Scatter in the star formation rate-halo mass relation: secondary bias and its impact on line-intensity mapping

TL;DR

This work quantifies how secondary bias—the correlation between star formation rate and halo bias at fixed mass—modifies the line-intensity mapping power spectrum. Using IllustrisTNG at z ~ 1.5, the authors show a ~5% enhancement of the two-halo term due to secondary bias and a ~10% boost of the one-halo term from central–satellite SFR correlations (galactic conformity). They demonstrate that halo concentration and total satellite mass are effective secondary parameters to mitigate these offsets, though residual bias remains, particularly for central galaxies. The findings stress the necessity of incorporating secondary properties into LIM mocks and analyses to avoid biased inferences of astrophysical and cosmological parameters, and highlight the role of sample variance and halo-mass dependence in shaping these effects.

Abstract

We use the IllustrisTNG cosmological hydrodynamical simulations to study the impact of secondary bias -- specifically, the correlation between star formation rate (SFR) and halo bias at fixed halo mass -- on the line-intensity mapping (LIM) power spectrum. In LIM, the galaxy contributions are flux-weighted, and therefore depend on the luminosity of emission line. We show that the (ensemble-averaged) large-scale two-halo term of the power spectrum depends only on the mean luminosity-halo mass relation if the scatter is uncorrelated with halo bias. However, when luminosity correlates with halo bias at fixed mass, this assumption breaks down. For many emission lines (e.g. H$α$), luminosity is strongly correlated with SFR, making the SFR-weighted power spectrum important to study. In IllustrisTNG, secondary bias increases the two-halo term of the SFR-weighted power spectrum by 5 per cent at $z \sim 1.5$ compared to a model with random scatter. We also find that SFRs of central and satellite galaxies are correlated, enhancing the one-halo term -- which depends on the distribution of SFR inside the halo -- by 10 per cent relative to random pairings. To mitigate secondary bias in the two-halo term, we identify halo concentration (for haloes with mass $\log M_h \lesssim 12$) and satellite mass (for $\log M_h \gtrsim 12$) as effective secondary parameters. These results highlight the need to account for secondary bias when building mock catalogues and interpreting LIM observations.

Figures (21)

• Figure 1: sfr-virial mass relation for haloes in TNG300-1 at $z = 1.5$ for the halo sfr (orange), central sfr (green) and satellite sfr (violet). The sfrs of all satellite subhaloes of a given friends-of-friends halo are summed to give the satellite sfr of the halo. The $\{5,25,50,75,95\}^{\mathrm{th}}$ percentiles are plotted from bottom to top. The lower panels show the fraction of haloes with sfr$> 10^{-2}$M_⊙ yr^-1. Left panel: The halo sfr (orange) largely follows the central sfr (green) relation up to $\log M_h \sim 12$, above which the group sfr becomes noticeably larger than the central sfr. The central sfr relation decreases due to agn feedback quenching the sfr of central galaxies. Each grey dot represents the total sfr of a halo. Right panel: The total satellite sfr (violet) is lower than the central sfr (green) relation for $\log M_h \lesssim$ 12, and increases to be higher than the central sfr relation for $\log M_h \gtrsim 12$. Each grey dot represents the central sfr of a halo. Summary: While there is a general relation between sfr and halo mass, there is significant scatter around this relation.
• Figure 2: Probability distribution functions (PDFs) of sfrs for haloes of a given mass, defined as PDF = ($n_{\mathrm{halo}}$ in sfr bin)/($n_{\mathrm{halo}}$ in mass bin $\times$sfr bin width). The halo masses considered are $\log M_h \in (11.3,11.4)$ (blue) and $\log M_h \in (12.3,12.4)$ (pink). The hatched area corresponds to haloes with sfr = 0 in the simulation. The distribution of sfrs is approximately Gaussian for lower halo masses but is non-Gaussian for higher halo masses due to agn quenching.
• Figure 3: The contribution from different halo mass ranges to the total sfr in tng. The fraction of the total sfr contributed by central galaxies (green), satellite galaxies (pink), and their combined contribution (orange) are shown. The contribution shown is from halo mass bins of width $\Delta \log_{10}(M_h\ [\unit{M_\odot h^{-1}}]) = 0.5$ dex; these are the bins we use to investigate the power spectrum in \ref{['sec:shuffling_method']}.
• Figure 4: Upper left panel: The blue solid line shows the $L$ - $M$ relation given by \ref{['eq:luminosity_mhalo_param']}. The red dots are obtained by applying a lognormal scatter to this relation with $\sigma = 0.4$ for $\log M_h < 12$ and $\sigma = 0.2$ for $\log M_h > 12$. The dashed blue lines indicate the standard deviation around the mean. Upper right panel: Same as upper left panel, with the addition of a purple solid line which shows the new linear mean $L$ - $M$ relation after applying the scatter (see text). Lower left panel: The ratio of the power spectra for the case of mass-dependent lognormal scatter (red dots in upper panel) against that for a sample with a one-to-one $L$ - $M$ relation given by \ref{['eq:luminosity_mhalo_param']} (blue line in upper panel) computed using the tng halo catalogue. The red lines represent the total power spectrum (solid), two-halo term (dotted), and shot noise (dash-dotted) averaged over five realisations of scatter. The shaded bands represent the 25th-75th percentile level. Lower right panel: Rather than taking the ratio with respect to the power spectrum for the case with the original logarithmic mean $L$ - $M$ relation (as in the lower left panel), the ratio is computed relative to that for a sample with the new (linear) mean $L$ - $M$ relation obtained after applying the mass-dependent scatter (purple line in the upper right panel). Summary: The mean two-halo term depends only on the linear mean $L$ - $M$ relation relation, regardless of the scatter (provided the scatter is random).
• Figure 5: Ratio of the power spectra for various assignment schemes relative to the case where all haloes have equal weighting. The linestyles are the same as in \ref{['fig:mass_dependent_scatter']}. The red colour corresponds to the case where weights are assigned randomly. The gold colour corresponds to the case where haloes with secondary property $\tilde{c}$ (correlated with halo bias) are assigned $W=1$ if $\tilde{c}$ is below the median and $W=5$ if above. The navy colour represents the reverse weighting scheme, with $W=5$ for haloes below the median and $W=1$ for those above. Correlation of weight with bias affects the two-halo term.