## International Summer Research Program in Gravitational-Wave Physics:

Research Experiences for Undergraduates around the world

**University of Birmingham**

*Testing General Relativity with Gravitational Waves*

Gravitational waves from merging black holes provide us with a unique opportunity to test the predictions of General Relativity. Using state-of-the-art waveform models with precession and higher multipoles, the student will undertake a parameter estimation campaign to understand future constraints on parameterized deformations from General Relativity and how imperfect waveform modelling can lead to systematic biases. The student will then explore how this couples to our understanding of astrophysical populations of binary black holes. The student will develop the skills to perform Bayesian inference and develop a basic understanding of data analysis with gravitational-wave observations.

**Mentors:**Patricia Schmidt and Geraint Pratten

*Massive black hole binaries and Pulsar Timing Array observations*:

Pulsar Timing Arrays (PTA) are galactic scale gravitational wave detectors that use radio pulsars as ultra-stable clocks to detect gravitational waves. Massive black hole binary systems are the primary sources of gravitational waves observable by PTAs. The goal of this project is to use the results from Monte Carlo simulations of the formation and evolution of these binaries to explore the sensitivity of current and future PTAs to this class of sources.

**Mentor:**Alberto Vecchio

**Past Projects: University of Birmingham**

- What can we learn about Black Holes with Gravitational Waves?

One of the main goals of gravitational-wave searches lies in the possibility of inferring the parameters of the sources from their gravitational-wave signature. For coalescing compact binaries, the parameter space can be quite large, e.g. 15 parameters for black-hole binaries with arbitrary spins. The presence of strong correlations and degeneracies in this large parameter space brings up a variety of challenges in searching for the true source parameters. We typically use stochastic techniques, such as Markov Chain Monte Carlo, to sample this parameter space. These techniques rely on accurate models of gravitational waveforms. We will explore the accuracy requirements for waveforms models, account for uncertainty in the waveforms, and develop techniques for computationally efficient parameter estimation on very long-duration waveforms.

**Mentor:**Ilya Mandel

**Related Project 2012:**"Improving Parameter Estimation on Gravitational-Wave Signals"

**Related Project 2013:**"Parameter Estimation Accuracy in Hybrid Gravitational Waveform Modeling"

- Improving Parameter Estimation on Gravitational-Wave Signals:

One of the main goals of gravitational-wave searches lies in the possibility of inferring the parameters of the sources from their gravitational-wave signature. For coalescing compact binaries, the parameter space can be quite large, e.g. 15 parameters for black-hole binaries with arbitrary spins. The presence of strong correlations and degeneracies in this large parameter space brings up a variety of challenges in searching for the true source parameters. We typically use stochastic techniques, such as Markov Chain Monte Carlo, to sample this parameter space. These techniques can be made more efficient by gaining a better understanding of the expected correlations. The goal of this project will be to search for such correlations and use the gained knowledge to improve jump proposal distributions.

**Mentor:**Ilya Mandel

**Related Project 2012:**"Improving Parameter Estimation on Gravitational-Wave Signals"

**Related Project 2013:**"Parameter Estimation Accuracy in Hybrid Gravitational Waveform Modeling"

- The dance of death of black hole binary systems:

The last few minutes of the dance macabre of a black hole binary can be studied in exquisite detail by gravitational-wave laser interferometers. These instruments record the signature of the structure of space-time in these extreme conditions by detecting the gravitational radiation that is emitted in the final stages of coalescence of binary black holes . Depending on the masses, spins and eccentricity of the binary, the orbit and space-time structure can be fantastically complex. The goal of the project is to develop a video and audio illustration of the structure of the space-time based on codes that we have developed within our group to model the evolution of these astrophysical systems. Such tools are extremely useful to develop a better intuition of the complex physics at work.

**Mentor:**Alberto Vecchio

**Related Project 2012:**"The dance of Death of Binary Black Hole Systems"

**Related Project 2013:**"The Impact of Gravitational Waves: Detectability and Signatures"

- Shaping a laser beam using a spatial light modulator:

Current gravitational wave detectors use the fundamental Gaussian beam mode of ultra-stable lasers for measuring a gravitational-wave induced differential position change of the end mirror test masses in a long baseline interferometer. Unfortunately, Brownian motion of the mirror surface couples into the phase of the reflected laser light. It is well known that employing lasers with a different, more uniform, mode shape can reduce this thermal noise. Commercially available 'spatial light modulators' can turn a Gaussian beam shape into an arbitrary user defined pattern. The goal of the project is to learn how the spatial light modulator can be used to produce so-called higher-order Laguerre-Gaussian modes (which feature concentric rings) and to optimize the optical setup such that a pure mode shape is generated.

**Mentor:**Andreas Freise

**Related Project 2011:**"Experimental Inquiry into the Feasibility of Generating Laguerre-Gauss Modes at Laser Powers of Order 100W"

- The Optical Resonator Calculator:

Optical resonators are a standard tool in precision optics and interferometry. They come in a variety of different shapes (linear, triangular, etc) and sizes (between microns and kilometers). Optical resonators are used in current gravitational wave detectors for various purposes, such as filtering or enhancing of individual light fields. The aim of this project is to develop an easy to use 'Optical Resonator Calculator' which would enable quick visualization of the characteristics of an optical resonator. The proposed application should have cross-platform operability, either through a web interface or by being based on JAVA. It should not only be fun to play with but also a useful illustrative tool for educational and outreach purposes.

**Mentor:**Andreas Freise

**Related Project 2009:**"Optical Resonator Calculator: Gravitational Wave Detector Cavity Simulations with Processing"

**Past IREU Projects**

**Other Prior Projects**