Search for intermediate mass black hole binaries in the first observing run of Advanced LIGO

TL;DR

This study conducted an all-sky search for gravitational waves from intermediate mass black hole binaries during LIGO's first observing run, setting new upper limits on merger rates due to no detections.

Contribution

It applied two independent search techniques to constrain the rate of IMBHB mergers, significantly improving previous upper limits.

Findings

No gravitational waves from IMBHBs were detected.

The merger rate for 100 solar mass black holes is constrained to less than 0.93 Gpc^{-3} yr^{-1}.

The upper limit improved by nearly two orders of magnitude.

Abstract

During their first observational run, the two Advanced LIGO detectors attained an unprecedented sensitivity, resulting in the first direct detections of gravitational-wave signals and GW151226, produced by stellar-mass binary black hole systems. This paper reports on an all-sky search for gravitational waves (GWs) from merging intermediate mass black hole binaries (IMBHBs). The combined results from two independent search techniques were used in this study: the first employs a matched-filter algorithm that uses a bank of filters covering the GW signal parameter space, while the second is a generic search for GW transients (bursts). No GWs from IMBHBs were detected, therefore, we constrain the rate of several classes of IMBHB mergers. The most stringent limit is obtained for black holes of individual mass $100\,M_\odot$, with spins aligned with the binary orbital angular momentum. For such systems, the merger rate is constrained to be less than $0.93~\mathrm{Gpc^{-3}\,yr}^{-1}$ in comoving units at the $90\%$ confidence level, an improvement of nearly 2 orders of magnitude over previous upper limits.

Figures

Tables

Table 1. Table 1: Results of our analysis for IMBHB systems with (source-frame) component masses m 1 , 2 subscript 𝑚 1 2 m_{1,2} and spins χ 1 , 2 subscript 𝜒 1 2 \chi_{1,2} parallel to the orbital angular momentum. For each set of parameters, we report the 90 % percent 90 90\% confidence combined upper limit on the rate density R 90 % subscript 𝑅 percent 90 R_{90\%} and the combined- and single-pipeline sensitive distance D ⟨ V ​ T ⟩ subscript 𝐷 delimited-⟨⟩ 𝑉 𝑇 D_{\langle VT\rangle} . Uncertainty in the detectors’ amplitude calibration introduces a ≈ 18 % absent percent 18 \approx 18\% uncertainty in the rates and a ≈ 6 % absent percent 6 \approx 6\% uncertainty in the sensitive distance.

$m_1$	$m_2$	${\chi }_{1,2}$	$R_{90\%}$		$D_{⟨VT⟩}{}_{\mathrm{cWB}}^{\mathrm{GstLAL}}$
$\left[M_{\odot }\right]$	$\left[M_{\odot }\right]$		$\left[{\mathrm{Gpc}}^{-3}{\mathrm{yr}}^{-1}\right]$	$\left[{\mathrm{GC}}^{-1}{\mathrm{Gyr}}^{-1}\right]$	$\left[\mathrm{Gpc}\right]$
$100$	$100$	$0.8$	$0.93$	$0.3$	${1.6}_{1.3}^{1.7}$
$100$	$100$	$0$	$2.0$	$0.7$	${1.3}_{1.0}^{1.3}$
$100$	$100$	$-0.8$	$3.5$	$1$	${1.1}_{0.89}^{1.1}$
$100$	$20$	$0$	$13$	$4$	${0.68}_{0.46}^{0.69}$
$100$	$50$	$0$	$3.3$	$1$	${1.1}_{0.78}^{1.1}$
$200$	$50$	$0$	$9.8$	$3$	${0.75}_{0.66}^{0.76}$
$200$	$100$	$0$	$4.6$	$2$	${0.97}_{0.84}^{0.98}$
$200$	$200$	$0$	$5.0$	$2$	${0.94}_{0.78}^{0.95}$
$300$	$50$	$0$	$45$	$20$	${0.45}_{0.37}^{0.46}$
$300$	$100$	$0$	$16$	$5$	${0.63}_{0.52}^{0.64}$
$300$	$200$	$0$	$12$	$4$	${0.69}_{0.58}^{0.70}$
$300$	$300$	$0$	$20$	$7$	${0.59}_{0.45}^{0.60}$

Equations

$$\overline{\mathcal{P}}=1-(1-\mathcal{P}{)}^2.$$

$$R_{90\%}=-\frac{\ln (0.1)}{⟨VT⟩}=\frac{2.303}{⟨VT⟩},$$

$$⟨VT⟩=T_0\int \mathrm{d}z\mathrm{d}\theta \frac{\mathrm{d}{V}_{\mathrm{c}}}{\mathrm{d}z}\frac{1}{1+z}s(\theta )f(z,\theta ),$$

$$⟨VT⟩=\frac{N_{\mathrm{below}\mathrm{cutoff}}}{N_{\mathrm{total}}}⟨VT{⟩}_{\mathrm{total}},$$

$$D_{⟨VT⟩}={\left(\frac{3⟨VT⟩}{4\pi T_{\mathrm{a}}}\right)}^{1/3},$$

Full text

I Introduction

The first observing run (O1) of the Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) detectors Aasi et al. (2015) took place from September 12, 2015 to January 19, 2016. During this period, there were a total of $51.5\leavevmode\nobreak\ \mathrm{days}$ of coincident analysis time between the two detectors, located in Hanford, Washington (H1), and Livingston, Louisiana (L1). This resulted in the detection of gravitational-wave (GW) signals from the coalescence of two binary black hole (BBH) systems with high statistical significance, GW150914 Abbott et al. (2016a) and GW151226 Abbott et al. (2016b), and a third lower-significance candidate, LVT151012 Abbott et al. (2016c), which is also likely to be a BBH coalescence Abbott et al. (2016d).

In all three cases, the estimated premerger individual source-frame masses, $(36.2^{+5.2}_{-3.8},29.1^{+3.7}_{-4.4})M_{\odot}$, $(14.2^{+8.3}_{-3.7},7.5^{+2.3}_{-2.3})M_{\odot}$, and $(23^{+18}_{-6},13^{+4}_{-5})M_{\odot}$, respectively Abbott et al. (2016e, d), are consistent with stellar evolutionary scenarios Abbott et al. (2016f).111Since GWs undergo a cosmological redshift between source and detector, we relate the observed detector-frame mass $m_{\mathrm{det}}$ and the physical source-frame mass $m_{\mathrm{source}}$ via $m_{\mathrm{det}}=(1+z)m_{\mathrm{source}}$, where $z$ is the redshift of the source assuming standard cosmology Ade et al. (2016). These systems were observed at relatively low redshifts, $z=0.09^{+0.03}_{-0.04}$, $0.09^{+0.03}_{-0.04}$, and $0.20^{+0.09}_{-0.09}$, respectively. If relatively heavy black hole remnants, similar to those already observed by Advanced LIGO, exist within dense globular clusters (GCs), further hierarchical merging of these objects could be a natural formation mechanism for intermediate mass black holes (IMBHs) Miller and Colbert (2004). IMBHs are normally defined as black holes with masses in the range $10^{2}\leq M_{\bullet}/M_{\odot}\leq 10^{5}$; in this paper, we consider any BBH with a total mass above $10^{2}\,M_{\odot}$ and mass ratio of $0.1\leq q\leq 1$ to be an IMBH binary (IMBHB).

It is possible that there will be numerous BBH detections in the next few years of GW astronomy Abbott et al. (2016g); Abbott et al. (2016d); Abbott et al. (2016h). In the near future, we should be able to place stringent astrophysical constraints on the formation and evolution of stellar-mass black holes. In addition to surveying stellar-mass black holes, we will also be able to investigate the astrophysics of IMBHs.

If they are found to exist, IMBHB mergers would be the LIGO–Virgo sources that emit the most gravitational-wave energy. Given an estimate of the power spectral density of a detector Abbott et al. (2016i), and assuming a matched-filter single-detector signal-to-noise ratio (SNR) threshold of $8$, in Fig. 1, we plot the horizon distance (the distance to which we can detect an optimally located and oriented source) as a function of source-frame total mass. As Fig. 1 displays, the O1 sensitivity for IMBHBs constitutes a factor of $\approx 6$ improvement in peak horizon distance ($\approx 200$ in search volume) as compared to the sensitivity achieved between 2009–2010, during the sixth and final science run (S6) of initial LIGO Aasi et al. (2014a). However, the matched-filter SNR is only an optimal detection statistic in stationary, Gaussian noise. Since LIGO data are known to contain non-stationary noise Abbott et al. (2016j), this figure is useful primarily as an approximate upper bound on the reach of a modeled search for IMBHBs.

In this paper, we report on the search for IMBHBs during O1. In previous IMBHB searches using LIGO–Virgo data taken in 2005–2010 Aasi et al. (2014a, b), an unmodeled transient search and a modeled matched-filter search using only the ringdown part of the waveform were separately employed to set distinct upper limits on the merger rates of IMBHBs. For this study, two distinct search pipelines were also used: a matched-filter search algorithm, GstLAL Cannon et al. (2012); Privitera et al. (2014); Messick et al. (2017), that uses inspiral–merger–ringdown waveform templates Abbott et al. (2016c, d) which are cross-correlated with the data, and an unmodeled transient search algorithm, coherent WaveBurst (cWB) Abbott et al. (2016k); Klimenko et al. (2016); Abbott et al. (2017a), which looks for excess power which is coherent across the network of GW detectors. Instead of setting distinct upper limits, however, the results presented in this paper are the combined statistics from both independent search techniques. No IMBHBs were detected in this combined search in O1; based on this, we set a $90\%$ confidence level limit on the rate of mergers (see Table 1 below).

The paper is organized as follows: Section II summarizes our search techniques and how they are combined for the current analysis. Section III describes how upper limits on rates are calculated and includes Table 1 and Fig. 2 as main results. Section IV discusses the astrophysical implications inferred from this analysis, and Section V presents our conclusions. We use the “TT+lowP+lensing+ext” parameters from Table 4 of the Planck 2015 results Ade et al. (2016) for cosmological calculations.

II Search Technique

For O1, a new search was inaugurated, in which both modeled and unmodeled analyses, specifically tuned to search for IMBHBs, were combined to form a single search. The modeled analysis employs a matched filter, which yields the optimal detection efficiency for signals of known form in stationary, Gaussian noise Wiener (1949) and thus requires a sufficiently accurate signal waveform model for use as a template. The unmodeled transient analysis, by contrast, can identify burst-like signals which do not correspond to any currently available waveform model. IMBHB signals, as a consequence of their sources’ high mass, have relatively few cycles in the LIGO frequency band; therefore, the IMBHB search benefits from the combination of the two complementary analysis techniques.

II.1 Modeled Analysis

The GstLAL pipeline, which is a matched-filter search algorithm for GWs from compact binary coalescences Cannon et al. (2012); Privitera et al. (2014); Messick et al. (2017), was used in its offline mode to analyze the entirety of O1 Abbott et al. (2016c, d).

The GstLAL IMBHB analysis is based on a discrete bank of GW templates constructed over a total mass between $50\,M_{\odot}$ and $600\,M_{\odot}$ in the detector frame, with mass ratios less extreme than $1$:$10$, and with dimensionless spin $\chi_{1,2}$ between $-0.99$ and $0.99$, where positive values are aligned with the orbital angular momentum of the system and negative values are antialigned. The templates used in this search are a reduced-order model of a double aligned-spin effective-one-body waveform Taracchini et al. (2014); Pürrer (2016). As a consequence of the noise characteristics at low frequencies Abbott et al. (2016i), GstLAL began its analysis at a frequency of $15\leavevmode\nobreak\ \mathrm{Hz}$.

In this analysis, the data are filtered through a singular-value decomposition of the template bank, and the matched-filter SNR time series for each template in the bank is reconstructed from the filtered output of the basis templates Messick et al. (2017). Maxima in the SNR, called triggers, are identified, and corresponding values of a signal consistency test, which is a comparison of the SNR time series for the data to the SNR time series expected from a real signal, are computed. Triggers found in one detector that are not coincident with triggers in another detector are assumed to be non-astrophysical and are used to estimate the probability distribution of noise events in each detector. Coincident triggers are considered GW candidates and are ranked against each other via a likelihood ratio, which compares the probability that each is a signal to the probability that each is noise Messick et al. (2017). Finally, a coincident trigger is assigned a $p$-value Messick et al. (2017), which is the probability of finding a noise fluctuation with such likelihood ratio or higher under the hypothesis that the data contains no GW signals.222See Ref. Capano et al. (2016) for a study of the properties of different methods to estimate the $p$-value in a coincident search for transient GW signals.

For validation, another independent matched-filter search algorithm, PyCBC Dal Canton et al. (2014); Usman et al. (2016), was also run over the same GW parameter space using a spin-aligned frequency-domain phenomenological waveform model Husa et al. (2016); Khan et al. (2016) as templates. PyCBC uses a different SNR-based ranking statistic Dal Canton et al. (2014); Usman et al. (2016); Babak et al. (2013); Abbott et al. (2016c). These two independent matched-filter algorithms find consistent results over the IMBH parameter space, which increases our confidence in their reliability and robustness.

The three most significant events from the GstLAL matched-filter analysis correspond to GW150914, LVT151012 and GW151226, which have already been reported Abbott et al. (2016a, b); Abbott et al. (2016c, d, e). Since parameter-estimation studies have placed these events outside of the IMBH mass range Abbott et al. (2016e, c); Abbott et al. (2016l); Abbott et al. (2016d), we have removed these triggers from our analysis. We discuss the production of our overall IMBHB results in Sec. II.3.

The bank of waveform templates used by the GstLAL IMBHB analysis notably overlaps with the O1 stellar-mass BBH search Abbott et al. (2016c, d) between $M=50\,M_{\odot}$ and $100\,M_{\odot}$. It was therefore expected that this new analysis would find GW150914 and LVT151012 as two of its most significant events, since the masses of these two signals have posterior support in this range Abbott et al. (2016c, e, d). Additionally, GW151226 being the third most significant event in this analysis demonstrates the robustness of modeled analyses to identify signals even outside of their covered parameter spaces.

This is the first modeled analysis that includes the inspiral, merger and ringdown portions of the compact binary coalescence waveform to extend above $M=100\,M_{\odot}$ and into the IMBHB parameter space. Even though IMBHB mergers potentially have large values of SNR, detecting them with this analysis can be difficult. Signal consistency checks are often inefficient at distinguishing true signals from background events. This problem is caused primarily by the short duration of signals produced by high-mass systems, especially those with antialigned spin configurations. Continuing to pursue improvements in IMBHB search methods will undoubtedly improve the sensitivity of the analysis.

II.2 Unmodeled Analysis

The unmodeled analysis was conducted with cWB, the data-analysis algorithm used for previous LIGO–Virgo unmodeled IMBHB searches Abadie et al. (2012); Aasi et al. (2014a). More recently, this algorithm has been used extensively on O1 data Abbott et al. (2017a).

cWB performs a coherent analysis on data from multiple detectors Klimenko et al. (2016); for the O1 analysis, just the H1 and L1 detectors were available. After decomposing the data into a time–frequency representation, the algorithm identifies coherent triggers from regions in the time–frequency domain with excess power relative to the noise level. GW candidate events are subsequently reconstructed in the framework of a constrained maximum-likelihood analysis.

As this reconstruction of signal is agnostic to the waveform modeling of the specific astrophysical source, this algorithm can be used in a variety of searches, including eccentric BBH mergers Tiwari et al. (2016). Past simulation studies have shown that the cWB unmodeled analysis is sensitive to BBH mergers over large regions of the binary parameter space accessible with initial GW detectors Mohapatra et al. (2014); analogous conclusions were reached for the case of advanced detectors Mazzolo et al. (2014).

For this analysis, we applied a further, weak constraint to favor the reconstruction of chirality-polarized waveforms Klimenko et al. (2016). Moreover, with respect to the generic burst search reported in Abbott et al. (2017a), frequency-dependent post-production selection cuts were tuned in order to minimize the impact of such cuts on IMBHB mergers: the low-frequency part of the spectrum of GW data is often polluted by various environmental and instrumental noises that effectively mimic the expected waveforms for massive binary mergers. The cWB analysis began at a frequency of $16\leavevmode\nobreak\ \mathrm{Hz}$.

The significance of any GW candidate event is estimated by comparing it with the noise background distribution in order to calculate its $p$-value. The background set was empirically produced by analyzing $\simeq 9000$ independent time-shifted O1 data sets.333Since the noise sources are uncorrelated between H1 and L1, introducing relative time delays larger than the GW travel time ($\lesssim 10\leavevmode\nobreak\ \mathrm{ms}$) is an effective way to generate an empirical noise distribution. Approximately $1100\leavevmode\nobreak\ \mathrm{yr}$ of effective background livetime was accumulated with this procedure. Additional time lags would have been analyzed had loud IMBHB candidates been identified and a more precise estimate of the background tails been required. The only GW signal found in the O1 data by cWB was GW150914, which is louder than all background events. Similarly to the aforementioned matched-filter searches, GW150914 was then removed from the unmodeled analysis.

II.3 Combining Analyses

After running on the data collected by the detectors, each search algorithm produces a trigger list with times and associated $p$-values $\mathcal{P}$. We combine the two lists together to form a single list of triggers ranked by their $p$-value. To avoid double counting of events, we remove triggers within $100\leavevmode\nobreak\ \mathrm{ms}$ of a more significant trigger found by the other search algorithm. To account for the use of two search algorithms, we apply a trials factor of $2$ to produce the final $p$-value of our search,

[TABLE]

This assumes that the triggers produced by the two algorithms are independent; a correlation in the two lists of triggers from the pipelines would reduce the effective trials factor, making $2$ a conservative choice. Of the top $150$ triggers output by the two pipelines, only GW150914 is common between the lists, indicating that the noise triggers are independent here. We consider $\overline{\mathcal{P}}$ as the ranking statistic for the combined search algorithm. Excluding GW150914, LVT151012 and GW151226, the most significant trigger has $\overline{\mathcal{P}}\simeq 0.26$, well below the significance needed to be considered as a detection candidate.

III Upper limits on rates

Since no IMBHB coalescences were detected during O1, we can calculate upper limits on the astrophysical rate (density) of such events. With the loudest-event method Biswas et al. (2009), if the most significant IMBHB trigger is consistent with noise, the $90\%$ confidence upper limit is given by

[TABLE]

where $\langle VT\rangle$ is the averaged spacetime volume to which our search is sensitive at the loudest-event threshold. We compute $\langle VT\rangle$ by injecting a large number of simulated waveforms into the O1 data, then analyzing the data with both pipelines (GstLAL and cWB) to produce a list of combined $p$-values $\overline{\mathcal{P}}$. A simulated signal is considered to be detected by the search if $\overline{\mathcal{P}}$ is smaller than the $p$-value of the loudest event, $0.26$. The sensitive $\langle VT\rangle$ is then given by

[TABLE]

where $T_{0}$ is the total time covered by the injections (in the detector frame), $V_{\mathrm{c}}(z)$ is the comoving volume contained within a sphere out to redshift $z$ Hogg (1999), $s(\theta)$ is the injected distribution of binary parameters $\theta$ (e.g., masses, spins, orientation angles, distance), and $0\leq f(z,\theta)\leq 1$ is the selection function indicating the fraction of injections with redshift $z$ and parameters $\theta$ that are detected by our search. We evaluate the integral (3) using a Monte Carlo technique.

The injected waveforms are generated using a spin-aligned effective-one-body model Taracchini et al. (2014), which is the waveform model used as a base for the reduced-order model Pürrer (2016) that the GstLAL search pipeline used for its template bank. Precession and higher-order modes are possibly important for IMBHB detection O’Shaughnessy et al. (2013); Schmidt et al. (2015); Capano et al. (2014); Varma et al. (2014); Harry et al. (2016); Calderón Bustillo et al. (2016a, b), particularly for sources with more extreme mass ratios; however, we neglect both effects due to current limitations in the waveform models.

Since the true population of IMBHBs, and thus the true function $s(\theta)$, is unknown, we focus on placing limits on twelve specific locations in the IMBHB parameter space. We choose ten specific combinations of masses (see Table 1). For nine of these mass combinations, we consider only nonspinning black holes. In the case $m_{1}=m_{2}=100\,M_{\odot}$, we consider nonspinning black holes and two spinning cases. In both spinning cases, we choose dimensionless spins $\chi_{1,2}$ of magnitude $0.8$ which are aligned with each other. In one case, the spins are also aligned with the orbital angular momentum of the system ($\chi_{1}=\chi_{2}=0.8$); in the other, they are antialigned ($\chi_{1}=\chi_{2}=-0.8$). Angular parameters (i.e., binary orientation and sky location) are chosen from a uniform distribution on a sphere.

The luminosity distances of the sources are chosen approximately uniformly in comoving volume out to a maximum redshift $z=1$.444A flat cosmology with an incorrect value of $\Omega_{\mathrm{m}}=0.3156$ (instead of $0.3065$) was used to generate the injection sets. We find that the error has no significant effect on our results, introducing an error of less than $1\%$. The sources are distributed uniformly in the O1 observation time ($T_{0}\simeq 130$ days), with a correction factor to account for time dilation. In the detector frame, the injections are spaced by $100\leavevmode\nobreak\ \mathrm{s}$ on average. The total number of injections in each set is $N_{\mathrm{total}}\simeq 112000$, with some slight variation between sets due to the random nature of assigning injection times. Each set includes times during which the detectors were not taking coincident data; the procedure is insensitive to their inclusion in the total. The total spacetime volume covered by the injection sets is $\langle VT\rangle_{\mathrm{total}}\simeq 35\leavevmode\nobreak\ \mathrm{Gpc^{3}\,yr}$. With these choices, expression (3) for the sensitive $\langle VT\rangle$ reduces to the form

[TABLE]

where $N_{\mathrm{below\ cutoff}}$ is the number of injections assigned a $p$-value lower than $0.26$.

The results are given in Table 1. The table shows the $90\%$ confidence rate upper limit for each of the twelve injection sets. Amplitude and phase errors arising from detector calibration Abbott et al. (2017b) have not been included in the analysis; we expect uncertainty in $R_{90\%}$ to be $\approx 18\%$ because of the $\approx 6\%$ uncertainty in the detectors’ amplitude calibration Abbott et al. (2016d). The tightest bound is placed on the merger of two $100\,M_{\odot}$ black holes whose spins are aligned with their orbital angular momentum: the rate of these mergers is constrained to be less than $0.93\leavevmode\nobreak\ \mathrm{Gpc^{-3}\,yr^{-1}}$. Since IMBHB merger rates are commonly expressed in events per GC per Gyr, we convert our results into these units by assuming, for the sake of simplicity, a redshift-independent GC density of $3\leavevmode\nobreak\ \mathrm{GC\,Mpc^{-3}}$ Portegies Zwart and McMillan (2000),555This density encompasses GCs with a range of masses and central concentrations; we make the further simplifying assumption that all GCs have the potential to form IMBHs with the masses we consider. yielding a minimal $R_{90\%}\approx 0.3\leavevmode\nobreak\ \mathrm{GC^{-1}\,Gyr^{-1}}$.

We also report a sensitive distance,

[TABLE]

where $T_{\mathrm{a}}<T_{0}$ is the total time analyzed by the search. The sensitive distance is analogous to the sense-monitor range Allen et al. (2012), except that (5) includes cosmological effects. It is given in Table 1 for the combined $\langle VT\rangle$, used to generate $R_{90\%}$, as well as for the GstLAL and cWB search algorithms individually. The searches are most sensitive to binaries with $m_{1}=m_{2}=100\,M_{\odot}$ and aligned spins. Fig. 2 also reports $R_{90\%}$ and $D_{\langle VT\rangle}$ for the combined search with lines of constant mass ratio $q=m_{2}/m_{1}$ and total mass $M=m_{1}+m_{2}$ to guide the eye.

IV Astrophysical Implications

There are currently few good candidates for IMBHs, but if one extrapolates the observed relation between supermassive black holes and the masses of their host galaxies to lower-mass systems, it is plausible to infer the existence of IMBHs Ferrarese and Merritt (2000); Gebhardt et al. (2000); Gültekin et al. (2009); Graham et al. (2011); McConnell and Ma (2013); Kormendy (1993); Marconi and Hunt (2003); Graham and Scott (2013). While the formation channel of IMBHs is unknown, there are a small number of proposed scenarios: (i) the direct collapse of massive first-generation, low-metallicity Population III stars Madau and Rees (2001); Schneider et al. (2002); Ryu et al. (2016); Kinugawa et al. (2014), (ii) runaway mergers of massive main sequence stars in dense stellar clusters Miller and Hamilton (2002); Portegies Zwart et al. (2004); Portegies Zwart and McMillan (2002); Atakan Gurkan et al. (2004); Mapelli (2016), (iii) the accretion of residual gas onto stellar-mass black holes Leigh et al. (2013) and (iv) chemically homogeneous evolution Marchant et al. (2016).666Since IMBHs are potentially formed via different channels than stellar-mass black holes, we do not attempt to extrapolate the BBH mass distribution to IMBHBs. The O1 BBH merger rate and mass distribution reported in Abbott et al. (2016g); Abbott et al. (2016d) were calculated assuming that the total mass is less than $100\,M_{\odot}$.

It has been suggested that the most likely locations to find IMBHs are at the centers of GCs  Godet et al. (2009); Askar et al. (2017); Lanzoni et al. (2007); Jalali et al. (2010); Noyola et al. (2008); Anderson and van der Marel (2010); Pasham et al. (2015); Brightman et al. (2016); Cseh et al. (2015); Mezcua et al. (2015); Lützgendorf et al. (2013); Koliopanos et al. (2016); Kızıltan et al. (2017). It follows that these are also the most likely places to find IMBHBs. Again, while the formation mechanisms are unknown, it is postulated that an IMBHB can be formed in a GC with a fraction of binary stars higher than $\approx 10\%$ Gurkan et al. (2006) or as a result of a merger of two clusters, each of which contains an IMBH Amaro-Seoane and Freitag (2006); Fregeau et al. (2006). While no direct observational evidence of IMBHBs exists, this hypothesis is supported by recent simulations of dense stellar systems Giersz et al. (2015). Measurements of an IMBHB’s components would allow us to not only constrain IMBH formation channels, but also make statements on the link between IMBHs and both ultra- Mezcua et al. (2013) and hyper-luminous Gao et al. (2003); Farrell et al. (2009); Sutton et al. (2012) X-ray systems.

As stated in Table 1, the minimal $R_{90\%}$ is found to be $\approx 0.3\leavevmode\nobreak\ \mathrm{GC^{-1}\,Gyr}^{-1}$. The improvement in detector sensitivity since the S6 run means that this result is nearly two orders of magnitude lower than the lowest upper limit set using previous LIGO–Virgo data Aasi et al. (2014b, a). This number is within a factor of a few of $0.1\leavevmode\nobreak\ \mathrm{GC^{-1}\,Gyr}^{-1}$, the IMBHB merger rate corresponding to one event occurring in each GC within the lifetime of the cluster (assumed equal to $10\leavevmode\nobreak\ \mathrm{Gyr}$), although it only refers to a single point in the IMBHB mass–spin parameter space and not to the full physical distribution of IMBHBs. The bounds are compatible with rate predictions coming from astrophysical models of IMBHB formation Fregeau et al. (2006); Giersz et al. (2016); Rodriguez et al. (2016). To make a full comparison of the upper limits with predictions, or with the BBH merger rate ($9$–$240\leavevmode\nobreak\ \mathrm{Gpc^{-3}\,{yr}^{-1}}$ Abbott et al. (2016g); Abbott et al. (2016d)), it would be necessary to assume a mass, spin and redshift distribution for IMBHB mergers; this distribution is currently uncertain, so we defer a comparison to future studies.

Further improvements to the detector sensitivity in the next observing runs will allow us to increasingly improve the IMBHB merger-rate estimation and provide relevant constraints on the merger rate in the local Universe. A single GW detection of an IMBHB merger could provide the first conclusive proof of the existence of IMBHs in the Universe Veitch et al. (2015); Graff et al. (2015); Haster et al. (2016). Multiple detections, where astrophysically important parameters, such as mass and spin, are measured, would allow us to make statements not only on the formation and evolutionary channels of IMBHs, but also on their link with other observed phenomena.

V Conclusion

This paper describes a search for intermediate mass black hole binaries during the first observing run of the Advanced LIGO detectors. Due to improvement in detector sensitivity, this run had an increase in search horizon of a factor of $\approx 6$ compared to the previous science run. The search uses the combined information from a modeled matched-filter pipeline and an unmodeled transient burst pipeline. While no IMBHBs were found, $90\%$ confidence limits were placed on the merger rates of IMBHBs in the local universe. The minimum merger rate of $\approx 0.3\leavevmode\nobreak\ \mathrm{GC^{-1}\,Gyr}^{-1}$ constitutes an improvement of almost two orders of magnitude over the previous search results. The results presented here are based on nonprecessing and, in most cases, nonspinning waveforms, that also omit higher modes. It is believed that these higher-order physical effects may be important for IMBHBs, but they should be less important for the near equal-mass systems where we can set best upper limits. We plan to include these effects in future analyses. It is also believed that continued improvements in the detector performance during future observing runs Aasi et al. (2016) will allow us to further tighten these bounds and may lead to the first detections of IMBHs.

Acknowledgments

The authors gratefully acknowledge the support of the United States National Science Foundation (NSF) for the construction and operation of the LIGO Laboratory and Advanced LIGO as well as the Science and Technology Facilities Council (STFC) of the United Kingdom, the Max-Planck-Society (MPS), and the State of Niedersachsen/Germany for support of the construction of Advanced LIGO and construction and operation of the GEO600 detector. Additional support for Advanced LIGO was provided by the Australian Research Council. The authors gratefully acknowledge the Italian Istituto Nazionale di Fisica Nucleare (INFN), the French Centre National de la Recherche Scientifique (CNRS) and the Foundation for Fundamental Research on Matter supported by the Netherlands Organisation for Scientific Research, for the construction and operation of the Virgo detector and the creation and support of the EGO consortium. The authors also gratefully acknowledge research support from these agencies as well as by the Council of Scientific and Industrial Research of India, Department of Science and Technology, India, Science & Engineering Research Board (SERB), India, Ministry of Human Resource Development, India, the Spanish Ministerio de Economía y Competitividad, the Vicepresidència i Conselleria d’Innovació, Recerca i Turisme and the Conselleria d’Educació i Universitat del Govern de les Illes Balears, the National Science Centre of Poland, the European Commission, the Royal Society, the Scottish Funding Council, the Scottish Universities Physics Alliance, the Hungarian Scientific Research Fund (OTKA), the Lyon Institute of Origins (LIO), the National Research Foundation of Korea, Industry Canada and the Province of Ontario through the Ministry of Economic Development and Innovation, the Natural Science and Engineering Research Council Canada, Canadian Institute for Advanced Research, the Brazilian Ministry of Science, Technology, and Innovation, International Center for Theoretical Physics South American Institute for Fundamental Research (ICTP-SAIFR), Russian Foundation for Basic Research, the Leverhulme Trust, the Research Corporation, Ministry of Science and Technology (MOST), Taiwan and the Kavli Foundation. The authors gratefully acknowledge the support of the NSF, STFC, MPS, INFN, CNRS and the State of Niedersachsen/Germany for provision of computational resources. This is LIGO document LIGO-P1600273.