The Harvard Banneker Institute Final Post

I know I have not made a new post in a while, reporting on the progress of my 2015 summer research with Dr. David Kipping, but I'm happy to say that I finished the project and I will be writing about my results below. The main purpose of this blog was for me to always keep making progress on my work because I knew that I had to write about it. This blog was mainly for me and I wrote as if I was telling myself what I did and what I still have to work on. This is why a lot of my post seemed to be "lacking details" but it's because those are post intended for me, very unorthodox writing style for blogs.

Just to summaries the main purpose of my summer research was to find the eccentricity of the planets in the planetary system EPIC 201367065 aka K2-3, the 3rd planetary system founded using the spacecraft Kepler 2. The system contains 3 planets the orbit a M-Dwarf star at a distance of 45 pc. Using these eccentricities I was able to find the if the planet's orbit is in the habitable zone, since the eccentricity determines the shape of the orbits and if the orbit is too eccentric than the planet will move out of the habitable zone.

The image below is the final plot that I made of K2-3, it shows the range of the semi-major axis of each planet, and the habitable zone in AU. I was very hopeful that my planets orbit in the habitable zone, unfortunately none of them orbit in the habitable zone. But this is only one of the characteristics that makes a planet habitable, we also need to take into account the atmospheric effects which I had no way of testing for these effects. As a scientist I must remember that my purpose is to figure out how the universe works, not show how I wanted it to work.

This summer was my best summer ever. Not only because of the things that I learned while doing research and taking grad level classes, but because of the people that I was with. My fellow Banneker students and affiliates were all people that helped me come closer towards becoming the BEST VERSION OF MYSELF. They are true friends for life and it was an honour to be a of part of the first Banneker class.

http://bannekerinstitute.fas.harvard.edu

“Walking with a friend in the dark is better than walking alone in the light.”

-Helen Keller

Day 33 Banneker Institute

This post will also be a special post, it will be about another Harvard graduate student, Luke Kelley. I was lucky enough to interview Luke about his work and the life of a graduate student. Luke also gave advise that will help future graduate students. Luke's main area of research is in massive black hole mergers. He studies what processes mediate this process, what mechanisms, and how long it takes for this process to occur.

Luke's love for Astrophysics began when he first watched Star Trek. His fascination for science took him to UC Santa Cruz where he did research in particle physics. He then change into Astrophysics where all aspects of physics are used, unlike in some Physics sub fields where only one or two aspects of Physics are used.

Graduate school differs a lot when compare to other level of education. In graduate school you suppose to be self motivated and independent. This is unlike other levels of education where you are guided trough the learning process. Luke advised undergraduate students to focus on getting research experience, and good recommendation letters that will speak about your research potential. These are the key elements that will help undergraduates get into graduate school.

Life in graduate school is also a lot different, in the sense that you choose when to work. Some work early in the morning and some late at night but the key is to not get sidetracked. Another important factor is finding a balance so you don't over work yourself.

Luke Kelley's websites and contact info:
https://www.cfa.harvard.edu/~lkelley
https://www.youtube.com/user/lzkelley

lkelley@cfa.harvard.edu

Two really interesting simulations:

https://www.youtube.com/watch?v=w7d-7Q0fGHE

https://www.youtube.com/watch?v=JVZEAA-0058

"There is no great genius without a mixture of madness."

-Aristotle

Day 32 Banneker Institute

Bayes' Theorem

Hola mundo,

Today I'll be explaining Bayes' Theorem and it's use in predicting events. The Bayes' Theorem uses a prior hypothesis based on a set of parameters and prior knowledge of the system that you are trying to predict, but you do not build a hypothesis of the model only of the result. The theorem uses a likelihood that event happening, giving that your parameters are true. The prior and the likelihood are completely independent of each other. Bayes' Theorem also uses a term named evidence (E) which in my case I am not using because it's a normalization term.

$$P(a|D) = \frac{{\Pi}(a)L(D|a)}{E}$$
$\Pi(a)$ is the prior where a is the hypothesis in the form of parameters a.

$L(D|a)$ is the likelihood where D is the data of the system in question.

I use this theorem to find the probability of getting heads after flipping a fair coin. I ran a few trials and plotted the results of the formula below.

$$P*H^{k}(1-H)^{n-k}$$
Where P is the prior, His the probability of getting heads, n is the number of trials, and k is the number of times we get heads. Below is a plot with the probability density distributions of my trials. As you can see the maximum probability of my trials are close to 0.5 which is the probability of getting heads using a fair coin if you flip the coin an infinite amount of times.

 

"Happiness is when what you think, what you say, and what you do are in harmony."

-Mahatma Gandhi

Day 31 Banneker Institute

This post is going to be different, I am not going to talk about my progress in my research, but instead about a Harvard Astronomy graduate student, Fernando Becerra. Fernando gave some advise for undergraduate students that want to go to graduate school. He spoke about the differences between graduate school and other levels of education. And he described how the lifestyle of a graduate student is like.

Fernando decided to study because he wants to understand how the physical world works. The way that he wants to do this is through the laws of Physics, and the language of Mathematics. Fernando is currently researching star formations, galaxy mergers ,and the first black holes in the universe. His work involves writing computer programs that will simulate the environments that these systems are born in. You can see some of his simulations in his website linked below.

Fernando described that biggest difference between graduate school and other levels of education is that you more independent. In High School and undergrad you mostly absorb knowledge, but graduate students generate knowledge. In graduate school is when people start to think and work like a researcher. Upcoming graduate students should have an open mind, and should know that research is not the same as the classroom. The skills needed to be a good researcher are different from the skills needed to get a good grade.

Upcoming graduate students need to able to explore to ideas and be flexible to change research projects at the beginning of their graduate careers. They need to know that academia is NOT THE ONLY PATH. Graduate school is the time to train yourself so you can obtain the skills necessary for your dream profession. In terms of the lifestyle of a graduate student, there is no one style. Everyone decides when to work and when not to work. Some people work early in the morning, and others late at night. The main thing to keep in mind is to be consistent.

Fernando's Website and Contact Information:
http://www.cfa.harvard.edu/~fbecerra
fbecerra@cfa.harvard.edu

"Even if you fall on your face, you're still moving forward."

-Victor Kiam

Day 30 Banneker Institute

I manage to fix the eccentricity calculation by changing the units to SI units. The values for the insolation of the planets is still a little strange, but I need to analyse this a little deeper.

"You must be the change you wish to see in the world."

-Mahatma Gandhi

Day 29 Banneker Institute

After calculating all of my parameters for all three planets, I noticed that the values for the insolation and the eccentricity are too large. These values don't make physical sense, but the mathematics seems to be correct. The only thing that I can do is to go back and double check my python code for any errors.

"A leader is best when people barely know he exists, when his work is done, his aim fulfilled, they will say: we did it ourselves."

-Lao Tzu

Day 28 Banneker Institute

I was able to calculate the insolation (S) and the eccentricity (e) of all three planets. The insolation of a planet is the amount of thermal energy that a planet obtains from its host star. The eccentricity is the shape of the orbit of an object as shown below.

$$e = \frac{|1 -  (\frac{\rho_{obs}}{\rho_{true}})^{2/3}|}{1 + (\frac{\rho_{obs}}{\rho_{true}})^{2/3}}$$

$$L = \frac{r_{*}^{2}*T_{*}^{4}}{T_{sun}^{4}}$$

$$S = \frac{\frac{L*a}{r_p}}{(\frac{r_{earth}}{a_{earth}})^{2}}$$

"Life is a series of natural and spontaneous changes. Don't resist them - that only creates sorrow. Let reality be reality. Let things flow naturally forward in whatever way they like."

-Lao Tzu