PTPlot: About

PTPlot is a tool for exploring the gravitational wave power spectrum from first-order phase transitions, and evaluating the likelihood of detecting a signal with the LISA mission.

Current version

This server is running version v1.1.0.

What PTPlot does

In addition to the papers cited below, you can read a Technical Note written by Jenni Häkkinen which describes which formulae PTPlot uses, and how they relate to other formulae in the literature.

About the output

  • All output figures are Scalable Vector Graphics (SVG) and can be downloaded and edited with free tools such as Inkscape. They are also easily converted to PDF or bitmapped formats by Inkscape or built-in OS tools, e.g.:
    $ inkscape input_snr_file.svg
    Note that on Macos, Inkscape requires the full path to the source and destination files in order to work.
  • The CSV files that can be downloaded on 'single point' plotting pages contain the following columns (these are labeled on the first row): $$ f,\, h^2 \Omega_\text{sensitivity}, \, h^2 \Omega_\text{GW, sw},\, [h^2 \Omega_\text{GW, turb}, \, h^2 \Omega_\text{GW, tot} ]. $$ There is therefore no explicit dependence on the Hubble rate in the data.

Crediting PTPlot

The results plotted by this tool are based on the papers arXiv:1704.05871, Shape of the acoustic gravitational wave power spectrum from a first order phase transition (note the erratum) and arXiv:1910.13125, Detecting gravitational waves from cosmological phase transitions with LISA: an update. You are welcome to include plots from PTPlot in your own work; if you do use PTPlot, please cite at least:

  • The above paper arXiv:1910.13125, as well as
  • The Zenodo snapshot of the latest version, i.e. doi:10.5281/zenodo.6949107. This helps us track interest and usage of PTPlot in particular and justify its continued development.

PTPlot now generates plots without a watermark. However if you use figures from PTPlot in a publication please do cite the sources above, and maybe write to let us know!


The source for PTPlot is available at The code is provided under the Creative Commons Attribution 4.0 International license. Please see the section Crediting PTPlot, above.

Feedback, issues

Please get in touch with the authors []. Unfortunately due to spam, we had to close the issue tracker, but we take all bug reports and issues seriously. We also try to help with other queries.

Recent news

  • 4.8.2023 - version 1.1.0
    • New technical note describing exactly what PTPlot does (thanks to Jenni Häkkinen).
    • Minor bugfixes to plotting code.
    • Ongoing clean-up and documentation of source code and Some files have been renamed.
    • Unneccessary multithreading removed (this does mean one needs to be careful when running locally).
    • LISA CosWG watermark has been removed.
    • Code for bulk downloading benchmark points is now included in the repo.
  • 1.8.2022 - version 1.0.2
    • Relicensed under CC BY 4.0 International and made available on Zenodo with a DOI.
    • Corrected value of sound wave power spectrum prefactor (per erratum of arXiv:1704.05871).
    • Changes to appearance for readability.
    • URLs which return SVG or CSV files now have the extension in the URL to make it a more pleasant experience when saving the file.
    • Use
      rather than some weird in-house code for calculating the integrated SNR.
  • 5.3.2020 - version 1.0.1
    • Can be installed with pip3 (for standalone use):
      pip3 install --upgrade
    • Fixes a systematic error due to having logarithmically spaced data for the sensitivity curve, while cannot cope with anything but evenly spaced points. Wrote a new replacement for the relevant commands that does numerical integration with an arbitrary interval.
    • Fixed the value of $\tilde{\Omega}_\text{gw}$ from 0.12 to 0.012. This was due to a typo in arXiv:1704.05871 below Equation 45, which will be corrected in a forthcoming erratum.
    • Power spectra and sensitivity data can now be downloaded as a CSV from individual point pages.
    • Minor fixes due to changes in Django.
    • Some improvements to the benchmark point database.
  • 7.11.2019 - version 1.0.0
    • Coincides with release of paper [arXiv:1910.13125].
    • Source data for plots now included in repo.
    • Minor tick marks now shown.
    • In plotting power spectra, only the sound wave curve is now shown (other curves remain available in the source code).
    • Bugfixes, including: corrections to definition of $\kappa$ and a missing factor of $h^2$ in the sound wave GW power spectrum.
  • 25.6.2019 - version 0.9.5
    • 3- and 7- year mission durations available.
    • Bugfixes to the "energy budget" calculation, which previously had some discrepancies at intermediate velocities.
    • Axis labels cleaned up.
    • "Theories" renamed to "Models" and another layer of granularity, "Scenarios", added to benchmark points.
    • More flexibility in terms of individual points and scenarios having their own $T_*$ and $v_\mathrm{w}$.
    • $\beta/H$ is now plotted (and used as a parameter) rather than $H/\beta$.
  • 21.12.2018 - version 0.9.2
    • The SNR curves and power spectra now use a single merged PowerSpectrum() class.
    • All plots use a conservative form of the sound wave source where it has lifetime set either by the shock formation time or the Hubble time, whichever is shorter.
    • All plots have a date and timestep to assist with debugging.
    • Power spectrum plots have the SNR (from sound waves only) overplotted, too.


  • arXiv:1512.06239 - Science with the space-based interferometer eLISA. II: Gravitational waves from cosmological phase transitions
  • arXiv:1910.13125 - Detecting gravitational waves from cosmological phase transitions with LISA: an update

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