We use cookies to ensure that we give you the best experience on our website. By continuing to browse this repository, you give consent for essential cookies to be used. You can read more about our Privacy and Cookie Policy.

Durham Research Online
You are in:

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

Han, Jiaxin and Wang, Wenting and Cole, Shaun and Frenk, Carlos S. (2016) 'The orbital PDF : general inference of the gravitational potential from steady-state tracers.', Monthly notices of the Royal Astronomical Society., 456 (1). pp. 1003-1016.


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

Item Type:Article
Keywords:Methods: data analysis, Galaxy: fundamental parameters, Galaxies: haloes, Galaxies: kinematics and dynamics, Dark matter.
Full text:(VoR) Version of Record
Download PDF
Publisher Web site:
Publisher statement:This article has been accepted for publication in Monthly Notices of the Royal Astronomical Society ©: 2015 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society. All rights reserved.
Date accepted:17 November 2015
Date deposited:12 February 2016
Date of first online publication:18 December 2015
Date first made open access:No date available

Save or Share this output

Look up in GoogleScholar