Detecting the orbital motion of nearby supermassive black hole binaries with Gaia

We show that a 10-yr Gaia mission could astrometrically detect the orbital motion of $\sim 1$ subparsec separation supermassive black hole binary in the heart of nearby, bright active galactic nuclei (AGN). Candidate AGN lie out to a redshift of $z=0.02$ and in the V-band magnitude range $10\lesssim m_V\lesssim 13$. The distribution of detectable binary masses peaks at a few times $\sim {10}^7{M}_{\odot }$ and is truncated above a few times $\sim {10}^8{M}_{\odot }$.

Figure 1

The number of AGN per V-band magnitude (left), log redshift (middle), and log binary mass (right) for four different populations. The dashed-black line shows all AGN. The teal-dashed line, labeled “Gaia-target” shows only the AGN for which the minimum Gaia-resolvable binary orbital period [Eq. (1)] is shorter than a 10-yr Gaia lifetime. The orange lines weight the Gaia-target distribution by the probability for finding an SBHB at the required orbital period (with $f_{\mathrm{bin}}=1$ and $\mathrm{SNR}=1$ for visualization). The dashed-orange lines show only those binaries with a $\ge 50\%$ detection rate ($\mathrm{SNR}\ge 2$). The gray histograms count known AGN with $m_V\le 16.0$ [66]. In the left panel, the purple dot-dashed line and corresponding right-vertical axis show the single-scan astrometric precision of Gaia.

Figure 2

Blue curve and left-bottom axes: the fraction of Gaia-detectable binaries vs maximum detectable orbital period $P_{\max }$ (for a total number referenced to $P_{\max }=20\mathrm{yr}$). Red curve and right-top axes: the fraction of Gaia-detectable binaries with orbital velocity of the secondary (mass ratio of 0.1) greater than the labeled x-axis value. The orbital velocity in units of the speed of light approximates the amplitude of modulations induced by the orbital Doppler boost.