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<h1>Multi-messenger inference</h1>
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<section id="multi-messenger-inference">
<h1>Multi-messenger inference<a class="headerlink" href="#multi-messenger-inference" title="Link to this heading">#</a></h1>
<p>A joint inference on gravitational-wave and electromagnetic signals requires NMMA to run on a supercomputer cluster because large memory space are required and need to be shared across many CPU cores. Here, we consider a full joint inference on the binary neutron star merger observed on 17th August 2017.</p>
<p>In order to run a multi-messenger inference, we need to follow to main steps:</p>
<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>nmma-generation config.ini
</pre></div>
</div>
<p>Perform the analysis or parameter estimation using:</p>
<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>nmma-analysis --data-dump <name_of_analysis>_data_dump.pickle
</pre></div>
</div>
<p>First of all, we set up the <code class="docutils literal notranslate"><span class="pre">config.ini</span></code> file and provide all required data and information.</p>
<p><strong>Observational data</strong></p>
<p>Firstly, all observational data is required that means observational data from single observed events:</p>
<ul class="simple">
<li><p>GW170817,</p></li>
<li><p>GRB170817A,</p></li>
<li><p>AT2017gfo.</p></li>
</ul>
<p>These observational data need to be provided in the <code class="docutils literal notranslate"><span class="pre">config.ini</span></code> file for the joint inference.</p>
<p><strong>Prior</strong></p>
<p>Moreover, a prior on all observed messengers is required and needs to be tailored to the models used in the inference. Here, we use the GRB afterglow light curve model <code class="docutils literal notranslate"><span class="pre">TrPi2018</span></code> from afterglowpy and the kilonova model <code class="docutils literal notranslate"><span class="pre">Bu2019lm</span></code>. For the gravitational-wave signal, we assume the model <code class="docutils literal notranslate"><span class="pre">IMRPhenomPv2_NRTidalv2</span></code> for a precessing neutron star binary. A prior for the joint inference can be found <a class="reference external" href="https://github.com/nuclear-multimessenger-astronomy/nmma/tree/main/example_files/prior">here</a>, called <code class="docutils literal notranslate"><span class="pre">GW170817_AT2017gfo_GRB170817A.prior</span></code>.</p>
<p><strong>Electroamagnetic data and models</strong></p>
<p>In order to not only sample on gravitational-wave data, we provide further electromagnetic signal related flags. The flag <code class="docutils literal notranslate"><span class="pre">with-grb=True</span></code> will turn on the sampling on a GRB data. As NMMA currently only includes one GRB model, this model does not need to be further specified. If <code class="docutils literal notranslate"><span class="pre">with-grb=False</span></code>, a joint inference of GW+KN data is possible, excluding the GRB part. With regard to the kilonova model, we need to provide a specific model under <code class="docutils literal notranslate"><span class="pre">kilonova-model</span></code>, its respective reduced model grid (if applicable) under <code class="docutils literal notranslate"><span class="pre">kilonova-model-svd</span></code> and a <code class="docutils literal notranslate"><span class="pre">kilonova-interpolation-type</span></code> which can be either <code class="docutils literal notranslate"><span class="pre">sklearn_gp</span></code> or <code class="docutils literal notranslate"><span class="pre">tensorflow</span></code>. The <code class="docutils literal notranslate"><span class="pre">light-curve-data</span></code> flag should include both GRB and kilonova data if a joint inference on GW-GRB-KN is desired (meaning use: <code class="docutils literal notranslate"><span class="pre">with-grb=True</span></code>) or should just include the kilonova data if a GW-KN inference is targeted (meaning use: <code class="docutils literal notranslate"><span class="pre">with-grb=False</span></code>). The kilonova start/end time and time steps apply to both the GRB and kilonova model which will generate light curves during the inference to match the observed data provided.</p>
<p><strong>Including EOS information</strong></p>
<p>NMMA enables to include nuclear information by using equations-of-state (EOS) and sample over the EOS during the inference. In order to include a set of EOSs, each EOS.dat file needs to include information on Mass, Radius and Tidal deformability. For the example shown in the <code class="docutils literal notranslate"><span class="pre">config.ini</span></code> file below, we see that <code class="docutils literal notranslate"><span class="pre">Neos</span> <span class="pre">=</span> <span class="pre">5000</span></code> meaning that we include 5000 EOS.dat files each containing information on mass, radius and tidal deformability. We also see that a constraint from NICER measurements has been folded in and thus the <code class="docutils literal notranslate"><span class="pre">eos-weight</span></code> reflects this in a weighting. The EOS set should be sorted according to this weighting in order to reduce runtime for the sampling on the EOSs.</p>
<p><strong>Running the config.ini generation</strong></p>
<p>In order to prepare the joint inference, a <code class="docutils literal notranslate"><span class="pre">config.ini</span></code> file is required which specifies all kind of models, observational data and inference settings. An example adjusted to the observed BNS merger can be found below:</p>
<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>################################################################################
## Data generation arguments
################################################################################
trigger_time = 1187008882.43
################################################################################
## Detector arguments
################################################################################
detectors = [H1, L1, V1]
psd_dict = {H1=data/GW170817/h1_psd.txt, L1=data/GW170817/l1_psd.txt, V1=data/GW170817/v1_psd.txt}
channel_dict = {H1=LOSC-STRAIN, L1=LOSC-STRAIN, V1=LOSC-STRAIN}
data_dict = {H1=data/GW170817/H-H1_LOSC_CLN_16_V1-1187007040-2048.gwf, L1=data/GW170817/L-L1_LOSC_CLN_16_V1-1187007040-2048.gwf, V1=data/GW170817/V-V1_LOSC_CLN_16_V1-1187007040-2048.gwf}
duration = 128
################################################################################
## Calibration arguments
################################################################################
calibration-model = CubicSpline
spline-calibration-nodes = 10
spline-calibration-envelope-dict = {H1:data/GW170817/Feb-20-2018_O2_LHO_GPSTime_1187008882_C02_RelativeResponseUncertainty_FinalResults.txt, L1:data/GW170817/Feb-20-2018_O2_LLO_GPSTime_1187008882_C02_RelativeResponseUncertainty_FinalResults.txt, V1:data/GW170817/V_calibrationUncertaintyEnvelope_magnitude5p1percent_phase40mraddeg20microsecond.txt}
################################################################################
## Job submission arguments
################################################################################
label = GW170817-AT2017gfo-GRB170817A
outdir = outdir
################################################################################
## Likelihood arguments
################################################################################
distance-marginalization=False
phase-marginalization=False
time-marginalization=False
################################################################################
## Prior arguments
################################################################################
prior-file = GW170817_AT2017gfo_GRB170817A.prior
################################################################################
## Waveform arguments
################################################################################
frequency-domain-source-model = lal_binary_neutron_star
waveform_approximant = IMRPhenomPv2_NRTidalv2
################################################################################
## EM arguments
################################################################################
binary-type=BNS
light-curve-data=data/AT2017gfo-GRB170817A/AT2017gfo_GRB170817A.dat
kilonova-model=Bu2019lm
kilonova-model-svd=data/AT2017gfo-GRB170817A/svdmodels_reduced
svd-mag-ncoeff=10
svd-lbol-ncoeff=10
kilonova-trigger-time=57982.5285236896
kilonova-tmin=0.1
kilonova-tmax=950
kilonova-error=1
kilonova-tstep=0.1
kilonova-interpolation-type=sklearn_gp
grb-resolution=12
with-grb=True
################################################################################
## EOS arguments
################################################################################
with-eos=True
eos-data=eos/with_NICER_J0740/EOS_024_uniform_5k_sorted
Neos=5000
eos-weight=eos/with_NICER_J0740/EOS_sorted_weight.dat
</pre></div>
</div>
<p>The joint inference generation can be performed by running:</p>
<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>nmma-generation config.ini
</pre></div>
</div>
<p>This will generate a <code class="docutils literal notranslate"><span class="pre">GW170817-AT2017gfo-GRB170817A_data_dump.pickle</span></code> file under <code class="docutils literal notranslate"><span class="pre">outdir/data/</span></code> which need to be provided for the joint inference function <code class="docutils literal notranslate"><span class="pre">nmma-analysis</span></code>.</p>
<p><strong>Running the analysis</strong></p>
<p>As detailed above, running the analysis with the command <code class="docutils literal notranslate"><span class="pre">nmma-analysis</span> <span class="pre">--data-dump</span> <span class="pre">outidr/data/GW170817-AT2017gfo-GRB170817A_data_dump.pickle</span></code> requires computational resources on a larger cluster. Below we show an example script for job submission called <code class="docutils literal notranslate"><span class="pre">jointinf.pbs</span></code> on a German cluster:</p>
<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>#!/bin/bash
#PBS -N <name of simulation>
#PBS -l select=16:node_type=rome:mpiprocs=128
#PBS -l walltime=24:00:00
#PBS -e ./outdir/log_data_analysis/err.txt
#PBS -o ./outdir/log_data_analysis/out.txt
#PBS -m abe
#PBS -M <email adress>
module load python
module load mpt
module load mpi4py
source <provide path to venv>
export MPI_UNBUFFERED_STDIO=true
export MPI_LAUNCH_TIMEOUT=240
cd $PBS_O_WORKDIR
mpirun -np 512 omplace -c 0-127:st=4 nmma-analysis --data-dump <absolute path to folder>/outdir/data/GW170817-AT2017gfo-GRB170817A_data_dump.pickle --nlive 1024 --nact 10 --maxmcmc 10000 --sampling-seed 20210213 --no-plot --outdir <absolute path to outdir/result folder>
</pre></div>
</div>
<p>Note that settings might differ from cluster to cluster and also the installation of NMMA might be changed (conda vs. python installation).</p>
<p><strong>Maximum mass constraint from a joint analysis</strong></p>
<p>From a joint posterior of GW and lightcurve data from a BNS, one can derive an upper limit on the TOV mass, if one assumes that the remnant collapsed to a black hole. The idea is to determine the posterior distribution on the remnant’s mass from the posterior distribution of the individual neutron star masses <span class="math notranslate nohighlight">\(m_1\)</span>, <span class="math notranslate nohighlight">\(m_2\)</span> and the ejecta and compare this to the TOV mass of EOSs.</p>
<p>This can be done via the command</p>
<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>maximum-mass-constraint --outdir <path to folder> --joint-posterior <path to the file with samples from GW+EM analysis> --prior <path to a bilby prior file> --eos-path-macro <path to macroscopic EOS> --eos-path-micro <path to microscopic EOS> [--use-M-Kepler]
</pre></div>
</div>
<p>The last flag determines whether the remnant mass is compared against the TOV mass or the maximum mass limit for a rotating NS (Kepler limit). The latter is less conservative. The joint posterior should contain the parameters chirp mass, eta_star, log10_mdisk, log10_mej_dyn as named columns. Here, eta_star is <span class="math notranslate nohighlight">\(η* = \ln(0.25-η)\)</span> from the symmetric mass ratio <span class="math notranslate nohighlight">\(η\)</span>. The macroscopic EOS curves must have the central pressure p0 in MeV/fm³ of each NS mass as last column.</p>
<p>If –use-M-Kepler is set, the prior file needs to contain two additional fiducial paramters for the quasi-universal relations:</p>
<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>ratio_R = Gaussian(name = "R", mu = 1.255, sigma = 0.024)
delta = Uniform(name="delta", minimum = -0.0125, maximum = 0.0125)
</pre></div>
</div>
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