio galaxy; or the bars on a bar-galaxy, it leads me to think there seems to be something out there; a gas that everything else is running into. And when you think about star formation, it seems like you need an initial bunch of stuff to start from, and we already know it was hydrogen gas.

So I'm thinking there must be a large portion of the stuff still out there that hasn't yet fallen into a clump to make stars.

 

[JDoolin]

The ISM has been enriched with "metals" (elements heavier than helium) through billions of years (several generations) of star formation in our galaxy. So it's no longer true that these elements are localized only to supernova remnants or planetary nebulae (relics of dead stars). They've had time to spread out somewhat homogeneously. In fact, the molecular gas in the galaxy is spread out over a fairly wide area. It exists in a large ring between 3.5 kpc - 7.5 kpc from the galactic centre, in the galactic plane (although I understand that there is also some diffuse stuff at high galactic latitudes i.e. off the plane). We know this from tracing CO emission ;)

The outer radius of this ring of detectable molecular gas is about where the sun orbits the galactic center. Now on the other hand, the part of the "galactic rotation curve" where the orbits are faster than expected due to dark matter starts around radius of 15 kpc and beyond.

Our galaxy is about 15 kpc in radius, though I'm looking at a "galactic rotation curve" in my text that extends out past 35 kpc. Its in that range of 15 to 35 kpc where the curve deviates heavily from keplerian motion, and indicates the presence of dark matter.

The Earth itself is a relic of a dead star. With an iron core, it was probably ejected from a type II supernova. Might it be possible that anything closer than 7.5 kpc to the center of the galaxy was a remnant of the same supernova? And more to the point--in the region from 15 to 35 kpc, there would be pure molecular hydrogen--so far unpolluted by supernova remnants.

 

[Chronos]

It appears your textbook is slightly misleading. Atomic hydrogen is easily detected via 21 cm band emissions. Molecular hydrogen is the more common, and stable species. It does not emit in the 21 cm band. It is normally detected by indirect means, as noted by cepheid.

 

[JDoolin]

So, just to reiterate... there is no known direct way to detect diffuse cold molecular hydrogen?

 

[Chronos]

Molecular hydrogen has a UV signature which is difficult to detect. It is readily absorbed and easily scattered.

 

[vociferous]

So, just to reiterate... there is no known direct way to detect diffuse cold molecular hydrogen?

It can be detected when gravitational potential energy causes it to coalesce and heat up. Any tiny variation in the density will cause the cloud to begin an isothermal and finally an adiabatic collapse.

Now, think about where all the dark matter is. Most of it is in the halo, exactly where there are very few stars. But how could there be very few stars if there are these huge, diffuse clouds of hydrogen? The hydrogen would have to be maintained in some kind of perfect density gradient that kept it from collapsing. Now, you suggest that the collapse is just extremely slow (on the order of 10 billion years). But this flies in the face of a multitude of globular clusters that are nearly as old as the Milky Way in the Halo. So why did those clouds of molecular hydrogen in the halo collapse but not this one? That sounds like special pleading to me. How does it sound to you?

 

[twofish-quant]

The main evidence for dark matter is that lots of things would break down if it turns out that dark matter were made of baryons.

Also I found this really interesting article...

http://arxiv.org/abs/1107.3314

 

[JDoolin]

It can be detected when gravitational potential energy causes it to coalesce and heat up. Any tiny variation in the density will cause the cloud to begin an isothermal and finally an adiabatic collapse.

Now, think about where all the dark matter is. Most of it is in the halo, exactly where there are very few stars. But how could there be very few stars if there are these huge, diffuse clouds of hydrogen? The hydrogen would have to be maintained in some kind of perfect density gradient that kept it from collapsing. Now, you suggest that the collapse is just extremely slow (on the order of 10 billion years). But this flies in the face of a multitude of globular clusters that are nearly as old as the Milky Way in the Halo. So why did those clouds of molecular hydrogen in the halo collapse but not this one? That sounds like special pleading to me. How does it sound to you?

Sorry I overlooked this response before.

I'm not entirely sure how to answer your question, but are you taking into account the changing density over time? Are you assuming that the local conditions were the same 10 billion years ago as they are now?

Consider that as we go back toward the Big Bang, each time you divide the age of the universe by two, you multiply the density by 8. If you agree with that reasoning, then consider, if the universe is 14 billion years old right now, at 7 billion years, it had 8 times its current density. At 3.5 billion years it had 64 times its current density.

The globular clusters formed sometime around at least 10 billion years ago, when the universe was at most 3.5 billion years old. Which would mean they formed when the gas was at least 60 times as dense as it is now. And since ALL the globular clusters are at least 10 billion years old, it suggests that they stopped forming, at a certain time, and my suggestion is that they stopped forming because the density of the universe dropped below some certain critical level.

Take that back another couple of steps. At 1.75 billion years, the universe would have had 64*8 = about 500 times its current density. At 900 million years, the universe would have had 500*8=4000 times its current density. At 450 million years, 32,000 times the density, etc, and you can keep going back in time and getting exponentially more and more density.

In this extremely dense environment, A supernova explosion, for instance, at that time could have a wildly different effect than a supernova explosion now, and could have made the perturbations that made our entire galaxy possible.

 

[Bobbywhy]

“Molecular hydrogen is difficult to detect by infrared and radio observations, so the molecule most often used to determine the presence of H2 is CO (carbon monoxide). The ratio between CO luminosity and H2 mass is thought to be constant, although there are reasons to doubt this assumption in observations of some other galaxies.”

http://en.wikipedia.org/wiki/Molecular_cloud

 

[JDoolin]

“Molecular hydrogen is difficult to detect by infrared and radio observations, so the molecule most often used to determine the presence of H2 is CO (carbon monoxide). The ratio between CO luminosity and H2 mass is thought to be constant, although there are reasons to doubt this assumption in observations of some other galaxies.”

http://en.wikipedia.org/wiki/Molecular_cloud

Right. I just think it is strange to ignore the possibility that there may be large amounts of H2 that is NOT accompanied by Carbon Monoxide. It seems to me, only that H2 which has interacted with supernovae and red giants should have any Carbon Monoxide in it.

It seems to me that this explanation (the thought that the ratio of H2 to CO is constant) must be assuming that all of the H2 was emitted from stars. It completely ignores the possibility that there was H2 without carbon monoxide long before there was H2 with carbon monoxide, and that some, or even most of that pure H2 might remain.

 

[vociferous]

Sorry I overlooked this response before.

I'm not entirely sure how to answer your question, but are you taking into account the changing density over time? Are you assuming that the local conditions were the same 10 billion years ago as they are now?

I'm assuming that the Jean's Mass formula is still applicable.

Consider that as we go back toward the Big Bang, each time you divide the age of the universe by two, you multiply the density by 8. If you agree with that reasoning, then consider, if the universe is 14 billion years old right now, at 7 billion years, it had 8 times its current density. At 3.5 billion years it had 64 times its current density.

I am assuming that you are referring to the density of the universe, not an individual galaxy. While galaxy formation is still something of a mystery, I believe I am correct in stating that early in a galaxy's formation, it is in the process of overall increasing its density, not decreasing it. I do not really know how that might affect the density of molecular clouds, but you could certainly research it in the published literature.

Remember, the density of the universe is not necessarily linearly proportional to the density of early galaxies or the density of the regions where globular clusters formed. For instance, the density of the visible universe is still decreasing, but the density of the Milky way is constant.

The globular clusters formed sometime around at least 10 billion years ago, when the universe was at most 3.5 billion years old. Which would mean they formed when the gas was at least 60 times as dense as it is now. And since ALL the globular clusters are at least 10 billion years old, it suggests that they stopped forming, at a certain time, and my suggestion is that they stopped forming because the density of the universe dropped below some certain critical level.

It seems like a reasonable hypothesis. The question is, where is the evidence?

Take that back another couple of steps. At 1.75 billion years, the universe would have had 64*8 = about 500 times its current density. At 900 million years, the universe would have had 500*8=4000 times its current density. At 450 million years, 32,000 times the density, etc, and you can keep going back in time and getting exponentially more and more density.

Showing a correlation between density and formation of clusters does not actually support your hypothesis. You need to model how the clusters formed and how the density of the universe would affect their formation.

In this extremely dense environment, A supernova explosion, for instance, at that time could have a wildly different effect than a supernova explosion now, and could have made the perturbations that made our entire galaxy possible.

I believe others have theorized this in regards to current stellar evolution. You might want to research papers on supernova-induced star formation if you have not already.

 

[Chronos]

Twofish-Quant is our supernova expert, I'm certain he could shed light on this issue.

 

[twofish-quant]

Twofish-Quant is our supernova expert, I'm certain he could shed light on this issue.

Not much. This is an ISM question and not a supernova question. :-) :-)

One thing that I found rather surprising is that it turns out that early universe chemistry is incredibly complicated.

 

[JDoolin]

I'm assuming that the Jean's Mass formula is still applicable.
I am assuming that you are referring to the density of the universe, not an individual galaxy. While galaxy formation is still something of a mystery, I believe I am correct in stating that early in a galaxy's formation, it is in the process of overall increasing its density, not decreasing it. I do not really know how that might affect the density of molecular clouds, but you could certainly research it in the published literature.

Remember, the density of the universe is not necessarily linearly proportional to the density of early galaxies or the density of the regions where globular clusters formed. For instance, the density of the visible universe is still decreasing, but the density of the Milky way is constant.
It seems like a reasonable hypothesis. The question is, where is the evidence?
Showing a correlation between density and formation of clusters does not actually support your hypothesis. You need to model how the clusters formed and how the density of the universe would affect their formation.
I believe others have theorized this in regards to current stellar evolution. You might want to research papers on supernova-induced star formation if you have not already.

I bolded a few statements here; mainly I need to model how the clusters formed and how the density of the universe would affect their formation.

I don't have a quantitative model, but I can qualitatively describe three distinct stages--perhaps four.
Stage 1--Universe Age: Very young. Galaxy forming stage. Extremely high density. Perturbation caused by supernova results in a gravitational gradient sufficient to overcome outward Hubble-velocity.
Stage 2--Universe Age, Less than a billion years. Globular Cluster forming stage: Medium density. Perturbation caused by supernova results in clumping of matter into stars, but insufficient to overcome outward Hubble-velocity.
(Stage 3)--Universe Age--Current. Spiral forming stage. Superluminal jets fire into already swirling gasses, causing it to clump into stars.
Stage 4--Universe Age--Current. Diffuse stage. Supernova explosion is not sufficient to cause clumping into stars

I made a little video to see if I could make this clearer:
http://screencast.com/t/QxU3YaeWAkXM

I hope this makes clear some of the other differences between this model and your model.
(1) in my hypothesis, the overall density of the universe equal to the overall density of a galaxy or a globular cluster at any given time. The difference is not in density but in clumpiness.
(2) You are correct in saying that galaxy formation involves increasing the density; not decreasing it; but I'm looking for a phenomenon sufficient to reverse the Hubble flow, and clump, surrounded by a homogeneous distribution of matter. In your model, you have the distribution already starting out pre-clumped, and it becomes more clumped.
(3) I don't have any additional evidence. You're already aware of spiral galaxies, bar galaxies, Hubble's law, and globular clusters.

The only thing we disagree about is the level of clumpiness in the universe. You think that the universe is clumpy on the scale of galaxies, and clumpy on the scale of solar systems. I think that the universe is homogeneous on every scale right down to the cubic meter, but clumps up on the scale of stars, because of perturbations.

 

[twofish-quant]

FYI, I'm going to put on my boxing gloves. If you want to propose a serious astrophysical model, then that means that you want to get into the boxing ring and treated like a professional boxer. So I'm not going to pull punches.

I don't have a quantitative model, but I can qualitatively describe three distinct stages--perhaps four.

A qualitative model is useless since it's impossible to make predictions that are detailed enough to compare with observations. Now it doesn't have to be a complicated quantitative model, but you need to run some numbers.

One quick thing to calculate is that age of the universe at which the average density of the universe reaches densities that are typical of the interstellar medium. My guess is that it's going to end up before you have any stars at all.

What you need to be able to generate are *NUMBERS*. How many globular clusters do we expect to see? What's the density of galaxies? What's the distribution of bright matter and dark matter? What's the temperature of the gas? I want correlation functions, spectral predictions, etc. etc.

Extremely high density. Perturbation caused by supernova results in a gravitational gradient sufficient to overcome outward Hubble-velocity.

I don't think this is going to work since you are dealing with different scales. Supernova explosions happen on length scales of kiloparsecs when you already have large local gravitational fields that overwhelm the Hubble flow. If you are talking about supernova shock waves then the Hubble flow is going to be irrelevant.

Supernova bubbles are smaller than galaxies and can't affect Hubble flow. Supernova bubbles also have negligible gravational gradients. The shock wave is purely a gas pressure phenonmenon.

The other thing is were did the supernova come from? If you have supernova then you already have stellar formation, and if you have stellar formation, then things are already clumping.

(2) You are correct in saying that galaxy formation involves increasing the density; not decreasing it; but I'm looking for a phenomenon sufficient to reverse the Hubble flow, and clump, surrounded by a homogeneous distribution of matter. In your model, you have the distribution already starting out pre-clumped, and it becomes more clumped.

Jeans instability.

The only thing we disagree about is the level of clumpiness in the universe. You think that the universe is clumpy on the scale of galaxies, and clumpy on the scale of solar systems. I think that the universe is homogeneous on every scale right down to the cubic meter, but clumps up on the scale of stars, because of perturbations.

Well, you are wrong.

The matter correlation spectrum is pretty well established, and it pretty clearly shows that things clumped top down rather than bottom up. During the 1980's it was an extremely big debate between the hot dark matter people that argued that galaxies first formed and then clustered into superclusters, and the cold dark matter people that argued that the superclusters formed first.

The data supports the CDM people.

 

[JDoolin]

You bring up a good point. I would be happy to work on this professionally. In many ways it would be a lot easier than what I'm doing now. But right now my time is divided, and this is only a hobby.

But regarding pulling your punches, realize that I am skirting the edges of the rules of the forum. I have to be very, very careful what I say, and I may already have said too much. At any time the moderators decide that I am in disagreement with the scientific consensus, or that I'm arguing for a "personal theory," they can delete my post and give me an infraction for my troubles. So you don't have to pull your punches here, but I am not permitted to block your punches in any substantial way, unless I can do it within the context of the standard model.

Within those limitations, (with one hand tied behind my back) I have to ask...

I presume you mean that the data supported that the matter was cold. The matter was dark. And it was some kind of matter. What was it that convinced them that that cold dark matter was nonbaryonic?

 

[twofish-quant]

You bring up a good point. I would be happy to work on this professionally. In many ways it would be a lot easier than what I'm doing now. But right now my time is divided, and this is only a hobby.

This is why "doing science" takes so much time. It's easy for me to come up with new ideas, but to get to the point where I can put that idea in the boxing ring, and not have it get instantly killed takes lots of time and effort.

At any time the moderators decide that I am in disagreement with the scientific consensus, or that I'm arguing for a "personal theory," they can delete my post and give me an infraction for my troubles.

1) You can step back and ask what *is* the scientific consensus. Asking, so why can't supernova trigger galaxy formation and then listening to the answers is within the rules of the game.

2) The rules are not that it's within the scientific consensus but rather than personal theories are not allowed on the main forums. If you can go into the standard preprint or paper archives, and pull out a paper that defends a theory that's similar to the one that you personally like, then you can discuss that.

There are a ton of papers talking about oddball theories. If you come up with something and it's something that no one has uploaded to Los Alamos, then chances are that it's not really worth discussing.

In the case of galaxy formation there *is* no scientific consensus.

I presume you mean that the data supported that the matter was cold. The matter was dark. And it was some kind of matter. What was it that convinced them that that cold dark matter was nonbaryonic?

Baryons sound different.

http://en.wikipedia.org/wiki/Baryon_acoustic_oscillations

Basically baryons will conduct sound waves and non-baryonic material won't. The CMB and location of the galaxies "freezes" the sound waves at the start of the universe, and the fact that baryons will conduct sound and non-baryonic material won't means that you end up with clumps of matter at certain locations.

 

[twofish-quant]

One other thing. You'll have to do a bit of digging to find computer simulations of baryon-only universes. They date from the late-1980's when this was still under dispute.

 

[twofish-quant]

Here's a graph showing what the universe looks like versus what it would look like with just baryons.

http://www.astro.caltech.edu/~george/ay21/eaa/eaa-powspec.pdf

It sounds different.

If you look at the baryon only graph, you see lots of peaks. Those are standing waves. A baryon-only universe would conduct sound really, really well, so if you imagine a string that goes from one end of the observable universe to the other, and pluck it, you end up with very strong harmonics.

We don't see extremely strong harmonics, but we do some some harmonics, which says that the universe is this mixture of stuff that conducts sound very well with stuff that doesn't conduct sound very well.

 

[JDoolin]

(If this is hard to read, I could probably do another Jing video running through it... But maybe you could address any number of items where I appear to be confused. I just picked one of your links http://www.astro.caltech.edu/~george/ay21/eaa/eaa-powspec.pdf and started reading, to the best of my ability; trying to figure out what you're saying.)

So for this Power function P(k) is the Fourier transform of the correlation function. xi(r) and w(theta). Now as for spatial and angular correlation functions xi(r) and w(theta), are they looking at r=0 from our position, and theta =0 in some specific direction? Are they using the orientation of our galaxy, or are they using the orientation of the CMBR dipole?

However, the article also says dP = nbar^2(1+xi(r12))dV1 dV2

$$dP = \bar n^2(1+\xi(r_{12}))dV_1 dV_2$$

I'd have to review Fourier transformations; Is that an equivalent definition? Now the idea of a Fourier transform, if I'm not mistaken, is to take something from distance or time domain into a frequency domain. It turns a function which is graphed in terms of time or distance into a function which is graphed in terms of frequency, or wave number.

The correlation function is xi(r)-the spatial distribution or w(theta)-the angular distribution. Now, “the spatial two-point or autocorrelation function is defined as the excess probability, compared with that expected for random distribution, of finding a pair of galaxies at a separation r12.” By “random” do they mean a “uniform random distribution?” And by “probability of finding a pair of galaxies at a separation r12” are they saying, “Given a galaxy at point 1, what is the probability of finding a galaxy at r2” or are they working from a single origin, and expecting to find galaxies in a more-or-less spherical distribution? Another question--on the correlation function itself. I think of “sound” as a causality relation; not a correlation relation. Is this really a sound wave traveling through the universe now, or is it a correlation function that may or may not be due to a sound wave that went through the universe a long, long, long time ago when the universe was significantly denser?

It says that between .1 h^-1 and 10 h^-1 MegaParsec's the spatial correlation function is well described by a power law (5 h^-1/r)^1.8. Unfortunately, the article never tells us what h^-1 actually stands for. There's also not really any explanation for where that came from; though it reminds me of an inverse square law that you might get, either from gravitational effects, or intensity effects--anything that is proportional to the surface area of a sphere at a certain distance from an object or event.

Also, they quickly change their mind, and decide, instead that xi(r) = 1 over 2 Pi times the integral of dk * k^2 P(k) sin (kr) over kr. $\xi(r) = \frac{1 }{2 \pi} \int{ dk * k^2 P(k) \frac{\sin(kr)}{kr}}$.
I gather that is some kind of representation of an inverse Fourier transform, though I don't fully see the resemblance to the Fourier transformations on Wikipedia. It seems like they have k/r sin(kr) but are fixing it up so there's something that looks like the sinc function in there.

The article says the paradigm is that “small fluctuations in density are amplified by gravity.” That is a qualitative sort of statement, that could mean just about anything. The main thing I'm questioning is their concept of scale--what is a “small” fluctuation in density if you go back in time to where the mean density of the universe in the first nanosecond? A quantum fluctuation in the first nanosecond or microsecond of the universe will expand over the next 13.7 billion years into the entire visible part of the universe.

So yes, essentially that might be what they are saying when they say “one possible explanation being that they are quantum fluctuations boosted to macroscopic scales by INFLATION.” I just don't see why this is in doubt. Given a few carefully chosen, well-reasoned axioms, I would think that this conclusion is virtually inescapable.

Now, the primordial power spectrum, assumed to be P(k) proportional k^n, where n=1 is a popular choice... They've defined the Power spectrum so abstractly, I'm not sure which way is up, but is it a useful interpretation to say that this assumption claims that “sound” in the universe is present equally at all wavelengths? I don't think I have this right, but I'm also in great doubt as to the wisdom of transforming the map of the universe from a spatial description to a wave-number description at all. (By the way, on further thinking, I'm not sure the "popular choice" of assuming that P(k) ~ k really makes any sense. Why should there be any a priori assumption about the distribution of wavelengths of perturbations in the universe, and why would it be distributed in this way?)

My own feeling is that wave-number-based descriptions of the universe are deeply counter-intuitive. It would be rather like trying to find a Bessel function and Legendre Polynomials to describe the surface of the Earth. Of course, you CAN model the Earth this way, but why would you want to? Would it really have any predictive or explanatory power? Could you, from that mapping, then find a useful theory of plate tectonics, volcanism, oceans, etc?

A second difficulty I have with what appears to be the Standard Model, and this discussion of “sound” in general, is that to have what we commonly think of as sound, you need to have a region of gas that is more-or-less in the same inertial reference frame, and has a great enough density . It's not a question of whether it happened, but when. It sounds as though most people who support the standard model are under the impression that we should be able to see evidence of sound passing through the universe now.

I agree that they should be able to see some evidence of sound passing through the universe long ago. When the universe was one hour old, the particles 1 mile away from each other were moving apart at 1 mile per hour. Yes, in that environment, sound might travel quite well, except for a few caveats. (1) we're talking about a fluid so dense that ANY fluctuation is going to result in massive gravitational instability, and (2) We're talking about a fluid that probably doesn't interact in any way similar to the spring-like molecular interactions we're familiar with. And that region would grow in the next 13.7 billion years to a volume on the scale of galaxies and superclusters.

I'm still interested in seeing why they think that Baryonic matter could not have produced what we're seeing, but I think that argument applies only to the early universe when the density was great enough that sound would carry through the plasma.

I think there would have been a time in the universe where the density got low enough when baryons would begin to form (then sound would really begin to flow), and then a time in the universe where the density of those baryons got low enough to become almost a vacuum, and sound basically stopped.

So if I am understanding properly (a big if, at this point) they think that when Baryons formed, Nuclear interactions start becoming a push/pull interaction rather than just pulling; Hooke's Law would have begun to apply en-masse to all the particles, making the system begin carrying sound. But they see some evidence for sound but not enough evidence for sound, so they decided that most of the mass of the universe is nonbaryonic.

You may think I'm trying to construct a straw-man here. If I am, please forgive me. I still mean to just be asking... “What makes you think the dark matter in the universe must be nonbaryonic.” What you've told me is that if it were baryonic, the universe would ring like a bell. What I'm trying to do here is make my best attempt to guess what you mean. I think you must mean that the universe ONCE rang like a bell; when the density was much greater. I'm suggesting that the universe stopped ringing like a bell because it became too diffuse for sound waves to carry through diffuse molecular hydrogen. You seem to be saying that the universe should be ringing still now, except for the presence of nonbaryonic dark matter. Do I have that right?

 

[George Jones]

The rules are not that it's within the scientific consensus but rather than personal theories are not allowed on the main forums. If you can go into the standard preprint or paper archives, and pull out a paper that defends a theory that's similar to the one that you personally like, then you can discuss that.

Not necessarily. What the Rules actually say:

Scientific Discussion Guidelines

Generally, in the science discussion forums we do not allow the following:

• Discussion of theories that appear only on personal web sites, self-published books, etc.
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[twofish-quant]

Now as for spatial and angular correlation functions xi(r) and w(theta), are they looking at r=0 from our position, and theta =0 in some specific direction?

No. What you do is to look at r=0 for some random point in the sky and then calculate the power spectrum with respect to that random point. If the universe is isotropic and homogenous, then you should get the same power spectrum for any random point (and people have checked and we do).

Given a galaxy at point 1, what is the probability of finding a galaxy at r2” or are they working from a single origin, and expecting to find galaxies in a more-or-less spherical distribution?

If the universe is isotropic then if you start with any random galaxy, you should get the same numbers.

Is this really a sound wave traveling through the universe now, or is it a correlation function that may or may not be due to a sound wave that went through the universe a long, long, long time ago when the universe was significantly denser?

For CMB baryon oscillations, it's a snapshot of the universe as it was when CMB was emitted. For galaxy counts, the expanding universe ends up "freezing" the sound waves.

Unfortunately, the article never tells us what h^-1 actually stands for.

Hubble's constant. What happens is that when you do the calculation, everything scales to the Hubble constant, so you can just put at in as a variable, that way you don't have to worry about what it really is.

The article says the paradigm is that “small fluctuations in density are amplified by gravity.” That is a qualitative sort of statement, that could mean just about anything.

There are two free parameters in LCDM for this. One gives you the size of the initial fluctuation. The other one gives you the steepness of the fluctuations. You can fit that to the data.

his assumption claims that “sound” in the universe is present equally at all wavelengths? I don't think I have this right, but I'm also in great doubt as to the wisdom of transforming the map of the universe from a spatial description to a wave-number description at all.

It's just math. You have a differerntial equation in space. You can do a coordinate transform to do the math in wavelengths.

(By the way, on further thinking, I'm not sure the "popular choice" of assuming that P(k) ~ k really makes any sense. Why should there be any a priori assumption about the distribution of wavelengths of perturbations in the universe, and why would it be distributed in this way?)

That's where inflation comes in...

Inflation says that the universe underwent a period in which it was expanding exponentially exp(ax). So if you have random gaussian flucutations at quantum scales, and you ask what that does to the total spectrum, you get a power law spectrum.

This is why doing the numbers is important. Inflation is more than merely saying that the universe expanded, but once you get the exact numbers, you end up with the initial perturbation spectrum.

My own feeling is that wave-number-based descriptions of the universe are deeply counter-intuitive. It would be rather like trying to find a Bessel function and Legendre Polynomials to describe the surface of the Earth. Of course, you CAN model the Earth this way, but why would you want to? Would it really have any predictive or explanatory power?

Yes, it shows that the universe isn't all baryons, and that baryons cause peaks.

When the universe was one hour old, the particles 1 mile away from each other were moving apart at 1 mile per hour. Yes, in that environment, sound might travel quite well, except for a few caveats. (1) we're talking about a fluid so dense that ANY fluctuation is going to result in massive gravitational instability, and (2) We're talking about a fluid that probably doesn't interact in any way similar to the spring-like molecular interactions we're familiar with.

1) This isn't true. There is a well known criterion for when something will undergo gravitational instability called the Jeans instability. What you basically do is to calculate the speed of sound in a gas, and if the sound waves spread out the gas faster than gravity can compress it, there is no instability.

2) Fluids are fluids. One thing that happens with the big bang is that the densities pretty quickly go down to the level of things that we run into in daily life. One hour after the big bang, you have a gas of hydrogen/helium at conditions we can simulate with Earth based experiments.

What you've told me is that if it were baryonic, the universe would ring like a bell. What I'm trying to do here is make my best attempt to guess what you mean. I think you must mean that the universe ONCE rang like a bell; when the density was much greater. I'm suggesting that the universe stopped ringing like a bell because it became too diffuse for sound waves to carry through diffuse molecular hydrogen.

We are looking at a snapshot of what the universe looked like at the time the CMB was emitted and the galaxies first formed. At that point the pressure waves got "frozen" which gives us what we see today.

You seem to be saying that the universe should be ringing still now, except for the presence of nonbaryonic dark matter. Do I have that right?

No. What I'm saying is that observations of CMB and galaxy counts show what the universe was like at the time CMB got emitted and the galaxies started to form. That gives us a snapshot of the that moment, which is inconsistent with all baryons.

Now you could argue that there is some process that converts non-baryonic matter to baryonic matter, but then you look at the list of possible particle physics processes, and none of them fit. If you were arguing for a dark matter->baryon process happening at 10^-2 seconds after the BB, that would be easy. But we are now BB+300,000 years, you have hydrogen gas at 3000K, so if there were some dark matter->baryon conversion process, you should be able to see it in action on earth.

 

[JDoolin]

What is the standard model regarding Hubble's constant? Is it a true constant; i.e. it does not change over time, or is it changing? Is it the reciprocal to the age of the universe, or is it regarded to be an unchanging parameter?

Never mind, I think I found it on Wikipedia:

http://en.wikipedia.org/wiki/Hubble's_law#.E2.80.98Ultimate_fate.27_and_age_of_the_universe

And a little calculation.

If q were zero, and the integration constant is zero, then it is the reciprocal to the age of the universe.

 

[twofish-quant]

One of way of thinking of the standard model is that it's like piece of software. Cosmological Model 2012 is going to be different from Cosmological Model 1995 in the same way that Windows 8 is different from Windows 95 or Linux 3.4 is different from Linux 1.5.

As time passes, people will put in more bug fixes and features, and rip out old obsolete stuff. Right now the big work in Standard Model 2012 involves adding in a galaxy formation model and an inflation model. The perturbation model for the standard model is linear. What that means is that you do a Fourier transform of the perturbations and then assume that the interaction between the wavelengths is small enough to ignore. Once you have galaxies forming, things will definitively "go non-linear" and things will break.

 

[JDoolin]

One hour after the big bang, you have a gas of hydrogen/helium at conditions we can simulate with Earth based experiments.

Was this a mis-statement?

From what I understand, we believe that hydrogen and helium first formed at 30,000 years after the Big Bang. By my calculation ,

1 mile/hour * 13.7 billion years = 20 light-years

at one hour after the Big bang, there would have been all the matter now distributed in the nearest 20 light years (the mass of the nearest 20 or 30 solar systems) compressed into the space of a radius of one mile.

This would be like neutron-star like density. I don't think that matter at those densities can be simulated in a laboratory.

 

[twofish-quant]

From what I understand, we believe that hydrogen and helium first formed at 30,000 years after the Big Bang.

No. Hydrogen and helium first formed at three minutes after the BB.

At 34 minutes after time zero, the density of the universe was 10 times the density of water...

http://hyperphysics.phy-astr.gsu.edu/hbase/astro/bbang.html

there would have been all the matter now distributed in the nearest 20 light years compressed into the space of a radius of one mile.

There's something wrong in that calculation.

This would be like neutron-star like density, prevented from collapse only by the fact that there was no gravitational gradient--no net direction of gravitational pull. I don't think that matter at those densities can be simulated in a laboratory.

At three minutes after BB, we are at densities which we can simulate (albeit briefly) on the earth, and it's typical of the densities you find in the sun.

https://lasers.llnl.gov/programs/nic/icf/

Also, we can generate these sorts of temperatures/pressures in hydrogen bombs.

 

[JDoolin]

$$\frac{1 mile}{1 hour}* \left (13.7\times 10^9 years \right )*\frac{8760 hours}{year}*\frac{1 light-year}{5.8785\times10^{12} miles}=20.4 ly$$

I have checked the math now about ten times. Please check, and see if you see an error in the calculation.

 

[twofish-quant]

You might start out by explaining how you are setting up the calculation.

Where did you get one mile/hour and why are you multiplying it by the age of the universe.

Most calculations start with a(t), which is the relative size of the universe. You put in gravity and pressure and then you come up with an equation for a(t). In some limits you end up with some proportions that you can use for quick calculations.

Unfortunately, I don't have time to put together a set of intro cosmology lecture notes, although since you know basic calculus, you can definitely follow the dervivations of the basic cosmology equations. I'm sure that someone has done it already on the internet.

 

[JDoolin]

Thanks for your reply. I wasn't sure whether you actually saw an error in the calculation or you were disagreeing with my underlying assumption that the bulk matter of the universe is spreading out at constant speed.

I felt that I had justified that assumption in post #28; and thought that I was staying within the Standard Model. I now wonder whether the equation given here$$q=-\left ( 1+\frac{\dot H}{H} \right )$$

is fully compatible with the equation given here: $$H=\frac{\dot a(t)}{a(t)}$$

There are basically two ways of looking at things. One is to expect that there would be a natural relationship between the velocities of distant objects, and their distance, which derives from the fact that they all originated at roughly the same place at the same time. That is essentially the meaning of the first equation.

Then there is another way of looking at things; to assume that things did NOT start out at the same place, but did start out at the same time, and that the natural relationship between redshifts and distance has to do with the scale factor, a(t) changing over time, and that is essentially the meaning of the second equation.

My calculation of 1 mile per hour times 13.7 billion years was coming from the first assumption, and I gather than Weinberg's calculation of a density 100 times greater than water after 3 minutes was coming from the second assumption.

I'll run out to the library, soon, and check out "The First Three Minutes" and see if I can find out why Mr. Weinberg's thought that the early density of the universe was so low.

To me, it appears that there are two different models for the universe, both actively in use by the astronomical community, as are summarized here:

http://en.wikipedia.org/wiki/Redshift#Redshift_formulae

One is for Minkowski spacetime, and the other is for the FLRW metric, and it refers to the cosmological scale factor. In my own reading, the reasoning behind gravitational redshift and velocity-based redshift is made fairly clear, and based on empirical data, and strong reasoning. Whereas the reasoning behind the FLRW metric generally begins with some hand-waving rationale based on a need for greater flexibility, like "What if the universe were spinning?" or "You can't have an expanding isotropic distribution that satisfies the cosmological principle."

I know in particular, since you quoted Weinberg, that he uses that latter argument in "The First Three Minutes" and he notably fails to apply the relativity of simultaneity. He makes some flawed argument about the density at point B as seen from A, versus the Density at point A as seen from B. I forget what figure it was in the book... I remember thinking to myself, there must be more than just this one mistake in the book.

I remember thinking at the time that I should really work my way through it, find a big collection of errors in Weinberg and others. The problem was that most of the book was much more hand-wavy than that diagram. So really, that one diagram, and his failure to apply the relativity of simultaneity--that was the only real error I saw in the whole book. Even so, if you want to quote Weinberg, it gives me the opportunity to mention that mistake. It is just one mistake, but I remember some quote from Einstein, when a whole lot of people were criticizing his theory, and pointing out lots and lots of mistakes.

You don't need lots and lots of mistakes--you just need one. If Weinberg's whole theory is based on his neglect of applying the relativity of simultaneity, then of course the whole theory falls. The only time you can really find an error in someone's reasoning is if they make their reasoning clear. And Weinberg made very clear that he was treating distant events as simultaneous in reference frames that are traveling away from each other at relativistic speeds.

Kudos to Weinberg here, though. It's incredibly rare for any proponent of the Standard Model to make their reasoning clear enough that you can find a flaw in it (or to be convinced by it, for that matter). Usually it's incredibly vague reasoning followed by page after page of dense tensor mathematics.

 

[twofish-quant]

One is to expect that there would be a natural relationship between the velocities of distant objects, and their distance, which derives from the fact that they all originated at roughly the same place at the same time. That is essentially the meaning of the first equation.

That's the wrong way of looking at it. The first equation doesn't describe anything. It's an equation that defines the deceleration parameter q.

My calculation of 1 mile per hour times 13.7 billion years was coming from the first assumption, and I gather than Weinberg's calculation of a density 100 times greater than water after 3 minutes was coming from the second assumption.

And the second way is the correct way of looking at things.

To me, it appears that there are two different models for the universe, both actively in use by the astronomical community, as are summarized here

Nope. Just one model, the second one. One thing about wikipedia is that it's a good resource, but I've often found it to be incorrect.

I remember thinking at the time that I should really work my way through it, find a big collection of errors in Weinberg and others.The problem was that most of the book was much more hand-wavy than that diagram.

You have to remember that Weinberg is writing for a general audience, and so he has to be hand-wavy in order not to bore people to death with equations. Also, often what appear to be errors in a popular work are simplifications. Finally, the first edition of that book was in 1977, and he wrote an updated addition in 1992, there are large parts of it that are out of date.

If you really want to do cosmology, you shouldn't start with his popular books. He's written some excellent textbooks that go through the equations in their full glory. The math isn't particularly difficult.

You don't need lots and lots of mistakes--you just need one. If Weinberg's whole theory is based on his neglect of applying the relativity of simultaneity, then of course the whole theory falls.

No it doesn't. Most "real world" theories aren't very brittle. If you make an assumption that turns out to be false, the theory still works as long as reality is "close enough" to the assumption.

The other thing is that it's usually a good idea to assume that people aren't idiots, and that maybe people have thought of an issue. For example, once you have a scale function, then you have a coordinate system and you can define simultaneity, so the principle of "no relativistic simultaneity" doesn't apply to cosmology calculations, because you've defined a fixed reference point which is the t=0 of the big bang.

The other thing is that if you have a conflict with a theoretical principle, you do the experiment and see what happens. It turns out that cosmology conflicts wildly with the principle of "no absolute reference frames". Oh well, that's what we observe. At that point you toss the theoretical principle.

And Weinberg made very clear that he was treating distant events as simultaneous in reference frames that are traveling away from each other at relativistic speeds.

Which you can do because you've defined a coordinate system based on the big bang. Once you've defined that coordinate system, then you can define simultaneous events and an absolute coordinate system.

There's no flaw. It happens that when talking about local stuff, you can use the "no simultaneity" principle to come up with a description of what happens, but it breaks down in cosmology.

Usually it's incredibly vague reasoning followed by page after page of dense tensor mathematics.

That's because people start with the physical principle and then work out the mathematical consequences of the principle. When you come up with physical principles, you just guess and hope you get lucky. You then work out the mathematical consequences of your guess, compare with observations. They may match. They may not. Repeat.

Sometimes the principle that you come up with happens to work in some situations but breaks in others. The idea that there are no preferred reference frames happens to work nicely in electrodynamics. It fails when you try to do cosmology with it, when there happens to be a absolute reference frame.