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Full list of authors: Delrez, L.; Murray, C. A.; Pozuelos, F. J.; Narita, N.; Ducrot, E.; Timmermans, M.; Watanabe, N.; Burgasser, A. J.; Hirano, T.; Rackham, B., V; Stassun, K. G.; Van Grootel, V.; Aganze, C.; Cointepas, M.; Howell, S.; Kaltenegger, L.; Niraula, P.; Sebastian, D.; Almenara, J. M.; Barkaoui, K.; Baycroft, T. A.; Bonfils, X.; Bouchy, F.; Burdanov, A.; Caldwell, D. A.; Charbonneau, D.; Ciardi, D. R.; Collins, K. A.; Daylan, T.; Demory, B-O; Guenther, N.; de Wit, J.; Dransfield, G.; Fajardo-Acosta, S. B.; Fausnaugh, M.; Fukui, A.; Furlan, E.; Garcia, L. J.; Gnilka, C. L.; Chew, Y. Gomez Maqueo; Gomez-Munoz, M. A.; Harakawa, H.; Heng, K.; Hooton, M. J.; Hori, Y.; Ikoma, M.; Jehin, E.; Jenkins, J. M.; Kagetani, T.; Kawauchi, K.; Kimura, T.; Kodama, T.; Kotani, T.; Krishnamurthy, V; Kudo, T.; Kunovac, V; Kusakabe, N.; Latham, D. W.; Littlefield, C.; McCormac, J.; Melis, C.; Mori, M.; Murgas, F.; Palle, E.; Pedersen, P. P.; Queloz, D.; Ricker, G.; Sabin, L.; Schanche, N.; Schroffenegger, U.; Seager, S.; Shiao, B.; Sohy, S.; Standing, M. R.; Tamura, M.; Theissen, C. A.; Thompson, S. J.; Triaud, A. H. M. J.; Vanderspek, R.; Vievard, S.; Wells, R. D.; Winn, J. N.; Zou, Y.; Zuniga-Fernandez, S.; Gillon, M.--This is an Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited., Context. In the age of JWST, temperate terrestrial exoplanets transiting nearby late-type M dwarfs provide unique opportunities for characterising their atmospheres, as well as searching for biosignature gases. In this context, the benchmark TRAPPIST-1 planetary system has garnered the interest of a broad scientific community. Aims. We report here the discovery and validation of two temperate super-Earths transiting LP 890-9 (TOI-4306, SPECULOOS-2), a relatively low-activity nearby (32 pc) M6V star. The inner planet, LP 890-9 b, was first detected by TESS (and identified as TOI-4306.01) based on four sectors of data. Intensive photometric monitoring of the system with the SPECULOOS Southern Observatory then led to the discovery of a second outer transiting planet, LP 890-9 c (also identified as SPECULOOS-2 c), previously undetected by TESS. The orbital period of this second planet was later confirmed by MuSCAT3 follow-up observations. Methods. We first inferred the properties of the host star by analyzing its Lick/Kast optical and IRTF/SpeX near-infrared spectra, as well as its broadband spectral energy distribution, and Gaia parallax. We then derived the properties of the two planets by modelling multi-colour transit photometry from TESS, SPECULOOS-South, MuSCAT3, ExTrA, TRAPPIST-South, and SAINT-EX. Archival imaging, Gemini-South/Zorro high-resolution imaging, and Subaru/IRD radial velocities also support our planetary interpretation. Results. With a mass of 0.118 ± 0.002 M⊙, a radius of 0.1556 ± 0.0086 R⊙, and an effective temperature of 2850 ± 75 K, LP 890-9 is the second-coolest star found to host planets, after TRAPPIST-1. The inner planet has an orbital period of 2.73 d, a radius of 1.320 −0.027+0.053 R⊕, and receives an incident stellar flux of 4.09 ± 0.12 S⊕. The outer planet has a similar size of 1.367 −0.039+0.055R⊕ and an orbital period of 8.46 d. With an incident stellar flux of 0.906 ± 0.026 S⊕, it is located within the conservative habitable zone, very close to its inner limit (runaway greenhouse). Although the masses of the two planets remain to be measured, we estimated their potential for atmospheric characterisation via transmission spectroscopy using a mass-radius relationship and found that, after the TRAPPIST-1 planets, LP 890-9 c is the second-most favourable habitable-zone terrestrial planet known so far (assuming for this comparison a similar atmosphere for all planets). Conclusions. The discovery of this remarkable system offers another rare opportunity to study temperate terrestrial planets around our smallest and coolest neighbours. © L. Delrez et al. 2022., Funding for the TESS mission is provided by NASA’s Science Mission Directorate. We acknowledge the use of public TESS data from pipelines at the TESS Science Office and at the TESS Science Processing Operations Center. This research has made use of the Exoplanet Follow-up Observation Program website, which is operated by the California Institute of Technology, under contract with the National Aeronautics and Space Administration under the Exoplanet Exploration Program. Resources supporting this work were provided by the NASA High-End Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center for the production of the SPOC data products. This paper includes data collected by the TESS mission that are publicly available from the Mikulski Archive for Space Telescopes (MAST). The research leading to these results has received funding from the European Research Council (ERC) under the FP/2007-2013 ERC grant agreement no 336480, and under the European Union’s Horizon 2020 research and innovation programme (grants agreements no 679030 & 803193/BEBOP); from an Action de Recherche Concertée (ARC) grant, financed by the Wallonia-Brussels Federation, from the Balzan Prize Foundation, from the BELSPO/BRAIN2.0 research program (PORTAL project), from the Science and Technology Facilities Council (STFC; grants no ST/S00193X/1, ST/00305/1, and ST/W000385/1), and from F.R.S-FNRS (Research Project ID T010920F). This work was also partially supported by a grant from the Simons Foundation (PI: Queloz, grant number 327127), as well as by the MERAC foundation (PI: Triaud). TRAPPIST is funded by the Belgian Fund for Scientific Research (Fond National de la Recherche Scientifique, FNRS) under the grant PDR T.0120.21, with the participation of the Swiss National Science Fundation (SNF). This work is partly supported by MEXT/JSPS KAKENHI Grant Numbers JP15H02063, JP17H04574, JP18H05439, JP18H05442, JP19K14783, JP21H00035, JP21K13975, JP21K20376, JP22000005, Grant-in-Aid for JSPS Fellows Grant Number JP20J21872, JST CREST Grant Number JPMJCR1761, the Astrobiology Center of National Institutes of Natural Sciences (NINS) (Grant Numbers AB031010, AB031014), and Social welfare juridical person SHIYUKAI (chairman MASAYUKI KAWASHIMA). This paper is based on data collected at the Subaru Telescope, which is located atop Maunakea and operated by the National Astronomical Observatory of Japan (NAOJ). We wish to recognise and acknowledge the very significant cultural role and reverence that the summit of Maunakea has always had within the indigenous Hawaiian community. This paper is based on observations made with the MuSCAT3 instrument, developed by the Astrobiology Center and under financial supports by JSPS KAKENHI (JP18H05439) and JST PRESTO (JPMJPR1775), at Faulkes Telescope North on Maui, HI, operated by the Las Cumbres Observatory. Some of the observations in the paper made use of the High-Resolution Imaging instrument Zorro obtained under Gemini LLP Proposal Number: GN/S-2021A-LP-105. Zorro was funded by the NASA Exoplanet Exploration Program and built at the NASA Ames Research Center by Steve B. Howell, Nic Scott, Elliott P. Horch, and Emmett Quigley. Zorro was mounted on the Gemini North (and/or South) telescope of the international Gemini Observatory, a program of NSF s OIR Lab, which is managed by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation on behalf of the Gemini partnership: the National Science Foundation (United States), National Research Council (Canada), Agencia Nacional de Investigación y Desarrollo (Chile), Ministerio de Ciencia, Tecnología e Innovación (Argentina), Ministério da Ciência, Tecnologia, Inovações e Comunicações (Brazil), and Korea Astronomy and Space Science Institute (Republic of Korea). We acknowledge funding from the European Research Council under the ERC Grant Agreement n. 3 37591-ExTrA. This work has been carried out within the framework of the NCCR PlanetS supported by the Swiss National Science Foundation. This work is based upon observations carried out at the Observatorio Astronómico Nacional at the Sierra de San Pedro Mártir (OAN-SPM), Baja California, México. We warmly thank the entire technical staff of the Observatorio Astronómico Nacional at San Pedro Mártir for their unfailing support to SAINT-EX operations. Research at Lick Observatory is partially supported by a generous gift from Google. L.D. is an F.R.S.-FNRS Postdoctoral Researcher. M.G. and E.J. are F.R.S.-FNRS Senior Research Associates. V.V.G. is an F.R.S.-FNRS Research Associate. B.V.R. thanks the Heising-Simons Foundation for support. Y.G.M.C. acknowledges support from UNAM-PAPIIT IG-101321. B.-O.D. acknowledges support from the Swiss National Science Foundation (PP00P2-163967 and PP00P2-190080). M.N.G. acknowledges support from the European Space Agency (ESA) as an ESA Research Fellow. A.H.M.J.T acknowledges funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no 803193/BEBOP), from the MERAC foundation, and from the Science and Technology Facilities Council (STFC; grants no ST/S00193X/1, ST/00305/1, and ST/W000385/1). E.D. acknowledges support from the innovation and research Horizon 2020 program in the context of the Marie Sklodowska-Curie subvention 945298. V.K. acknowledges support from NSF award AST2009343. This publication benefits from the support of the French Community of Belgium in the context of the FRIA Doctoral Grant awarded to M.T., With funding from the Spanish government through the Severo Ochoa Centre of Excellence accreditation SEV-2017-0709.