arXiv subjects

Paul J. McMillan

Publications and source records attributed to Paul J. McMillan.

24 records · Page 2Linked to original sources

arXiv2011

Mass models of the Milky Way

We present a simple method for fitting parametrized mass models of the Milky Way to observational constraints. We take a Bayesian approach which allows us to take into account input from photometric and kinematic data, and expectations from theoretical modelling. This provides us with a best-fitting model, which is a suitable starting point for dynamical modelling. We also determine a probability density function on the properties of the model, which demonstrates that the mass distribution of the Galaxy remains very uncertain. For our choices of parametrization and constraints, we find disc scale lengths of 3.00 \pm 0.22 kpc and 3.29 \pm 0.56 kpc for the thin and thick discs respectively; a Solar radius of 8.29 \pm 0.16 kpc and a circular speed at the Sun of 239 \pm 5 km/s; a total stellar mass of 6.43 \pm 0.63 * 10^10 M_sun; a virial mass of 1.26 \pm 0.24 * 10^12 M_sun and a local dark matter density of 0.40 \pm 0.04 GeV/cm^3. We find some correlations between the best-fitting parameters of our models (for example, between the disk scale lengths and the Solar radius), which we discuss. The chosen disc scale-heights are shown to have little effect on the key properties of the model.

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arXiv2009

The uncertainty in Galactic parameters

We reanalyse the measurements of parallax, proper motion, and line-of-sight velocity for 18 masers in high mass star-forming regions presented by Reid et al. (2009). We use a likelihood analysis to investigate the distance of the Sun from the Galactic centre, R_0, the rotational speed of the local standard of rest, v_0, and the peculiar velocity of the Sun, vsol, for various models of the rotation curve, and models which allow for a typical peculiar motion of the high mass star-forming regions. We find that these data are best fit by models with non-standard values for vsol or a net peculiar motion of the high mass star-forming regions. We argue that a correction to vsol is much more likely, and that these data support the conclusion of Binney (2009) that V_sol should be revised upwards from 5.2 km/s to 11 km/s. We find that the values of R_0 and v_0 that we determine are heavily dependent on the model we use for the rotation curve, with model-dependent estimates of R_0 ranging from 6.7 \pm 0.5kpc to 8.9 \pm 0.9kpc, and those of v_0 ranging from 200 \pm 20 km/s to 279 \pm 33 km/s. We argue that these data cannot be thought of as implying any particular values of R_0 or v_0. However, we find that v_0/R_0 is better constrained, lying in the range 29.9-31.6 km/s/kpc for all models but one.

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arXiv2009

The dangers of deprojection of proper motions

We re-examine the method of deprojection of proper motions, which has been used for finding the velocity ellipsoid of stars in the nearby Galaxy. This method is only legitimate if the lines of sight to the individual stars are uncorrelated with the stars' velocities. Very simple models are used to show that spurious results similar to ones recently reported are obtained when velocity dispersion decreases with galactocentric radius in the expected way. A scheme that compensates for this bias is proposed.

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arXiv2008

Disassembling the Galaxy with angle-action coordinates

Angle-action coordinates are used to study the relic of an N-body simulation of a self-gravitating satellite galaxy that was released on a short-period orbit within the disc of the Galaxy. Satellite stars that lie within 1.5 kpc of the Sun are confined to a grid of patches in action space. As the relic phase-mixes for longer, the patches become smaller and more numerous. These patches can be seen even when the angle-action coordinates of an erroneous Galactic potential are used, but using the wrong potential displaces them. Diagnostic quantities constructed from the angle coordinates both allow the true potential to be identified, and the relic to be dated. Hence when the full phase space coordinates of large numbers of solar-neighbourhood stars are known, it should be possible to identify members of particular relics from the distribution of stars in an approximate action space. This would then open up the possibility of determining the time since the relic was disrupted and gaining better knowledge of the Galactic potential. The availability of angle-action coordinates for arbitrary potentials is the key to these developments. The paper includes a brief introduction to the torus technique used to generate them.

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arXiv2007

Initial conditions for disc galaxies

We present a general recipe for constructing N-body realizations of galaxies comprised of near-spherical and disc components. First, an exact spherical distribution function for the spheroids (halo & bulge) is determined, such that it is in equilibrium with the gravitational monopole of the disc components. Second, an N-body realisation of this model is adapted to the full disc potential by growing the latter adiabatically from its monopole. Finally, the disc is sampled with particles drawn from an appropriate distribution function, avoiding local-Maxwellian approximations. We performed test simulations and find that the halo and bulge radial density profile very closely match their target model, while they become slightly oblate due to the added disc gravity. Our findings suggest that vertical thickening of the initially thin disc is caused predominantly by spiral and bar instabilities, which also result in a radial re-distribution of matter, rather than scattering off interloping massive halo particles.

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arXiv2005

Halo evolution in the presence of a disc bar

Angular momentum transfer from a rotating stellar bar has been proposed by Weinberg & Katz (2002) as a mechanism to destroy dark-matter cusps in a few rotation periods. The N-body simulations performed by these authors in support of their claim employed spherical harmonics for the force computation and were, as shown by Sellwood (2003), very sensitive to inclusion of asymmetric terms (odd l,m). In order to disentangle possible numerical artifacts due to the usage of spherical harmonics from genuine stellar dynamical effects, we performed similar experiments using a tree code and find that significant cusp destruction requires substantially more angular momentum than is realistically available. However, we find that the simplified model (a N-body halo torqued by a rotating bar pinned to the origin) undergoes an instability in which the cusp moves away from the origin. In presence of this off-centring, spherical density profiles centred on the origin display an apparent cusp-removal. We strongly suspect that it is this effect which Weinberg & Katz observed. When suppressing the artificial instability, cusp removal is very slow and requires much more angular momentum to be transferred to the halo than a realistic stellar bar possibly possesses.

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