Relativistic boost as the cause of periodicity in a massive black-hole binary candidate

Abstract

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...

Minidisks in Binary Black Hole Accretion

“…Minidisks are soft X-ray sources undergoing orbital motion at potentially relativistic velocities. In the Earth's frame, relativistic beaming will induce a periodic variation in each minidisk's emission that should be absent in the emission from the global circumbinary disk (D'Orazio et al 2015). Discriminating the minidisk emission from the circumbinary disk may be possible if the SED of the entire system has a "notch," as suggested in Roedig et al (2014).…”

Spectroscopic Indication of a Centi-Parsec Supermassive Black Hole Binary in the Galactic Center of Ngc 5548

“…One needs to carefully investigate the dynamics of accretion disks around binary black holes and the influences of the tidal torques (e.g., Liu & Shapiro 2010). On the other hand, recently D'Orazio et al (2015b) interpreted the periodicity of the light curve by relativistic Doppler boosting and successfully applied their model to the periodic light curve of PG1302-102 (Graham et al 2015b). For NGC5548, Doppler boosting is unimportant because the line-of-sight velocities of the binary are non-relativistic ( < -V c 10 ; 2 see Figure 10(b)).…”

A transition in circumbinary accretion discs at a binary mass ratio of 1:25

“…Accreting MBHBs below the critical mass ratio will prove difficult to detect in time-domain electromagnetic surveys due to accretion variability alone. For such low mass, steadily-accreting MBHBs, other mechanism could cause variability, such as a precessing jet, disc instabilities, or relativistic Doppler boost in the case of compact binaries (D'Orazio et al 2015b). Because of the drastic change in disc lopsidedness across the q = 0.04 transition, there may be an equally drastic change in the binary orbital parameters.…”