wolffem / 12p5yr_stochastic_analysis

Analysis and tutorial materials associated with the NANOGrav Collaboration's search for an isotropic stochastic gravitational-wave background in 12.5-years of precision millisecond pulsar timing data.

NANOGrav_12yr_tutorial

Tutorial to go with the 12.5 year isotropic GWB analysis

Authors: Aaron Johnson, Bence Becsy, Stephen Taylor, Sarah Vigeland, and Joe Simon for the NANOGrav Collaboration

Please send questions about this tutorial to aaron.johnson (at) nanograv.org

Installing PTA software

1. Install Miniconda

   • Either...download and install the relevant Miniforge file from here: https://github.com/conda-forge/miniforge
   • OR... use Terminal command line installation
     • Download the right one for your architecture
       • Mac: wget -q https://github.com/conda-forge/miniforge/releases/latest/download/Miniforge3-Linux-x86_64.sh
     • bash Miniforge3-MacOSX-x86_64.sh -b
       • rm Miniforge3-MacOSX-x86_64.sh (careful with “rm”)
       • Linux: wget -q https://github.com/conda-forge/miniforge/releases/latest/download/Miniforge3-MacOSX-x86_64.sh
     • bash Miniforge3-Linux-x86_64.sh -b
       • rm Miniforge3-Linux-x86_64.sh (careful with “rm”)
     • enterprise dependencies do not currently support Windows or M1 Macs natively

2. To install a new environment: conda create -n enterprise_extensions la_forge

• Note: if you use Miniconda or Anaconda instead of Miniforge, you will need to use conda create -n enterprise -c conda-forge enterprise_extensions la_forge jupyterlab
• M1 Macs can make a conda environment and install enterprise by first following the instructions here

3. This will create a conda environment that can be activated by conda activate enterprise

4. Next run jupyter lab

5. Set the Kernel

• when opening a new notebook: click New and select Python [conda env:enterprise]
• when opening an existing notebook (like this tutorial): click Kernel --> Change Kernel --> Python [conda env:enterprise]

Tutorials

These tutorials are split into several different files. The topic of each tutorial is shown below. These are roughly in the order that they should be viewed in to get a complete picture of how our isotropic GWB analysis is performed in NANOGrav.

Exploring NANOGrav Data

NANOGrav uses data files that may be unfamiliar to users that are new to pulsar timing or data analysis. Here, we investigate what information exists inside each par and tim file, how to load them into enterprise, and what information enterprise can use.

Single Pulsar GWB Analysis

This tutorial is meant to be a quick introduction to one of the simplest analyses we can perform. We go through the Bayesian red noise analysis of J1909 and J1713. These are two of the longest timed pulsars in the NANOGrav data set. One of the pulsars supports a common red process at spectral indices that are indicative of gravitational waves from a population of supermassive black hole binaries, while the other does not.

White Noise Single Pulsar Analysis

Here we go through the Bayesian analysis of white noise on a single pulsar. This is done for every pulsar in the NANOGrav data set to find the maximum marginalized posterior values of each white noise parameter. White noise parameters are then set to their maximum posterior values in the GWB analysis to reduce the number of parameters required from ~600 to ~90.

PTA GWB Analysis

This tutorial is split into two files, one for parameter estimation and one for model selection. We work through the Bayesian analysis of the full NANOGrav 12.5 year data to show what values each of the searched-over parameters prefers. After going through a generalized process of the single pulsar GWB analysis, we show how to compare models and compute Bayes factors. Figures 1 and 2 from the 12.5 year GWB search paper are reproduced in a separate file.

Optimal Statistic Analysis

This tutorial gives an introduction to frequentist methods we can use to look for the stochastic gravitational-wave background. It calculates the optimal statistic using the maximum likelihood noise parameters and also the noise marginalized optimal statistic using the parameter posteriors from a Bayesian analysis. It reproduces Figure 4 and 5 of the stochastic background paper.

Data Download

Output from NANOGrav analyses include chain files from PTMCMCSampler. These files contain samples of the posterior that tell us information about the parameters that go into our models. This file downloads the data products that are output by our sampler and used in Bayesian post-processing and frequentist analyses.