My role in this research paper was to test the linearity of the CCD detector attached to the 20-inch telescope we used at the Highland Road Park Observatory in Baton Rouge, Louisiana. Appendix 1 is the part that I wrote that summarizes why having proper linearity in the CCD detector is important and the methodology I used to find a cutoff point to ensure that all data collected is accurate. The code we used to organize and filter the images was written by me and I used this data to add a warning flag to any image with pixels brighter than the cutoff point, indicating that image may not give completely accurate data. I also assisted with data collection for the overall project, writing and editing parts of the rest of the paper, and writing and testing code for other parts of the project.

View the paper at the link below. 

https://drive.google.com/file/d/1lvTcL7qj_2rFKu1z3jA7tXatpsIX52Zq/view

https://drive.google.com/file/d/1CRLleM2pWSGpj8EotHHSmozhAGh6XyRw/view?usp=sharing

https://drive.google.com/file/d/1Wa84qCnanqd9R--CBhAysW3FKXQqNU3G/view?usp=sharing 

I worked with Dr. Geoffrey Clayton analyzing and organizing data from over a thousand images of a specific star and its neighbors. This star is a variable type star that Dr. Clayton specialized in researching, allowing me to gain insight from one of the top experts in this particular star type. 

***

My Distinguished Communicator project for Astronomy 1402 (Astrophysics of Stars and Galaxies) presents course relevant work using the visual and technological communication modes. I worked with my professor, Dr. Geoffrey Clayton, to analyze, organize, and plot data from a specific R Coronae Borealis star, V854 Cen.

R Coronae Borealis (RCB) stars are a rare type of star with specific properties. Their signature property is their variable brightness—changing by multiple magnitudes in as little as a few weeks—because of the extreme amount of dust they produce at seemingly random intervals. This dust blocks our ability to see these RCB stars and can lead to them significantly dropping in visibility for years at a time. The particular star we were working with was visible sporadically throughout the first half of the 1900s, but dropped out of visibility until the late 1970s.

All RCB stars are hydrogen deficient, which is very unusual since most stars are 90% Hydrogen. All stars eventually burn through their hydrogen in the core and many begin to fuse heavier elements throughout their lifetime. For the more massive stars, they will eventually supernova after burning through their hydrogen and become either a neutron star or a black hole. Less massive stars (like our sun), will not supernova, but instead shrink back down and become a very dense, small, and dim star known as a white dwarf.

RCB stars are predicted to be created from the merger of two white dwarfs in a binary system. If two low mass stars are near enough to each other when they eventually both become white dwarfs, then they can possibly merge. Many, however, will stay orbiting around each other for their entire lifetimes and never get close enough to merge.

Another major property of RCB stars is that they are rich in carbon, meaning the stars that merged to form the RCB star were fusing elements up to carbon when they were burning. These stars are thought to be in just a relatively short phase of their lifespan, emitting a lot of dust in that short span.

For this project, we took data primarily from the Harvard Observatory Plate Lightcurve database. A lightcurve is a plot of the variations of brightness of a star versus time.  We used data attributed to V854 Cen and also to two nearby stars, TYC 7810-110-1 and UCAC2 14839501. Using the data from the two nearby stars, we could compare the brightness when V854 was visible and when it was too dim to be seen by the plates. V854 had over 100 plate images in the database, while the other two stars had nearly 2000 plate images each. I exported the data from each of the plate images and used Excel to line up the data for each star from their individual and shared plates and organized it all by date, listing when the variable V854 was visible for each plate.

I then imported the newly organized data into Python to create plots showing the lightcurves of all three stars compared to the limiting magnitude (the dimmest brightness the plates could pick up) on the plates, showing the variability of V854 Cen over the nearly 100 years shown in the plate database.

The following is a paper I wrote to be my notes for my final presentation in a Modern Optics class summarizing a high-level astronomical optics paper for an audience of undergraduate physics students. It highlights my ability to distill complex information into more approachable language for a specific audience, condensing the main ideas and important take-aways into a ten minute presentation.

Link to the paper cited in the presentation:  https://arxiv.org/abs/2109.14557

Modeling the microlensing of circumbinary systems

1.        Introduction

Gravitational lensing, a key prediction of general relativity, describes the bending of light by massive objects. This phenomenon occurs when a massive object, such as a galaxy or black hole, lies between a distant light source and an observer. The massive object warps spacetime, causing light rays from the source to bend around it. This can create multiple images of the source or a distorted, magnified view.

Gravitational microlensing, the focus of the cited paper, operates on a smaller scale. Instead of objects on the scale of galaxies bending the light, we are looking at the light bent by planets and stars. This technique is used to detect exoplanets in a similar way to transit detection, which relies on the planet passing in front of a star from our perspective.

In a binary star system, one star can act as a lens for the light from the other. This results in a temporary increase in the background star's brightness. If a planet orbits the foreground star, it can also produce a smaller peak in brightness as it passes in front of the background star.

Since the first discovery of an exoplanet using microlensing in 2004, over a hundred exoplanets have been detected using this method (according to the paper, which was written in 2021). Microlensing offers a significant advantage over the transit method: it is more sensitive to small planets at larger orbital distances from their host stars, providing valuable insights into the diversity of planetary systems.

Most exoplanets discovered from other methods are orbiting a single star, but it is estimated that as many as 50% of the stars in our galaxy are a part of binary or multiple star systems. A planet that orbits a binary star system is called a circumbinary planet, and a binary star system with a known planet is called a circumbinary system. As of the writing of this paper, only around 20 circumbinary planets have been discovered using different methods, and only one has been discovered using microlensing. It was found in 2016.

The primary focus of the paper is analyzing a triple lens system using the lens equation and applying that method to the one circumbinary system found using microlensing.

2.        The Lens Equation

The lens equation describes the relationship between the deflection angle alpha (α), the angle beta (β) between the lens and the source, and the angle theta (θ) between the lens and the image. Using small angle approximations, as these angles are extremely small in realistic scenarios, gives us the lens equation.

When beta is zero (the source is aligned with the lens), we get what is called the Einstein angle. This results in the image appearing as a ring around the lens, known as an Einstein ring.

The lens equation can be generalized for N lenses. In this generalized form, the angles become vectors. The deflection angle alpha becomes more complex in this multi-lens scenario. These angles are then parameterized in units of the Einstein angle, and the lens equation is rewritten using complex coordinates. This results in new complex variables for the source, image, and lens positions, and a corresponding new lens equation.

3.        The Triple-Lens System

The simplified equation for a triple-lens system involves five parameters: the mass ratios of each mass to the total mass (ε), with the third mass ratio expressed in terms of the other two; the distance of the stars (l); the distance of the planet (l’); and the angle of the system (Φ).

The authors of the source paper performed complex calculations to derive an equation for the total magnification of a general lens system. They aimed to create magnification maps that highlight regions of highest magnification. This process resulted in an 18th-order polynomial, the roots of which represent the individual magnifications for each image. The total magnification is then calculated by summing the absolute values of these roots.

For a double lens system, they could use Mathematica to find roots and plot the magnification. This was actually impossible to do for the triple lens system so they instead evaluated the magnification at random points using a random number generator.

4.        Parameter Variation and Results

Using this data, the authors generated plots simulating changes in the magnification maps and light curves by changing one parameter at a time.

-            Planetary Mass: Increasing the planetary mass resulted in a more pronounced microlensing signal.

-            Planetary Distance: Opposite to what would be expected from transit detection, increasing the planet's distance from the stars made the microlensing signal more easily detectable.

-            Stellar Distance: Closer stellar separation made it harder to distinguish the individual stars and the planet, sometimes making planet detection difficult. At larger separations, the planet's influence remained visible near its host star.

-            System Angle: Smaller system angles led to increased planet visibility.

-            Stellar Mass Ratio: Varying the stellar mass ratio, while keeping the ratio of the largest to smallest mass constant, produced different magnification maps. Scenarios included two equal-mass stars with a planet, a star with a brown dwarf and a planet, and two unequal-mass stars with a planet.

The authors applied their model to the single circumbinary system discovered through microlensing. They generated two magnification maps: one treating the system as two planets and a star, and the other as a true circumbinary system.

5.        Conclusion

The authors concluded that their model can be further improved by incorporating orbital motion and potentially adding more lenses. This work demonstrates the power of microlensing for detecting and characterizing circumbinary planetary systems.

References

• Shvartzvald, Y., Maoz, D., & Udalski, A. (2021). Microlensing of Circumbinary Systems. arXiv preprint arXiv:2109.14557.

The following is a paper I wrote to be my notes for my final presentation in Planetary Astrophysics. In the paper and presentation, I discuss the concept of the Fermi Paradox and its potential answers, from scientific to speculative. 

***

            Humans have always been fascinated with the unknown. One of the biggest mysteries humans ponder is: “are we alone in the universe?” Physicist Enrico Fermi is quoted asking, “Where is everybody?” The question is a valid one. The universe is very old, and our solar system is relatively young. Life emerged quickly on Earth once conditions were right, so it’s reasonable to think it probably happened in other places too. Any civilization older than ours would be far more advanced than us; some estimations say that it would take only a few million years of civilization for a species to colonize a large portion of a galaxy.[1] Yet we don’t see any evidence of species that are more advanced than us. So where are they? Plenty of answers have been proposed, from us just not knowing how or what to look for to more outlandish like the Zoo Hypothesis or the Simulation Argument.[2] Occam’s Razor suggests that we go with the simplest answer that requires the least assumptions. In this case, that would mean we are alone in the universe.

            If there has been plenty of time for life to arise and advance in the universe and we still don’t see it, something must be getting in the way. This idea is known as the Great Filter.[3] It says that at some point, there is an obstacle so difficult to overcome that almost nothing makes it past. We have two options when considering the Great Filter. Either we are one of (if not the only) species to make it past the Great Filter and the universe is ours for the taking, or we have yet to reach the Great Filter and we will likely end up like every other intelligent species that hit the Filter before us.[4]

            The first option is of course the more optimistic view. We faced the Great Filter at some point in our past and somehow managed to make it through. There are a few possible contenders for the Great Filter in our past. An idea called the “Rare Earth” hypothesis says that all the necessary conditions for complex life to arise may be a very unlikely combination of circumstances.[5] Things like a star in its main sequence, a planet at the right distance to allow water, gas giants reducing the likelihood of cosmic impacts, a large moon to stabilize the orbit, plate tectonics, and the right amount of oxygen at the right time all made Earth a great place for life and having all of those may be exceedingly rare. A similar argument is called the “Gaian Bottleneck”.[6] It follows the idea that for a planet to remain habitable, it must be inhabited. The Gaian Bottleneck says that life must evolve in the right timing to keep a planet habitable and stable for future growth into complex organisms. Both ideas suggest that getting past single cell life, for one reason or another, may be the Great Filter. Asteroid impacts, gamma ray bursts, and other cosmological disasters could also sterilize a planet. It is also possible the universe is only recently stable enough to allow life to evolve for a long stretch of time, making us one of the first to make it this far.[7]

            The second option is much less optimistic. The Great Filter is ahead of us and we are likely going to face extinction one day. This option tells us that it is likely aliens reached around where we are in other parts of the universe, but something killed them all off before getting much further. This could be some inevitable advancement that has catastrophic consequences. Or maybe intelligent life is just adept at wiping themselves out; nuclear apocalypse, biological weapons, runaway climate change, super bugs or viruses, or even an AI Singularity all have the potential to be Great Filters.[8] There could also be a hard limit to technological advancement or other existential risks we haven’t even considered yet.

            One of the more terrifying possible future Filters is the Dark Forest theory. This is an artificial Great Filter, but not one of our own creation. The Dark Forest says that somewhere in the universe is a hyper advanced civilization that eliminates any life that gets past a certain point.[9] They could use something like berserker probes, an object that could ram a planet or star at a significant fraction of the speed of light, completely obliterating any life before they even would have seen it coming.[10] This is a terrifying idea and just the thought of it could prevent other intelligent species from trying to communicate with the universe. Or maybe they have already targeted us, and their berserkers just haven’t gotten here yet. It’s possible that a species that advanced would have moved completely past violence though, making this a primitive idea.

            Wherever the Great Filter is, finding life in our solar system could be a very bad sign. Single cell life would still support a Gaian Bottleneck, but anything more complex than would be both one of the greatest and worst discoveries of all time. It would suggest that complex life evolves frequently and that the Great Filter is almost definitely ahead of us.

            From what we currently see, we are the only intelligent life in the universe, or at least anywhere close to us. Life may be abundant, but something seems to prevent it from advancing too far. What seems to make the most sense is the Gaian Bottleneck being the largest Great Filter to life getting past single cell life forms. We are possibly the first to make it this far and we likely have some huge hurdles (though not necessarily Filters) to overcome in the future. If we survive, we may become one of the first spacefaring, super-intelligent civilizations to ever emerge in the universe. 

[1] (Urban, 2014)

[2] (Webb, 2015)

[3] (Urban, 2014)

[4] (Urban, 2014)

[5] (Adler, 2022)

[6] (Chopra & Lineweaver, 2016)

[7] (Urban, 2014)

[8] (Webb, 2015)

[9] (Urban, 2014)

[10] (Webb, 2015)

Works Cited

Adler, D. (2022, July 29). Rare Earth hypothesis: Why we might really be alone in the universe. Retrieved from Astronomy.com: https://astronomy.com/news/2022/07/rare-earth-hypothesis-why-we-might-really-be-alone-in-the-universe

Chopra, A., & Lineweaver, C. (2016). The Case for a Gaian Bottleneck: The Biology of Habitability. Astrobiology.

Urban, T. (2014, May 21). The Fermi Paradox. Retrieved from Wait But Why: https://waitbutwhy.com/2014/05/fermi-paradox.html

Webb, S. (2015). If the Universe is Teeming with Aliens... Where is Everybody? Springer International Publishing.