Abdurashidova, The HERA Collaboration: ZaraAdams, TyroneAguirre, James E.Alexander, PaulAli, Zaki S.Baartman, RushelleBalfour, YangaBarkana, RennanBeardsley, Adam P.Bernardi, GianniBillings, Tashalee S.Bowman, Judd D.Bradley, Richard F.Breitman, DanielaBull, PhilipBurba, JacobCarey, SteveCarilli, Chris L.Cheng, CarinaChoudhuri, SamirDeBoer, David R.de Lera Acedo, EloyDexter, MattDillon, Joshua S.Ely, JohnEwall-Wice, AaronFagnoni, NicolasFialkov, AnastasiaFritz, RandallFurlanetto, Steven R.Gale-Sides, KingsleyGarsden, HughGlendenning, BrianGorce, AdélieGorthi, DeepthiGreig, BradleyGrobbelaar, JasperHalday, ZiyaadHazelton, Bryna J.Heimersheim, StefanHewitt, Jacqueline N.Hickish, JackJacobs, Daniel C.Julius, AustinKern, Nicholas S.Kerrigan, JoshuaKittiwisit, PiyanatKohn, Saul A.Kolopanis, MatthewLanman, AdamLa Plante, PaulLewis, DavidLiu, AdrianLoots, AnitaMa, Yin ZheMacMahon, David H.E.Malan, LourenceMalgas, KeithMalgas, CresshimMaree, MatthysMarero, BradleyMartinot, Zachary E.McBride, LisaMesinger, AndreiMirocha, JordanMolewa, MathakaneMorales, Miguel F.Mosiane, TshegofalangMuñoz, Julian B.Murray, Steven G.Nagpal, VighneshNeben, Abraham R.Nikolic, BojanNunhokee, Chuneeta D.Nuwegeld, HansParsons, Aaron R.Pascua, RobertPatra, NipanjanaPieterse, SamanthaQin, YuxiangRazavi-Ghods, NimaRobnett, JamesRosie, KathrynSantos, Mario G.Sims, PeterSingh, SaurabhSmith, CraigSwarts, HiltonTan, JianrongThyagarajan, NithyanandanWilensky, Michael J.Williams, Peter K.G.van Wyngaarden, PieterZheng, Haoxuan2025-06-302025-06-300004-637Xhttp://www.scopus.com/inward/record.url?scp=85150531114&partnerID=8YFLogxKhttps://hdl.handle.net/1885/733765735We report the most sensitive upper limits to date on the 21 cm epoch of reionization power spectrum using 94 nights of observing with Phase I of the Hydrogen Epoch of Reionization Array (HERA). Using similar analysis techniques as in previously reported limits, we find at 95% confidence that Δ2(k = 0.34 h Mpc−1) ≤ 457 mK2 at z = 7.9 and that Δ2(k = 0.36 h Mpc−1) ≤ 3496 mK2 at z = 10.4, an improvement by a factor of 2.1 and 2.6, respectively. These limits are mostly consistent with thermal noise over a wide range of k after our data quality cuts, despite performing a relatively conservative analysis designed to minimize signal loss. Our results are validated with both statistical tests on the data and end-to-end pipeline simulations. We also report updated constraints on the astrophysics of reionization and the cosmic dawn. Using multiple independent modeling and inference techniques previously employed by HERA Collaboration, we find that the intergalactic medium must have been heated above the adiabatic cooling limit at least as early as z = 10.4, ruling out a broad set of so-called “cold reionization” scenarios. If this heating is due to high-mass X-ray binaries during the cosmic dawn, as is generally believed, our result’s 99% credible interval excludes the local relationship between soft X-ray luminosity and star formation and thus requires heating driven by evolved low-metallicity stars.The authors wish to thank the anonymous referee for providing insightful feedback. J.S.D. gratefully acknowledges the support of the NSF AAPF award No. 1701536. N.K. gratefully acknowledges support from the MIT Pappalardo fellowship. P.K. and M.G.S. acknowledge support from the South African Radio Astronomy Observatory (SARAO; www.sarao.ac.za ) and the National Research Foundation (grant No. 84156). This result is part of a project that has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement No. 948764; P.B. and M.J.W.). P.B. and H.G. acknowledge support from STFC grant ST/T000341/1. Y.Q. would like to acknowledge the support from the High Performance Computing centers of the Scuola Normale Superiore (Italy), the Council for Scientific and Industrial Research (South Africa), the OzSTAR national facility (Australia), and XSEDE (U.S.) for computational resources. J.M. acknowledges computational resources and support on the supercomputer Cedar at Simon Fraser University, which is managed by Compute Canada and funded by the Canada Foundation for Innovation (CFI). Parts of this research were supported by the Australian Research Council Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), through project No. CE170100013. S.H. acknowledges support from STFC studentship 2277533 in project ST/T505985/1. J.B.M. is supported by a Clay Fellowship at the Smithsonian Astrophysical Observatory. G.B. acknowledges funding from the INAF PRIN-SKA 2017 project 1.05.01.88.04 (FORECaST), support from the Ministero degli Affari Esteri della Cooperazione Internazionale—Direzione Generale per la Promozione del Sistema Paese Progetto di Grande Rilevanza ZA18GR02 and the National Research Foundation of South Africa (grant No. 113121) as part of the ISARP RADIOSKY2020 Joint Research Scheme, from the Royal Society and the Newton Fund under grant NA150184 and from the National Research Foundation of South Africa (grant No. 103424). E.d.L.A. acknowledges the funding support of the UKRI Science and Technology Facilities Council SKA grant. A.L. acknowledges support from the New Frontiers in Research Fund Exploration grant program, the Canadian Institute for Advanced Research (CIFAR) Azrieli Global Scholars program, a Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grant and a Discovery Launch Supplement, the Sloan Research Fellowship, and the William Dawson Scholarship at McGill. This material is based upon work supported by the National Science Foundation under grant Nos. 1636646 and 1836019 and institutional support from the HERA collaboration partners. This research is funded in part by the Gordon and Betty Moore Foundation through grant GBMF5212 to the Massachusetts Institute of Technology. HERA is hosted by the South African Radio Astronomy Observatory, which is a facility of the National Research Foundation, an agency of the Department of Science and Innovation. This work used the Extreme Science and Engineering Discovery Environment (XSEDE; Towns et al. ), which is supported by National Science Foundation grant No. ACI-1548562. We acknowledge the use of the Ilifu cloud computing facility ( www.ilifu.ac.za ) and the support from the Inter-University Institute for Data Intensive Astronomy (IDIA; https://www.idia.ac.za ).enPublisher Copyright: © 2023. The Author(s). Published by the American Astronomical Society.2023-03-0110.3847/1538-4357/acaf5085150531114