Biased tracers of two fluids in the Lagrangian picture

Abstract

We explore Lagrangian perturbation theory (LPT) for biased tracers in the presence of two fluids, focusing on the case of cold dark matter (CDM) and baryons. The presence of two fluids induces corrections to the Lagrangian bias expansion and tracer advection, both of which we formulate as expansions in the three linear modes of the Lagrangian equations of motion. We compute the linear-order two-fluid corrections in the Zeldovich approximation, finding that modifications to the bias expansion and tracer advection both enter as percentlevel corrections over a large range of wavenumbers at low redshift and draw parallels with the Eulerian formalism. We then discuss nonlinear corrections in the two-fluid picture, and calculate contributions from the relative velocity effect (∝ v 2 r ) at one loop order. Finally, we conduct an exploratory Fisher analysis to assess the impact of two-fluid corrections on baryon acoustic oscillations (BAO) measurements, finding that while modest values of the relative bias parameters can introduce systematic biases in the measured BAO scale of up to 0.5 σ, fitting for these effects as additional parameters increases the error bar by less than 30% across a wide range of bias values. Linear Equations of Motion in Lagrangian SpaceIn the Lagrangian picture, fluid dynamics is encoded in the displacements Ψ σ (q) of fluid elements of each species, σ, originally situated at Lagrangian positions q, such that their Eulerian positions at conformal time τ (dτ = a −1 dt) are given by [28,37,38] x σ (q, τ ) = q + Ψ σ (q, τ ).(2.1)The subscript σ = {c, b} denotes the species, either cold dark matter (CDM) or baryons, respectively, whose motion we are tracking. Assuming that initial displacements are infinitesimally small compared to those at the redshifts of interest, the overdensity, δ σ , of each species at Eulerian

Large-scale dark matter simulations

“…This question was indeed investigated by using simulations with adaptive softening (Khoraminezhad et al 2021) and by using an extension of the separate universe approach (Barreira et al 2020a), which does not suffer from the numerical inaccuracies described above. These authors showed that halo formation is actually sensitive to baryon-dark matter fluctuations, in agreement with analytic arguments (Chen et al 2019;Schmidt 2016). At a fixed matter overdensity, halos tend to form more efficiently in regions with smaller baryon-dark matter differences.…”

The reconstructed power spectrum in the Zeldovich approximation

“…fields. Similar behavior is seen in the evaluation of unequal-time correlation functions [47] and the baryon-cold dark matter cross-correlation [48,49], though the physical mechanisms are of course different. At large scales, we similarly have…”

Baryonic effects on CMB lensing and neutrino mass constraints

“…2 Ergo, we must 1 The CMB lensing power spectra we have computed for this work are available at https://github.com/sjforeman/cmblensing_ baryons. 2 There is hope that perturbation theory could provide such an analytical theory on quasi-linear scales, even in the presence of baryonic effects [45,46], but the corresponding predictions will still involve free parameters whose values must either be calibrated using simulations or fit to observations. resort to simulations that implement large-scale gravitational clustering alongside hydrodynamics and subgrid models of baryon behavior such as gas cooling, star formation, and feedback.…”