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

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

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Authors

Jiaxin Han

Wenting Wang



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.

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Copyright 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.







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