Determining the Hubble Constant with Black Hole Mergers in Active Galactic Nuclei

Determining the Hubble Constant with AGN-assisted Black Hole Mergers

Y. Yang,1 V. Gayathri,1 S. Márka,2 Z. Márka,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 measure 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 represent a valuable, independent probe of the expansion of the Universe [1]. The Hubble constant, which describes 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 accretion 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 measured 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 {H0, Ωr, Ωm, Ωk, ΩΛ} = Even for those mergers where no electromagnetic coun- {67.8km s−1 Mpc−1, 0, 0.306, 0, 0.694}. 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 Hˆ . −5 −3 0 0 their density is only nAGN ≈ 2 × 10 Mpc [37, 38]. ˆ Therefore, we find Hˆ0/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 mergers 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, {Hˆ0,1, Hˆ0,2, ..., Hˆ0,N}. 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 Hˆ0 is asymp- simulation of 25,000 binaries. We randomly drew binary totically normal and its standard deviation is σ(Hˆ0) ∝ 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 mergers will have a detected electromagnetic counterpart. " # 1 (log d − log dˆ )2 While there are theoretical predictions [18–20], the emis- p(d |dˆ , σ2 ) = exp − L L L L dL q 2 2 ˆ 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- ˆ 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%. with this event. Such a counterpart can help us identify We conservatively estimate this number by considering the host galaxy of the merger and thus the redshift of the all LIGO/Virgo’s public alerts as detections. 3

will be able to measure the Hubble constant. Our results AGN 1% BNS 10% are shown in Fig.2 (top). We see that within 5 years we AGN 10% BNS 100%

] expect to reach an uncertainty of σH0 /H0 ≈ 1% and 0.5%

% 1 [ 10 for our 1% and 10% models, respectively. This precision

0 is suﬃcient to help resolve (or deepen) the discrepancy H /

0 between H0 measurements using Type Ia supernovae and H 0 the cosmic microwave background. 10 no observation For comparison, we also estimated σH0 /H0 expected for neutron star mergers. We carried out this calculation similarly to that above for black hole mergers, with 102 the appropriate merger rate and detector sensitivity. We neglected the eﬀect of galaxy peculiar velocities that are N 101 important in the case of neutron star mergers, making our neutron-star-merger estimate optimistic. 100 We took into account that not all neutron star mergers 2020 2022 2023 2025 2026 will have an electromagnetic counterpart. For currently published detections by LIGO/Virgo this fraction is 50%, but it is likely to drop further as more distant events are FIG. 2. Projected relative uncertainty of Hubble con- found by more sensitive gravitational-wave detectors. We stant measurements. Top: Relative uncertainties assuming that 1% (black) or 10% (red) of black hole mergers dis- therefore considered a realistic electromagnetic detection covered by LIGO/Virgo are AGN-assisted with identiﬁed host fraction of 10%, as well as the optimistic case of 100%. galaxies. For comparison we show relative uncertainties for Our results for neutron star mergers are shown in Fig. neutron star mergers assuming that all (blue) or only 10% 2. We see that if all neutron star mergers have a detected

(green) of them discovered by LIGO/Virgo have identified electromagnetic counterpart, then the obtained σH0 /H0 host galaxies. The squares in 2020 show uncertainties derived is similar to that for our AGN model with 1% host galaxy for GW190521 [42–45] and neutron star merger GW170817 fraction. For comparison, a similar calculation was car- [10, 46]. Bottom: Expected number of detections for the ried out for neutron star mergers by Chen et al. [47] same categories as above. whose results are similar to ours assuming 100% electromagnetic detection fraction. If only 10% of neutron star mergers have an identi- In addition, we may be able to identify the host galaxy fied host galaxy, or if 10% of AGN-assisted mergers have of some of the AGN-assisted black hole mergers due to identified host galaxies then we find that the precision of their accurate gravitational wave localization. As dis- AGN-assisted black hole mergers is potentially as much cussed above, this could represent 1 − 5% of the AGN- as an order of magnitude better. assisted mergers, or . 2% of all black hole mergers de- More research is needed to better understand possi- tected by LIGO/Virgo. ble multi-messenger emission mechanisms in black hole Based on the above estimates, we considered two obser- mergers in AGN disks. Equally importantly, future black vation scenarios, in which 1% and 10% of LIGO/Virgo’s hole merger discoveries by LIGO/Virgo/KAGRA will black hole detections are both AGN-assisted and have need to be followed up by electromagnetic observatories, identified host galaxies. For both scenarios, we com- an effort that will need significant prioritization given puted the anticipated detection rate based on expected shear rate of such detections. LIGO/Virgo/KAGRA sensitivities for the next five years [14]. Our results are shown in Fig.2 (bottom). We see that by the end of this period we expect about Ngal = 20 ACKNOWLEDGMENTS and Ngal = 200 detections for the 1% and 10% scenarios, respectively. The authors thank Karan Jani, Jon Gair and Hsin-Yu Chen for useful suggestions. IB acknowledges support from the Alfred P. Sloan Foundation and the University of Florida. This research has made use of data, software IV. MEASURING THE HUBBLE CONSTANT and/or web tools obtained from the Gravitational Wave Open Science Center (https://www.gw-openscience.org), Using the expected Ngal shown in Fig.2 (bottom), we a service of LIGO Laboratory, the LIGO Scientific Col- computed the expected uncertainty σH0 with which we laboration and the Virgo Collaboration.

[1] B. F. Schutz, Nature (London) 323, 310 (1986). [2] A. G. Riess, S. Casertano, W. Yuan, et al., Astrophys. J. 4

876, 85 (2019), arXiv:1903.07603 [astro-ph.CO]. [26] Y. Yang, I. Bartos, Z. Haiman, et al., Astrophys. J. 876, [3] N. Aghanim, Y. Akrami, M. Ashdown, et al., 122 (2019), arXiv:1903.01405 [astro-ph.HE]. arXiv:1807.06209 (2018). [27] Y. Yang, I. Bartos, Z. Haiman, et al., Astrophys. J. 896, [4] I. Bartos, P. Brady, and S. Mrka, Classical and Quantum 138 (2020). Gravity 30, 123001 (2013). [28] Y. Yang, V. Gayathri, I. Bartos, et al., arXiv:2007.04781 [5] B. D. Metzger and E. Berger, Astrophys. J. 746, 48 (2020). (2012), arXiv:1108.6056 [astro-ph.HE]. [29] Y. Yang, I. Bartos, V. Gayathri, et al., Phys. Rev. Lett. [6] J. Aasi et al., Class. Quantum Grav. 32, 074001 (2015). 123, 10.1103/physrevlett.123.181101 (2019). [7] F. Acernese et al., Class. Quantum Grav. 32, 024001 [30] B. Zackay, L. Dai, T. Venumadhav, et al., arXiv (2015). e-prints , arXiv:1910.09528 (2019), arXiv:1910.09528 [8] B. P. Abbott et al., Nature 551, 85 (2017). [astro-ph.HE]. [9] C. Guidorzi, R. Margutti, D. Brout, et al., Astrophys. J. [31] V. Gayathri, I. Bartos, Z. Haiman, et al., Astrophys. J. Lett. 851, L36 (2017), arXiv:1710.06426 [astro-ph.CO]. 890, L20 (2020). [10] K. Hotokezaka, E. Nakar, O. Gottlieb, et al., Nature As- [32] A. H. Nitz, T. Dent, G. S. Davies, et al., Astrophys. J. tronomy 3, 940 (2019), arXiv:1806.10596 [astro-ph.CO]. 891, 123 (2020), arXiv:1910.05331 [astro-ph.HE]. [11] G. Hosseinzadeh, P. S. Cowperthwaite, S. Gomez, et al., [33] R. Abbott, T. D. Abbott, S. Abraham, et al., Astrophys. Astrophys. J. 880, L4 (2019). J. 896, L44 (2020). [12] S. Anand, M. W. Coughlin, and M. M. o. Kasliwal, [34] B. P. Abbott, R. Abbott, T. D. Abbott, et al., Phys. Rev. Nature Astronomy 10.1038/s41550-020-1183-3 (2020), D 100, 064064 (2019). arXiv:2009.07210 [astro-ph.HE]. [35] B. P. Abbott, R. Abbott, T. D. Abbott, et al., Phys. Rev. [13] B. P. Abbott et al., Phys. Rev. X 9, 031040 (2019). D 96, 022001 (2017), arXiv:1704.04628 [gr-qc]. [14] B. P. Abbott et al., Living Rev. Relativ. 21, 3 (2018). [36] L. Hao, M. A. Strauss, X. Fan, et al., Astron. J 129, 1795 [15] W. Del Pozzo, Physical Review D 86, 10.1103/phys- (2005), arXiv:astro-ph/0501042 [astro-ph]. revd.86.043011 (2012). [37] J. E. Greene and L. C. Ho, Astrophys. J. 667, 131 (2007). [16] M. Soares-Santos, A. Palmese, W. Hartley, et al., Astro- [38] J. E. Greene and L. C. Ho, Astrophys. J. 704, 1743 phys. J. Lett. 876, L7 (2019), arXiv:1901.01540 [astro- (2009). ph.CO]. [39] C. Cutler and E. E. Flanagan, Phys. Rev. D 49, 2658 [17] S. Mukherjee, B. D. Wandelt, S. M. Nissanke, and (1994), arXiv:gr-qc/9402014. A. Silvestri, arXiv e-prints , arXiv:2007.02943 (2020), [40] Y. Aso, Y. Michimura, K. Somiya, et al. (The KAGRA arXiv:2007.02943 [astro-ph.CO]. Collaboration), Phys. Rev. D 88, 043007 (2013). [18] I. Bartos, B. Kocsis, Z. Haiman, and S. M´arka, Astro- [41] B. Iyer, T. Souradeep, C. S. Unnikrishnan, et al., LIGO- phys. J. 835, 165 (2017). M1100296 (2011). [19] N. C. Stone, B. D. Metzger, and Z. Haiman, Mon. Notices [42] V. Gayathri, J. Healy, J. Lange, et al., arXiv e-prints Royal Astron. Soc 464, 946 (2017). , arXiv:2009.05461 (2020), arXiv:2009.05461 [astro- [20] B. McKernan, K. E. S. Ford, I. Bartos, et al., Astrophys. ph.HE]. J. 884, L50 (2019). [43] V. Gayathri, J. Healy, J. Lange, B. O’Brien, M. Szczep- [21] R. M. O’Leary, B. Kocsis, and A. Loeb, Mon. Notices anczyk, I. Bartos, M. Campanelli, S. Klimenko, Royal Astron. Soc 395, 2127 (2009). C. Lousto, and R. O’Shaughnessy, in preparation (2020). [22] C. J. Hailey, K. Mori, F. E. Bauer, M. E. Berkowitz, [44] Mukherjee S. and Ghosh A. and Graham M.J. and others, J. Hong, and B. J. Hord, Nature (London) 556, 70 in preparation (2020). (2018). [45] Chen H.Y. and Haster C.J. and Vitale S. and others, in [23] M. Graham, K. Ford, B. McKernan, et al., Phys. Rev. preparation (2020). Lett. 124, 10.1103/physrevlett.124.251102 (2020). [46] B. P. Abbott, R. Abbott, T. D. Abbott, et al., Astrophys. [24] R. Abbott, T. D. Abbott, S. Abraham, et al. (LIGO J. 848, L12 (2017). Scientiﬁc Collaboration and Virgo Collaboration), Phys. [47] H.-Y. Chen, M. Fishbach, and D. E. Holz, Nature (Lon- Rev. Lett. 125, 101102 (2020). don) 562, 545 (2018), arXiv:1712.06531 [astro-ph.CO]. [25] R. Abbott et al., Astrophys. J. Lett. 900, L13 (2020).