Gravitational-Wave Localization Alone Probes AGN Origin of Stellar-Mass Black Hole Mergers

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by  I. Bartos

Gravitational-Wave Localization Alone Probes AGN Origin of
Stellar-Mass Black Hole Mergers
I. Bartos,1,∗ Z. Haiman,2,3 Z. Marka,1 B.D. Metzger,1 N.C. Stone,1,† and S. Marka1
1Columbia Astrophysics Laboratory, Columbia University, New York, NY 10027, USA
2Department of Astronomy, Columbia University, New York, NY 10027, USA
3Department of Physics, New York University, New York, NY 10003, USA
Stellar-massbinaryblackholemergersarepoisedtorepresentthemajorityofgravitational-wave
(GW) observations by Advanced LIGO and Virgo. Probing their origin will be difficult due to the
expectedlackofelectromagneticemissionandlimitedlocalizationaccuracy. Associationswithrare
hostgalaxytypes–suchasactivegalacticnuclei(AGN)–canneverthelessbeidentifiedstatistically
through spatial correlation. We show that (i) fractional contributions f =50−100% from AGN
agn
hosts to the total BBH merger rate can be statistically established with 70-300 detected events
7
(expectedin0.5-2yearsofobservationwithAdvancedLIGO-Virgoatdesignsensitivityandcurrent
1
rate estimates); (ii) fractional contributions as low as f = 25% can be tested with 1000 events
0 agn
(∼5yearsofobservation);(iii)the∼5%bestlocalizedGWsdrivetheseconstraints. Thepresented
2
methodandresultsaregenerallyapplicabletobinaryformationchannelswithrarehostpopulations.

n
a
J
I. INTRODUCTION AccurateGWlocalization,andtheidentificationofthe

9 hostgalaxy[31],couldbeanadditionalimportantcluein

The recent discovery of gravitational waves (GWs) constraining the formation channel. However, the large
]
E fromstellar-massbinaryblackholemergersbytheLaser number of possible host galaxies will require highly ac-
H Interferometer Gravitational-wave Observatory (LIGO; curatelocalizationthatmayonlybeachievedforasmall
. [1]) opened the door to alternative probes of stellar and fraction of GW observations [32], or with future GW de-
h galactic evolution, cosmology and fundamental physics. tector networks. The situation is complicated further if
p AsLIGO’ssensitivitywillgraduallyincreaseinthecom- multiple formation channels are present, ultimately re-
-
o ingyears,andotherGWdetectorscomeonline[2–4],the quiring the statistical study of rare events.
r rateofGWobservationswillincreaseto∼1day−1 [5,6], In this paper we investigate the prospects of statisti-
t
s making it possible to comprehensively study GW source cally proving the connection of BBH mergers with rare
a populations. hosts, focusing on luminous AGN. Copious gas inflow to
[
The majority of detected GWs will come from binary the nuclei of bright AGN (i.e. quasars) provides a po-

1 blackhole(BBH)mergers[5],makingitpossibletostudy tential site for finding massive black holes [33] that can
v these sources in detail. At the same time, while there is enhance the merger rate as BBHs embedded in their ac-
8
significant effort invested in finding electromagnetic or cretiondisksrapidlymergeduetogasdynamicalfriction
2
neutrino emission from GW sources [7–9], it is not clear [10, 11]. Active galactic nuclei (AGN) represent a small
3
2 if any BBH mergers will have detectable multimessenger fraction(∼1%)ofgalaxies,makingtheiridentificationas
0 signatures. Such counterparts can be produced only if hostsfeasible. Wewillestablishthefeasibilityofstatisti-
. thebinaryissurroundedbysufficientgasthatcanbeac- callyprovingtheconnectionwithAGNashostsforaset
1
creted,whichisnotexpectedformostformationchannels of observed BBH mergers, even if only a sub-population
0
7 (but see [10–14]). of the detected mergers originate from AGN. This tech-
1 BBHs can be formed either from massive stellar bina- niquecanprobethephysicaloriginofBBHmergers,and
: ries [15–18] or via dynamical interactions in dense stel- allowcosmologicalmeasurementsoftheHubbleconstant
v
i lar systems, including globular clusters and galactic nu- using plausible AGN host redshifts (as previously pro-
X clei [19–27]. Identifying the BBH formation channel will posed for extreme mass ratio inspiral events in galaxies
r be a key step in using BBH mergers as cosmic probes. detectablebyLISA;[34])withoutEMcounterparts. The
a
However,thisidentificationforasinglemergerisdifficult method can be extended and applied to other similarly
without an electromagnetic counterpart [5]. Possible ob- rare host populations.
servational clues include the binary mass ratio [5], mass
distribution [28], black-hole spin [29, 30], and orbital ec-
II. SEARCH STRATEGY
centricity close to merger [22]. However, the efficiency
of these clues in differentiating between formation chan-
We aim to take advantage of spatial correlation be-
nels is uncertain, and is dependent on complex stellar
tweenthedistributionofahostpopulation,namelyAGN,
evolution and dynamics processes.
and the location of origin of detected GWs. The origin
of each detected GW can be localized to within a finite
volume at high confidence [35]. GWs originating from
∗ [email protected] anAGNpopulationwillpreferentiallycomefromregions
† EinsteinFellow in the universe with higher AGN number density, while
2
GWs of other origin will show no such preference. The test statistic of a set of detected GWs will be the
Thesourcepopulationisassumedtobeaknownsetof likelihood ratio
point sources. Since Advanced LIGO-Virgo will only be
sensitivetomergersatredshiftz (cid:46)1[36],itispossibleto (cid:20)L(f )(cid:21)
λ=2log agn (4)
achieve a sufficiently complete AGN catalog within this L(0)
range. Additionally, even the closest AGN have much
smaller angular diameter than the precision of GW re-
The significance of an ensemble of GW observations will
construction, hence we can treat AGN as point sources.
be determined by comparing the observed λ value to λ’s
We will further assume that AGN are randomly, uni-
backgrounddistributionP (λ). Thisbackgrounddistri-
formly distributed within the local universe, a conserva- bg
butioncouldinprinciplebedeterminedbydirectintegra-
tiveassumptiongiventhattheyareknowntocluster[37].
tion,butforsimplicity,weusedMonteCarlosimulations
WewillalsoassumethatAGNarespatiallyuncorrelated
verysimilartoourpreviouswork[39]. Wewillrejectthe
withalternativemergersources(seefurtherdiscussionof
nullhypothesisinfavoroff fractionoftheGWsorigi-
this point below). agn
natingfromAGNiftheGWs’λcorrespondstoap-value
A network of GW detectors can constrain the location
less than 3σ (=0.00135).
of origin of a GW, generating a 3D probability density.
We now determine how many GW detections will be
This probability distribution is typically expressed as a
sufficient to reject the null hypothesis with 3σ signifi-
3D localization comoving volume (hereafter localization
cance, given an f fraction. We characterize this num-
volume),atathresholdconfidenceorcrediblelevel(CL), agn
ber, N (f ), by the median number of detections
oftenchosentobe90%[6]. Forsimplicity,wewillusethis gw,3σ agn
that is sufficient to reject the null hypothesis at 3σ level.
localizationvolumeat90%CL,withouttakingadvantage
of the inner probability density.
Let the localization volume of the ith detected GW be
V . ForaGWnot originatingfromanAGN,thenumber
i
A. Monte Carlo Simulations
of AGN within V will follow a Poisson distribution with
i
mean λ = ρ V , where ρ is the number density of
i agn i agn
AGN. The probability of having N AGN’s within V To find N (f ), we use Monte Carlo simulations
agn,i i gw,3σ agn
for our null-hypothesis is (see [39]). We adopt the distribution of GW localization
volumes obtained by Chen & Holz [32] for the LIGO-
Bi(Nagn,i)=Poiss(Nagn,i,ρagnVi). (1) Virgo GW detector network at design sensitivity. We
take their results for 10M –10M BBH mergers as a
(cid:12) (cid:12)
If the GW originated in an AGN, then there will be 1 characteristicbinary,notingthatthelocalizationvolume
guaranteed AGN, with the number of additional AGN increases for greater binary mass due to the lower GW
followingaPoissondistributionwithλi mean. Theprob- frequencies as well as the larger horizon distances. The
ability of having Nagn,i AGN in Vi volume for our alter- localization volumes found by Chen & Holz are given
native hypothesis is therefore at 90% confidence level. As only 90% of GWs will be
locatedwithintheselocalizationsvolumes,thisdecreases
Si(Nagn,i)=Poiss(Nagn,i−1,ρagnVi). (2) the effective AGN fraction fagn by a factor of 0.9, which
we take into account in the following calculations.
While a single GW detection may not be sufficient to
For one Monte Carlo realization, we assume a GW de-
determine its host population of origin, combining mul-
tection number N , and (effective) AGN fraction f .
tiple GW observations will increase the likelihood that gw agn
ForeachGWdetection,werandomlyassignanAGNori-
we can statistically prove the connection between BBH
gin with 0.9f probability, otherwise it is considered to
mergers and AGN. For the alternative hypothesis that a agn
originatefromanotherhosttype. ForGWdetectioni,we
fraction f of the detected GWs originated from AGN
agn assign a random localization volume V drawn from the
and(1−f )fromsomeotherhostpopulation,weobtain i
agn Chen-Holz distribution described above, and generate a
the likelihood
random AGN number within this volume, using the dis-
(cid:89) tributionsinEqs. 2and1forAGNandnot-AGNorigins,
L(f )= [f S +(1−f )B ] (3)
agn agn i agn i respectively. We then calculate λ corresponding to this
i
realization using Eq. 4. We similarly obtain background
wheretheproductisoveralldetectedBBHmergersdur- realizations following the same calculation, except that
ing the observation period. the number of AGN for all GW detections are drawn
While we do not know f a priori, here we will use fromthebackgrounddistributioninEq. 1. Weusethese
agn
a specific value in the likelihood ratio test. For estimat- background realizations to determine the p-values corre-
ing f , one can maximize L(f ) with respect to f sponding to the realizations with GWs from AGN.
agn agn agn
(e.g., [38]). Since we focus here on sensitivity and not We repeat the above Monte Carlo analysis for a range
the precision of parameter reconstruction, we will ignore of N values for a given f in order to determine the
gw agn
this step. threshold number N (f ).
gw,3σ agn
3
III. RESULTS
111000111
We carried out the Monte Carlo analysis described
above for a range of fagn values. We found the scaling 111000333
relation
N ∝f−2. (5)
gw,3σ agn
TogfehttihsheecratsnocatbaleelsinnwutumitihbtievNrel1oy/f2eAxp,GewNchteifldoe:rttahhlelenGsutWamnbddeaerrtdoecfdt”eiovsinigasntiatooln”- NNN333,,,wwwggg111000222 11[1[11MM00000-----pp44444cc.. 55[--M33]]pc-3] 111000000 ]]]rrryyy[[[TTT sssbbbooo
AGN scales with N gw,3σf , corresponding to a signal- 111000---444...75755
gw,3σ agn
to-noise ratio SNR∝N1/2 f . Interpreting our detec- 111000---545.75
tion threshold as a fixedgwS,3NσRa,gnwe get back Eq. 5. 111000---656 111000---111
111000---767
Our results for N are shown in Fig. 1. Here, we
gw,3σ 111000111
applied Monte Carlo analysis to evaluate the case fagn = 000 000...222 000...444 000...666 000...888 111
1, and used Eq. 5 to show scaling with f . fff
agn aaagggnnn
For a fiducial AGN density ρ = 10−4.75Mpc−3
agn
[40, 41], we find that ∼ 70 detections would be suffi-
FIG. 1. Number of detections needed for the identification
cient to statistically prove the BBH-AGN connection if
of an AGN host population at a median 3σ significance, as
allBBHmergersoccurredinAGN.FortheexpectedBBH
a function of the fraction (f ) of GW detections originat-
agn
merger rate of ∼ 60Gpc−3yr−1 [5], this corresponds to ing from AGN. The results are shown for different assumed
a few months of LIGO-Virgo observation time at design AGN number densities (see legend), with fiducial density
sensitivity, indicating that this scenario would yield re- ρ =10−4.75Mpc−3 [40,41],fortheAdvancedLIGO-Virgo
agn
sultsquickly(possiblyevenbeforeLIGOandVirgoreach networkatdesignsensitivity. Ontherightside,wemarkthe
designsensitivity). WiththecurrentuncertaintyinBBH necessary observation duration corresponding to numbers of
mergerrateof9−240Gpc−3yr−1 [5],therequiredtimeis detection, using 200 detections/year.
withinamonthandafewyears. Evenifonlyafractionof
mergersoccurinAGN,wefindthata5-yearobservation
Toanswerthisquestion,wereranourMonteCarlostudy
period is likely sufficient to statistically prove the BBH-
for ρ = 10−4.75Mpc−3 and f = 1, with the modifi-
AGN connection if the AGN fraction is at least 25%. agn agn
cation that the analysis only used GW localization vol-
To understand our results’ dependence on the un-
umesbelowacutoffvolumeV . WemeasuredN
certain AGN number density, and to demonstrate the cutoff gw,3σ
as a function of the fraction f (V ) of localization
method’s applicability to other rare host types, we also V cutoff
volumesbelowV . WefoundthatV (cid:38)105Mpc3
obtainedresultsforarangeofdifferentρ numberden- cutoff cutoff
agn
didnotmeaningfullychangeN ,butforlowerV ,
sities. While a sparser source population leads to even gw,3σ cutoff
we found a quick deterioration. We conclude that those
less detections needed for the identification of a host
events drive our constraints in whose localization vol-
population, we found that, even for number densities of
10−4Mpc−3, a 5-year observation period will establish umes we expect (cid:46) 2 interloper quasars on average. For
the BBH-AGN connection for f (cid:38) 0.5. With higher ρagn =10−4.75Mpc−3,thisisthetop∼5%bestlocalized
agn
events.
host number densities it becomes difficult to prove an
AGNconnectionsolelyusingGWlocalizations,although
the construction of additional GW detectors (KAGRA
[42] and LIGO India [43]), and potentially the inclusion IV. DISCUSSION AND CONCLUSIONS
ofmarginallysignificantGWevents,willfurtherimprove
the situation. We examined the prospects of using GW localization
HowmuchdoGWswithdifferentlocalizationvolumes to probe GW host galaxy populations. In particular,
contribute to the results? To better understand the we were interested in BBH mergers in AGN, where the
role of the GW localization volume, we carried out the inflowofgascansignificantlyincreasemergerratescom-
Monte Carlo analysis described above, but with fixed lo- pared to other galactic nuclei, and may lead to multi-
calization volume size. This analysis confirmed that, for messenger emission. AGN represent a small fraction of
fixed localization volume, our method described above is galaxies, making it easier to identify correlation between
equivalent to combining AGN from all GW detections, their position and the localization of GWs. We consid-
and looking for a 3σ deviation in the overall number. ered the Advanced LIGO-Virgo detector network at its
The GW detection number threshold in this case, for design sensitivity.
N (cid:29) 1, is N = 9ρ V, where V is the fixed We calculated the number of GW observations needed
gw,3σ gw,3σ agn
localization volume. to statistically establish the connection of BBH mergers
Are we mainly relying on a few well-localized GWs for with AGN as hosts, as a function of the AGN number
this analysis, or are less-well-localized GWs also useful? density ρ and the fraction f of BBH mergers origi-
agn agn
4
nating in AGN. Our findings are the following: There are important next steps that will further en-
(1) For our fiducial number density ρ = hance the prospects of our analysis. (i) AGN are rela-
agn
10−4.75Mpc−3 and f = 1, ∼ 70 observations tively strongly clustered, which can enhance the signal
agn
will be sufficient, on average, to statistically establish to noise ratio over a random AGN distribution assumed
the BBH-AGN connection at 3σ significance. With an here. (ii)Differenthostpopulationscanbespatiallycor-
expected rate of BBH merger detection of 200yr−1, this related, which needs to be taken into account before the
corresponds to 6 months of observation time. BBHscanbeinferredtoresideinAGN(ratherthanjust
(2) We quantified the efficiency of establishing BBH- correlated with them statistically). (iii) Combining our
AGN for fractional AGN contributions (Fig. 1). For error region analysis with other ”observables” (binary
a fractional contribution f , the number of detections mass, spins, etc.) and host galaxy properties that cor-
agn
sufficient on average to establish the BBH-AGN connec- relate with binary rate will significantly enhance search
tion is N =70f−2. sensitivity (iv) If suitable models are available, recon-
gw,3σ agn
(3) Incorporating the ∼5% best localized BBH mergers structed BBH properties can add to the differentiating
is sufficient to produce close to optimal constraints. power of a search.
Our results demonstrate that correlation between the We further emphasize the need for detailed AGN cat-
locationofAGNandGWsalone canbeusedtoestablish alogs out to redshift of z ∼ 0.2; these catalogs will pro-
theBBH-AGNconnectionwithafewyearsofobservation vide the backbone of any statistical BBH-AGN connec-
withAdvancedLIGO-Virgoatdesignsensitivity,making tion [49, 50]. In principle, the nearby AGN which host
thisacompetitiveapproachcomparedtomoremodelde- mostLIGOevents,withM (cid:38)106M )shouldbebright
bh (cid:12)
pendent probes that use reconstructed BBH properties, enough to be detectable in large all-sky surveys [51]. In
or uncertain electromagnetic counterparts. practice, however, existing spectroscopically confirmed
In principle, LIGO events can be spatially correlated quasar catalogs appear incomplete. In the full comov-
with AGN even if they are unrelated to AGN, but occur ing volume out to z =0.1 (∼0.3Gpc3) we expect to find
in galaxies whose spatial distribution is correlated with ∼ 10,000AGN. This number is based on extrapolating
AGN.Thecross-correlationlengthbetweenlocalgalaxies spectroscopicmeasurementsforfaintnearbyAGNtothe
and quasars is ∼ 6Mpc [44], which is an order of mag- rest of the sky. On the other hand, the latest quasar
nitude smaller than the linear size of the typical LIGO catalog from SDSS, covering ≈10,000deg2 [52] contains
errorvolume[32],soweexpectthiseffecttobesmall,un- only232quasarsatz <0.1, implyingthatitisonly10%
less the events occur in rare galaxy sub-types that have complete. Deeper spectroscopic surveys exist but target
a stronger correlation with AGN. onlyasmallfractionofthesky. TheSwiftBAT70-month
The technique and results presented here can also be survey covers the entire sky, but contains only a total of
applied to other rare host populations. For instance, in 523 quasars and AGN at z ≤ 0.1, the vast majority of
the standard dynamical formation scenario, BBHs form whichareSeyfertgalaxies[53]. Moretargetedcataloging
in globular clusters. The number of globular clusters efforts are needed to take full advantage of GW obser-
within a galaxy strongly correlates with the mass of the vations. With no full-sky catalogs, it is also sufficient to
central supermassive black hole [45], so relatively rare, identify galaxies in follow-up surveys of individual GW
largeblackholesneartheturnoverintheSchechterfunc- localization volumes [50, 54].
tion are the dominant contributors. Another relevant We thank Jules Halpern for useful discussions. IB,
channel is BBHs formed by GW capture in the dense ZM and SM are thankful for the generous support of
stellarmassblackholepopulationsofgalacticnuclei[22]. Columbia University in the City of New York. ZH ac-
This scenario preferentially occurs in the densest nuclei, knowledges support from NASA grant NNX15AB19G
and therefore could be strongly correlated with E+A and a Simons Fellowship for Theoretical Physics. BDM
galaxies. E+As are post-starburst galaxies that repre- acknowledges support from NASA grant NNX16AB30G
sent ≈0.2% of all z ≈0 galaxies but host an order unity and the Research Corporation for Science Advancement
fraction of stellar tidal disruption events [46, 47]; pre- Scialog Program grant RCSA23810. NCS acknowledges
liminary evidence suggests that this is due to overdense supportbyNASAthroughEinsteinPostdoctoralFellow-
central star clusters [48]. ship Award Number PF5-160145.
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