Subaru High-z Exploration of Low-luminosity Quasars (SHELLQs). XVIII. The Dark Matter Halo Mass of Quasars at z ∼ 6

Abstract

Abstract We present, for the first time, dark matter halo (DMH) mass measurement of quasars at z ∼ 6 based on a clustering analysis of 107 quasars. Spectroscopically identified quasars are homogeneously extracted from the Hyper Suprime-Cam Strategic Survey Program wide layer over 891 deg 2 . We evaluate the clustering strength by three different autocorrelation functions: projected correlation function, angular correlation function, and redshift–space correlation function. The DMH mass of quasars at z ∼ 6 is evaluated as <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mn>5.0</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>4.0</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>7.4</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo>×</mml:mo> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>12</mml:mn> </mml:mrow> </mml:msup> <mml:mspace width="0.25em"/> <mml:msup> <mml:mrow> <mml:mi>h</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:msub> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>⊙</mml:mo> </mml:mrow> </mml:msub> </mml:math> with the bias parameter b = 20.8 ± 8.7 by the projected correlation function. The other two estimators agree with these values; though, each uncertainty is large. The DMH mass of quasars is found to be nearly constant ∼10 12.5 h −1 M ⊙ throughout cosmic time, suggesting that there is a characteristic DMH mass where quasars are always activated. As a result, quasars appear in the most massive halos at z ∼ 6, but in less extreme halos thereafter. The DMH mass does not appear to exceed the upper limit of 10 13 h −1 M ⊙ , which suggests that most quasars reside in DMHs with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>M</mml:mi> <mml:mi>halo</mml:mi> </mml:msub> <mml:mo>&lt;</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>13</mml:mn> </mml:msup> <mml:mo> </mml:mo> <mml:msup> <mml:mi>h</mml:mi> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:msub> <mml:mi>M</mml:mi> <mml:mo>⊙</mml:mo> </mml:msub> </mml:math> across most of the cosmic time. Our results supporting a significant increasing bias with redshift are consistent with the bias evolution model with inefficient active galactic nucleus feedback at z ∼ 6. The duty cycle ( f duty ) is estimated as 0.019 ± 0.008 by assuming that DMHs in some mass interval can host a quasar. The average stellar mass is evaluated from stellar-to-halo mass ratio as <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>*</mml:mo> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:msubsup> <mml:mrow> <mml:mn>6.5</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>5.2</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>9.6</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo>×</mml:mo> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> </mml:msup> <mml:mspace width="0.25em"/> <mml:msup> <mml:mrow> <mml:mi>h</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:msub> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>⊙</mml:mo> </mml:mrow> </mml:msub> </mml:math> , which is found to be consistent with [C ii ] observational results.