This is my BS thesis with Prof. Pawan Kumar (UT, Austin). I am exploring Alfven wave propagation in an ultra-strong magnetic field (e.g., in a magnetar) and how it can generate coherent radio emission. This is a proposed model to explain Fast Radio Bursts (FRBs).

 I'm doing Particle-In-Cell (PIC) simulations using the TRISTAN code and analytical calculations to explore this problem. 

STATUS:

 Work in progress... I'll keep this updated as I make progress

My first astrophysics project with Prof. Banibrata Mukhopadhyay focused on the dynamical states of GRS 1915+105 (GRS), specifically analyzing whether its temporal classes were driven by chaotic dynamics or stochastic processes responsible for the observed variability in luminosity.

 After verifying the well-known dynamical states of GRS, I was introduced to IGR J17091-3624 (IGR), a source considered a "twin" of GRS. However, IGR's low photon count and high Poisson noise contamination made it challenging to distinguish true stochastic dynamics from noise using standard non-linear time series analysis. I saw this as an opportunity to apply my experience in noise filtering from a previous research project in atmospheric physics.

 I began by denoising the IGR light curves using simple moving averages, which significantly improved the signal-to-noise ratio and revealed deterministic behavior in certain temporal classes. Motivated by these results, I tested various filtering algorithms to minimize Poisson noise and employed newer unsupervised machine learning algorithms to distinguish between deterministic and stochastic classes.

 To our surprise, we discovered that IGR exhibits transitions between deterministic and stochastic dynamics similar to GRS, reinforcing the idea that these sources are indeed "twins" in terms of their dynamics. We have since written a manuscript detailing our findings.

STATUS:

• Submitted to ApJ!

• Presented at ISRA 2023 (Sikkim, India)

• Abstract selected at AstroAI 2024 conference by Harvard-Smithsonian CfA!

This was a very interesting problem that Prof. Christian Fendt (MPIA) gave me: 

How do you incorporate the effect of gravity on the galactic scale into GR-MHD simulations of AGN jet launching (a much smaller length scale)?

 My first idea was to use the weak-field limit of GR; i.e., I can add the galaxies (Newtonian) potential as a correction term to the Kerr background metric of the black hole. This would connect the weak curvature of space-time due to the galaxy at faraway regions (essentially Newtonian gravity) to the strong gravity near the black hole, where the curvature due to the Kerr metric part dominates. Quite simple, really!

 But, there is a problem with the way the HARM code implements the metric! All the metric components and their derivatives (i.e., Christoffel symbols, Riemann, Ricci, etc.) have been hard-coded with a particular choice of coordinates. So I could not simply add a correction term to the metric and call it a day. 

I came up with another idea... 

What if we model the galaxy's gravity as an external force acting on the plasma without changing the Kerr metric background? 

You see, in GR, the "force" of gravity is not really a force! It's a kinematic effect where test particles follow straight lines in curved space (a.k.a geodesics). This checks out only when the underlying metric is derived from the entire stress tensor,  globally. If I don't allow the galaxy's stress tensor to affect our black hole's metric (for numerical convenience), a test particle's motion solely under the effect of gravity will not follow the geodesics of the Kerr metric! The external gravity will manifest as a 4-force acting on the particles, causing them to deviate from the perfect geodesics.

 In practice, this introduces additional flux terms in the GR-MHD system of equations. I perturbatively calculated all these extra terms (up to first-order), which can be easily implemented in HARM. This method is useful because it works without drastically changing its architecture yet capturing the same physics!

I was given this problem by Prof. Christian Fendt (MPIA). Firstly, I had to learn the complete theory of ideal GR-MHD and the effect of magnetic diffusion (non-zero resistivity). I then learned about the primitive-variable solver techniques used for codes like HARM. In short, it was an intensive and rewarding learning experience!

 The research problem involved identifying the terms in the resistive GR-MHD equations responsible for Ohmic heating in accreting plasma. Higher heating rates increase thermal pressure, causing the disk to "puff" up. In non-relativistic MHD simulations, an "instantaneous" cooling term can be added to the energy equation to study the effect of Ohmic dissipation on disk dynamics by controlling the extent of heating. The goal was to apply a similar approach in resistive GR-MHD codes like rHARM, developed by Prof. Fendt's group.

 In standard GR-MHD, we evolve the combined stress tensor of the electromagnetic field and plasma. However, I figured that to isolate Ohmic dissipation, which converts electromagnetic energy into thermal energy in the co-moving frame of the fluid, one needs to track the evolution of the individual fluid and electromagnetic stress tensors! The total stress tensor can be conserved with or without Ohmic dissipation, meaning no explicit term in the resistive GR-MHD equations captures this process.

 To address this, I proposed a modified set of equations that would allow us to control the energy-momentum exchange between matter and the electromagnetic field. Essentially, my idea was to evolve the field and the fluid stress tensors separately, such that the interaction between the two becomes explicit. These can be implemented in a future iteration of the rHARM code. 

Apart from learning an absolutely essential tool for astrophysics, this project was highly instructive in another aspect: formalizing a research problem, understanding its physical implications, and working within the constraints of available resources such as algorithms and codes.

I went to ARIES, Nainital during the summer of 2023 to work with Dr. Saurabh Sharma to study star formation in globular clusters. Primarily, this was a training in observational astrophysics. 

I was fortunate to have learned to operate and use the 3.6 m Devasthal Optical Telescope (DOT), India's largest optical telescope!

 My focus was studying the globular cluster NGC 2316. Starting from data reduction using PyRAF/ IRAF to photometry, it was an immensely rewarding learning experience. For this project, I also did photometry with infrared data from 2MASS. To convert the measured apparent magnitude of my source of interest to absolute magnitude, I parallelly did photometry for the standard Landolt field: SA-98, whose absolute magnitudes are known. What I admire the most about this field of research is "precision." Absolutely no stone is left unturned to remove every known source of error; truly, the devil lies in the details! 

To study the kinematics of this cluster, I used Gaia DR3 proper motion data of some stars from NGC 2316 and calculated the membership probabilities. 

True to my nature, I saw scope for optimizing the workflow and wrote a Python pipeline to automate the entire photometry and kinematic analysis; this allowed me to focus more on the underlying physics rather than just the process. I also introduced a new clustering algorithm based on DBSCAN to evaluate the membership probabilities of the stars.

 All in all, the two months spent in the foothills of the Himalayas, traveling 4 hours by bus through the mountainous forests every day- 5 days a week - each week, staying up 5 nights at the observatory with cup-noodles and bone-shattering cold... all the while doing something I really love. I couldn't ask for more!

In my 2nd year, I took a "General Relativity and Cosmology" course by Prof. Rajeev Kr. Jain. As a part of this course, we had to do a project on a related topic to this field given by our instructor. 

I was interested in emergent gravity and analog gravity models even before entering university. So, I took this opportunity to propose this new project idea to my professor, and he happily agreed.

 In very plain words, the idea is this: we can form a mathematical duality between the physics of condensed matter systems and the kinematics of matter/ radiation in curved space-time. For example, one can study the propagation of a sound wave packet in a barotropic fluid with a background flow and map it to null-geodesics of photons in a curved spacetime given by a corresponding metric. The key-word here is kinematics! : analog models of gravity don't try to emulate Einstein's field equation to evolve the metric dynamically. Hence, it works best for massless, minimally coupled particles. 

A similar theoretical setup can also be done with a coherent quantum system, such as Bose-Einstein condensates (BEC), to experiment with curved spacetime quantum field theory on a lab scale. This is extremely useful for better understanding and validating theoretical models in cosmology, such as inflation, baryogenesis, etc. 

In this project, I derived the Gross-Pitaevskii equations for the dynamics of a weakly interacting BEC, starting from the second quantization of a boson field using the mean-field theory approach. I used it to derive the "acoustic metric," whose null-geodesics give the equations of motion of phonons in the condensates. I analyzed the setup of the "analog" of the FLRW metric in an atomic BEC. I discussed how recent experiments have successfully used these analogies to demonstrate cosmological principles in the lab. I went to the extent of emailing authors of various studies in analog gravity experiments and interviewing grad students who did these experiments! 🙃

 In summary, for me, this project was a harmony between GR, cosmology, condensed matter physics, and experiments. With a much better understanding of analog gravity from this project, I firmly believe that it has the potential to be a handy tool to validate a lot of theories and possibly discover yet unknown physical effects that can help refine the standard model of cosmology. At least mathematically, the correspondence is gratifying. I am glad that I chose to do something out of the box!