Evolution of Retrograde Orbiters in an AGN Disk
Amy Secunda, Betsy Hernandez, Jeremy Goodman, Nathan W. C. Leigh, Barry McKernan, K.E. Saavik Ford, Jose I. Adorno
DDraft version September 10, 2020
Typeset using L A TEX twocolumn style in AASTeX63
Evolution of Retrograde Orbiters in an AGN Disk
Amy Secunda,
1, 2
Betsy Hernandez,
1, 2
Jeremy Goodman, Nathan W. C. Leigh,
3, 1
Barry McKernan,
1, 4, 5
K.E. Saavik Ford,
1, 4, 5 and Jose I. Adorno
1, 6 Department of Astrophysics, American Museum of Natural History, Central Park West at 79th Street, New York, NY 10024, USA Department of Astrophysical Sciences, Princeton University, Peyton Hall, Princeton, NJ 08544, USA Departamento de Astronom´ıa, Facultad de Ciencias F´ısicas y Matem´aticas, Universidad de Concepci´on, Concepci´on, Chile Department of Science, Borough of Manhattan Community College, City University of New York, New York, NY 10007 Physics Program, The Graduate Center, CUNY, New York, NY 10016 Department of Physics, Queens College, City University of New York, Queens, NY, 11367, USA (Received June 1, 2019; Revised January 10, 2019; Accepted September 10, 2020)
Submitted to ApJLABSTRACTAGN disks have been proposed as promising locations for the mergers of stellar mass black holebinaries (BBHs). Much recent work has been done on this merger channel, but the majority focuseson stellar mass black holes (BHs) orbiting in the prograde direction. Little work has been done toexamine the impact of retrograde orbiters (ROs) on the formation and mergers of BBHs in AGNdisks. Quantifying the retrograde contribution is important, since roughly half of all orbiters shouldinitially be on retrograde orbits when the disk forms. We perform an analytic calculation of theevolution of ROs in an AGN disk. Because this evolution could cause the orbits of ROs to cross thoseof prograde BBHs, we derive the collision rate between a given RO and a given BBH orbiting in theprograde direction. ROs experience a rapid decrease in the semi-major axis of their orbits while alsobecoming highly eccentric in less than a million years. This rapid orbital evolution leads to very lowcollision rates between retrograde BHs and prograde BBHs, meaning that ROs are unlikely to breakapart or ionize existing BBHs in AGN disks. The rapid orbital evolution of ROs could instead leadto extreme mass ratio inspirals and gravitationally lensed BBH inspirals. Both could be detected bythe Laser Interferometer Space Antenna (LISA), and even disrupt the inner disk, which may produceelectromagnetic signatures.
Keywords: black holes INTRODUCTIONActive galactic nucleus (AGN) disks are promising lo-cations (McKernan et al. 2012, 2014; Bellovary et al.2016; Bartos et al. 2017; Stone et al. 2016; McKernanet al. 2018; Leigh et al. 2018; Secunda et al. 2019, 2020;Yang et al. 2019a,b; Tagawa et al. 2020; McKernan et al.2019; Gr¨obner et al. 2020; Ishibashi & Gr¨obner 2020;The LIGO Scientific Collaboration & the Virgo Collabo-ration 2020) for producing the stellar mass black hole bi-nary (BBH) mergers detected by the Advanced Laser In-
Corresponding author: Amy [email protected] terferometer Gravitational Wave Observatory (aLIGO)and Advanced Virgo (Acernese et al. 2014; Aasi et al.2015; Abbott et al. 2019). An AGN disk is a favor-able location for BBH mergers detectable by aLIGObecause the gas disks will act to decrease the inclina-tion of intersecting orbiters and harden existing BBHs(McKernan et al. 2014; Yang et al. 2019a). Additionally,stellar mass black holes (BHs) on prograde orbits willexchange energy and angular momentum with the gasdisk, causing migration in both the inward and outwardradial directions (Bellovary et al. 2016; Secunda et al.2019, 2020). In particular these orbiters will migratetowards regions of the disk where positive and negativetorques cancel out, known as migration traps. As theseprograde orbiters (POs) migrate towards the migration a r X i v : . [ a s t r o - ph . H E ] S e p Secunda et al. traps, they will encounter each other at small relativevelocities. Consequently, BBHs form that could mergeon timescales of 10 −
500 years (Baruteau et al. 2011;McKernan et al. 2012, 2018; Leigh et al. 2018; Baruteau& Lin 2010).Despite an abundance of recent publications on BHsin AGN disks, thus far studies have largely ignored theimpact of retrograde orbiters (ROs) in an AGN disk.We could expect that since bulges have little net rota-tion, perhaps nuclei lack net rotation as well. Conse-quently, roughly half of the initial BH population of anuclear star cluster should be on retrograde orbits whenthe gas disk forms. While MacLeod & Lin (2020) foundthat orbiters with high initial inclinations will flip fromprograde to retrograde orbits as they are ground downinto alignment with the disk, the population of orbitersinitially aligned with the disk or on slightly inclined or-bits should be roughly half retrograde. These ROs willbe impacted by the disk in a significantly different wayfrom POs due to their larger velocities relative to thegas disk. Additionally, ROs will encounter POs in thedisk with large relative velocities, meaning they are lesslikely to form BBHs with POs and more likely to ionizebinaries in the disk (Leigh et al. 2018). Therefore ROscould have a significant affect on the number of BBHsand mergers in AGN disks.We aim to calculate the evolution of BHs initially or-biting in the retrograde direction when the gas disk ap-pears, and predict whether these ROs interact with BHsand/or BBHs orbiting in the prograde direction. In § § §
4. Finally, in § ORBITAL EVOLUTIONFor a BH orbiting in an AGN disk in the retrogradedirection the relative velocity ( v rel = v − v disk ) betweenthe orbiter and the disk is highly supersonic, with Machnumber v rel /c s ∼ ( h/r ) − (cid:29)
1, where h/r is the diskaspect ratio. The gas drag force on a BH of mass m canbe approximated as dynamical friction (Binney 1987;Ostriker 1999), F drag = − π ln Λ( Gm ) ρv v rel , (1) where ρ is the local mass density of the disk, andΛ ∼ hv /Gm , where h is the scale height of the disk, m the mass of the RO, and G is the gravitational con-stant. We assume m is small enough that Λ (cid:29)
1. Theadditional contribution to the drag from Bondi-Hoyle-Lyttleton accretion onto the BH will be smaller by afactor of ∼ (ln Λ) − , and so we neglect it.The orbital energy of the BH is, E = − GM m a , (2)where M is the mass of the SMBH and a is the semi-major axis of the orbit. Neglecting accretion onto theBH, d ln adt = − d ln Edt , (3)and dEdt = F drag · v = − π ln Λ( Gm ) ρv v · v rel , (4)where v is the velocity of the RO. Defining the angularmomentum of the AGN disk as positive, the angularmomentum for a RO becomes L = − m (cid:112) GM a (1 − e ) , (5)where e is the eccentricity. The torque on the orbiter is dLdt = F drag · ˆ e φ r = − π ln Λ( Gm ) ρv ( rv φ − √ GM r ) , (6)where ˆ e φ is a unit vector in the azimuthal direction and r is the radial distance of the RO from the central SMBH.Using Equations 2 and 5, for small changes da , de in a and e we get dE = GM m a da, (7)and dL = m (cid:34)(cid:114) GMa (1 − e ) da − (cid:114) GM a − e de (cid:35) . (8)Using equation 7 to put equation 8 in terms of dE instead of da and substituting in the mean motion, n = − (cid:112) GM/a , gives the change in eccentricity interms of the change in energy and angular momentum, de dt = 2 aGM m (1 − e ) (cid:18) dEdt − n √ − e dLdt (cid:19) . (9)Using the fact that E = m ( v / − GM/r ), L = mrv φ = m (cid:112) GM a (1 − e ) and v disk = ˆ e φ (cid:112) GM/r , weobtain | v − v disk | = − GMa + 3
GMr + 2 GM (cid:112) a (1 − e ) r − / , (10) etrograde Orbiters in an AGN Disk v · ( v − v disk ) = − GMa + 2
GMr + GM (cid:112) a (1 − e ) r − / , (11)and rv φ − √ GM r = − (cid:112) GM a (1 − e ) − √ GM r, (12)which allows us to eliminate the velocities in equations4 and 6 in favor of r . r , as a function of the azimuthalangle φ , is r = a (1 − e )1 + e cos ( φ − φ p ) , (13)where φ p is the angle at pericenter. We set φ p = 0,because our disk is axisymmetric. By Kepler’s SecondLaw, the time interval dt corresponding to the angularinterval dφ are related by, dtP = r dφ πa √ − e , (14)where P is the orbital period. We can use Equation14 to write the average the change in energy, angularmomentum, and eccentricity over one orbital in termsof dφ .Apart from the velocities, dE/dt and dL/dt dependon r through the midplane density ρ ( r ) and Λ. In aSirko & Goodman (2003) AGN disk, we have ρ ( r ) ∝ r γ ,with γ = 3 / f ( a ) = 4 π ln Λ( Gm ) ρ ( a ) (cid:112) a/GM , (15)which has the same dimensions as dE/dt and ndL/dt .We can now write (cid:104) dEdt (cid:105) = − f ( a ) I E ( γ, e ) , (16) (cid:104) dLdt (cid:105) = − f ( a ) n I L ( γ, e ) , (17)and (cid:104) de dt (cid:105) = − f ( a ) 2 aGM m (1 − e )[ I E ( γ, e )+ 1 √ − e I L ( γ, e )] , (18)where I E and I L are the dimensionless integrals, I E ( γ, e ) = 12 π √ − e (cid:90) π ( − u + √ − e u / ) u − γ − dφ ( − u + 2 √ − e u / ) / (19) and I L ( γ, e ) = 12 π √ − e (cid:90) π ( −√ − e − u − / ) u − γ − dφ ( − u + 2 √ − e u / ) / , (20)where, u ( φ ) ≡ a/r = 1 + e cos φ − e . (21)We integrate these equations numerically to solve for theeccentricity and semi-major axis of a RO as a function oftime. We discuss the orbital evolution of ROs for threedifferent fiducial initial eccentricities in § COLLISION RATESIn this section we estimate the collision rate of a RO(body 1) and a prograde BBH (body 2). We assume thatthe apsidal precession rate due to both relativistic effectsand disk self-gravity is rapid compared to the interactionrate, such that the probability of finding an orbiter ina given area element rdrdφ is independent of azimuth, φ . Therefore, the collision probability is proportional tothe fraction ( dt/P ) i of the orbit of body i spent between r and r + dr , d P i dr dr = 2 P i dr | v r | = 2 P i dr (cid:113)
2[ ˆ E − ˆΦ( r ) − ˆ L / r ]= 1 πa i rdr (cid:112) ( r + ,i − r )( r − r − ,i ) , r ± ,i = a i (1 ± e i )(22)where ˆ E , ˆΦ, and ˆ L , are the total energy, potentialenergy, and angular momentum per unit mass. Thefactor of 2 occurs in the numerator because the or-bit crosses a given radius r twice per orbit, providedthat a (1 − e ) < r < a (1 + e ). The second line fol-lows from plugging in the relations P = 2 π (cid:112) a /GM ,ˆ E = − GM/ a , ˆΦ( r ) = − GM/r and ˆ L = GM a (1 − e ).Orbiters in an AGN disk will be excited onto slightlyinclined orbits by turbulent motions in the disk, but theinclination will also be damped by drag forces from thegas. Without a specific model for turbulence, we assumefor simplicity that the probability of finding an orbiterat height z to z + dz is gaussian,exp( − z / h ) (cid:112) πh dz , (23)with a scale height h BH estimated as follows.At ∼
500 R s in a Sirko & Goodman (2003) diskwith a 10 M (cid:12) SMBH, Σ ≈ × g cm − and h ≈ . × . The eddy turnover speed will be v edd (cid:39) α / c s , (24) Secunda et al. where α is the ShakuraSunyaev (Shakura & Sunyaev1973) viscosity parameter (10 − for a Sirko & Goodman(2003) disk) and c s is the isothermal sound speed at themidplane. The turnover time of eddies of size l edd is τ edd = (cid:18) v edd l edd (cid:19) − . (25)If we limit τ edd to τ edd (cid:46) Ω − , where Ω =( GM/r ) − / = c s /h is the orbital frequency, l edd /h (cid:46) v edd /c s = α / . Therefore the eddy mass is m edd (cid:39) α / ρh = 12 α / Σ h . (26)The eddy mass m edd at 500 R s in our AGN disk isroughly 3 × − M (cid:12) .Assuming equipartition of vertical kinetic energies, h BH (cid:39) h v edd c s (cid:18) m edd m bh (cid:19) / . (27)For a 10 M (cid:12) BH in our AGN disk h BH (cid:39) . × − h (cid:39) . × cm. For simplicity we assume that h BH isindependent of radius.Since the area of the annulus is 2 πrdr and the distri-bution over height is given by eq. (23), the probabilityper unit volume dV = rdrdφdz of finding the body neara given point ( r, φ, z ) is d P i dV = 12 π a i (2 πh ) / exp( − z / h ) (cid:112) ( r + ,i − r )( r − r − ,i ) . (28)We will assume e , the eccentricity of the BBH orbit-ing in the prograde direction, is ∼
0, because the diskacts to circularize POs (Tanaka & Ward 2004). Thisassumption gives d P dV ≈ exp( − z / h ) (cid:112) πh δ ( r − a )2 π a , if e (cid:28) τ − = (cid:90) dV d P dV d P dV v rel σ ( v rel ) . (30)The interaction cross section of the BBH and the RO is, σ ∼ πs f ln(1 /f ) . (31)Here s bin is the semi-major axis of the binary itself,which we take to be the mutual Hill radius of the twoBHs in the binary R mH = (cid:18) m i + m j M (cid:63) (cid:19) / (cid:18) r i + r j (cid:19) . (32) f is the Safronov number, a dimensionless “gravitationalfocusing” factor, f ≡ Gm s bin v , (33)where m is the total mass of the BBH and v =( v φ, − v φ, ) + ( v r, − v r, ) + ( v z, − v z, ) is the relativevelocity between the BBH and the RO. σ is taken in thelimit that f (cid:28)
1. Because v rel will be very large, theencounters will be fast and gravitational focusing willnot be important.Next, we assume that the z components of the veloc-ities, v z,i , are negligible and that e ∼
0. Since e ∼ r = a giving v rel = (cid:34) GM (cid:32) a − a + 2 a / (cid:113) a (1 − e ) (cid:33)(cid:35) / . (34)Substituting into eq. (30) gives, τ − = 1 (cid:112) πh × π a (cid:112) ( a (1 + e ) − a )( a − a (1 − e )) × v rel σ ( v rel ) , (35)with v rel given by eq. (34) and σ ( v rel ) by eq. (31). Thetwo terms in parentheses in the denominator of the sec-ond term define the limits where a collision is possiblegiven our assumptions, since both terms must be pos-itive. That is, it is not possible for a collision to takeplace if a is greater than the apocenter of the RO or lessthan the pericenter of the RO. We discuss the collisionrate for three different fiducial eccentricities in § RESULTSThe solid lines in Figure 1 show the evolution ofthe semi-major axis (top) and eccentricity (bottom) forROs orbiting a 10 M (cid:12) SMBH with initial eccentrici-ties e =0.1, 0.5, and 0.7, calculated through numericalintegration of Equations 7, 16, 17, and 18. All orbiterswere initiated with a = 500 R s and integrated over timeuntil they reached e = 0 . e see a dra-matic increase in their eccentricity and decrease in theirsemi-major axis within 10 years. All orbiters reach aneccentricity of 0.99 in under a Myr. ROs with greater e become highly eccentric on shorter timescales. Forexample, orbiters with e (cid:38) e = 0 .
999 within100 kyr.For the special case of a BH on a circular retrogradeorbit, v = − v disk , where v disk is the velocity of the disk( (cid:112) GM/r ), and the relative velocity between the orbiter etrograde Orbiters in an AGN Disk Figure 1.
The colored lines show the evolution of the semi-major axis (top panel) and eccentricity (bottom panel) of10 M (cid:12)
ROs with different initial eccentricities, calculated bynumerically integrating Equations 7, 16, 17 and 18 in §
2. Thedashed black lines show the evolution of these orbiters whenwe include GW circularization (Peters 1964) in our integra-tion. All orbiters begin with a semi-major axis of 500 R s and are evolved until they reach an eccentricity of 0.999 forthe integration that does not include GW circularization, ormerge with the SMBH for the integration that does. and the disk is v rel = 2 v disk . Equations 3 and 4 from § (cid:12) BH on this circular, retrograde orbitaround a 10 M (cid:12) SMBH in a Sirko & Goodman (2003)AGN disk. If the BH is initially at a radius of ∼ R s ,Λ ∼ (4 M/m )( h/r ) ∼ and ρ ∼ − g cm − , which Figure 2.
The collision rate as a function of time predictedby Equation 35 for a RO with three different initial eccen-tricities, and a BBH orbiting in the prograde direction withrespect to the disk on a ciruclar orbit. The integrated proba-bility of an interaction occurring before the RO reaches an ec-centricity of 0.999 is 5 . × − , 1 . × − , and 4 . × − for a RO with e = 0.1, 0.5, and 0.7, respectively. gives d ln adt ≈ . × yr (cid:18) a R s (cid:19) . (36)The dashed black lines in Figure 1 show the evolutionof ROs with the same initial conditions as the coloredlines, when accounting for gravitational wave (GW) cir-cularization (Peters 1964). We evolve e and a by therates in Peters (1964) at the values we find for e and a after evolving them with Equations 7, 16, 17 and18 from §
2. These rates are integrated over time un-til a = 0. GW circularization becomes more rapid asthe eccentricity of the orbiter increases, slowing the ec-centricity driving once a high eccentricity is reached.The maximum eccentricity reached is now 0.982, 0.997,and 0.998, and the eccentricity at the time of merger is0.932, 0.984, and 0.983 for ROs with e =0.1, 0.5, and0.7, respectively.Figure 2 shows the collision rate per orbit, τ − , asa function of time calculated with Equation 35 for thethree example e . The mass of the RO is 10 M (cid:12) and thetotal mass of the binary m = 20 M (cid:12) . For simplicity wetake the semi-major axis of the BBH, a , to be constantat 330 R s , i.e. the location of the migration trap in aSirko & Goodman (2003) AGN disk (Bellovary et al.2016). a and e evolve over time as calculated above,with GW circularization and a =500 R s , initially. If a is greater than the apocenter distance or less than thepericenter distance of the RO for a given orbit we take τ − = 0. Secunda et al.
We choose these initial parameters to resemble themost common conditions in Secunda et al. (2019) andSecunda et al. (2020), who find that BHs migrate to-wards the migration trap at ∼ R s in a Sirko &Goodman (2003) AGN disk, where they start formingBBHs on timescales similar to the orbital evolution ofROs ( ∼ − years) and remain for the lifetime ofthe disk. This over-dense population of BBHs is a primetarget for a RO to interact with. However, future workshould look at a wider range of BBH orbital parameters,AGN disk parameters, and actively migrating progradeBBHs to determine collision rates for a wider range ofinitial conditions (see e.g. McKernan et al. 2019; McK-ernan et al. 2020; Tagawa et al. 2020, on the prevalenceof BBH mergers away from a trap). Preliminary testsshow that changing the location of the BBH and havingBBHs migrate within the inner 500 R s does not have asignificant affect on τ − . τ − ∼ O (10 − ) yr − initially for ROs with e =0.5,0.7 and then increases to ∼ O (10 − ) yr − as GWcircularization becomes important. At first, τ − = 0 forthe RO with e =0.1, since its orbit will not cross the or-bit of the BBH until its semi-major axis has decreasedand its eccentricity has increased. Once the orbits docross τ − starts out relatively high, around O (10 − ).Then, while the eccentricity is still low, τ − decreasesas the semi-major axis decreases reaching a minimum ofaround 6 × − . Next, as the eccentricity increases,the decrease in semi-major axis causes τ − to increaseto ∼ − yr − . Finally, the semi-major axis becomestoo small for the RO to cross the orbit of the BBH, and τ − = 0.The total probability of an encounter summed overall orbits before the RO reaches a = 0 is 5 . × − ,1 . × − , and 4 . × − for our fiducial runs with e =0.1, 0.5, and 0.7, respectively. Our calculations sug-gest that an interaction between a RO and a BBH or-biting in the prograde direction is most likely to occurfor ROs with smaller e , because their orbits have moretime to evolve to smaller semi-major axes before they aredriven to high eccentricities. However, our calculatedprobability of interaction is still very small for these or-biters, suggesting that the likelihood of an interactionbetween a prograde BBH and a RO is small. DISCUSSIONROs migrate to the inner disk on timescales of tens tohundreds of kiloyears, depending on their initial eccen-tricity. They also experience a rapid increase in theireccentricity, reaching e (cid:38) .
999 or e (cid:38) .
98 in less thana megayear, without and with GW circularization, re-spectively. The collision rate per orbit between ROs and prograde orbiting 20 M (cid:12)
BBHs in the migration trap ofa Sirko & Goodman (2003) AGN disk is small. There-fore, the probability of a RO interacting with these pro-grade BBHs before it reaches a high eccentricity in ourfiducial examples is low.GW circularization only has a minimal affect on our10 M (cid:12)
ROs until they reach e (cid:38) .
98. Afterwards, GWsquickly lead to coalescence with the SMBH before theorbits of the retrograde BHs can become much morecircular. However, as the mass of the RO increases, therate of GW circularization increases while the rate ofeccentricity driving from the gas decreases. As a re-sult, more massive ROs take longer to reach their maxi-mum eccentricities and never become as eccentric as thefiducial examples shown here. In some cases, such as a50 M (cid:12)
RO with e =0.1, ROs will circularize after theyreach their maximum eccentricity before merging withthe SMBH.In the fiducial calculation in § § (cid:12) for the BBH, but Secundaet al. (2020) found that BBHs near the migration trapoften grow as massive as 100 M (cid:12) , and occasionally even1000 M (cid:12) . The former BBH mass would increase theprobability of interaction for ROs with e =0.1 to about4 . (cid:12) BBH would be almost certain to col-lide with a RO with e =0.1, and has a probability ofinteraction of ∼
11% with a RO with e =0.5. However,in our fiducial examples ROs take under a megayear tomerge with the SMBH, and in (Secunda et al. 2020)these 1000 M (cid:12) BBHs take several megayears to form.ROs from further out in the disk or that are grounddown from inclined orbits into the disk could perhapsreplenish the supply of ROs at later times, althoughMacLeod & Lin (2020) find that ROs on inclined or-bits will flip to prograde orbits as they align with thedisk.If a RO were to interact with a PO the two couldpotentially merge or form a BBH. This interaction out-come would be most likely to occur at apocenter of theretrograde BH’s orbit where the relative velocities of thePOs and ROs would be smallest. A merger would alsobe more likely if the orbiters are very far out from thecentral SMBH, where both of their orbital velocities willbe lower. However, due to the high relative velocities ofPOs and ROs, the total interaction energy is likely tobe positive. As a result, ROs would most likely act toionize existing prograde BBHs (e.g. Leigh et al. 2016,2018). For example, the hard-soft boundary describesthe binary separation over which a BBH will tend tobe disrupted or ionized when it encounters a tertiary.The hard-soft boundary for a RO with e =0.1 interact-ing with a 100 M (cid:12) BBH in our fiducial model, would etrograde Orbiters in an AGN Disk . × − AU, depending on when the ROand BBH interact. A BBH this compact would likelymerge rapidly due to GW emission and not survive longenough to undergo a collision.Whether ROs will form BBHs with each other is un-certain. ROs’ large eccentricities may lead to largerelative velocities among them, preventing them frombecoming bound. However, if ROs after experiencingorbital decay did undergo a GW inspiral in the inner-most disk, they would have a higher probability of be-ing gravitationally lensed by the SMBH, which couldbe detected by the Laser Interferometer Space Antenna(LISA) (Amaro-Seoane et al. 2017; Nakamura 1998;Takahashi & Nakamura 2003; Kocsis 2013; D’Orazio &Loeb 2019; Chen et al. 2019). This population of or-biters in the innermost disk could also perturb the innerdisk, which may be detectable by electromagnetic obser-vations (McKernan et al. 2013; McKernan et al. 2014;Blanchard et al. 2017; Ross et al. 2018; Ricci et al. 2020).Finally, the rapid orbital decay of these retrogradeBHs would likely lead to extreme mass ratio inspi-rals (EMRIs), from coalescence of these BHs with theSMBH. LISA is most sensitive to EMRIs where theSMBH is 10 − M (cid:12) (Babak 2017), i.e. 2-3 ordersof magnitude less massive than the SMBH mass usedhere. Nonetheless, EMRIs involving a 10 M (cid:12) SMBHcould be detectable at low redshift by LISA. ROs inmost cases will still be on eccentric orbits when theymerge. As a result they will produce exotic waveforms,that would identify them as ROs. LISA could also po-tentially localize its detections to only a few candidateAGN (Babak 2017). The examples studied here provide evidence that ROswill not change previously predicted BH merger rates,because we find the probability of interaction betweena RO and a BBH to be low. However, wider parame-ter studies including initially inclined orbits,(e.g., Justet al. 2012; Kennedy et al. 2016; Panamarev et al. 2018;MacLeod & Lin 2020; Fabj et al. 2020), lower massSMBH, higher mass BBH, varying disk density and scaleheight profiles, and POs away from the migration trapshould investigate where RO-BBH interactions may be-come important. Instead of interacting with BBHs, wefind that ROs are likely to become EMRIs. Becausethese EMRIs are often on highly eccentric orbits at thetime of merger, their LISA-observable waveforms will beextremely distinctive and may even allow for measure-ment of gas effects (Derdzinski et al. 2019, 2020). Suchobservations will provide critical insights for our modelsof both nuclear star clusters and AGN disks.ACKNOWLEDGMENTSA.S. would like to thank Charles Emmett Maher foruseful conversations. A.S. is supported by a fellow-ship from the Helen Gurley Brown Revocable Trust andthe NSF Graduate Research Fellowship Program un-der Grant No. DGE-1656466. NWCL gratefully ac-knowledges the support of a Fondecyt Iniciacion grant
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