Determining the Hubble Constant with AGN-assisted Black Hole Mergers Y. Yang,1 V. Gayathri,1 S. M´arka,2 Z. M´arka,2 and I. Bartos1, ∗ 1Department of Physics, University of Florida, PO Box 118440, Gainesville, FL 32611, USA 2Department of Physics, Columbia University in the City of New York, New York, NY 10027, USA Gravitational waves from neutron star mergers have long been considered a promising way to mea- sure the Hubble constant, H0, which describes the local expansion rate of the Universe. While black hole mergers are more abundantly observed, their expected lack of electromagnetic emission and poor gravitational-wave localization makes them less suited for measuring H0. Black hole mergers within the disks of Active Galactic Nuclei (AGN) could be an exception. Accretion from the AGN disk may produce an electromagnetic signal, pointing observers to the host galaxy. Alternatively, the low number density of AGNs could help identify the host galaxy of 1 − 5% of mergers. Here we show that black hole mergers in AGN disks may be the most sensitive way to determine H0 with gravitational waves. If 1% of LIGO/Virgo's observations occur in AGN disks with identified host galaxies, we could measure H0 with 1% uncertainty within five years, likely beyond the sensitivity of neutrons star mergers. I. INTRODUCTION Multi-messenger gravitational-wave observations rep- resent a valuable, independent probe of the expansion of the Universe [1]. The Hubble constant, which de- scribes the rate of expansion, can measured using Type Ia supernovae, giving a local expansion rate of H0 = 74:03 ± 1:42 km s−1 Mpc−1 [2]. It can also be measured through cosmic microwave background observations fo- cusing on the early Universe, which gives a conflicting −1 −1 H0 = 67:4 ± 0:5 km s Mpc [3]. These results differ at about 3σ level, which may be the signature of new FIG. 1. Illustration of black hole mergers in AGN physics beyond our current understanding of cosmology. disks. A binary black hole system migrates into the accre- tion disk around the central supermassive black hole. It then Gravitational waves from a binary merger carry infor- rapidly merges due to dynamical friction within the disk. Fol- mation about the luminosity distance of the source. To lowing the merger the remnant black hole produces an optical determine H0 one also needs to measure redshift, which signal due to accretion from the disk. is not directly accessible from the source but can be mea- sured from the spectrum of the merger's host galaxy. The identification of the host galaxy typically requires Black hole mergers are detected by LIGO/Virgo at a the detection of electromagnetic emission given the lim- rate more than an order of magnitude higher than neu- ited localization available through gravitational waves. trons star mergers [13, 14]. In addition, they are typically Neutrons star mergers are natural targets for such mea- detected at much greater distances, therefore they are surements due to the broad range of electromagnetic less affected by the proper motion of galaxies. Nonethe- emission they produce [4,5]. The first neutron star less, black hole mergers are mostly not expected to pro- merger discovered by LIGO [6] and Virgo [7], GW170817, duce electromagnetic counterparts, limiting their utility was also observed across the electromagnetic spectrum, (although see [15{17]). and was used to constrain H [8{10]. 0 Active galactic nuclei (AGN) represent a unique envi- Not all neutron star mergers detected by LIGO/Virgo ronment that facilitates the merger of black holes and can arXiv:2009.13739v1 [astro-ph.HE] 29 Sep 2020 will have identified electromagnetic counterparts [11, 12]. potentially also lead to electromagnetic emission from Especially more distant events will be difficult to observe them [18{20]. Galactic centers harbor a dense popula- electromagnetically due to their weaker flux and poorer tion of thousands of stellar mass black holes that mi- gravitational-wave localization. In addition, as neutron grated there through mass segregation [21, 22]. These star mergers are relatively nearby, the redshift of their black holes interact with the accretion disk of the cen- host galaxies will be affected by significant proper mo- tral supermassive black hole, driving their orbit to align tion, introducing a systematic uncertainty in H mea- 0 with the disk plane. The disk hence becomes an ultra- surements. dense 2D collection of black holes. The black holes then migrate within the disk. Once two of them get close and form a binary, they rapidly merge due to dynamical friction within the gas or binary single encounters with ∗ imrebartos@ufl.edu other nearby objects. The gas-rich environment of these 2 mergers enables the black holes to accrete and produce event can be determined. The true distance of the event electromagnetic radiation. is linked to its redshift by: Recently, such a candidate electromagnetic counter- Z z 0 part has been observed by the Zwicky Transient Facil- c(1 + z) dz dL = 0 (2) ity (ZTF), in coincidence with the black hole merger H0 0 E(z ) GW190521 [23, 24]. In addition, the mass and spin of GW190521 suggest an AGN origin [25{28]. While with this is the clearest case, some of the other black hole p 4 3 2 E(z) = Ωr(1 + z) + Ωm(1 + z) + Ωk(1 + z) + ΩΛ : mergers recorded by LIGO/Virgo may have also orig- (3) inated in AGN disks, including GW170729 [13, 29], Here, Ω is the radiation energy density, Ω is mat- GW170817A [30, 31], GW151205 [25, 32] or possibly r m ter density, ΩΛ is the dark energy density and Ωk GW190814 [28, 33]. LIGO/Virgo's heaviest black holes is the curvature of our Universe. We adopted a set are particularly promising [34, 35]. of cosmology parameters of fH0; Ωr; Ωm; Ωk; ΩΛg = Even for those mergers where no electromagnetic coun- f67:8km s−1 Mpc−1; 0; 0:306; 0; 0:694g. Since black terpart is observed, the rarity of AGNs can help the iden- holes are typically found at Gpc distances, we neglected tification of their host galaxies. Counting even the less the peculiar velocity of the host galaxy. active Seyfert galaxies, the AGN number density in the The measured luminosity distance d can also be −3 L local universe is nSeyfert ≈ 0:02 Mpc [36]. Considering linked to the redshift z similarly to Eq.2 above but the contribution of only the more active galactic nuclei, by replacing H with the measured Hubble constant H^ . −5 −3 0 0 their density is only nAGN ≈ 2 × 10 Mpc [37, 38]. ^ Therefore, we find H^0=H0 = dL=dL. Given these number densities, 1−5% of black hole merg- For this we assumed that the other cosmological pa- ers detected in the future by LIGO/Virgo could be suffi- rameters are fixed at the values obtained by Planck 2018 ciently well localized such that only a single AGN resides [3]. in their localization volume [14]. If we detect multiple AGN-assisted black hole merg- ers and identify their host galaxies either through their electromagnetic counterpart or through accu- II. MONTE CARLO SIMULATION OF rate gravitational-wave localization, we will obtain MERGERS a set of measurement of the Hubble constant, fH^0;1; H^0;2; :::; H^0;Ng. We adopted the arithmetic mean We obtained a sample of reconstructed distances for of our simulated values as our overall estimate H0 of AGN-assisted black hole mergers using a Monte Carlo the Hubble constant. The distribution of H^0 is asymp- simulation of 25,000 binaries. We randomly drew binary totically normal and its standard deviation is σ(H^0) / parameters, including the masses and spins of the black N −1=2. holes, from the AGN model of Yang et al. [28, 29]. We placed these binaries at random distances from Earth assuming uniform density in comoving volume, similar III. DETECTION RATE OF MERGERS WITH to our expectation for AGN-assisted mergers [27]. We HOST GALAXIES then selected a random inclination angle for the binary. We reconstructed the distance of each merger us- With the improving sensitivity of LIGO/Virgo, and ing simulated gravitational-wave data through a Fisher- with the construction of KAGRA [40], and later the con- matrix technique. This Fisher matrix approach enables struction of LIGO-India [41], the rate of gravitational- the estimation of parameter errors. It is based on the wave discoveries will rapidly increase over the next few partial derivatives of an analytic gravitational-wave sig- years [14]. While currently uncertain, the fraction of nal model with respect to its parameters [39]. For each detected mergers that originate from AGNs could be merger, we obtained a log-normal luminosity distance 10 − 50% [26]. distribution It also uncertain what fraction of AGN-assisted merg- ers will have a detected electromagnetic counterpart. " # 1 (log d − log d^ )2 While there are theoretical predictions [18{20], the emis- p(d jd^ ; σ2 ) = exp − L L L L dL q 2 2 ^ 2σ sion process is not yet well understood. To estimate 2πσ dL dL dL this fraction, we considered the fact that one black hole (1) merger has a candidate electromagnetic counterpart so where dL is the true luminosity distance of this event, far, detected by ZTF [23]. If this candidate is a real coun- ^ while dL and σdL are the reconstructed luminosity dis- terpart of an AGN-assisted merger, and assuming that tance and its uncertainty, respectively. no other one will be found by ongoing archival searches, If the merger occurs within the AGN disk, it could pro- then the expected fraction of LIGO/Virgo's detections duce a detectable electromagnetic counterpart associated that has an electromagnetic counterpart is about 2%.