What is Our Actual Hubble Speed and How Does it Relate to CMB?

[marcus]

The "Hubble speed" of Imagine

whereever Imagine goes, a crowd of people always collects, trying to explain the world----Imagine exerts a kind of magnetism or enchantment----and being no exception I also feel compelled to explain the world to Imagine.

Most recently Imagine has written:
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What is our actual Hubble "speed" ?
...
What is our own recession speed? Zero ? Since temperature seems to decrease with time, is it, or could it be, related to CMB?
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A THOUGHT EXPERIMENT for Imagine

The CMB temperature has been measured in each direction of the sky very carefully and although the basic temp is 2.7 kelvin it is just slightly warmer in the direction of Leo (that very nice spring constellation). It is between 3 and 4 MILLIkelvins warmer in the Leo direction and the same amount colder in the away-from-Leo direction.

So the uniformity of the temperature around us is not perfect. But suppose we had a rocket ship with enough room and supplies for several friends and able to achieve a speed AWAY from Leo just fast enough so that the sky is now the same temperature in all directions.

Then we in the ship would be AT REST vis a vis the CMB. Our solar system and our galaxy are both almost at rest relative to the CMB already, but by means of this rocket ship we can arrange to be perfectly at rest in respect to CMB.

Now suppose that 100 million light years away from us there are also some nice people who wish, like us, to be at rest with respect to the CMB and they too have a rocket ship. They measure the temperature carefully and find the hot spot and then they speed away from the hotspot at just the right speed so that it seems cooler to them and the whole sky is also for them the same temperature. They are in some other galaxy because 100 million light years is an intergalactic distance.
So those people are also now at rest relative to the CMB, like we are.


Suppose that we unroll a long tape measure, marked in centimeters, between them and us. We take care not to let the tape measure touch any stars, which might burn it and spoil the thought experiment.

Does the distance measured by the tape measure, between these two points (both at rest) change with time?
And if so, by how many centimeters per second is it changing?

 

[marcus]

Ned Wright's Cosmology Website is now in Italian and French as well in English!

main URL:
http://www.astro.ucla.edu/~wright/cosmolog.htm

French URL:
http://www.chez.com/cosmosaf/FAQ/Wright.htm

http://www.chez.com/cosmosaf/FAQ/Cours-cosmo-1.htm

This is "La Cosmologie par Ned Wright", a translation
by Jacques Fric of the original online Cosmology Tutorial.

By the way Ned Wright (a cosmologist teaching at UCLA) has a more realistic version of this tape measure at the top of his "distance" page:

http://www.astro.ucla.edu/~wright/cosmo_02.htm

There he imagines measuring the "now" distance from A to Z by having a chain of observers in galaxies along the line from point A to point Z.

So A measures the distance to B
B measures the distance to C
...
Y measures the distance to Z
all at the same instant
and they add up the results

When all the reports are in and totaled up then
the total is the distance from A to Z at the moment
when the measurements were made.

I thought it would be simpler to simply stretch a tape measure.

 

[marcus]

how many centimeters per second?

I think most people at PF who read and post about these things know that the current value of the Hubble parameter is
the reciprocal of 13.8 billion years.

It is the simplest way to express this important parameter

H₀ = 1/(13.8 billion years)

The meaning of the Hubble law
v = HD

is simply that at the present moment ( we can call this t = t₀) the present recessionvelocity of a point at rest in the space around it is equal to the present value of H multiplied by the present distance. Written with the irritating subscripts it would be:

v₀ = H₀ D₀

But in the thought experiment we imagined that we have two points which are each at rest and that the distance between them as measured by the tape measure is 100 million LY

The righthand side of the law
D₀ H₀ = (100 million LY) (1/(13.8 billion years)) = (100 million LY)/(13.8 billion years) = (1/138) c

Therefore the lefthand side, v₀, the current speed of recession, is 1/138 of the speed of light.

So the distance is getting larger, as measured by the tape measure, at a certain number of centimeters per second (this is intended as a courtesy to Imagine who is French-Canadian) and
the number of centimeters per second is calculated by dividing
29979245800 by 138.

It is the speed of light in cm/second divided by 138, or
about 217 million centimeters per second.

 

[Imagine]

Bonjour Marcus,

I am happy to know that I generate a kind of magnetism or enchantment. I would precise that I don't use voodooism. Merci pour votre courtoisie mais I use meter/sec as light speed's unit.

I think that I really understand your explanation and I will read both the "englishly and frenchly" referred document. I will have to work further on "present moment" meanings since it seams to me that it's specified to make provision in case of H(t).

After reading your posts, I presume that you answered your own question, to fullfill pedagogical objectives. Merci beaucoup.

I suspect relation between CMB and Hubble's speed in my question "could it be, related to CMB?" because I have tortuous mind.

1) Hubble's speed increase with distance from us.
2) Temperature of the Universe drops with the expansion scale factor.

I imagined that some relation exists, between Hubble's speed and CMB, and that the actual CMB temperature would give our own actual Hubble's speed.

In supplement to your link, I will read carefully THE QUEST FOR THE COSMOLOGICAL PARAMETERS, M. Plionis
. He use present "epoch" instead of "moment".

 

[selfAdjoint]

While we're on this topic, why would the wavelength of the CMB increase with the expansion but not the distance between ticks on the tape measure?

 

[marcus]

Originally posted by Imagine
In supplement to your link, I will read carefully THE QUEST FOR THE COSMOLOGICAL PARAMETERS, M. Plionis
. He use present "epoch" instead of "moment".

This paper (by Plionis) is a very good one! I noticed that it is available in at least two places on the web. There is an HTML version which you gave the link to:

http://nedwww.ipac.caltech.edu/level5/March02/Plionis/Plionis1_1.html

However on my browser parts of this HTML version are almost illegible because of typography----the greek letters serving as symbols fall in the wrong place on the page!

To remedy this, I have downloaded the PDF version from

http://lanl.arxiv.org/abs/astro-ph/0205166

This is typographically perfect and printable. I printed out the first 14 pages.

Plionis paper strikes a resonant chord because it is from a summer 2001 cosmology course on Samos Island in the Aegean near the coast of Turkey. This island is not only the birthplace of the ancestor of mathematical science Pythagoras but also Samos is the birthplace of the first person to imagine the heliocentric solar system----Aristarchus of Samos who flourished around 250 BC.

<<BACKGROUND - PREREQUISITES
The main task of Observational Cosmology is to identify which of the idealized models, that theoretical Cosmologists construct, relates to the Universe we live in. One may think that since we cannot perform experiments and study, in a laboratory sense, the Universe as a whole, this is a futile task. Nature however has been graceful, and through the detailed and exhaustive analysis of the detected electromagnetic radiation emitted from the different photon-generating processes, we can do wonders!

Among the many important tasks of Observational Cosmology is the determination of the total mass-energy density of the Universe, the rate of its expansion, its age, the amount of ordinary and exotic matter that it contains, as well as to quantify in a objective and bias free manner the large-scale distribution of matter, as traced by galaxies, clusters of galaxies and AGN's for example. >>

BTW Active Galaxy Nucleus (AGN) is sort of the same thing as a quasar---a supermassive black hole is causing matter to spiral in and meanwhile get very hot and release much energy. Writers use too many enigmatic abbreviations like "AGN".

In the Abstract, Plionis speaks of the "concordance model" which refers to the very happy and reassuring fact that Cosmologists (ordinarily a very argumentative bunch of individuals each with their own opinion) have lately come to agree on the approximate sizes of certain basic parameters and features of a kind of "consensus" model.

<<Abstract. The following review is based on lectures given in the First Samos Cosmology summer school. It presents an attempt to discuss various issues of current interest in Observational Cosmology, the selection of which as well as the emphasis given, reflects my own preference and biases. After presenting some Cosmological basics, for which I was aided by excellent textbooks, I emphasize on attempts to determine some of the important cosmological parameters; the Hubble constant, the curvature and total mass content of the Universe. The outcome of these very recent studies is that the concordance model, that fits the majority of observations, is that with

&Omega;_m + &Omega;_&Lambda; = 1
&Omega;_&Lambda; ~ 0.7
H₀ ~ 70 km/s per Mpc
&Omega;_{baryonic matter} ~ 0.04
spectral index of primordial fluctuations-the inflationary value n~1.>>
------------------------------

 

[marcus]

Originally posted by selfAdjoint
While we're on this topic, why would the wavelength of the CMB increase with the expansion but not the distance between ticks on the tape measure?

selfAdjoint, this is a very sensible question which Frank Shu
addressed very carefully and at length in his introductory Astro textbook "The Physical Universe" (University Science Press, 1982)

Everytime someone asks this I am impressed with the wisdom of Frank Shu for taking the trouble to answer back then what is a completely natural question to ask! But in more recent textbooks the authors seem not to realize that it is something that students will want to know so they don't even bother to deal with it!

The distance between atoms in a solid is determined by minimizing some functions so it will always stay some number of angstroms or (fractional) centimeters.

But nothing like that is holding the wave peaks or wavefronts together. So while the Maxwell equations are working space is very gradually expanding and the solution of M. equations in gradually expanding space involve a corresponding expansion of the wavelength a tiny-tiny bit with every cycle.

The wave has no "memory" of its earlier wavelength and no way to re-contract itself back to a "normal" size. So the effect of a little spreading out with every cycle is cumulative.

So the solid matter of a measuring tape or measuring rod is very different from a wave! A wave can be progressively stretched out from 1 centimeter to 2 centimeters, while a crystal that is 1 centimeter wide will stay 1 centimeter wide!

One would think that every introductory textbook in General Astronomy would discuss this, but in several textbooks I have glanced at the authors just take it for granted that the students understand this and do not bother explaining!

Frank Shu (on pages 373 and 374) does bother to explain. He is a worldclass astronomer known among other things for having first developed the density wave model of spiral structure in galaxies. Was the ranking cosmologist in the UC berkeley Astro department for many years, now probably emeritus.

If you find that some more recent textbook writers take adequate trouble to explain the cosmological redshift, which is not a doppler shift, please let me know.