Eddington's Demon: Inferring Galaxy Mass Functions and other Distributions from Uncertain Data

Abstract

We present a general modified maximum likelihood (MML) method for inferring generative distribution functions from uncertain and biased data. The MML estimator is identical to, but easier and many orders of magnitude faster to compute than the solution of the exact Bayesian hierarchical modelling of all measurement errors. As a key application, this method can accurately recover the mass function (MF) of galaxies, while simultaneously dealing with observational uncertainties (Eddington bias), complex selection functions and unknown cosmic large-scale structure. The MML method is free of binning and natively accounts for small number statistics and non-detections. Its fast implementation in the R-package "dftools" is equally applicable to other objects, such as haloes, groups and clusters, as well as observables other than mass. The formalism readily extends to multi-dimensional distribution functions, e.g. a Choloniewski function for the galaxy mass-angular momentum distribution, also handled by dftools. The code provides uncertainties and covariances for the fitted model parameters and approximate Bayesian evidences. We use numerous mock surveys to illustrate and test the MML method, as well as to emphasise the necessity of accounting for observational uncertainties in MFs of modern galaxy surveys.

24 pages, 22 figures

References in corpus (5)

• The galaxy stellar mass function at 3.5<z<7.5 in the CANDELS/UDS, GOODS-South, and HUDF fields
• Galaxy And Mass Assembly (GAMA): The galaxy stellar mass function to $z=0.1$ from the r-band selected equatorial regions
• Simultaneous Falsification of LCDM and Quintessence with Massive, Distant Clusters
• A Model for Multi-property Galaxy Cluster Statistics
• A deep Parkes HI survey of the Sculptor group and filament: HI mass function and environment

Cited by in corpus (18)

• Galaxy And Mass Assembly (GAMA): Data Release 4 and the z < 0.1 total and z < 0.08 morphological galaxy stellar mass functions
• Deep Extragalactic VIsible Legacy Survey (DEVILS): SED Fitting in the D10-COSMOS Field and the Evolution of the Stellar Mass Function and SFR-$M_{\star }$ relation
• Constraints on the Faint End of the Galaxy Stellar Mass Function at z ~ 4-8 from Deep JWST Data
• MIGHTEE-HI: The first MeerKAT HI mass function from an untargeted interferometric survey
• The Arecibo Ultra-Deep Survey
• Deep Extragalactic VIsible Legacy Survey (DEVILS): The emergence of bulges and decline of disk growth since $z=1$
• Towards the first detection of strongly lensed HI emission
• Deep Extragalactic VIsible Legacy Survey (DEVILS): Stellar Mass Growth by Morphological Type since $z=1$
• Stellar Masses of Clumps in Gas-rich, Turbulent Disk Galaxies
• The SAMI Galaxy Survey: The contribution of different kinematic classes to the stellar mass function of nearby galaxies
• PAC in DESI. I. Galaxy Stellar Mass Function into the $10^6{\mathrm{M}}_{\odot }$ Frontier
• The miniJPAS survey. Evolution of the luminosity and stellar mass functions of galaxies up to $z\sim 0.7$
• The circular velocity and halo mass functions of galaxies in the nearby Universe
• The FAST Ursa Major supergroup HI survey (FUMaS): catalog and HI mass function
• The MeerKAT Fornax Survey VI. The collapse of the galaxy HI Mass Function in Fornax
• Galaxy and black hole coevolution in dark matter haloes not captured by cosmological simulations
• Galaxy And Mass Assembly (GAMA): Deconstructing the galaxy stellar mass function by star formation and environment
• The contribution of stars, dust, neutral gas and supermassive black holes in galaxies to the cosmic baryon inventory