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Different traces give different gravitational mass distributions
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Chakrabarty, Dalia (2009) Different traces give different gravitational mass distributions. Working Paper. Coventry: University of Warwick. Centre for Research in Statistical Methodology. Working papers, Vol.2009 (No.47).

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Abstract
Context. Charting the extent and amount of dark matter (DM) in the Universe is highly appealing but is
equally hard since it is only through the interpretation of its effect that we can track the DM distribution, i.e.
the problem is fundamentally inverse. Given the implementational problems, it is nontrivial to quantify the
effects of DM on the motion of individual test particles in an elliptical galaxy, with the aim of identifying its
total gravitational (i.e. luminous+dark) mass distribution; expectedly, this has caused controversy.
Aims. Leaving such technical details aside, in this article we report on the danger of the very notion that test
particle velocities can reliably imply total mass distribution in galaxies.
Methods. We expose the fallibility of this mass determination route, by undertaking a nonparametric
Bayesian analysis (using the algorithm CHASSIS) of the observed lineofsight velocities of individual test
particles belonging two distinct particle (or mass tracer) populations: planetary nebulae (PNe) and globular
clusters (GCs) that span the outskirts of the galaxy NGC 3379.
Results. The PNe and GC data are shown to be drawn from independent phase space density distributions
and total gravitational mass density distributions that are derived from implementation of the two kinematic
data sets are found to be significantly different, leading to significant (at 1¾ level) differences in the corresponding
solutions for the gravitational potential. CHASSIS currently assumes isotropy in phase space,
so this assumption is tested with a robust Bayesian hypothesis test; the GC velocities are found to be more
supportive of the assumption of isotropy than are the PNe data. We find that this recovered difference in
the state of isotropy between the phase space distributions that the data are drawn from, cannot be used to
reconcile the differences in the recovered gravitational mass density distributions.
Conclusions. This recovered dichotomy in the potential structure of the galaxy is indicative of the multistability
of the dynamical system at hand, i.e. the galaxy. In light of this, we advance the risk involved in
the interpretation of gravitational mass distributions obtained from individual tracer samples, as equivalent
to the mass distribution of the whole galaxy.
Item Type:  Working or Discussion Paper (Working Paper) 

Subjects:  Q Science > QA Mathematics Q Science > QB Astronomy 
Divisions:  Faculty of Science > Statistics 
Library of Congress Subject Headings (LCSH):  Dark matter (Astronomy)  Mathematical models, Dark matter (Astronomy)  Statistics 
Series Name:  Working papers 
Publisher:  University of Warwick. Centre for Research in Statistical Methodology 
Place of Publication:  Coventry 
Official Date:  2009 
Volume:  Vol.2009 
Number:  No.47 
Number of Pages:  18 
Status:  Not Peer Reviewed 
Access rights to Published version:  Open Access 
Funder:  Royal Society (Great Britain), Warwick Centre of Analytical Sciences 
References:  Banerjee, P., 2003, Nonlinear Optics Theory, Numerical Modeling and Applications, Marcel Dekker Inc., New York, Basel. 
URI:  http://wrap.warwick.ac.uk/id/eprint/35233 
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