oLIMpus: An Effective Model for Line Intensity Mapping Auto- and Cross- Power Spectra in Cosmic Dawn and Reionization

TL;DR

oLIMpus delivers a fully analytic, fast framework to model line intensity mapping auto- and cross-power spectra across cosmic dawn and the EoR by extending Zeus21 with a second-order lognormal treatment of the density field. It couples line luminosity through $L(M_h,z)$ or $L(\dot{M}_*,M_h)$ to a lognormal luminosity density $\rho_L$, accounts for shot noise and redshift-space distortions, and produces coeval boxes and lightcones suitable for parameter inference. The approach yields rapid, scalable spectra computations (and cross-spectra with the 21-cm signal) while maintaining physical connections to the density field, halo mass function, and SFRD, enabling efficient MCMC-style analyses for multi-line LIM data. Its modular, pluggable design supports easy addition of lines, stochasticity, and cross-correlations, with demonstrated consistency against other public codes in overlapping regimes, and broad potential for SPHEREx, COMAP, and cross-survey studies.

Abstract

Line-intensity mapping (LIM) is emerging as a powerful probe of the high-redshift Universe, with a growing number of LIM experiments targeting various spectral lines deep into the epochs of reionization and cosmic dawn. A key remaining challenge is the consistent and efficient modeling of the diverse emission lines and of the observables of different surveys. Here, we present oLIMpus, a fully analytical effective model to study LIM auto- and cross- power spectra. Our work builds on the 21-cm effective model presented in Zeus21, applying it to star-forming lines and improving it in different aspects. Our code accounts for shot noise and linear redshift-space distortions and it includes by default prescriptions for OII, OIII, H$α$, H$β$, CII, CO line luminosities, together with the 21-cm model inherited from Zeus21. Beyond auto- and cross-power spectra, oLIMpus can produce mock coeval boxes and lightcones, and with a computational time of $\sim s$ it is ideal for parameter-space exploration and inference. Its modular implementation makes it easy to customize and extend, enabling various applications, such as MCMC analyses and consistent multi-line cross-correlations.

Figures (12)

• Figure 1: Flowchart of oLIMpus. The top panel indicates the building blocks inherited from Zeus21 to model the cosmology and the star formation rate$\dot{M_*}(M_h)$. On top of these, oLIMpus introduces a new building block to model the line luminosity of the star forming lines of interest $L(\dot{M}_*(M_h))$, for which we also account for lognormal scattering. Combined with $dn/dM_h$, the star formation rate and the line luminosity provide the star formation rate density $\dot{\rho}_{*}$ and the luminosity density $\rho_L$. The central panel recalls the key assumption in oLIMpus: both $\dot{\rho}_{*}$ and $\rho_L$ can be estimated as lognormal functions of the smoothed density field $\delta_R$. The approximation $\dot{\rho}_{*}(\delta_R)\propto e^{\gamma_R\delta_R}$ was already introduced in Zeus21 to estimate the evolution of the 21-cm signal; here, we improve over the previous work by adding the second-order dependence on $\delta_R^2$, and by extending this formalism to the star-forming lines. Moreover, Zeus21 can now be used as a submodel of oLIMpus, hence producing the 21-cm signal during cosmic dawn and the epoch of reionization consistently with the evolution of the other lines. Finally, the green panels in the bottom row represent the main outputs of our code: the lognormal approximation allows us to estimate fully analytically the auto- and cross- power spectra of star forming lines, including shot noise and redshift space distortions. The auto-power spectra, in turn, can be used to produce coeval boxes and lightcones of the expected LIM signal, which correlate with the underlying density field. oLIMpus can also produce coeval boxes and lightcones through a cell-by-cell computation of the relevant quantities, including the reionization field that drives the evolution of the ionizing bubble and their effect on the 21-cm signal. The reionization model is part of an upcoming new release of Zeus21Sklansky:2025; for the moment, oLIMpus relies on a reduced version, which enters in the steps indicated with (*) in the flowchart; these will be updated in subsequent work.
• Figure 2: Density-modulated luminosity density $\rho_L(z|\delta_R)$ for different choices of redshift and smoothing radius $R$. The top panel shows $R=1\,{\rm Mpc}$, the bottom $R=5\,{\rm Mpc}$; in both of them, solid lines and filled points are associated with $z=6$, while dashed lines and empty points with $z=10$. While the lines are obtained relying on the first (blue) and second (red) order lognormal approximation in Eq. \ref{['eq:lognormal']}, the points indicate the binned $\rho_L(\vec{x},z)$ in coeval boxes having side $L_{\rm box}=150\,$Mpc and $N_{\rm cell}=$150 cells per side. The boxes are obtained using the cell-by-cell algorithm introduced at the end of Sec. \ref{['sec:line_model']}. In all scenarios, the second-order lognormal approximation shows better agreement with the mock coeval boxes, particularly for small $R$, low $z$ or high $\delta_R$.
• Figure 3: Line intensity power spectrum $\Delta_{\nu}^2(k,z)$ for different choices of redshift and smoothing radius $R$. The top panel shows $R=1\,{\rm Mpc}$, the bottom $R=5\,{\rm Mpc}$; the color legend is the same as Fig. \ref{['fig:lognormal_approx']}. The points show the power spectrum measured using powerbox on $\{L_{\rm box},N_{\rm cell}\}=\{150\,{\rm Mpc},150\}$ boxes produced through the cell-by-cell algorithm introduced at the end of Sec. \ref{['sec:line_model']}. In all scenarios, the second-order lognormal approximation shows remarkable agreement with the mock coeval boxes; the first order case, instead, overestimates the power spectrum on small scales.
• Figure 4: Left: normalized auto-power spectra for OIII, H$\alpha$, CII and CO(2-1), each of which is divided by the observed intensity $\bar{I}_\nu^2(z)$. Except for OIII and H$\alpha$, oLIMpus uses different models for different lines (see Appendix \ref{['app:lines']}). We made this choice in order to include by default in our code models that are actively used in the literature, each of which is calibrated on state-of-the art simulations; other models can be easily customized into the code. The choice of a larger smoothing radius $R_0$ for CO is illustrative. Right: cross power spectra between OIII and the other lines at $z=6$. In both plots, the points are obtained using powerbox on {$L_{\rm box}, N_{\rm cell}$}={150 Mpc, 150} boxes produced with the cell-by-cell alghorithm described at the end of Sect. \ref{['sec:line_model']}.
• Figure 5: LIM power spectrum with (solid and black dots) and without (dashed and white dots) shot noise contribution, see Sect. \ref{['sec:shot_noise']}. The red lines include spherically-averaged RSD, see Appendix \ref{['app:RSD']}. The points are measured with powerbox in coeval boxes $L_{\rm box}=150\,$Mpc and $N_{\rm cell}=$150. For the white points, we use the intensity box produced with the cell-by-cell algorithm at the end of Sec. \ref{['sec:line_model']}; the black points, instead, are measured from a box produced by summing the intensity box with the shot noise box, realized as a Gaussian field in powerbox based on $P_{\rm shot}(z)$ in Eq. \ref{['eq:shot']}; the smoothing over different radii (top, $R=1\,$Mpc, bottom $R=5\,$Mpc) is done a posteriori. The cell-by-cell algorithm does not include RSD.