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