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> </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> </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> </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> </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> </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> ...