Can quasars, triggered by mergers, account for NANOGrav’s stochastic gravitational wave background?

Abstract The stochastic gravitational wave (GW) background recently discovered by several pulsar timing array experiments is consistent with arising from a population of coalescing super-massive black hole binaries. The amplitude of the background is somewhat higher than expected in most previous population models or from the local mass density observations. Such binaries are expected to be produced in galaxy mergers, which are also thought to trigger bright quasar activity. Under the assumptions that (i) a fraction <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>f</mml:mi> <mml:mrow> <mml:mrow> <mml:mi>bin</mml:mi> </mml:mrow> </mml:mrow> </mml:msub> <mml:mo>∼</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> of all quasars are associated with mergers, (ii) the typical quasar lifetime is <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>t</mml:mi> <mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">Q</mml:mi> </mml:mrow> </mml:mrow> </mml:msub> <mml:mo>∼</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>8</mml:mn> </mml:msup> <mml:mtext> </mml:mtext> <mml:mtext>yr</mml:mtext> </mml:mrow> </mml:math> , and (iii) adopting Eddington ratios <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>f</mml:mi> <mml:mrow> <mml:mrow> <mml:mi>Edd</mml:mi> </mml:mrow> </mml:mrow> </mml:msub> <mml:mo>∼</mml:mo> <mml:mn>0.25</mml:mn> </mml:mrow> </mml:math> for the luminosity of quasars, we compute the GW background associated directly with the empirically measured quasar luminosity function. This approach bypasses the need to model the cosmological evolution of black holes or galaxy mergers from simulations or semi-analytical models. We find the amplitude matching the value measured by NANOGrav. Our results are consistent with most quasars being associated with black hole binaries and being the sources of the GW background, and imply a joint constraint on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>t</mml:mi> <mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">Q</mml:mi> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>f</mml:mi> <mml:mrow> <mml:mrow> <mml:mi>Edd</mml:mi> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> and the typical mass ratio <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>q</mml:mi> <mml:mo>≡</mml:mo> <mml:msub> <mml:mi>M</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:msub> <mml:mi>M</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:mrow> </mml:math> . The signal in this case would be dominated by relatively distant <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mo>∼</mml:mo> </mml:mrow> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>9</mml:mn> </mml:msup> <mml:mrow> <mml:msub> <mml:mi mathvariant="normal">M</mml:mi> <mml:mo>⊙</mml:mo> </mml:msub> </mml:mrow> </mml:mrow> </mml:math> sources at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>z</mml:mi> <mml:mo>≈</mml:mo> <mml:mn>2</mml:mn> <mml:mo>−</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:math> , at the peak of quasar activity. Similarly to other models, our results remain in tension with the local super-massive black hole mass density.