{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T23:12:08Z","timestamp":1790723528862,"version":"4.1.0"},"reference-count":99,"publisher":"American Physical Society (APS)","issue":"6","license":[{"start":{"date-parts":[[2026,2,12]],"date-time":"2026-02-12T00:00:00Z","timestamp":1770854400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000271","name":"Science and Technology Facilities Council","doi-asserted-by":"publisher","award":["ST\/W000903\/1"],"award-info":[{"award-number":["ST\/W000903\/1"]}],"id":[{"id":"10.13039\/501100000271","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["journals.aps.org"],"crossmark-restriction":true},"short-container-title":["Phys. Rev. Lett."],"accepted":{"date-parts":[[2025,12,2]]},"abstract":"<jats:p>\n                    Supermassive black hole (SMBH) binary systems are an unavoidable outcome of galaxy mergers. Their dynamics encode valuable information about their formation and growth, the composition of their host galactic nuclei, the evolution of galaxies, and the nature of gravity. Many SMBH binaries with separations pc-kpc have been found, but closer (subparsec) binaries remain to be confirmed. Identifying these systems may elucidate how binaries evolve past the \u201cfinal parsec\u201d until gravitational radiation drives them to coalescence. Methods to discover and characterize SMBH binaries can shed light on these important questions and potentially open new multimessenger channels. Here we show that SMBH binaries in nonactive galactic nuclei can be identified and characterized by the gravitational lensing of individual bright stars, located behind them in the host galaxy. The rotation of \u201ccaustics\u201d\u2014regions where sources are hugely magnified due to the SMBH binary\u2019s orbit and inspiral\u2014leads to quasiperiodic lensing of starlight (QPLS). The extreme lensing magnification of individual bright stars produces a significant variation in the host galaxies\u2019 luminosity; their lightcurve traces the orbit of the SMBH binary and its evolution, analogous to the waveforms recorded by gravitational-wave (GW) detectors. QPLS probes the population of sources observable by pulsar timing arrays and space detectors (LISA, TianQin), offering advance warning triggers for merging SMBHs for coincident or follow-up GW detections. SMBH population models predict 1\u201350\n                    <a:math xmlns:a=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <a:mrow>\n                        <a:mo stretchy=\"false\">[<\/a:mo>\n                        <a:mn>190<\/a:mn>\n                        <a:mi>\u2013<\/a:mi>\n                        <a:mn>5000<\/a:mn>\n                        <a:mo stretchy=\"false\">]<\/a:mo>\n                        <a:mrow>\n                          <a:mo stretchy=\"false\">(<\/a:mo>\n                          <a:msub>\n                            <a:mrow>\n                              <a:mi>n<\/a:mi>\n                            <\/a:mrow>\n                            <a:mrow>\n                              <a:mo>\u22c6<\/a:mo>\n                            <\/a:mrow>\n                          <\/a:msub>\n                          <a:mo>\/<\/a:mo>\n                          <a:msup>\n                            <a:mrow>\n                              <a:mi>pc<\/a:mi>\n                            <\/a:mrow>\n                            <a:mrow>\n                              <a:mo>\u2212<\/a:mo>\n                              <a:mn>3<\/a:mn>\n                            <\/a:mrow>\n                          <\/a:msup>\n                          <a:mo stretchy=\"false\">)<\/a:mo>\n                        <\/a:mrow>\n                      <\/a:mrow>\n                    <\/a:math>\n                    QPLS binaries with period less than 10[40]\u00a0yr with comparable masses and redshift\n                    <g:math xmlns:g=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <g:mi>z<\/g:mi>\n                      <g:mo>&lt;<\/g:mo>\n                      <g:mn>0.3<\/g:mn>\n                    <\/g:math>\n                    , where\n                    <i:math xmlns:i=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n                      <i:msub>\n                        <i:mi>n<\/i:mi>\n                        <i:mo>\u22c6<\/i:mo>\n                      <\/i:msub>\n                    <\/i:math>\n                    is the stellar number density. Additionally, stellar and orbital motion will lead to frequent instances of single or double flares caused by SMBHBs with longer periods. This novel signature can be searched for in a wealth of existing and upcoming time-domain photometric data: identifying quasiperiodic variability in galactic lightcurves will reveal an ensemble of binary systems and illuminate outstanding questions around them.\n                  <\/jats:p>","DOI":"10.1103\/1sfl-87t4","type":"journal-article","created":{"date-parts":[[2025,12,2]],"date-time":"2025-12-02T20:24:21Z","timestamp":1764707061000},"update-policy":"https:\/\/doi.org\/10.1103\/crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["Black Holes as Telescopes: Discovering Supermassive Binaries through Quasiperiodic Lensed Starlight"],"prefix":"10.1103","volume":"136","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0106-4757","authenticated-orcid":true,"given":"Hanxi","family":"Wang","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/052gg0110","id-type":"ROR","asserted-by":"publisher"}],"name":"University of Oxford"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9943-6490","authenticated-orcid":true,"given":"Miguel","family":"Zumalac\u00e1rregui","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/03sry2h30","id-type":"ROR","asserted-by":"publisher"}],"name":"Max Planck Institute for Gravitational Physics (Albert Einstein Institute)"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4865-7517","authenticated-orcid":true,"given":"Bence","family":"Kocsis","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/052gg0110","id-type":"ROR","asserted-by":"publisher"}],"name":"University of Oxford, Clarendon Laboratory"},{"id":[{"id":"https:\/\/ror.org\/052gg0110","id-type":"ROR","asserted-by":"publisher"}],"name":"University of Oxford"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"16","published-online":{"date-parts":[[2026,2,12]]},"reference":[{"key":"1sfl-87t4Cc1R1","doi-asserted-by":"publisher","DOI":"10.1038\/287307a0","type":"journal-article"},{"key":"1sfl-87t4Cc2R1","doi-asserted-by":"publisher","DOI":"10.1086\/386278","type":"journal-article"},{"key":"1sfl-87t4Cc3R1","doi-asserted-by":"publisher","DOI":"10.1007\/s00159-010-0029-x","type":"journal-article"},{"key":"1sfl-87t4Cc4R1","doi-asserted-by":"publisher","DOI":"10.1086\/378086","type":"journal-article"},{"key":"1sfl-87t4Cc5R1","doi-asserted-by":"publisher","DOI":"10.1007\/s41114-022-00041-y","type":"journal-article"},{"key":"1sfl-87t4Cc6R1","doi-asserted-by":"publisher","DOI":"10.1086\/344675","type":"journal-article"},{"key":"1sfl-87t4Cc7R1","doi-asserted-by":"publisher","DOI":"10.1146\/annurev-astro-082708-101811","type":"journal-article"},{"key":"1sfl-87t4Cc8R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.133.021401","type":"journal-article"},{"key":"1sfl-87t4Cc9R1","doi-asserted-by":"publisher","DOI":"10.1086\/590230","type":"journal-article"},{"key":"1sfl-87t4Cc10R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.newar.2020.101525","type":"journal-article"},{"key":"1sfl-87t4Cc12R1","doi-asserted-by":"publisher","DOI":"10.1007\/s41114-022-00037-8","type":"journal-article"},{"key":"1sfl-87t4Cc13R1","doi-asserted-by":"publisher","DOI":"10.1093\/mnras\/stab3713","type":"journal-article"},{"key":"1sfl-87t4Cc14R1","doi-asserted-by":"publisher","DOI":"10.3847\/2041-8213\/acdac6","type":"journal-article"},{"key":"1sfl-87t4Cc15R1","doi-asserted-by":"publisher","DOI":"10.1051\/0004-6361\/202346844","type":"journal-article"},{"key":"1sfl-87t4Cc16R1","doi-asserted-by":"publisher","DOI":"10.3847\/2041-8213\/acdd02","type":"journal-article"},{"key":"1sfl-87t4Cc17R1","doi-asserted-by":"publisher","DOI":"10.1088\/1674-4527\/acdfa5","type":"journal-article"},{"key":"1sfl-87t4Cc18R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.109.L021302","type":"journal-article"},{"key":"1sfl-87t4Cc19R1","doi-asserted-by":"publisher","DOI":"10.1103\/1br7-s1rc","type":"journal-article"},{"key":"1sfl-87t4Cc22R1","doi-asserted-by":"publisher","DOI":"10.1088\/0264-9381\/33\/3\/035010","type":"journal-article"},{"key":"1sfl-87t4Cc23R1","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6382\/adda8a","type":"journal-article"},{"key":"1sfl-87t4Cc24R1","doi-asserted-by":"publisher","DOI":"10.1007\/s41114-023-00045-2","type":"journal-article"},{"key":"1sfl-87t4Cc25R1","doi-asserted-by":"publisher","DOI":"10.1088\/0004-637X\/700\/2\/1952","type":"journal-article"},{"key":"1sfl-87t4Cc26R1","doi-asserted-by":"publisher","DOI":"10.1038\/nature15262","type":"journal-article"},{"key":"1sfl-87t4Cc27R1","doi-asserted-by":"publisher","DOI":"10.1093\/mnras\/sty215","type":"journal-article"},{"key":"1sfl-87t4Cc28R1","doi-asserted-by":"publisher","DOI":"10.1093\/mnras\/stz2766","type":"journal-article"},{"key":"1sfl-87t4Cc29R1","doi-asserted-by":"publisher","DOI":"10.1093\/mnras\/staa299","type":"journal-article"},{"key":"1sfl-87t4Cc30R1","volume-title":"Gravitational 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Schneider","year":"1986","journal-title":"Astron. Astrophys.","ISSN":"https:\/\/id.crossref.org\/issn\/0004-6361","issn-type":"print"},{"key":"1sfl-87t4Cc47R1","unstructured":"See Supplemental Material at http:\/\/link.aps.org\/supplemental\/10.1103\/1sfl-87t4, Sec.\u00a0A for details on methods and assumptions used when computing the magnification of the binary lens equation, which includes Refs.\u00a0[48\u201356]; Sec.\u00a0B for details on the topology and size of the caustic curves, which includes Ref.\u00a0[57]; Sec.\u00a0C for details on computing the magnification of an extended source near the caustic curve of a binary lens, which includes Ref.\u00a0[58]; Sec. D for details on the magnification estimate at the trough and near merger for the lensing light curve, which includes Ref.\u00a0[59]; Sec.\u00a0F for details on the time duration estimate of caustic crossing; Sec.\u00a0H for details on detection thresholds, which includes Refs.\u00a0[60\u201362]; Sec.\u00a0I for details on the GW-driven evolution of the binary and the detectability of the GWs of eccentric binaries, which includes Refs.\u00a0[63\u201367]; Sec.\u00a0J for details on the QPLS and caustic crossing rates, which includes Refs.\u00a0[68,69]; and Sec.\u00a0K for the special case of multiple QPLS sources.","type":"other"},{"key":"1sfl-87t4Cc48R1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1745-3933.2009.00777.x","type":"journal-article"},{"key":"1sfl-87t4Cc49R1","doi-asserted-by":"publisher","DOI":"10.3847\/1538-4357\/aab617","type":"journal-article"},{"key":"1sfl-87t4Cc50R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.97.023518","type":"journal-article"},{"key":"1sfl-87t4Cc51R1","doi-asserted-by":"publisher","DOI":"10.3847\/1538-4357\/aa9575","type":"journal-article"},{"key":"1sfl-87t4Cc52R1","doi-asserted-by":"publisher","DOI":"10.1093\/mnras\/stae2652","type":"journal-article"},{"key":"1sfl-87t4Cc53R1","first-page":"453","type":"journal-article","volume":"268","author":"H. 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Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.aps.org\/article\/10.1103\/1sfl-87t4","content-type":"unspecified","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/harvest.aps.org\/v2\/journals\/articles\/10.1103\/1sfl-87t4\/fulltext","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T22:47:18Z","timestamp":1790722038000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.aps.org\/doi\/10.1103\/1sfl-87t4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,2,12]]},"references-count":99,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2026,2]]}},"URL":"https:\/\/doi.org\/10.1103\/1sfl-87t4","relation":{"has-preprint":[{"id-type":"doi","id":"10.48550\/arXiv.2506.16544","asserted-by":"subject"}]},"ISSN":["0031-9007","1079-7114"],"issn-type":[{"value":"0031-9007","type":"print"},{"value":"1079-7114","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,2,12]]},"assertion":[{"value":"2025-07-10","name":"date_received","label":"Date 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