A direct and robust method to observationally constrain the halo mass function via the submillimeter magnification bias: Proof of concept

Abstract

Aims. The main purpose of this work is to provide a proof-of-concept method to derive tabulated observational constraints on the halo mass function (HMF) by studying the magnification bias effect on high-redshift submillimeter galaxies. Under the assumption of universality, we parametrize the HMF according to two traditional models, namely the Sheth and Tormen (ST) and Tinker fits, derive posterior distributions for their parameters, and assess their performance in explaining the measured data within the Λ cold dark matter model. We also study the potential influence of the halo occupation distribution (HOD) parameters in this analysis and discuss two aspects regarding the HMF parametrization, namely its normalization and the possibility of allowing negative values for the parameters. Methods. We measure the cross-correlation function between a foreground sample of GAMA galaxies with spectroscopic redshifts in the range 0.2 < z < 0.8 and a background sample of H-ATLAS galaxies with photometric redshifts in the range 1.2 < z < 4.0 and carry out a Markov chain Monte Carlo algorithm in the context of Bayesian inference to check this observable against its mathematical prediction within the halo model formalism, which depends on both the HOD and HMF parameters. Results. Under the assumption that all HMF parameters are positive, the ST fit only seems to fully explain the measurements by forcing the mean number of satellite galaxies in a halo to increase substantially from its prior mean value. The Tinker fit, on the other hand, provides a robust description of the data without relevant changes in the HOD parameters, but with some dependence on the prior range of two of its parameters. When the normalization condition for the HMF is dropped and we allow negative values of the p1 parameter in the ST fit, all the involved parameters are better determined, unlike the previous models, thus deriving the most general HMF constraints. While all the aforementioned cases are in agreement with the traditional fits within the uncertainties, the last one hints at a slightly higher number of halos at intermediate and high masses, raising the important point of the allowed parameter range.

Cosmological and astrophysical results exploiting magnification bias with high-z sub-millimetre galaxies

“…In particular, Cueli et al in Ref. 18 successfully test such possibility according to two common parametrisations: the Sheth & Tormen and Tinker fits. They find general agreement with traditional values for the involved parameters, with a slight difference in the Sheth & Tormen fit for intermediate and high masses, where the results suggest a hint at a somewhat higher number of halos.…”

Tomography-based observational measurements of the halo mass function via the submillimeter magnification bias

“…Several comments should be made about this. Firstly, the choice of the ST fit over other models follows from the results of Cueli et al (2021): for our study, this model seems to compare favorably with other fits, where an important degeneration among parameters is bound to arise together, thus compromising the statistical conclusions, especially when they depend on the prior range. Secondly, the original work by Sheth & Tormen (1999) imposed a normalization condition accounting for the fact that all mass should be bound up in halos, which allowed them to fix A in terms of p (and resulted in the commonly used bestfit triple A = 0.33, a = 0.707 and p = 0.3).…”

“…Secondly, the original work by Sheth & Tormen (1999) imposed a normalization condition accounting for the fact that all mass should be bound up in halos, which allowed them to fix A in terms of p (and resulted in the commonly used bestfit triple A = 0.33, a = 0.707 and p = 0.3). Following the results from Cueli et al (2021), we opted to leave the A parameter free in most cases, provided however that the condition ∞ 0 f (ν)/ν dν ≤ 1 is met so as to have a meaningful physical interpretation of the HMF. Lastly, it should be noted that the original ST function f (ν, z) does not depend on redshift, but given the tomographic character of this work, we aim to study the possible time evolution of its parameters to quantify deviations from universality.…”

Cosmological direct detection of dark energy: non-linear structure formation signatures of dark energy scattering with visible matter

“…This is a task which goes significantly beyond the scope of the present work, but which once more is a priority for follow-up work. Finally, it is worth mentioning the existence of proposals for directly measuring the halo mass function using combinations of weak lensing, galaxy cluster counts, galaxy cluster power spectra, and lensed Type Ia Supernovae data (Castro et al 2016), as well as using sub-mm magnification bias (Cueli et al 2021): should applying these methods ultimately prove feasible on real data, they would undoubtedly provide a very interesting pathway towards directly probing signatures of DE-baryon scattering on the halo mass function.…”