Shubham

Research Overview

Below, I provide a slightly more elaborate (and mostly self-contained) overview of my research. Still, the best way to learn about my research is to read my articles. You can find them on the Publications page.

Background

Laser Interferometer Space Antenna (LISA)

LISA image
Figure 1: The space-based gravitational wave observatory LISA. Image from ESA.

I primarily work on developing the data analysis pipeline in various contexts (as you will see below) for the upcoming space-based gravitational wave observatory, i.e. the Laser Interferometer Space Antenna (LISA) (NASA). LISA was recently adopted by the European Space Agency (ESA), and is on track to be launched sometime in the middle of the next decade (ESA). Notably, the milli-Hz frequency band of LISA will be sensitive to many source-types, including a swarm of compact binaries evolving in the Milky Way, supermassive black hole binaries in the late-inspiral stage, and extreme-mass-ratio inspirals (EMRIs) in which a stellar-mass black hole is gravitationally bound to a supermassive black hole (LISA Collaboration). EMRIs are the primary target of my study.

Extreme-mass-ratio inspirals (EMRIs)

Figure 2: Animation of a late-stage extreme-mass-ratio inspiral. Credits: Steve Drasco, MPIGP (AEI), Potsdam.

EMRIs are inspirals of a compact object (CO) — most relevant to the context of LISA a stellar-origin black hole with mass \(\sim 10 M_\odot\) — orbiting a supermassive black hole (MBH) of mass \(\sim 10^6 M_\odot\). Their gravitational wave signals are expected to spend years in the LISA band spanning hundreds of thousands of strong-field orbits. This will allow a unique opportunity to map the curvature of spacetime around MBHs, testing General Relativity (GR) to unprecedented precision. In addition, any environmental forces (for e.g. from an accretion disk surrounding the MBH) will have a cummulative effect on the binary’s long-term inspiral, making measurements extremely sensitive to such effects.

Measurability of “Beyond-Vacuum-GR” effects in EMRIs

biases intrinsic
Figure 3: Biases induced on the EMRI's intrinsic parameters due to an environmental effect in the signal which was not accounted for in the inference. The biases scaled by the \(1\sigma\) measurement precision on each parameter are plotted along the vertical axis, showing biases of order \(10-100\sigma\). The horizontal axis shows the average correlations of the intrinsic and the unmeasured environmental effect parameter, showing a weak trend. Diagram from Kejriwal et al. (2023).

Mathematically, environmental effects and beyond-GR modifications are generally expressed using simple power law expressions, added perturbatively to the leading-order equations of motion of the binary, see e.g. Kocsis et al. (2011) and Barausse et al. (2014), or directly to the final waveform in frequency domain, see e.g. Yunes and Pretorius (2009). When multiple such effects, which we generically tag as “beyond-vacuum-GR” effects, are being tested for during inference, the general expectation in the literature is then that they can simply be added together. However, using a generic mathematical framework, we show in our work (Kejriwal et al. (2023)), that such setups can lead to extremely correlated posterior surfaces. Along with worsened inference efficiency, this also degrades the precision with which EMRI parameters can be measured. On the flip side, if such effects are excluded from the analysis but are present in the true signal, this can significantly bias the inference of EMRI’s intrinsic parameters (more than \(10\sigma\)), effectively washing away any prospects of testing GR. Our study is a first of its kind to establish the severe impact that beyond-vacuum-GR effects can have on EMRI systems, and motivates further work to develop a consistent and systematic procedure to include such effects in the data analysis pipeline.

biases intrinsic
Figure 4: (Left panel): Schematic representation of how biases are induced to the set of signal parameters \(\psi_S, \varphi_S\) (blue cross) in a larger "signal space" (red cube) when inferred over a template space (grey manifold) which holds fixed one or more signal parameters to a fixed null value, in this case \(\varphi = \varphi_0\). The "best-fit" point is obtained at a biased location: \(\psi_{\rm MAP}, \varphi_0\). (Right panel): The scheme proposed in Kejriwal et al. (2025) to correct the biases by obtaining posterior samples along the restricted axis (green stars along the vertical axis) and measuring the corresponding probability that \(\varphi \neq \varphi_0\).

A major challenge in developing a systematic framework for inferring beyond-vacuum-GR effects is the shear number of such effects proposed in the literature. Given the cost of sampling the posterior surface in a single run with techniques like Markov Chain Monte Carlo (MCMC), and especially in the context of the LISA global fit inference pipeline, it is impractical to try and constrain all such effects simultaneously. Our latest work (Kejriwal et al. (2025)) proposes an inference-based method to consistently and inexpensively obtain samples from the posterior surface in alternate beyond-vacuum-GR hypothesis, given just posterior samples from the vacuum-GR hypothesis. Within this novel framework, beyond-vacuuum-GR hypotheses can be quickly tested in a “post-processing” inference step.

Electromagnetic Counterparts of EMRIs

biases intrinsic
Figure 5: A schematic depiction of an EMRI evolving in a matter-rich environment (yellow disk). Diagram from Kejriwal et al. (2024) courtesy of Vojtěch Witzany.
biases intrinsic
Figure 6: Time-domain signal from the August 2020 run of eRO-QPE2 quasi-periodic eruption source. Diagram from Pasham, Kejriwal et al. (2024) courtesy of Dheeraj R. Pasham.

Quasi-periodic eruption (QPE) events, which are low-frequency (\(\sim 10^{-4}\) Hz) signals of soft X-ray peaks over a quiescent background, are theorized to be electromagnetic (EM) counterparts of EMRIs. While EMRIs evolving in a vacuum are not expected to host EM counterparts, the presence of a disk around the MBH allows interactions with the compact object that can lead to EM counterparts in the X-ray or even ultraviolet bands, see e.g. Linial and Metzger (2023). This poses an exciting prospect of multimessenger astronomy with EMRIs. In our work, (Kejriwal et al. (2024)), we calculated the frequency band of QPE sources that are emitting an EM signal “today”, such that they may also be observed in the future by LISA as GW sources. We extended our analysis to a particularly promising QPO source (where the ‘O’ now stands for oscillations, not eruptions, distinguishing their intensity), RE J1034+396. REJ has shown a decreasing time period over two observations separated by a decade, which is expected of EMRIs. We found that a compact object orbiting the MBH in REJ may be of mass \(\approx 47 M_\odot\) and that there is a \(\approx 25\%\) probability that REJ (if it is an EMRI and follows its current inspiral trend) would be detected in the LISA band. Our study is a first of its kind to comment on the multimessenger prospects of LISA EMRIs.

Developing Waveform Models and Data Analysis Tools

These are ongoing projects under this theme:

© 2025 Shubham Kejriwal