Paul J. McMillan

Gaia Data Release 1 - Astrometry: one billion positions, two million proper motions and parallaxes

Gaia Data Release 1 (Gaia DR1) contains astrometric results for more than 1 billion stars brighter than magnitude 20.7 based on observations collected by the Gaia satellite during the first 14 months of its operational phase. We give a brief overview of the astrometric content of the data release and of the model assumptions, data processing, and validation of the results. For stars in common with the Hipparcos and Tycho-2 catalogues, complete astrometric single-star solutions are obtained by incorporating positional information from the earlier catalogues. For other stars only their positions are obtained by neglecting their proper motions and parallaxes. The results are validated by an analysis of the residuals, through special validation runs, and by comparison with external data. Results. For about two million of the brighter stars (down to magnitude ~11.5) we obtain positions, parallaxes, and proper motions to Hipparcos-type precision or better. For these stars, systematic errors depending e.g. on position and colour are at a level of 0.3 milliarcsecond (mas). For the remaining stars we obtain positions at epoch J2015.0 accurate to ~10 mas. Positions and proper motions are given in a reference frame that is aligned with the International Celestial Reference Frame (ICRF) to better than 0.1 mas at epoch J2015.0, and non-rotating with respect to ICRF to within 0.03 mas/yr. The Hipparcos reference frame is found to rotate with respect to the Gaia DR1 frame at a rate of 0.24 mas/yr. Based on less than a quarter of the nominal mission length and on very provisional and incomplete calibrations, the quality and completeness of the astrometric data in Gaia DR1 are far from what is expected for the final mission products. The results nevertheless represent a huge improvement in the available fundamental stellar data and practical definition of the optical reference frame.

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. We use a likelihood analysis to investigate the distance of the Sun from the Galactic Centre, R o , the rotational speed of the local standard of rest, v 0 , and the peculiar velocity of the Sun, v ⊙ , 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 v ⊙ or a net peculiar motion of the high-mass star-forming regions. We argue that a correction to v ⊙ is much more likely and these data support the conclusion of Binney that V ⊙ should be revised upwards from 5.2 to 11 km s ―1 . We find that the values of R o and v 0 that we determine are heavily dependent on the model we use for rotation curve, with model-dependent estimates of R 0 ranging from 6.7 ± 0.5 to 8.9 ± 0.9 kpc, and those of v 0 ranging from 200 ± 20 to 279 ± 33 km s ―1 . We argue that these data cannot be thought of as implying any particular values of R o or v 0 . However, we find that v 0 /R 0 is better constrained, lying in the range 29.9 -31.6 km s ―1 kpc ―1 for all models but one.

Gaia Data Release 2 - The astrometric solution

Context. Gaia Data Release 2 (Gaia DR2) contains results for 1693 million sources in the magnitude range 3 to 21 based on observations collected by the European Space Agency Gaia satellite during the first 22 months of its operational phase. Aims. We describe the input data, models, and processing used for the astrometric content of Gaia DR2, and the validation of these resultsperformed within the astrometry task. Methods. Some 320 billion centroid positions from the pre-processed astrometric CCD observations were used to estimate the five astrometric parameters (positions, parallaxes, and proper motions) for 1332 million sources, and approximate positions at the reference epoch J2015.5 for an additional 361 million mostly faint sources. These data were calculated in two steps. First, the satellite attitude and the astrometric calibration parameters of the CCDs were obtained in an astrometric global iterative solution for 16 million selected sources, using about 1% of the input data. This primary solution was tied to the extragalactic International Celestial Reference System (ICRS) by means of quasars. The resulting attitude and calibration were then used to calculate the astrometric parameters of all the sources. Special validation solutions were used to characterise the random and systematic errors in parallax and proper motion. Results. For the sources with five-parameter astrometric solutions, the median uncertainty in parallax and position at the reference epoch J2015.5 is about 0.04 mas for bright (G < 14 mag) sources, 0.1 mas at G = 17 mag, and 0.7 masat G = 20 mag. In the proper motion components the corresponding uncertainties are 0.05, 0.2, and 1.2 mas yr−1, respectively.The optical reference frame defined by Gaia DR2 is aligned with ICRS and is non-rotating with respect to the quasars to within 0.15 mas yr−1. From the quasars and validation solutions we estimate that systematics in the parallaxes depending on position, magnitude, and colour are generally below 0.1 mas, but the parallaxes are on the whole too small by about 0.03 mas. Significant spatial correlations of up to 0.04 mas in parallax and 0.07 mas yr−1 in proper motion are seen on small (< 1 deg) and intermediate (20 deg) angular scales. Important statistics and information for the users of the Gaia DR2 astrometry are given in the appendices.

Constraining the Galaxy's dark halo with RAVE stars

We use the kinematics of ∼200000 giant stars that lie within ∼1.5kpc of the plane to measure the vertical profile of mass density near the Sun. We find that the dark mass contained within the isodensity surface of the dark halo that passes through the Sun ((6 ± 0.9) × 10 10 M� ), and the surface density within 0.9kpc of the plane ((69 ± 10)Mpc −2 ) are almost inde- pendent of the (oblate) halos axis ratio q. If the halo is spherical, 46 per cent of the radial force on the Sun is provided by baryons, and only 4.3 per cent of the Galaxys mass is baryonic. If the halo is flattened, the baryons contribute even less strongly to the local ra- dial force and to the Galaxys mass. The dark matter density at the location of the Sun is 0.0126q −0.89 Mpc −3 = 0.48q −0.89 GeVcm −3 . When combined with other literature results we find hints for a mildly oblate dark halo with q � 0.8. Our value for the dark mass within the solar radius is larger than that predicted by cosmological dark-matter-only simulations but in good agreement with simulations once the effects of baryonic infall are taken into account. Our mass models consist of three double-exponential discs, an oblate bulge and a Navarro- Frenk-White dark matter halo, and we model the dynamics of the RAVE (RAdial Velocity Experiment) stars in the corresponding gravitational fields by finding distribution functions f(J) that depend on three action integrals. Statistical errors are completely swamped by systematic uncertainties, the most important of which are the distance to the stars in the pho- tometric and spectroscopic samples and the solar distance to the Galactic Centre. Systematics other than the flattening of the dark halo yield overall uncertainties ∼15percent.

New distances to RAVE stars

Probability density functions (pdfs) are determined from new stellar parameters for the distance moduli of stars for which the RAdial Velocity Experiment (RAVE) has obtained spectra with S/N >= 10. Single-Gaussian fits to the pdf in distance modulus suffice for roughly half the stars, with most of the other half having satisfactory two-Gaussian representations. As expected, early-type stars rarely require more than one Gaussian. The expectation value of distance is larger than the distance implied by the expectation of distance modulus; the latter is itself larger than the distance implied by the expectation value of the parallax. Our parallaxes of Hipparcos stars agree well with the values measured by Hipparcos, so the expectation of parallax is the most reliable distance indicator. The latter are improved by taking extinction into account. The effective temperature-absolute magnitude diagram of our stars is significantly improved when these pdfs are used to make the diagram. We use the method of kinematic corrections devised by Schonrich, Binney and Asplund to check for systematic errors for general stars and confirm that the most reliable distance indicator is the expectation of parallax. For cool dwarfs and low-gravity giants, tends to be larger than the true distance by up to 30 per cent. The most satisfactory distances are for dwarfs hotter than 5500 K. We compare our distances to stars in 13 open clusters with cluster distances from the literature and find excellent agreement for the dwarfs and indications that we are overestimating distances to giants, especially in young clusters.

Models of our Galaxy – II

Stars near the Sun oscillate both horizontally and vertically. In a previous paper by Binney it was assumed that the coupling between these motions can be modelled by determining the horizontal motion without reference to the vertical motion, and recovering the coupling between the motions by assuming that the vertical action is adiabatically conserved as the star oscillates horizontally. Here, we show that, although the assumption of adiabatic invariance works well, more accurate results can be obtained by taking the vertical action into account when calculating the horizontal motion. We use orbital tori to present a simple but fairly realistic model of the Galaxys discs in which the motion of stars is handled rigorously, without decomposing it into horizontal and vertical components. We examine the ability of the adiabatic approximation to calculate the models observables, and find that it performs perfectly in the plane, but errs slightly away from the plane. When the new correction to the adiabatic approximation is used, the density, mean-streaming velocity and velocity dispersions are in error by less than 10per cent for distances up to 2.5kpc from the Sun. The torus-based model reveals that at locations above the plane, the long axis of the velocity ellipsoid points almost to the Galactic centre, even though the model potential is significantly flattened. This result contradicts the widespread belief that the shape of the Galaxys potential can be strongly constrained by the orientation of velocity ellipsoid near the Sun. An analysis of individual orbits reveals that in a general potential the orientation of the velocity ellipsoid depends on the structure of the models distribution function as much as on its gravitational potential, contrary to what is the case for Stackel potentials. We argue that the adiabatic approximation will provide a valuable complement to torus-based models in the interpretation of current surveys of the Galaxy. (Less)

The mass distribution and gravitational potential of the Milky Way

We present mass models of the Milky Way created to fit observational constraints and to be consistent with expectations from theoretical modelling. The method used to create these models is that demonstrated in our previous study, and we improve on those models by adding gas discs to the potential, considering the effects of allowing the inner slope of the halo density profile to vary, and including new observations of maser sources in the Milky Way amongst the new constraints. We provide a best-fitting model, as well as estimates of the properties of the Milky Way. Under the assumptions in our main model, we find that the Sun is R0 = 8.20 ± 0.09 kpc from the Galactic Centre, with the circular speed at the Sun being v0 = 232.8 ± 3.0 kms-1; and that the Galaxy has a total stellar mass of (54.3 ± 5.7) × 109 M⊙, a total virial mass of (1.30 ± 0.30) × 1012M⊙ and a local dark-matter density of 0.40 ± 0.04 GeV cm-3, where the quoted uncertainties are statistical. These values are sensitive to our choice of priors and constraints. We investigate systematic uncertainties, which in some cases may be larger. For example, if we weaken our prior on R0, we find it to be 7.97 ± 0.15 kpc and that v0 = 226.8 ± 4.2 kms-1.We find that most of these properties, including the local dark-matter density, are remarkably insensitive to the assumed power-law density slope at the centre of the dark-matter halo. We find that it is unlikely that the local standard of rest differs significantly from that found under assumptions of axisymmetry. We have made code to compute the force from our potential, and to integrate orbits within it, publicly available. (Less)

Initial conditions for disc galaxies

We present a general recipe for constructing N-body realizations of galaxies comprising near spherical and disc components. First, an exact spherical distribution function for the spheroids (halo and bulge) is determined, such that it is in equilibrium with the gravitational monopole of the disc components. Second, an N-body realization 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.

In the thick of it: metal-poor disc stars in RAVE

By selecting in the Radial Velocity Experiment-fourth data release (RAVE-DR4) survey the stars located between 1 and 2 kpc above the Galactic plane, we question the consistency of the simplest three-component model (thin disc, thick disc and halo) for the Milky Way. We confirm that the metallicity and azimuthal velocity distribution functions of the thick disc are not Gaussian. In particular, we find that the thick disc has an extended metallicity tail going at least down to [M/H] = 2 dex, contributing roughly 3 per cent of the entire thick disc population and having a shorter scalelength compared to the canonical thick disc. The mean azimuthal velocity of these metal-poor stars allows us to estimate the correlation between the metallicity ([M/H]) and the orbital velocity (V-phi), which is an important constraint on the formation mechanisms of the Galactic thick disc. Given our simple approach, we find V-phi[M/H] 50 km s(-1) dex(-1), which is in very good agreement with previous literature values. We complete the study with a brief discussion on the implications of the formation scenarios for the thick disc and suggest that given the above-mentioned characteristics, a thick disc mainly formed by radial migration mechanisms seems unlikely.

The rich are different : evidence from the RAVE survey for stellar radial migration

Using the RAdial Velocity Experiment fourth data release (RAVE DR4), and a new metallicity calibration that will be also taken into account in the future RAVE DR5, we investigate the existence and the properties of supersolar metallicity stars ([M/H] ≳ +0.1 dex) in the sample, and in particular in the solar neighbourhood. We find that RAVE is rich in supersolar metallicity stars, and that the local metallicity distribution function declines remarkably slowly up to +0.4 dex. Our results show that the kinematics and height distributions of the supersolar metallicity stars are identical to those of the [M/H] ≲ 0 thin-disc giants that we presume were locally manufactured. The eccentricities of the supersolar metallicity stars indicate that half of them are on a roughly circular orbit (e ≤ 0.15), so under the assumption that the metallicity of the interstellar medium at a given radius never decreases with time, they must have increased their angular momenta by scattering at corotation resonances of spiral arms from regions far inside the solar annulus. The likelihood that a star will migrate radially does not seem to decrease significantly with increasing amplitude of vertical oscillations within range of oscillation amplitudes encountered in the disc.