Rotation Curves Research Articles

Six spiral galaxies lacking dark matter

Dark matter is believed to be the essential building blocks of galaxy formation. While instances of galaxies lacking dark matter have been observed, these occurrences are typically linked to specific formation mechanisms, making them stand out as unique cases. In spiral galaxies, the presence of flat rotation curves is a common observation, indicating the need for dark matter to support these dynamics. However, the galaxies displaying minimal or no dark matter are likely not exceptional cases. We report several spiral galaxies where the flat rotation areas exhibit an average dynamical to baryonic mass ratio value of Mdyn/Mbary∼1.09\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M_{dyn}/M_{bary}\\sim 1.09$$\\end{document}. The low dynamical to baryonic mass ratios indicate that the kinematics of these galaxies can be supported by their baryonic mass only. The existence of spiral galaxies devoid of dark matter suggests that, in specific scenarios, the influence of dark matter on galaxy formation may not be as universally essential as previously believed.

Swimming Velocity Analysis Using Wearable Inertial Sensors and Speedometer: A Comparative Study.

The speedometer is widely used to evaluate swimming velocity but has some constraints. With the constant development of inertial units (IMUs), it is expected that they will become a good alternative to the speedometer. This study aimed to compare the data retrieved by an IMU and a speedometer when breaststroke is performed at maximum speed. Sixteen swimmers, nine males and seven females (20.3 ± 3.3 vs. 18.7 ± 1.1 years old, 65.8 ± 11.2 vs. 57.7 ± 9.1 kg of body mass and 1.75 ± 0.07 vs. 1.61 ± 0.10 m of height, respectively), performed 4 × 25 m of breaststroke sprint. They were equipped with an IMU fixed to the sacrum and with the line of an electromechanical speedometer (acquisition frequency of 50 Hz) fixed at the central point in the lumbar region. Statistical parametric mapping was used to compare the velocity curves, IBM SPSS was used for descriptive statistics and Bland-Altman plots were used for agreement of measurements. The results show that the IMU and speedometer do not show similar patterns, and the velocity values measured by the IMU are lower (p < 0.001). Bland-Altman plots presented a larger bias in terms of coefficient of variation and intracycle velocity variation. It can be concluded that IMUs and speedometers are not substitutes for each other as methods for evaluating intracycle velocity variations.

A study of centaur (54598) Bienor from multiple stellar occultations and rotational light curves

Centaurs, distinguished by their volatile-rich compositions, play a pivotal role in understanding the formation and evolution of the early Solar System, as they represent remnants of the primordial material that populated the outer regions. Stellar occultations offer a means to investigate their physical properties, including shape and rotational state, and the potential presence of satellites and rings. This work aims to conduct a detailed study of the centaur (54598) Bienor through stellar occultations and rotational light curves from photometric data collected during recent years. We successfully predicted three stellar occultations by Bienor that were observed from Japan, Western Europe, and the USA. In addition, we organized observational campaigns from Spain to obtain rotational light curves. At the same time, we developed software to generate synthetic light curves from three-dimensional shape models, enabling us to validate the outcomes through computer simulations. We resolved Bienor's projected ellipse for December 26, 2022; determined a prograde sense of rotation; and confirmed an asymmetric rotational light curve. We also retrieved the axes of its triaxial ellipsoid shape as a = (127 pm 5) km, b = (55 pm 4) km, and c = (45 pm 4) km. Moreover, we refined the rotation period to 9.1736 pm 0.0002 hours and determined a geometric albedo of (6.5 pm 0.5) &lt;!PCT!&gt;, which is higher than previously determined by other methods. Finally, by comparing our findings with previous results and simulated rotational light curves, we analyzed whether an irregular or contact-binary shape, an additional element such as a satellite, or significant albedo variations on Bienor's surface may be present.

Relationships Between Force-Time Curve Variables and Tennis Serve Performance in Competitive Tennis Players.

Fourel, L, Touzard, P, Fadier, M, Arles, L, Deghaies, K, Ozan, S, and Martin, C. Relationships between force-time curve variables and tennis serve performance in competitive tennis players. J Strength Cond Res 38(9): 1667-1674, 2024-Practitioners consider the role of the legs in the game of tennis as fundamental to achieve high performance. But, the exact link between leg actions and high-speed and accurate serves still lacks understanding. Here, we investigate the correlation between force-time curve variables during serve leg drive and serve performance indicators. Thirty-six competitive players performed fast serves, on 2 force plates, to measure ground reaction forces (GRF). Correlation coefficients describe the relationships between maximal racket head velocity, impact height, and force-time curve variables. Among all the variables tested, the elapsed time between the instants of maximal vertical and maximal anteroposterior GRF ( r = -0.519, p < 0.001) and the elapsed time between the instant of maximal anteroposterior GRF and ball impact ( r = -0.522, p < 0.001) are the best predictors of maximal racket velocity. Maximal racket head velocity did not significantly correlate with the mean or maximal vertical GRF or with the mean or maximum rate of vertical force development. The best predictor for impact height is the relative net vertical impulse during the concentric phase ( r = 0.772, p < 0.001). This work contributes to a better understanding of the mechanical demands of tennis serve motion and gives guidelines to improve players preparation and performance. Trainers should encourage their players to better synchronize their upward and forward pushing action during the serve to increase maximal racket head velocity. Players should also aim to improve their relative net vertical impulse to increase impact height through strength training and technical instructions.

Wormholes in dwarf and spiral galactic halo regions

In this article, we study solutions which describe wormholes in the halos of dwarf and massive spiral galaxies with different morphologies, masses, sizes and gas fractions by taking observed flat rotation curves as input. We assume Singular Isothermal Sphere (SIS) dark matter density profile. This result confirms the possible existence of wormholes in both dwarf and massive spiral galaxies.

Revisiting flat rotation curves in Chern-Simons modified gravity

We revisit slow rotating black hole (BH) solutions in Chern-Simons modified gravity (CSMG) by considering perturbative solution about Schwarzschild BH. In particular, the case when nondynamical CSMG with noncanonical CS scalar is considered. We provide a new solution different from the previously obtained one [1] which we refer to as KMT model. The present solution accounts for frame dragging effect which includes not only radial dependence as in the KMT. Nevertheless, it reduces to KMT as a particular case. We show that the tidal gravitational force (Kretschmann invariant) associated to the present solution contains a term of order 1/r3 additional to Schwarzschild but absent from directional divergence, unlike KMT model which diverges along the axis of symmetry. We derive the corresponding circular velocity of a massive test particle in which the KMT velocity is recovered in addition to an extra term ∝r. We investigate possible constraints on KMT and the present solutions from the observed rotation curve of UGC11455 galaxy as an example. We show that perturbation solutions cannot physically explain the flattening of galactic rotation curves.

Spatial rotational behaviour of intact and damaged column foot joints: numerical modelling

Columns in traditional Chinese timber structures barely rest on stone bases, and the column foot joints are capable of resisting moment around any direction. This study numerically investigated the spatial rotational behaviour of intact and damaged columns based on experiments. Unidirectional cyclic loading tests were carried out on two intact and three damaged column foot joint specimens. A fibre element-based numerical model for the column foot joints was developed and validated by use of the unidirectional loading test results. Numerical analyses were performed based on the fibre element-based model to obtain the rotational behaviour of the intact and damaged column foot joints under spatial loading. The analyses indicated that the moment–rotation curve of an intact column foot joint under spatial loading was on an umbrella-shaped surface. The damage at the column foot not only unidirectionally decreased the moment-resisting capacity of a column foot joint but also resulted in a rotational performance degradation valley on the moment–rotation surface of the joint. The rotational behaviour of both the intact and damaged column foot joints under spatial loading was highly non-linear. This developed fibre element-based model can be further utilised to analyse the structural performance of traditional timber structures under three-dimensional excitations.

Investigation of a W UMa-type contact binary GZ And in a physical triple system

GZ And is a variable star within the visually observed multiple-star system ADS 1693. Recent observations have yielded new light curves for GZ And, obtained using the Xinglong 85-cm telescope and the Transiting Exoplanet Survey Satellite (TESS) satellite. These light curves, along with radial velocity curves, were analyzed simultaneously to ascertain the fundamental physical parameters of GZ And’s components. The findings indicate that the primary star has a mass of M1 = 0.57 (4)M⊙, radius of R1 = 0.75 (2)R⊙, and luminosity of L1 = 0.42 (2)L⊙. The secondary star is characterized by a mass of M2 = 1.19 (9)M⊙, radius of R2 = 1.04 (3)R⊙, and luminosity of L2 = 0.63 (3)L⊙. Their orbital separation is determined to be a = 2.30 (6)R⊙. An analysis of the accumulated times of light minima reveals that GZ And is undergoing orbital period variations at a rate of dP/dt = −7.58 (7) × 10−8day ⋅ year−1, likely due to mass transfer from the more massive component to its lighter counterpart at a rate of dM2/dt = −9.06 (8) × 10−8M⊙⋅ year−1. Additionally, distance measurements for the component stars in ADS 1693, derived from Gaia DR3 astrometric data, suggest that ADS 1693A (GZ And) and ADS 1693B are gravitationally bound and likely originated from the same molecular cloud, sharing similar ages. This evidence supports the classification of GZ And as a W UMa-type contact binary within a physically associated triple system.

Bow-shock structure of Sgr-B molecular-cloud complex in the Galactic Centre inferred from 3D CO-line kinematics

ABSTRACT Three-dimensional (3D) bubble structure of the Sgr-B molecular-cloud complex is derived by a kinematical analysis of CO-line archival cube data of the Galactic Centre (GC) observed with the Nobeyama 45-m telescope. The line-of-sight depth is estimated by applying the face-on transformation method of radial velocity to the projected distance on the Galactic plane considering the Galactic rotation of the central molecular zone (CMZ). The 3D complex exhibits a conical-horn structure with the Sgr-B2 cloud located in the farthest end on the line of sight at radial velocity $v_{\rm lsr} \sim 70$ km s$^{-1}$, and the entire complex composes a lopsided bubble opening toward the Sun at $v_{\rm lsr}\sim 50$ to 30 km s$^{-1}$. The line-of-sight extent of the complex is $\sim 100$ pc according to the large velocity extent for several tens of km s$^{-1}$ from Sgr-B2 to the outskirts. The entire complex exhibits a flattened conical bubble with full sizes $\sim 40 \ {\rm pc} \times 20 \ {\rm pc} \times 100 \ {\rm pc}$ in the l, b and line-of-sight directions, respectively. Based on the 3D analysis, we propose a formation scenario of the giant molecular bubble structure due to a galactic bow shock, and suggest that the star formation in Sgr-B2 was enhanced by dual-side compression (DSC) of the B2 cloud by the Galactic shock wave from up-stream and expanding H ii region from the down-stream side of the GC Arm I in Galactic rotation.

Low temperature coefficient of frequency AlN Lamb wave resonator using groove structure between interdigital transducers

The lithographically tunable and small size features of Lamb wave resonators (LWRs) take a bright future for their use in high frequency narrow band filters. Resonant frequency drift due to temperature variation has a large impact on the narrower passband and a temperature coefficient of frequency (TCF) closer to 0 can broaden the stable temperature range of the resonator. This paper proposes a method of etching grooves in the area of the piezoelectric layer not covered by the Interdigital transducer (IDT) electrodes to improve the temperature stability of the Lamb resonator. Through the finite element method and theoretical analysis, the phase velocity, group velocity, and TCF dispersion curve of different modes of the resonator with groove structure were determined. The reason for the change of TCF under different normalized thicknesses of AlN was explained through the conversion of the LWR from a contour mode resonator (CMR) to a Cross-Sectional Lamé Mode Resonator. Simulation and test have shown that etching grooves have the effect of reducing TCF by adjusting the electromechanical coupling coefficient. The test shows that 205 nm-depth grooves can lower the TCF of the S0 mode IDT-Open LWR from −13.3 to −5.1 ppm/°C and S1 mode from −36.8 to −9.0 ppm/°C, respectively. The TCF of S0 and S1 mode LWRs decreased by 61.7% and 75.5%, respectively, after 205 nm groove etching. The groove etching method greatly raises the temperature stability of the LWR, enabling Lamb wave filters to operate stably over a wider temperature range.

Deformation, shape transformations, and stability of elastic rod loops within spherical confinement

Mechanical insight into the packing of slender objects within confinement is essential for understanding how polymers, filaments, or wires organize and rearrange in limited space. Here we combine theoretical modeling, numerical optimization, and experimental studies to reveal spherical packing behavior of thin elastic rod loops of homogeneous or inhomogeneous stiffness. Across varying loop lengths, a rich array of configurations including circle, saddle, figure-eight, and more intricate patterns are identified. A theoretical framework rooted in the local equilibrium of force and moment is proposed for the rod loop deformation, facilitating the determination of internal and contact forces experienced by the rods during deformation. For the confined homogeneous rod loops, their stable and metastable configurations are well described using proposed Euler rotation curves, which offer a concise and effective approach for configuration prediction. Moreover, formulated analysis on the stability and critical force for homogeneous rod loops on great circles of the spherical confinement are performed. For inhomogeneous rod loops with two segments of differing stiffness, the stiffer segment exhibits less deviation from the great circle, while the softer segment undergoes more pronounced deformation. These findings not only enhance our understanding of buckling and post-buckling phenomena but also offer insights into filament patterning within confining environments.

Possibility of the Traversable Wormholes in the Galactic Halos within 4D Einstein–Gauss–Bonnet Gravity

AbstractRecently, there has been significant interest regarding the regularization of a limit of Einstein–Gauss–Bonnet (EGB) gravity. This regularization involves re‐scaling the Gauss–Bonnet (GB) coupling constant as , which bypasses Lovelock's theorem and avoids Ostrogradsky instability. A noteworthy observation is that the maximally or spherically symmetric solutions for all the regularized gravities coincide in the scenario. Considering this, the wormhole solutions in the galactic halos are investigated based on three different choices of dark matter (DM) profiles, such as Universal Rotation Curve, Navarro–Frenk–White, and Scalar Field Dark Matter with the framework of EGB gravity. Also, the Karmarkar condition is used to find the exact solutions for the shape functions under different non‐constant redshift functions. The energy conditions for each DM profile are discussed and the influence of GB coefficient in violating energy conditions are noticed, especially null energy conditions. Further, some physical features of wormholes, viz. complexity factor, active gravitational mass, total gravitational energy, and embedding diagrams, have been explored.

Recent observations of the rotation of distant galaxies and the implication for dark matter

Context. Recent measurements of gas velocity in the outer parts of high redshift galaxies suggest that steeply falling rotation curves may be common or even universal in these galaxies, in contrast to the near universal flat, non-declining rotation curves in nearby galaxies. Aims. The aim was to investigate the implications of these postulated steeply falling rotation curves for the role of dark matter in galaxy formation. Methods. Using an established computer code, the collapse of dark matter and baryonic matter together, starting with a variety of initial conditions, was simulated for comparison with the observed rotation curves. A simulation of collapsing baryonic matter on its own without dark matter was also carried out. The masses of the protogalaxies were chosen to produce a stellar disc in the same mass range as the observed galaxies at roughly the same redshift. Results. As soon as a smooth stellar disc was formed in the baryonic matter, with properties similar to the observed high redshift galaxies, the computed rotation curves were without exception relatively flat to large radius in the gas disc. Only a simulation without a dark matter halo was able to reproduce the observed rotation curves. Conclusions. This implies that if the high redshift steeply falling rotation curves turn out to be common, then the standard scenario of galaxy formation by baryonic matter falling into the potential well of a massive dark matter halo must be wrong, unless there is pressure support via velocity dispersion significantly higher than has so far been observed or resulted from our simulations. It would also imply that for these galaxies the flat rotation curves at low redshift must be due to dark matter which has subsequently fallen into the galactic potential well, or there must be some other explanation for their contemporary flat rotation curves other than dark matter.

Black Hole–Halo Mass Relation from UNIONS Weak Lensing

This Letter presents, for the first time, direct constraints on the black hole–halo mass relation using weak gravitational-lensing measurements. We construct type I and type II active galactic nucleus (AGN) samples from the Sloan Digital Sky Survey, with a mean redshift of 0.4 (0.1) for type I (type II) AGNs. This sample is cross correlated with weak-lensing shear from the Ultraviolet Near Infrared Optical Northern Survey. We compute the excess surface mass density of the halos associated with 36,181 AGNs from 94,308,561 lensed galaxies and fit the halo mass in bins of black hole mass. We find that more massive AGNs reside in more massive halos. The relation between halo mass and black hole mass is well described by a power law of slope 0.6 for both type I and type II samples, in agreement with models that link black hole growth to baryon feedback. We see no dependence on AGN type or redshift in the black hole–halo mass relation below a black hole mass of 108.5 M ⊙. Above that mass, we find more massive halos for the low-z type II sample compared to the high-z type I sample, but this difference may be interpreted as systematic error in the black hole mass measurements. Our results are consistent with previous measurements for non-AGN galaxies. At a fixed black hole mass, our weak-lensing halo masses are consistent with galaxy rotation curves but significantly lower than galaxy-clustering measurements. Finally, our results are broadly consistent with state-of-the-art hydrodynamical cosmological simulations, providing a new constraint for black hole masses in simulations.

Probing the Galactic Halo with RR Lyrae Stars. VI. The Radial Velocity Curve Templates of RRc Stars

We present radial velocity (RV) curve templates of RR Lyrae first-overtone (RRc) stars constructed with the Mg i b triplet and Hα lines using time-domain Medium-Resolution Survey spectra of seven RRc stars from Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) Data Release 9. Additionally, we derive the relation between the stellar RV curve amplitudes and g-band light curve amplitudes from Zwicky Transient Facility (ZTF) public survey. For those RRc stars without ZTF g-band light curves, we provide the conversions from the light curve amplitudes in ZTF r- and i-bands, Gaia G-band, and V-band from the All-Sky Automated Survey for Supernovae to those in ZTF g-band. We validate our RV curve templates using the RRc star SV Scl and find the uncertainties of systemic RV are less than 2.11 km s −1 and 6.08 km s −1 based on the Mg i b triplet and Hα lines, respectively. We calculate the systemic RVs of 30 RRc stars using the RV curve templates constructed with the Mg i b triplet and Hα lines and find the systemic RVs are comparable with each other. This RV curve template will be particularly useful for obtaining the systemic RV of RRc using the LAMOST spectroscopy.

A Strong Falsification of the Universal Radial Acceleration Relation in Galaxies

In the past few decades, many studies revealed that there exist some apparent universal relations that can describe the dynamical properties in galaxies. In particular, the radial acceleration relation (RAR) is one of the most popular relations discovered recently that can be regarded as a universal law to connect the dynamical radial acceleration with the baryonic acceleration in galaxies. This has revealed an unexpected close connection between dark matter and baryonic matter in galaxies. In this article, by following the recent robust Galactic rotation curve analyzes, we derive the Galactic RAR (GRAR) and show for the first time that the alleged best-fit universal RAR deviates from the GRAR data at more than 5σ. This provides a strong evidence to falsify the universal nature of RAR in galaxies claimed in past studies.

Open Star Clusters and Their Asymmetrical Tidal Tails

Stars that evaporate from their star cluster by the energy equipartition process end up in either a leading or a trailing tidal tail. In Newtonian gravitation and for open star clusters in the solar vicinity, the tidal threshold, or práh, for escape is symmetrical, such that the leading and trailing tails are equally populated. The data from six independent teams that applied the convergent point method to map out the tidal tails of four open clusters (the Hyades, Praesepe, Coma Berenices, and COIN-Gaia 13) using Gaia DR2 and DR3 are here applied to test for the expected symmetry. All tidal tails contain more stars in the leading tail. The combined confidence amounts to an 8σ falsification of the práh symmetry. The same test using Milgromian dynamics leads to consistency with the data. More effort needs to be exerted on this matter, but the data indicate with high confidence that the tidal práh of an open star cluster is asymmetrical, with the corresponding confidence that Newtonian gravitation is falsified. Open star clusters depopulate more rapidly in Milgromian than in Newtonian dynamics, and the COIN-Gaia 13 cluster is here found to be nearly completely dissolved. In view of these results, the wide-binary star test and the finding of a Keplerian Galactic rotation curve are briefly discussed.

Comparing bulge RR Lyrae stars with bulge giants

Context. The structure and kinematics of the old component of the Galactic bulge are still a matter of debate. It is clear that the bulk of the bulge as traced by red clump stars includes two main components, which are usually identified as the metal-rich and metal-poor components. They have different shapes, kinematics, mean metallicities, and alpha-element abundances. It is our current understanding that they are associated with a bar and a spheroid, respectively. On the other hand, RR Lyrae variables trace the oldest population of the bulge. While it would be natural to think that they follow the structure and kinematics of the metal-poor component, the data analysed in the literature show conflicting results. Aims. We aim to derive a rotation curve for bulge RR Lyrae stars in order to determine that the old component traced by these stars is distinct from the two main components observed in the Galactic bulge. Methods. This paper combines APOGEE-2S spectra with OGLE-IV light curves, near-infrared photometry, and proper motions from the VISTA Variables in the Vía Láctea survey for 4193 RR Lyrae stars. Six-dimensional phase-space coordinates were used to calculate orbits within an updated Galactic potential and to isolate the stars. Results. The stars that stay confined within the bulge represent 57% of our sample. Our results show that bulge RR Lyrae variables rotate more slowly than metal-rich red clump stars and have a lower velocity dispersion. Their kinematics is compatible with them being the low-metallicity tail of the metal-poor component. We confirm that a rather large fraction of halo and thick disc RR Lyrae stars pass by the bulge within their orbits, increasing the velocity dispersion. A proper orbital analysis is therefore critical to isolate bona fide bulge variables. Finally, bulge RR Lyrae seem to trace a spheroidal component, although the current data do now allow us to reach a firm conclusion about the spatial distribution.

The High-resolution Fe K Spectrum of Cygnus X-3

We analyze features of the Fe K spectrum of the high-mass X-ray binary Cygnus X-3. The spectrum was obtained with the Chandra High Energy Transmission Grating Spectrometer in the third diffraction order. The increased energy resolution of the third order enables us to fully resolve the Fe xxv Heα complex and the Fe xxvi Lyα lines. The emission-line spectrum shows the expected features of photoionization equilibrium, excited in the dense stellar wind of the companion star. We detect discrete emission from inner-shell transitions, in addition to absorption likely due to multiple unresolved transitions in lower ionization states. The emission-line intensity ratios observed in the range of the spectrum occupied by the Fe xxv n = 1–2 forbidden and intercombination lines suggest that there is a substantial contribution from resonantly scattered inner-shell emission from the Li- and Be-like ionization states. The Fe xxv forbidden and intercombination lines arise in the ionization zone closest to the compact object, and since they are not subject to radiative-transfer effects, we can use them in principle to constrain the radial velocity amplitude of the compact object. We infer that the results indicate a compact object mass of the order of the mass of the Wolf–Rayet companion star, but we note that the presence of resonantly scattered radiation from Li-like ions may complicate the interpretation of the He-like emission spectrum, and specifically of the radial velocity curve of the Fe xxv forbidden line.

The torsion of stellar streams and the overall shape of galactic gravity’s source

Context. Flat rotation curves, v(r), are naturally explained by elongated (prolate) dark matter (DM) distributions, and we have provided competitive fits to the SPARC database. To further probe the geometry of the halo, or the equivalent source of gravity in other formulations, one needs observables outside the galactic plane. Stellar streams, poetically analogous to airplane contrails, but caused by tidal dispersion of massive substructures such as satellite dwarf galaxies, would lie on their own plane (consistently with angular momentum conservation) should the DM-halo gravitational field be spherically symmetric. Tracks resembling entire orbits are seldom available because their periods are commensurable with Hubble time, with streams often presenting themselves as short segments. Aims. Therefore, we aim to establish stellar stream torsion, a local observable that measures the deviation from planarity in differential curve geometry, as a diagnostic providing sensitivity to aspherical DM distributions and ensuring the use of even relatively short streams. Methods. We performed small-scale simulations of tidally distorted star clusters to check that indeed a central force center produces negligible torsion, while distorted halos can generate it. Turning to observational data, we identified among the known streams those that are at the largest distance from the Galactic center, and that are likely not affected by the Magellanic clouds, as the most promising for the study, and by means of polynomial fits we extracted their differential torsion. Results. We find that the torsion of the few known streams that should be sensitive to most of the Milky Way’s DM halo is much larger than expected for a central spherical bulb alone. This is consistent with the nonsphericity of the halo. Conclusions. Future studies of stellar stream torsion with larger samples and further out of the galactic plane should be able to extract the ellipticity of the halo to see whether it is just a slight distortion of a spherical shape or whether it rather resembles a more elongated cigar.