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.