Selection bias in dynamically-measured super-massive black hole samples: consequences for pulsar timing arrays
MMon. Not. R. Astron. Soc. , 1–6 (2016) Printed 6 November 2018 (MN L A TEX style file v2.2)
Selection bias in dynamically-measured super-massive black holesamples: consequences for pulsar timing arrays
Alberto Sesana (cid:63) , Francesco Shankar , Mariangela Bernardi & Ravi K. Sheth School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom Department of Physics and Astronomy, University of Southampton, Highfield, SO17 1BJ, UK Department of Physics and Astronomy, University of Pennsylvania, 209 South 33rd St, Philadelphia, PA 19104
ABSTRACT
Supermassive black hole – host galaxy relations are key to the computation of the expectedgravitational wave background (GWB) in the pulsar timing array (PTA) frequency band. Ithas been recently pointed out that standard relations adopted in GWB computations are in factbiased-high. We show that when this selection bias is taken into account, the expected GWB inthe PTA band is a factor of about three smaller than previously estimated. Compared to otherscaling relations recently published in the literature, the median amplitude of the signal at f =1 yr − drops from . × − to × − . Although this solves any potential tension betweentheoretical predictions and recent PTA limits without invoking other dynamical effects (suchas stalling, eccentricity or strong coupling with the galactic environment), it also makes theGWB detection more challenging. Key words: black hole physics - galaxies: evolution - gravitational waves - pulsars: general
The first gravitational wave (GW) detection by advanced LIGOAbbott et al. (2016) put the field of GW astronomy in the spot-light. At nHz frequency (inaccessible to ground based interferom-eters), pulsar timing arrays (PTAs) brings the promise of GW de-tection from inspiralling supermassive black hole (SMBH) bina-ries. This is the primary goal of the European Pulsar Timing Ar-ray (EPTA, Desvignes & Others 2016), the Parkes Pulsar TimingArray (PPTA, Manchester et al. 2013) and the North AmericanNanohertz Observatory for Gravitational Waves (NANOGrav, TheNANOGrav Collaboration 2015), that join forces under the aegis ofthe International Pulsar Timing Array (IPTA, Verbiest et al. 2016).At those low frequencies, the superposition of individual sig-nal coming from SMBH binaries is expected to produce a stochas-tic gravitational wave background (GWB Sesana et al. 2008). Itsnormalization is set by the cosmic merger rates of SMBH binarysystems and their typical masses, whereas its shape is affected bythe interaction of the binaries with their stellar and gaseous en-vironment, possibly suppressing the signal at the lowest frequen-cies. Both the amplitude and the spectral shape of the signal areaffected by significant uncertainties, some of which have been re-cently explored by several authors (see, e.g. Kocsis & Sesana 2011;Sesana 2013b,a; Ravi et al. 2014). In particular the signal amplitudestrongly depends on the SMBH masses, which is set by the intrin-sic relation between SMBHs and either the host galaxy stellar bulge( M • − M b relation) or the stellar velocity dispersion ( M • − σ re- (cid:63) E-mail: [email protected] lation). In recent years, improvements in SMBH dynamical massmeasurements, together with the discovery of few “overmassive”black holes in brightest cluster galaxies (McConnell & Ma 2013a)resulted in a upward revision of the SMBH-host galaxy relations(Kormendy & Ho 2013, hereinafter KH13), implying a median ex-pected GWB signal with strain amplitude A ∼ − at f = 1 / yr(although values of A < − are not excluded). Therefore, re-cent PTA non detections of the GWB at the A ∼ − level(Shannon et al. 2015) has been interpreted as being somewhat intension with currently favoured SMBH assembly scenarios, point-ing to a possible important role of SMBH binary eccentricity orenvironmental coupling (Arzoumanian et al. 2015).However, recently Shankar et al. (2016) (S16, hereafter), con-firming the earlier finding of Bernardi et al. (2007), showed that theset of local galaxies with dynamically-measured SMBHs is biased.It has significantly higher velocity dispersions than local galaxies ofsimilar stellar mass as determined from the Sloan Digital Sky Sur-vey (e.g. Bernardi et al. 2014) and this bias also affects the SMBH -host galaxy relations. Using targeted Monte-Carlo simulations, S16showed that this bias could have been induced by the observationalselection requirement that the black hole sphere of influence mustbe resolved to measure black hole masses with spatially resolvedkinematics. By studying the impact of this bias on the local SMBHscaling relations, they found this selection effect to artificially in-crease the normalization of the intrinsic M • − σ relation by a factor (cid:38) , and the intrinsic M • − M b relation by up to an order of magni-tude at low stellar masses. The underlying unbiased relations wouldthus lie significantly below all previous estimates found in the lit- c (cid:13) a r X i v : . [ a s t r o - ph . GA ] M a r A. Sesana et al. erature, naturally implying a lower normalization of the expectedGWB.The aim of this Letter is to quantify the impact of the biasin local SMBH scaling relations on the detectability of the GWBwith PTAs. In Section 2 we review our model for the computationof the GWB, and in Section 3 we focus on the SMBH-host galaxyscaling relations. We present our results in Section 4, discussingtheir implication for PTA campaigns and we summarize our find-ings in Section 5. Throughout the paper we assume a concordance Λ –CDM universe with h = 0 . , Ω M = 0 . and Ω λ = 0 . . Unlessotherwise specified, we use geometric units where G = c = 1 . The method we adopt to extract the GWB from observed proper-ties of low redshift galaxies is fully described in Sesana (2013b)(S13, hereafter). In the following we provide a short summary. Weneglect issues related to possible binary coupling with the envi-ronment, eccentricity, and the possibility of resolving individualsources, which are beyond the scope of this Letter. We consider acosmological population of SMBH binaries, inspiralling in quasi-circular orbit, driven by GW back-reaction. Each merging pair ischaracterized by the masses of the two black holes M • , > M • , ,defining the mass ratio q • = M • , /M • , . The characteristic am-plitude h c of the generated GWB is given by Sesana et al. (2008) h c ( f ) = 4 πf (cid:90) (cid:90) (cid:90) dzdM • , dq • d ndzdM • , dq • ,
11 + z dE gw ( M ) d ln f r . (1)Although the integrals formally run through the whole allowedrange of each variable, Sesana et al. (2008); Sesana (2013b) showedthat > of the signal comes from major mergers ( q • > / )involving massive binaries ( M • , > M (cid:12) ) at low redshift( z < . ). The energy emitted per log-frequency interval is dE gw d ln f r = π / M / f / r . (2)Here M = ( M • , M • , ) / / ( M • , + M • , ) / is the chirp massof the binary and f r = (1 + z ) f is the GW rest frame frequency(twice the orbital frequency). It then follows (Jenet et al. 2006) that h c ( f ) = A (cid:18) f yr − (cid:19) − / (3)where the normalization constant A depends on the SMBH binarymerger rate density per unit redshift, mass and mass ratio givenby the term d n/ ( dzdM • , dq • ) in equation (1). PTA limits on astochastic GWB are usually quoted in terms of A (Lentati et al.2015; Arzoumanian et al. 2015; Shannon et al. 2015). We summarize here the approach taken by S13 to determine d n/dzdM • , dq • . The procedure is twofold: (i) we determine fromobservations the galaxy merger rate d n G /dzdMdq (in a merg-ing galaxy pair, M and q < are the stellar mass of the primarygalaxy and the mass ratio respectively), and (ii) we populate merg-ing galaxies with SMBHs according to empirical SMBH – host We use M • , , M • , , q • for SMBH binaries, and M and q for galaxies Figure 1.
Top panel: average galaxy stellar mass growth, M ( z =0) /M ( z = 1) , predicted by all combinations of pair fractions and mergertime-scales considered in this work (light blue lines), compared to a com-pilation of theoretical and observational estimates. Dark green squares aresimulations from Oser et al. (2010), the magenta triangle is from Naab et al.(2009), the blue circles are a compilation of BCG simulations by Laporteet al. (2013) and the brown open square is from Shankar et al. (2015). Ob-servational estimates are from McIntosh et al. (2008) (purple circles), vanDokkum et al. (2010) (orange pentagon) and Lidman et al. (2012) (yellowcircle). Red lines highlight models featuring an average mass growth in linewith what observed for BCGs (upper), and with typical massive galaxies(lower). Bottom panel, average number of mergers as a function of galaxymass since z = 1 . Light blue lines are the models presented in this paper,with fiducial ones highlighted in red. Dark green square are estimates fromHopkins et al. (2010), the blue pentagon from Xu et al. (2012), the violettriangle from De Lucia & Blaizot (2007) and the yellow circle from Trujilloet al. (2011). galaxy scaling relations. In this procedure, we assume a one-to-one correspondence between galaxy and SMBH mergers; signif-icant delays between the two or possible stalling of SMBH pairswill naturally reduce the integrated GWB. The galaxy differential merger rate can be written as (S13) d n G dzdMdq = φ ( M, z ) M ln 10 F ( z, M, q ) τ ( z, M, q ) dt r dz . (4) φ ( M, z ) = ( dn/d log M ) z denotes the galaxy mass function (MF)at redshift z ; F ( M, q, z ) = ( df/dq ) M,z is the differential fractionof galaxies with mass M at redshift z paired to a secondary galaxywith mass ratio in the range q, q + δq ; τ ( z, M, q ) is the merger time-scale for a galaxy pair and is a function of M , q and z . dt r /dz provides the conversion between proper time and redshift in theadopted cosmology. Equation (4) conveniently expresses the rate asa function of the directly observable quantities φ and F , whereas τ can be inferred from numerical simulations (see below).Improving on S13, we explore four different mass functions(labelled, MF1-4). MF1-3 are constructed by matching individu-ally the MFs at z > provided by Ilbert et al. (2013); Muzzin et al. c (cid:13)000
Top panel: average galaxy stellar mass growth, M ( z =0) /M ( z = 1) , predicted by all combinations of pair fractions and mergertime-scales considered in this work (light blue lines), compared to a com-pilation of theoretical and observational estimates. Dark green squares aresimulations from Oser et al. (2010), the magenta triangle is from Naab et al.(2009), the blue circles are a compilation of BCG simulations by Laporteet al. (2013) and the brown open square is from Shankar et al. (2015). Ob-servational estimates are from McIntosh et al. (2008) (purple circles), vanDokkum et al. (2010) (orange pentagon) and Lidman et al. (2012) (yellowcircle). Red lines highlight models featuring an average mass growth in linewith what observed for BCGs (upper), and with typical massive galaxies(lower). Bottom panel, average number of mergers as a function of galaxymass since z = 1 . Light blue lines are the models presented in this paper,with fiducial ones highlighted in red. Dark green square are estimates fromHopkins et al. (2010), the blue pentagon from Xu et al. (2012), the violettriangle from De Lucia & Blaizot (2007) and the yellow circle from Trujilloet al. (2011). galaxy scaling relations. In this procedure, we assume a one-to-one correspondence between galaxy and SMBH mergers; signif-icant delays between the two or possible stalling of SMBH pairswill naturally reduce the integrated GWB. The galaxy differential merger rate can be written as (S13) d n G dzdMdq = φ ( M, z ) M ln 10 F ( z, M, q ) τ ( z, M, q ) dt r dz . (4) φ ( M, z ) = ( dn/d log M ) z denotes the galaxy mass function (MF)at redshift z ; F ( M, q, z ) = ( df/dq ) M,z is the differential fractionof galaxies with mass M at redshift z paired to a secondary galaxywith mass ratio in the range q, q + δq ; τ ( z, M, q ) is the merger time-scale for a galaxy pair and is a function of M , q and z . dt r /dz provides the conversion between proper time and redshift in theadopted cosmology. Equation (4) conveniently expresses the rate asa function of the directly observable quantities φ and F , whereas τ can be inferred from numerical simulations (see below).Improving on S13, we explore four different mass functions(labelled, MF1-4). MF1-3 are constructed by matching individu-ally the MFs at z > provided by Ilbert et al. (2013); Muzzin et al. c (cid:13)000 , 1–6 BHB mass bias and pulsar timing arrays (2013); Tomczak et al. (2014) to the local mass function estimatedby Bernardi et al. (2013). Conversely MF4 simply assumes an ex-tension of Bernardi et al. (2013) at all considered redshifts with-out evolution (therefore providing an upper limit to the inferredGWB). This is also in line with the recent observational findingsby Bernardi et al. (2016) at z ∼ . . We also explore four differ-ent differential pair fractions (PFs) = ( df/dq ) M,z , extracted from(Bundy et al. 2009; de Ravel et al. 2009; L´opez-Sanjuan et al. 2012;Xu et al. 2012) following the same procedure as in S13 (see alsodetailed description in Gerosa & Sesana 2015). We checked thatthose broadly match recent compilations of galaxy PFs from, e.g,Conselice et al. (2014). Considering different MFs and PFs helpsin folding into our computation possible systematic errors due tothe specific samples and techniques adopted in each work. To ac-count for statistical uncertainties, each MF and PF comes with afiducial value plus an upper and lower limits derived from the un-certainty range quoted in each paper. As in S13, we explore a ’fast’and ’slow’ merger scenario where τ is specified by (i) adoptingequation (10) of Kitzbichler & White (2008) τ = 1 .
32 Gyr (cid:18) M × h − M (cid:12) (cid:19) − . (cid:16) z (cid:17) , (5)and (ii) complementing equation (5) with fits to the results of a setof full hydrodynamical simulation of galaxy mergers presented byLotz et al. (2010), which gives τ = 0 .
79 Gyr (cid:18) M × h − M (cid:12) (cid:19) . q − . (cid:16) z (cid:17) . (6)We interpolate all the measured φ, F , τ on a fine 3-D grid in ( z, M, q ) , to numerically obtain × × differentialgalaxy merger rates. Note that typical values of τ are up to fewGyr, therefore, the merger rate at a given ( z, M, q ) point in the gridis obtained by evaluating φ and F at ( z + δz, M, q ) , where δz is theredshift delay corresponding to the merging time τ . By doing this,we implicitly assume that SMBH binaries coalesce instantaneouslyat the merger time of their hosts. We extend our calculations to allgalaxies with M > M (cid:12) merging at z < . , ensuring that wecapture the bulk of the GWB (see Sesana 2013b).Using the same formalism of equation 4 and following Gerosa& Sesana (2015), the differential number of mergers experiencedby each individual galaxy with mass M is given by d Ndzdq (cid:12)(cid:12)(cid:12)(cid:12) M = dfdq (cid:12)(cid:12)(cid:12)(cid:12) M,z τ ( z, M, q ) dt r dz . (7)We can then compute the number of mergers experienced by eachindividual galaxy with a given mass at z = 1 ( M z =1 ) as N ( M z =1 ) = (cid:90) dz (cid:90) q min dq (cid:90) dM d Ndzdq (cid:12)(cid:12)(cid:12)(cid:12) M δ [ M − M ( z )] , (8)where the integral is consistently evaluated at the redshift-evolvinggalaxy mass M ( z ) through the Dirac delta function. If we multi-ply the integrand of equation (8) by a factor qM , we then obtainthe mass growth of the galaxy, M z =0 /M z =1 , since z = 1 . Resultsfor all MFs and PFs considered in this work are compared to var-ious estimates from the literature in figure 1.The average numberof galaxy mergers and mass growth are in line with observationsand other theoretical estimates, validating the viability of our mod-elling. The last ingredient in the computation of the GWB from equation(1) is the connection between the host galaxy and the SMBH mass.This issue is overcome by employing scaling relations between M • and either the galaxy bulge stellar mass M b or velocity dispersion σ , measured on a limited sample of nearby galaxies. Recent esti-mates of the GWB are usually based on relations provided by Mc-Connell & Ma (2013b) and KH13. In particular, we consider herethe relations reported by KH13: log (cid:18) M • M (cid:12) (cid:19) = 8 . . (cid:18) σ / s (cid:19) , (9) log (cid:18) M • M (cid:12) (cid:19) = 8 .
69 + 1 . (cid:18) M b M (cid:12) (cid:19) , (10)with intrinsic scatter (cid:15) = 0 . dex, and (cid:15) = 0 . dex respectively.However, S16 have shown that both Monte Carlo simula-tions and the analysis of the residuals around the scaling relationssuggest that σ is most fundamental galaxy property correlated toSMBH mass, with a possible additional (weak) dependence on stel-lar mass. In particular the M • − M b relation is mostly induced bythe relation between M • - σ and σ − M b . S16 find the preferredintrinsic relation log (cid:18) M • M (cid:12) (cid:19) = 7 . (cid:18) σ / s (cid:19) +0 . (cid:18) M b M (cid:12) (cid:19) , (11)with intrinsic scatter (cid:15) = 0 . dex. In the following we will con-sider the three scaling relations given above; models adopting ei-ther equation (9) or (10) will be referred to as KH13, whereas thoseadopting equation (11) will be referred to as S16.The relations link M • to the bulge properties, whereas ourgalaxy merger rates are function of the total stellar mass. We derivethe bulge mass of each galaxy by multiplying the total stellar massby a factor f b taken from Bernardi et al. (2014) for SerExp galaxieswith a probability P > . of being ellipticals/lenticulars, whichwe fit as f b = . M b − .
5) 9 . (cid:54) log M b < . . M b − .
6) 10 . (cid:54) log M b < . . M b − .
4) log M b (cid:62) . (12)with an intrinsic scatter (cid:15) = 0 . dex. Velocity dispersion σ , cor-rected to the Hyperleda aperture of . kpc for consistency withS16, is computed from the corresponding bulge mass and fitted as log σ = 2 . − . M b − . , (13)characterized by an intrinsic scatter (cid:15) = 0 . − . M b − . dex . (14)In equations (12)-(14), M b and σ are expressed in units of M (cid:12) andkm s − , respectively. We assume no redshift evolution in any of theaforementioned relations up to z = 1 . .Finally, each merger event, involves three bulges: the progen-itors M b , , M b , and the remnant M b , r . We associate to thesespheroids SMBH masses M • , , M • , and M • ,r , taken from thesame scaling relation, and imposing the only constrain that M • , + M • , < M • ,r . We therefore allow, during the merger, an amountof accretion M acc = M • ,r − ( M • , + M • , < M • ,r ) . This masscan be accreted with a different timing with respect to the SMBHbinary merger, and in different amount on the two SMBHs. We fol-low the three prescriptions described in Section 2.2 of Sesana et al.(2009). We stress that the exact details of the accretion model are c (cid:13) , 1–6 A. Sesana et al.
Figure 2.
Characteristic amplitude of the GWB assuming the scaling re-lations indicated in the panels. In each panel, the shaded areas representthe 68% 95% and 99.7% confidence intervals of the signal amplitude.The jagged curves are current PTA sensitivities: EPTA (dot-dashed green),NANOGrav (long-dashed blue), and PPTA (short-dashed red). For eachsensitivity curve, stars represent the integrated upper limits to an f − / background – cf. equation (3) –, and the horizontal ticks are their extrapo-lation at f = 1 yr − not crucial as we are specifically interested in evaluating the impactof the bias in SMBH scaling relations for PTA searches.The combination of the × SMBH population pre-scription with the 288 galaxy merger rates results in 2592 differ-ent SMBH binary merger rates d n/dzdM • , dq • . By constructionthey are consistent with current observations of the evolution of thegalaxy mass function, pair fractions at z < . and M > M (cid:12) ,and with published empirical SMBH-host relations. They also re-produce observational constraints on the number of galaxy mergersand mass growth (cf. figure 1). Since we are primarily interested in assessing the impact of theSMBH-galaxy relations selection bias on the expected GWB, wedivide the 2592 models in two sub-sample featuring either theKH13 or the S16 relations. The expected characteristic amplituderanges obtained in the two cases are compared in figure 2, togetherwith current upper limits placed by the three pulsar timing arrays:EPTA (Lentati et al. 2015), NANOGrav (Arzoumanian et al. 2015)and PPTA (Shannon et al. 2015). Including the S16 scaling rela-tions in the model lowers the median value of the expected signalat f = 1 yr − by a factor of three, from . × − to × − .This is further elucidated in figure 3, where we show the result-ing probability density distributions of A – cf. equation (3) – forthe two cases. Although recent limits show some tension with theKH13 models, they are fully consistent with the S16 models, whichpredict . × − < A < . × − at 95% confidence. In theupper panel of figure 3 we further separate models featuring MF1-3to those featuring MF4. As expected, the latter provides an upperlimit to the signal, placing the median value at A = 2 × − and A = 6 × − for KH13 and S16 models respectively.Conversely, the more realistic MF1-3, place the median signals at A = 1 . × − and A = 3 . × − .In figure 1, we highlighted in red two ’fiducial’ models; oneproviding a good fit to the overall mass growth of medium-sizegalaxies (fiducial1, lower red curve), and one matching the massgrowth of brightest cluster galaxies (fiducial2, upper curve). The re- Shankar et al. 2016Kormendy & Ho 2013Shankar et al. 2016Kormendy & Ho 2013
Figure 3.
Probability distribution of the signal amplitude A assuming dif-ferent scaling relations, as indicated in figure. Top panel: all pair fractionsand merger time-scale are considered. The solid distributions include all theadopted MFs, the long-dashed ones include MF 1-3, and the short-dashedone assumes MF 4. Bottom panel: amplitude distributions assuming the twofiducial models highlighted in figure 1: fiducial1 (long–dashed) and fidu-cial2 (short–dashed). sulting A distributions from these models are reported in the lowerpanel of figure 3. Obviously, model fiducial2 results in a highersignal, but only by just about 0.2 dex. Median values remain in therange A = 1 − × − and A = 3 − × − for the KH13and S16 models respectively. To investigate the consequences for PTA detection we followRosado et al. (2015) (hereinafter R15). We consider an ideal IPTA-type array with N = 50 pulsars, timed with an rms residual σ rms = 200 ns at intervals ∆ t = 2 weeks. We compute detec-tion probabilities versus time by means of equation (15) in R15,fixing a false alarm rate p = 0 . . We mimic the effect of fittingfor the pulsar spin-down by excluding the two lowest frequencybins from the computation. Although this is a crude approximation,it has little impact on our investigation, since we are interested incomparative results. We take two GWBs with A = 1 . × − and A = 4 × − , representative of the KH13 and S16 models respec-tively. Results are shown in figure 4. In the latter case, there is a sig-nificant delay in detection probability build-up, reaching 95% aboutseven year later. Since, for any given T , S/N ∝ Nh c / ( σ ∆ t ) , adrop of a factor of three in h c can be compensated by an equiva-lent improvement of the rms residuals (i.e. from σ rms = 200 nsto σ rms = 70 ns), by monitoring pulsars every couple of days, orby increasing the number of pulsars in the array. Note that resultsin figure 4 are shown from the start of the PTA experiment; forcomparison, an A = 1 . × − signal would have a detectionprobability of only few% in current IPTA data, which is marked c (cid:13)000
Probability distribution of the signal amplitude A assuming dif-ferent scaling relations, as indicated in figure. Top panel: all pair fractionsand merger time-scale are considered. The solid distributions include all theadopted MFs, the long-dashed ones include MF 1-3, and the short-dashedone assumes MF 4. Bottom panel: amplitude distributions assuming the twofiducial models highlighted in figure 1: fiducial1 (long–dashed) and fidu-cial2 (short–dashed). sulting A distributions from these models are reported in the lowerpanel of figure 3. Obviously, model fiducial2 results in a highersignal, but only by just about 0.2 dex. Median values remain in therange A = 1 − × − and A = 3 − × − for the KH13and S16 models respectively. To investigate the consequences for PTA detection we followRosado et al. (2015) (hereinafter R15). We consider an ideal IPTA-type array with N = 50 pulsars, timed with an rms residual σ rms = 200 ns at intervals ∆ t = 2 weeks. We compute detec-tion probabilities versus time by means of equation (15) in R15,fixing a false alarm rate p = 0 . . We mimic the effect of fittingfor the pulsar spin-down by excluding the two lowest frequencybins from the computation. Although this is a crude approximation,it has little impact on our investigation, since we are interested incomparative results. We take two GWBs with A = 1 . × − and A = 4 × − , representative of the KH13 and S16 models respec-tively. Results are shown in figure 4. In the latter case, there is a sig-nificant delay in detection probability build-up, reaching 95% aboutseven year later. Since, for any given T , S/N ∝ Nh c / ( σ ∆ t ) , adrop of a factor of three in h c can be compensated by an equiva-lent improvement of the rms residuals (i.e. from σ rms = 200 nsto σ rms = 70 ns), by monitoring pulsars every couple of days, orby increasing the number of pulsars in the array. Note that resultsin figure 4 are shown from the start of the PTA experiment; forcomparison, an A = 1 . × − signal would have a detectionprobability of only few% in current IPTA data, which is marked c (cid:13)000 , 1–6 BHB mass bias and pulsar timing arrays Figure 4.
Detection probability as a function of time T . The dashed greenand solid purple lines are for signals with A = 1 . × − (KH13) and A = 4 × − (S16) respectively, assuming an array of N = 50 pulsars, σ rms = 200 ns and ∆ t = 2 weeks. The black dotted line marks a detectionprobability of 95%. by the vertical dotted line. However, one cannot simply extrapolateIPTA detection times based on this plot, since the S/N build-up pacedepends on the number of pulsars, on their timing accuracy, on theaddition of new pulsars and availability of novel instrumentation. We investigated the impact of the selection bias in dynamical mea-surement of SMBH masses on the expected GWB at nHz frequen-cies, accessible to PTAs. We found that the revised SMBH-hostgalaxy relations imply a drop of a factor of three in the signal am-plitude, shifting its median to A = 4 × − . Note that since A is proportional to the number of mergers, compensating thisdrop would require ≈ more SMBH binary mergers, which isseverely inconsistent with observational and theoretical estimatesof galaxy merger rate (cf. figure 1). This result resolves any po-tential tension between recent PTA non-detections and theoreticalpredictions, without invoking any additional physics related to thedynamics of SMBH binaries, such as stalling, high eccentricity orstrong coupling with the surrounding stellar and gaseous environ-ment. On the other hand, it also poses a significant challenge to on-going PTA efforts. If SMBH-galaxy relations are in fact affected bythe strong bias reported by S16, the resulting GWB might be out-side the reach of current PTAs for several years to come. This pic-ture is consistent with the ’stalling scenario’ of Taylor et al. (2016),in which a 95% detection probability is expected only in the next 8-to-12 years depending on the array. This is not surprising since their’stalling scenario’ has a mean A consistent with the implication ofthe selection bias in the SMBH-host relations described here. Ourresults call for a more extensive investigation along the lines ofJanssen et al. (2015) and Taylor et al. (2016), properly weighting-in new ultra-precise timing measurement with MeerKAT (Booth &Jonas 2012) and FAST (Nan et al. 2011) starting next year, andeventually data collected with SKA from 2021 (Smits et al. 2009) ACKNOWLEDGEMENTS
A.S. is supported by a University Research Fellow of the Royal So-ciety, and acknowledge the continuous support of colleagues in theEPTA. A.S. thanks A. Possenti and S. Taylor for useful comments.
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