Quick update, I went to JPL this Summer!!!!!!

I go to AAS!

The last few year have been a series of amazing experiences, and it has been incredible to spend this week presenting my research at the 231st Meeting of the American Astronomical Society! Check out the full text of the poster here!

This year

We are bounded in a nutshell of Infinite Space: Week 12: Free Form #17: This year

One more semester is about to end. I’ve been a year at Harvard, and it’s hard to believe 4 seasons have gone by. But this year has only gone by so quickly simply because of the sheer lack of pause. Every day, there are more than enough activities and events of every kind, be it presentations, classes, concerts, free food, or incredible opportunities. One such use of my time has been this class, Astronomy 16, an introduction to the physics of stars, planets, and the formation of the individual objects we study. After taking astronomy 17 last semester, I guess I had a bit of an insight going into the class, being less daunted by most of the material, and comfortable with the style of the class.

This being said, the difficulty between the courses was hardly noticeable, both requiring different approaches to learning and facing different kinds of problems astronomy is constantly berated with. From finding ways to cope with a huge source of light blocking our view for most of the day (Thank you, Sun, we love you (and need you to survive)), to coming to terms with only seeing the past as we look at the stars, Astronomy certainly has its unconventional problems. Furthermore, the portions of astronomical thought which deal with these realities (so pretty much all of it), are my favorite parts of the discipline. Throughout the semester, we consistently dealt with the origin of the light we see, stars and other objects which tell us how “life” (?) is in other sectors of the cosmos, and understanding the radiative processes have been my favorite components of the semester. However, I need to give a shout out to binary and locked systems, because actually observing one during a lab project and the exoplanet challenge was amazing!

Hello Mr Planet!

The most difficult parts of the semester would probably be the portions of the class when quantum mechanics, astrochemistry, and similar topics which became very abstract. Notwithstanding, I enjoyed these portions as much as the rest of the class, understanding these components to be integral in comprehending the way all the processes of astronomy work and the way we are currently able to observe anything at all. Without a doubt, this semester became easier than the last one had been, in part I am sure because of just being here longer and knowing what pace needed to be kept, but also because I’ve started to feel more comfortable, more at home in this occasional frozen-over hell, but truly hopeful of the next stages of college life, and learning more and more about this strange and beautiful universe we inhabit.  

I'll let the pictures do the talking

We are bounded in a nutshell of Infinite Space: Week 11: Free Form #16: I'll let the pictures do the talking 

 Stephen Hawing came to Harvard. Possibly one of the most influential physicists, cosmologists, science promoters, writers, of the last century, Dr. Hawking is a true stalwart. Not only because of his disability and the drive it takes to continue living and working to change the world, he is an unadulterated view of someone who has fought every step of the way to finally be the top in their field. Now, he came to Harvard as part of the opening of the Black Hole Initiative (hopefully I get a chance to work there for a while), where mathematicians, physicists, philosophers, and astrophysicists will work on better understanding the nature of black holes and the important role they play for the universe. Professor Hawking, on his part, went on to give a full lecture on quantum black holes. He started out with the basic premises, the nature of general relativity and space time, to later move on to the more interesting portions. The talk shifted to Schwarzschild, the dawn of the theory of black holes, and then to Richard Feynman and Arthur Penrose, people who further developed the theory and saw the consequences of black holes on structure formation. 

He then spoke of the components of black hole theory he had established in the past, especially the understanding of how black holes begin to fade due to radiation emission, called Hawking Radiation. This allows for a black hole to disappear after a great deal of time, but in this come the theoretical and frontiers of new black hole science: information theory. This aspect of black holes, thought up by Hawking, Strominger, and Perry, attempts to explain how black holes are a way that, originally, information could be completely vanished from the universe. Imagine you were to place an encyclopedia into a black hole, all the pages with all their facts would fall towards the singularity, ripped apart by tidal forces and spaghettified (for not humongous black holes), never to be seen again in our universe (yes, he got into the idea that black holes could very well be a gateway to another dimension). However, this is where the idea becomes very interesting, for black holes grow larger and their radius expands as they become more massive, as more things are thrown into it, and as the black hole eventually radiates out its existence, in theory the information first lost beyond the event horizon could come back in the form of thermal energy, technically not impossible to be turned into physical matter with all the pages on the Rhine, rhinitis, and rhinoceroses. If you want to learn more on how these black holes become the unification of quantum mechanics and general relativity, one of the main pursuits of modern physics. 

A Night at the Observatory

We are bounded in a nutshell of Infinite Space: Week 11: Free Form #15: A Night at the Observatory

Oh to be doing the Exoplanet Challenge. Here I am, awake during the daytime after being conscious throughout the night, and the weight on my eyelids is as strong as its ever going to be, and the fact I tried reading Plato this morning for my Ancient Greek class didn’t help at all. These are the thoughts that echo after spending last night (this morning) looking at HAT P 37b, a transiting exoplanet crossing in front of a star found in the Draco Constellation. As part of the Astronomy 16 course, we have the option of taking on the Exoplanet Challenge, a chance to use some of the more advanced tools available to undergraduates to try and find evidence of a planet crossing in front of a star we are observing. The challenge gives the unique opportunity of having to go up to the 8th floor of the Harvard Science Center, open the Astronomy Lab, and start prepping for the use of the Clay Telescope, all on our own (in groups of 2 or 3). As such, my partner and I went up to the telescope at midnight, set up all the systems, and waited until we had the data to be analyzed to find evidence of the transit and understand what it means. However, around 4:30 am, as we made the second batch of warm water for tea and coffee, we started comparing the photometry (brightness signatures) from the stars, waning to be sure we had indeed looked at the right object. As we plotted the graph, we could hardly make sense of the data, it shifting several times and having strange reference stars of which the main object’s signature was calculated by the software. We were lost for a bit. Soon after, around 5:30 am, the Sun started coming up on the horizon, and as such we started closing up shop and preparing to leave to a proximate future of a couch somewhere near. Leaving, we weren’t sure we had done it correctly, even though there was no step we could have missed, and we worried over having to go through this ordeal again.  

All this being said, we definitely lucked out with weather. And as we spoke coming out of the building, we knew there were slight places to grow and be more precise. We also understood that there was a definite value to being in the observatory all night, seeing how the sky moved throughout the night, and having the lab became not only be workspace, but starting to see it and the telescope as an extension of our senses. We grew to appreciate the instrument, and be fond of it the way one is of ones hands and eyes, but now having a dear appreciation of how they allow us to peer into the unknown. Ultimately, we were able to fix the data analysis, seeing as how we were using bad stars as references, and with the correction we could now clearly make out the light curve of the planet transit, the white whale we had been hunting throughout the night, with a better understanding of how difficult the job of the hunting sea captain, the searching astronomer, is, and what he can become.

Squiggle Math III, The Time Conundrum

We are bounded in a nutshell of Infinite Space: Week 11: Worksheet #20: Problem #2: Squiggle Math III, The Time Conundrum

2.

a. Time for some more squiggle math!! So from the previous problem on this worksheet relating temperature, luminosity, and the distance between the star and the object, we can rewrite it in terms of its variables as: \[ T \sim L_\star^{1/4} a^{-1/2},\] but since the temperature we can consider it to be constant for the purposes of this problem, we find that:  \[ a^{1/2} \sim L_\star^{1/4}\]

b. We can take the previous result relating the temperature to the distance, and find the relationship is also: \[ a^2 \sim L .\] Also, we know from a previous worksheet we did a couple of months ago that luminosity and mass are inherently linked in a star, which can be described with its proportion as:  \[ L \sim\ M^4,\] and by plugging these in, we find that:  \[ a^2 \sim M^4\] \[ a \sim M^2,\] which means \[ a_{HZ} \sim M_\star^2 ,\] where the looked for variable becomes: \[ \alpha = 2\]

c.  Furthermore, we can use these proportions to establish how Kepler’s third law works according to squiggle math: \[ P^2 = \frac{4\pi^2 a^3}{G M_\star}, \] becomes \[ P^2 \sim \frac{a^3}{M_\star} ,\] and according to our previous part, we can substitute in and find that: \[ P^2 \sim \frac{M_\star^{2^{3}} }{M_\star},\] which means \[ P^2 \sim M_\star^5\] \[ P \sim M^{5/2}.\]

Now, we want ot find the period of the Earth if the Sun were half its current mass, such that: \[ P \sim \left(\frac{1}{2} M_\star \right)^{5/2} ,\] turns into  \[ P \sim {\frac{1}{2}}^\frac{5}{2} M_\star^{5/2}\] \[ \sqrt{32} P \sim M_\star^{5/2},\] which means the new Earth period is related to the original period by:  \[ \frac{1}{\sqrt{32}} P_\oplus = P_{\frac{1}{2} M_\star },\] and thus, the Period of rotation becomes \[  P_{\frac{1}{2} M_\star} = \frac{365}{\sqrt{32} } = 64 ~days,\] our new definition of a year.

This is where you live

We are bounded in a nutshell of Infinite Space: Week 11: Worksheet #20: Problem #1: This is where you live 

1.

a.

b. For this problem, we are attempting to find the range of the distance around a star in which a planet may have liquid water, what we know as the habitable zone. In order to understand this, we must find the correlation of temperature and the brightness of stellar objects. For a planet, we know the Flux it receives from the star it orbits is: \[ \frac{L_\star}{4\pi a^2}  = F_P ,\] which can be re written to better represent all the energy impacting the planet in a specified time: \[ F = \frac{Energy}{time \cdot area}\] \[   \frac{L_\star}{4\pi a^2} \cdot \pi R_P^2 = \frac{Energy}{time}~received~by~planet\]

Furthermore, we should understand the energy the planet then radiates back into space, which can be described with the equation for bolometric flux: \[F = \sigma T_P^4,\] and from previous worksheets we know that the flux can be turned into luminosity by just multiplying by the surface area \[ L_P = \sigma T_P^4 \cdot 4\pi R_P^2\]  

c. Next we set these equations equal to each other and find the expression for the temperature of the planet: \[   \frac{L_\star}{4\pi a^2} \cdot \pi R_P^2 = \frac{Energy}{time}~received~by~planet = L_P = \sigma T_P^4 \cdot 4\pi R_P^2\]  \[   \frac{L_\star}{4\pi a^2} \cdot \pi R_P^2 = \sigma T_P^4 \cdot 4\pi R_P^2,\] we start simplifying the equation and find that \[ \frac{L_\star}{4a^2} = \sigma T_P^4 \cdot 4\pi ,\] which finally turns into: \[ T_P = \left(\frac{L_\star}{16 a^2 \pi \sigma}\right)^{1/4}\]

Also, we can keep on simplifying the expression were we to consider the definition of the star’s luminosity: \[L_\star = 4\pi R_\star^2 \cdot \sigma T_{eff}^4,\] which can be placed into the equation we just derived to further understand the factors involved: \[ T_P = \left(\frac{4\pi R_\star^2 \cdot \sigma T_{eff}^4}{16 a^2 \pi \sigma}\right)^{1/4},\] \[ T_P = \left(\frac{ R_\star^2 T_{eff}^4}{4 a^2 }\right)^{1/4},\] This results in the simplified version of the equation which expresses the relationship between the planet’s temperature, and the radius and temperature of the star: \[ T_P = T_{eff} \sqrt{\frac{R_\star}{2a}}\]

d. As we can see from the equations, the radius of the planet becomes insignificant, it not being a factor in establishing the temperature of the planet, rather the radius of the star comes into play.  

e. Now, we can assume some energy gets reflected from the surface, yielding an equation similar to: \[ T_P = \left(\frac{L_\star}{16 a^2 \pi \sigma}\right)^{1/4},\] but where A is the energy per time reflected: \[ T_P = \left(\frac{L_\star - A}{16 a^2 \pi \sigma}\right)^{1/4},\] which simplifies to: \[ T_P = T_{eff} \sqrt{\frac{R_\star}{2a}} - \left(\frac{A}{16 a^2 \pi \sigma}\right)^{1/4}.\] Therefore, the temperature most definitely goes down as the reflectivity increases.