Solving Cosmology Question: Redshift where Radiation = Matter Energy Density

  • Thread starter dum-dum
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CMB radiation.And the density of matter, as I said, is 0.2 x 10-9 joule per cubic meter.So once you have both energy densities it is easy to take the ratio and then the redshift.In summary, the conversation discusses a problem involving finding the redshift at which the energy density in radiation equals the energy density in matter. The givens include assumptions about the baryon-photon ratio, scale factors for matter and radiation, and using simple equations such as E=mc^2 and E=hv to calculate the energy densities. The conversation also touches on the concept of the radiation constant and using the temperature of 2.7K to find the
  • #1
dum-dum
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Hi guys, I'm in a pickle here with an assignment.

I'm required to find the redshift at which the energy density in radiation equals the energy density in matter.
The following are the givens we were...well, given:
1) assume 1 baryon = 10^9 photon
2) assume all photons have energy to the wavelength of the peak of a 2.73K black-body radiation curve
3) scale factor (a) of matter: Pm = a^-3
4) scale factor of radiation: Pr = a^-4
5) we are to work out the energy density of a photon & baryon in present time and then apply the scale factor

Apparently this isn't using complicated formulas, just simple E=mc^2 & E=h*nu.

me right now = lost...need major help

Thanks in advance
 
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  • #2
I don't know what assumption #1 means exactly

but suppose it gives you a way of comparing today's radiation energy density with today's matter density.

Just to use different numbers, suppose that TODAY the CMB radiation density is one MILLIONTH of the matter density (expressed as energy equivalent)


then that means if you go back to redshift z+1 = 1,000,000 the densities will be equal


Because if you go back to redshift z+1 = N
then the radiation density will be N4 times what it is today
and the matter density will be N3 times what it is today
so the ratio of radiation to matter densities will increase a factor of N.

If matter, today, has an advantage of a factor of N, then you have to go back to redshift z+1 = N in order to bring them into balance


so the problem is easy once you know what the ratio is today. (of CMB radiation to matter)

the other kinds of radiation are minor compared to CMB so can forget about them
 
  • #3
well, the prof wanted us to solve the redshift using the photon-baryon ratio, hence the first assumption...and combined w/ your explanation marcus, I'm deducing that i can use E=mc2 to work out the energy density for matter & use E=hv to work out the energy density for radiation...which will give me the radiation-matter ratio, then apply the scale factor.

would that be correct?
 
  • #4
im trying to do this problem too dum-dum so when you get an answer send me an email and we can compare answers(sndhooper@hotmail.com)

and marcus #1 just means that there are and always have been approximately 10^9 photons for every baryon in the universe
 
  • #5
The baryon/photon ratio remains approximately constant over between matter/radiation equality and now. So i) compute the energy in a 2.73K CMB photon and compare the energy in 10^9 of them with that of a single baryon (use E=mc^2). If you change the scale factor a by a factor of 1/N, each photon gains in energy by a factor of N and the baryon remains unchanged. This is because the energy density (NOT scale factor) of matter goes like 1/a^3 and that of radiation by 1/a^4. Now just figure out what change in scale factor a will render them approximately equal.
 
  • #6
Hey dick, about the E=mc^2 would you plug in 2.73 and 10^9 into E since mass is not given and c is speed of light. So we need to find m then? Sorry I'm not great with math especially physics lol.
 
  • #7
we are to use the mass of a proton for 'm'...

you don't plug 109 into anything, you need to multiple that to the energy density of a photon (representing the radiation) to make it on par w/ the energy density of a baryon (representing the matter)
 
  • #8
I see ok so you find the proton mass which represent the baryon mass. I calculated the photon energy using E=hv is that right? since v=1.9 when it is at 2.7K. What does "a" mean in a^-3. So what do you do with all the numbers you find? do you sub it with a?
 
  • #9
hmmm just a quick question like we know v=1.9nm so in order to like match up with proton SI units, do we need to convert the 1.9nm into meters and then do the E=hv? Because I got a 10^-42 and it looks awfully small! thnx again

this is my email harvey_shadowfalcon@hotmail.com I think discussing this over msn is better
 
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  • #10
so is the energy density of photon is E=(6.63 10^-34)(1.9 10^-9)?
 
  • #11
use the E=hv equation for energy density of photon (meaning radiation)
h = Planck's constant
v = frequency (you're giving wavelength, so freq = spd of light/wavelength)
 
  • #12
can you explain a bit more what i do after i find the ratio between photons and baryons. this whole scale factor thing is a bit confusing
 
  • #13
look at marcus's explanation...it's about as thorough as i can think of as well.
 
  • #14
so the ratio of Ephoton/Ebaryon = n?
 
  • #15
is anyone else getting 2.414x10^11 baryons : 1 photon ?
 
  • #16
umm, i don't think that's right mixx.

we're trying to solve for "z"...
 
  • #17
http://www.astro.washington.edu/astro323/WebLectures/lec10_small.pdf

try this guys if you are having trouble w/ scale factor and how to incorporate them.
 
  • #18
woe is me. i just redid my calculations... I am getting my ratio as 7.24 x 10^19 baryons:photon
 
  • #19
this is clearly a homework so I can't just say the answer and you all seem well on the way.

but I will describe a DIFFERENT WAY TO DO IT.

You can get the energy density of CMB radiation in terms of joules per cubic meter
using a need trick which I will show you (the fourth power law)

And the energy density of matter (dark and baryonic combined) is 0.2 joule per cubic kilometer, which is 0.2 x 10-9 joule per cubic meter. So once you have the two energy densities it is easy to take the ratio----which is essentially the same as the redshift.

It is a blackbody radiation law that if the temperature is T then the density of radiation is arad T4

where arad is called the RADIATION CONSTANT
Many times people simply use the symbol "a" for the radiation constant but we already have that letter used in this problem for the scale factor, so to avoid confusion let's call it arad , like I said.

So it is really trivial. You just take the temperature 2.7 kelvin and raise to fourth power and multiply by arad and that will give you some small quantity of joule per cubic meter. then you take the ratio, and you are done.

But be warned, this does not seem to be the way the teacher wants you to solve the problem. So don't get sidetracked by my method. It is just for comparison.
 
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  • #20
the radiation constant is 7.566 x 10-17 joules per cubic meter per kelvin4

and I guess 2.73 kelvin raised to the fourth power is roughly 55 kelvin4

so multiply that by the radiation constant and you get roughly 42 x 10-16 joules per cubic meter

that is 4.2 millionths of a joule per cubic kilometer. that is the energy density of the CMB.

and we already said that the energy density of all types matter (baryonic + dark) was 0.2 joules per cubic kilometer. that is 200,000 millionths

so as a rough calculation the ratio is about 200,000/4.2 which is about 50,000

I wonder if that is approximately right. Or have I made a mistake.

In any case the professor won't like it if you solve it this way, even if the answer is right. Because he did not say to use the radiation constant.
====================
It makes a huge difference whether you count dark matter or not. This professor seems only to be concerned with baryonic matter
which I estimate has a presentday density of 34,000 millionths of a joule per cubic kilometer. And the CMB density is currently 4.2 millionths. So the ratio is only 34000/4.2 = 8100.
So getting back to a time when radiation balances baryonic matter just requires a redshift of 8100! That sounds kind of reasonable.
But I still wonder if it is right.

Right or wrong the prof won't like my method, which uses the radiation constant.

this radiation constant has an interesting formula in terms of k, hbar, and c. It is

[tex]\frac{1}{15} \frac {k^4}{(\hbar c)^3}[/tex]

So if you go to google and put "k^4/(hbar*c)^3/15" in the window, google will give you the value
that I said earlier-----the 7.566 etc etc.
 
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  • #21
i don't understand where i am going wrong. maybe i can lay out my steps and you can show me what i am not doing correct.

PHOTONS:

-By weins law: using 2.73 k, find wavelength
- by E=hc/wavelength find energy of photon
-multiply by 10^9

BARYONS:

- E=mc^2

and then i divide Ephoton/Eproton

and from there i am hopelessly stuck. the numbers i am getting are rediculous and do not work
 
  • #22
marcus, i have another small question...if we are looking for the age of the universe at certain redshift...do we need the Einstein de Sitter model (a = time2/3?

is the redshift and the current (assumed) age of universe enough??
 
  • #23
for some reason i doubt the second question is that easy. I am banging my head against the wall for the first question still
 
  • #24
hey man check your pm
 
  • #25
dum-dum said:
marcus, i have another small question...if we are looking for the age of the universe at certain redshift...do we need the Einstein de Sitter model (a = time2/3?

is the redshift and the current (assumed) age of universe enough??

Although no expert, I would say NOT enough.
I would suggest playing around with Ned Wright's calculator.
Put in the redshift and it will tell the age at that redshift.
Experiment and see how changing the parameters of the model affects the estimated age.

Just google Ned Wright, or cosmology calculator
 
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  • #26
marcus said:
...
It makes a huge difference whether you count dark matter or not. This professor seems only to be concerned with baryonic matter
which I estimate has a presentday density of 34,000 millionths of a joule per cubic kilometer. And the CMB density is currently 4.2 millionths. So the ratio is only 34000/4.2 = 8100...

I am not sure that 8000 is right, but just to have something for comparison I went to Ned Wright's cosmology calculator and put in z = 8000. It said the age of the universe at that redshift was about 10 thousand years.

If that is right then when the expansion was 10,000 years old, or thereabouts, the radiation energy density as equal to the baryonic energy density.

There are some real sloppy steps in the way I have estimated this, so could be off by an order of magnitude. There are several people that could help get more certainty: Wallace, Hellfire, George Jones, Kurdt, to name a few. Maybe I will start a thread in cosmology forum to try to get answers to my own questions.
 
  • #27
thanks for all your hard work marcus
 

What is redshift in cosmology?

Redshift is a phenomenon in which light from distant galaxies appears to have longer wavelengths, or shifts to the red end of the electromagnetic spectrum. This is caused by the expansion of the universe stretching out the wavelengths of light as it travels through space.

How is redshift related to the energy density of matter and radiation in the universe?

In cosmology, the energy density of matter and radiation are important factors in understanding the expansion of the universe. As the universe expands, the energy density of matter decreases, causing the wavelength of light to stretch and resulting in redshift. This redshift can help scientists determine the age and composition of the universe.

What is the significance of solving the cosmology question of redshift where radiation equals matter energy density?

Solving this question can provide valuable insights into the structure and evolution of the universe. It can help us understand the relationship between matter and radiation and how they contribute to the expansion of the universe. Additionally, it can lead to a better understanding of the origins of the universe and its future fate.

What methods are used to solve the cosmology question of redshift where radiation equals matter energy density?

Scientists use a variety of methods and techniques to study the redshift phenomenon and its relation to matter and radiation energy density. These include observations of distant galaxies and their redshift values, mathematical models and simulations, and data from experiments such as the Cosmic Microwave Background Radiation.

What are the potential implications of solving the cosmology question of redshift where radiation equals matter energy density?

Understanding the relationship between redshift, matter, and radiation in the universe can have significant implications for our understanding of the universe and its origins. It can also have practical applications, such as improving our ability to make precise measurements of distances in space and potentially leading to new technologies and advancements in cosmology and astrophysics.

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