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# gwbinning

I. General description

This Python tutorial code demonstrates the technique of relative binning for efficient evaluation of the likelihood function for gravitational wave data (See Zackay, Dai, Venumadhav 2018, https://arxiv.org/abs/1806.08792 for theoretical description of the method). Using GW170817 as an example, the tutorial shows a sample code to construct frequency-binned summary data, and compute the likelihood function using the summary data.

As an application, we also provide a sample code to find the best-fit waveform parameters by numerically maximizing the likelihood.

II. Required python packages

This tutorial code only requires the common python packages numpy and scipy. For demonstration, the analytical TaylorF2 waveform (including the effects of aligned spins and tidal deformation) is implemented as a python function. In order to make the tutorial as accessible as possible, we do not require the LIGO data analysis package LALSuite to be installed.

III. Description of Python code files

waveform.py: This analytically implements the TaylorF2 waveform model, as well as other functions to be used in the tutorial binning.py: This contains the algorithms to construct frequency bins and to generate the summary data GW170817_binning.py: This is the Python tutorial file to apply the binning technique to the case of GW170817.

IV. LIGO data

The user has to download the strain data for GW170817 from the LIGO website:

https://losc.ligo.org/events/GW170817/

In the example we give, we use T = 2048 sec chunk of data at a sampling rate of 4096Hz after noise subtraction:

https://dcc.ligo.org/public/0146/P1700349/001/H-H1_LOSC_CLN_4_V1-1187007040-2048.txt.gz https://dcc.ligo.org/public/0146/P1700349/001/L-L1_LOSC_CLN_4_V1-1187007040-2048.txt.gz

V. Posterior samples for GW170817

We generate posterior samples for GW170817 utilizing the relative binning technique. We provide posterior samples based on two different waveform models from LAL: IMRPhenomD_NRTidal and TaylorF2.

The samples are provided in terms of a set of 8 parameters. The columns are:

Mc: detector-frame chirp mass [Msun] eta: symmetric mass ratio s1z: aligned spin component for the primary s2z: aligned spin component for the secondary lambda1: tidal deformability for the primary lambda2: tidal deformability for the secondary tc1: merger time for the primary [sec] tc2: merger time for the secondary [sec]

Posterior sample files:

GW170817_IMRPhenomDNRTidal_emcee.txt ------ [IMRPhenomD_NRTidal; using emcee] GW170817_IMRPhenomDNRTidal_MultiNest.txt ------ [IMRPhenomD_NRTidal; using pyMultiNest] GW170817_TaylorF2_MultiNest.txt ------ [TaylorF2; using pyMultiNest]