Computational Advancements for Analyzing Binary Systems with LISA

Katz, Michael

doi:https://doi.org/10.21985/n2-rh5g-5820

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Computational Advancements for Analyzing Binary Systems with LISA

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I present the body of work I have pursued over the course of my doctoral study at Northwestern University. First, I conduct an analysis of the measurement abilities of distinctive LISA detector designs, examining the influence of LISA's low-frequency performance on the detection and characterization of massive black hole binaries. We are particularly interested in LISA's ability to measure massive black holes merging at frequencies near the low-frequency band edge, with masses in the range of $\sim 10^6-10^{10}M_\odot$. We examine the signal-to-noise ratio (SNR) using phenomenological waveforms for inspiral, merger, and ringdown over a wide range of massive black hole binary parameters. We employ a broad palette of possible LISA configurations with different sensitivities at low frequencies. For this analysis, we created a tool\footnote{BOWIE, \href{ https://github.com/mikekatz04/BOWIE}{github.com/mikekatz04/BOWIE}} that evaluates the change in SNR between two parameterized situations. The shifts in SNR are computed as gains or losses as a function of binary parameters, and graphically displayed across a two dimensional grid of parameter values. We illustrate the use of this technique for both parameterized LISA mission designs, as well as for considering the influence of astrophysical parameters on gravitational wave signal models. In terms of low-frequency sensitivity, acceleration noise or armlength is found to be the most important factor in observing the largest massive black hole binaries, followed by break frequency and then spectral index. LISA's ability to probe the astrophysical population of $\sim10^7-10^9M_\odot$ black holes is greatly influenced by these aspects of its sensitivity. The importance of the constituent black hole spins is also highlighted. With data from the Illustris cosmological simulation, we provide analysis of LISA detection rates accompanied by characterization of the merging massive black hole population. Massive black holes of total mass $\sim10^5-10^{10} M_\odot$ are the focus of this study. We evolve Illustris massive black hole mergers, which form at separations on the order of the simulation resolution ($\sim$kpc scales), through coalescence with two different treatments for the binary massive black hole evolutionary process. The coalescence times of the population, as well as physical properties of the black holes, form a statistical basis for each evolutionary treatment. From these bases, we Monte Carlo synthesize many realizations of the merging massive black hole population to build mock LISA detection catalogs. We analyze how our massive black hole binary evolutionary models affect detection rates and the associated parameter distributions measured by LISA. With our models, we find massive black hole binary detection rates with LISA of $\sim0.5-1$ yr$^{-1}$ for massive black holes with masses greater than $10^5M_\odot$. This should be treated as a lower limit primarily because our massive black hole sample does not include masses below $10^5M_\odot$, which may significantly add to the observed rate. We suggest reasons why we predict lower detection rates compared to much of the literature. I present a parameter estimation analysis for a variety of massive black hole binaries. This analysis is performed with a graphics processing unit (GPU) implementation comprising the \phenomhm waveform with higher-order harmonic modes and aligned spins; a fast frequency-domain LISA detector response function; and a GPU-native likelihood computation. The computational performance achieved with the GPU is shown to be 500 times greater than with a similar CPU implementation, which allows us to analyze full noise-infused injections at a realistic Fourier bin width for the LISA mission in a tractable and efficient amount of time. With these fast likelihood computations, we study the effect of adding aligned spins to an analysis with higher-order modes by testing different configurations of spins in the injection, as well as the effect of varied and fixed spins during sampling. Within these tests, we examine three different binaries with varying mass ratios, redshifts, sky locations, and detector-frame total masses ranging over three orders of magnitude. We discuss varied correlations between the total masses and mass ratios; unique spin posteriors for the larger mass binaries; and the constraints on parameters when fixing spins during sampling, allowing us to compare to previous analyses that did not include aligned spins. Many inspiraling and merging stellar remnants emit both gravitational and electromagnetic radiation as they orbit or collide. These gravitational wave events together with their associated electromagnetic counterparts provide insight about the nature of the merger, allowing us to further constrain properties of the binary. With the future launch of LISA, follow up observations and models are needed of ultracompact binary (UCB) systems. Current and upcoming long baseline time domain surveys will observe many of these UCBs. We present a new fast periodic object search tool based on the Conditional Entropy algorithm. This new implementation of Conditional Entropy is fast enough to allow for a grid search over both period ($P$) and the time derivative of the period ($\pdot$). To demonstrate the performance and usage of this tool, we use a galactic population of UCBs generated from the population synthesis code \cosmic, as well as a Curated catalog for varying periods at fixed intrinsic parameters. We simulate light curves as likely to be observed by future time domain surveys by using an existing eclipsing binary light curve model accounting for the change in orbital period due to gravitational radiation. We find that a search with $\pdot$ values is necessary for detecting binaries at orbital periods less than $\sim$10 min. We also show it useful in finding and characterizing binaries with longer periods, but at a higher computational cost. Our code is called \texttt{gce} (GPU-Accelerated Conditional Entropy).\footnote{gce, \href{ https://github.com/mikekatz04/gce/tree/c166a9059a5a544fb8ed996a2a94f2b52724cc19}{github.com/mikekatz04/gce}} Finally, I present a framework for fast and accurate waveforms for extreme mass ratio inspirals, a prime source for the LISA mission. LISA data analysts to date have used so-called ``kludge'' waveforms for LISA-related analysis. These waveforms use a set of approximations to ensure their speed while sacrificing accuracy. Fully accurate waveforms are not theoretically available, and the advanced theory that is available is too slow for any tractable analysis. To achieve full accuracy, the LISA community needs waveforms built from the so-called gravitational self-force. I introduce this topic and discuss moving from kludge waveforms to self-force-based waveforms. My collaborators and I present the first framework to generate fast self-forced waveforms using advanced hardware and a variety of interpolation techniques, including artificial neural networks. I present in detail how this framework is built, as well as how it can be extended as more theoretical results are discovered by the gravitational self-force community. Within this framework, we build a waveform on GPUs that can create an advanced, accurate waveform with sub-second timing for an entire year-long waveform.

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