Parameter Estimation Horizon of Core-Collapse Supernovae with Current and Next-Generation Gravitational-Wave Detectors

Author(s)

Akhmetali, Almat, Abylkairov, Y. Sultan, Orel, Daniil, Nunes, Solange, Sakan, Aknur, Zhunuskanov, Alisher, Zaidyn, Marat, Ussipov, Nurzhan, Font, José Antonio, Abdikamalov, Ernazar

Abstract

Core-collapse supernovae (CCSNe) are powerful sources of gravitational waves (GWs). These signals propagate essentially unobstructed, providing a unique probe of the supernova central engine. In this work, we investigate parameter estimation from the bounce and early ring-down GW signal of rotating CCSNe using machine learning. We infer the peak frequency and peak amplitude of the signal as well as the rotation of the core. We extend previous studies in several directions. We consider a range of progenitor models and nuclear equations of state, and we assess the impact of key physical uncertainties, including bounce-time uncertainty and source inclination. We incorporate both current detector noise and the projected sensitivities of next-generation observatories. We find that uncertainty in the bounce time does not significantly affect parameter estimation when the analysis is performed in the Fourier domain. In contrast, orientations when the rotation axis is near the line of sight substantially degrade performance. For optimal orientations, next-generation detectors can constrain rotation out to distances exceeding 100 kpc.

Figures

True vs. predicted values of the estimated parameters using the FD representation with $\Delta t_{\mathrm b}=20$\,ms and signals at a distance of 10\,kpc. The black dashed diagonal line corresponds to the ideal prediction. Gray dashed lines and shaded regions indicate the $1\sigma$ and $2\sigma$ deviation intervals. MAPE values are $7.10\%$, $3.14\%$, $6.43\%$ for $T/|W|$, $f_\mathrm{peak}$, and $D\Delta h$, respectively.
Caption True vs. predicted values of the estimated parameters using the FD representation with $\Delta t_{\mathrm b}=20$\,ms and signals at a distance of 10\,kpc. The black dashed diagonal line corresponds to the ideal prediction. Gray dashed lines and shaded regions indicate the $1\sigma$ and $2\sigma$ deviation intervals. MAPE values are $7.10\%$, $3.14\%$, $6.43\%$ for $T/|W|$, $f_\mathrm{peak}$, and $D\Delta h$, respectively.
P-P plot for the estimated parameters at 10\,kpc using the FD-based model. The curve shows the fraction of true parameter values contained within the predicted credible intervals as a function of the nominal confidence level. The dashed diagonal line indicates perfect calibration.
Caption P-P plot for the estimated parameters at 10\,kpc using the FD-based model. The curve shows the fraction of true parameter values contained within the predicted credible intervals as a function of the nominal confidence level. The dashed diagonal line indicates perfect calibration.
Fraction of signals with Absolute Percentage Error (APE) $\le20\%$ as a function of source distance for different parameters and detectors. The blue, orange, and green lines correspond to $T/|W|$, $f_{\mathrm{peak}}$, and $D\Delta h$, respectively. Solid lines represent the A+ detector, while dashed and dotted lines correspond to the ET and CE 3G detectors. The gray horizontal dashed line at 0.9 indicates a threshold for reasonably accurate practical predictions. Vertical black dashed lines mark reference distances to the Galactic Center (8.5\,kpc), the Large Magellanic Cloud (49.8\,kpc), and M31 (780\,kpc).
Caption Fraction of signals with Absolute Percentage Error (APE) $\le20\%$ as a function of source distance for different parameters and detectors. The blue, orange, and green lines correspond to $T/|W|$, $f_{\mathrm{peak}}$, and $D\Delta h$, respectively. Solid lines represent the A+ detector, while dashed and dotted lines correspond to the ET and CE 3G detectors. The gray horizontal dashed line at 0.9 indicates a threshold for reasonably accurate practical predictions. Vertical black dashed lines mark reference distances to the Galactic Center (8.5\,kpc), the Large Magellanic Cloud (49.8\,kpc), and M31 (780\,kpc).
References
  • [1] The LIGO Scientific Collaboration, the Virgo Col- laboration, the KAGRA Collaboration, A. G. Abac, I. Abouelfettouh, F. Acernese, and K. e. a. Ackley, GWTC-4.0: Updating the Gravitational-Wave Transient Catalog with Observations from the First Part of the Fourth LIGO-Virgo-KAGRA Observing Run, arXiv e-prints , arXiv:2508.18082 (2025), arXiv:2508.18082 [gr-qc].
  • [1] The LIGO Scientific Collaboration, the Virgo Col- laboration, the KAGRA Collaboration, A. G. Abac, I. Abouelfettouh, F. Acernese, and K. e. a. Ackley, GWTC-4.0: Updating the Gravitational-Wave Transient Catalog with Observations from the First Part of the Fourth LIGO-Virgo-KAGRA Observing Run, arXiv e-prints , arXiv:2508.18082 (2025), arXiv:2508.18082 [gr-qc].
  • [2] A. Mezzacappa and M. Zanolin, Gravitational Waves from Neutrino-Driven Core Collapse Supernovae: Predictions, Detection, and Parameter Estimation, arXiv e-prints , arXiv:2401.11635 (2024), arXiv:2401.11635 [astro-ph.HE].
  • [2] A. Mezzacappa and M. Zanolin, Gravitational Waves from Neutrino-Driven Core Collapse Supernovae: Predictions, Detection, and Parameter Estimation, arXiv e-prints , arXiv:2401.11635 (2024), arXiv:2401.11635 [astro-ph.HE].
  • [3] D. Vartanyan, A. Burrows, T. Wang, M. S. B. Coleman, and C. J. White, Gravitational-wave signature of corecollapse supernovae, Phys. Rev. D 107, 103015 (2023), arXiv:2302.07092 [astro-ph.HE].
  • [4] B. Müller, Core-Collapse Supernovae and their Gravitational Wave Signals: The Status of Theory and Modeling, arXiv e-prints , arXiv:2603.24243 (2026), arXiv:2603.24243 [astro-ph.HE].
  • [4] B. Müller, Core-Collapse Supernovae and their Gravitational Wave Signals: The Status of Theory and Modeling, arXiv e-prints , arXiv:2603.24243 (2026), arXiv:2603.24243 [astro-ph.HE].
  • [5] B. P. Abbott, R. Abbott, T. D. Abbott, S. Abraham, and F. Acernese (LIGO Scientific Collaboration and Virgo Collaboration and ASAS-SN Collaboration and DLT40 Collaboration), Optically targeted search for gravitational waves emitted by core-collapse supernovae during the first and second observing runs of advanced ligo and advanced virgo, Phys. Rev. D 101, 084002 (2020).
  • [6] M. J. Szczepańczyk, Y. Zheng, J. M. Antelis, M. Benjamin, M.-A. Bizouard, A. Casallas-Lagos, P. CerdáDurán, D. Davis, D. Gondek-Rosińska, S. Klimenko, C. Moreno, M. Obergaulinger, J. Powell, D. Ramirez, B. Ratto, C. Richardson, A. Rijal, A. L. Stuver, P. Szewczyk, G. Vedovato, M. Zanolin, I. Bartos, S. Bhaumik, T. Bulik, M. Drago, J. A. Font, F. De Colle, J. Garcı́a-Bellido, V. Gayathri, B. Hughey, G. Mitselmakher, T. Mishra, S. Mukherjee, Q. L. Nguyen, M. L. Chan, I. Di Palma, B. J. Piotrzkowski, and N. Singh, Optically targeted search for gravitational waves emitted by core-collapse supernovae during the third observing run of advanced ligo and advanced virgo, Phys. Rev. D 110, 042007 (2024).
  • [7] V. Srivastava, S. Ballmer, D. A. Brown, C. Afle, A. Burrows, D. Radice, and D. Vartanyan, Detection prospects of core-collapse supernovae with supernova-optimized third-generation gravitational-wave detectors, Phys. Rev. D 100, 043026 (2019), arXiv:1906.00084 [gr-qc].
  • [8] H.-T. Janka, T. Melson, and A. Summa, Physics of Core-Collapse Supernovae in Three Dimensions: A Sneak Preview, Annual Review of Nuclear and Particle Science 66, 341 (2016), arXiv:1602.05576 [astro-ph.SR].
  • [9] T. Ertl, H.-T. Janka, S. E. Woosley, T. Sukhbold, and M. Ugliano, A Two-parameter Criterion for Classifying the Explodability of Massive Stars by the Neutrinodriven Mechanism, Astrophys. J. 818, 124 (2016), arXiv:1503.07522 [astro-ph.SR].
  • [10] L. Boccioli, D. Vartanyan, E. P. O’Connor, and D. Kasen, Neutrino heating in 1D, 2D, and 3D corecollapse supernovae: characterizing the explosion of high-compactness stars, MNRAS 540, 3885 (2025), arXiv:2501.06784 [astro-ph.HE].
  • [11] H.-T. Janka, Conditions for shock revival by neutrino heating in core-collapse supernovae, A&A 368, 527 (2001), arXiv:astro-ph/0008432 [astro-ph].
  • [12] A. Burrows, L. Dessart, E. Livne, C. D. Ott, and J. Murphy, Simulations of Magnetically Driven Supernova and Hypernova Explosions in the Context of Rapid Rotation, Astrophys. J. 664, 416 (2007), arXiv:astroph/0702539.
  • [13] A. Burrows, Colloquium: Perspectives on core-collapse supernova theory, Reviews of Modern Physics 85, 245 (2013), arXiv:1210.4921 [astro-ph.SR].
  • [14] E. O’Connor and C. D. Ott, Black Hole Formation in Failing Core-Collapse Supernovae, Astrophys. J. 730, 70 (2011), arXiv:1010.5550 [astro-ph.HE].
  • [15] K. Nakamura, S. Horiuchi, M. Tanaka, K. Hayama, T. Takiwaki, and K. Kotake, Multimessenger signals of long-term core-collapse supernova simulations: synergetic observation strategies, Mon. Not. Roy. Astron. Soc. 461, 3296 (2016), arXiv:1602.03028 [astro-ph.HE].
  • [16] J. R. Westernacher-Schneider, E. O’Connor, E. O’Sullivan, I. Tamborra, M.-R. Wu, S. M. Couch, and F. Malmenbeck, Multimessenger asteroseismology of core-collapse supernovae, Phys. Rev. D 100, 123009 (2019), arXiv:1907.01138 [astro-ph.HE].
  • [17] B. Müller, H.-T. Janka, and A. Marek, A New Multidimensional General Relativistic Neutrino Hydrodynamics Code of Core-collapse Supernovae. III. Gravitational Wave Signals from Supernova Explosion Models, Astrophys. J. 766, 43 (2013), arXiv:1210.6984 [astroph.SR].
  • [18] V. Morozova, D. Radice, A. Burrows, and D. Vartanyan, The Gravitational Wave Signal from Corecollapse Supernovae, Astrophys. J. 861, 10 (2018), arXiv:1801.01914 [astro-ph.HE].
  • [19] A. Torres-Forné, P. Cerdá-Durán, M. Obergaulinger, B. Müller, and J. A. Font, Universal Relations for Gravitational-Wave Asteroseismology of Protoneutron Stars, Phys. Rev. Lett. 123, 051102 (2019), arXiv:1902.10048 [gr-qc].
  • [20] J. Powell and B. Müller, Inferring astrophysical parameters of core-collapse supernovae from their gravitationalwave emission, Phys. Rev. D 105, 063018 (2022), arXiv:2201.01397 [astro-ph.HE].
  • [21] A. Burrows and J. Goshy, A Theory of Supernova Explosions, ApJ Lett. 416, L75 (1993).
  • [22] B. Müller, H.-T. Janka, and A. Heger, New Twodimensional Models of Supernova Explosions by the Neutrino-heating Mechanism: Evidence for Different Instability Regimes in Collapsing Stellar Cores, Astrophys. J. 761, 72 (2012), arXiv:1205.7078 [astro-ph.SR].
  • [23] D. Radice, C. D. Ott, E. Abdikamalov, S. M. Couch, R. Haas, and E. Schnetter, Neutrino-driven Convection in Core-collapse Supernovae: High-resolution Simulations, Astrophys. J. 820, 76 (2016), arXiv:1510.05022 [astro-ph.HE].
  • [24] J. W. Murphy, C. D. Ott, and A. Burrows, A Model for Gravitational Wave Emission from Neutrino-Driven Core-Collapse Supernovae, Astrophys. J. 707, 1173 (2009), arXiv:0907.4762 [astro-ph.SR].
  • [25] C. D. Ott, E. Abdikamalov, P. Mösta, R. Haas, S. Drasco, E. P. O’Connor, C. Reisswig, C. A. Meakin, and E. Schnetter, General-relativistic Simulations of Three-dimensional Core-collapse Supernovae, Astrophys. J. 768, 115 (2013), arXiv:1210.6674 [astroph.HE].
  • [26] K. N. Yakunin, A. Mezzacappa, P. Marronetti, S. Yoshida, S. W. Bruenn, W. R. Hix, E. J. Lentz, O. E. Bronson Messer, J. A. Harris, E. Endeve, J. M. Blondin, and E. J. Lingerfelt, Gravitational wave signatures of ab initio two-dimensional core collapse supernova explosion models for 12 -25 M⊙ stars, Phys. Rev. D 92, 084040 (2015), arXiv:1505.05824 [astro-ph.HE].
  • [27] H. Andresen, B. Müller, E. Müller, and H. T. Janka, Gravitational wave signals from 3D neutrino hydrodynamics simulations of core-collapse supernovae, MNRAS 468, 2032 (2017), arXiv:1607.05199 [astro-ph.HE].
  • [28] A. Mezzacappa, P. Marronetti, R. E. Landfield, E. J. Lentz, R. D. Murphy, W. Raphael Hix, J. A. Harris, S. W. Bruenn, J. M. Blondin, O. E. Bronson Messer, J. Casanova, and L. L. Kronzer, Core collapse supernova gravitational wave emission for progenitors of 9.6, 15, and 25M⊙, Phys. Rev. D 107, 043008 (2023), arXiv:2208.10643 [astro-ph.SR].
  • [29] H. Sotani, B. Müller, and T. Takiwaki, Universality in supernova gravitational waves with protoneutron star properties, Phys. Rev. D 109, 123021 (2024), arXiv:2405.09030 [astro-ph.HE].
  • [30] J. Ehring, S. Abbar, H.-T. Janka, G. Raffelt, K. Nakamura, and K. Kotake, Gravitational-Wave Signatures of Nonstandard Neutrino Properties in Collapsing Stellar Cores, Phys. Rev. Lett. 136, 021201 (2026), arXiv:2412.02750 [astro-ph.HE].
  • [31] A. Lella, G. Lucente, D. Kresse, R. Glas, H.-T. Janka, and A. Mirizzi, Gravitational-Wave Signals for Supernova Explosions of Three-Dimensional Progenitors, arXiv e-prints , arXiv:2602.02651 (2026), arXiv:2602.02651 [astro-ph.HE].
  • [31] A. Lella, G. Lucente, D. Kresse, R. Glas, H.-T. Janka, and A. Mirizzi, Gravitational-Wave Signals for Supernova Explosions of Three-Dimensional Progenitors, arXiv e-prints , arXiv:2602.02651 (2026), arXiv:2602.02651 [astro-ph.HE].
  • [32] S. M. Couch and C. D. Ott, Revival of the Stalled Corecollapse Supernova Shock Triggered by Precollapse Asphericity in the Progenitor Star, ApJ Lett. 778, L7 (2013), arXiv:1309.2632 [astro-ph.HE].
  • [33] S. M. Couch, E. Chatzopoulos, W. D. Arnett, and F. X. Timmes, The Three-dimensional Evolution to Core Collapse of a Massive Star, ApJ Lett. 808, L21 (2015), arXiv:1503.02199 [astro-ph.HE].
  • [34] B. Müller, T. Melson, A. Heger, and H.-T. Janka, Supernova simulations from a 3D progenitor model - Impact of perturbations and evolution of explosion properties, MNRAS 472, 491 (2017), arXiv:1705.00620 [astroph.SR].
  • [35] H. Nagakura, K. Takahashi, and Y. Yamamoto, On the importance of progenitor asymmetry to shock revival in core-collapse supernovae, MNRAS 483, 208 (2019), arXiv:1811.05515 [astro-ph.HE].
  • [36] R. Kazeroni and E. Abdikamalov, The impact of progenitor asymmetries on the neutrino-driven convection in core-collapse supernovae, MNRAS 494, 5360 (2020), arXiv:1911.08819 [astro-ph.SR].
  • [37] D. Vartanyan, M. S. B. Coleman, and A. Burrows, The collapse and three-dimensional explosion of threedimensional massive-star supernova progenitor models, MNRAS 510, 4689 (2022), arXiv:2109.10920 [astroph.SR].
  • [38] Y. Telman, E. Abdikamalov, and T. Foglizzo, Convective vortices in collapsing stars, MNRAS 535, 1388 (2024), arXiv:2409.17737 [astro-ph.SR].
  • [39] J. M. Blondin, A. Mezzacappa, and C. DeMarino, Stability of Standing Accretion Shocks, with an Eye toward Core-Collapse Supernovae, Astrophys. J. 584, 971 (2003), arXiv:astro-ph/0210634 [astro-ph].
  • [40] T. Foglizzo, L. Scheck, and H. T. Janka, Neutrino-driven Convection versus Advection in Core-Collapse Supernovae, Astrophys. J. 652, 1436 (2006), arXiv:astroph/0507636 [astro-ph].
  • [41] T. Kuroda, K. Kotake, and T. Takiwaki, A New Gravitational-wave Signature from Standing Accretion Shock Instability in Supernovae, ApJ Lett. 829, L14 (2016), arXiv:1605.09215 [astro-ph.HE].
  • [42] T. Kuroda, K. Kotake, K. Hayama, and T. Takiwaki, Correlated Signatures of Gravitational-wave and Neutrino Emission in Three-dimensional Generalrelativistic Core-collapse Supernova Simulations, Astrophys. J. 851, 62 (2017), arXiv:1708.05252 [astroph.HE].
  • [43] A. C. Buellet, T. Foglizzo, J. Guilet, and E. Abdikamalov, Effect of stellar rotation on the development of post-shock instabilities during core-collapse supernovae, A&A 674, A205 (2023), arXiv:2301.01962 [astroph.HE].
  • [44] B. Müller and H.-T. Janka, Non-radial instabilities and progenitor asphericities in core-collapse supernovae, MNRAS 448, 2141 (2015), arXiv:1409.4783 [astroph.SR].
  • [45] S. W. Bruenn, E. J. Lentz, W. R. Hix, A. Mezzacappa, J. A. Harris, O. E. B. Messer, E. Endeve, J. M. Blondin, M. A. Chertkow, E. J. Lingerfelt, P. Marronetti, and K. N. Yakunin, The Development of Explosions in Axisymmetric Ab Initio Core-collapse Supernova Simulations of 12-25 M Stars, Astrophys. J. 818, 123 (2016), arXiv:1409.5779 [astro-ph.SR].
  • [46] A. Heger, S. E. Woosley, and H. C. Spruit, Presupernova Evolution of Differentially Rotating Massive Stars Including Magnetic Fields, Astrophys. J. 626, 350 (2005), arXiv:astro-ph/0409422 [astro-ph].
  • [47] C. D. Ott, E. Abdikamalov, E. O’Connor, C. Reisswig, R. Haas, P. Kalmus, S. Drasco, A. Burrows, and E. Schnetter, Correlated gravitational wave and neutrino signals from general-relativistic rapidly rotating iron core collapse, Phys. Rev. D 86, 024026 (2012), arXiv:1204.0512 [astro-ph.HE].
  • [48] J. Fuller, H. Klion, E. Abdikamalov, and C. D. Ott, Supernova seismology: gravitational wave signatures of rapidly rotating core collapse, MNRAS 450, 414 (2015), arXiv:1501.06951 [astro-ph.HE].
  • [49] S. Scheidegger, T. Fischer, S. C. Whitehouse, and M. Liebendörfer, Gravitational waves from 3D MHD core collapse simulations, A&A 490, 231 (2008), arXiv:0709.0168 [astro-ph].
  • [50] S. Shibagaki, T. Kuroda, K. Kotake, and T. Takiwaki, A new gravitational-wave signature of low-T/—W— instability in rapidly rotating stellar core collapse, MNRAS 493, L138 (2020), arXiv:1909.09730 [astro-ph.HE].
  • [51] K.-C. Pan, M. Liebendörfer, S. M. Couch, and F.-K. Thielemann, Stellar Mass Black Hole Formation and Multimessenger Signals from Three-dimensional Rotating Core-collapse Supernova Simulations, Astrophys. J. 914, 140 (2021), arXiv:2010.02453 [astro-ph.HE].
  • [52] E. Mueller and H. T. Janka, Gravitational radiation from convective instabilities in Type II supernova explosions., A&A 317, 140 (1997).
  • [53] T. Takiwaki and K. Kotake, Anisotropic emission of neutrino and gravitational-wave signals from rapidly rotating core-collapse supernovae, MNRAS 475, L91 (2018), arXiv:1711.01905 [astro-ph.HE].
  • [54] D. Vartanyan and A. Burrows, Gravitational Waves from Neutrino Emission Asymmetries in Corecollapse Supernovae, Astrophys. J. 901, 108 (2020), arXiv:2007.07261 [astro-ph.HE].
  • [55] L. Choi, A. Burrows, and D. Vartanyan, Gravitationalwave and Gravitational-wave Memory Signatures of Core-collapse Supernovae, Astrophys. J. 975, 12 (2024), arXiv:2408.01525 [astro-ph.HE].
  • [56] D. Radice, V. Morozova, A. Burrows, D. Vartanyan, and H. Nagakura, Characterizing the Gravitational Wave Signal from Core-collapse Supernovae, ApJL 876, L9 (2019), arXiv:1812.07703 [astro-ph.HE].
  • [57] O. Birnholtz and T. Piran, Gravitational wave memory from gamma ray bursts’ jets, Phys. Rev. D 87, 123007 (2013), arXiv:1302.5713 [astro-ph.HE].
  • [58] M. Pais, T. Piran, and E. Nakar, The velocity distribution of outflows driven by choked jets in stellar envelopes, MNRAS 519, 1941 (2023), arXiv:2208.14459 [astro-ph.HE].
  • [59] P. Mösta, S. Richers, C. D. Ott, R. Haas, A. L. Piro, K. Boydstun, E. Abdikamalov, C. Reisswig, and E. Schnetter, Magnetorotational Core-collapse Supernovae in Three Dimensions, ApJL 785, L29 (2014), arXiv:1403.1230 [astro-ph.HE].
  • [60] M. Obergaulinger and M. Á. Aloy, Magnetorotational core collapse of possible GRB progenitors I. Explosion mechanisms, MNRAS 492, 4613 (2020), arXiv:1909.01105 [astro-ph.HE].
  • [61] T. Kuroda, A. Arcones, T. Takiwaki, and K. Kotake, Magnetorotational Explosion of a Massive Star Supported by Neutrino Heating in General Relativistic Three-dimensional Simulations, Astrophys. J. 896, 102 (2020), arXiv:2003.02004 [astro-ph.HE].
  • [62] M. Cusinato, M. Obergaulinger, M. Á. Aloy, and J. A. Font, Resonant amplification of multimessenger emission in rotating stellar core collapse, Physical Review Research 8, 013180 (2026).
  • [63] M. A. Pajkos, M. L. Warren, S. M. Couch, E. P. O’Connor, and K.-C. Pan, Determining the Structure of Rotating Massive Stellar Cores with Gravitational Waves, Astrophys. J. 914, 80 (2021), arXiv:2011.09000 [astro-ph.HE].
  • [64] E. Abdikamalov, G. Pagliaroli, and D. Radice, Gravitational Waves from Core-Collapse Supernovae, in Handbook of Gravitational Wave Astronomy, edited by C. Bambi, S. Katsanevas, and K. D. Kokkotas (2022) p. 21.
  • [65] A. Casallas-Lagos, J. M. Antelis, C. Moreno, M. Zanolin, A. Mezzacappa, and M. J. Szczepańczyk, Characterizing the temporal evolution of the high-frequency gravitational wave emission for a core collapse supernova with laser interferometric data: A neural network approach, Phys. Rev. D 108, 084027 (2023).
  • [66] A. Mitra, B. Shukirgaliyev, Y. S. Abylkairov, and E. Abdikamalov, Exploring supernova gravitational waves with machine learning, MNRAS 520, 2473 (2023), arXiv:2209.14542 [astro-ph.HE].
  • [67] J. Logue, C. D. Ott, I. S. Heng, P. Kalmus, and J. H. C. Scargill, Inferring core-collapse supernova physics with gravitational waves, Phys. Rev. D 86, 044023 (2012), arXiv:1202.3256 [gr-qc].
  • [68] J. Powell, A. Iess, M. Llorens-Monteagudo, M. Obergaulinger, B. Müller, A. Torres-Forné, E. Cuoco, and J. A. Font, Determining the core-collapse supernova explosion mechanism with current and future gravitational-wave observatories, Phys. Rev. D 109, 063019 (2024), arXiv:2311.18221 [astro-ph.HE].
  • [69] E. Abdikamalov, S. Gossan, A. M. DeMaio, and C. D. Ott, Measuring the angular momentum distribution in core-collapse supernova progenitors with gravitational waves, Phys. Rev. D 90, 044001 (2014), arXiv:1311.3678 [astro-ph.SR].
  • [70] M. A. Pajkos, S. M. Couch, K.-C. Pan, and E. P. O’Connor, Features of Accretion-phase Gravitationalwave Emission from Two-dimensional Rotating Corecollapse Supernovae, Astrophys. J. 878, 13 (2019), arXiv:1901.09055 [astro-ph.HE].
  • [71] M.-A. Bizouard, P. Maturana-Russel, A. Torres-Forné, M. Obergaulinger, P. Cerdá-Durán, N. Christensen, J. A. Font, and R. Meyer, Inference of protoneutron star properties from gravitational-wave data in corecollapse supernovae, Phys. Rev. D 103, 063006 (2021), arXiv:2012.00846 [gr-qc].
  • [72] T. Bruel, M.-A. Bizouard, M. Obergaulinger, P. Maturana-Russel, A. Torres-Forné, P. Cerdá-Durán, N. Christensen, J. A. Font, and R. Meyer, Inference of protoneutron star properties in core-collapse supernovae from a gravitational-wave detector network, Phys. Rev. D 107, 083029 (2023), arXiv:2301.10019 [astro-ph.HE].
  • [73] P. Cerdá-Durán, N. DeBrye, M. A. Aloy, J. A. Font, and M. Obergaulinger, Gravitational Wave Signatures in Black Hole Forming Core Collapse, ApJL 779, L18 (2013), arXiv:1310.8290 [astro-ph.SR].
  • [74] K.-C. Pan, M. Liebendörfer, S. M. Couch, and F.K. Thielemann, Equation of State Dependent Dynamics and Multi-messenger Signals from Stellar-mass Black Hole Formation, Astrophys. J. 857, 13 (2018), arXiv:1710.01690 [astro-ph.HE].
  • [75] S. Shibagaki, T. Kuroda, K. Kotake, and T. Takiwaki, Characteristic time variability of gravitationalwave and neutrino signals from three-dimensional simulations of non-rotating and rapidly rotating stellar core collapse, MNRAS 502, 3066 (2021), arXiv:2010.03882 [astro-ph.HE].
  • [76] A. Burrows, D. Vartanyan, and T. Wang, Black Hole Formation Accompanied by the Supernova Explosion of a 40 M ⊙ Progenitor Star, Astrophys. J. 957, 68 (2023), arXiv:2308.05798 [astro-ph.SR].
  • [77] J. Powell and B. Müller, Gravitational waves from core-collapse supernovae with no electromagnetic counterparts, arXiv e-prints , arXiv:2506.03581 (2025), arXiv:2506.03581 [astro-ph.HE].
  • [77] J. Powell and B. Müller, Gravitational waves from core-collapse supernovae with no electromagnetic counterparts, arXiv e-prints , arXiv:2506.03581 (2025), arXiv:2506.03581 [astro-ph.HE].
  • [78] O. Eggenberger Andersen, E. O’Connor, H. Andresen, A. da Silva Schneider, and S. M. Couch, Black Hole Supernovae, Their Equation of State Dependence, and Ejecta Composition, Astrophys. J. 980, 53 (2025), arXiv:2411.11969 [astro-ph.HE].
  • [79] C. D. Ott, C. Reisswig, E. Schnetter, E. O’Connor, U. Sperhake, F. Löffler, P. Diener, E. Abdikamalov, I. Hawke, and A. Burrows, Dynamics and Gravitational Wave Signature of Collapsar Formation, Phys. Rev. Lett. 106, 161103 (2011), arXiv:1012.1853 [astroph.HE].
  • [80] T. Kuroda and M. Shibata, Failed supernova simulations beyond black hole formation, MNRAS 526, 152 (2023), arXiv:2307.06192 [astro-ph.HE].
  • [81] S. Richers, C. D. Ott, E. Abdikamalov, E. O’Connor, and C. Sullivan, Equation of state effects on gravitational waves from rotating core collapse, Phys. Rev. D 95, 063019 (2017), arXiv:1701.02752 [astro-ph.HE].
  • [82] M. C. Edwards, Classifying the equation of state from rotating core collapse gravitational waves with deep learning, Phys. Rev. D 103, 024025 (2021), arXiv:2009.07367 [astro-ph.IM].
  • [83] Y.-S. Chao, C.-Z. Su, T.-Y. Chen, D.-W. Wang, and K.-C. Pan, Determining the Core Structure and Nuclear Equation of State of Rotating Core-collapse Supernovae with Gravitational Waves by Convolutional Neural Networks, Astrophys. J. 939, 13 (2022), arXiv:2209.10089 [astro-ph.HE].
  • [84] N. E. Wolfe, C. Fröhlich, J. M. Miller, A. TorresForné, and P. Cerdá-Durán, Gravitational Wave Eigenfrequencies from Neutrino-driven Core-collapse Supernovae, Astrophys. J. 954, 161 (2023), arXiv:2303.16962 [astro-ph.HE].
  • [85] A. Mitra, D. Orel, Y. S. Abylkairov, B. Shukirgaliyev, and E. Abdikamalov, Probing nuclear physics with supernova gravitational waves and machine learning, MNRAS 529, 3582 (2024), arXiv:2310.15649 [astro-ph.HE].
  • [86] Y. Sultan Abylkairov, M. C. Edwards, A. Ostrikov, Y. Tleukhanov, A. Torres-Forné, P. Cerdá-Durán, J. A. Font, M. J. Szczepańczyk, and E. Abdikamalov, Assessing the distance for probing the nuclear equation of state with supernova gravitational waves, Phys. Rev. D , (2025).
  • [87] A. Akhmetali, Y. Sultan Abylkairov, M. Zaidyn, A. Sakan, A. Zhunuskanov, N. Ussipov, J. A. Font, A. Torres-Forné, and E. Abdikamalov, Toward More Realistic Machine-Learning Inference of the DenseMatter Equation of State from Supernova Gravitational Waves, arXiv e-prints , arXiv:2603.27680 (2026), arXiv:2603.27680 [astro-ph.HE].
  • [87] A. Akhmetali, Y. Sultan Abylkairov, M. Zaidyn, A. Sakan, A. Zhunuskanov, N. Ussipov, J. A. Font, A. Torres-Forné, and E. Abdikamalov, Toward More Realistic Machine-Learning Inference of the DenseMatter Equation of State from Supernova Gravitational Waves, arXiv e-prints , arXiv:2603.27680 (2026), arXiv:2603.27680 [astro-ph.HE].
  • [88] R. D. Murphy, A. Casallas-Lagos, A. Mezzacappa, M. Zanolin, R. E. Landfield, E. J. Lentz, P. Marronetti, J. M. Antelis, and C. Moreno, Dependence of the reconstructed core-collapse supernova gravitational wave high-frequency feature on the nuclear equation of state in real interferometric data, Phys. Rev. D 110, 083006 (2024), arXiv:2406.01784 [astro-ph.HE].
  • [89] A. Rusakov, A. S. Burrows, T. Wang, and D. Vartanyan, An Exploration of the Equation of State Dependence of Core-Collapse Supernova Explosion Outcomes and Signatures, arXiv e-prints , arXiv:2602.09025 (2026), arXiv:2602.09025 [astro-ph.HE].
  • [89] A. Rusakov, A. S. Burrows, T. Wang, and D. Vartanyan, An Exploration of the Equation of State Dependence of Core-Collapse Supernova Explosion Outcomes and Signatures, arXiv e-prints , arXiv:2602.09025 (2026), arXiv:2602.09025 [astro-ph.HE].
  • [90] J. Powell and B. Müller, Impact of the nuclear equation of state on the explodability of massive stars, arXiv e-prints , arXiv:2510.20076 (2025), arXiv:2510.20076 [astro-ph.HE].
  • [90] J. Powell and B. Müller, Impact of the nuclear equation of state on the explodability of massive stars, arXiv e-prints , arXiv:2510.20076 (2025), arXiv:2510.20076 [astro-ph.HE].
  • [91] C. D. Ott, H. Dimmelmeier, A. Marek, H. T. Janka, B. Zink, I. Hawke, and E. Schnetter, Rotating collapse of stellar iron cores in general relativity, Classical and Quantum Gravity 24, S139 (2007), arXiv:astroph/0612638 [astro-ph].
  • [92] Y. S. Abylkairov, M. C. Edwards, D. Orel, A. Mitra, B. Shukirgaliyev, and E. Abdikamalov, Evaluating machine learning models for supernova gravitational wave signal classification, Machine Learning: Science and Technology 5, 045077 (2024), arXiv:2409.14508 [astroph.HE].
  • [93] M. C. Edwards, R. Meyer, and N. Christensen, Bayesian parameter estimation of core collapse supernovae using gravitational wave simulations, Inverse Problems 30, 114008 (2014), arXiv:1407.7549 [physics.data-an].
  • [94] C. Pastor-Marcos, P. Cerdá-Durán, D. Walker, A. Torres-Forné, E. Abdikamalov, S. Richers, and J. A. Font, Bayesian inference from gravitational waves in fast-rotating, core-collapse supernovae, Phys. Rev. D 109, 063028 (2024), arXiv:2308.03456 [astro-ph.HE].
  • [95] S. Nunes, G. Escrig, O. G. Freitas, J. A. Font, T. Fernandes, A. Onofre, and A. Torres-Forné, Deep-learning classification and parameter inference of rotational corecollapse supernovae, Phys. Rev. D 110, 064037 (2024), arXiv:2403.04938 [astro-ph.HE].
  • [96] L. O. Villegas, C. Moreno, M. A. Pajkos, M. Zanolin, and J. M. Antelis, Parameter estimation from the corebounce phase of rotating core collapse supernovae in real interferometer noise, Classical and Quantum Gravity 42, 115001 (2025).
  • [97] G. Pagliaroli, F. Vissani, E. Coccia, and W. Fulgione, Neutrinos from Supernovae as a Trigger for Gravitational Wave Search, Phys. Rev. Lett. 103, 031102 (2009), arXiv:0903.1191 [hep-ph].
  • [98] F. Halzen and G. G. Raffelt, Reconstructing the supernova bounce time with neutrinos in IceCube, Phys. Rev. D 80, 087301 (2009), arXiv:0908.2317 [astro-ph.HE].
  • [99] S. Hild, M. Abernathy, F. Acernese, P. Amaro-Seoane, N. Andersson, K. Arun, F. Barone, B. Barr, M. Barsuglia, M. Beker, N. Beveridge, S. Birindelli, S. Bose, L. Bosi, S. Braccini, C. Bradaschia, T. Bulik, E. Calloni, G. Cella, E. Chassande Mottin, S. Chelkowski, A. Chincarini, J. Clark, E. Coccia, C. Colacino, J. Colas, A. Cumming, L. Cunningham, E. Cuoco, S. Danilishin, K. Danzmann, R. De Salvo, T. Dent, R. De Rosa, L. Di Fiore, A. Di Virgilio, M. Doets, V. Fafone, P. Falferi, R. Flaminio, J. Franc, F. Frasconi, A. Freise, D. Friedrich, P. Fulda, J. Gair, G. Gemme, E. Genin, A. Gennai, A. Giazotto, K. Glampedakis, C. Gräf, M. Granata, H. Grote, G. Guidi, A. Gurkovsky, G. Hammond, M. Hannam, J. Harms, D. Heinert, M. Hendry, I. Heng, E. Hennes, J. Hough, S. Husa, S. Huttner, G. Jones, F. Khalili, K. Kokeyama, K. Kokkotas, B. Krishnan, T. G. F. Li, M. Lorenzini, H. Lück, E. Majorana, I. Mandel, V. Mandic, M. Mantovani, I. Martin, C. Michel, Y. Minenkov, N. Morgado, S. Mosca, B. Mours, H. Müller—Ebhardt, P. Murray, R. Nawrodt, J. Nelson, R. Oshaughnessy, C. D. Ott, C. Palomba, A. Paoli, G. Parguez, A. Pasqualetti, R. Passaquieti, D. Passuello, L. Pinard, W. Plastino, R. Poggiani, P. Popolizio, M. Prato, M. Punturo, P. Puppo, D. Rabeling, P. Rapagnani, J. Read,
  • [100] A. Abac and et al, The Science of the Einstein Telescope, J. Cosmol. Astropart. Phys. 2026, 081 (2026), arXiv:2503.12263 [gr-qc].
  • [101] E. D. Hall, Cosmic Explorer: A Next-Generation Ground-Based Gravitational-Wave Observatory, Galaxies 10, 10.3390/galaxies10040090 (2022).
  • [102] H. Dimmelmeier, J. A. Font, and E. Müller, Relativistic simulations of rotational core collapse I. Methods, initial models, and code tests, A&A 388, 917 (2002), arXiv:astro-ph/0204288 [astro-ph].
  • [103] H. Dimmelmeier, J. Novak, J. A. Font, J. M. Ibáñez, and E. Müller, Combining spectral and shock-capturing methods: A new numerical approach for 3D relativistic core collapse simulations, Phys. Rev. D 71, 064023 (2005), astro-ph/0407174.
  • [104] M. Liebendörfer, A Simple Parameterization of the Consequences of Deleptonization for Simulations of Stellar Core Collapse, Astrophys. J. 633, 1042 (2005), arXiv:astro-ph/0504072 [astro-ph].
  • [105] S. E. Woosley and A. Heger, Nucleosynthesis and remnants in massive stars of solar metallicity, Physics Reports 442, 269 (2007), arXiv:astro-ph/0702176 [astroph].
  • [106] S. E. Woosley, A. Heger, and T. A. Weaver, The evolution and explosion of massive stars, Rev. Mod. Phys. 74, 1015 (2002).
  • [107] S. Banik, M. Hempel, and D. Bandyopadhyay, New Hyperon Equations of State for Supernovae and Neutron Stars in Density-dependent Hadron Field Theory, Astrophys. J. Suppl. Ser. 214, 22 (2014), arXiv:1404.6173 [astro-ph.HE].
  • [108] A. W. Steiner, M. Hempel, and T. Fischer, Corecollapse Supernova Equations of State Based on Neutron Star Observations, Astrophys. J. 774, 17 (2013), arXiv:1207.2184 [astro-ph.SR].
  • [109] J. M. Lattimer and F. D. Swesty, A generalized equation of state for hot, dense matter, Nucl. Phys. A 535, 331 (1991).
  • [110] M. Hempel and J. Schaffner-Bielich, A statistical model for a complete supernova equation of state, Nucl. Phys. A 837, 210 (2010), arXiv:0911.4073 [nucl-th].
  • [111] M. Hempel, T. Fischer, J. Schaffner-Bielich, and M. Liebendörfer, New Equations of State in Simulations of Core-collapse Supernovae, Astrophys. J. 748, 70 (2012), arXiv:1108.0848 [astro-ph.HE].
  • [112] G. Shen, C. J. Horowitz, and E. O’Connor, Second relativistic mean field and virial equation of state for astrophysical simulations, Phys. Rev. C 83, 065808 (2011).
  • [113] A. G. Abac and et al (LIGO-Virgo-KAGRA Collaboration), GWTC-4.0: An Introduction to Version 4.0 of the Gravitational-Wave Transient Catalog, ApJ Lett. 995, L18 (2025), arXiv:2508.18080 [gr-qc].
  • [114] A. Nitz, I. Harry, D. Brown, C. M. Biwer, J. Willis, T. D. Canton, C. Capano, T. Dent, L. Pekowsky, G. S. C. Davies, S. De, M. Cabero, S. Wu, A. R. Williamson, B. Machenschalk, D. Macleod, F. Pannarale, P. Kumar, S. Reyes, dfinstad, S. Kumar, M. Tápai, L. Singer, P. Kumar, veronica villa, maxtrevor, B. U. V. Gadre, S. Khan, S. Fairhurst, and A. Tolley, gwastro/pycbc: v2.3.3 release of pycbc (2024).
  • [115] J. W. Tukey, An introduction to the calculation of numerical spectrum analysis, Spectra Analysis of Time Series , 25 (1967).
  • [116] J. Alzubi, A. Nayyar, and A. Kumar, Machine learning from theory to algorithms: An overview, Journal of Physics: Conference Series 1142, 012012 (2018).
  • [117] A. E. Hoerl and R. W. Kennard, Ridge regression: Applications to nonorthogonal problems, Technometrics 12, 69 (1970).
  • [118] R. Tibshirani, Regression shrinkage and selection via the lasso, Journal of the Royal Statistical Society. Series B (Methodological) 58, 267 (1996).
  • [119] L. Breiman, Random forests, Mach. Learn. 45, 5–32 (2001).
  • [120] A. Smola and B. Scholkopf, A tutorial on support vector regression, Statistics and Computing 14, 199 (2004).
  • [121] L. Prokhorenkova, G. Gusev, A. Vorobev, A. V. Dorogush, and A. Gulin, Catboost: unbiased boosting with categorical features, in Proceedings of the 32nd International Conference on Neural Information Processing Systems, NIPS’18 (Curran Associates Inc., Red Hook, NY, USA, 2018) p. 6639–6649.
  • [122] G. Ke, Q. Meng, T. Finley, T. Wang, W. Chen, W. Ma, Q. Ye, and T.-Y. Liu, Lightgbm: a highly efficient gradient boosting decision tree, in Proceedings of the 31st International Conference on Neural Information Processing Systems, NIPS’17 (Curran Associates Inc., Red Hook, NY, USA, 2017) p. 3149–3157.
  • [123] T. Chen and C. Guestrin, Xgboost: A scalable tree boosting system, in Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD ’16 (Association for Computing Machinery, New York, NY, USA, 2016) p. 785–794.
  • [124] F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, et al., Scikit-learn: Machine learning in python, the Journal of machine Learning research 12, 2825 (2011).
  • [125] C. D. C. D. Lewis, Industrial and business forecasting methods : a practical guide to exponential smoothing and curve fitting (Butterworth Scientific, 1982).
  • [126] F. J. Massey, The kolmogorov-smirnov test for goodness of fit, Journal of the American Statistical Association 46, 68 (1951).
  • [127] B. Müller, Multi-dimensional relativistic simulations of core-collapse supernovae with energy-dependent neutrino transport, Ph.D. thesis, Technische Universität München, München, Germany (2009).
  • [128] A. Sakan, N. Ussipov, E. Abdikamalov, A. Akhmetali, M. Zaidyn, A. Zhunuskanov, J. A. Font, M. C. Edwards, and S. Abylkairov, Probing Supernovae through gravitational wave entropy, arXiv e-prints , arXiv:2511.08010 (2025), arXiv:2511.08010 [astro-ph.HE].
  • [128] A. Sakan, N. Ussipov, E. Abdikamalov, A. Akhmetali, M. Zaidyn, A. Zhunuskanov, J. A. Font, M. C. Edwards, and S. Abylkairov, Probing Supernovae through gravitational wave entropy, arXiv e-prints , arXiv:2511.08010 (2025), arXiv:2511.08010 [astro-ph.HE].
  • [129] S. E. Gossan, P. Sutton, A. Stuver, M. Zanolin, K. Gill, and C. D. Ott, Observing gravitational waves from corecollapse supernovae in the advanced detector era, Phys. Rev. D 93, 042002 (2016), arXiv:1511.02836 [astroph.HE].
  • [130] M. J. Szczepańczyk, J. M. Antelis, M. Benjamin, M. Cavaglià, D. Gondek-Rosińska, T. Hansen, S. Klimenko, M. D. Morales, C. Moreno, S. Mukherjee, G. Nurbek, J. Powell, N. Singh, S. Sitmukhambetov, P. Szewczyk, O. Valdez, G. Vedovato, J. Westhouse, M. Zanolin, and Y. Zheng, Detecting and reconstructing gravitational waves from the next galactic core-collapse supernova in the advanced detector era, Phys. Rev. D 104, 102002 (2021), arXiv:2104.06462 [astro-ph.HE].