The Impact of Galaxy Formation on Galaxy Biasing, and Implications for Primordial non-Gaussianity Constraints

Abstract

The parameter $f_{\textrm{NL}}$ measures the local non-Gaussianity in the primordial energy fluctuations of the Universe, with any deviation from $f_{\textrm{NL}}=0$ providing key constraints on inflationary models. Galaxy clustering is sensitive to $f_{\textrm{NL}}$ at large scale modes and the next generation of galaxy surveys will approach a statistical error of $σ_{f_{\textrm{NL}}}\sim1$. However, the systematic errors on these constraints are dominated by the degeneracy of $f_{\textrm{NL}}$ with the galaxy bias parameters $b_1$ (galaxy overdensities caused by mass perturbations) and $b_φ$ (galaxy overdensities caused by primordial potential perturbations). It has been shown that the assumed scaling of $b_φ(z)=2δ_c (b_1(z)-1)$ is not accurate for realistically simulated galaxies, and depends both on the galaxy selection and the way that galaxies are modeled. To address this, we leverage the CAMELS-SAM pipeline to explore how varying parameters of galaxy formation affects $b_φ$ and $b_1$ for various galaxy selections. We run separate-universe N-body simulations of $L=205 h^{-1}$ cMpc and $N=1280^3$ to measure $b_φ$, and run 55 unique instances of the Santa Cruz semi-analytic model with varying parameters of stellar and AGN feedback. We find the behavior and evolution of a SC-SAM model's stellar-, SFR- and sSFR- to halo mass relationships track well with how $b_1$ and $b_φ(b_1)$ change across redshift and selection for the SC-SAM. We find our variations of the SC-SAM encapsulate the $b_φ$ behavior previously measured in IllustrisTNG, the Munich SAM, and Galacticus.Finally, we identify sSFR selections as particularly robust to varied galaxy modeling.

Figures (23)

• Figure 1: Comparison of halo bias relations $b_1$ vs. $M_{\textrm{tot}}$ (left) and $b_{\phi}$ vs. $b_1$ (right) measured in SC-SAM galaxies and results from the literature, validating out separate-universe simulations. Galaxies are selected by total (halo) mass across the 56 models at $z=0, 1, 2$. As expected for N-body simulations, $b_1$ vs. $M_{\textrm{tot}}$ is consistent with what the Tinker2010 model (dashed lines, left), and $b_{\phi}$ vs. $b_1$ closely follows the universality relationship for dark matter $b_{\phi}=2 \delta_c (b_1 -1)$ (dashed line, right) or known deviations from this relationship given halo definitions $b_{\phi}=q \times 2 \delta_c (b_1 -1)$, $q \in [0.7, 0.9]$ (dark grey shading). The size of points in the right plot corresponds to the total mass selection (following those in the left plot), with higher mass selections plotted as larger and proceeding in dex-bins of 0.5.
• Figure 2: The $z=0$ stellar mass function (left) and stellar-halo mass relationship (right) for the 'one-at-a-time' SC-SAM models, showing the effect of the minimum and maximum of each parameter with all others held constant (including cosmology). The fiducial model is plotted in black. The $z=0$ SMF observations used for assessing 'realism' are shown in blue and green stars. A$_{\text{AGN}}$ affects the just the high mass end of the SMF, but raises/lowers the SHMR at its minimum/maximum, respectively. The two A$_{\text{SN}}$ parameters strongly warp the SMF and SHMR in unique ways.
• Figure 3: The $z=0$ instantaneous SFR vs. M$_{\textrm{halo}}$ (upper) and specific SFR vs. M$_{\textrm{halo}}$ (lower) 'main sequences' for central galaxies in the 'one-at-a-time' SC-SAM models. (See $z=1$ and $z=2$ in Appendix \ref{['app:bphi_zevol']}.) The fiducial SC-SAM is plotted in black alongside the other parameter pairs: A$_{\text{SN1}}$ min/max in cyan/magenta (left), A$_{\text{SN2}}$ min/max in blue/teal (center), and A$_{\text{AGN}}$ min/max in red/gold (right). For emphasis, we highlight a region of massive and quenched galaxies with M$_{\textrm{halo}}> 10^{11.9}$ M$_{\odot}$ and SFR $< 0$ M$_{\odot}$ yr$^{-1}$ or sSFR $< -1$ Gyr$^{-1}$. The contours include all galaxies in the approximate 'massive and quenched' corner and the first 70,000 galaxies of each model (for figure legibility). The legends indicate the total number of central galaxies in each model, and what percentage of galaxies are in the grey 'massive and quenched' regions. All models share the same fundamental shape in their sSFR vs. M$_{*}$ distribution by design in the SC-SAM, but differences in their stellar-halo mass relationships change their SFR vs. M$_{\textrm{halo}}$ relationship.
• Figure 4: The $z=0$ stellar mass function (SMF, left) and stellar-halo mass relationship (SHMR, right) for the 56 SC-SAM models in this work. Each model is colored by its relative 'realism' when compared to the Bernardi2018$z=0$ SMF measurements (green and blue) between 9 $< \log M_{*} (M_{\odot}) <$ 11, with least-to-most realistic as beige-to-black.
• Figure 5: The behavior of $b_{\phi}$ as a function of stellar mass (top row), SFR (middle row), and specific SFR (bottom row) when changing the selected SC-SAM astrophysical parameters one at a time, for $z=0, 1, 2$ (left, middle, right columns respectively). The black curve is the fiducial model, fit to several $z=0$ scaling relations. The colored lines correspond to SC-SAM runs where each parameter was varied to its minimum or maximum while all others were held to the fiducial values. We exclude bins whose selections led to fewer than 500 galaxies, and errors are calculated as described in Eq. \ref{['eq:bphi_def_error']}.