Sub-Torque-Balance Upper Limits on Continuous Gravitational Waves from Scorpius X-1
Using LIGO data from the first part of the fourth observing run, this study sets the first sub-torque-balance upper limits on continuous gravitational waves from Scorpius X-1 in the 50–200 Hz range, arguing against torque balance for a hadronic neutron star and significantly improving sensitivity depth over previous searches.
Original authors: The LIGO Scientific Collaboration, the Virgo Collaboration, the KAGRA Collaboration, the Precision Ephemerides for Gravitational-Wave Searches (PEGS), Project, :, A. G. Abac, I. Abouelfettouh, F. Acernese, K. Ackley, A. Adam, C. Adamcewicz, S. Adhicary, D. Adhikari, N. Adhikari, R. X. Adhikari, V. K. Adkins, S. Afroz, A. Agapito, D. Agarwal, M. Agathos, N. Aggarwal, S. Aggarwal, O. D. Aguiar, I. -L. Ahrend, L. Aiello, A. Ain, P. Ajith, T. Akutsu, S. Albanesi, L. Albers, W. Ali, S. Al-Kershi, C. Alléné, A. Allocca, S. Al-Shammari, P. A. Altin, S. Alvarez-Lopez, W. Amar, O. Amarasinghe, A. Amato, F. Amicucci, C. Amra, C. Anand, A. Ananyeva, S. B. Anderson, W. G. Anderson, M. Andia, M. Ando, M. Andrés-Carcasona, J. L. Andrey, T. Andrić, J. Anglin, J. Anna, S. Ansoldi, J. M. Antelis, S. Antier, M. Aoumi, E. Z. Appavuravther, S. Appert, S. K. Apple, K. Arai, A. Araya, M. C. Araya, M. Arca Sedda, F. Arciprete, J. S. Areeda, N. Aritomi, F. Armato, S. Armstrong, N. Arnaud, M. Arogeti, S. M. Aronson, G. Ashton, Y. Aso, L. Asprea, M. Assiduo, S. Assis de Souza Melo, S. M. Aston, P. Astone, F. Attadio, F. Aubin, K. AultONeal, G. Avallone, E. A. Avila, S. Babak, C. Badger, S. Bae, S. Bagnasco, L. Baiotti, R. Bajpai, T. Baka, K. A. Baker, T. Baker, G. Balbi, G. Baldi, N. Baldicchi, M. Ball, G. Ballardin, S. W. Ballmer, S. Banagiri, B. Banerjee, D. Bankar, T. M. Baptiste, P. Baral, M. Baratti, J. C. Barayoga, K. Baric, B. C. Barish, D. Barker, N. Barman, P. Barneo, F. Barone, B. Barr, M. Barrios, L. Barsotti, M. Barsuglia, D. Barta, M. A. Barton, I. Bartos, A. Basalaev, R. Bassiri, A. Basti, M. Bawaj, P. Baxi, J. C. Bayley, A. C. Baylor, P. A. Baynard II, M. Bazzan, V. M. Bedakihale, F. Beirnaert, M. Bejger, D. Belardinelli, A. S. Bell, C. Bellani, L. Bellizzi, D. Beltran-Martinez, W. Benoit, I. Bentara, M. Ben Yaala, S. Bera, F. Bergamin, B. K. Berger, S. Bernuzzi, M. Beroiz, I. Berry, D. Bersanetti, T. Bertheas, A. Bertolini, J. Betzwieser, D. Beveridge, G. Bevilacqua, N. Bevins, R. Bhandare, R. Bhatt, A. Bhattacharjee, D. Bhattacharjee, S. Bhattacharyya, S. Bhaumik, V. Biancalana, A. Bianchi, F. Bianchi, I. A. Bilenko, G. Billingsley, A. Binetti, S. Bini, C. Binu, S. Biot, O. Birnholtz, S. Biscoveanu, A. Bisht, M. Bitossi, M. -A. Bizouard, S. Blaber, J. K. Blackburn, L. A. Blagg, C. D. Blair, D. G. Blair, N. Bode, N. Boettner, P. Bogdan, G. Boileau, M. Boldrini, G. N. Bolingbroke, A. Bolliand, L. D. Bonavena, R. Bondarescu, F. Bondu, V. A. Bonhomme, E. Bonilla, M. S. Bonilla, A. Bonino, R. Bonnand, A. Borchers, N. Borghi, V. Boschi, S. Bose, V. Bossilkov, Y. Bothra, A. Boudon, M. Boyle, A. Bozzi, C. Bradaschia, M. J. Brady, P. R. Brady, A. Branch, M. Branchesi, T. Briant, A. Brillet, M. Brinkmann, P. Brockill, E. Brockmueller, A. F. Brooks, B. C. Brown, D. D. Brown, M. L. Brozzetti, S. Brunett, G. Bruno, R. Bruntz, J. Bryant, Y. Bu, F. Bucci, J. Buchanan, O. Bulashenko, T. Bulik, H. J. Bulten, A. Buonanno, K. Burtnyk, R. Buscicchio, D. Buskulic, C. Buy, R. L. Byer, R. Cabrita, V. Cáceres-Barbosa, L. Cadonati, G. Cagnoli, C. Cahillane, A. Calafat, T. A. Callister, E. Calloni, S. R. Callos, M. Canepa, G. Caneva Santoro, K. C. Cannon, H. Cao, L. A. Capistran, E. Capocasa, G. Capoccia, E. Capote, G. Capurri, G. Carapella, F. Carbognani, K. J. Cardona-Martínez, M. Carlassara, J. B. Carlin, T. K. Carlson, M. F. Carney, M. Carpinelli, G. Carrillo, J. J. Carter, G. Carullo, A. Casallas-Lagos, J. Casanueva Diaz, C. Casentini, S. Caudill, M. Cavaglià, R. Cavalieri, G. Cella, S. Cepic, P. Cerdá-Durán, E. Cesarini, N. Chabbra, W. Chaibi, A. Chakraborty, P. Chakraborty, S. Chakraborty, S. Chalathadka Subrahmanya, R. Chalmers, C. Chan, J. C. L. Chan, M. Chan, K. Chang, P. Charlton, E. Chassande-Mottin, C. Chatterjee, Debarati Chatterjee, Deep Chatterjee, M. Chaturvedi, S. Chaty, A. Chen, A. H. -Y. Chen, D. Chen, H. Chen, H. Y. Chen, S. Chen, Y. Chen, G. Cheng, H. P. Cheng, P. Chessa, T. Cheunchitra, H. T. Cheung, S. Y. Cheung, F. Chiadini, G. Chiarini, A. Chiba, A. Chincarini, D. Chintala, M. L. Chiofalo, A. Chiummo, C. Chou, S. Choudhary, N. Christensen, S. S. Y. Chua, G. Ciani, P. Ciecielag, M. Cieślar, M. Cifaldi, B. Cirok, F. Clara, J. A. Clark, T. A. Clarke, P. Clearwater, S. Clesse, F. Cleva, S. M. Clyne, E. Coccia, E. Codazzo, P. -F. Cohadon, D. E. Cohen, S. Colace, E. Colangeli, O. Cole, M. Colleoni, C. G. Collette, J. Collins, S. Colloms, A. Colombo, C. M. Compton, G. Connolly, L. Conti, T. R. Corbitt, I. Cordero-Carrión, S. Corezzi, N. J. Cornish, I. Coronado, A. Corsi, L. A. Corubolo, L. Cotnoir, R. Cottingham, M. W. Coughlin, P. Couvares, D. M. Coward, D. C. Coyne, R. Coyne, A. Cozzumbo, J. D. E. Creighton, T. D. Creighton, S. Crook, R. Crouch, J. Csizmazia, J. R. Cudell, T. J. Cullen, A. Cumming, E. Cuoco, M. Cusinato, L. V. Da Conceição, T. Dal Canton, S. Dall'Osso, S. Dal Pra, G. Dálya, O. Dan, Y. Dang, B. D'Angelo, S. Danilishin, S. D'Antonio, K. Danzmann, K. E. Darroch, L. P. Dartez, R. Das, A. Dasgupta, V. Dattilo, A. Daumas, I. Dave, A. Davenport, M. Davier, T. F. Davies, D. Davis, L. Davis, M. C. Davis, P. Davis, E. J. Daw, M. Dax, J. De Bolle, M. Deenadayalan, J. Degallaix, M. De Laurentis, C. J. Delgado Mendez, F. De Lillo, S. Della Torre, W. Del Pozzo, O. M. del Rio, A. Demagny, F. De Marco, G. Demasi, F. De Matteis, N. Demos, T. Dent, A. Depasse, N. DePergola, R. De Pietri, R. De Rosa, C. De Rossi, M. Desai, V. Deshmukh, R. De Simone, S. Determan, A. Dhani, R. Dhurkunde, R. Diab, C. Diaz, M. C. Díaz, M. Di Cesare, G. Dideron, T. Dietrich, L. Di Fiore, C. Di Fronzo, M. Di Giovanni, T. Di Girolamo, D. Diksha, J. Ding, S. Di Pace, I. Di Palma, D. Di Piero, F. Di Renzo, Divyajyoti, A. Dmitriev, J. P. Docherty, Z. Doctor, N. Doerksen, E. Dohmen, A. Doke, A. Domiciano De Souza, L. D'Onofrio, F. Donovan, K. L. Dooley, T. Dooney, S. Doravari, O. Dorosh, F. Dosopoulou, W. J. D. Doyle, M. Drago, J. C. Driggers, M. Dubois, R. R. Dumbreck, L. 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Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer
Imagine the universe is a giant, cosmic dance floor, and one of the most energetic dancers is a tiny, super-dense star called a neutron star, hidden inside a binary system known as Scorpius X-1. This star is spinning so fast it's a blur, and as it twirls, it might be wobbling just enough to send out ripples in the fabric of space-time called gravitational waves. Think of these waves like the ripples you see when a stone hits a pond, but instead of water, it's the universe itself stretching and squeezing.
For years, scientists have been listening for these ripples with giant detectors called LIGO, hoping to catch a glimpse of this cosmic dancer. But there's a catch: the star is spinning so fast and the signals are so faint that finding them is like trying to hear a single pin drop in a hurricane.
The Great "Torque Balance" Theory
A popular idea in the physics world was that this neutron star has reached a perfect "torque balance." Imagine a child on a swing. If you push them (accretion, or matter falling onto the star) at the exact same rate that air resistance slows them down (gravitational waves), they stay at a steady height. Scientists thought Scorpius X-1 was exactly like that: the matter falling onto it was spinning it up, and the gravitational waves it was creating were spinning it down, keeping it in a perfect, steady groove. If this were true, the star should be sending out a very specific, loud signal that our detectors should have easily found by now.
The Big Search
In this new study, a massive team of scientists used data from the first part of the fourth major observing run (O4a) of the LIGO, Virgo, and KAGRA detectors. They didn't just listen; they used a clever new trick called "resampling." Imagine trying to listen to a song that keeps speeding up and slowing down slightly. Instead of trying to hear it as it is, they digitally rearranged the audio data so the song played at a perfectly steady speed, making it much easier to spot the melody. They searched for signals in a frequency range between 25 and 200 Hz (which corresponds to the star spinning between 12.5 and 100 times a second, or slightly faster if the waves come from a different kind of wobble).
The Result: The Silence is Loud
Here is the exciting part: They didn't find the signal. But that silence is actually a huge discovery.
The team set a new record for how quiet the universe must be in this specific frequency range. Their limits are so sensitive that they have now argued strongly against the idea that Scorpius X-1 is in that perfect "torque balance" state for a neutron star made of normal, ordinary nuclear matter (specifically, a hadronic equation of state).
Think of it like this: If the "torque balance" theory were true for a standard neutron star, the star would be shouting so loudly that our detectors would have heard it from a mile away. Instead, the star is whispering so softly that it's below the level we expected. The data suggests that the balance is broken for these types of stars, though scientists note that uncertainties in how we model the star's interior mean we can't say it's impossible with absolute certainty. However, the theory remains hypothetically possible if the star is a very strange, exotic object—like a quark star—which could still fit the theory.
The "Outliers" That Vanished
During the search, the team did find a few "outliers"—tiny blips in the data that looked a little suspicious, like a faint noise that might be a signal. One of the loudest was at 129.20 Hz. But when they zoomed in and checked the data with different methods, and even looked at data from later in the observing run, those blips disappeared. They turned out to be just random noise or glitches, not a real cosmic dance. It's like hearing a rustle in the bushes, thinking it's a tiger, but then realizing it was just the wind.
How Sensitive Were They?
The team's search was incredibly sharp. At the higher end of their search (around 200 Hz), they could detect a gravitational wave amplitude as small as 5×10−26 (if we average over all possible angles) or as low as 2×10−26 if the star is tilted in the most favorable way. To put that in perspective, they improved their sensitivity depth to about 70−75 Hz−1/2, which is a significant jump over previous searches.
What Does This Mean?
While they didn't find the gravitational waves, they did find something very important: the "torque balance" scenario, where the star is perfectly balanced, is likely not happening for a standard neutron star in this frequency range. It's possible the star is a very strange, exotic object (like a quark star) that could still fit the theory, but for a normal neutron star, the balance is broken.
The search continues! The star might be spinning faster than 100 Hz, or the gravitational waves might be coming from a different mechanism entirely. But for now, the universe has told us that Scorpius X-1 isn't playing the "perfect balance" game we thought it was for ordinary matter. The hunt for the true nature of this cosmic dancer goes on.
Technical Summary: Sub-Torque-Balance Upper Limits on Continuous Gravitational Waves from Scorpius X-1
Problem and Motivation
Low-mass X-ray binaries (LMXBs), particularly Scorpius X-1 (Sco X-1), are prime targets for continuous gravitational wave (GW) searches. Theoretical models suggest that asymmetries in the neutron star (NS) mass distribution (triaxiality) or fluid oscillations (r-modes) could emit persistent, quasimonochromatic GWs. A key astrophysical motivation is the "torque balance" hypothesis, which posits that the spin-up torque from accretion is balanced by a spin-down GW torque, naturally explaining the observed cutoff in NS spin frequencies around 750 Hz. If this equilibrium holds, the GW amplitude from Sco X-1 should be detectable by current ground-based detectors. Previous searches using Advanced LIGO, Virgo, and KAGRA data have set upper limits, but none had yet definitively probed below the standard torque balance prediction across a broad frequency range independent of the NS spin inclination.
Methodology
This paper presents a search for continuous GWs from Sco X-1 using data from the first part of the fourth observing run (O4a) of the LIGO-Virgo-KAGRA (LVK) network (May 2023 – January 2024). During O4a, only the two LIGO detectors (H1 and L1) were operational; Virgo and KAGRA were offline.
- Search Algorithm: The analysis employs the resampling version of the cross-correlation (CrossCorr) pipeline. Unlike the "demod" pipeline used in previous runs, which correlates Short Fourier Transform (SFT) pairs with start times differing by a coherence time Tmax, the resampling method reconstructs the data into a time series evenly sampled in the neutron star's reference frame. This allows for more efficient computation and the use of longer coherence times.
- Parameters: The search covers GW signal frequencies f0 between 25 and 200 Hz. This corresponds to NS spin frequencies of 12.5–100 Hz (for triaxiality, where f0=2νs) or ∼15–20 to ∼120–150 Hz (for r-modes). The search grid includes the signal frequency, projected semi-major axis (asini), time of ascension (tasc′), and a "sheared" orbital period (P~) to account for correlations in the ephemeris.
- Data Processing: The analysis uses calibrated strain data with "self-gating" applied to remove transient instrumental glitches. The coherence time was fixed at Tmax=24 hours (86,400 s), significantly longer than in previous resampling searches, to maximize sensitivity.
- Candidate Follow-up: Candidates exceeding a frequency-dependent signal-to-noise ratio (S/N) threshold (ranging from 7.2 to 7.6) underwent a hierarchical follow-up. This involved:
- Clustering candidates in frequency.
- A "Level 0" targeted search using the non-resampling "demod" pipeline to veto candidates associated with known instrumental lines.
- "Level 1" refinement with a finer grid.
- "Level 2" and "Level 3" follow-ups with increasing coherence times (Tmax=4 days and 16 days, respectively) to distinguish persistent signals from noise outliers.
- Validation: The follow-up procedure was tested on 350 simulated signal injections, 289 of which exceeded thresholds. The search candidates were compared against these injections to assess their likelihood of being real signals.
Key Results
- No Detection: No convincing detection candidates were found. The most significant outliers (e.g., at 129.20 Hz) failed to exhibit the expected S/N scaling with increasing coherence time and were not recovered in independent searches of the subsequent O4b observing run data.
- Upper Limits: In the absence of a detection, the authors set 95% confidence upper limits on the GW amplitude h0.
- Sensitivity: The search achieved a sensitivity depth of D≈70–75 Hz−1/2, a significant improvement over previous searches (D≈50–60 Hz−1/2).
- Amplitude Limits: The most sensitive limits occur at the upper end of the frequency band (f0≈200 Hz), reaching h0≈5×10−26 (marginalized over inclination) and 2×10−26 (assuming the most favorable inclination).
- Torque Balance Constraint: Crucially, for frequencies 50 Hz≲f0≲200 Hz, the upper limits fall below the standard torque balance prediction for any neutron star spin inclination angle. This holds even under conservative assumptions regarding the NS radius (R=10 km) and mass (M=1.4M⊙).
- Physical Implications:
- Triaxiality: The limits correspond to ellipticities ϵ between 3×10−5 (at 75 Hz) and 3×10−6 (at 200 Hz). These values approach the theoretical maximum deformations supportable by ordinary nuclear matter.
- r-modes: The constraints on the r-mode amplitude α reach ≲5×10−4 at 200 Hz. While this is within the plausible range for newborn NSs, it is slightly above expectations for an accreting NS like Sco X-1.
Significance and Claims
The paper claims that these results represent the most sensitive search for continuous GWs from Sco X-1 to date. The primary significance is that the search has, for the first time, set upper limits below the standard torque balance prediction across a broad frequency range (50–200 Hz) without relying on assumptions about the neutron star's spin inclination.
The authors argue that these results effectively exclude the scenario where Sco X-1 contains a neutron star in equilibrium between accretion and GW torques within this frequency range, assuming a standard hadronic equation of state. They note that the torque balance scenario remains hypothetically possible only for extremely compact objects, such as quark stars with masses M≲0.5M⊙ and radii R≲8 km, which are not the standard interpretation for Sco X-1. The paper concludes that while the spin frequency of Sco X-1 could still be higher than the searched range (implying f0>200 Hz), the current data strongly disfavors the torque balance model for the searched frequencies.
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