Assembly bias and local Primordial non-Gaussianity from DESI DR1 Quasars

1. Problem Statement

The paper addresses a critical degeneracy in constraining local Primordial Non-Gaussianity (PNG), parameterized by $f_{\text{NL}}$, using large-scale structure (LSS) surveys like the Dark Energy Spectroscopic Instrument (DESI).

• The Physics: Local PNG induces a scale-dependent bias in the clustering of dark matter halos and tracers (like quasars). The amplitude of this bias is proportional to the product $f_{\text{NL}} b_\phi$, where $b_\phi$ is the response of tracer number density to large-scale potential fluctuations.
• The Degeneracy: Current analyses cannot separate $f_{\text{NL}}$ from $b_\phi$ without an external prior on $b_\phi$.
• The Unknown Parameter: The standard theoretical prediction for $b_\phi$ relies on the "universality relation":
  $$b_\phi = 2\delta_c(b_1 - p)$$
  where $b_1$ is the linear bias, $\delta_c \approx 1.686$, and $p$ is a parameter describing the assembly bias.
  • Standard Assumption: For mass-selected halos, $p=1$.
  • Quasar Specifics: Quasars (QSOs) are believed to reside in halos undergoing recent major mergers. Previous work suggested $p=1.6$ for such halos.
• The Issue: DESI Data Release 1 (DR1) analysis had to assume either $p=1$ or $p=1.6$, resulting in two separate, degenerate constraints on $f_{\text{NL}}$. There was no physically motivated, data-driven prior for $p$ specific to the DESI quasar selection, leaving the true value of $f_{\text{NL}}$ unconstrained.

2. Methodology

The authors developed a robust, simulation-based prior for the assembly bias parameter $p$ by combining hydrodynamical simulations with the extended Press-Schechter (ePS) formalism.

A. Theoretical Framework

• ePS Formalism: They utilized the extended Press-Schechter theory to model the conditional mass function $P(z_f|M)$, linking halo formation redshift ($z_f$) to the parameter $p$.
• Variable $\omega_f$: They introduced a variable $\omega_f$ (dependent on formation redshift, halo mass, and cosmology) to parameterize assembly bias.
• Derivation: Using the analytical expression for the conditional mass function, they derived an explicit relation for $p$ as a function of $\omega_f$ (Eq. 2.4). This allows $p$ to be calculated directly from the merger history of a halo.

B. Simulation Analysis: IllustrisTNG

• Sample Construction: Using the TNG300-1 hydrodynamical simulation, they constructed a "DESI-like" quasar sample at redshift $z \approx 1.5$.
  • Selection Criteria: Halos with mass $M > 10^{12.2} h^{-1}M_\odot$.
  • Quasar Identification: They selected black holes (BHs) with high Eddington ratios ($\chi > 0.1$), representing the most luminous, actively accreting quasars.
  • Control Sample: A mass-matched sample of halos with random formation histories was created to isolate the effect of merger history.
• Calculation: For each selected quasar host, they traced the merger tree to determine the formation redshift ($z_f$) and calculated the corresponding $p$ value using the ePS prediction.

C. Robustness Checks

1. Selection Noise: They tested the stability of the $p$ distribution by introducing stochasticity into the quasar selection (randomly replacing up to 34% of the sample). The mean $\bar{p}$ remained stable.
2. CAMELS Validation: To quantify dependence on subgrid physics and cosmic variance, they utilized the CAMELS simulation suite:
   • CV Set: 26 realizations with different initial conditions (testing cosmic variance).
   • 1P Set: 36 realizations varying 9 astrophysical parameters related to AGN feedback and BH growth (testing model dependence).

3. Key Contributions

• Physically Motivated Prior: The paper moves beyond arbitrary assumptions ($p=1$ or $p=1.6$) by deriving a probability distribution $\Pi(p)$ based on the actual merger history of quasar-hosting halos in state-of-the-art hydrodynamical simulations.
• Breaking the Degeneracy: By providing a robust prior for $p$, the authors break the degeneracy between $f_{\text{NL}}$ and $b_\phi$, allowing for a single, unified constraint on primordial non-Gaussianity.
• Validation of Assembly Bias: The study confirms that the enhanced $p$ value is driven by the merger history of quasar hosts (recent mergers) rather than halo mass alone, and that this result is robust against variations in astrophysical feedback models.

4. Key Results

• Distribution of $p$:
  • The DESI-like quasar sample in IllustrisTNG yields a distribution of $p$ skewed toward higher values, with a mean $\bar{p} \simeq 1.41$ at $z \approx 1.5$.
  • The control (random) sample yields $\bar{p} \approx 0.99$, confirming the universality relation for mass-selected halos.
  • The quasar sample sits between the universality limit ($p=1$) and the "recent merger" limit ($p=1.6$).
• Robustness:
  • Selection Effects: The mean $\bar{p}$ is stable even with significant selection noise (34% replacement).
  • Astrophysics: In CAMELS-1P, varying AGN feedback parameters shifts the mean only slightly to $\bar{p} \simeq 1.38$.
  • Cosmic Variance: The CAMELS-CV set shows a negligible impact of cosmic variance.
  • Redshift Dependence: The dependence of $\bar{p}$ on redshift is weak across the relevant range ($z \sim 1.5 - 2.1$).
• Updated DESI DR1 Constraints:
  • Applying the prior $\Pi(p)$ (with $\bar{p} \approx 1.4$) to the DESI DR1 quasar power spectrum data yields a single, updated constraint:
    $$f_{\text{NL}} = -3.3 \pm 9.2$$
  • This result is statistically indistinguishable from marginalizing over the full distribution or fixing $p$ to the mean, and it is consistent with previous DESI results but provides a more physically grounded interpretation.

5. Significance

• Improved Cosmological Constraints: This work provides the first simulation-validated, physically motivated prior for the assembly bias parameter $p$ in quasar samples. This eliminates the need to report multiple $f_{\text{NL}}$ constraints based on arbitrary choices of $p$.
• Future-Proofing: While the impact on current DESI DR1 precision is modest (due to current statistical errors), the methodology is crucial for future data releases (DESI DR2, DR3, etc.) where statistical precision will improve, and the systematic uncertainty in $p$ will become the limiting factor.
• Astrophysical Insight: The results reinforce the theoretical picture that luminous quasars are hosted by halos with recent major merger histories, providing a quantitative link between AGN activity and halo assembly bias.
• Methodological Standard: The paper establishes a framework for using hydrodynamical simulations to calibrate bias parameters for LSS analyses, a technique that can be applied to other tracers and surveys.