Tutorials

In NMMA, it is possible to use the results from GW, kilonova and GRB afterglow inferences to get estimates on the binary properties. This is based on phenomenological relations, i.e., via fits based on numerical-relativity relations. The dynamical ejecta mass, \(M_{ej}^{dyn}\), is connected to the binary properties through quasi-universal relations, see Pang et al. 2022.

For the GW-EM resampling, the following input files are required:

• EMsamples - is the posterior sample file from a previous Bayesian inference (e.g. Kilonova+GRB inference) on electromagnetic (EM) signals,
• EMprior - is the prior file that was used for the previous EM inference
• EOS - number of equation of state (EOS) files used in the resampling,
• EOSpath - path to the folder of all EOS files,
• GWsamples - some fiducial randomly generated posterior samples for masses \(m_{1,2}\), chirp mass \(\mathcal{M}_{c}\), mass ratio \(q\), luminosity distance \(D_{L}\), and EOS samples,
• GWprior - a prior file for sources observed via gravitational waves

Here, we illustrate the resampling on the example of a previous Bayesian inference on the observed data of the event GRB211211A, see section Combined light curve inference.

For the GWsamples input file, we need to generate some fiducial dummy GW samples. A script for the generation can be found here. The GW sample generation is based on the EOS set 15nsat_cse_uniform_R14 which can be found on Zenodo. The EMprior file is the same as specified here, and for the GWprior file we can use this example prior file.

Finally, to run the GW-EM-resampling, we can use this command:

mpiexec -np 6 gwem_resampling --outdir outdir --GWsamples ./GWsamples.dat --GWprior ./GW.prior --EMsamples ./GRB211211A_posterior_samples.dat --EOSpath ./15nsat_cse_uniform_R14/macro/ --Neos 5000 --EMprior ./Bu2019lm_TrPi2018GRB211211A.prior --nlive 1024

The result will be a posterior file containing information on:

• the chirp mass \(M_{c}\),
• mass ratio \(q\),
• Tidal deformability \(\tilde{\Lambda}\),
• dynamical ejecta mass error \(\alpha\),
• dynamical ejecta mass fraction \(\zeta\)

A corner plot is shown below:

In order to estimate the properties of a NSBH system, you need to adjust the GWsamples and GWprior file accordingly and run the resampling with the argument withNSBH (otherwise, you will run for a BNS system).

gwem_resampling --outdir outdir --GWsamples GWsamples_NSBH.dat --GWprior GWNSBH.prior --withNSBH --EMsamples GRB211211A_NSBH_posterior_samples.dat --EOSpath 15nsat_cse_uniform_R14/macro/ --Neos 5000 --EMprior Bu2019nsbh_TrPi2018_GRB211211A.prior --nlive 1024