Big Bang Nucleosynthesis

What happened in the first few minutes after the Big Bang? Usually astronomers work on time scales of thousands to billions of years for objects in the sky to develop and change. However, after the Big Bang it took just a few minutes for light elements to form. All of our activites have been based on one key assumption; that the universe began as an extremely small, hot, condensed object and that the Big Bang is what changed it all. In the past two days we have seen that the Universe is expanding as galaxies race away from us, and there is a remenant Cosmic Microwave Background that can give us a temperature of the universe. If we accept our assumption and experienced its truth in the last few days we can apply the laws of physics and examine what happened in the first seventeen minutes of the Universe and what we see today that supports those claims.

Helium Abundance

One of the predictions that the Big Bang theory leads to, concerns the abundance by mass of Helium we should see in the universe. The "conditions" during Big Bang Nucleosynthesis were just perfect to create about 25% Helium, 75% Hydrogen, and much less than 1% of everything else. But don't just take our word for it, lets prove it. Hang on because this is where the tricky math comes in. So when I said "the conditions," you probably wondered, "What were those conditions?" The most important condition was the temperature. The universe started as a very very hot object. Immediately following the big bang it began to cool down. Once the temperature passed through the area around 1 MeV, cool stuff started happening. Here we go with the units again. Apparently F, c, and K are not enough to describe temperatures. Astronomres have to use electron volts too. An electron volt (eV) is a unit used to express an extremely hot temperature. 1 eV = 11,604 K. That is approximately 20,000 degrees Farenheit. Very hot! Another condition is the mass difference of the neutron to the proton (Q).

Q = mass of neutron/mass of proton = 1.293 MeV

This condition is true today because the masses of neutrons and protons hasn't changed. You see the electron volt again, only this time its being used as a mass measurement. This comes straight from the famouse E=mc2 relationship. Although it seems silly to be changing everything around, now you see that we have a temperature and a mass both in MeV. The units will cancel out (which is usually a good thing). But the important point is that we are beginning to use the math that determined what formed in the beginning of the universe.

A useful analogy for this phenomenon has to do with parking lots. Lets say there is a small parking lot with only sixteen spots. Four of those spots are in the shade. It is a really hot summer day, so when cars start to fill the parking lot, the first four will most likely choose the spots in the shade. The other 12 spots remain in the sun and cars drive around picking their spot for a different reason other than the shade. However, the first spots to fill are the shady ones and you can bet that they will be filled on a hot summer day. In the same way, there are sixteen nucleons bouncing around in the universe and four of them (two protons and two neutrons) will bind together to form a Helum-4 nucleus. If it is a hot summer day you can bet they will form that nucleus and the other 12 will be left to fend for themselves until more "shady spots" open up.

The next thing we look at is the abundance ratio of the neutron to proton. This ratio goes as follows

n/p = exp(-Q/T)

with Q being the mass difference, T being the Temperature, and exp(x) = ex. So with the above stated conditions,

n/p = exp(-1.293 MeV/1 MeV) = .2744

The temperature starts to rapidly decrease as the Universe expands. The temperature continues to decrease and reaches an equilibrium point where the temperature is about .72 MeV and the abundance ratio of the neutron to proton (n/p) also changes.

n/p=exp(-1.293 MeV/.72 MeV) = .166 which is approximately 1/6

So the universe has expanded and cooled off to a point where for every 1 neutron, there are 6 protons. Neutrons and protons are both considered nucleons. This just means they are objects found in the nucleus of an atom. However, we must take into consideration that neutrons decay. A neutron decays into a proton, electron, and anti-neutrino. The decaying neutron means there are less neutrons than we originally though. Taking this into consideration the actual neutron to proton abundance ratio is actually 1/7.

n/p = 1/7

At this equilibrium point, elements begin to form. A Helium-4 nucleus is made up of 2 protons and 2 neutrons. So if two neutrons grab two protons that leaves 12 extra protons bumping around. So four of the nucleons are wrapped up in a helium nucleus and the other twelve nucleons are hydrogen nuclei. Thus,

4/16 = 25% Helium

If the Big Bang Theory is accurate, everywhere we look in the Universe should be 25% helium. Now let's examine what to look for and how we can determine that.

Stellar Spectra

By now you should all be spectrum experts. Yesterday we saw how to take a spectrum from an object and determine its temperature in the case of it being a blackbody. Perhaps you are familiar with the concept of using a spectrum to determine the composition of an object. When a spectrum is taken of an object, the spectrometer separates the light into different wavelengths. Every element emits a specific wavelength. Therefore we can determine the makeup of an object by looking at its spectrum. This is exacly how they do it on shows like "CSI," where they find a paint chip and are able to look at where it was made and what model car that was. Light emits certain wavelengths. For Helium these wavelengths are measured in angstroms. An angstrom is a small unit of distance equal to 10^-10 meters. The specific Helium wavelengths we are examining are 4026, 4471, and 4686 Angstroms. Below is a spreadsheet template. It is set up with actual data from five different stars. The data comes from the SDSS database. The template is also set up with some simulated data. This data is generated by a computer program and has specific temperature and gravity constants programmed in. The synthetic data also has a key quality that it is set up to have around a 25% Helium abundance since that is what Big Bang Nucleosynthesis is predicting, and also what we want to test.

Big Bang Nucleosynthesis Excel Worksheet

Directions for the Excel Sheet

  1. Once the Excel sheet is open make sure you are clicked on the tab called "Spec 585." This corresponds to the spectrum of the star who's ID# ends in 585.
  2. You will see that the first six columns with actual data in them are titles "Stellar Data." This data was taken during the Sloan Digital Sky Survey. It is the spectrum of the star. When graphing, exel wants to take the first two columns and assign an integer number to each point instead of using the "wavelength" column as the point. One way to "trick" excel is to divide column A by a common number, and then multiply it by that again. This is what has been done for you in columns D and G. The green columns are the actual data we will use to plot to the graph.
  3. Column J is where we have put in some synthetic data. In the "Spec 585" tab the synthesized data has a known Temperature to be 22,000 K, a known gravity constant 4.0, and as previously stated, this data was synthesized to have 25% Helium abundance. The data needs to be multiplied by a unitless scaling constant which is found in cell O7 and highlighted yellow.
  4. We want to compare the stellar data to the synthetic data. Plotting them on the same graph is a good way of doing this.
  5. In excel, highlight columns M and N and click the chart wizard button on the top toolbar. A window will open and should show your data.
  6. Next click "Series" at the top of the new window. When on that page click "Add new series" and highlight the values you want to input for x and y columns.
  7. Click "next" and you will be prompted to give your graph a title, and label the axes. Once that is finished, finish your chart and it will appear on your spreadsheet.
  8. A few useful steps that are unneccessary but helpful include, changing the size of the data points to size "2," changing the colors of the data points to match the green and blue columns they correspond with, and changing the scaling constant to get the synthetic data to better match the stellar data.
  9. Another useful step is to zoom in the graph so we are examining the wavelenths of He. I suggest an xrange of [4000:4900].
  10. Hopefully now you can compare the synthetic and stellar spectra and the depth, width, and position of the He absorbtion lines. Record your observations

Further Data Analysis

You can now move onto the tabs labeled "Spec 564," "Spec 388," and "Spec 242." It is the same set up, but instead of being given the correct synthetic spectrum with a given temperature and gravity constant you must choose the correct fit. These stars are both different and hopefully you can find a fit that you are comfortable with and observe whether or not the stars have an observable abundance of Helium and if it is 25% or not. It is worth thinking about why or why not the synthetic spectra fits.

For an even more advanced activity we can use the SDSS Navigation Link (used in the Hubble Digram Activity) to pull stellar spectrum off of the database.

SDSS Navigation

After clicking the above link there are two things you need to be sure to look for. On the left side, make sure "objects with spectra," is clicked. Once you find an object with a red box around it you can click on it and on the top right it should say whether the selected object is a galaxy or a star. For this activity we are looking for stars. Once you find a star with a red box around it, click on it and on the lower right hand side click, "Quick Look." If SDSS has a spectrum for a star it will say under the picture of the spectrum, "Get spectrum on CSV." This button opens up the spectral data in Excel. See how many stars you can find and whether you believe they fit with one of the synthetic spectra. If they do, are they in agreement on the Helium abundance? Why or why not?

The data you are pulling off of SDSS is probably not fitting very well with the limited amount of synthetic data you have. Below is a fairly advanced activity to use for picking synthetic data from a large document.

Synthetic Data

Synthetic Data File

  1. First download the synthetic data file onto your desktop.
  2. Next, open up a terminal window. To get to the desktop type in "cd Desktop/"
  3. You want to look up a certain line of data in the file to see what the data in that place looks like. For an example type in "awk 'NR==18 || NR==19 {print $240;}' HRESm10.vis"
  4. Hopefully the terminal will say, "10500.0, 4.00." These numbers correspond to the temperature and gravity of the synthetic star. You can play around with the number inside the brackets (in our example 240) and print out a temp and g that you think will fit with your spectrum. Once you have picked a temperature and a g you can print out to a file the synthetic spectrum for a star of that temperature and gravity.
  5. To print it out type in terminal "awk 'NR>20 {print $1, $240/2e8;}' HRESm10.vis >t10500g4" Doing this will export a data file with the name "t10500g4" to your desktop with that data. You can then open it with a text editing window and copy and paste it into excel to put it with your stellar data you got from SDSS.