Spectroastrometry and Reverberation Mapping: The Mass and Geometric Distance of the Supermassive Black Hole in the Quasar 3C 273
Yanrong Li, Jian‐Min Wang, Yu-Yang Songsheng, Zhi-Xiang Zhang, Pu Du, Hu Chen, Ming Xiao
Abstract
Abstract The quasar 3C 273 has been observed with infrared spectroastrometry (SA) of the broad Pa α line and optical reverberation mapping (RM) of the broad H β line. SA delivers information about the angular size and structure of the Pa α broad-line region (BLR), while RM delivers information about the physical size and structure of the H β BLR. Based on the fact that the two BLRs share the mass of the supermassive black hole (SMBH) and viewing inclination, a combination of SA and velocity-resolved RM (SARM) thereby allows us to simultaneously determine the SMBH mass and geometric distance through dynamically modeling the two BLRs. We construct a suite of dynamical models with different geometric configurations and apply a Bayesian approach to obtain the parameter inferences. Overall the obtained masses and distances are insensitive to specific BLR configurations but more or less depend on parameterizations of the vertical distributions. The most probable model, chosen in light of the Bayes factor, yields an angular-size distance <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>log</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mrow> <mml:mi>D</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">A</mml:mi> </mml:mrow> </mml:msub> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:mi>Mpc</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>=</mml:mo> <mml:msubsup> <mml:mrow> <mml:mn>2.83</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.28</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.32</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> and an SMBH mass <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>log</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>•</mml:mo> </mml:mrow> </mml:msub> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:msub> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>⊙</mml:mo> </mml:mrow> </mml:msub> <mml:mo stretchy="false">)</mml:mo> <mml:mo>=</mml:mo> <mml:msubsup> <mml:mrow> <mml:mn>9.06</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.27</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.21</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> , which agree with the relationships between SMBH masses and bulge properties. The BLRs have an inclination of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mn>5</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> degrees, consistent with that of the large-scale jet in 3C 273. Our approach reinforces the capability of SARM analysis to measure SMBH masses and distances of active galactic nuclei and quasars even though SA and RM observations are undertaken with different emission lines and/or in different periods.