KDE Representations of the Gravitational Wave Background Free Spectra Present in the NANOGrav 15-Year Dataset

OVERVIEW

----------------

This is a downloadable file of probability densities from KDEs (Kernel Density Estimator) of free spectrum analyses of the NANOGrav 15yr Dataset (DOI 10.5281/zenodo.7967584) that can be used with the Ceffyl and PTArcade packages. Please see the GitHub page for Ceffyl/PTArcade installation details and usage information.

Details on how this data product was produced can be found in Lamb, Taylor & van Haasteren 2023 (DOI 10.1103/PhysRevD.108.103019).

DIRECTORY AND FILE STRUCTURE

----------------------------------------------------

Each directory contains a file with log-pdfs representing their corresponding free spectra (`density.npy`), the frequencies at which they were analysed (`freqs.npy`), the grid-points at which each log-pdf was computed (`log10rhogrid.npy`), frequency labels (`log10rholabels.txt`), analysis label (`pulsar_list.txt`), an array of bandwidths computed using the Sheather-Jones method (see Lamb et al. 2023; 'bandwidths.npy'), and a file with some metadata about the data (`log.txt`).

./30f_fs{cp}_ceffyl 

• A representation of a 30 frequency CURN free spectrum.

./30f_fs{hd}_ceffyl

• A representation of a 30 frequency HD-correlated free spectrum

./30f_fs{hd+mp+dp+cp}_ceffyl_hd-only

• A representation of an analysis that simultaneously modeled a HD-correlated free spectrum, a MP-correlated free spectrum, a DP-correlated free spectrum, and a CURN free spectrum. Only the HD component is represented here.

./README

• this is a readme

SOFTWARE

------------------

This data should ideally be used with the latest versions of:

• ceffyl (https://github.com/astrolamb/ceffyl)
• PTArcade (https://github.com/andrea-mitridate/PTArcade)

PLANNED REVISIONS

---------------------------------

None

CHANGE LOG

----------------------

07/08/2026 - Corrected data set after finding a bug in our sampler

• A bug was found in the parallel tempering sub-routine of `PTMCMCSampler`, an MCMC sampler that was used to estimate the free spectrum posteriors of the NANOGrav 15yr data set. This release corrects the posteriors which were biased by this bug.
  • Details of the bug can be found here: Pull Release 58
  • This bug affected population inference of SMBHBs. See the following erratum: Agazie et al 2026 ApJL1006 L67
• We re-ran every free spectrum with the exception of `30f_fs{hd+mp+dp}_ceffyl_hd-only` and `30f_fs{hd}_100fDMGP_ceffyl`

10/12/2023 - updated KDE representations

A bug was found that produced a poor reflection at the lower prior boundary. Hence, data was being represented well at the lower prior boundary. This has now been corrected.