Determining the Hubble Constant with Black Hole Mergers in Active Galactic Nuclei
DDetermining the Hubble Constant with AGN-assisted Black Hole Mergers
Y. Yang, V. Gayathri, S. M´arka, Z. M´arka, and I. Bartos ∗ Department of Physics, University of Florida, PO Box 118440, Gainesville, FL 32611, USA Department 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, H , which describes the local expansion rate of the Universe. While blackhole mergers are more abundantly observed, their expected lack of electromagnetic emission andpoor gravitational-wave localization makes them less suited for measuring H . Black hole mergerswithin the disks of Active Galactic Nuclei (AGN) could be an exception. Accretion from the AGNdisk 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 weshow that black hole mergers in AGN disks may be the most sensitive way to determine H withgravitational waves. If 1% of LIGO/Virgo’s observations occur in AGN disks with identified hostgalaxies, we could measure H with 1% uncertainty within five years, likely beyond the sensitivityof neutrons star mergers. I. INTRODUCTION
Multi-messenger gravitational-wave observations rep-resent a valuable, independent probe of the expansionof the Universe [1]. The Hubble constant, which de-scribes the rate of expansion, can measured using TypeIa supernovae, giving a local expansion rate of H =74 . ± .
42 km s − Mpc − [2]. It can also be measuredthrough cosmic microwave background observations fo-cusing on the early Universe, which gives a conflicting H = 67 . ± . − Mpc − [3]. These results differat about 3 σ level, which may be the signature of newphysics beyond our current understanding of cosmology.Gravitational waves from a binary merger carry infor-mation about the luminosity distance of the source. Todetermine H one also needs to measure redshift, whichis 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 requiresthe detection of electromagnetic emission given the lim-ited localization available through gravitational waves.Neutrons star mergers are natural targets for such mea-surements due to the broad range of electromagneticemission they produce [4, 5]. The first neutron starmerger discovered by LIGO [6] and Virgo [7], GW170817,was also observed across the electromagnetic spectrum,and was used to constrain H [8–10].Not all neutron star mergers detected by LIGO/Virgowill have identified electromagnetic counterparts [11, 12].Especially more distant events will be difficult to observeelectromagnetically due to their weaker flux and poorergravitational-wave localization. In addition, as neutronstar mergers are relatively nearby, the redshift of theirhost galaxies will be affected by significant proper mo-tion, introducing a systematic uncertainty in H mea-surements. ∗ imrebartos@ufl.edu FIG. 1.
Illustration of black hole mergers in AGNdisks . A binary black hole system migrates into the accre-tion disk around the central supermassive black hole. It thenrapidly merges due to dynamical friction within the disk. Fol-lowing the merger the remnant black hole produces an opticalsignal due to accretion from the disk.
Black hole mergers are detected by LIGO/Virgo at arate more than an order of magnitude higher than neu-trons star mergers [13, 14]. In addition, they are typicallydetected at much greater distances, therefore they areless affected by the proper motion of galaxies. Nonethe-less, black hole mergers are mostly not expected to pro-duce electromagnetic counterparts, limiting their utility(although see [15–17]).Active galactic nuclei (AGN) represent a unique envi-ronment that facilitates the merger of black holes and canpotentially also lead to electromagnetic emission fromthem [18–20]. Galactic centers harbor a dense popula-tion of thousands of stellar mass black holes that mi-grated there through mass segregation [21, 22]. Theseblack holes interact with the accretion disk of the cen-tral supermassive black hole, driving their orbit to alignwith the disk plane. The disk hence becomes an ultra-dense 2D collection of black holes. The black holes thenmigrate within the disk. Once two of them get closeand form a binary, they rapidly merge due to dynamicalfriction within the gas or binary single encounters withother nearby objects. The gas-rich environment of these a r X i v : . [ a s t r o - ph . H E ] S e p mergers enables the black holes to accrete and produceelectromagnetic radiation.Recently, such a candidate electromagnetic counter-part has been observed by the Zwicky Transient Facil-ity (ZTF), in coincidence with the black hole mergerGW190521 [23, 24]. In addition, the mass and spinof GW190521 suggest an AGN origin [25–28]. Whilethis is the clearest case, some of the other black holemergers recorded by LIGO/Virgo may have also orig-inated in AGN disks, including GW170729 [13, 29],GW170817A [30, 31], GW151205 [25, 32] or possiblyGW190814 [28, 33]. LIGO/Virgo’s heaviest black holesare particularly promising [34, 35].Even for those mergers where no electromagnetic coun-terpart is observed, the rarity of AGNs can help the iden-tification of their host galaxies. Counting even the lessactive Seyfert galaxies, the AGN number density in thelocal universe is n Seyfert ≈ .
02 Mpc − [36]. Consideringthe contribution of only the more active galactic nuclei,their density is only n AGN ≈ × − Mpc − [37, 38].Given these number densities, 1 −
5% of black hole merg-ers detected in the future by LIGO/Virgo could be suffi-ciently well localized such that only a single AGN residesin their localization volume [14].
II. MONTE CARLO SIMULATION OFMERGERS
We obtained a sample of reconstructed distances forAGN-assisted black hole mergers using a Monte Carlosimulation of 25,000 binaries. We randomly drew binaryparameters, including the masses and spins of the blackholes, from the AGN model of Yang et al. [28, 29]. Weplaced these binaries at random distances from Earthassuming uniform density in comoving volume, similarto our expectation for AGN-assisted mergers [27]. Wethen selected a random inclination angle for the binary.We reconstructed the distance of each merger us-ing simulated gravitational-wave data through a Fisher-matrix technique. This Fisher matrix approach enablesthe estimation of parameter errors. It is based on thepartial derivatives of an analytic gravitational-wave sig-nal model with respect to its parameters [39]. For eachmerger, we obtained a log-normal luminosity distancedistribution p ( d L | ˆ d L , σ d L ) = 1 (cid:113) πσ d L ˆ d L exp (cid:34) − (log d L − log ˆ d L ) σ d L (cid:35) (1)where d L is the true luminosity distance of this event,while ˆ d L and σ d L are the reconstructed luminosity dis-tance and its uncertainty, respectively.If the merger occurs within the AGN disk, it could pro-duce a detectable electromagnetic counterpart associatedwith this event. Such a counterpart can help us identifythe host galaxy of the merger and thus the redshift of the event can be determined. The true distance of the eventis linked to its redshift by: d L = c (1 + z ) H (cid:90) z dz (cid:48) E ( z (cid:48) ) (2)with E ( z ) = (cid:112) Ω r (1 + z ) + Ω m (1 + z ) + Ω k (1 + z ) + Ω Λ . (3)Here, Ω r is the radiation energy density, Ω m is mat-ter density, Ω Λ is the dark energy density and Ω k is the curvature of our Universe. We adopted a setof cosmology parameters of { H , Ω r , Ω m , Ω k , Ω Λ } = { . − Mpc − , , . , , . } . Since blackholes are typically found at Gpc distances, we neglectedthe peculiar velocity of the host galaxy.The measured luminosity distance d L can also belinked to the redshift z similarly to Eq. 2 above butby replacing H with the measured Hubble constant ˆ H .Therefore, we find ˆ H /H = d L / ˆ d L .For this we assumed that the other cosmological pa-rameters are fixed at the values obtained by Planck 2018[3].If we detect multiple AGN-assisted black hole merg-ers and identify their host galaxies either throughtheir electromagnetic counterpart or through accu-rate gravitational-wave localization, we will obtaina set of measurement of the Hubble constant, { ˆ H , , ˆ H , , ..., ˆ H , N } . We adopted the arithmetic meanof our simulated values as our overall estimate H ofthe Hubble constant. The distribution of ˆ H is asymp-totically normal and its standard deviation is σ ( ˆ H ) ∝ N − / . III. DETECTION RATE OF MERGERS WITHHOST GALAXIES
With the improving sensitivity of LIGO/Virgo, andwith the construction of KAGRA [40], and later the con-struction of LIGO-India [41], the rate of gravitational-wave discoveries will rapidly increase over the next fewyears [14]. While currently uncertain, the fraction ofdetected mergers that originate from AGNs could be10 −
50% [26].It also uncertain what fraction of AGN-assisted merg-ers will have a detected electromagnetic counterpart.While there are theoretical predictions [18–20], the emis-sion process is not yet well understood. To estimatethis fraction, we considered the fact that one black holemerger has a candidate electromagnetic counterpart sofar, detected by ZTF [23]. If this candidate is a real coun-terpart of an AGN-assisted merger, and assuming thatno other one will be found by ongoing archival searches,then the expected fraction of LIGO/Virgo’s detectionsthat has an electromagnetic counterpart is about 2%.We conservatively estimate this number by consideringall LIGO/Virgo’s public alerts as detections. H / H [ % ] n o o b s e r v a t i o n AGN 1%AGN 10% BNS 10%BNS 100% N FIG. 2.
Projected relative uncertainty of Hubble con-stant measurements. Top:
Relative uncertainties assum-ing that 1% (black) or 10% (red) of black hole mergers dis-covered by LIGO/Virgo are AGN-assisted with identified hostgalaxies. For comparison we show relative uncertainties forneutron star mergers assuming that all (blue) or only 10%(green) of them discovered by LIGO/Virgo have identifiedhost galaxies. The squares in 2020 show uncertainties derivedfor GW190521 [42–45] and neutron star merger GW170817[10, 46].
Bottom:
Expected number of detections for thesame categories as above.
In addition, we may be able to identify the host galaxyof some of the AGN-assisted black hole mergers due totheir accurate gravitational wave localization. As dis-cussed above, this could represent 1 −
5% of the AGN-assisted mergers, or (cid:46)
2% of all black hole mergers de-tected by LIGO/Virgo.Based on the above estimates, we considered two obser-vation scenarios, in which 1% and 10% of LIGO/Virgo’sblack hole detections are both AGN-assisted and haveidentified host galaxies. For both scenarios, we com-puted the anticipated detection rate based on expectedLIGO/Virgo/KAGRA sensitivities for the next five years[14]. Our results are shown in Fig. 2 (bottom). We seethat by the end of this period we expect about N gal = 20and N gal = 200 detections for the 1% and 10% scenarios,respectively. IV. MEASURING THE HUBBLE CONSTANT
Using the expected N gal shown in Fig. 2 (bottom), wecomputed the expected uncertainty σ H with which we will be able to measure the Hubble constant. Our resultsare shown in Fig. 2 (top). We see that within 5 years weexpect to reach an uncertainty of σ H /H ≈
1% and 0.5%for our 1% and 10% models, respectively. This precisionis sufficient to help resolve (or deepen) the discrepancybetween H measurements using Type Ia supernovae andthe cosmic microwave background.For comparison, we also estimated σ H /H expectedfor neutron star mergers. We carried out this calcula-tion similarly to that above for black hole mergers, withthe appropriate merger rate and detector sensitivity. Weneglected the effect of galaxy peculiar velocities that areimportant in the case of neutron star mergers, makingour neutron-star-merger estimate optimistic.We took into account that not all neutron star mergerswill have an electromagnetic counterpart. For currentlypublished detections by LIGO/Virgo this fraction is 50%,but it is likely to drop further as more distant events arefound by more sensitive gravitational-wave detectors. Wetherefore considered a realistic electromagnetic detectionfraction of 10%, as well as the optimistic case of 100%.Our results for neutron star mergers are shown in Fig.2. We see that if all neutron star mergers have a detectedelectromagnetic counterpart, then the obtained σ H /H is similar to that for our AGN model with 1% host galaxyfraction. For comparison, a similar calculation was car-ried out for neutron star mergers by Chen et al. [47]whose results are similar to ours assuming 100% electro-magnetic detection fraction.If only 10% of neutron star mergers have an identi-fied host galaxy, or if 10% of AGN-assisted mergers haveidentified host galaxies then we find that the precision ofAGN-assisted black hole mergers is potentially as muchas an order of magnitude better.More research is needed to better understand possi-ble multi-messenger emission mechanisms in black holemergers in AGN disks. 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