Towards a Model-Independent Measurement of the Halo Mass Function with Observables

Abstract

In the CDM paradigm, the halo mass function is a sensitive probe of the cosmic structure. In observations, halo mass is typically estimated from its relation with other observables. The resulting halo mass function is subject to systematic bias, such as the Eddington bias, due to the scatter or uncertainty in the observable - mass relation. Exact correction for the bias is not easy, as predictions for the observables are typically model-dependent in simulations. In this paper, we point out an interesting feature in the halo mass function of the concordence $\Lambda$CDM model: the total halo mass within each evenly-spaced logarithmic mass bin is approximately the same over a large mass range. We show that this property allows us to construct an almost bias-free halo mass function using only an observable (as a halo mass estimator) and stacked weak lensing measurements as long as the scatter between the true halo mass and the observable-inferred mass has a stable form in logarithmic units. The method is not sensitive to the form of the mass-observable relation. We test the idea using cosmological simulations, and show that the method performs very well for realistic observables.

10 pages,16 figures

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• Halo Properties and Mass Functions of Groups/Clusters from the DESI Legacy Imaging Surveys DR9
• An empirical measurement of the Halo Mass Function from the combination of GAMA DR4, SDSS DR12, and REFLEX II data
• The intrinsic SFRF and sSFRF of galaxies: comparing SDSS observation with IllustrisTNG simulation
• A Stochastic Theory of the Hierarchical Clustering I. Halo Mass Function