Gravitational waves are disturbances in the curvature of spacetime, generated by accelerated… 1 answer below »

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Gravitational waves are disturbances in the curvature of spacetime, generated by accelerated masses, that propagate as waves outward from their source at the speed of light. They are predicted in General Relativity and other theories of gravity and since 2017, they have now been observed! In this exercise we will analyse some mock gravitational wave data from two unknown astrophysical objects merging together and coelescing. We will use a Monte Carlo Markov Chain (MCMC) to compare a scaled model that predicts how the wave changes depending on the total mass of the merging objects and their distance from us to the observed waveform. This will allow us to determine the nature of the orbiting objects that merged to form the gravitational wave using MCMC, whether for instance they could be originating from merging white dwarfs, neutron stars or black holes. The mock or simulated waveforms measure the strain as two compact, dense astrophysical objects coalesce. The strain describes the amplitude of the wave. The system is parameterised by the masses of the merging objects, ??1M1 and ??2M2, and their distance from the observer ??D. Other useful parameters are: The mass ratio ??=??2/??1q=M2/M1, with convention that ??1=??2M1=M2 and so ??=1q=1. The “Chirp mass”, which is a quantity used in general relativity, is given by: ????h=(??1??2)3/5(??1+??2)1/5Mch=(M1M2)3/5(M1+M2)1/5 General tips: • Explain all your reasoning for each step. A significant fraction of the marks are given for explanations and discussion, as they evidence understanding of the analysis. • Some of these steps will take a while to run and compile. It’s a good idea to add in print statements to your code throughout eg print(‘this step is done’) to make sure that your bit of code has finished. • Add the import packages statements in the cell below to the top of your Jupyter notebook. We will use the pandas package to read in the data, with eg dataIn=pd.read_csv(‘filename.csv’). • You may find it useful to look at the following publication from the LIGO consortium. https://arxiv.org/pdf/1608.01940.pdf

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