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

## TL;DR

This paper proposes a model-independent method to measure the halo mass function using observables and stacked weak lensing, reducing systematic bias without relying on specific mass-observable relations.

## Contribution

The authors introduce a novel approach leveraging a property of the halo mass function to obtain bias-free measurements from observables and lensing data, independent of the mass-observable relation.

## Key findings

- Method performs well in cosmological simulations.
- Approach reduces systematic bias in halo mass function measurement.
- Effective over a large mass range.

## 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.