A near-equal-mass binary black hole can clear a central cavity in a circumbinary accretion disc; however, previous works have revealed accretion streams entering this cavity. Here we use 2D hydrodynamical simulations to study the accretion streams and their periodic behavior. In particular, we perform a suite of simulations, covering different binary mass ratios q = M 2 /M 1 in the range 0.003 q 1. In each case, we follow the system for several thousand binary orbits, until it relaxes to a stable accretion pattern. We find the following results: (i) The binary is efficient in maintaining a low-density cavity. However, the time-averaged mass accretion rate into the cavity, through narrow coherent accretion streams, is suppressed by at most a factor of a few compared to a disc with a single BH with the same mass; (ii) for q ∼ > 0.05, the accretion rate is strongly modulated by the binary, and depending on the precise value of q, the power spectrum of the accretion rate shows either one, two, or three distinct periods; and (iii) for q ∼ < 0.05, the accretion rate becomes steady, with no time-variations. Most binaries produced in galactic mergers are expected to have q ∼ > 0.05. If the luminosity of these binaries tracks their accretion rate, then a periodogram of their light-curve could help in their identification, and to constrain their mass ratio and disc properties.

Because most large galaxies contain a central black hole, and galaxies often merge 1 , blackhole binaries are expected to be common in galactic nuclei 2 . Although they cannot be imaged, periodicities in the light curves of quasars have been interpreted as evidence for binaries [3][4][5] , most recently in PG 1302-102, with a short rest-frame optical period of 4 yr 6 . If the orbital period matches this value, then for the range of estimated black hole masses the components would be separated by 0.007-0.017 pc, implying relativistic orbital speeds. There has been much debate over whether black hole orbits could be smaller than 1 pc 7 . Here we show that the amplitude and the sinusoid-like shape of the variability of PG 1302-102 can be fit by relativistic Doppler boosting of emission from a compact, steadily accreting, unequal-mass binary. We predict that brightness variations in the ultraviolet light curve track those in the optical, but with a 2-3 times larger amplitude. This prediction is relatively insensitive to the details of the emission process, and is consistent with archival UV data. Follow-up UV and optical observations in the next few years can test this prediction and confirm the existence of a binary black hole in the relativistic regime.Assuming PG 1302-102 is a binary, it is natural to attribute its optical emission to gas that is bound to each black hole, forming circumprimary and circumsecondary accretion flows. Such flows, forming "minidisks", are generically found in high-resolution 2D and 3D hydrodynamical simulations that include the black holes in their simulated domain [8][9][10][11][12][13][14][15] . Assuming a circular orbit, the velocity of the lower-mass secondary black hole isor ∼ 0.03c for the fiducial parameters above, where M = M 1 + M 2 is the total binary mass, M 1,2 are the individual masses, q = M 2 /M 1 ≤ 1 is the mass ratio, P is the orbital period, and c is the speed of light. The primary's orbital velocity is v 1 = qv 2 . Even if a minidisk has a steady intrinsic rest-frame luminosity, its apparent flux on Earth is modulated by relativistic Doppler beaming. The photon frequencies suffer relativistic Doppler shift by the factor D = [Γ(1 − β || )] −1 , where Γ = (1 − β 2 ) −1/2 is the Lorentz factor, β = v/c is the three-dimensional velocity v in units of the speed of light, and β || = β cos φ sin i is the component of the velocity along the line of sight, with i and φ the orbital inclination and phase. Because the photon phase-space density ∝ F ν /ν 3 is invariant in special relativity, the apparent flux F ν at a fixed observed frequency ν is modified from the flux of 1 arXiv:1509.04301v1 [astro-ph.HE] 14 Sep 2015The last step assumes an intrinsic power-law spectrum F 0 ν ∝ ν α . To first order in v/c, this causes a sinusoidal modulation of the apparent flux along the orbit, by a fractional amplitude ∆F ν /F ν = ±(3 − α)(v cos φ/c) sin i. Although lighttravel time modulations appear at the same order, they are subdominant to the Doppler modulation. This modulation is analogo...

Most standard descriptions of Type II migration state that massive, gap-opening planets must migrate at the viscous drift rate. This is based on the idea that the disk is separated into an inner and outer region and gas is considered unable to cross the gap. In fact, gas easily crosses the gap on horseshoe orbits, nullifying this necessary premise which would set the migration rate. In this work, it is demonstrated using highly accurate numerical calculations that the actual migration rate is dependent on disk and planet parameters, and can be significantly larger or smaller than the viscous drift rate. In the limiting case of a disk much more massive than the secondary, the migration rate saturates to a constant which is sensitive to disk parameters and is not necessarily of order viscous rate. In the opposite limit of a low-mass disk, the migration rate decreases linearly with disk mass. Steady-state solutions in the low disk mass limit show no pile-up outside the secondary's orbit, and no corresponding drainage of the inner disk.

Using numerical hydrodynamics calculations and a novel method for densely sampling parameter space, we measure the accretion and torque on a binary system from a circumbinary disk. In agreement with some earlier studies, we find that the net torque on the binary is positive for mass ratios close to unity, and that accretion always drives the binary toward equal mass. Accretion variability depends sensitively on the numerical sink prescription, but the torque and relative accretion onto each component do not depend on the sink timescale. Positive torque and highly variable accretion occurs only for mass ratios greater than around 0.05. This means that for mass ratios below 0.05, the binary would migrate inward until the secondary accreted sufficient mass, after which it would execute a U-turn and migrate outward. We explore a range of viscosities, from α = 0.03 to α = 0.15, and find that this outward torque is proportional to the viscous torque, so that torque per unit accreted mass is independent of α. Dependence of accretion and torque on mass ratio is explored in detail, densely sampling mass ratios between 0.01 and unity. For mass ratio q > 0.2, accretion variability is found to exhibit a distinct sawtooth pattern, typically with a five-orbit cycle that provides a smoking gun prediction for variable quasars observed over long periods, as a potential means to confirm the presence of a binary.

We study circumbinary accretion discs in the framework of the restricted three-body problem (R3Bp) and via numerically solving the height-integrated equations of viscous hydrodynamics. Varying the mass ratio of the binary, we find a pronounced change in the behaviour of the disc near mass ratio q ≡ M s /M p ∼ 0.04. For mass ratios above q = 0.04, solutions for the hydrodynamic flow transition from steady, to stronglyfluctuating; a narrow annular gap in the surface density around the secondary's orbit changes to a hollow central cavity; and a spatial symmetry is lost, resulting in a lopsided disc. This phase transition is coincident with the mass ratio above which stable orbits do not exist around the L4 and L5 equilibrium points of the R3B problem. Using the DISCO code, we find that for thin discs, for which a gap or cavity can remain open, the mass ratio of the transition is relatively insensitive to disc viscosity and pressure. The q = 0.04 transition has relevance for the evolution of massive black hole binary+disc systems at the centers of galactic nuclei, as well as for young stellar binaries and possibly planets around brown dwarfs. INTRODUCTIONBinaries embedded in gas discs are ubiquitous astrophysical systems. They are realized in the proto-planetary nebulae surrounding young stars and their growing planets (Kley & Nelson 2012) and possibly in young binary star systems as evidenced by circumbinary planets (e.g. Orosz et al. 2012). They also arise at the centers of galactic nuclei to which gas can be funneled to accompany an inspiraling massive black hole binary (MBHB) (Barnes & Hernquist 1996, and see recent reviews by Dotti et al. (2012);Mayer (2013)).Understanding the long-term evolution of the binary+disc system is complicated by the coupled nature of mass, angular momentum, and energy conservation for the total binary+disc system. The binary affects the structure of the disc, and the disc alters the orbital parameters of the binary. For planets and stars enveloped by a gas disc, the binary+disc interaction determines the migration and growth of the planets, dictating the post-disc-configuration of the planetary system. For a MBHB+disc system, gas torques can alter the inspiral rate of the binary. The effect is important for deciphering the final parsec problem and predicting the rate of gravitational wave events due to MBHB mergers (Begelman et al. 1980 Additionally, interaction of the binary and disc can lead to periodic accretion (Hayasaki et al. 2007;MacFadyen & Milosavljević 2008;Cuadra et al. 2009;Roedig et al. 2011;Noble et al. 2012;Shi et al. 2012;Roedig et al. 2012;D'Orazio et al. 2013;Farris et al. 2014;Dunhill et al. 2015;Shi & Krolik 2015) which can aid in identifying MBHB candidates in electromagnetic (EM) surveys (Haiman et al. 2009). As has been recently been made clear by the discovery of multiple MBHB candidates in EM time-domain surveys (Graham et al. 2015b,a;Liu et al. 2015), the interpretation of variability in EM surveys will rely heavily on our knowledge of how accretion ...

We show that nearly half of all binary black hole (BBH) mergers dynamically assembled in globular clusters have measurable eccentricities (e > 0.01) in the LISA band (10 −2 Hz), when General Relativistic corrections are properly included in the N-body evolution. If only Newtonian gravity is included, the derived fraction of eccentric LISA sources is significantly lower, which explains why recent studies all have greatly underestimated this fraction. Our findings have major implications for how to observationally distinguish between BBH formation channels using eccentricity with LISA, which is one of the key science goals of the mission. We illustrate that the relatively large population of eccentric LISA sources reported here originates from BBHs that merge between hardening binary-single interactions inside their globular cluster. These results indicate a bright future for using LISA to probe the origin of BBH mergers.

Supermassive black hole binaries (SMBHBs) should be common in galactic nuclei as a result of frequent galaxy mergers. Recently, a large sample of sub-parsec SMBHB candidates was identified as bright periodically variable quasars in optical surveys. If the observed periodicity corresponds to the redshifted binary orbital period, the inferred orbital velocities are relativistic (v/c ≈ 0.1). The optical and UV luminosities are expected to arise from gas bound to the individual BHs, and would be modulated by the relativistic Doppler effect. The optical and UV light curves should vary in tandem with relative amplitudes which depend on the respective spectral slopes. We constructed a control sample of 42 quasars with aperiodic variability, to test whether this Doppler colour signature can be distinguished from intrinsic chromatic variability. We found that the Doppler signature can arise by chance in ∼20% (∼37%) of quasars in the nUV (fUV) band. These probabilities reflect the limited quality of the control sample and represent upper limits on how frequently quasars mimic the Doppler brightness+colour variations. We performed separate tests on the periodic quasar candidates, and found that for the majority, the Doppler boost hypothesis requires an unusually steep UV spectrum or an unexpectedly large BH mass and orbital velocity. We conclude that at most ∼1/3rd of these periodic candidates can harbor Doppler-modulated SMBHBs.

The coalescence of a compact object with a 10 4 − 10 7 M supermassive black hole (SMBH) produces mHz gravitational waves (GWs) detectable by the future Laser Interferometer Space Antenna (LISA). If such an inspiral occurs in the accretion disc of an active galactic nucleus (AGN), the gas torques imprint a small deviation in the GW waveform. Here we present two-dimensional hydrodynamical simulations with the moving-mesh code DISCO of a BH inspiraling at the GW rate in a binary system with a mass ratio q = M 2 /M 1 = 10 −3 , embedded in an accretion disc. We assume a locally isothermal equation of state for the gas (with Mach number M = 20) and implement a standard α-prescription for its viscosity (with α = 0.03). We find disc torques on the binary that are weaker than in previous semi-analytic toy models, and are in the opposite direction: the gas disc slows down, rather than speeds up the inspiral. We compute the resulting deviations in the GW waveform, which scale linearly with the mass of the disc. The SNR of these deviations accumulates mostly at high frequencies, and becomes detectable in a 5-year LISA observation if the total phase shift exceeds a few radians. We find that this occurs if the disc surface density exceeds Σ 0 10 2−3 g cm −2 , as may be the case in thin discs with near-Eddington accretion rates. Since the characteristic imprint on the GW signal is strongly dependent on disc parameters, a LISA detection of an intermediate mass ratio inspiral would probe the physics of AGN discs and migration.If a coalescing compact BH binary encounters a sufficient amount of gas, it will experience a gravitational torque that can act to either accelerate or hinder a GW-driven inspiral. The presence of gas also provides the opportunity for