Modeling the Black hole Merger of QSO 3C 186

TL;DR

This paper models the properties of a supermassive black hole merger in quasar 3C 186, using observations of recoil velocity and numerical relativity to estimate mass ratios, spins, and gravitational wave emission.

Contribution

It provides the first detailed modeling of the black hole merger in 3C 186, constraining progenitor parameters and energy radiated based on observational data and simulations.

Findings

Black holes had comparable masses with q>1/4.

At least 4% of total mass was radiated as gravitational waves.

Merger was the most energetic event observed, radiating about 10% of total mass.

Abstract

Recent detailed observations of the radio-loud quasar 3C 186 indicate the possibility that a supermassive recoiling black hole is moving away from the host galaxy at a speed of nearly 2100km/s. If this is the case, we can model the mass ratio and spins of the progenitor binary black hole using the results of numerical relativity simulations. We find that the black holes in the progenitor must have comparable masses with a mass ratio $q=m_1/m_2>1/4$ and the spin of the primary black hole must be $\alpha_2=S_2/m_2^2>0.4$. The final remnant of the merger is bounded by $\alpha_f>0.45$ and at least $4\%$ of the total mass of the binary system is radiated into gravitational waves. We consider four different pre-merger scenarios that further narrow those values. Assuming, for instance, a cold accretion driven merger model, we find that the binary had comparable masses with $q=0.70^{+0.29}_{-0.21}$ and the normalized spins of the larger and smaller black holes were $\alpha_2=0.94^{+0.06}_{-0.22}$ and $\alpha_1=0.95^{+0.05}_{-0.09}$. We can also estimate the final recoiling black hole spin $\alpha_f=0.93^{+0.02}_{-0.03}$ and that the system radiated $9.6^{+0.8}_{-1.4}\%$ of its total mass, making the merger of those black holes the most energetic event ever observed.

Tables

Table 1. Table 1 Parameters of the progenitor binary assuming a dry, hot, cold, uniform volume merger. μ 1 , 2 = cos ⁡ θ 1 , 2 subscript 𝜇 1 2 subscript 𝜃 1 2 \mu_{1,2}=\cos\theta_{1,2} is the cosine of the angle each spin makes with the direction of the orbital angular momentum, α 1 , 2 subscript 𝛼 1 2 \alpha_{1,2} are the dimensionless spin magnitudes, and q = m 1 / m 2 ≤ 1 𝑞 subscript 𝑚 1 subscript 𝑚 2 1 q=m_{1}/m_{2}\leq 1 is the mass ratio. The errors are given at 1- σ 𝜎 \sigma level. We also provide the final spin of the merged hole and the total radiated energy in units of the binary’s total mass based on the binary-parameter distributions in Fig.  2 . Lastly, we include the probabilities, given hot, cold Dry, or uniform distributions for recoils of 2000 ​ km / s 2000 km s 2000\ \rm km/s or larger.

	${\mu }_1$	${\mu }_2$	${\alpha }_1$	${\alpha }_2$	$q$
Cold	${0.99}_{-0.07}^{+0.01}$	${0.93}_{-0.07}^{+0.06}$	${0.94}_{-0.22}^{+0.06}$	${0.95}_{-0.09}^{+0.05}$	${0.70}_{-0.21}^{+0.29}$
Hot	${1.00}_{-0.28}^{+0.00}$	${0.88}_{-0.19}^{+0.11}$	${0.78}_{-0.34}^{+0.21}$	${0.96}_{-0.24}^{+0.04}$	${0.60}_{-0.25}^{+0.36}$
Dry	${0.52}_{-0.51}^{+0.42}$	${0.45}_{-0.44}^{+0.48}$	${0.74}_{-0.39}^{+0.08}$	${0.71}_{-0.14}^{+0.14}$	${0.56}_{-0.17}^{+0.39}$
Uni.	${0.09}_{-0.08}^{+0.91}$	${0.63}_{-0.59}^{+0.31}$	${1.00}_{-0.49}^{+0}$	${1.00}_{-0.29}^{+0}$	${0.55}_{-0.24}^{+0.28}$

Full text

1. Introduction

A recent detailed study Chiaberge et al. (2017) of the radio-loud quasar 3C 186, which has an active nucleus offset from the galactic center by $1.3\pm 0.1$ arcsec (i.e. $\sim 11$ kpc) and broad line emissions offset from the narrow line spectra by $2140\pm 390$ km/s, has concluded that the most likely explanation is that the central supermassive black is recoiling away from the center of the galaxy at $\sim 2000$ km/s.

Studies of this sort have been carried in the past Bonning et al. (2007); Komossa et al. (2008); Bogdanović et al. (2009); Heckman et al. (2009); Shields et al. (2009); Strateva & Komossa (2009); Decarli et al. (2009); Lauer & Boroson (2009); Vivek et al. (2009); Robinson et al. (2010); Shields & Bonning (2013); Decarli et al. (2014) prompted by the numerical relativity simulations that predicted large recoil velocities from the merger of binary black holes Campanelli et al. (2007a, b). A review of those early efforts is summarized in Komossa (2012).

This new case of the QSO 3C 186 is of particular interest since its differential velocity (if interpreted in terms of gravitational wave recoil) may be used to determine the parameters of the progenitor binary black hole system and the final black hole being ejected from the merged galaxies.

Full numerical simulations of the merger of binary black holes have produced detailed predictions for the remnant final black hole mass, spin and recoil velocity Lousto et al. (2010a); Lousto & Zlochower (2013, 2014); Zlochower & Lousto (2015) and the probability of a given recoil velocity to be observed Schnittman & Buonanno (2007); Lousto et al. (2010b, 2012). Those “phenomenological” formulas relate the binary parameters of the progenitor, i.e. individual masses and spins, to the final mass, spin and (recoil) velocity of the merged hole with high accuracy. The large value of the measured differential redshift of the broad and narrow lines can only be the result of the gravitational recoil if the progenitor binary had a mass ratio close to unity and highly spinning progenitor black holes (BHs). We can also determine the direction of the recoil velocity with respect to the merger orbital plane.

These techniques, used here for QSO 3C 186, clearly apply to any highly recoiling system, as for example those candidates cited above. In order to cover different pre-merger scenarios, we study binaries with parameters based on hot and cold accretion models, as well as two gas-poor merger models, as shown in Fig. 1

2. Results

For our statistical analysis, we consider the recoils from binaries sampled from the following distributions. For the mass ratio, we use a distribution motivated by cosmological simulations, $P(q)\propto q^{-0.3}(1-q)$, as given in Ref. Yu et al. (2011); Stewart et al. (2009); Hopkins et al. (2010). For the spins, we consider four different distributions which we will denote by Hot, Cold, Dry, and Uniform. The Hot and Cold distributions are based on the hot and cold accretion models given in Lousto et al. (2012). In these models, the merger is assumed to be gas rich and the subsequent accretion both reorients the spins (towards partial alignment) and induces relatively large spin magnitudes. The cold model, in particular, severely constrains the polar orientations of the spin, which severely limits the magnitude of the recoil. Because of the very low probability for large recoils in the dry model, our sample size was $3.1\times 10^{8}$ binaries for the cold model. For all other models, the sample size was $10^{7}$ binaries. The dry model is based on Zlochower & Lousto (2015). For the dry model, we assume accretion is inefficient at aligning the spins, and thus assume a uniform distribution of spin directions. The magnitude of the spin is determined by assuming past mergers were also gas poor. This leads to the spin-magnitude distribution shown in Fig. 1. Finally, the Uniform model simply assumes uniform probabilities for the spin magnitudes and directions within the unit sphere (i.e., uniform probabilities for all directions and a probability density of $3\alpha^{2}$ for the magnitude of the spin). This uniform model has a strong bias towards high spins (that could be the product of gas-rich pre-merger scenarios) combined with random distributions of the spin directions (that could be the product of anisotropic accretion, see Figs. 4 and 7 in Perego et al. (2009), or retrograde circumbinary accretion Schnittman & Krolik (2015)). Thus, while the uniform distribution is geometrical in origin, it represents a series of astrophysically plausible scenarios and provides the most favorable distributions for observing high recoils of thousand of km/s.

These distributions are summarized in Fig. 1.

To model the recoil, we use the formulas given in Zlochower & Lousto (2015). Based on those formulas, we can conclude that a binary with mass ratio $q<0.23$ cannot recoil as fast as $2000\ \rm km/s$. This holds true regardless of the progenitors spin magnitudes and orientations. If we further assume, for instance, the dry distribution of spin magnitudes, then the mass ratio cannot be smaller than $0.28$. Thus, if the supermassive black hole (SMBH) in QSO 3C 186 resulted from the quasicircular 111Comparable masses binary black holes are very efficient in reducing any initial eccentricity through radiation of gravitational waves Peters (1964) down to the merger Mroue et al. (2010); Lousto et al. (2016). inspiral of two SMBHs, the progenitor BHs must have had similar masses.

Figure 2 shows the probabilities for a recoil of $2000\ \rm km/s$ or larger as a function of the two spins $\alpha_{1}$ and $\alpha_{2}$ for each distribution, as well as the probabilities as a function of mass ratio and the polar orientation of the spin of the larger BH, $\mu_{2}=\cos\theta_{2}$. Note that the probability of any binary recoiling at $2000\ \rm km/s$ or larger for the four models are $3\times 10^{-4}\%$, $0.19\%$, $0.23\%$, and $2.14\%$ for cold, hot, dry, and uniform volume distributions, respectively. Finally, we show probabilities for the remnant spin and total radiated mass (in terms of the binary’s initial mass).

Based on Fig. 2, we can estimate the parameters of the progenitor binary. Assuming a dry, hot, cold, uniform volume merger, we get the parameters in Table 1. Furthermore, using the empirical formulas in Zlochower & Lousto (2015), we find that the final remnant black hole spin and total radiated energy. For instance, for the dry mergers, the final spin is $\alpha_{f}=0.75^{+0.08}_{-0.13}$ and the binary converted $5.5^{+1.1}_{-1.1}$% of its total mass into gravitational radiation. The other models lead to even higher final remnant spins and radiated gravitational energy.

3. Conclusion and discussion

While for the ideal configuration Lousto & Zlochower (2011) of equal-mass binaries and maximally spinning black holes with spins at nearly 50-degrees from the orbital angular momentum and opposite phases, recoil velocities can reach up to 5000km/s. By demanding high velocities, above 2000km/s, one can place important constraints on the parameters of the progenitor binary. We find that, independent of the merger model we adopt, the mass ratio has to be $q>1/4$ and that the spin of the holes are likely above $50\%$ of their maximum value. Note that according to Fig. 1, (bottom-right panel) of Chiaberge et al. (2017) the presence of low signal to noise shells or tidal tails in the host galaxy are typical of major galaxy merger remnants, i.e. the two merging galaxies have masses that are equal to within a factor of 3.

Those highly-recoiling configurations also require a misalignment of the spins with the orbital angular momentum of the binary, which suggests that any circumbinary accretion did not have enough time to align spins Bogdanović et al. (2007); Coleman Miller & Krolik (2013), i.e. the merger was either gas-poor or the black holes were too massive for accretion to make an impact on the direction of the spins. Note that the estimates of the final black hole mass in Chiaberge et al. (2017) sets its value in the range $3-6\times 10^{9}M_{\odot}$. Increasing the measured recoil velocity can dramatically narrow the possible region of the binary parameter space, and even exclude some of the pre-merger scenarios, such as the cold accretion one. This also suggest, that if one had an independent way of measuring another parameter of the system, for instance the final spin of the remnant, one could choose, based on Table 1or Fig. 2 among the different models for the pre-merger stage of the binary black hole.

If we assume that the 11kpc of offset between the AGN and the host galaxy is due to a transverse component of the recoil velocity of nearly 1000km/s, the time elapsed from the merger of the black hole is around $10^{7}$ years. This in turn, allows us to claim that our bounds, based on recoil velocities $v>2000$km/s is a conservative one (since the total recoil velocity, including transversal and potential of the host galaxy components, would be even larger), and that the actual parameters of the precursor binary are even closer to more comparable masses and higher spins.

In relation to the above time scale another important factor to consider is the lifetime of accretion disks carried by recoiling black holes Blecha & Loeb (2008); Blecha et al. (2011). In Chiaberge et al. (2017), assuming a radiative efficiency of $\epsilon=0.1$ and the luminosity and BH mass estimated for 3C 186, they derive a lifetime for the disk of $t_{disk}\sim 10^{8}$yr. This is an order of magnitude longer than the estimate above and hence the transverse velocities would not need to be much larger than $100$ km/s for the accretion disk to survive until a 11kpc offset is reached.

Finally, large recoil velocities are strongly beamed along the orbital angular momentum (see Figs. 11-14 of Ref. Lousto et al. (2012) and Fig. 7 in Ref. Zlochower & Lousto (2015)). This means that we must be seeing the system in a rather face-on angle with respect to the late merger orbital plane. It is interesting to correlate this with the radio, optical and x-ray maps of QSO 3C 186.

The authors thank T.Bogdanovic, E.Bonning, M.Chaberge, Cole-Miller, M.Dotti, J.Krolik and J.Schnittman for discussions and gratefully acknowledge the NSF for financial support from NSF Grants No. PHY-1607520, No. ACI-1550436, No. AST-1516150, and No. ACI-1516125.