Determining the velocity dispersion of the thick disc

We attempt to recover the mean vertical velocity and vertical velocity dispersion as a function of the Galactic height for a sample drawn from a realistic Galaxy distribution function by following the method presented in Moni Bidin et al. (2012). We find that, for the sample size used, the observational error in the velocities is much smaller than the Poisson noise which has not been accounted for by Moni Bidin et al. We repeat the analysis on a large number of samples to estimate the contribution of the Poisson noise and to uncover any systematics. We find that the dispersion is systematically overestimated at low Galactic heights and slightly underestimated at high Galactic heights leading to an underestimate of the gradient of the dispersion with Galactic height. The causes of the systematics are revealed by repeating the calculation using a method inspired by Girard et al. (2006). This method recovers the expected dispersion much more successfully and in particular yields a gradient of the dispersion with Galactic height which is approximately three times that found using the method presented by Moni Bidin et al.Comment: 7 pages, 7 figures, accepted for publication in MNRAS - included more information on DF, small change to DF has slightly altered the result

Angle-action estimation in a general axisymmetric potential

The usefulness of angle-action variables in galaxy dynamics is well known, but their use is limited due to the difficulty of their calculation in realistic galaxy potentials. Here we present a method for estimating angle-action variables in a realistic Milky Way axisymmetric potential by locally fitting a St\"ackel potential over the region an orbit probes. The quality of the method is assessed by comparison with other known methods for estimating angle-action variables of a range of disc and halo-type orbits. We conclude by projecting the Geneva-Copenhagen survey into angle-action space.Comment: 13 pages, 12 figures, accepted for publication in MNRA

Chemodynamical modelling of the Milky Way

Chemodynamical models of our Galaxy that have analytic Extended Distribution Functions (EDFs) are likely to play a key role in extracting science from surveys in the era of Gaia.Comment: 6 pages to appear in "Reconstructing the Milky Way history: spectroscopic surveys, asteroseismology and chemodynamical models", eds C Chiappini, J Montalban & M Steffe

Stream-orbit misalignment I: The dangers of orbit-fitting

Tidal streams don't, in general, delineate orbits. A stream-orbit misalignment is expected to lead to biases when using orbit-fitting to constrain models for the Galactic potential. In this first of two papers we discuss the expected magnitude of the misalignment and the resulting dangers of using orbit-fitting algorithms to constrain the potential. We summarize data for known streams which should prove useful for constraining the Galactic potential, and compute their actions in a realistic Galactic potential. We go on to discuss the formation of tidal streams in angle-action space, and explain why, in general, streams do not delineate orbits. The magnitude of the stream-orbit misalignment is quantified for a logarithmic potential and a multi-component Galactic potential. Specifically, we focus on the expected misalignment for the known streams. By introducing a two-parameter family of realistic Galactic potentials we demonstrate that assuming these streams delineate orbits can lead to order one errors in the halo flattening and halo-to-disc force ratio at the Sun. We present a discussion of the dependence of these results on the progenitor mass, and demonstrate that the misalignment is mass-independent for the range of masses of observed streams. Hence, orbit-fitting does not yield better constraints on the potential if one uses narrower, lower-mass streams.Comment: 13 pages, 7 figures, accepted for publication in MNRA

Stream-orbit misalignment II: A new algorithm to constrain the Galactic potential

In the first of these two papers we demonstrated that assuming streams delineate orbits can lead to order one errors in potential parameters for realistic Galactic potentials. Motivated by the need for an improvement on orbit-fitting, we now present an algorithm for constraining the Galactic potential using tidal streams without assuming that streams delineate orbits. This approach is independent of the progenitor mass so is valid for all observed tidal streams. The method makes heavy use of angle-action variables and seeks the potential which recovers the expected correlations in angle space. We demonstrate that the method can correctly recover the parameters of a simple two-parameter logarithmic potential by analysing an N-body simulation of a stream. We investigate the magnitude of the errors in observational data for which the method can still recover the correct potential and compare this to current and future errors in data. The errors in the observables of individual stars for current and near future data are shown to be too large for the direct use of this method, but when the data are averaged in bins on the sky, the resulting averaged data are accurate enough to constrain correctly the potential parameters for achievable observational errors. From pseudo-data with errors comparable to those that will be furnished in the era of Gaia (20 per cent distance errors, 1.2 mas/yr proper motion errors, and 10 km/s line-of-sight velocity errors) we recover the circular velocity, V_c=220 km/s, and the flattening of the potential, q=0.9, to be V_c=223+/-10km/s and q=0.91+/-0.09.Comment: 11 pages, 5 figures, accepted for publication in MNRA

The period--luminosity relation for Mira variables in the Milky Way using Gaia DR3: a further distance anchor for H0H_0

Gaia DR3 parallaxes are used to calibrate preliminary period--luminosity relations of O-rich Mira variables in the 2MASS $J$, $H$ and $K_s$ bands using a probabilistic model accounting for variations in the parallax zeropoint and underestimation of the parallax uncertainties. The derived relations are compared to those measured for the Large and Small Magellanic Clouds, the Sagittarius dwarf spheroidal galaxy, globular cluster members and the subset of Milky Way Mira variables with VLBI parallaxes. The Milky Way linear $JHK_s$ relations are slightly steeper and thus fainter at short period than the corresponding LMC relations suggesting population effects in the near-infrared are perhaps larger than previous observational works have claimed. Models of the Gaia astrometry for the Mira variables suggest that, despite the intrinsic photocentre wobble and use of mean photometry in the astrometric solution of the current data reduction, the recovered parallaxes should be on average unbiased but with underestimated uncertainties for the nearest stars. The recommended Gaia EDR3 parallax zeropoint corrections evaluated at $\nu_\mathrm{eff}=1.25\,\mu\mathrm{m}^{-1}$ require minimal ($\lesssim5\,\mu\mathrm{as}$) corrections for redder five-parameter sources, but over-correct the parallaxes for redder six-parameter sources, and the parallax uncertainties are underestimated, at most by a factor $\sim1.6$ at $G\approx12.5\,\mathrm{mag}$. The derived period--luminosity relations are used as anchors for the Mira variables in the Type Ia host galaxy NGC 1559 to find $H_0=(73.7\pm4.4)\,\mathrm{km\,s}^{-1}\mathrm{Mpc}^{-1}$.Comment: 31 pages, 18 figures, accepted for publication in MNRA