287,872 Supermassive Black Holes Masses: Deep Learning Approaching Reverberation Mapping Accuracy

287,872 Supermassive Black Holes Masses: Deep Learning Approaching Reverberation Mapping Accuracy Yuhao Lu1a,b, HengJian SiTu2c, Jie Li3c, Yixuan Li4c,b, Yang Liu5a,b,d, Wenbin Lin6a,c,e and Yu Wang7f,b,e,g,∗ aSchool of Computer Science, University of South China, Hengyang, 421001, China bICRANet-AI, Brickell Avenue 701, Miami, FL 33131, USA cSchool of Mathematics and Physics, University of South China, Hengyang, 421001, China dDepartment of Physics E. Pancini, University Federico II, Naples, 80126, Italy eICRANet, Piazza della Repubblica 10, Pescara, 65122, Italy fICRA and Dipartimento di Fisica, Sapienza Università di Roma, P.le Aldo Moro 5, Rome, 00185, Italy gINAF – Osservatorio Astronomico d’Abruzzo, Via M. Maggini snc, Teramo, I-64100, Italy A R T I C L E I N F O Keywords: supermassive black holes quasars machine learning black hole mass estimation SDSS-RM A B S T R A C T We present a population-scale catalogue of 287,872 supermassive black hole masses with high accuracy. Using a deep encoder-decoder network trained on optical spectra with reverberation- mapping (RM) based labels of 849 quasars and applied to all SDSS quasars up to 𝑧= 4, our method achieves a root-mean-square error of 0.058 dex, a relative uncertainty of ≈14%, and coefficient of determination 𝑅2 ≈0.91 with respect to RM-based masses, far surpassing traditional single-line virial estimators. Notably, the high accuracy is maintained for both low (< 107.5 𝑀⊙) and high (> 109 𝑀⊙) mass quasars, where empirical relations are unreliable. 1. Introduction Supermassive black holes (SMBHs) with masses span- ning from roughly 105 𝑀⊙to 1010 𝑀⊙are commonly ob- served at the centers of most massive galaxies (Kormendy and Richstone, 1995; Ferrarese and Ford, 2005; Kormendy and Ho, 2013). Recent breakthroughs, particularly the Event Horizon Telescope’s imaging of the SMBH at the core of the elliptical galaxy M 87, have provided unprecedented direct observational evidence (Event Horizon Telescope Collabo- ration et al., 2019). It is now firmly established that SMBH masses are strongly correlated with the characteristics of their host galaxies, including bulge mass, stellar velocity dispersion, surface brightness, and luminosity (Ferrarese and Merritt, 2000; Merritt and Ferrarese, 2001; Häring and Rix, 2004; Saglia et al., 2016). These correlations appear to persist across both local and high-redshift galaxies (Graham and Scott, 2013; Schramm and Silverman, 2013; Izumi et al., 2019), suggesting a fundamental co-evolutionary link de- spite the vast difference in physical scales between SMBHs and their hosts (Hopkins et al., 2008; Schawinski et al., 2010; Izumi et al., 2019). Nevertheless, significant challenges remain, particularly in understanding how such massive black holes could have formed within the universe’s first billion years (Wu et al., 2015; Inayoshi et al., 2020). Current models suggest that SMBHs grow predominantly through gas accretion and galaxy mergers, releasing substantial energy that profoundly affects host galaxy evolution (Alexander and Hickox, 2012; Ciotti and Ostriker, 2007; Sijacki et al., 2007). ∗Corresponding author lwb@usc.edu.cn (W. Lin); yu.wang@icranet.org (Y. Wang) ORCID(s): Observationally, SMBHs manifest as active galactic nuclei (AGNs) or quasars, whose extreme luminosities offer key insights into accretion processes and black hole growth (Soltan, 1982). However, directly measuring SMBH masses remains challenging. Spectroscopic techniques, though widely used, are labor-intensive and have yielded only about one million estimates over the past two decades (Shen et al., 2011; Kelly and Shen, 2013). The advent of large-scale surveys such as the Vera C. Rubin Observatory’s Legacy Survey of Space and Time (LSST), expected to detect nearly 108 quasars (Ivezić et al., 2019), will require far more efficient and scalable mass estimation methods. Alternative approaches based on variability measurements in optical and X-ray bands show promise (McHardy et al., 2006; Burke et al., 2021), but are complicated by nonlinear physical dependencies and the massive data volumes involved. Mean- while, direct dynamical measurements of SMBH masses remain limited to only a small sample of nearby galaxies (Kuo et al., 2011; Kormendy and Ho, 2013; McConnell and Ma, 2013; Shankar et al., 2016, 2019). While classical machine learning techniques, such as symbolic regression, random forests, and photometric re- gressions, have contributed to early progress in black hole mass estimation by extending traditional scaling relations (Jin and Davis, 2023; He et al., 2022), their performance remains fundamentally constrained by shallow architectures and limited feature representations. In contrast, deep learn- ing approaches have shown greater promise in capturing the non-linear dependencies inherent in high-dimensional astrophysical data. For instance, variability-based models such as AGNet achieve a scatter of approximately 0.37 dex Lu et al.: Preprint sub

This content is AI-processed based on open access ArXiv data.