HMcode-2020: Improved modelling of non-linear cosmological power spectra with baryonic feedback

TL;DR

HMcode-2020 advances non-linear cosmological power-spectrum modelling by extending the halo-model framework with BAO damping, an updated massive-neutrino treatment, and a physically motivated baryonic feedback component. The method blends de-wiggled linear theory, tuned damping of 2H and 1H terms, and Halo-model ingredients calibrated against hydrodynamical simulations, producing RMS errors around 2% across $k<10\,h\mathrm{Mpc}^{-1}$ and $z<2$. A six-parameter baryonic feedback model (and a single-parameter variant) maps AGN-driven gas expulsion and star formation to the power spectrum, achieving sub-1% fits to hydrodynamic simulations for $z<1$ and $k<20\,h\mathrm{Mpc}^{-1}$. The code is publicly available and integrated with CAMB (and soon CLASS), enabling fast, physically-informed exploration of cosmologies including baryonic processes for current and future weak-lensing analyses.

Abstract

We present an updated version of the HMcode augmented halo model that can be used to make accurate predictions of the non-linear matter power spectrum over a wide range of cosmologies. Major improvements include modelling of BAO damping in the power spectrum and an updated treatment of massive neutrinos. We fit our model to simulated power spectra and show that we can match the results with an RMS error of 2.5 per cent across a range of cosmologies, scales $k < 10\,h\mathrm{Mpc}^{-1}$, and redshifts $z<2$. The error rarely exceeds 5 per cent and never exceeds 16 per cent. The worst-case errors occur at $z\simeq2$, or for cosmologies with unusual dark-energy equations of state. This represents a significant improvement over previous versions of HMcode, and over other popular fitting functions, particularly for massive-neutrino cosmologies with high neutrino mass. We also present a simple halo model that can be used to model the impact of baryonic feedback on the power spectrum. This six-parameter physical model includes gas expulsion by AGN feedback and encapsulates star formation. By comparing this model to data from hydrodynamical simulations we demonstrate that the power spectrum response to feedback is matched at the $<1$ per cent level for $z<1$ and $k<20\,h\mathrm{Mpc}^{-1}$. We also present a single-parameter variant of this model, parametrized in terms of feedback strength, which is only slightly less accurate. We make code available for our non-linear and baryon models at https://github.com/alexander-mead/HMcode and it is also available within CAMB and soon within CLASS.

Figures (8)

• Figure 1: Comparison of different matter power spectrum prediction schemes to the node cosmologies of the franken emu version of the cosmic emulator Heitmann2014. These cosmologies span a range of values of $\omega_\mathrm{m}$, $\omega_\mathrm{b}$, $h$, $n_s$, $\sigma_8$ and $w$. Each coloured line shows a different cosmology and the columns show $z=0$ (left) $0.5$, $1$ and $2$ (right). The different rows show different prediction: hmcode-2020 presented in this paper (top), followed by Mead2016, and Mead2015b, halofit from Takahashi2012 followed by Smith2003 and linear theory (bottom). Dashed horizontal lines show $5$ per cent errors, and accuracy (and publication date) increases from the bottom to the top. All the hmcode models were fitted to data from these emulator nodes. The grey band, most obvious in the bottom two rows, indicates the $2\sigma$ region of the noise floor in the emulator predictions which we calculate from the scatter in the linear predictions are large scales. No prediction scheme can do better than this for these data.
• Figure 2: As Fig. \ref{['fig:FrankenEmu']} but for the nodes of the mira titan version of the cosmic emulator. Compared to franken emu the emulator here additionally covers the extra parameters: time-varying dark energy equation of state, $w_a$; neutrino density, $\omega_\nu$. None of the models presented here were fitted to cosmologies from the nodes of this emulator, so this provides a fair comparison. Power spectra here are coloured by the value of neutrino mass so that the correlation of error with neutrino mass is clearly visible. Note that the minimal $m_\nu \simeq 0.06\,\mathrm{eV}$ corresponds almost to the bluest colour here and that the upper range probed by the emulator is quite high $\sim 1\,\mathrm{eV}$ compared to current constraints on the neutrino mass: $m_\nu < 0.12\,\mathrm{eV}$Planck2018VI. Once again, the grey band indicates the $2\sigma$ region of the noise floor of the emulator node predictions.
• Figure 3: Halo-model predictions for the matter--matter power for different choices of model ingredients. The top $5$ rows show comparison to the $37$ node cosmologies of franken emu. In the left-hand column we show the mean prediction across the different node cosmologies, while in the right-hand column we show the standard deviation of the prediction between the different cosmologies. In each panel the purple curve shows the baseline model, from which all others deviate. The coloured curves in the rows show different choices for the two-halo term (top), halo mass function, halo definition, spherical-collapse calculation and concentration--mass relation. The bottom row compares to the $26$ massive-neutrino node cosmologies of mira titan, because massive neutrinos are not included in the cosmologies of franken emu. In this row ingredients that effect only the massive-neutrino implementation in the halo model are varied. In this Figure we show results at $z = 0$, but the results are broadly similar for other redshifts, although some of the trends are less extreme.
• Figure 4: Comparison of the ratio of power spectra for hmcode-2020 compared to that from the regular halo-model calculation with the same basic ingredients. The models are shown for a standard $\Lambda$CDM cosmology at $z=0$. The two-halo term (long dashed), the one-halo term (short-dashed), and the total (solid) are shown for each model to illustrate the main differences between them.
• Figure 5: Comparison of our single-parameter baryonic feedback response model against three different versions of bahamas AGN feedback simulations with the WMAP9 cosmology that differ only by their values of the 'sub-grid heating' temperature (blue, grey, and light-red for $\log_{10}(T_\mathrm{AGN}/\mathrm{K})=7.6$, $7.8$, and $8.0$). The dots show the simulation measurements while the lines show the hmcode model. In all cases we see that baryonic feedback suppresses power, starting at $k\sim0.1\,h\mathrm{Mpc}^{-1}$ with a maximum suppression effect of tens of per cent at $k\sim7\,h\mathrm{Mpc}^{-1}$, which is followed by a sharp rise in power. The suppression is caused by AGN feedback expelling gas from haloes while the rise in power is caused by galaxy formation in halo centres. The dark-red curve shows the cosmo-owls extreme AGN simulation with the Planck2013 cosmology. This feedback scenario is quite well matched with the same single-parameter feedback model with an increased effective AGN temperature of $\log_{10}(T_\mathrm{AGN}/\mathrm{K})=8.3$. The dashed-grey line shows the AGN feedback model from the previous versions of hmcode, which suppresses the power more than any of the scenarios shown here for $k>5\,h\mathrm{Mpc}^{-1}$ and the onset of the suppression is at slightly smaller scales compared to the bahamas and cosmo-owls simulations.