Ultralight Bosonic Field Mass Bounds from Astrophysical Black Hole Spin Matthew J. Stott Theoretical Particle Physics and Cosmology Group, Department of Physics, Kings College London, University of London, Strand, London, WC2R 2LS, United Kingdom∗ (Dated: September 16, 2020) Black Hole measurements have grown significantly in the new age of gravitation wave astronomy from LIGO observations of binary black hole mergers. As yet unobserved massive ultralight bosonic fields represent one of the most exciting features of Standard Model extensions, capable of providing solutions to numerous paradigmatic issues in particle physics and cosmology. In this work we explore bounds from spinning astrophysical black holes and their angular momentum energy transfer to bosonic condensates which can form surrounding the black hole via superradiant instabilities. Using recent analytical results we perform a simplified analysis with a generous ensemble of black hole parameter measurements where we find superradiance very generally excludes bosonic fields in −14 −11 −20 the mass ranges; Spin-0: f3:8 × 10 eV ≤ µ0 ≤ 3:4 × 10 eV; 5:5 × 10 eV ≤ µ0 ≤ 1:3 × −16 −21 −20 −15 −11 10 eV; 2:5×10 eV ≤ µ0 ≤ 1:2×10 eVg, Spin-1: f6:2×10 eV ≤ µ1 ≤ 3:9×10 eV; 2:8× −22 −16 −14 −11 −20 10 eV ≤ µ1 ≤ 1:9×10 eVg and Spin-2: f2:2×10 eV ≤ µ2 ≤ 2:8×10 eV; 1:8×10 eV ≤ −16 −22 −21 µ2 ≤ 1:8 × 10 eV; 6:4 × 10 eV ≤ µ2 ≤ 7:7 × 10 eVg respectively. We also explore these bounds in the context of specific phenomenological models, specifically the QCD axion, M-theory models and fuzzy dark matter sitting at the edges of current limits. In particular we include recent measurements of event GW190521 and M87* used to constrain both the masses and decay constants of axion like fields. Finally we comment a simple example of a spectrum of fields for the spin-0 and spin-1 cases. I. INTRODUCTION including neutron star (NS) binaries [27{29] and possible BH-NS binaries [30]. Recently the first direct detection of +28 Black holes (BHs) as solutions to Einsteins field equa- an IMBH [31, 32] (MBH = 142 16M ) from LIGO event − tions offer a vital probe into the fundamental interac- GW190521 appears to have involved two merger objects tions and potential constituents of theories that deter- heavier than previously expected limits from models of mine the nature of our Universe [1{6]. Populations supernova dynamics. The apparent shadow from the of BHs are often classified into mass bounds based on event horizon of the SMBH M87* was also recently pre- observational evidence to date. Common designations sented by the Event Horizon Telescope (EHT) collabo- across the BH mass spectrum normalised to the solar ration [33{37]. This work representing the first direct mass unit M , are: stellar mass BHs [7, 8] (5M . experimental evidence of a BH. Collectively these land- 2 marks indicate the initial footings of a wealth of data to MBH . 10 M ), intermediate mass BHs [9{11] (IMBHs: 2 5 come. This exciting prospect potentially capable of deep- 10 M . MBH . 10 M ) , low mass BHs (LMBHs) 5 6 ening our understanding of pertinent questions in both [12, 13] (10 M . MBH . 10 M ), supermassive BHs 6 10 the broader pictures of astrophysics and particle physics, [14, 15] (SMBHs: 10 M . MBH . 10 M ) and ul- 10 where objects on the largest scales might enlighten us tramassive BHs [16, 17] (UMBHs: 10 M . MBH . 1012M ). To date numerous BHs have been documented about physics operating on some of the smallest. in the Milky Way and nearby galaxies from observed X- ray binaries [18]. Some decades after their discovery it is Ultralight bosonic matter with weak couplings to the now also well understood most galaxies or active galactic standard matter content of the Universe are common fea- nuclei (AGN) [19] harbour a SMBH at their core. Phe- tures of many grand unified theories (GUTs) [38{40]. Common place in these theoretical frameworks are ex- arXiv:2009.07206v1 [hep-ph] 15 Sep 2020 nomenologically BHs themselves may provide interest- ing candidates to observational issues, such as primor- tended sectors of massive scalar (spin-0), vector (spin- dial BHs representing the total dominant non-baryonic 1) and tensor (spin-2) quantum fields, which prove chal- matter in the Universe [20{22]. lenging to probe experimentally due to their highly sup- Recent successful probes of BHs have also taken place pressed couplings. A archetypal example is the QCD in the new era of gravitational wave (GW) observational axion [41{43], a pseudoscalar boson proposed to provide astronomy, ushered in by their historic first direct detec- a dynamical field solution to the issue of CP violation in tion from the coalescence of a binary BH (BBH) system the Standard Model, via the Peccei-Quinn (PQ) mech- by the Laser Interferometer Gravitational-Wave Obser- anism [44, 45]. The mass of this field is light, of the QCD 12 6 10 GeV vatory (LIGO)/ VIRGO collaboration [24, 25]. This suc- order, µ0 5:71 10− eV ( =fa) [23], where fa ' × cess has continued with dozens of new observations [26], is the mass-scale where the anomalous global symmetry the field is charged under, is broken. String and M-theory compactification models often predict a plethoric land- scape (string axiverse [46{48]) of ultralight pseudoscalars ∗ [email protected] or axion-like particles (ALPs), the dynamical scales of 2 in non-linear extensions of massive gravity. Example so- lutions have been formulated [88, 89], such as bimetric 1.0 MPl QCD GUT FDM gravity theories [90{93]. These ghost-free theories allow for an understanding of massive spin-2 fields coupled to 10 18.0 0.8 − gravity (i.e. multi-vielbeins [82] or multi-metrics [94] ap- proaches), though the specifics are certainly non-trivial f to ensure no significant deviations from general relativity 0.6 a 10 17.5 − [GeV] [eV]) etc. Recent progress on the stability on particular fami- µ ( lies of bimetric gravity theories has opened up the poten- ex 0.4 tial of exploring the dynamics of massive spin-2 particles P 17.0 10− [88, 95{99] via unique non-linear solutions [89, 91, 100] Spin-0 0.2 coupling two tensors which interact via non-derivative Spin-1 Spin-2 terms. Under fixed conditions this scenario can be con- 16.5 10− sidered as traditional gravity theory with an extended 0.0 10 12 14 16 18 20 22 sector of spin-2 fields [101, 102]. It is also possible to 10− 10− 10− 10− 10− 10− 10− µ [eV] extend these investigations to theories of massive gravity in order to explore properties of the graviton [95, 103]. Figure 1. Total probability of exclusion functions for mas- If we are to seriously consider the low energy effec- sive ultralight bosonic fields of spin-0 (solid line), spin-1 (dot- tive limits of extensions to the Standard Model such as ted line) and spin-2 (dashed line) from the collective BH string theoretic frameworks, then it is natural to ask data ensemble in Appendix A ,using the measurements in what constraints can we place on these extended sectors shaded grey Table IV, Table V and Table VI. The region of ulralight bosonic fields. Fortunately a novel solution represents expected mass limits of FDM (10−(21−22) eV)(see Section III C 3). The coloured shaded region represents the to this problem has been highlighted recently, stemming from the spacetime dynamics of rotating astrophysical bounds on the QCD axion in the limit fa ≤ MPl, its mass/decay constant defined according to Ref. [23]. The dip BHs and the universal nature of the gravitational cou- in the exclusions function represents an absence of measure- plings ultralight bosons possess [95, 103{107]. A rotat- ments for IMBHs which for spin-0 bosons is associated to the ing astrophysical BH in a four-dimensional asymptoti- GUT axion mass window defined in Eq. (31). cally flat spacetime is described by the Kerr geometry [108], parameterised according to its mass, MBH and an- gular momentum, J = aMBH. The phenomena of su- these ubiquitous degrees of freedom potentially spanning perradiance from rotational bodies is a general feature many decades1. These fields may offer solutions to a which can occur with systems that present a dissipat- number of core issues in cosmology through their sym- ing surface with a non-vanishing angular moment com- metry properties [42, 52{54], such as cold dark matter ponent, leading to many fascinating outcomes [95, 109]. (DM) [55{57], quintessence/ dark energy (DE) [58{60], The presence of perturbations close to a rotating BH are solutions to the electroweak hierarchy problem [61] and amplified [110, 111] when enclosed in a suitable reflecting cosmic inflation [62{66] etc. cavity. This instability is known as the BH bomb scenario Extended sectors of spin-1 vector fields [67{69] or dark [112]. Assuming on-shell production of yet unseen bosons photons come from motivations for new abelian U(1) from quantum fluctuations of the vacuum, naturally a gauge bosons in a hidden sector, possessing highly sup- suitable confining mechanism is supplied from the mass pressed couplings to electrically charged particles induced of bosonic fields leading to such an instability. The so- through kinetic mixing with the photon. These often called no-hair and uniqueness theorems permit precision arise in numerous extensions of the standard model such cosmology of BHs, inturn allowing us to probe the ex- as supersymmetric theories [70] or general hidden portal istence of quasi-equilibrium configurations consisting of models [71].