Investigating the amplitude and rotation of the phase spiral in the Milky Way outer disc

Context: With the data releases from the astrometric space mission Gaia, the exploration of the structure of the Milky Way has developed in unprecedented detail and unveiled many previously unknown structures in the Galactic disc and halo. One such feature is the phase spiral where the stars in the Galactic disc form a spiral density pattern in the $Z-V_Z$ plane. Aims: We aim to characterize the shape, rotation, amplitude, and metallicity of the phase spiral in the outer disc of the Milky Way. This will allow us to better understand which physical processes caused the phase spiral and can give further clues to the Milky Way's past and the events that contributed to its current state. Methods: We use Gaia data release 3 (DR3) to get full position and velocity data on approximately 31.5 million stars, and metallicity for a subset of them. We then compute the angular momenta of the stars and develop a model to characterise the phase spiral in terms of amplitude and rotation at different locations in the disc. Results: We find that the rotation angle of the phase spiral changes with Galactic azimuth and Galactocentric radius, making the phase spiral appear to rotate about $3^\circ$ per degree in Galactic azimuth. Furthermore, we find that the phase spiral in the $2200 - 2400$ kpc km s$^{-1}$ range of angular momentum is particularly strong compared to the phase spiral that can be observed in the solar neighbourhood. The metallicity of the phase spiral appears to match that of the Milky Way disc field stars. Conclusions: We created a new model capable of fitting several key parameters of the phase spiral. We have been able to determine the rotation rate of the phase spiral and found a peak in the phase spiral amplitude which manifests as a very clear phase spiral when using only stars with similar angular momentum.Comment: Submitted to A&A. Abridge

Development of a theoretical model for upright postural control in lower limb prosthesis users

Methods used to assess quiet standing in unilateral prosthesis users often assume validity of an inverted pendulum model despite this being shown as invalid in some instances. The aim of the current study was to evaluate the validity of a proposed unilaterally-constrained pin-controller model in explaining postural control in unilateral prosthesis users. Prosthesis users were contrasted against the theoretical model as were able-bodied controls that stood on a platform which unilaterally constrained movement of the CoP. All participants completed bouts of quiet standing with eyes open, eyes closed and with feedback on inter-limb weight bearing asymmetry. Correlation coefficients were used to infer inverted pendulum behavior in both the anteroposterior and mediolateral directions and were derived from both kinematic (body attached markers) and kinetic (centre of pressure) experimental data. Larger, negative correlation coefficients reflected better model adherence, whilst low or no correlation reflected poorer model adherence. Inverted pendulum behavior derived from kinematic data, indicated coefficients of high magnitude in both mediolateral (all cases range 0.71–0.78) and anteroposterior (0.88–0.91) directions, irrespective of groups. Inverted pendulum behavior derived from kinetic data in the anteroposterior direction indicated validity of the model with large negative coefficients associated with the unconstrained/intact limbs (prosthesis users: − 0.45 to − 0.65, control group: − 0.43 to − 0.72), small coefficients in constrained/prosthetic limbs (prosthesis users: − 0.02 to 0.07, control group: 0.13–0.26) and large negative coefficients in combined conditions (prosthesis users: − 0.36 to − 0.56, control group: − 0.71 to − 0.82). For the mediolateral direction, coefficients were negligible for individual limbs (0.03–0.17) and moderate to large negative correlations, irrespective of group (− 0.31 to − 0.73). Data suggested both prosthesis users’ and able-bodied individuals’ postural control conforms well to that predicted by a unilaterally-constrained pin-controller model, which has implications for the fundamental control of posture in transtibial prosthesis users