Standard Deviation

Hello everyone!

This week was a bit slower than other weeks, but that was because I hit a complication in the project. When I say complication, I mean standard deviation...

I was in contact with my ASU advisor and I had a difficult time understanding what he was trying to get me to do. Really, that was the complication because finding the standard deviation itself is not hard. Thank you chemistry!! Just in case you are not familiar with the term standard deviation, it refers to how far data is from the mean (average). It's on a scale from 0 to 1. If your data gives you a standard deviation of 1, it means your data is pretty scattered.

After a reading a great deal about standard deviation, I realized what he was asking me to do. He wanted me to find the standard deviation of the data and the standard deviation of the data with a fitted line (trendline). I had to do all of this in Excel, for it's the easiest way to graph, use trendlines, and input equations. In case you didn't read my last post, I am using two scenarios for my data. I am graphing the peak magnitudes (maximum brightness) of the supernovae (explosions) against the time it takes for the supernovae to reach 95% of their peak magnitudes. I am also graphing the peak magnitudes of the supernovae against the time it takes for the supernovae to gain 1 magnitude from its peak magnitude. Since we are dealing with negatives, the magnitude will be heading towards zero.

For the Peak Magnitude vs 95% Magnitude data, I had to find two standard deviations. I found a standard deviation of 0.817 for the fitted trendline and a standard deviation of 0.941 for the data without the fitted line. As you can see, the data is pretty scattered.

For the Peak Magnitude vs 1 + Peak Magnitude data, I had to find two more standard deviations. I found a standard deviation of 0.922 for the trendline and a standard deviation of .941 for the data without the fitted line. Similarly, the data is scattered.

That's pretty much what I have been up to this week. In summary, I had to find the standard deviation of my data. This would show me how scattered my data is. However, with supernovae type II, there is usually a great deal of scatter, as the explosions are usually varied.

Now, you may be asking yourself, "what does this all mean?" Great Question!!

See you next week!

Standard Candles: Type IIb Supernovae

Hi!!

Last week, I mentioned that I had a new task assigned to me from my on-site advisor. I had some trouble understanding what he was trying to say, but after a few emails, I realized he was asking me to standardize supernovae type II.

At first, I had no idea where to start. Supernovae type Ia (explosions of white dwarf stars) all have a absolute magnitude near -19.3. This is because these stars all explode when they reach a certain mass limit. Hence, they explode at roughly the same size and burn off the same amount of energy. That makes things easier for standardization of type Ia supernovae, but supernovae type II are a different scenario.

In order to standardize the supernovae (find a similar luminosity in all super massive explosions), I needed to measure the peak magnitudes of my selected supernovae and plot them against the amount of time it takes for them to decrease to 95% of their peak magnitudes. In other the words, plot them against the fading supernovae. I came up with this with the help of my BASIS advisor, Dr. Whaley. We met on Tuesday this week, for about an hour, and tried to figure out how to go about doing this. The method we came up with was then passed on to my professor at ASU. He said that was correct, but he also wanted me to try another method. Instead of 95%, he wanted me to add 1 to the peak magnitudes. It's essentially the same thing, just different values.

I've done both, and the next step is to find the standard deviation of the magnitudes. That will be my task for next week, for afterwards, I will have to plot my corrected mags. I am reaching a conclusion, and to know that I am on the right track is exciting.

I am still looking at my emails, waiting for him to email me about night time observing. It's been especially difficult recently, due to the clouds that have been above us for the last few days.

That's what I have been up to this week. I hope you enjoyed reading. As always, any questions you have, please leave them below. Check back next week for updated progress.

I have attached a picture of my table for the data values. Unfortunately, I could not get a big enough picture on here. That said, you probably won't be able to read the values. I just attached it to show you the size of the table that was required to reach a plausible conclusion.

Hubble Constant: Data!

Hello everyone.

I hope everyone enjoyed their break. I know I had a nice time escaping the work for a week. Now, I am back to completing my project.

This week has been the week where I have begun to compile all the data needed for determining the Hubble Constant. All the work I have done before this week has been such a help because with all the numbers I have looked at, I am now able to determine what data I actually need.

I am using most of my data from a source called "sne.space". This website is an open supernova catalog, meaning that most, if not all, supernovae data has been logged here. I am able to look at it's redshift, and most importantly, their absolute and apparent magnitudes. Knowing the magnitudes is a great help when it comes to finding the distance to an object. So far, I have taken data from around 15 supernovae. If I am doing the calculations correctly, I am reaching a Hubble Constant value of 67.1 km/s/Mpc. Considering that the astronomers get values around 70 km/s/Mpc, I'm pretty happy with what I have done so far.

I sent the data I had to the professor, just to make sure I was doing it correctly, and he replied that I had been doing it right. He did mention that he wanted me to try to find the distance in a different way, a standardization of supernovae type IIb. Supernovae type II are explosions of massive stars, much larger than ours. Most people use type Ia supernovae (the explosion of white dwarf stars) because of their brightness. They have been dubbed "standard candles". Because they are standard candles, they all have magnitudes (brightness) of 19.3. Not many people have considered type II supernovae "standard candles", so he wants me to standardize type II supernovae. I'll need to find a magnitude consistent for all supernovae type IIb. In my view, it's pretty complicated, but I'll figure it out with the help of my advisor.

I think this will be an interesting next step for my project. It's a way to determine the Hubble Constant with the standard candle method. Because I'm not too familiar with this method, I am currently reading two papers that deal with the standardization of supernovae type IIb. Once I finish them, I should have a good idea of what I'll need to do to complete the task.

Thanks for reading!!

Finding the Hubble Constant

Welcome readers!

This week was a slower week, for most of my work consisted of reading up on how to determine the Hubble Constant. This was valuable though because I found out what to do with the data once I receive it. I've come to realize, however, that I have not properly discussed what I need to do to find the rate at which the universe is expanding. I will do my best to explain it in a way that won't be dry.

There are a few ways to measure the universe's rate of expansion, including the use of supernovae or cepheid variable stars. In case you don't know, a supernova is an explosion of a star while cepheid variable stars are stars that have periods of luminosity (similar to a slow flicker of a lightbulb). Astronomers use these objects because of the amount of light that they emit. Supernovae are one of the brightest objects in the sky. One was recorded as 20 times brighter than the combined amount of light from the Milky Way galaxy's 100 billion stars! Because they can be so bright, making them easier to observe, they are optimal for finding distance. In order to find the distance of the stars, astronomers need to know their apparent magnitude (how bright they look to us) and absolute magnitude (how bright they are with a standard distance of 32.6 light-years), and/or luminosity (the amount of energy emitted from the star). Once researchers have found the apparent magnitude (m) and absolute magnitude (M), they can plug it into the equation d = 10^{[(m-M) + 5]/5}.

To find the velocity of the star, or galaxy, astronomers need to determine the redshift. When objects move away from us, light shifts toward the red end of the spectrum, meaning that wavelengths get longer. Some have described this by relating it to a police siren. As the siren approaches, the pitch gets higher, but as it passes, their is a sudden decrease in the pitch. This arises because the sound waves are closer together when moving towards the listener, but the sounds waves stretch once they make their way past the listener. This is known as the Doppler Effect! Galaxies have the same effect. Because most galaxies are moving away from us, the light is stretched. Redshift can be described, in other words, as the shift in wavelengths of light. The equation for this is z = (observed wavelength - rest wavelength)/(rest wavelength). Rest wavelength is the wavelength of a star, or galaxy, not moving. If we have the redshift (z), we can multiply it by the speed of light, which is 300,000 km/s, to find the velocity of the object.

Now that we have both the velocity and distance, we can find the Hubble Constant. The Hubble Constant is the relationship between both velocity and distance. With both values, we can plot them on a graph. If we do this using several supernovae, we can determine the slope. The slope is the value of the Hubble Constant. The Constant is defined in terms of km/s/Mpc. Mpc is an abbreviation for Mega parsecs, a distance value. That tells us how far the object is. The km/s tells us how fast that object is receding from us.

I hope this cleared up any questions you had about how I am approaching this problem. If there are any questions, feel free to leave them below. Hope you guys have a good weekend!