The baryonic Tully-Fisher relation as an independent direct probe of cosmology and of the nature of dark matter

Technical Summary: The Baryonic Tully-Fisher Relation as a Direct Probe of Cosmology and Dark Matter Nature

Problem Statement
The baryonic Tully-Fisher relation (BTFR) is a well-established empirical scaling law linking the total baryonic mass of rotation-supported galaxies to their asymptotic rotation velocity. Historically, the BTFR has been utilized primarily as a calibrated distance indicator to estimate the Hubble constant ($H_0$) and as a tool for testing galaxy formation theories, dark matter halo properties, and alternative gravity models. However, its potential as a direct probe for constraining fundamental cosmological parameters (beyond $H_0$) and the nature of dark matter has remained underexplored. This paper addresses the gap in understanding whether the BTFR is sensitive to cosmological parameters such as matter density ($\Omega_m$) and the amplitude of matter fluctuations ($\sigma_8$), as well as the mass of warm dark matter (WDM) particles and astrophysical feedback mechanisms.

Methodology
The authors employ a simulation-based inference (SBI) framework utilizing deep neural networks to explore the sensitivity of the BTFR to a six-dimensional parameter space. The study relies on the DREAMS (DaRk mattEr and Astrophysics with Machine learning and Simulations) suite, a large collection of 1,024 cosmological magneto-hydrodynamic simulations. These simulations, run with the AREPO code and the IllustrisTNG model, vary the following parameters following a Sobol sequence:

• Cosmological: Matter density ($\Omega_m \in [0.1, 0.5]$) and amplitude of fluctuations ($\sigma_8 \in [0.6, 1.0]$).
• Dark Matter: Mass of WDM particles ($M_{\text{WDM}} \in [1.8, 16]$ keV).
• Astrophysical Feedback: Parameters regulating supernova (SN) feedback ($A_{\text{SN1}}, A_{\text{SN2}}$) and active galactic nucleus (AGN) feedback ($A_{\text{AGN}}$).

For each simulation, the BTFR is derived by selecting rotation-supported galaxies ($V_{\text{max}}/\sigma_{\text{disp}} > 1.5$) and computing the median baryonic mass ($M_{b,\text{med}}$) and its standard deviation ($\sigma_M$) across 10 bins of maximum circular velocity ($V_{\text{max}}$). Data is extracted at three redshifts ($z=0, 0.54, 1.05$) to mimic the observational capabilities of the future Square Kilometer Array (SKA).

To infer the posterior distributions of the parameters given a BTFR measurement, the authors train a neural density estimator using Masked Autoregressive Flows (MAF). The network is trained on 974 simulations and tested on 50 held-out realizations. The input consists of stacked arrays of $V_{\text{max}}$, $M_{b,\text{med}}$, and $\sigma_M$, while the output is the set of true model parameters used to generate the simulation.

Key Results
The inference framework demonstrates the ability to recover unbiased values for the input parameters with varying degrees of precision:

• Cosmological Parameters: The model recovers $\Omega_m$ and $\sigma_8$ with sub-percent average deviation accuracy. The median precision is approximately 2.6% for $\Omega_m$ and 3.9% for $\sigma_8$. The predictions show a strong Spearman rank-order correlation with true values ($R=0.99$ for $\Omega_m$ and $R=0.93$ for $\sigma_8$). An anti-correlation ($R=-0.74$) between $\Omega_m$ and $\sigma_8$ is recovered, consistent with other cosmological probes.
• Dark Matter Mass: The mass of WDM particles ($M_{\text{WDM}}$) is recovered with a median precision of $\sim 29\%$ (standard deviation $\sim 33\%$) and an average deviation of $\sim 3\%$. The correlation is lower ($R=0.83$) compared to cosmological parameters. The results indicate an anti-correlation between $\sigma_8$ and $M_{\text{WDM}}$, suggesting that a "warmer" (lighter) dark matter particle suppresses low-mass halo formation, requiring a higher $\sigma_8$ to fit the BTFR.
• Astrophysical Feedback: The framework successfully constrains the SN feedback parameters ($A_{\text{SN1}}$ and $A_{\text{SN2}}$) with median precisions of 10.5% and 12.6%, respectively. However, the AGN feedback parameter ($A_{\text{AGN}}$) cannot be reliably constrained due to the sparsity of AGNs in the simulation volumes, leading to shot noise that overwhelms the signal.

Significance and Claims
The paper claims to provide the first demonstration that the BTFR is simultaneously sensitive to cosmological parameters ($\Omega_m, \sigma_8$), the nature of dark matter ($M_{\text{WDM}}$), and specific astrophysical feedback mechanisms. The authors position the BTFR as a novel, independent probe of cosmology and fundamental physics, distinct from traditional methods like galaxy clustering, weak lensing, or the Cosmic Microwave Background (CMB).

The significance of this work lies in its potential to:

1. Offer a low-redshift cosmological probe to help resolve tensions in cosmological parameters, such as the $\sigma_8$ tension.
2. Provide constraints on dark matter models (specifically WDM) independent of Lyman-$\alpha$ forest data.
3. Enable the precise characterization of supernova feedback mechanisms.

The authors note that while this study serves as a theoretical proof of concept using idealized simulations, future work must address the lack of convergence between different galaxy formation models and the modeling of observational systematics before applying this method to real data. The upcoming capabilities of the Square Kilometer Array (SKA) to measure the BTFR up to $z \sim 1$ are identified as the critical next step for realizing these prospects.