On the Connection between Supermassive Black Holes and Galaxy Growth in the Reionization Epoch

<jats:title>Abstract</jats:title> <jats:p>The correlation between the mass of supermassive black holes (SMBHs; <jats:inline-formula> <jats:tex-math> <?CDATA ${{ \mathcal M }}_{\mathrm{BH}}$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi mathvariant="italic"></mml:mi> </mml:mrow> <mml:mrow> <mml:mi>BH</mml:mi> </mml:mrow> </mml:msub> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjlac6de8ieqn1.gif" xlink:type="simple" /> </jats:inline-formula>) and their host galaxies (<jats:inline-formula> <jats:tex-math> <?CDATA ${{ \mathcal M }}_{\star }$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi mathvariant="italic"></mml:mi> </mml:mrow> <mml:mrow> <mml:mo>⋆</mml:mo> </mml:mrow> </mml:msub> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjlac6de8ieqn2.gif" xlink:type="simple" /> </jats:inline-formula>) in the reionization epoch provides valuable constraints on their early growth. High-redshift quasars typically have an <jats:inline-formula> <jats:tex-math> <?CDATA ${{ \mathcal M }}_{\mathrm{BH}}$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi mathvariant="italic"></mml:mi> </mml:mrow> <mml:mrow> <mml:mi>BH</mml:mi> </mml:mrow> </mml:msub> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjlac6de8ieqn3.gif" xlink:type="simple" /> </jats:inline-formula>/<jats:inline-formula> <jats:tex-math> <?CDATA ${{ \mathcal M }}_{\star }$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi mathvariant="italic"></mml:mi> </mml:mrow> <mml:mrow> <mml:mo>⋆</mml:mo> </mml:mrow> </mml:msub> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjlac6de8ieqn4.gif" xlink:type="simple" /> </jats:inline-formula> ratio significantly elevated in comparison to the local value. However, the degree to which this apparent offset is driven by observational biases is unclear for the most distant quasars. To address this issue, we model the sample selection and measurement biases for a compilation of 20 quasars at <jats:italic>z</jats:italic> ∼ 6 with host properties based on ALMA observations. We find that the observed distribution of quasars in the <jats:inline-formula> <jats:tex-math> <?CDATA ${{ \mathcal M }}_{\mathrm{BH}}\mbox{--}{{ \mathcal M }}_{\star }$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi mathvariant="italic"></mml:mi> </mml:mrow> <mml:mrow> <mml:mi>BH</mml:mi> </mml:mrow> </mml:msub> <mml:mo>–</mml:mo> <mml:msub> <mml:mrow> <mml:mi mathvariant="italic"></mml:mi> </mml:mrow> <mml:mrow> <mml:mo>⋆</mml:mo> </mml:mrow> </mml:msub> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjlac6de8ieqn5.gif" xlink:type="simple" /> </jats:inline-formula> plane can be reproduced by assuming that the underlying SMBH population at <jats:italic>z</jats:italic> ∼ 6 follows the relationship in the local universe. However, a positive or even a negative evolution in <jats:inline-formula> <jats:tex-math> <?CDATA ${{ \mathcal M }}_{\mathrm{BH}}$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi mathvariant="italic"></mml:mi> </mml:mrow> <mml:mrow> <mml:mi>BH</mml:mi> </mml:mrow> </mml:msub> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjlac6de8ieqn6.gif" xlink:type="simple" /> </jats:inline-formula>/<jats:inline-formula> <jats:tex-math> <?CDATA ${{ \mathcal M }}_{\star }$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi mathvariant="italic"></mml:mi> </mml:mrow> <mml:mrow> <mml:mo>⋆</mml:mo> </mml:mrow> </mml:msub> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjlac6de8ieqn7.gif" xlink:type="simple" /> </jats:inline-formula> can also explain the data, depending on whether the intrinsic scatter evolves and on the strength of various systematic uncertainties. To break these degeneracies, an improvement in the accuracy of mass measurements and an expansion of the current sample to lower <jats:inline-formula> <jats:tex-math> <?CDATA ${{ \mathcal M }}_{\mathrm{BH}}$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi mathvariant="italic"></mml:mi> </mml:mrow> <mml:mrow> <mml:mi>BH</mml:mi> </mml:mrow> </mml:msub> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjlac6de8ieqn8.gif" xlink:type="simple" /> </jats:inline-formula> limits are needed. Furthermore, assuming a radiative efficiency of 0.1 and quasar duty cycles estimated from the active SMBH fraction, significant outliers in <jats:inline-formula> <jats:tex-math> <?CDATA ${{ \mathcal M }}_{\mathrm{BH}}$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi mathvariant="italic"></mml:mi> </mml:mrow> <mml:mrow> <mml:mi>BH</mml:mi> </mml:mrow> </mml:msub> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjlac6de8ieqn9.gif" xlink:type="simple" /> </jats:inline-formula>/<jats:inline-formula> <jats:tex-math> <?CDATA ${{ \mathcal M }}_{\star }$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi mathvariant="italic"></mml:mi> </mml:mrow> <mml:mrow> <mml:mo>⋆</mml:mo> </mml:mrow> </mml:msub> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjlac6de8ieqn10.gif" xlink:type="simple" /> </jats:inline-formula> tend to move toward the local relation given their instantaneous BH growth rate and star formation rate. This may provide evidence for a self-regulated SMBH–galaxy coevolution scenario that is in place at <jats:italic>z</jats:italic> ∼ 6, with active galactic nucleus feedback being a possible driver.</jats:p>