Relativity and Cosmology Blog

# Relativity and Cosmology

This is a Blog on relativity and cosmology for engineers and the like. You are welcome to comment upon or question anything said on my website (relativity-4-engineers), in the eBook or in the snippets I post here.

Comments/questions of a general nature should preferably be posted to the FAQ section of this Blog (http://cr4.globalspec.com/blogentry/316/Relativity-Cosmology-FAQ).

A complete index to the Relativity and Cosmology Blog can be viewed here: http://cr4.globalspec.com/blog/browse/22/Relativity-and-Cosmology"

Regards, Jorrie

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# Galactic Puzzle (take 2)

Posted September 23, 2014 12:49 PM by Jorrie
Pathfinder Tags: Expansion rate Hubble flow

Galaxies usually occur in galactic clusters or super-clusters, where from a few tens to a few thousand galaxies move in huge orbits around some gravitational center. But there are also galaxies inside the so-called cosmic voids - just not too many of them.

For the purpose of this discussion we are going to consider two such galaxies, sitting rather lonely inside a large void. So lonely that the gravitational influence of other galaxies upon them are negligible and we can say they just move with the Hubble flow. This means that they should be drifting apart according to Hubble's law, at a speed of about 68 km/s per Mpc of their present separation.

To make things easy, let's say the two typical, identical galaxies (A and B) are located near the center of the void and around 14.7 Mpc (or 47.5 million light years) apart. They should be receding from each other at some 68 * 14.7 ~ 1000 km/s. Divide this by c (300,000 km/s) and we get the expected redshift z=0.0033. This is the fractional increase (Δλ/λ) in the wavelength of light emitted in one galaxy and observed in the other, caused by cosmic expansion.

Now let's also say that astronomers living on a planet inside galaxy A find, to their surprise, that galaxy B is observed at just about zero redshift. This means the galaxy is neither receding from them, nor falling towards them, just sitting at 47.5 Mly away. This could obviously also mean that the galaxies are in circular orbit around each other, because tangential speed will not show up in the redshift value.

If civilization and astronomy on that planet were to survive for another million years, what do you reckon will happen to the redshift observations between those two galaxies? Will they just remain at a stable distance, or do you think the cosmic expansion will make them move farther apart? No need for calculations, just give a gut-feel on the possible outcomes.

-J

PS: I seem to have not tick all the boxes in the previous one, so it never showed up in the "New Blog Entries" list. Will try to remove the old one.

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#1

### Re: Galactic Puzzle (take 2)

09/23/2014 1:12 PM

Yes I think they would recede from each other....Although I'm not clear on the nature of dark energy and dark matter, they do seem to be ubiquitous and common....

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#2

### Re: Galactic Puzzle (take 2)

09/24/2014 12:11 AM

How about, as the universe expands, it creates large empty areas, cosmic voids, that become white holes (WH), the effect being that dark matter becomes white matter? (hydrogen) and in doing so releases large amounts of energy that heats up the hydrogen to cause nuclear fusion and give birth to new galaxies? A miniature Big Bang? Just some thoughts.

Regards JD.

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#5

### Re: Galactic Puzzle (take 2)

09/24/2014 3:50 AM

JD, yes cosmic voids exist, but they are practically devoid of dark matter as well. Dark matter appears to be associated with the galactic structures, actually must have been clumping first and then drawing normal matter into the clumps.

I have no idea how white holes could form in the voids, or anywhere else, for that matter. We surely have no observed data to support that.

-J

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#15

### Re: Galactic Puzzle (take 2)

09/24/2014 5:07 PM

There is a theory that primordial black holes were created in the first instants of the

Big Bang with a mass of much less than 4 billion tons, but they would have

evaporated by now, but ones that exceeded this threshold could still exist today.

The event horizon would be so steep that virtual particles could be separated,with the

result that the unpaired virtual particle would transform into a real particle,

of intense energy,a gamma ray.

This output of energy from this primordial black hole would look like a white hole,an

invisible source of gamma rays.

In fact,Hawking proved that,at the quantum level,a primordial black hole was

indistinguishable from a white hole.

He also stated in his randomicity principle that information is also spewing out from

these white holes that has never existed in our universe before,

and since these actions occur at random,it places limitations on our ability to

understand reality.

There was even a speculation of the possibility that some of these white holes could

exist within our solar system.

A white hole of several billion tons could be placed in orbit and the gamma rays

converted to microwaves and beamed down to receivers on Earth.

Hawking estimated the power output of one of these white holes at 6 Gigawatts.

Please take with a grain of salt that my information may have been outdated by more

recent theories and data about gamma ray sources.

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#19

### Re: Galactic Puzzle (take 2)

09/25/2014 3:45 AM

HTRN, I do not know too much about it - it's quantum mechanical in nature... :(

Here is a modern view of possibly exploding black holes and the fact that they may actually already have been observed. "Fast Radio Bursts and White Hole Signals". A little technical, but quite an easy-read 5-pager.

-J

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#22

### Re: Galactic Puzzle (take 2)

09/25/2014 9:25 AM

Very interesting,and loaded with plenty of reference material for me to digest.

This should keep me busy for a while!

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#23

### Re: Galactic Puzzle (take 2)

09/25/2014 12:48 PM

Easy for you, perhaps! For me, it simply confirms how old I and my cosmological and quantum knowledge are...

Next year it will have been half a century since I drove past Arecibo. At least I DO still remember doing so!

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#7

### Re: Galactic Puzzle (take 2)

09/24/2014 10:03 AM

Interesting theory, sounds a lot like another theory about the universe:

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#9

### Re: Galactic Puzzle (take 2)

09/24/2014 10:58 AM

Yup, but "Steady State Theory" has been declared 'dead in the void'. :)

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#11

### Re: Galactic Puzzle (take 2)

09/24/2014 12:30 PM

I know, I was reserving 'official judgement' to be polite, allowing people to look at the two theories, see that they are so similar as to be indistinguishable (one merely gives a name to the 'nothing' that the new hydrogen pops out of)and then make their own conclusion about how much credit should be given to the detailed version of the discredited theory.

It also gives the poster of the theory time to say "Oh, I didn't realize that, my mistake" before the Unkind Mob lunges i with the pointing and jeering.

People make mistakes, often several in a single say (thanks to computers, now it's up to several in a single MINUTE, several a second if they set things up for the computer to 'batch process,' as the computer, as a tool of the human, can make mistakes based on improper input at blinding speed) and it's fair to give them a chance to correct them. If the person continues to defend a mistake after it's been proven wrong, THEN the laughing ant pointing can commence.

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#3

### Re: Galactic Puzzle (take 2)

09/24/2014 12:36 AM

I'm more than a little bit embarrassed to say that I have so little understanding of the concepts involved, that I don't have any gut feelings on the matter! I'm definitely a Newtonian physicist, and have much willingness, but little success in advancing beyond that point!

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#4

### Re: Galactic Puzzle (take 2)

09/24/2014 2:42 AM

Yes, it is not easy to have a gut feeling on this issue, because it is a part Newtonian, part relativistic problem. Actually, it is closer to the Newton side than to the Einstein side, because the distances of 47.5 million light year (Mly) and the speeds of 1000 km/s are not very relativistic values.

To get a feeling, we must do a few rather simple sums. To have zero observed redshift, means that Galaxy B must have a radial speed of -1000 km/s (-0.003333c) relative to its 'local space',* creating a Doppler blueshift that exactly cancels the cosmological redshift for the distance of 47.5 Mly. If B moves at 0.003333c for a million years (Myr), it can only move through space a distance of 0.003333 Mly. So it should end up at 47.496667 Mly.

The issue is now, what did cosmic expansion do to the distance of 47.496667 in the million years? The present Hubble constant implies that all spatial distances will increase by 1% every 144 Myr.** In one million years, the 47.496667 Mly will hence increase by 47.496667/(100*144)=0.0032984 Mly.

As a first result, the 47.5 Gly will end up being 47.496667+0.003298 = 47.499965 Gly. So, it appears as if the two galaxies have moved marginally closer to each other, some one part in a million closer. There are other second order effects that are not considered yet, but unless astronomy/cosmology is orders of magnitude more precise in a million years, I think it is to close to call. For all practical purposes, no difference will be detected over the million years.

-J

* 'Relative to local space' is effectively relative to an observer that measures the CMB as perfectly isotropic, or static relative to the local gravitational field.

** The Cosmo-Calculator gives the 1% per 144 million years in the bottom-left box.

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#6

### Re: Galactic Puzzle (take 2)

09/24/2014 9:52 AM

It' easy - the "gut feeling" as well as "common sense" gives the same answer: no change. If the present relative speed is zero, it will remain zero as there are no active forces - only an inertial movement opposed to the cosmic expansion. Of course, this means that we neglect both the gravitational attraction between the 2 galaxies (which doesn't apply at all if they are in circular orbit around each other) and the accelerated expansion.

The fact that you obtained a small difference in your calculations is because you neglected the approximations in the values. First, 14.7Mpc = 47.946Mly (and not 47.5). Second, 68km/s per Mpc do not correspond to 1% for 144My but to 1.00142%. You also considered a closer distance (47Mly - 0.003333Mly) to which you applied the expansion - why didn't you consider the expansion of 47.5Mly and then subtract the 0.003333Mly? In fact, both methods are wrong but the second one is closer to the real distance. Finally, c = 299792.458km/s and the 1000km/s is in fact 999.6km/s. If you apply all the above corrections you obtain the same value of 0.00333430Mly for both distances - the expansion corresponding to 47.946Mly and the distance traveled at 999.6km/s during 1000000y, so that the final distance remains the same.

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#8

### Re: Galactic Puzzle (take 2)

09/24/2014 10:55 AM

Alex, you wrote: "Of course, this means that we neglect both the gravitational attraction between the 2 galaxies (which doesn't apply at all if they are in circular orbit around each other) and the accelerated expansion."

So what is the use of all the accuracy in the calculation if we neglect a real physical phenomenon like dark energy? Although too small to measure at the sort of distances and times discussed here, it will eventually make those galaxies recede from each other. In short, they will settle into receding exactly according to the Hubble flow.

In this respect, SolarEagle's intuition was right. If we use all the higher order cosmological effects to the limit, the galaxies will recede.

-J

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#17

### Re: Galactic Puzzle (take 2)

09/25/2014 2:27 AM

"So what is the use of all the accuracy in the calculation if we neglect a real physical phenomenon like dark energy?"

It was only to show that in this simplified conditions the result is "no change" (and not a slight decrease of distance). After all, you also neglected these two conditions. Of course, if we consider them, the accelerated expansion will win.

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#18

### Re: Galactic Puzzle (take 2)

09/25/2014 3:32 AM

"It was only to show that in this simplified conditions the result is "no change" (and not a slight decrease of distance). After all, you also neglected these two conditions."

Not a big issue, but it is important to take note that when we neglect accelerated expansion (the cosmological constant) and also the mutual gravity of the two galaxies, but we use the accurate cosmological equations, there would still be a decrease in distance, due to decelerating expansion:

d2D/dt2 = D H02Λ - Ωm/2)

which with ΩΛ= 0 and Ωm= 1 gives d2D/dt2 = -1.158*10-7 Mly/My2, for the distances involved. Using the standard distance from rest: S = ½ (d2D/dt2) t2 over the million years in question, it gives a decrease in distance of 5.8*10-8 Mly and speed simply -1.158*10-7 c; still quite undetectable over such a 'short' time.

The only case where the distance really remained constant would have been about 7 billion years ago, when decelerating expansion changed over to accelerating expansion.

-J

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#10

### Re: Galactic Puzzle (take 2)

09/24/2014 12:17 PM

"As a first result, the 47.5 Gly will end up being 47.496667+0.003298 = 47.499965 Gly. So, it appears as if the two galaxies have moved marginally closer to each other, some one part in a million closer."

I am confused (unless it's you). Dont you mean farther away? Cosmic expansion should increase the distance. I believe you have said that galaxies do not expand because they are "gravitationally bound." Would the same be true for galaxies that are in orbit around each other? If so, they would not move farther apart. I personally question that assertion, so I think they will get farther apart.

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#12

### Re: Galactic Puzzle (take 2)

09/24/2014 1:00 PM

Hi SG, you wrote: "I am confused (unless it's you). Dont you mean farther away? Cosmic expansion should increase the distance."

I meant to write "first order result", but be that as it may, I have partially answered it to Alex above. If we ignore accelerating or decelerating expansion (i.e. just take the expansion rate as constant) and go to the exact values, then galaxies of typical mass and at the distance of 47.5 Gly apart will stay at that distance, as Alex pointed out. The gravitational influence on each other is quite negligible (I calculated it to be of the order 10-12 m/s2 acceleration for two M-way mass galaxies at that distance).

However, since we have the cosmological constant to deal with today, giving us accelerated expansion, the galaxies will eventually recede from each other. They are too far apart to be gravitationally bound, i.e. being in stable orbit around each other.

The equation for the 'cosmic tidal acceleration' is actually quite simple:

d2D/dt2 = D H02Λ - Ωm/2)

where D is distance and the Omegas the cosmological constant and matter density parameters (0.7 and 0.3) of the universe respectively. For this case the outward acceleration works out to the order 10-9 m/s2, which is about one tenth nano-g, I think. ;)

Note that the equation says that if it was not for the cosmological constant term, the acceleration would have been negative, meaning that despite expansion, the galaxies would have fallen towards each other with order one tenth nano-g acceleration.

-J

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#14

### Re: Galactic Puzzle (take 2)

09/24/2014 4:05 PM

"the galaxies will eventually recede from each other. They are too far apart to be gravitationally bound, i.e. being in stable orbit around each other."

So how do you know that? At what distance would they be gravitationally bound? Keep your answer simple by assuming no expansion if you like.

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#16

### Re: Galactic Puzzle (take 2)

09/25/2014 1:28 AM

How do I know the galaxies will recede?

The "pushing" force of the cosmological constant exceeds their gravitational attraction by a factor 600.* Even if they were in an unlikely orbit around each other, they would spiral away in a relatively short time, cosmologically speaking.

Bring them as close as the Andromeda galaxy from us and they could be in a bound orbit.

-J

* The Gly/Mly goof also slipped into my calculations, so the approximate values for the scenario are: cosmic force = 0.1 femto-g; gravitational force = 1/600 th of the cosmic force.

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#13

### Re: Galactic Puzzle (take 2)

09/24/2014 2:03 PM

Hi again SG, in order to avoid any confusion, I did goof with the units in that post. The original problem was in terms of of 47.5 million light years (Mly), not Gly as I wrote. Sorry about that; it invited misunderstanding.

Secondly, it does not mean that galaxies in a void and 47.5 Mly apart, static in their local space, will not recede from each other. The specific problem statement required galaxy B to have a peculiar velocity that canceled the cosmic expansion at that distance. It is the classic "Tethered Galaxy" problem that Tamara Davis mentioned in her doctorate thesis (http://arxiv.org/abs/astro-ph/0402278).

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#20

### Re: Galactic Puzzle (take 2)

09/25/2014 4:53 AM

Beyond my level, but I'm fascinated...

I believe cosmic expansion must inevitably cause them to move further apart, but I am not convinced that 1 million years is a suitable time-span to observe this.

Maybe after a million years, they would not be monitoring red shift ? Surely, after a few thousand years they would simply expect and believe the constant? That's why I say I'm not convinced re: time span.

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#21

### Re: Galactic Puzzle (take 2)

09/25/2014 8:56 AM

Yes, a million years is 'nothing' in present cosmological terms, but eventually everything tends to follow the Hubble flow, even if it had a peculiar velocity to start with (like the 1000 km/s of the example). In cosmology it is also called "particle momentum decay". In an expanding cosmos, ordinary momentum is not a conserved quantity because peculiar velocity ("through space", not "with space") decreases over cosmological timescales.

-J

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