Black Hole Mass Estimates and Rapid Growth of Supermassive Black Holes in Luminous $z \sim$ 3.5 Quasars

TL;DR

This study uses near-infrared spectroscopy to estimate black hole masses in luminous quasars at z~3.5, confirming MgII as a reliable proxy for Hβ, and demonstrates rapid black hole growth consistent with cosmic timescales.

Contribution

It provides new near-IR measurements of Hβ and MgII lines in high-redshift quasars, validating MgII as a substitute for Hβ in black hole mass estimates and analyzing their growth within cosmic time.

Findings

MgII FWHM correlates well with Hβ FWHM.

High-redshift quasars host supermassive black holes (~10^9 to 10^10 solar masses).

Quasars can grow their black holes within the age of the universe at z~3.5.

Abstract

We present new near-infrared (IR) observations of the H$\beta\ \lambda4861$ and MgII $\lambda2798$ lines for 32 luminous quasars with $3.2<z<3.9$ using the Palomar Hale 200 inch telescope and the Large Binocular Telescope. We find that the MgII Full Width at Half Maximum (FWHM) is well correlated with the H$\beta$ FWHM, confirming itself as a good substitute for the H$\beta$ FWHM in the black hole mass estimates. The continuum luminosity at 5100 \AA\ well correlates with the continuum luminosity at 3000 \AA\ and the broad emission line luminosities (H$\beta$ and MgII). With simultaneous near-IR spectroscopy of the H$\beta$ and MgII lines to exclude the influences of flux variability, we are able to evaluate the reliability of estimating black hole masses based on the MgII line for high redshift quasars. With the reliable H$\beta$ line based black hole mass and Eddington ratio estimates, we find that the $z\sim3.5$ quasars in our sample have black hole masses $1.90\times10^{9} M_{\odot} \lesssim M_{\rm BH} \lesssim 1.37\times10^{10} M_{\odot}$, with a median of $\sim 5.14\times10^{9} M_{\odot}$ and are accreting at Eddington ratios between 0.30 and 3.05, with a median of $\sim1.12$. Assuming a duty cycle of 1 and a seed black hole mass of $10^{4} M_{\odot}$, we show that the $z\sim3.5$ quasars in this sample can grow to their estimated black hole masses within the age of the Universe at their redshifts.