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SkipNChurch

Cosmology, Peanut Gallery

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Okay, so let us talk about standard candles. A particular example will involve a type of star known as a Cepheid variable. These are stars that vary their brightness over a highly predictable period of time. This is generally days to months, as I understand. In the early 1900's, folks were attempting to understand some of the distant observations that they were seeing. One particular story involves a woman by the name of Henrietta Leavitt. Back in those days, women were not allowed to do "serious" work in astronomy, so she was stuck looking at photographic plates of the large and small Magellanic clouds; two small dwarf galaxies that are "relatively" close to our own galaxy. Back then I believe the dominant thinking was that these were objects in our own galaxy, as most people did not accept the hypothesis that there was anything beyond our galaxy.

 

She noticed that there were stars that became brighter and dimmer, and that this cycle occurred in a predictable manner.  She decided to plot the intensity (how bright the stars appeared) over time. She noticed something startling. The brighter stars had a longer cycle and the dimmer stars had a shorter cycle.  Reference the picture that I have attached below for a rough drawing of what she found.  You can see intensity/luminosity on the Y axis and time on the X axis. The star that cycles the fastest © has the lowest intensity and the star that cycles the slowest (  A  ), has the largest intensity. This led to her to make the hypothesis regarding cycling and intensity.  Unfortunately, nobody knew the distance to the large and small Magellanic clouds at that time, so she did not know the "actual" luminosity of the stars, but it was quite certain that the cycle of a star reliably predicted the luminosity. This eventually led to a breakthrough in using these stars as so called "standard candles" for distance measurement. More about that later however...

 

Cepheid Graph 1

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Following her work Hertzsprung, using a technique known as spectroscopic parallax, was able to accurately identify the distance to the magellanic clouds. This is the same Hertsprung who was part of the development of the Hertzsprung-Russell diagrammes for main sequence stars. A link to describe that concept here: http://en.wikipedia.org/wiki/Hertzsprung%E2%80%93Russell_diagram

 

A link to describe spectroscopic parallax: https://www.e-education.psu.edu/astro801/content/l7_p7.html

 

Now that we had a reliable distance to the variables that Leavitt looked at, we could identify the "actual" luminosity of the stars and calibrate her findings.  This was done using a logarithmic graph where the luminosity of the stars could be graphed on the Y axis in terms of our suns luminosity. As you can see, even the dimmest variable is hundreds to thousands of times "brighter" than our sun. See the picture of this graph below with luminosity on the Y axis and the period in days on the X axis.

 

Actual Cepheid Brightness

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So how does this work? Let us use a famous example. Star V1 in the andromeda galaxy is a cepheid variable. It has a cycle of about 30 days. Using the picture in the prior post, let us plot the cycle and see the star's luminosity. Notice the blue lines on the chart? I actually plotted this for you. Find the 30 day mark on the X axis and follow it up to where it intercepts the black line of "best fit." Then, go across, back toward the Y axis and see where it lands. This tells us that star V1 has a luminosity of about 16,000 times that of our sun.

 

A link to basic information about star V1: http://www.nasa.gov/mission_pages/hubble/science/star-v1.html

 

Now that we know the luminosity of the star in question, we can use a formula that relates the flux and luminosity into a single concept. However, it is probably important that I explain the difference between flux and luminosity first. For that, I will be back after lunch to explain and perhaps actually calculate the distance to V1. Stay tuned everybody.

 

Please feel free to correct me...

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Luminosity can be roughly though of as how "bright" something is general. Flux is roughly how much of that light passes through a specific area. The basic idea behind flux can be located here: http://hyperphysics.phy-astr.gsu.edu/hbase/vision/isql.html#c1

 

This should make sense. Basically, the brighter something is and the closer you are to it, the more light will pass through a certain area. The flux drops off not in a linear way, but via a so called "inverse square." In other words, it becomes exponentially smaller as the distance from the source increases. Using these ideas and the fact that we know the actual luminosity of the star V1 based on what has already been described above, we can create an equation that will tell us the distance to the star as long as we know the flux and the luminosity of said star.  We know the luminosity and simply measure the flux through our telescope and then plug and chug.

 

So, the luminosity of the sun is about 3.9 * 10(26) Watts

 

The Luminosity of the star V1 is about 16,000 times that of our sun

 

Find a good calculator and do the math.  You should get a luminosity of about 6.2 * 10(30) Watts for V1.

 

Now that we have the luminosity, we just measure the flux through our telescope.

 

The flux of V1 is about 1.0 *10(-15) Watts/Meter (2)

 

I believe that value can be referenced here: http://arxiv.org/pdf/1111.0262v1.pdf

 

Finally, we can use a Flux/Luminosity Formula: Flux (F)  = Luminosity (L)  /4Pi *radial distance from the star ® (3)

 

We can rearrange the formula: r = square root of L/4 Pi F

 

Plug in the numbers and crunch and you get a value of about 2.2 * 10(22) meters

 

Using basic dimensional analysis, this gives us about 2.4 million light years

 

See the picture below for how I set up this calculation and the basic values I obtained.

 

Distance to V1

 

 

Hopefully that helps anybody interested in knowing a bit about finding distances of these far off objects. Of course, this method is only good for relatively nearby galaxies and other methods are needed for more distant objects.

 

EDIT: The best known distance is around 2.5 million light years, so my ad hoc calculations are off by about 100,000 light years. The answer I obtained was still only about + or - 5% off from the best measured answer, so not too bad.

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Outstanding RS, I really appreciate you taking the time to walk me through this. That makes things much more clear. I also think it adds depth to the overall discussion. I'm sure it will be valuable to others who are reading as well. Excellent stuff.

 

BAA, thanks for the link to the wiki page about the cosmic distance ladder. That was also very informative, and it answered my question about how the Earth-Sun distance is measured.

 

I never had the opportunity to delve into this area of physics when I was at University, so this is fun for me. I'm really interested to see where the discussion goes from here.

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Thanks for the feedback. I ended up just finding a video that actually explains what I went through without the half a dozen or so posts and cheesy pictures. It is probably better to watch it instead of slogging through all my posts and It actually covers what I did, including the distance to V1.

 

Hope it helps:https://www.youtube.com/watch?v=iyisAjHdhas

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Something for Disillusioned.

 

http://www.jpl.nasa.gov/news/news.php?feature=4522

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