Image created by taking a 3x3 grid image three times in the three color filters, for a total of 81 images. All images were reduced and combined using code I wrote during the class. The final image was edited to clean up hot pixels and brighten colors in a photo editing software.

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.

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

Introduction

Gravitational lensing was a major prediction of general relativity. It says that a large concentration of mass will curve space and the light that passes close to that mass will follow that curved space. Something that is directly behind an object like a galaxy or black hole can be seen as the light that would go past it is bent around it and directed towards the other side.

**Images of lensing**

Gravitational microlensing, which this paper focuses on, is like gravitational lensing but on a smaller scale, as the name implies. Instead of objects on the scale of galaxies bending the light, we are looking at the light bent by planets and stars. This is used to detect exoplanets in a similar way to transit detection, which has the planet passing in front of a star from our perspective.

When looking at two stars, one passing in front of the other, we can see a gravitational lensing effect where the background star increases in brightness temporarily. When a planet is orbiting the foreground star, we can also see a smaller peak in brightness due to the planet passing in front of the background star.

**Images**

According to this paper, which was written in 2021, over a hundred exoplanets have been discovered from this method since the first was discovered in 2004.

The biggest advantage to this method as opposed to the transit method is that microlensing is much more sensitive for detecting small planets further from their host stars, which helps us get a better understanding of the types of planets that are common.

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. So far, only about 20 circumbinary planets have been discovered using different methods, and only 1 has been discovered using microlensing, as of the writing of this paper. It was found in 2016.

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

The lens equation

We’re not going to go through all the math here because that would take a lot longer than we have, but I do want to give a quick overview of the math.

This slide shows a single lens system. We have the deflection angle alpha, the angle beta between the lens and the source, and the angle theta between the lens and the image. Using small angle approximations because these angles are extremely small in realistic situations 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 creates the image as a ring around the lens.

So from the lens equation they give a generalized lens equation for N lenses. We have the same variables here but now they are vectors. Our alpha angle is a bit more complicated here. They then parameterize the angles in units of the Einstein angle and rewrite the lens equation in complex coordinates using those parameterized vectors.

Then we get new complex variable for the source, images, and lenses positions and a new lens equation.

Triple lens

Here is the equation they give for the triple lens system after it has been simplified a bit. It gives us five parameters to account for. The epsilons are the mass ratios for each mass in the system to the total mass, with the third one rewritten in terms of the other two. The distance of the stars is l, and the distance of the planet is l’. Phi is the angle of the system.

The paper goes through some fairly complicated and lengthy calculations to get an equation to find the total magnification for a general lens system. One of the things they wanted to do was create magnification maps which highlight where magnification is greatest.

They end up with an 18th order polynomial, with the roots of that polynomial being the individual magnification for each image. They add the absolute values of those roots to get the total magnification.

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.

Changing the variables

Using this data, they created plots simulating the change in the magnification maps and light curves based on one changing variable at a time.

When changing the mass of the planet, you can clearly see that the heavier planet in the top is much more noticeable.

When changing the distance of the planet, you can see that the farther away the planet is, the easier it is to see. This is the opposite of what we would expect from other methods like transit detection.

For the star distance, the closer the stars are, the harder it becomes to separate them and it looks like a single star and planet, but it can also be difficult to detect the planet at all. Here the planet is larger so we can see the spike in the light curve still. The second image is magnification maps for farther distances, with the planet still being visible by the star it orbits.

Changing the angle of the system shows that as the angle gets smaller, the planet becomes more visible.

For the mass of the stars, they had the two masses equal for the other sections but varied them here. The three scenarios shown are a star with two equal mass planets at the top; a star, a brown dwarf, and a planet in the middle; and two stars of unequal mass with a planet on the bottom. The ratio of the largest to smallest mass stayed the same throughout.

Conclusion

To finish out the paper, they applied their system to the one star that has been discovered using microlensing. They produced two separate magnification maps, the left one looking at it as two planets and a star, and the right as a circumbinary system.

Their conclusion talks about how they could continue to improve their data, including accounting for orbital motion and potentially adding more lenses.

            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.