Al een decennium lang kunnen we zwaartekrachtgolven bestuderen met kilometerslange detectoren. Hiermee “kijken” we niet naar het universum zoals met een telescoop, maar we “luisteren” eerder. En dat is heel handig want nu hebben we als het ware een extra zintuig waarmee we het universum op nieuwe wijze kunnen onderzoeken. Momenteel kunnen we met zwaartekrachtgolven de laatste doemdans van zwarte gaten en neutronensterren die op elkaar inspiraleren en samensmelten bestuderen.
Hoe weten we juist welke objecten betrokken waren bij die fatale dans? Daarvoor kunnen we het zwaartekrachtgolfsignaal op twee manieren onderzoeken:
Bij de eerste manier hebben we een theoretisch model met een aantal parameters. Die parameters werken als draaiknoppen voor de eigenschappen van de bron. Door deze eigenschappen, zoals massa, spin, afstand, ... te veranderen, proberen we het ontvangen signaal na te maken. Als we dan iets krijgen dat overeenkomt met het ontvangen signaal, hebben we de juiste parameters gevonden! Zo kunnen we dus achterhalen wat we gezien hebben. Voor een klein aantal parameters is dit niet zo moeilijk, maar de modellen die wij gebruiken hebben er heel wat, dus is dit een lastig en tijdrovend karwei. Daarom gebruiken we hiervoor supercomputers.
De tweede techniek wordt ook wel de “ongemodelleerde” techniek genoemd. Hierbij tellen we een heleboel simpele signaaltjes, wavelets genaamd, op om zo het originele signaal na te maken. Dit heeft het voordeel dat er geen aannames worden gemaakt over de bron en is heel nuttig om bijvoorbeeld eerst ruis uit het signaal te verwijderen en dan met de eerste methode parameters te verkrijgen. Maar hoe weet je hoeveel van die wavelets je moet gebruiken? Te weinig en je krijgt waarschijnlijk een te simpele reconstructie terug. Te veel, en je reconstructie heeft ook de ruis gereconstrueerd! We moeten dus op zoek naar een gulden middenweg. Gelukkig kunnen we hierbij steunen op William of Ockham: een rebelse priester uit de 14e eeuw die er niet voor terugdeinsde de paus openlijk tegen te spreken. Vandaag staat hij vooral bekend om Ockhams Scheermes. Dit principe komt er ongeveer op neer dat als twee theorieën of modellen dezelfde voorspellingskracht hebben, maar de één complexer is dan de ander, je altijd het simpelere model moet kiezen. In de context van zwaartekrachtgolfanalyse willen we dus zo min mogelijk wavelets gebruiken om het signaal goed genoeg te reconstrueren.
Tot nu toe zijn de gemodelleerde en ongemodelleerde technieken zo goed als gescheiden gebleven. Maar door ze te combineren kunnen we fenomenen in onze modellen opnemen waarvan we niet goed weten hoe ze exact tot uiting komen of, nog spannender, waarvan we het bestaan niet eens kennen!
Met dit in het achterhoofd heb ik voor mijn thesis een proof-of-concept hiervan uitgewerkt. Ik heb dus onderzocht of het überhaupt mogelijk is om deze technieken te combineren aangezien dit nog nooit is gedaan. Indien dit kan, zouden we bijvoorbeeld getijdenresonanties van neutronensterren kunnen bestuderen.
Net als een stemvork kent een neutronenster resonanties. Als je een stemvork naast een andere gelijkgestemde stemvork plaatst en eentje aanslaat, zal de andere ook meetrillen doordat de geluidsgolven deze aan nét de juiste frequentie doen trillen. Dit noemen we een resonantie. Als een neutronenster tijdens het inspiraleren aan de juiste frequentie vervormd wordt door de zwaartekracht van zijn danspartner, zal deze resoneren en kan dit een afdruk achterlaten op het signaal.
Een stemvork zal, afhankelijk van het materiaal, resoneren bij een bepaalde toonhoogte (frequentie) en bij neutronensterren is dit ook zo. Door zo’n resonanties te meten, kunnen we dus iets leren over de samenstelling van neutronensterren, iets waar er nog heel wat onzekerheid over heerst in de literatuur. Deze resonanties kunnen we modelleren met wavelets, wat de gecombineerde methode interessant maakt voor zo’n onderzoek.
Maar nog spannender dan neutronensterren beter begrijpen, is het potentieel om iets exotisch te vinden. Er zijn namelijk een heleboel hypothetische objecten die heel erg zouden lijken op neutronensterren en zwarte gaten door een "gewone" telescoop. Maar ze zouden zich wel kunnen onderscheiden door hun resonantiefrequenties, iets wat we met deze gecombineerde techniek zouden kunnen onderzoeken.
Een ander, meer direct toepasbaar gebruik is het wegwerken van detector glitches. Dit zijn kortstondige toenames in de ruis van een zwaartekrachtgolfdetector waarvan de oorzaak ongekend is, een beetje als een oorsuizing. Ze kunnen overlappen met een signaal of zelfs op een signaal lijken. Het is dus heel belangrijk om deze weg te werken! Dit vergt wel wat werk aangezien de glitch eerst apart gemodelleerd moet worden en daarna van het signaal moet worden afgetrokken. Maar met de gecombineerde techniek zouden we de glitch en het astrofysische signaal tegelijkertijd kunnen modelleren en onderscheiden van elkaar.
Ik heb deze twee toepassingen verkend in mijn thesis door een gesimuleerd signaal te maken, wavelets toe te voegen en alles vervolgens in detectorruis onder te dompelen. Dan probeert een programma het signaal te reconstrueren waarbij het ook moet bepalen hoeveel wavelets erin zitten. De figuur hieronder toont een reconstructie van zo’n gesimuleerd signaal in de toekomstige Einstein Telescoop waarbij er ingezoomd is op de wavelet. Zoals je kan zien, is het een heel klein, maar niet onzichtbaar, effect.
Voor de volgende generatie aan zwaartekrachtgolfdetectoren zoals de Einstein Telescoop (die misschien in het drielandenpunt komt) is de techniek veelbelovend. Meerdere wavelets kunnen erbij worden teruggevonden en alleen de allerstilste ontbreken in de reconstructie. Bij de huidige detectoren ben ik nog niet overtuigd van het potentieel van deze methode aangezien het ruisniveau nog redelijk hoog ligt.
Bij deze detectoren lukt het echter wel om een glitch van een zwaartekrachtgolfsignaal te onderscheiden. Deze glitch heeft op de meeste fysische parameters ook maar een kleine impact, wat zeer goed nieuws is.
De volgende stap lijkt me om resultaten van complexe computersimulaties te gebruiken die zo’n getijdenresonanties simuleren om te onderzoeken of ze daadwerkelijk detecteerbaar zijn en of we er iets uit kunnen leren.
Wie weet, misschien vinden we zo ooit wel volledig nieuwe objecten die onze verbeelding ver overstijgen...
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and Zieminska, D. and Zimin, N.I. and Zimmermann, R. and Zimmermann, S. and Zimmermann, S. and Ziolkowski, M. and Zitoun, R. and Živković, L. and Zmouchko, V.V. and Zobernig, G. and Zoccoli, A. and zur Nedden, M. and Zutshi, V. and Zwalinski, L.},
journal = {Physics Letters B},
title = {Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC},
year = {2012},
issn = {0370-2693},
month = sep,
number = {1},
pages = {1--29},
volume = {716},
doi = {10.1016/j.physletb.2012.08.020},
publisher = {Elsevier BV},
}
@Article{Barack2019,
author = {Barack, Leor and Cardoso, Vitor and Nissanke, Samaya and Sotiriou, Thomas P and Askar, Abbas and Belczynski, Chris and Bertone, Gianfranco and Bon, Edi and Blas, Diego and Brito, Richard and Bulik, Tomasz and Burrage, Clare and Byrnes, Christian T and Caprini, Chiara and Chernyakova, Masha and Chruściel, Piotr and Colpi, Monica and Ferrari, Valeria and Gaggero, Daniele and Gair, Jonathan and García-Bellido, Juan and Hassan, S F and Heisenberg, Lavinia and Hendry, Martin and Heng, Ik Siong and Herdeiro, Carlos and Hinderer, Tanja and Horesh, Assaf and Kavanagh, Bradley J and Kocsis, Bence and Kramer, Michael and Le Tiec, Alexandre and Mingarelli, Chiara and Nardini, Germano and Nelemans, Gijs and Palenzuela, Carlos and Pani, Paolo and Perego, Albino and Porter, Edward K and Rossi, Elena M and Schmidt, Patricia and Sesana, Alberto and Sperhake, Ulrich and Stamerra, Antonio and Stein, Leo C and Tamanini, Nicola and Tauris, Thomas M and Urena-López, L Arturo and Vincent, Frederic and Volonteri, Marta and Wardell, Barry and Wex, Norbert and Yagi, Kent and Abdelsalhin, Tiziano and Aloy, Miguel Ángel and Amaro-Seoane, Pau and Annulli, Lorenzo and Arca-Sedda, Manuel and Bah, Ibrahima and Barausse, Enrico and Barakovic, Elvis and Benkel, Robert and Bennett, Charles L and Bernard, Laura and Bernuzzi, Sebastiano and Berry, Christopher P L and Berti, Emanuele and Bezares, Miguel and Blanco-Pillado, Jose Juan and Blázquez-Salcedo, Jose Luis and Bonetti, Matteo and Bošković, Mateja and Bosnjak, Zeljka and Bricman, Katja and Brügmann, Bernd and Capelo, Pedro R and Carloni, Sante and Cerdá-Durán, Pablo and Charmousis, Christos and Chaty, Sylvain and Clerici, Aurora and Coates, Andrew and Colleoni, Marta and Collodel, Lucas G and Compère, Geoffrey and Cook, William and Cordero-Carrión, Isabel and Correia, Miguel and de la Cruz-Dombriz, Álvaro and Czinner, Viktor G and Destounis, Kyriakos and Dialektopoulos, Kostas and Doneva, Daniela and Dotti, Massimo and Drew, Amelia and Eckner, Christopher and Edholm, James and Emparan, Roberto and Erdem, Recai and Ferreira, Miguel and Ferreira, Pedro G and Finch, Andrew and Font, Jose A and Franchini, Nicola and Fransen, Kwinten and Gal’tsov, Dmitry and Ganguly, Apratim and Gerosa, Davide and Glampedakis, Kostas and Gomboc, Andreja and Goobar, Ariel and Gualtieri, Leonardo and Guendelman, Eduardo and Haardt, Francesco and Harmark, Troels and Hejda, Filip and Hertog, Thomas and Hopper, Seth and Husa, Sascha and Ihanec, Nada and Ikeda, Taishi and Jaodand, Amruta and Jetzer, Philippe and Jimenez-Forteza, Xisco and Kamionkowski, Marc and Kaplan, David E and Kazantzidis, Stelios and Kimura, Masashi and Kobayashi, Shiho and Kokkotas, Kostas and Krolik, Julian and Kunz, Jutta and Lämmerzahl, Claus and Lasky, Paul and Lemos, José P S and Levi Said, Jackson and Liberati, Stefano and Lopes, Jorge and Luna, Raimon and Ma, Yin-Zhe and Maggio, Elisa and Mangiagli, Alberto and Montero, Marina Martinez and Maselli, Andrea and Mayer, Lucio and Mazumdar, Anupam and Messenger, Christopher and Ménard, Brice and Minamitsuji, Masato and Moore, Christopher J and Mota, David and Nampalliwar, Sourabh and Nerozzi, Andrea and Nichols, David and Nissimov, Emil and Obergaulinger, Martin and Obers, Niels A and Oliveri, Roberto and Pappas, George and Pasic, Vedad and Peiris, Hiranya and Petrushevska, Tanja and Pollney, Denis and Pratten, Geraint and Rakic, Nemanja and Racz, Istvan and Radia, Miren and Ramazanoğlu, Fethi M and Ramos-Buades, Antoni and Raposo, Guilherme and Rogatko, Marek and Rosca-Mead, Roxana and Rosinska, Dorota and Rosswog, Stephan and Ruiz-Morales, Ester and Sakellariadou, Mairi and Sanchis-Gual, Nicolás and Sharan Salafia, Om and Samajdar, Anuradha and Sintes, Alicia and Smole, Majda and Sopuerta, Carlos and Souza-Lima, Rafael and Stalevski, Marko and Stergioulas, Nikolaos and Stevens, Chris and Tamfal, Tomas and Torres-Forné, Alejandro and Tsygankov, Sergey and İ Ünlütürk, Kıvanç and Valiante, Rosa and van de Meent, Maarten and Velhinho, José and Verbin, Yosef and Vercnocke, Bert and Vernieri, Daniele and Vicente, Rodrigo and Vitagliano, Vincenzo and Weltman, Amanda and Whiting, Bernard and Williamson, Andrew and Witek, Helvi and Wojnar, Aneta and Yakut, Kadri and Yan, Haopeng and Yazadjiev, Stoycho and Zaharijas, Gabrijela and Zilhão, Miguel},
journal = {Classical and Quantum Gravity},
title = {Black holes, gravitational waves and fundamental physics: a roadmap},
year = {2019},
issn = {1361-6382},
month = jun,
number = {14},
pages = {143001},
volume = {36},
doi = {10.1088/1361-6382/ab0587},
publisher = {IOP Publishing},
}
@Article{Mazur2001,
author = {Mazur, Pawel O. and Mottola, Emil},
title = {Gravitational Condensate Stars: An Alternative to Black Holes},
year = {2001},
copyright = {Creative Commons Attribution 4.0 International},
doi = {10.48550/ARXIV.GR-QC/0109035},
keywords = {General Relativity and Quantum Cosmology (gr-qc), Astrophysics (astro-ph), High Energy Physics - Theory (hep-th), FOS: Physical sciences, FOS: Physical sciences},
publisher = {arXiv},
}
@Article{Cornish2015,
author = {Cornish, Neil J and Littenberg, Tyson B},
journal = {Classical and Quantum Gravity},
title = {Bayeswave: Bayesian inference for gravitational wave bursts and instrument glitches},
year = {2015},
issn = {1361-6382},
month = jun,
number = {13},
pages = {135012},
volume = {32},
doi = {10.1088/0264-9381/32/13/135012},
publisher = {IOP Publishing},
}
@Article{Littenberg2015,
author = {Littenberg, Tyson B. and Cornish, Neil J.},
journal = {Physical Review D},
title = {Bayesian inference for spectral estimation of gravitational wave detector noise},
year = {2015},
issn = {1550-2368},
month = apr,
number = {8},
pages = {084034},
volume = {91},
doi = {10.1103/physrevd.91.084034},
publisher = {American Physical Society (APS)},
}
@Article{Flanagan2007,
author = {Flanagan, Éanna É. and Racine, Étienne},
journal = {Physical Review D},
title = {Gravitomagnetic resonant excitation of Rossby modes in coalescing neutron star binaries},
year = {2007},
issn = {1550-2368},
month = feb,
number = {4},
pages = {044001},
volume = {75},
doi = {10.1103/physrevd.75.044001},
publisher = {American Physical Society (APS)},
readstatus = {skimmed},
}
@Article{Balachandran2007,
author = {Balachandran, Prakash and Flanagan, Eanna E.},
title = {Detectability of Mode Resonances in Coalescing Neutron Star Binaries},
year = {2007},
month = jan,
abstract = {Inspirals of neutron star-neutron star binaries are a promising source of gravitational waves for gravitational wave detectors like LIGO. During the inspiral, the tidal gravitational field of one of the stars can resonantly excite internal modes of the other star, resulting in a phase shift in the gravitational wave signal. We compute using a Fisher-matrix analysis how large the phase shift must be in order to be detectable. For a $1.4 M_\odot, 1.4 M_\odot$ binary the result is $\sim 8.1, 2.9$ and 1.8 radians, for resonant frequencies of $16, 32$ and 64 Hz. The measurement accuracies of the other binary parameters are degraded by inclusion of the mode resonance effect.},
archiveprefix = {arXiv},
copyright = {Assumed arXiv.org perpetual, non-exclusive license to distribute this article for submissions made before January 2004},
doi = {10.48550/ARXIV.GR-QC/0701076},
eprint = {gr-qc/0701076},
file = {:Balachandran2007 - Detectability of Mode Resonances in Coalescing Neutron Star Binaries.pdf:PDF:http\://arxiv.org/pdf/gr-qc/0701076v1},
keywords = {General Relativity and Quantum Cosmology (gr-qc), FOS: Physical sciences},
primaryclass = {gr-qc},
publisher = {arXiv},
readstatus = {skimmed},
}
@Article{Faber2002,
author = {Faber, Joshua A. and Grandclément, Philippe and Rasio, Frederic A. and Taniguchi, Keisuke},
journal = {Physical Review Letters},
title = {Measuring Neutron-Star Radii with Gravitational-Wave Detectors},
year = {2002},
issn = {1079-7114},
month = nov,
number = {23},
pages = {231102},
volume = {89},
doi = {10.1103/physrevlett.89.231102},
publisher = {American Physical Society (APS)},
readstatus = {skimmed},
}
@Article{Mastrogiovanni2025,
author = {Mastrogiovanni, Simone and Maggio, Elisa and Mascioli, Adriano Frattale},
title = {Limits on the existence of totally reflective exotic compact objects with current and future gravitational-wave detectors},
year = {2025},
month = feb,
abstract = {Exotic compact objects (ECOs) are a theorized class of compact objects that solve the paradoxes of black holes by replacing the event horizon with a physical surface located at $r=r_+(1+\epsilon)$ from the would-be horizon at $r_+$. Spinning horizonless objects are prone to the ergoregion instability, which would prevent their existence if their spin is higher than a critical threshold. In this paper, we set upper limits on the existence of a population of merging ECOs from the spin distribution of the population of compact binary coalescences (CBCs) detected by the LIGO, Virgo and KAGRA collaboration. Using spin measurements from 104 compact objects, we find that if ECOs have $\epsilon \in [10^{-42}-10^{-3}]$ and their surface is totally reflective, the population of CBCs cannot be composed (at 90% credible level) by more than 71% (59%) of ECOs for polar (axial) perturbations. If we restrict the ECOs to be ultracompact ($\epsilon<10^{-30}$), at 90% credible level, ECOs cannot compose more than 28% and 25% of the CBC population for polar and axial perturbations. The constraints from current data are a factor of two more precise than the ones obtained from a non-detection of a stochastic GW background due to spin loss. We also study how next generation gravitational-wave detectors, such as the Einstein Telescope, can constrain the ECO population. We find that 1 day of data taking would be enough to constrain the fraction of ECOs to be lower than 20% for $\epsilon \in [10^{-42}-10^{-3}]$.},
archiveprefix = {arXiv},
copyright = {Creative Commons Attribution 4.0 International},
doi = {10.48550/ARXIV.2502.07675},
eprint = {2502.07675},
file = {:Mastrogiovanni2025 - Limits on the Existence of Totally Reflective Exotic Compact Objects with Current and Future Gravitational Wave Detectors.pdf:PDF:http\://arxiv.org/pdf/2502.07675v1},
keywords = {General Relativity and Quantum Cosmology (gr-qc), FOS: Physical sciences},
primaryclass = {gr-qc},
publisher = {arXiv},
}
@Article{Maggio2019,
author = {Maggio, Elisa and Cardoso, Vitor and Dolan, Sam R. and Pani, Paolo},
journal = {Physical Review D},
title = {Ergoregion instability of exotic compact objects: Electromagnetic and gravitational perturbations and the role of absorption},
year = {2019},
issn = {2470-0029},
month = mar,
number = {6},
pages = {064007},
volume = {99},
doi = {10.1103/physrevd.99.064007},
publisher = {American Physical Society (APS)},
}
@Article{Abbott2017,
author = {Abbott, B.P. and Abbott, R. and Abbott, T.D. and Acernese, F. and Ackley, K. and Adams, C. and Adams, T. and Addesso, P. and Adhikari},
journal = {Physical Review Letters},
title = {GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral},
year = {2017},
issn = {1079-7114},
month = oct,
number = {16},
pages = {161101},
volume = {119},
doi = {10.1103/physrevlett.119.161101},
publisher = {American Physical Society (APS)},
}
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@Comment{jabref-meta: databaseType:bibtex;}