Preliminary cosmological results using extreme accretors Quasar formalism

Technical Summary: Preliminary Cosmological Results Using Extreme Accretors Quasar Formalism

Problem Statement
The standard cosmological model ($\Lambda$CDM) faces significant challenges, most notably the "Hubble tension" (discrepancies in $H_0$ measurements) and the $S_8$ amplitude of matter fluctuations. While Type Ia Supernovae (SNIa) provide precise constraints at low redshifts, they lack coverage at high redshifts ($z > 1$). Quasars offer a potential solution for probing these higher distances, but their utility as standard candles has been historically limited by a large intrinsic dispersion in luminosity and sample heterogeneity. This paper addresses the need for a standardized, homogeneous quasar sample capable of constraining cosmological parameters with precision comparable to SNIa, specifically to test the $\Lambda$CDM model against dynamical dark energy scenarios ($w$CDM and $w_0w_a$CDM).

Methodology
The authors compile and standardize a sample of "extreme accretor" quasars (xA), which are objects radiating near the Eddington limit. The selection relies on the Eigenvector 1 (E1) formalism, utilizing the 4DE1 parameter space to isolate objects with specific physical conditions:

• Low-$z$ ($z \lesssim 0.8$): Selection based on $FWHM(H\beta) < 4000$ km s$^{-1}$ and strong FeII emission ($R_{FeII} > 1$).
• High-$z$ ($z \gtrsim 2$): Selection based on UV line ratios ($CIII]/SiIII] > 1$ and $AlIII/SiIII] > 0.5$).

The luminosity of these objects is derived spectroscopically, assuming the Broad Line Region (BLR) is virialized and the objects radiate at a limiting Eddington ratio ($L/L_{Edd} \sim 1$). The luminosity is approximated as $L \propto FWHM^4$, allowing the calculation of a distance modulus ($\mu$) purely from spectroscopic quantities.

The final curated sample comprises 266 objects spanning $z = 0.06$ to $z \sim 7.5$. The authors perform a Bayesian analysis using Markov Chain Monte Carlo (MCMC) methods (NAUTILUS algorithm) to constrain parameters for three models:

1. $\Lambda$CDM: Fixed dark energy equation of state ($w = -1$).
2. $w$CDM: Constant dark energy equation of state ($w_0$).
3. $w_0w_a$CDM (CPL): Redshift-dependent dark energy ($w(z) = w_0 + w_a z/(1+z)$).

To ensure robustness, the xA sample is analyzed both in isolation and in combination with external probes: Pantheon+ SNIa, Cosmic Chronometers (CC), CMB distance priors (Planck), Reverberation Mapping (nRL), UV-X non-linear relation (nUVX), and Angular Distance measurements (Angular QSO).

Key Results

• Hubble Constant ($H_0$):

  • Using the xA sample alone within the $\Lambda$CDM framework, the authors derive $H_0 = 68.8 \pm 2.2$ km s$^{-1}$ Mpc$^{-1}$.
  • When combined with SNIa, CC, and CMB priors ("Base" combination), the constraint tightens to $H_0 = 69.0 \pm 0.9$ km s$^{-1}$ Mpc$^{-1}$.
  • In the $w$CDM and $w_0w_a$CDM models, the xA sample alone yields higher central values ($H_0 \approx 75-76$ km s$^{-1}$ Mpc$^{-1}$) with significantly larger uncertainties, showing consistency with SH0ES measurements but with low precision.

• Dark Energy Dynamics:

  • When the xA sample is analyzed in isolation, there is a weak Bayesian preference for dynamical dark energy models over $\Lambda$CDM (negative Bayes factors).
  • However, this preference vanishes when the xA sample is combined with the "Base" datasets (SNIa + CC + CMB). The combined analysis yields strong Bayesian evidence favoring the standard $\Lambda$CDM model (positive Bayes factors, e.g., $\ln B_{ij} = +3.04$ for $w_0w_a$CDM).

• Comparative Analysis:

  • The study compares xA results with other AGN-based methods (nRL, nUVX, Angular QSO). While some individual quasar samples show preferences for dynamical dark energy or high $H_0$, these trends generally disappear or become consistent with $\Lambda$CDM when combined with standard probes.
  • The nUVX sample, for instance, shows significant tension with CMB priors when used alone but converges to consensus values when combined with the Base dataset.

Significance and Claims
The paper concludes that while the xA formalism provides a viable path to high-redshift cosmology, significant intrinsic dispersion remains a critical limitation across all quasar samples. This dispersion prevents tight constraints on complex dynamical dark energy models when the quasar data is used in isolation.

The authors assert that the apparent deviations from $\Lambda$CDM (such as preferences for $w \neq -1$ or high $H_0$) observed in some quasar-only analyses are likely artifacts of systematic uncertainties and sample dispersion rather than evidence of new physics. The robustness of the $\Lambda$CDM model is reinforced when quasar data is combined with established probes.

The paper emphasizes that establishing xA and other AGN samples as precise cosmological tools requires:

1. Reducing intrinsic dispersion through better physical understanding of accretion conditions and BLR structure.
2. Filling observational gaps in the redshift ranges $1 < z < 2$ and $z > 3$.
3. Developing a full physical and dynamical model for the core regions of black holes to better constrain the luminosity-distance relation.

Ultimately, the work presents the xA sample as a promising but currently "tentative" cosmological probe, highlighting that overcoming systematic errors is the key prerequisite for resolving cosmological tensions using quasars.