AbacusPNG: A modest set of simulations of local-type primordial non-Gaussianity in the DESI era

Abstract

A measurement of a primordial non-Gaussianity (PNG) signal through late- or early-Universe probes has the potential to transform our understanding of the physics of the primordial Universe. $N$-body simulations, such as the public \textsc{AbacusPNG} set presented in this study, consisting of 9 boxes, each of size $L_{\rm box} = 2~{\rm Gpc}/h$ and particle mass of $1.01 \times 10^{10} \ M_\odot/h$, provide a viable path forward. As validation, we find good agreement between the simulations and our expectations from one-loop perturbation theory and the `separate universe' method for the matter bispectrum, matter power spectrum and the halo bias parameter associated with PNG, $b_φ$. As a science application, we investigate the link between halo assembly bias and $b_φ$ for halo properties known to play a vital role in accurately predicting galaxy clustering: concentration, shear (environment), and accretion rate. We find a strong response for all three parameters, suggesting that the connection between $b_φ$ and the assembly history of halos needs to be taken into account by future PNG analyses. We further perform the first study of the $b_φ$ parameter from fits to early DESI data of the luminous red galaxy (LRG) and quasi-stellar object (QSO) samples and comment on the effect on $f_{\rm NL}$ constraints for the allowed galaxy-halo models (note that $σ[f_{\rm NL}] \propto \frac{σ[b_φ]}{b_φ}$). We find that the error on $f_{\rm NL}$ is 21, 6, 22 for the LRGs at $z = 0.5$ and $z = 0.8$ and QSOs at $z = 1.4$, respectively, suggesting that a thorough understanding of galaxy assembly bias is warranted so as to perform robust high-precision analysis of local-type PNG with future surveys. Simulations publicly available at https://app.globus.org/file-manager?origin_id=ffc65d7a-0bf9-11ec-90b4-41052087bc27

Figures (7)

• Figure 1: Validation of the effect of local-type PNG on the matter bispectrum at the initial conditions, $z_{\rm IC} = 99$. We show the derivative of the power spectrum with respect to local-type $f_{\rm NL}$ as computed from the AbacusPNG_c302_ph000 simulation as well as from theory using the tree-level approximation (see Eq. \ref{['eq:B']}). We see that they are in very good agreement with each other for all three triangle configurations considered in this study: equilateral ($k_1 = k_2 = k_3$), squeezed ($k_1 = k_2 = k$, $k_3 = 3 k_{\rm F}$), folded ($k_1 = k_2 = k$, $k_3 = 2k$)). The squeezed limit yields the strongest response to local-type PNG (across all $k$-modes) and thus has the smallest error bars. For $k \gtrsim 0.15$, we see a deviation from theory, which we attribute to mild non-linearities we find in the simulation power spectrum on these scales, compared with linear theory. The noise in the theory curve is due to the fact it is computed on a grid so as to match the noise of the measurement.
• Figure 2: Validation of the effect of local-type PNG on the matter power spectrum at $z = 0.5$. We show the derivative of the power spectrum with respect to $f_{\rm NL}$ as computed from the AbacusPNG_c302_ph000 simulation as well as from theory, using 1-loop EFT (see Eq. \ref{['eq:dpdfnl']}). We notice that local-type PNG has a very weak effect on the matter power spectrum -- $\sim$0.01% at $k \approx 0.2 h/{\rm Mpc}$ The effect on large scales is negligible, whereas on small scales it grows exponentially. As expected, the agreement between theory and simulation is very good on large scales and starts to break down on non-linear scales $k \gtrsim 0.15 h/{\rm Mpc}$, where non-linearities start to become relevant.
• Figure 3: Comparison between $b_\phi$ obtained from the AbacusPNG set by fitting the power spectrum ratio (see Eq. \ref{['eq:ratio_bphi']}) and $b_\phi$ obtained from the Separate Universe approach by using a pair of the AbacusSummit suite of simulations (see Eq. \ref{['eq:bphimeasure']}). We note that the PNG result is obtained by fitting the ratio separately for AbacusPNG_c302_ph000 and AbacusPNG_c302_ph001 (with their respective $f_{\rm NL} = 0$ simulations) and then averaging the two values of $b_\phi$. We also show in blue the curve coming from the modified universality relation (see Eq. \ref{['eq:bphiuniv']}). We see that the halos in the Separate Universe approach are in perfect agreement with the modified universality relation. On the other hand, the AbacusPNG curve is substantially more noisy, as despite the fact that we have canceled most of the cosmic variance, the power spectrum ratio retains some intrinsic noise.
• Figure 4: Response of the primordial bias parameter $b_\phi$ to the halo assembly bias properties: concentration (see Eq. \ref{['eq:conc']}), accretion rate (see Eq. \ref{['eq:gamma']}) and shear (see Eq. \ref{['eq:shear']}). The dashed curves come from the AbacusPNG set of simulations, whereas the solid curves come from the Separate Universe pair of simulations, which uses the original AbacusSummit suite. The halos are split into 12 mass bins and then each bin is further split into 3 bins of equal sizes (33%, 66% percentile) based on the secondary property being considered (low, mid, high). Here, for all mass bins, we report the pairs $[b_1^{\rm high}, b_\phi^{\rm high}/b_\phi^{\rm mid}]$ in blue and $[b_1^{\rm low}, b_\phi^{\rm low}/b_\phi^{\rm mid}]$ in red. The Separate Universe and AbacusPNG curves are in good agreement with each other. For all three properties, the low-mass (low-bias) bins exhibit the largest variations in their values of $b_\phi$. If a given galaxy sample preferentially occupies low- or high-concentration (accretion rate) halos, then that may not reflect on the inference from the two-halo clustering, but it will affect PNG analysis. The concentration response is stronger than that of the accretion rate, and that the trend is reversed between the two, which makes sense, as actively accreting objects have lower concentration (have more spread out substructure). We note that a different definition of accretion rate might yield a stronger response. To see a change in $b_\phi$ for shear, one needs to vary the linear bias significantly at fixed halo mass.
• Figure 5: Scatter plot of $b_\phi$ and mean halo mass for the three samples of interest to this study: LRGs at $z = 0.5$ (red) and $z = 0.8$ (blue), and QSOs at $z = 1.4$ (green). Dots are shown for the HOD samples that satisfy the condition $\Delta \chi^2 \leq {\rm d.o.f.}$ as described in Section \ref{['sec:bphi']}. We show the mean and fiducial values for each sample with a cross and large circle, respectively, as well as the universality relation (dashed) with $c = 0.8$ (see Eq. \ref{['eq:bphiuniv']}; note that a lower value of $c$ is found for the galaxies compared with the halos, $c = 0.9$). We see that the samples follow a thin slanted contour on the $b_\phi$-$\bar{M}_{\rm halo}$ plane. We attribute this to the fact that the mean halo mass (which is a proxy of linear bias) is relatively well constrained compared with $b_\phi$. The standard deviation of $b_\phi$ for the three samples is roughly 11%, 6% and 5%, respectively.