Inferring the Neutron Star Maximum Mass and Lower Mass Gap in Neutron Star–Black Hole Systems with Spin Christine Ye 1 and Maya Fishbach 2,3 1 Eastlake High School, 400 228th Avenue NE, Sammamish, WA 98074, USA 2 Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA) and Department of Physics and Astronomy, Northwestern University, 1800 Sherman Avenue, Evanston, IL 60201, USA Received 2022 January 30; revised 2022 July 6; accepted 2022 July 7; published 2022 September 29 Abstract Gravitational-wave (GW) detections of merging neutron star–black hole (NSBH) systems probe astrophysical neutron star (NS) and black hole (BH) mass distributions, especially at the transition between NS and BH masses. Of particular interest are the maximum NS mass, minimum BH mass, and potential mass gap between them. While previous GW population analyses assumed all NSs obey the same maximum mass, if rapidly spinning NSs exist, they can extend to larger maximum masses than nonspinning NSs. In fact, several authors have proposed that the ∼2.6 M e object in the event GW190814—either the most massive NS or least massive BH observed to date—is a rapidly spinning NS. We therefore infer the NSBH mass distribution jointly with the NS spin distribution, modeling the NS maximum mass as a function of spin. Using four LIGO–Virgo NSBH events including GW190814, if we assume that the NS spin distribution is uniformly distributed up to the maximum (breakup) spin, we infer the maximum nonspinning NS mass is  - + M 2.7 0.4 0.5 (90% credibility), while assuming only nonspinning NSs, the NS maximum mass must be >2.53 M e (90% credibility). The data support the mass gap’s existence, with a minimum BH mass at  - + M 5.4 1.0 0.7 . With future observations, under simplified assumptions, 150 NSBH events may constrain the maximum nonspinning NS mass to ±0.02 M e , and we may even measure the relation between the NS spin and maximum mass entirely from GW data. If rapidly rotating NSs exist, their spins and masses must be modeled simultaneously to avoid biasing the NS maximum mass. Unified Astronomy Thesaurus concepts: Gravitational waves (678); Neutron stars (1108); Black holes (162) 1. Introduction The transition between neutron star (NS) and black hole (BH) masses is key to our understanding of stellar evolution, supernova physics, and nuclear physics. In particular, the maximum mass that an NS can support before collapsing to a black hole (BH), known as the Tolman–Oppenheimer–Volkoff (TOV) mass M TOV for a nonspinning NS, is governed by the unknown high-density nuclear equation of state (EOS)(Bombaci 1996; Kalogera & Baym 1996; Lattimer 2012). Constraints on the maximum NS mass can therefore inform the nuclear EOS, together with astrophysical observations such as X-ray timing of pulsar hot spots (Bogdanov et al. 2019), gravitational-wave (GW) tidal effects from mergers involving NSs (Abbott et al. 2018; Lim & Holt 2019; Landry et al. 2020; Dietrich et al. 2020), and electromagnetic observations of binary neutron star (BNS) merger remnants (Margalit & Metzger 2017; Rezzolla et al. 2018), as well as lab experiments (e.g., Adhikari et al. 2021). Recent theoretical and observational constraints on the EOS have placed M TOV = 2.2–2.5 M e (e.g., Legred et al. 2021). If astrophysical NSs exist up to the maximum possible NS mass, M TOV can be measured by fitting the NS mass distribution to Galactic NS observations (Valentim et al. 2011; Özel et al. 2012; Alsing et al. 2018; Farrow et al. 2019; Farr & Chatziioannou 2020). A recent fit to Galactic NSs finds a maximum mass of  - + M 2.22 0.23 0.85 (Farr & Chatziioannou 2020). In particular, observations of massive pulsars (Antoniadis et al. 2013; Cromartie et al. 2020) set a lower limit of M TOV  2 M e . Meanwhile, the minimum BH mass and the question of a mass gap between NSs and BHs is of importance to supernova physics (Fryer & Kalogera 2001; Fryer et al. 2012; Belczynski et al. 2012; Liu et al. 2021). Observations of BHs in X-ray binaries first suggested a mass gap between the heaviest NSs (limited by M TOV ) and the lightest BHs (∼5 M e ; Özel et al. 2010; Farr et al. 2011), although recent observations suggest that the mass gap may not be empty (Thompson et al. 2019; Abbott et al. 2020c). Over the last few years, the GW observatories Advanced LIGO (Aasi et al. 2015) and Virgo (Acernese et al. 2015) have revealed a new astrophysical population of NSs and BHs in merging binary black holes (BBHs)(Abbott et al. 2016), BNS (Abbott et al. 2017, 2020a), and NSBH systems (Abbott et al. 2021a). These observations can be used to infer the NS mass distribution in merging binaries and constrain the maximum NS mass (Chatziioannou & Farr 2020; Galaudage et al. 2021; Landry & Read 2021; Li et al. 2021; Zhu et al. 2021; The LIGO Scientific Collaboration et al. 2021a). Furthermore, jointly fitting the NS and BH mass distribution using GW data probes the existence of the mass gap (Mandel et al. 2017; Fishbach et al. 2020; Farah et al. 2021). Recent fits of the BNS, BBH, and NSBH mass spectrum find a relative lack of objects between 2.6 and 6 M e (Abbott et al. 2021b; Farah et al. 2021; The LIGO Scientific Collaboration et al. 2021a). Gravitational-wave NSBH detections can uniquely explore both the maximum NS mass and the minimum BH mass simultaneously with the same system. In particular, the NS and BH masses in the first NSBH detections (Abbott et al. 2021a) The Astrophysical Journal, 937:73 (14pp), 2022 October 1 https://doi.org/10.3847/1538-4357/ac7f99 © 2022. The Author(s). Published by the American Astronomical Society. 3 NASA Hubble Fellowship Program Einstein Postdoctoral Fellow. Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. 1