Hurray! After the long and stressful application process, we finally got the acceptance email from Incubate Nepal. A marvelous journey of exploration awaited us. Who would have thought these two months will be the most challenging, yet productive and fun? Who would have thought that 26 different strangers from different corners of Nepal would be an integral part of this beautiful Incubate Nepal family?
Five multi-disciplinary teams: Team Kishan, Team Drishti, Team Arthasastra, Team Diabeters, and Team Brahmanda were formed with a mentor in each team. Everything in nature is believed to be made up of five basic elements: earth, water, fire, air, and space; each element with their distinct characteristics giving their own contribution which is quite similar to our team Brahmanda. We were five different individuals having different skill sets, views, and perceptions but when we got united, we formed our own Universe(termed as Brahmanda in Nepali)
The drive for understanding the Universe where we live led us to conduct our research on the topic “Exploring the history and the fate of the universe.” Our ultimate goal was to calculate the approximate density of the dark matter of the Universe, but before taking such a giant leap, we needed to build up a strong foundation of theoretical understanding. What is the Universe? How is it expanding? What are the factors that make it expand? These were a few questions that we wanted to understand to have a clear picture of the dynamics of the universe. So, we spent ample time on the theories that gave answers to those questions.
The Big Picture
The Universe is simply everything we can feel, sense, or detect, including us, other living beings, planets, stars, galaxies, and all the different forms of matter and energy. It began to expand 13.8 billion years ago and has continued to expand ever since.
We human beings, compared to the Universe, are merely even the size of an atom. But this has never confined us from exploring and delving deeper into the mysteries that are yet to be unraveled like the mysterious “95 percent” of the Universe. However, we are unknown about this huge portion of the Universe because all the planets, stars, and galaxies we see today only make up to 5 percent of the Universe. Our research was on this same matter that we knew was there, but we couldn’t see/observe it.
Universe: a balloon
We mentioned earlier that the Universe has been expanding, but what does it mean? In the first few weeks, we studied intensely why the Universe is expanding? When scientists talk about the expansion of the Universe, they suggest that the expansion has been growing ever since it began with the Big Bang. The galaxies outside of our own are moving away from us, and the ones that are farthest away are moving the fastest.
Let’s make it simple, take a balloon, draw a few dots using a marker. Now, blow up the balloon. Think of this balloon as our Universe and the points as the galaxies. We can observe that the points are moving farther away from each other, which means that all the galaxies are moving away from each other. There is no centre of expansion; everything is moving away from everything else. While talking about the expansion, we can never leave out two crucial elements that have shaped the way we define the expansion: Dark Matter and Dark Energy. While the name might suggest it to be some mysterious demonic substance, its existence is scientifically inclined.
You can’t see me!
So, what’s the matter with dark matter? The Universe is full of exhilarating mysteries, and ‘Dark Matter’ is no stranger to it. Dark matter is the term given to non-luminous mass whose presence is presumed from the gravitational effects. By non-luminous, it means something that does not interact with electromagnetic radiation making it “invisible”. The story of Dark matter started when a Swiss astronomer, Fritz Zwicky, detected a phenomenon, which would later change how we see the Universe. In 1933, while trying to calculate the mass of the Coma cluster using two methods: rotation curves and mass-luminosity ratio, he found that the average mass of the cluster measured from rotational curves was about 100 times more than the expected mass calculated from Mass-light ratio. Staggering, isn’t it? Thus, he termed the phenomenon as ‘Dunkle Materie’, a German word later translated as ‘dark matter’.
This discovery made by Zwicky languished for decades. But an American astronomer Vera Rubin brought light to it in the 1970s while observing spectra of stars in the Andromeda Galaxy to determine their velocities. Vera found something strange in the behavior of stars. She found that the rotation curve of the stars in the galaxy was flat, which could mean only one thing: the stars in the outer spirals of the galaxy were orbiting at the same speed as stars near the center. More astounding, the stars in the outer spirals were orbiting so fast that they should have flown apart. There was no ample amount of luminous mass to hold the galaxy together, so there must be something mysterious. Dark matter is responsible for the Universe to hold onto itself as it provides the extra gravitational force necessary for the Universe to stay put even if it’s expanding.
We don’t know much about the dark matter except the fact that it exists. It’s more common than ordinary matter and doesn’t interact with normal matter or itself except gravitationally. It is presumed that the dark matter accounts for approximately 25% of the energy density of the Universe. The discovery of dark matter has revolutionized how we see the Universe and has pushed scientists to their limits to unravel this uncanny substance.
Hold on my beer! I am the cause.
Dark energy is the name given to the cause of a bizarre phenomenon accelerating the Universe’s expansion. So hypothetically, it is some sort of energy intrinsic to space which has anti-gravitational effects. Since we don’t know much about it, there are different assumptions regarding the obsolete expansion of the Universe. The idea of the cosmological constant is one hypothesis, while there are lots and lots of speculations on this. Some even argue that it might be some property of the space itself caused by the outward pressure caused during vacuum field fluctuation. On the one hand, these mysteries are so distressing; on the other hand, these are the frontier of cosmology. There are so many things about the scaffolds of these peculiar things yet to be unveiled. It makes young physics enthusiasts, like us, fascinated by these sorts of mysteries.
Likewise, we had talked about the uncertainties that one might get while trying to calculate the amount of dark energy in the Universe. Since it would only add to more confusion and error, we decided not to be involved much with the dark energy term in Friedmann’s equation.
I decide the Universe’s fate!
Friedmann’s equations are the sets of equations that represent the war between gravity and dark matter and also govern the expansion of the Universe. Rather than complex General Relativity, we derived the Friedmann equations using the simple Newtonian Mechanics assuming that our Universe is ‘isotropic’ and ‘homogeneous’, meaning that it is the same in all the directions. This equation has helped us understand how the matter present in the Universe affects its expansion. ‘K’, in the aforementioned equation, deals with the geometrical curvature of space, whereas ‘a’ deals with the scale factor of the expansion. Another application of the Friedmann equation is it can be used to determine the age of the Universe. We first calculated the dark matter density in the Universe and plugged in that value in the Friedmann equation and by integrating this equation. And using simple mathematical manipulations, we could determine the age of the Universe. Though the age we calculated was not exact, the result was quite close to the right value.
Furthermore, with the Friedmann equations and the Laws of Thermodynamics, we then derived the continuity equation, which tells us how the density of the matter and energy changes as the Universe expands. Along with the derivation of formulae, we also focused on its application by solving different olympiad problems. It helped us to find out and understand the actual meaning of those formulae.
Since our predetermined goal was to find the density of the dark matter present in the Universe, we worked on finding out several ways to do this. Velocity dispersion, Virial theorem, Gravitational lensing, and X-ray emission are quite famous methods for measurement of the density of galaxies. We agreed to choose the ‘velocity dispersion’ method. In astronomy, the velocity dispersion (σ) is the statistical dispersion of velocities about the mean velocity for a group of astronomical objects. For this, we need radial velocity, which can be gained from astronomical spectroscopy.
How can you forget me? I am omnipresent.
Many scientific discoveries result from serendipity. Cosmic Microwave Background (CMB) radiation also falls under the same hood. In 1964, Physicists Arno A. Penzias and Robert W. Wilson were using the antenna in Holmdel, New Jersey, to study the Milky Way when they started hearing some parasitic noises. They initially thought the noise was coming due to the malfunctioning of their devices, which led them to check every nook and corner- but the noise remained. Penzias and Wilson took no time to contact their colleagues at Princeton University and tell them about this incident. Unbelievably, one of the astrophysicists John Peebles immediately remarked that the experiments had detected the cosmic microwave background radiation, which was predicted years earlier by scientists like Ralph Apher. This discovery led them to win the Nobel Prize in 1978.
The Universe is believed to be opaque during its initial moments because no photon of that time is observable. But about 380,000 years later, the expansion had dilated the Universe enough for photons to start moving freely, creating the CMB. The discovery of CMB was a huge deal to the scientific community. It supported the claims of the big bang theory and made it the best theory that describes the birth and evolution of the Universe.
Our earlier expectations
After we spent the first few weeks learning equations and understanding the concepts, we had to search for the exact data to estimate the density of dark matter. We chose to study M31 (Andromeda galaxy) in-depth to understand the distribution of dark matter throughout its volume and generalise later to the whole universe. We had expected that the statistical dispersion of the velocities of the mean velocities of star clusters in the galaxy can help us derive the mass of the cluster using the Virial theorem. The virial theorem relates the total kinetic energy with the potential energy of a system. To make our research accurate, we also decided to follow X-ray emission methods.
How scientists discovered dark matter using an X-ray technique has an exciting story. They detected an unidentified 3.5kev spectral line originally in Andromeda and different other galaxy clusters. Although several X-ray detectors detected the line, the origin was still unclear, but they found out the possibility that the observed line is a signal from decaying dark matter particles. The data to use in this method could be extracted from sources like XMM Newton Telescope and Chandra X-ray observatory. The mathematical calculations also seemed to be more comfortable. We searched for data from those sources with the hope of studying and drawing out the conclusions by analyzing the velocity and the spectral lines. We eventually found out that the X-ray emission method could only be used for the detection of dark matter and not for the calculation of its density. So, we had to change the entire process that we were planning to work on. This journey of choosing different methods, failing, and then opting for other ideas taught us a lot of essential skills. For instance, we learned how to read research papers and to extract accurate data from different sources. The most challenging task for us was to find the relevant information from a pool of data and papers, but this journey was a learning process for all of us. We spent countless hours surfing through the internet, finding reliable data, and understanding the research papers. There were even times when the paper we were reading made no sense to us, but that didn’t stop us from exploring more! Prof. Robert Scherrer from Vanderbilt University also helped us throughout our journey to search and find relevant papers to our research work for which we are always grateful to him.
Our current work in brief
Since the method we chose didn’t seem to work out, we did a review of research works that does the study of the density profile in the andromeda galaxy. Yet again, we had to go through bulks of paper and, at the same time, work on the data extraction and plotting. So, we divided our tasks according to our knowledge and skills in different fields. It helped us achieve more in a shorter time. We extracted data from those papers and plotted the graph of mass VS radius and velocity VS radius graph. We also plotted a new density profile graph of both luminous and non-luminous matter with the help of the mass-radius profile we obtained. We then hypothesized a ratio of stellar mass and non-luminous mass of M31 to assume a general ratio of densities of observable and non-observable matter throughout the universe. We are working to create a review research paper that sums up all the things we have done in this project.
All things considered, what we talked about and read about was based on some sort of theories. We have to wait and watch-and be alive- to see what the future-universe holds for us.
Even these descriptions will fail to describe the experience we have gained over these two months. From the lame inside jokes to the late-night meetings, everything has given us life-long memories to cherish forever. Years later, when we look back at our pictures and remember memories we made, we will have a broad smile on our faces and will still be thanking the whole Incubate Nepal family for such a great experience. And no matter where our destiny will take us, we will always be a part of this beautiful family.