Periodic Reporting for period 1 - StochRewind (Stochastic Rewind and fast-forward: calibrating LISA with LIGO's black holes and stochastic background)
Reporting period: 2023-09-01 to 2025-08-31
Since the first direct measurement of a gravitational wave (GW) from a merging binary system of stellar-mass black holes (BH) in 2015 by the Laser Interferometer GW Observatory (LIGO), the field of GW astronomy has made giant leaps, counting now over 100 events. The catalogue of individually detected events grows with each new data run, and is used to infer the properties of the underlying population of merging binary BHs (BBHs) in the Universe. Furthermore, ground-based GW detectors such as LIGO, Virgo, and KAGRA (LVK) can potentially see much more than the individual signals; the resolved events counted in the catalogues make up a tiny fraction of all the GWs which reach our detectors, while most lie below the confusion limit and go undetected. Like voices in a crowded room, the collection of unresolved events gives rise to a background signal, referred to as the stochastic GW background (SGWB).
While we witness the explosion of ground-based detector science, the GW community is actively preparing for the upcoming revolution: the Laser Interferometer Space Antenna (LISA). Led by the European Space Agency, the LISA constellation will provide a deep coverage of the low-frequency GW sky, which is populated not only by unique sources (e.g. supermassive BHs, extreme mass ratio inspirals) but also by the same stellar-mass BHs observed by LIGO; crucially, these are observed at a much earlier phase of their lives. The overlapping of many sources, both in time and in frequency, will make LISA data analysis an extremely challenging task, which is why the so-called “LISA global fit” is now the holy grail of GW astronomy.
It is necessary to fully exploit the data from LVK today to dig deeper in the LISA data of tomorrow: Calibrating LISA with LIGO’s black holes and stochastic background is exactly the bold idea behind the StochRewind project. We (i) deliver crucial improvements to current measurements of the stochastic GW background, (ii) combine it with LIGO’s individual detections, and (iii) exploit it to predict the stochastic background of stellar-mass BHs in LISA. This is a novel handle to anchor one of the many moving parts of the LISA global fit using products from the current ground-based detector network.
Why now: The LISA ground segment is under active development and many of its foundational choices are still being made. Completing StochRewind now is vital to fully realise the promise of GW astronomy. Combining both individual and stochastic BBH signals in LVK and LISA, StochRewind will pioneer an holistic view of GW astronomy, bound to have repercussions for decades to come.
While we witness the explosion of ground-based detector science, the GW community is actively preparing for the upcoming revolution: the Laser Interferometer Space Antenna (LISA). Led by the European Space Agency, the LISA constellation will provide a deep coverage of the low-frequency GW sky, which is populated not only by unique sources (e.g. supermassive BHs, extreme mass ratio inspirals) but also by the same stellar-mass BHs observed by LIGO; crucially, these are observed at a much earlier phase of their lives. The overlapping of many sources, both in time and in frequency, will make LISA data analysis an extremely challenging task, which is why the so-called “LISA global fit” is now the holy grail of GW astronomy.
It is necessary to fully exploit the data from LVK today to dig deeper in the LISA data of tomorrow: Calibrating LISA with LIGO’s black holes and stochastic background is exactly the bold idea behind the StochRewind project. We (i) deliver crucial improvements to current measurements of the stochastic GW background, (ii) combine it with LIGO’s individual detections, and (iii) exploit it to predict the stochastic background of stellar-mass BHs in LISA. This is a novel handle to anchor one of the many moving parts of the LISA global fit using products from the current ground-based detector network.
Why now: The LISA ground segment is under active development and many of its foundational choices are still being made. Completing StochRewind now is vital to fully realise the promise of GW astronomy. Combining both individual and stochastic BBH signals in LVK and LISA, StochRewind will pioneer an holistic view of GW astronomy, bound to have repercussions for decades to come.
The activities and results are presented here in relation to the four main research objectives of this action:
RO1: Add a new fully functioning stochastic search pipeline for LIGO-Virgo-KAGRA (LVK) data analysis, to detect the intermittent background signal arising from binary black hole (BBH) mergers.
RO1 was mostly achieved: the methods paper was published [1] and the data-ready pipeline has been developed, however has not been published yet due to a minor but persistent bias that the analysis presents. This bias has been investigated thoroughly, and the researcher and collaborators are currently preparing a publication to explain the source of the bias.
RO2: Successfully analyse LVK data and detect/constrain the BBH gravitational-wave background (GWB).
RO2 was achieved by analysing the LVK O4a data, now public. This involved further developing and employing the analysis pipeline [2,3], the development of which was led by the researcher, and performing the search as a part of the LVK collaboration. Due to the delay in the start of the project due to the deferral of the start date, the researcher led the analysis of the newest version of LVK data (Observing run O4), as co-chair of the LVK isotropic stochastic group. This led to publication [4], which sets the most recent and most constraining upper limits on the BBH SGWB.
RO3: Deliver a comprehensive profile of the BBH population in our Universe.
RO3 was pursued both as a part of the LVK collaboration, using new datasets (O4a) which have now been released, and independently using older datasets: The researcher co-coordinated and contributed to the analysis presented in [4], which includes joint constraints on the BBH population using resolved BBH events within the LVK data and the GWB upper limit obtained. Furthermore, the researcher developed popstock [5], a library and pipeline to efficiently and accurately compute the BBH GWB spectrum starting from a parametric population model. The library is tailored to expect a set of posterior draws from standard population models, either obtained from data or from astrophysical modelling assumptions. This library was used to produce part of the results shown in [4]. The library was subsequently employed by the researcher together with local U. Bicocca collaborators and the PI to train a neural network and provide faster parameter estimation for BBH population parameters with future data [6].
RO4: Predict the stellar-mass BBH SGWB in the Laser Interferometer Space Antenna (LISA).
By the time the researcher started on WP2, a calculation of the BBH SGWB in LISA starting from the measured LVK population of BBHs already existed in the literature. This calculation was verified by the researcher using popstock, which was specifically extended to describe the LISA band. The researcher and local collaborators are extending this work to produce more accurate predictions of the BBH SGWB in LISA including eccentricity and spin effects. This work is in progress and is now being pursued also as a part of the LISA scientific ground segment.
[1] A stochastic search for intermittent gravitational-wave backgrounds, J. Lawrence, K. Turbang, A. Matas, A. I. Renzini, N. van Remortel and J. D. Romano, Phys. Rev. D 107 (2023) no.10 103026
[2] pygwb: A Python-based Library for Gravitational-wave Background Searches, A. I. Renzini and others, Astrophysical Journal 952 (2023) no.1 25
[3] pygwb: a Python-based library for gravitational-wave background searches, A. I. Renzini et al., Journal of Open Science Software, 9 (02/2024) no. 94, 5454
[4] Upper Limits on the Isotropic Gravitational-Wave Background from the first part of LIGO, Virgo, and KAGRA's fourth Observing Run, LIGO-Virgo-KAGRA Collaborations, arXiv: 2508.20721 (08/2025)
[5] Projections of the uncertainty on the compact binary population background using popstock, A. I. Renzini and J. Golomb, A&A 691 (11/2024) A238
[6] Accelerated inference of binary black-hole populations from the stochastic gravitational-wave background, G. Giarda, A. I. Renzini, C. Pacilio, D. Gerosa, CQG 42 (11/2025) 195015
RO1: Add a new fully functioning stochastic search pipeline for LIGO-Virgo-KAGRA (LVK) data analysis, to detect the intermittent background signal arising from binary black hole (BBH) mergers.
RO1 was mostly achieved: the methods paper was published [1] and the data-ready pipeline has been developed, however has not been published yet due to a minor but persistent bias that the analysis presents. This bias has been investigated thoroughly, and the researcher and collaborators are currently preparing a publication to explain the source of the bias.
RO2: Successfully analyse LVK data and detect/constrain the BBH gravitational-wave background (GWB).
RO2 was achieved by analysing the LVK O4a data, now public. This involved further developing and employing the analysis pipeline [2,3], the development of which was led by the researcher, and performing the search as a part of the LVK collaboration. Due to the delay in the start of the project due to the deferral of the start date, the researcher led the analysis of the newest version of LVK data (Observing run O4), as co-chair of the LVK isotropic stochastic group. This led to publication [4], which sets the most recent and most constraining upper limits on the BBH SGWB.
RO3: Deliver a comprehensive profile of the BBH population in our Universe.
RO3 was pursued both as a part of the LVK collaboration, using new datasets (O4a) which have now been released, and independently using older datasets: The researcher co-coordinated and contributed to the analysis presented in [4], which includes joint constraints on the BBH population using resolved BBH events within the LVK data and the GWB upper limit obtained. Furthermore, the researcher developed popstock [5], a library and pipeline to efficiently and accurately compute the BBH GWB spectrum starting from a parametric population model. The library is tailored to expect a set of posterior draws from standard population models, either obtained from data or from astrophysical modelling assumptions. This library was used to produce part of the results shown in [4]. The library was subsequently employed by the researcher together with local U. Bicocca collaborators and the PI to train a neural network and provide faster parameter estimation for BBH population parameters with future data [6].
RO4: Predict the stellar-mass BBH SGWB in the Laser Interferometer Space Antenna (LISA).
By the time the researcher started on WP2, a calculation of the BBH SGWB in LISA starting from the measured LVK population of BBHs already existed in the literature. This calculation was verified by the researcher using popstock, which was specifically extended to describe the LISA band. The researcher and local collaborators are extending this work to produce more accurate predictions of the BBH SGWB in LISA including eccentricity and spin effects. This work is in progress and is now being pursued also as a part of the LISA scientific ground segment.
[1] A stochastic search for intermittent gravitational-wave backgrounds, J. Lawrence, K. Turbang, A. Matas, A. I. Renzini, N. van Remortel and J. D. Romano, Phys. Rev. D 107 (2023) no.10 103026
[2] pygwb: A Python-based Library for Gravitational-wave Background Searches, A. I. Renzini and others, Astrophysical Journal 952 (2023) no.1 25
[3] pygwb: a Python-based library for gravitational-wave background searches, A. I. Renzini et al., Journal of Open Science Software, 9 (02/2024) no. 94, 5454
[4] Upper Limits on the Isotropic Gravitational-Wave Background from the first part of LIGO, Virgo, and KAGRA's fourth Observing Run, LIGO-Virgo-KAGRA Collaborations, arXiv: 2508.20721 (08/2025)
[5] Projections of the uncertainty on the compact binary population background using popstock, A. I. Renzini and J. Golomb, A&A 691 (11/2024) A238
[6] Accelerated inference of binary black-hole populations from the stochastic gravitational-wave background, G. Giarda, A. I. Renzini, C. Pacilio, D. Gerosa, CQG 42 (11/2025) 195015
This action has led/contributed to several impactful scientific publications. New key results that go beyond the state of the art include:
- A new a library and pipeline, popstock [3], to efficiently and accurately compute the BBH GWB spectrum starting from a population model. The library is tailored to expect a set of posterior draws from standard population models, either obtained from data or from astrophysical modelling assumptions. This provides a key piece of the inference and implications calculations to convert a measurement of the GWB into information on the population of BBHs.
- The most stringent upper limits on the GWB spectrum of BBHs by the LVK collaboration [2]. This upper limit is now consistent with the upper end of the expected amplitude of this signal, signifying that these analyses are beginning to exert real constraining power, and the LVK detectors will soon become sensitive to the GWB signal as more data is taken.
- A new neural network-based method for inference of BBH populations starting from GWB measurements [4], focusing on next generation detectors.
- A new reversible-jump MCMC method for inference of BBH populations starting from GWB measurements [5], compatible with both current and next generation detectors.
These publications are all publicly available to the scientific community and contribute to the growth of the community’s common knowledge of compact binary populations, gravitational-wave backgrounds (GWB), and data analysis methodologies. Together with other publications supported by this action, they paint a clear picture of (i) what the necessary conditions (sensitivity, signal amplitude) are for the detection of the GWB, (ii) what astrophysical information we will extract from this detection, and beyond this (iii) what avenues next generation detectors will open.
A crucial discovery has been that the original design of the SSI analysis published by researcher and collaborators in [1] does not capture the full complexity of the real data analysis problem. Furthermore, the capabilities of an SSI-like analysis to constrain the merger rate history o BBHs has been probed and compared to pre-existing methodologies and found that it may have reduced performance if implemented as originally designed. New research solutions are being explored to fully realise the potential of SSI.
[1] A stochastic search for intermittent gravitational-wave backgrounds, J. Lawrence, K. Turbang, A. Matas, A. I. Renzini, N. van Remortel and J. D. Romano, Phys. Rev. D 107 (2023) no.10 103026
[2] Upper Limits on the Isotropic Gravitational-Wave Background from the first part of LIGO, Virgo, and KAGRA's fourth Observing Run, LIGO-Virgo-KAGRA Collaborations, arXiv: 2508.20721 (08/2025)
[3] Projections of the uncertainty on the compact binary population background using popstock, A. I. Renzini and J. Golomb, A&A 691 (11/2024) A238
[4] Accelerated inference of binary black-hole populations from the stochastic gravitational-wave background, G. Giarda, A. I. Renzini, C. Pacilio, D. Gerosa, CQG 42 (11/2025) 195015
[5] A model-agnostic gravitational-wave background characterization algorithm, Taylor Knapp, Patrick M. Meyers, Arianna I. Renzini, arXiv:2507.08095 (07/2025)
- A new a library and pipeline, popstock [3], to efficiently and accurately compute the BBH GWB spectrum starting from a population model. The library is tailored to expect a set of posterior draws from standard population models, either obtained from data or from astrophysical modelling assumptions. This provides a key piece of the inference and implications calculations to convert a measurement of the GWB into information on the population of BBHs.
- The most stringent upper limits on the GWB spectrum of BBHs by the LVK collaboration [2]. This upper limit is now consistent with the upper end of the expected amplitude of this signal, signifying that these analyses are beginning to exert real constraining power, and the LVK detectors will soon become sensitive to the GWB signal as more data is taken.
- A new neural network-based method for inference of BBH populations starting from GWB measurements [4], focusing on next generation detectors.
- A new reversible-jump MCMC method for inference of BBH populations starting from GWB measurements [5], compatible with both current and next generation detectors.
These publications are all publicly available to the scientific community and contribute to the growth of the community’s common knowledge of compact binary populations, gravitational-wave backgrounds (GWB), and data analysis methodologies. Together with other publications supported by this action, they paint a clear picture of (i) what the necessary conditions (sensitivity, signal amplitude) are for the detection of the GWB, (ii) what astrophysical information we will extract from this detection, and beyond this (iii) what avenues next generation detectors will open.
A crucial discovery has been that the original design of the SSI analysis published by researcher and collaborators in [1] does not capture the full complexity of the real data analysis problem. Furthermore, the capabilities of an SSI-like analysis to constrain the merger rate history o BBHs has been probed and compared to pre-existing methodologies and found that it may have reduced performance if implemented as originally designed. New research solutions are being explored to fully realise the potential of SSI.
[1] A stochastic search for intermittent gravitational-wave backgrounds, J. Lawrence, K. Turbang, A. Matas, A. I. Renzini, N. van Remortel and J. D. Romano, Phys. Rev. D 107 (2023) no.10 103026
[2] Upper Limits on the Isotropic Gravitational-Wave Background from the first part of LIGO, Virgo, and KAGRA's fourth Observing Run, LIGO-Virgo-KAGRA Collaborations, arXiv: 2508.20721 (08/2025)
[3] Projections of the uncertainty on the compact binary population background using popstock, A. I. Renzini and J. Golomb, A&A 691 (11/2024) A238
[4] Accelerated inference of binary black-hole populations from the stochastic gravitational-wave background, G. Giarda, A. I. Renzini, C. Pacilio, D. Gerosa, CQG 42 (11/2025) 195015
[5] A model-agnostic gravitational-wave background characterization algorithm, Taylor Knapp, Patrick M. Meyers, Arianna I. Renzini, arXiv:2507.08095 (07/2025)