The orbital PDF: general inference of the gravitational potential from steady-state tracers

Han, Jiaxin; Wang, Wenting; Cole, Shaun; Frenk, Carlos S.

Abstract

We develop two general methods to infer the gravitational potential of a system using steady-state tracers, i.e. tracers with a time-independent phase-space distribution. Combined with the phase-space continuity equation, the time independence implies a universal orbital probability density function (oPDF) dP(λ|orbit) ∝ dt, where λ is the coordinate of the particle along the orbit. The oPDF is equivalent to Jeans theorem, and is the key physical ingredient behind most dynamical modelling of steady-state tracers. In the case of a spherical potential, we develop a likelihood estimator that fits analytical potentials to the system and a non-parametric method (‘phase-mark’) that reconstructs the potential profile, both assuming only the oPDF. The methods involve no extra assumptions about the tracer distribution function and can be applied to tracers with any arbitrary distribution of orbits, with possible extension to non-spherical potentials. The methods are tested on Monte Carlo samples of steady-state tracers in dark matter haloes to show that they are unbiased as well as efficient. A fully documented c/python code implementing our method is freely available at a GitHub repository linked from http://icc.dur.ac.uk/data/#oPDF.

Citation

Han, J., Wang, W., Cole, S., & Frenk, C. S. (2016). The orbital PDF: general inference of the gravitational potential from steady-state tracers. Monthly Notices of the Royal Astronomical Society, 456(1), 1003-1016. https://doi.org/10.1093/mnras/stv2707

• Journal Article Type: Article
• Acceptance Date: Nov 17, 2015
• Online Publication Date: Dec 18, 2015
• Publication Date: Feb 11, 2016
• Deposit Date: Feb 9, 2016
• Publicly Available Date: Feb 12, 2016
• Journal: Monthly Notices of the Royal Astronomical Society
• Print ISSN: 0035-8711
• Electronic ISSN: 1365-2966
• Publisher: Royal Astronomical Society
• Peer Reviewed: Peer Reviewed
• Volume: 456
• Issue: 1
• Pages: 1003-1016
• DOI: https://doi.org/10.1093/mnras/stv2707
• Keywords: Methods: data analysis, Galaxy: fundamental parameters, Galaxies: haloes, Galaxies: kinematics and dynamics, Dark matter.
• Public URL: https://durham-repository.worktribe.com/output/1412699