Sub-parsec supermassive Binary Quasars: expectations at z
We investigate the theoretical expectations for detections of supermassive binary black holes that can be identified as sub-parsec luminous quasars. To-date, only two candidates have been selected in a sample comprising 17,500 sources selected from the Sloan Digital Sky Survey (SDSS) Quasar Catalog at (Boroson & Lauer, 2009). In this Letter, we use models of assembly and growth of supermassive black holes (SMBHs) in hierarchical cosmologies to study the statistics and observability of binary quasars at sub-parsec separations. Our goal is twofold: (1) test if such a scarce number of binaries is consistent with theoretical prediction of SMBH merger rates, and (2) provide additional predictions at higher redshifts, and at lower flux levels. We determine the cumulative number of expected binaries in a complete, volume limited sample. Motivated by Boroson & Lauer (2009), we apply the SDSS Quasar luminosity cut (M) to our theoretical sample, deriving an upper limit to the observable binary fraction. We find that sub-parsec quasar binaries are intrinsically rare. Our best models predict deg sub-parsec binary quasars with separations below Schwarzschild radii () at , which represent a fraction of unabsorbed quasars in our theoretical sample. In a complete sample of 10,000 sources, we therefore predict an upper limit of 10 sub-parsec binary quasars. The number of binaries increases rapidly with increasing redshift. The decreasing lifetime with SMBH binary mass suggests that lowering the luminosity threshold does not lead to a significant increase in the number of detectable sub-parsec binary quasars.
Subject headings:black hole physics — cosmology: theory — galaxies: nuclei — quasars: general
SMBHs appear to inhabit most galaxy centers (e.g., Richstone et al., 1998; Ferrarese & Ford, 2005), and in CDM cosmologies galaxies experience multiple mergers during their cosmic assembly. SMBH binaries (SMBHBs) are therefore expected to be recurrent, albeit transient features of most galactic bulges. Observationally, the paucity of quasar pairs (0.1%) on galactic scales (Foreman et al., 2009) points toward rapid inspiral of the SMBHs down to (sub-)parsec scales where they form a gravitationally bound pair (Mayer et al., 2007). As discussed in Foreman et al. (2009) if we assume that every galaxy hosts a SMBH and that quasar activity is triggered by galaxy mergers, the probability of observing a double quasar scales with the ratio of the quasar lifetime to the total merger timescale as , if the two quasars light up at different, random times. This is consistent with the fraction of quasar pairs found in the SDSS (Hennawi et al., 2006), if and (for more details, see Foreman et al., 2009). At lower level of activity, Comerford et al. (2008) find that about 2% of early-type galaxies host candidate AGN pairs in the same galaxy.
Detecting sub-parsec binaries by imaging techniques is extremely difficult. However, the presence of SMBHBs in AGNs can be discovered spectroscopically, as double broad–line emission systems (see Gaskell (1996) and references therein). The two sets of broad emission lines originate in gas associated with the two SMBHs, and the velocity separation between the two emission line systems traces the projected orbital velocity of the binary. Dotti et al. (2008) and Bogdanovic et al. (2008) extended the pre–existent spectroscopical technique, discovering that, depending on the SMBH mass ratio, the AGN spectrum shows two sets of broad lines (equal mass binaries) or a single set of broad lines and two sets of narrow emission lines at different redshifts (unequal mass binaries). In the latter case, only one of the two SMBHs is active, and the two sets of narrow emission lines correspond to emission from low density gas in the potential well of the binary and from the “standard” narrow line region (NLR) of the AGN.
Dotti et al. (2008) and Bogdanovic et al. (2008) apply the binary model to the peculiar quasar SDSS J092712.65+294344.0. This quasar exhibits two distinct sets of lines. The first set of very narrow emission lines is assumed to be emitted in the NLR of the host and trace the redshift of the host galaxy (). The second set comprises two blue–shifted systems featuring different FWHM: the broad Mg II and Balmer emission lines with FWHM km s, and narrow lines with FWHM km s, both consistent with a redshift of 0.698. In this model, the source emitting the blue–shifted line system is gas inside or near the broad line region (BLR) of the secondary, comoving with the SMBH with a light-of-sight velocity of 2630 km s relative to the rest-frame of the host.
Boroson & Lauer (2009) developed a principal components analysis technique that identifies sources having peculiar spectral characteristics. They applied this procedure to the restframe optical spectrum of 17,500 quasars. Their sample comprises all quasars having from the fifth release of the SDSS Quasar Catalog (Schneider et al., 2007) plus all sources classified as quasars in the seventh SDSS data release. Of the 17,500 objects in their entire sample, only two objects have multiple redshift systems consistent with the presence of a candidate SMBHB, SDSS J092712.65+294344.0, and SDSS J153636.22+044127.0 (but see Chornok et al. 2009; Heckman et al., 2009; Shields et al., 2008; Wrobel & Laor, 2009; Gaskell, 2009).
In this paper we assess the expected number of merging SMBHBs based on realistic merger rates of SMBHs in hierarchical cosmologies, and determine an upper limit to sub-parsec binary quasars detectable as double broad-line emission quasars
2. Black hole merger rate and quasar activity
We trace the evolution of SMBHs within a plausible scenario for the hierarchical assembly, growth, and dynamics of SMBHs in a CDM cosmology. Our model has been shown to capture many features of the SMBH population (e.g., luminosity function of quasars, X–ray background, SMBH mass density). The main features of the models have been discussed elsewhere (Volonteri et al., 2003, 2005; Volonteri & Rees, 2006; Sesana et al., 2007b, and references therein). We summarize in the following the relevant assumptions.
SMBH “seeds” form at high redshift () in highly biased halos, corresponding to 3.5–4 peaks of the density fluctuation field (Volonteri et al., 2007). The initial SMBH occupation fraction is therefore low, but along the cosmic hierarchy SMBHs are incorporated into massive and massive systems, as galaxies grow in a CDM cosmology.
The occupation fraction of SMBHs increases with time, and approaches unity for massive galaxies at low redshift (Marulli et al., 2006; Volonteri et al., 2007). In our scheme, therefore, not all galaxy mergers lead to SMBH mergers, but only those involving two galaxies both hosting SMBHs. We further assume that SMBHs merge within the merger timescale of their hosts, which is a likely assumption for SMBH binaries formed after gas rich galaxy mergers (Escala et al., 2004, 2005; Dotti et al., 2006, 2007). This is the most likely scenario in the context of this work, as quasar fueling requires a substantial gas supply. We explored an alternative scenario where at late cosmic times SMBHBs shrink via three-body interactions, i.e., by capturing and ejecting at much higher velocities the stars passing by within a distance comparable to the binary separation (Merritt, 2006; Volonteri et al., 2003; Sesana et al., 2007a), and we found that the merger rate in the redshift range is very similar, as already found in previous tests (Sesana et al., 2005). Sesana et al. (2008) compare our theoretical merger rates with the merger rates inferred by observations of the fraction of close galaxy pairs (assuming that SMBH masses scale with bulge masses). Our SMBH merger rate is consistent Ð within a factor of 2 Ð with the merger rate of massive spheroidal found in Bell et al. (2006), who quote a factor of 2 uncertainty in their rate estimate.
We base our model for SMBH mass growth on a set of simple assumptions, supported by both simulations of AGN triggering and feedback (Springel et al., 2005), and analysis of the relationship between SMBH masses () and the properties of their hosts (Gebhardt et al., 2000; Ferrarese & Merritt, 2000; Ferrarese, 2002). SMBHs in galaxies undergoing a major merger (i.e. having a mass ratio ) undergo accretion. Each SMBH accretes an amount of mass, , that scales with the relation of its hosts (see Volonteri & Natarajan 2009). Accretion starts after a dynamical timescale and lasts until the SMBH has accreted .
The accretion rate during the active phase is derived from the empirical distribution of Eddington ratios, , found in Merloni & Heinz (2008). We adopt a fitting function of the Eddington ratio distribution as a function of SMBH mass and redshift (Merloni 2009). The distributions of Eddington ratios, , are computed in 10 redshift intervals (from to ) for 4 different mass bins (, , , ), and then fit with an analytic function which is the sum of a Schechter function and a log-normal. The Eddington ratio distributions are normalized so that at a given mass and redshift, . We adopt the bolometric corrections presented in Richards et al. (2006), and we correct for absorbed quasars according to model 4 in La Franca et al. (2005).
Our first check is on the cumulative number counts of quasars, regardless of binarity. We select all accreting SMBHs in our theoretical sample, and apply the same luminosity cut as in the SDSS Quasar Catalog, M. This choice is motivated by the SDSS being the largest quasar catalog currently available, however we stress here that our models provide upper limits to the number of observable binaries, in a complete volume limited sample. We compare our number counts to the expected number from the integration of the bolometric luminosity function of quasars (Hopkins et al., 2007) at M. The comparison is shown in the top panels of Fig. 1 (top histogram and dashed curve).
3. Sub-parsec binary quasars
To evaluate the expected number of binary quasars, we start from the SMBHB merger rate. Our theoretical models indicate which of these binaries are in an active phase, following a major merger. We initially analyze the complete sample of SMBHBs, that is, we consider all merging SMBHs, regardless of their activity status. This first model (model I) provides a strong upper limit to the number of theoretical sub-parsec binary quasars. To each SMBH in our sample we randomly assign an Eddington ratio, , from the normalized distribution (Merloni 2009). Note that, since for most masses/redshift this model does not allow for ‘quiescent’ SMBHs at, e.g., the level of Sgr A* (Quataert et al., 1999).
We further assume that only SMBHBs with a mass ratio, , above a certain threshold ( or ) create distinguishable double broad emission line systems. We regard as our best choice, because of an additional independent motivation, as follows. Callegari et al. (2008) study the formation of SMBHBs during galaxy mergers, and how SMBH pairing depends on the interplay between different physical processes (dynamical friction, tidal and ram–pressure stripping). From this analysis, Callegari et al. (2008) find that is the minimum mass ratio between two merging galaxies (and as a consequence between the two SMBHs) to guarantee the formation of a SMBHB. However, tidal and gas–pressure stripping can be reduced for extreme structural properties and orbital parameters of merging galaxies. We consider the very conservative case of SMBHBs with to take into account every possible merger configuration (e.g., plunging radial orbits).
Finally, we assign a lifetime to SMBH binaries detectable at sub-parsec separations following the detailed study of SMBHB dynamical evolution in circumbinary disks performed by Haiman et al. (2009). The lifetime corresponds to the time spent by the SMBHB at a separation such that the shift between the BLRs (or the NLR and the BLR) is a few thousand , becoming comparable with the widths of typical broad lines (Shen et al., 2008). Blending of profiles with smaller velocity differences would be missed (Gaskell, 1996). For , the typical separation is Schwarzschild radii, and for these conditions, Haiman et al. (2009) give a lifetime:
where , and we have chosen the longest residence time, thus providing an upper limit to SMBHBs lifetime.
The results of this model (model I) are shown in Fig. 1 (bottom panels). We find that at the total expected number of binaries with M per deg is for and for . These detectable binaries represent a fraction and respectively of the unabsorbed quasars. Within the sample of 17,500 sources analyzed by Boroson & Lauer (2009), 9895 objects, including the two putative binary SMBHs, belong to the uniformly selected statistical sample of SDSS quasars (Boroson, private communication). The statistical sample reaches a completeness larger than 90% at for sources with apparent magnitude , roughly corresponding to M at (Richards et al. 2002). Given these caveats, our results must be considered upper limits to the number of detectable sub-parsec binary quasars. We therefore find marginal agreement, within the uncertainties, with Boroson & Lauer (2009) findings111We have calculated the error by using the simple Poisson statistics, 1– confidence. The errors are lower limits given the small number statistics. See Gehrels (1986).. If binaries with do produce distinguishable double broad emission line systems, then the expected SMBHB merger rate must be lower than we predict. The high luminosity selection criterion leads to a sample composed of actively accreting () massive () SMBHs.
In a second model (model II) we select only SMBHBs where at least one of the SMBHs is active, according to our merger-driven quasar activity scheme. The results of this model are shown in the top panels of Fig. 1. In this case the expected number of binaries per deg is for and for . Detectable binaries represent a fraction of the unabsorbed quasars, consistent with Boroson & Lauer (2009) findings (a fraction ).
If we decrease the luminosity threshold we expect two factors enter into play: on the one hand, the merger rate of SMBHs is expected to increase at lower SMBH masses, where the mass function is less steep (Gültekin et al., 2009). This is indeed what we find in our models (Fig. 2; see also Dotti et al. 2009 and Sesana et al. 2005). On the other hand, however, the lifetime of detectable binaries decreases with decreasing mass (Haiman et al., 2009), making the detection harder. Using the scaling for lifetimes presented in Haiman et al. 2009, we indeed expect that the number of detectable sub-parsec binary quasars does not increase dramatically with decreasing luminosity, because of the shorter timescale over which they are observable. For instance, if we decrease the flux limit by a factor of ten, we find negligible changes in model II, and a mild increase in the number of binaries by a factor of 3 in model (I): for and for .
Stimulated by the recent putative discovery of two candidate sub-parsec SMBHBs identified as quasars with multiple redshift line systems (BLR and NRL), SDSS J092712.65+294344.0 and SDSS J153636.22+044127.0, we investigate theoretically the occurrence of sub-parsec SMBHBs that can be identified as sub-parsec binary quasars. We study the SMBH cosmic evolution via a Monte-Carlo merger tree approach. We trace the growth and dynamical history of SMBHs from high redshift via physically motivated prescriptions, that allow us to reproduce many observational constraints.
Our approach provides us with a catalog of SMBHBs, for which we know the masses and the redshift. We further assume that only SMBHBs with a mass ratio, , above a certain threshold ( or ) create distinguishable double broad emission line systems. Motivated by the work by Boroson & Lauer (2009), we apply to our theoretical sample the same luminosity cut as in the SDSS Quasar Catalog, M, thus deriving upper-limits to the fraction of detectable binaries. We stress here that the theoretical sample is complete and volume limited. Since the SDSS quasar catalog is not a complete sample (Schneider et al., 2007), a direct comparison with Boroson & Lauer (2009) is not appropriate. However, our results are consistent with the binary fraction derived for the subset of the 17,500 quasars used by Boroson & Lauer that are part of the statistical sample of the SDSS.
Our merger-driven quasar scheme provides us also with an accretion rate, hence a luminosity. We analyze two models that likely bracket the theoretical uncertainties. Model I ignores merger-driven quasar activity and we assume that each SMBH is at some level “active”. Each SMBH in our binary sample is assigned an Eddington ratio, , from the normalized distribution derived from synthesis model for AGN evolution (Merloni & Heinz, 2008). Model I is therefore our strong upper limit to the number of detectable SMBHBs. Model II is more rooted into our quasar activity scheme, as we select SMBHBs where at least one of the SMBHs is active, according to our merger-driven scenario.
Our main findings are as follows:
Sub-parsec binary quasars are intrinsically rare, due to a combination of strict requirements: the time over which SMBHB are detectable through line shifts decreases with decreasing binary mass. On the other hand, the merger rate of SMBHBs increases with increasing mass.
In a volume limited, complete sample of 10,000 sources at , our best models (II), that relate quasar activity to galaxy mergers, predict an upper limit of 5-10 sub-parsec binary quasars. Model I, that does not associate quasars to mergers, is only marginally compatible with Boroson & Lauer (2009) who find only 2 candidate sub-parsec binary quasars in the statistical SDSS quasar sample.
Fig. 1 extends our predictions out to . The number of detectable binaries increases by a factor from to .
The lifetime over which SMBHBs can be detected as sub-parsec quasars decreases with decreasing binary mass (Haiman et al., 2009). This effect is stronger than the increase in the merger rate of SMBHB at lower masses. Lowering the luminosity threshold is unlikely to lead to a large increase in the number of detectable sub-parsec binary quasars.
SDSS-III will increase the spectroscopic quasar sample and will provide a good testing ground for our predictions. The masses of SMBHBs that can be identified as sub-parsec binary quasars are too large for the gravitational waves emitted by these binaries to be detectable at merger by the Laser Interferometer Space Antenna (LISA), which will instead focus on the mass range . However, such massive binaries (in a later evolutionary stage, when the binary has shrunk by an additional factor of ten and the dynamical evolution is driven by emission of gravitational radiation) are typical candidates for detection via Pulsar Timing Arrays (PTAs, e.g. the Parkes radio-telescope). PTAs rely on the effect of gravitational waves on the propagation of radio signals from a pulsar to the Earth, producing a characteristic signature in the time of arrival of radio pulses. Sesana et al. (2008) find that the mass distribution of the SMBHBs detectable via PTAs peaks at , with most binaries at , the same mass range probed by sub-parsec binary quasars identifiable in the SDSS.
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