Circular Velocity Curves Research Articles

Assessing the robustness of the Galactic rotation curve inferred from the Jeans equations using Gaia DR3 and cosmological simulations

Several authors have recently applied Jeans modelling to -based datasets to infer the circular velocity curve for the Milky Way. These works have consistently found evidence for a continuous decline in the rotation curve beyond $ kpc $, which may indicate the existence of a light dark matter (DM) halo. Using a large sample of Gaia DR3 data, we aim to derive the rotation curve of the Milky Way using the Jeans equations, and to quantify the role of systematic effects, both in the data and those inherent to the Jeans methodology under the assumptions of axisymmetry and time independence. We used data from the Gaia DR3 radial velocity spectrometer sample, supplemented with distances inferred through Bayesian frameworks, to determine the radial variation of the second moments of the velocity distribution for stars close to the Galactic plane. We used these profiles to determine the rotation curve using the Jeans equations under the assumption of axisymmetry and explored how they vary with azimuth and position above and below the plane of the Galactic disc. We applied the same methodology to an N-body simulation of a Milky Way-like galaxy impacted by a satellite akin the Sagittarius dwarf, and to the Auriga suite of cosmological simulations. The circular velocity curve we infer for the Milky Way is consistent with previous findings out to $ 15$ kpc, where our statistics are robust. Due to the larger number of stars in our sample, we are able to reveal evidence of disequilibrium and deviations from axisymmetry closer in. For example, we find that the second moment of $V_R$ flattens out at $R kpc, and that the second moment of $V_ is different above and below the plane for $R kpc. Our exploration of the simulations indicates that these features are typical of galaxies that have been perturbed by external satellites. From the simulations, we also estimate that the difference between the true circular velocity curve and that inferred from Jeans equations can be as high as $15<!PCT!>$, but that it is likely of the order of $10<!PCT!>$ for the Milky Way. This is higher than the systematic uncertainties associated with the observations or those linked to most modelling assumptions when using the Jeans equations. However, if the density of the tracer population were truncated at large radii instead of being exponential as often assumed, this could lead to the erroneous conclusion of a steeply declining rotation curve. We find that steady-state axisymmetric Jeans modelling becomes less robust at large radii, indicating that particular caution must be exercised when interpreting the rotation curve inferred in those regions. A more careful and sophisticated approach may be necessary for precision measurements of the DM content of our Galaxy.

Indefinitely Flat Circular Velocities and the Baryonic Tully–Fisher Relation from Weak Lensing

We use a new deprojection formula to infer the gravitational potential around isolated galaxies from weak gravitational lensing. The results imply circular velocity curves that remain flat for hundreds of kiloparsecs, greatly extending the classic result from 21 cm observations. Indeed, there is no clear hint of a decline out to 1 Mpc, well beyond the expected virial radii of dark matter halos. Binning the data by mass reveals a correlation with the flat circular speed that closely agrees with the baryonic Tully–Fisher relation known from kinematic data. These results apply to both early- and late-type galaxies, indicating a common universal behavior.

Asymmetric Drift Map of the Milky Way Disk Populations between 8 -16 kpc with LAMOST and Gaia datasets

The application of asymmetric drift (AD) tomography across different populations provides valuable insights into the kinematics, dynamics, and rotation curves of the Galactic disk. By leveraging common stars identified in both the LAMOST and Gaia surveys, alongside Gaia DR3’s circular velocity curve, we conducted a qualitative exploration of asymmetric drift distributions within the Galactic disk spanning distances from 8 to 16 kpc. In the R-Z plane, we observed that the asymmetric drift is minimal near the mid-plane of the Galactic disk and gradually increases with vertical distance, resulting in a distinctive “horn” shape. Additionally, our analysis revealed that populations with higher [ α/Fe] ratios exhibit greater asymmetric drift compared to those with lower [ α/Fe] ratios. Specifically, we found the asymmetric drift around the solar location to be approximately 6 km s −1, with a median value of 16 km s −1 across the entire sample. Notably, the median asymmetric drift in the northern region of the Galactic disk (20 km s −1) surpasses that in the southern region (13 km s −1), with errors remaining within 2 km s −1. Furthermore, our investigation into mono-age stellar populations unveiled that older stellar populations tend to exhibit larger asymmetric drift and velocity dispersion, aligning closely with predictions from previous numerical models. Finally, based on chemical compositions, we observed that the median asymmetric drift of the thick disk significantly exceeds that of the thin disk and found that star formation within the thick disk primarily occurred 8-10 billion years ago, whereas the thin disk’s predominant star formation period spanned 6-8 billion years ago.

Radial and azimuthal gradients of the moving groups in Gaia DR3: The slow and fast bar degeneracy problem

The structure and dynamics of the central bar of the Milky Way (MW) are still under debate whilst being fundamental ingredients for the evolution of our Galaxy. The recent Gaia DR3 offers an unprecedented detailed view of the 6D phase space of the MW, allowing for a better understanding of the complex imprints of the bar on the phase space. We aim to identify and characterise the dynamical moving groups across the MW disc, and use their large-scale distribution to help constrain the properties of the Galactic bar. We used 1D wavelet transforms of the azimuthal velocity ($V_ distribution in bins of radial velocity to robustly detect the kinematic substructure in the Gaia DR3 catalogue. We then connected these structures across the disc to measure the azimuthal (phi ) and radial ($R$) gradients of $V_ of the moving groups. We simulated thousands of perturbed distribution functions using backward integration, sweeping a large portion of parameter space of feasible Galaxy models that include a bar, in order to compare them with the data and to explore and quantify the degeneracies. The radial gradient of the Hercules moving group ($ V_ R$ = 28.1pm 2.8 $) cannot be reproduced by our simple models of the Galaxy that show much larger slopes both for a fast and a slow bar. This suggests the need for more complex dynamics (e.g. a different bar potential, spiral arms, a slowing bar, a complex circular velocity curve, external perturbations, etc.). We measured an azimuthal gradient for Hercules of $ V_ = -0.63pm $deg$^ $ and find that it is compatible with both the slow and fast bar models. Our analysis points out that in using this type of analysis, at least two moving groups are needed to start breaking the degeneracies. We conclude that it is not sufficient for a model to replicate the local velocity distribution; it must also capture its larger-scale variations. The accurate quantification of the gradients, especially in the azimuthal direction, will be key for the understanding of the dynamics governing the disc.

Tracing the Galactic disk with planetary nebulae using Gaia DR3

Aims. We study the population of Galactic planetary nebulae (PNe) and their central stars (CSPNe) through the analysis of their distances and Galactic distribution. The PN distances are obtained by means of a revised statistical distance scale, based on an astrometrically-defined sample of their central stars from the third Gaia Data Release (DR3) as calibrators. The new statistical distances, together with the proper motion of the CSPNe (also from DR3) with published PN abundances as well as radial velocities, are used to characterize the PN populations in the Galaxy and to derive the radial metallicity gradient. Methods. The statistical scale was applied to infer the distances of a significant number (∼850) of Galactic PNe, for which we deliver a new catalog of PN distances. By adopting a circular velocity curve of the Galaxy, we also obtained peculiar 3D velocities for a large sample of PNe (∼300). The elemental abundances of the PNe were culled from the literature for an updated catalog, to be used in our analysis and other external applications. Results. The radial chemical gradient of the Galactic disk is traced by PNe with available chemical abundances and distances, and kinematic data of the CSPNe are employed to identify the halo PN population. We date PN progenitors based both on abundances and kinematic properties, finding a confirmation of the first method with the second. For all PNe with at least one oxygen determination in the literature, we find a slope of the radial oxygen gradient equal to Δ log(O/H)/ΔRG = −0.0144 ± 0.00385 [dex kpc−1]. Furthermore, we estimate radial oxygen gradients for the PNe with old (> 7.5 Gyr) and young (< 1 Gyr) progenitors to be Δ log(O/H)/ΔRG = −0.0121 ± 0.00465 and −0.022 ± 0.00758 [dex kpc−1], respectively, thus disclosing a mild steepening of the gradient since Galaxy formation, with a slope change of 0.01 dex. The time evolution is slightly higher (∼0.015 dex) when we select the best available abundances in the literature. This result broadly agrees with previous PN results, but is now based on Gaia DR3 analysis, and it also agrees with what has been traced by most other Galactic probes. We also find a moderate oxygen enrichment when comparing the PNe with young and old progenitors.

A Bayesian estimation of the Milky Way’s circular velocity curve using Gaia DR3

Aims. Our goal is to calculate the circular velocity curve of the Milky Way, along with corresponding uncertainties that quantify various sources of systematic uncertainty in a self-consistent manner. Methods. The observed rotational velocities are described as circular velocities minus the asymmetric drift. The latter is described by the radial axisymmetric Jeans equation. We thus reconstruct the circular velocity curve between Galactocentric distances from 5 kpc to 14 kpc using a Bayesian inference approach. The estimated error bars quantify uncertainties in the Sun’s Galactocentric distance and the spatial-kinematic morphology of the tracer stars. As tracers, we used a sample of roughly 0.6 million stars on the red giant branch stars with six-dimensional phase-space coordinates from Gaia Data Release 3 (DR3). More than 99% of the sample is confined to a quarter of the stellar disc with mean radial, rotational, and vertical velocity dispersions of (35 ± 18) km s−1, (25 ± 13) km s−1, and (19 ± 9) km s−1, respectively. Results. We find a circular velocity curve with a slope of 0.4 ± 0.6 km s−1 kpc−1, which is consistent with a flat curve within the uncertainties. We further estimate a circular velocity at the Sun’s position of vc(R0) = 233 ± 7 km s−1 and that a region in the Sun’s vicinity, characterised by a physical length scale of ∼1 kpc, moves with a bulk motion of VLSR = 7 ± 7 km s−1. Finally, we estimate that the dark matter (DM) mass within 14 kpc is log10 MDM(R < 14kpc)/ M⊙ =(11.2+2.0-2.3) and the local spherically averaged DM density is ρDM(RO)=(0.41+0.10-0.09) GeV cm-3 = (0.011+0.003-0.002) M⊙pc-3. In addition, the effect of biased distance estimates on our results is assessed.

The Circular Velocity Curve of the Milky Way from 5–25 kpc Using Luminous Red Giant Branch Stars

We present a sample of 254,882 luminous red giant branch (LRGB) stars selected from the APOGEE and LAMOST surveys. By combining photometric and astrometric information from the Two Micron All Sky Survey and Gaia survey, the precise distances of the sample stars are determined by a supervised machine-learning algorithm: the gradient-boosted decision trees. To test the accuracy of the derived distances, member stars of globular clusters (GCs) and open clusters are used. The tests by cluster member stars show a precision of about 10% with negligible zero-point offsets, for the derived distances of our sample stars. The final sample covers a large volume of the Galactic disk(s) and halo of 0 < R < 30 kpc and ∣Z∣ ≤ 15 kpc. The rotation curve (RC) of the Milky Way across the radius of 5 ≲ R ≲ 25 kpc has been accurately measured with ∼54,000 stars of the thin disk population selected from the LRGB sample. The derived RC shows a weak decline along R with a gradient of −1.83 ± 0.02 (stat.) ± 0.07 (sys.) km s−1 kpc−1, in excellent agreement with the results measured by previous studies. The circular velocity at the solar position, yielded by our RC is 234.04 ± 0.08 (stat.) ± 1.36 (sys.) km s−1, again in great consistency with other independent determinations. From the newly constructed RC, as well as constraints from other data, we have constructed a mass model for our Galaxy, yielding a mass of the dark matter halo of M 200 = (8.05 ± 1.15) × 1011 M ⊙ with a corresponding radius of R 200 = 192.37 ± 9.24 kpc and a local dark matter density of 0.39 ± 0.03 GeV cm−3.

The many reasons that the rotation curves of low-mass galaxies can fail as tracers of their matter distributions

ABSTRACT It is routinely assumed that galaxy rotation curves are equal to their circular velocity curves (modulo some corrections) such that they are good dynamical mass tracers. We take a visualization-driven approach to exploring the limits of the validity of this assumption for a sample of 33 low-mass galaxies ($60\lt v_\mathrm{max}/\mathrm{km}\, \mathrm{s}^{-1}\lt 120$ ) from the APOSTLE suite of cosmological hydrodynamical simulations. Only three of these have rotation curves nearly equal to their circular velocity curves at z = 0, the rest are undergoing a wide variety of dynamical perturbations. We use our visualizations to guide an assessment of how many galaxies are likely to be strongly perturbed by processes in several categories: mergers/interactions (affecting 6/33 galaxies), bulk radial gas inflows (19/33), vertical gas outflows (15/33), distortions driven by a non-spherical DM halo (17/33), warps (8/33), and winds due to motion through the intergalactic medium (5/33). Most galaxies fall into more than one of these categories; only 5/33 are not in any of them. The sum of these effects leads to an underestimation of the low-velocity slope of the baryonic Tully–Fisher relation (α ∼ 3.1 instead of α ∼ 3.9, where Mbar ∝ vα) that is difficult to avoid, and could plausibly be the source of a significant portion of the observed diversity in low-mass galaxy rotation curve shapes.

The diversity of rotation curves of simulated galaxies with cusps and cores

ABSTRACTWe use ΛCDM cosmological hydrodynamical simulations to explore the kinematics of gaseous discs in late-type dwarf galaxies. We create high-resolution 21-cm ‘observations’ of simulated dwarfs produced in two variations of the EAGLE galaxy formation model: one where supernova-driven gas flows redistribute dark matter and form constant-density central ‘cores’, and another where the central ‘cusps’ survive intact. We ‘observe’ each galaxy along multiple sightlines and derive a rotation curve for each observation using a conventional tilted-ring approach to model the gas kinematics. We find that the modelling process introduces systematic discrepancies between the recovered rotation curve and the actual circular velocity curve driven primarily by (i) non-circular gas orbits within the discs; (ii) the finite thickness of gaseous discs, which leads to overlap of different radii in projection; and (iii) departures from dynamical equilibrium. Dwarfs with dark matter cusps often appear to have a core, whilst the inverse error is less common. These effects naturally reproduce an observed trend which other models struggle to explain: late-type dwarfs with more steeply rising rotation curves appear to be dark matter-dominated in the inner regions, whereas the opposite seems to hold in galaxies with core-like rotation curves. We conclude that if similar effects affect the rotation curves of observed dwarfs, a late-type dwarf population in which all galaxies have sizeable dark matter cores is most likely incompatible with current measurements.

Investigating the link between inner gravitational potential and star-formation quenching in CALIFA galaxies

It has been suggested that gravitational potential can have a significant role in suppressing star formation in nearby galaxies. To establish observational constraints on this scenario, we investigated the connection between the dynamics – taking the circular velocity curves (CVCs) as a proxy for the inner gravitational potential – and star formation quenching in 215 non-active galaxies across the Hubble sequence from the Calar Alto Legacy Integral Field Area (CALIFA) survey. Our results show that galaxies with similar CVCs tend to have a certain star-formation quenching pattern. To explore these findings in more details, we constructed kiloparsec(kpc)-resolved relations of the equivalent width of the Hα (WHα) versus the amplitude (Vc) and shape (β = dlnVc/dlnR) of the circular velocity at given radii. We find that the WHα − Vc is a declining relationship, where the retired regions of the galaxies (the ones with WHα values of below 3 Å) tend to have higher Vc. Concurrently, WHα − β is a bimodal relationship, which is characterised by two peaks: concentration of the star forming regions at a positive β (rising CVC) and a second concentration of the retired regions with a negative β (declining CVC). Our results show that both the amplitude of the CVC – driven by the mass of the galaxies – and its shape – which reflects the internal structure of the galaxies – play an important role in the quenching history of a galaxy.

Kinematics and mass distributions for non-spherical deprojected Sérsic density profiles and applications to multi-component galactic systems

Using kinematics to decompose the mass profiles of galaxies, including the dark matter contribution, often requires parameterization of the baryonic mass distribution based on ancillary information. One such model choice is a deprojected Sérsic profile with an assumed intrinsic geometry. The case of flattened, deprojected Sérsic models has previously been applied to flattened bulges in local star-forming galaxies (SFGs), but can also be used to describe the thick, turbulent disks in distant SFGs. Here, we extend this previous work that derived density (ρ) and circular velocity (vcirc) curves by additionally calculating the spherically-enclosed 3D mass profiles (Msph). Using these profiles, we compared the projected and 3D mass distributions, quantified the differences between the projected and 3D half-mass radii (Re; r1/2, mass, 3D), and compiled virial coefficients relating vcirc(R) and Msph(&lt; r = R) or Mtot. We quantified the differences between mass fraction estimators for multi-component systems, particularly for dark matter fractions (ratio of squared circular velocities versus ratio of spherically enclosed masses), and we considered the compound effects of measuring dark matter fractions at the projected versus 3D half-mass radii. While the fraction estimators produce only minor differences, using different aperture radius definitions can strongly impact the inferred dark matter fraction. As pressure support is important in analyses of gas kinematics (particularly, at high redshifts), we also calculated the self-consistent pressure support correction profiles, which generally predict less pressure support than for the self-gravitating disk case. These results have implications for comparisons between simulation and observational measurements, as well as for the interpretation of SFG kinematics at high redshifts. We have made a set of precomputed tables and the code to calculate the profiles publicly available.

Kinematics of the Milky Way from the Gaia EDR3 red giants and subgiants

ABSTRACT We present the results of the kinematic investigations carried out with the use of spatial velocities of red giants and subgiants contained in the Gaia EDR3 catalogue. The 12 kinematic parameters of the Ogorodnikov–Milne model have been derived for stellar systems with radii of 0.5 and 1.0 kpc, located along the direction of the Galactic Centre–the Sun–the Galactic anticentre within the range of Galactocentric distances R = 0–8–16 kpc. By combining some of the local parameters, the information related to the Galaxy as a whole has been received in the distance range of 4–12 kpc, in particular the circular velocity curve of red giant and subgiant centroids, its slope, and velocity gradients. We show that when using this approach, there is an alternative possibility to infer the behaviour of the circular velocity curve of red giant and subgiant centroids and its slope without using the Galactocentric distance R⊙. The kinematic parameters derived within the solar vicinity of 1 kpc radius are in good agreement with those given in the literature.

Formation of the Stellar System and the Central Gravitation-Potential Vessel of Galaxies

AbstractThe formation of the global stellar system of galaxies are studied through the circular velocity curves of CALIFA nearby galaxies by sequencing the depth and size of the central gravitation-potential vessel and its dynamical mass, relative to the masses of the stellar system and of the parent halo, with the population or age parameters, to explore the dynamical characteristics of the dissipative contracting baryonic matter.

Circular Orbit Structure and Thin Accretion Disks around Kerr Black Holes with Scalar Hair

Abstract In this paper, we first investigate the equatorial circular orbit structure of Kerr black holes with scalar hair (KBHsSH) and highlight their most prominent features, which are quite distinct from the exterior region of ordinary bald Kerr black holes, i.e., peculiarities that arise from the combined bound system of a hole with an off-center, self-gravitating distribution of scalar matter. Some of these traits are incompatible with the thin-disk approach; thus, we identify and map out various regions in parameter space. All of the solutions for which the stable circular orbital velocity (and angular momentum) curve is continuous are used for building thin and optically thick disks around them, from which we extract the radiant energy fluxes, luminosities, and efficiencies. We compare the results in batches with the same spin parameter j but different normalized charges, and the profiles are richly diverse. Because of the existence of a conserved scalar charge, Q, these solutions are nonunique in the (M, J) parameter space. Furthermore, Q cannot be extracted asymptotically from the metric functions. Nevertheless, by constraining the parameters through different observations, the luminosity profile could in turn be used to constrain the Noether charge and characterize the spacetime, should KBHsSH exist.

Gravitational potential from small-scale clustering in action space: application to Gaia Data Release 2

ABSTRACT Most measurements of mass in astronomy that use kinematics of stars or gas rely on assumptions of equilibrium that are often hard to verify. Instead, we develop a novel idea that uses the clustering in action space, as a probe of the underlying gravitational potential: the correct potential should maximize small-scale clustering in the action space. We provide a first-principle derivation of likelihood using the two-point correlation function in action space, and we test it against simulations of stellar streams. We then apply this method to the second data release of Gaia, and we use it to measure the radial force fraction fh and logarithmic slope α of the dark matter halo profile. We investigate stars within 9–11 kpc and 11.5–15 kpc from the Galactic Centre, and we find (fh, α) = (0.391 ± 0.009, 1.835 ± 0.092) and (0.351 ± 0.012, 1.687 ± 0.079), respectively. We also confirm that the set of parameters that maximize the likelihood function does correspond to the most clustering in the action space. The best-fitting circular velocity curve for the Milky Way potential is consistent with past measurements (although it is ∼5–10 per cent lower than previous methods that use masers or globular clusters). Our work provides a clear demonstration of the full statistical power that lies in the full phase space information, relieving the need for ad hoc assumptions such as virial equilibrium, circular motion or steam-finding algorithms.

On the estimation of the local dark matter density using the rotation curve of the Milky Way

The rotation curve of the Milky Way is commonly used to estimate the local dark matter density ρDM,⊙. However, the estimates are subject to the choice of the distribution of baryons needed in this type of studies. In this work we explore several Galactic mass models that differ in the distribution of baryons and dark matter, in order to determine ρDM,⊙. For this purpose we analyze the precise circular velocity curve measurement of the Milky Way up to ∼ 25 kpc from the Galactic centre obtained from Gaia DR2 [1]. We find that the estimated value of ρDM,⊙ stays robust to reasonable changes in the spherical dark matter halo. However, we show that ρDM,⊙ is affected by the choice of the model for the underlying baryonic components. In particular, we find that ρDM,⊙ is mostly sensitive to uncertainties in the disk components of the Galaxy. We also show that, when choosing one particular baryonic model, the estimate of ρDM,⊙ has an uncertainty of only about 10% of its best-fit value, but this uncertainty gets much bigger when we also consider the variation of the baryonic model. In particular, the rotation curve method does not allow to exclude the presence of an additional very thin component, that can increase ρDM,⊙ by more than a factor of 8 (the thin disk could even be made of dark matter). Therefore, we conclude that exclusively using the rotation curve of the Galaxy is not enough to provide a robust estimate of ρDM,⊙. For all the models that we study without the presence of an additional thin component, our resulting estimates of the local dark matter density take values in the range ρDM,⊙ ≃ 0.3−0.4 GeV/cm3, consistent with many of the estimates in the literature.

Peculiar motions of the gas at the centre of the barred galaxy UGC 4056

We derive the circular velocity curves of the gaseous and stellar discs of UGC 4056, a giant barred galaxy with an active galactic nucleus (AGN). We analyse UGC 4056 using the 2D spectroscopy obtained within the framework of the Mapping Nearby Galaxies at APO (MaNGA) survey. Using images and the colour index g − r from the Sloan Digital Sky Survey (SDSS), we determined the tilt of the galaxy, which allows us to conclude that the galaxy rotates clockwise with trailing spiral arms. We found that the gas motion at the central part of the UGC 4056 shows peculiar features. The rotation velocity of the gaseous disc shows a bump within around three kiloparsecs while the rotation velocity of the stellar disc falls smoothly to zero with decreasing galactocentric distance. We demonstrate that the peculiar radial velocities in the central part of the galaxy may be caused by the inflow of the gas towards the nucleus of the galaxy. The unusual motion of the gas takes place at the region with the AGN-like radiation and can be explained by the gas response to the bar potential.

The Circular Velocity Curve of the Milky Way from 5 to 25 kpc

Abstract We measure the circular velocity curve v c(R) of the Milky Way with the highest precision to date across Galactocentric distances of 5 ≤ R ≤ 25 kpc. Our analysis draws on the six-dimensional phase-space coordinates of ≳23,000 luminous red giant stars, for which we previously determined precise parallaxes using a data-driven model that combines spectral data from APOGEE with photometric information from WISE, 2MASS, and Gaia. We derive the circular velocity curve with the Jeans equation assuming an axisymmetric gravitational potential. At the location of the Sun we determine the circular velocity with its formal uncertainty to be = with systematic uncertainties at the ∼2%–5% level. We find that the velocity curve is gently but significantly declining at (−1.7 ± 0.1) km s−1 kpc−1, with a systematic uncertainty of 0.46 km s−1 kpc−1, beyond the inner 5 kpc. We exclude the inner 5 kpc from our analysis due to the presence of the Galactic bar, which strongly influences the kinematic structure and requires modeling in a nonaxisymmetric potential. Combining our results with external measurements of the mass distribution for the baryonic components of the Milky Way from other studies, we estimate the Galaxy’s dark halo mass within the virial radius to be = and a local dark matter density of = .

Kinematics of the outer halo of M 87 as mapped by planetary nebulae

Aims. We present a kinematic study of a sample of 298 planetary nebulas (PNs) in the outer halo of the central Virgo galaxy M 87 (NGC 4486). The line-of-sight velocities of these PNs are used to identify subcomponents, to measure the angular momentum content of the main M 87 halo, and to constrain the orbital distribution of the stars at these large radii. Methods. We use Gaussian mixture modelling to statistically separate distinct velocity components and identify the M 87 smooth halo component, its unrelaxed substructures, and the intra-cluster (IC) PNs. We compute probability weighted velocity and velocity dispersion maps for the smooth halo, and its specific angular momentum profile (λR) and velocity dispersion profile. Results. The classification of the PNs into smooth halo and ICPNs is supported by their different PN luminosity functions. Based on a Kolmogorov–Smirnov (K–S) test, we conclude that the ICPN line-of-sight velocity distribution (LOSVD) is consistent with the LOSVD of the galaxies in Virgo subcluster A. The surface density profile of the ICPNS at 100 kpc radii has a shallow logarithmic slope, −αICL ≃ −0.8, dominating the light at the largest radii. Previous B − V colour and resolved star metallicity data indicate masses for the ICPN progenitor galaxies of a few ×108 M⊙. The angular momentum-related λR profile for the smooth halo remains below 0.1, in the slow rotator regime, out to 135 kpc average ellipse radius (170 kpc major axis distance). Combining the PN velocity dispersion measurements for the M 87 halo with literature data in the central 15 kpc, we obtain a complete velocity dispersion profile out to Ravg = 135 kpc. The σhalo profile decreases from the central 400 km s−1 to about 270 km s−1 at 2–10 kpc, then rises again to ≃300 ± 50 km s−1 at 50–70 kpc, to finally decrease sharply to σhalo ∼ 100 km s−1 at Ravg = 135 kpc. The steeply decreasing outer σhalo profile and the surface density profile of the smooth halo can be reconciled with the circular velocity curve inferred from assuming hydrostatic equilibrium for the hot X-ray gas. Because this rises to νc,X ∼ km s−1 at 200 kpc, the orbit distribution of the smooth M 87 halo is required to change strongly from approximately isotropic within Ravg ∼ 60 kpc to very radially anisotropic at the largest distances probed. Conclusions. The extended LOSVD of the PNs in the M 87 halo allows the identification of several subcomponents: the ICPNs, the “crown” accretion event, and the smooth M 87 halo. In galaxies like M 87, the presence of these subcomponents needs to be taken into account to avoid systematic biases in estimating the total enclosed mass. The dynamical structure inferred from the velocity dispersion profile indicates that the smooth halo of M 87 steepens beyond Ravg = 60 kpc and becomes strongly radially anisotropic, and that the velocity dispersion profile is consistent with the X-ray circular velocity curve at these radii without non-thermal pressure effects.

Non-circular motions and the diversity of dwarf galaxy rotation curves

We use mock interferometric HI measurements and a conventional tilted-ring modelling procedure to estimate circular velocity curves of dwarf galaxy discs from the APOSTLE suite of {\Lambda}CDM cosmological hydrodynamical simulations. The modelling yields a large diversity of rotation curves for an individual galaxy at fixed inclination, depending on the line-of-sight orientation. The diversity is driven by non-circular motions in the gas; in particular, by strong bisymmetric fluctuations in the azimuthal velocities that the tilted-ring model is ill-suited to account for and that are difficult to detect in model residuals. Large misestimates of the circular velocity arise when the kinematic major axis coincides with the extrema of the fluctuation pattern, in some cases mimicking the presence of kiloparsec-scale density 'cores', when none are actually present. The thickness of APOSTLE discs compounds this effect: more slowly-rotating extra-planar gas systematically reduces the average line-of-sight speeds. The recovered rotation curves thus tend to underestimate the true circular velocity of APOSTLE galaxies in the inner regions. Non-circular motions provide an appealing explanation for the large apparent cores observed in galaxies such as DDO 47 and DDO 87, where the model residuals suggest that such motions might have affected estimates of the inner circular velocities. Although residuals from tilted ring models in the simulations appear larger than in observed galaxies, our results suggest that non-circular motions should be carefully taken into account when considering the evidence for dark matter cores in individual galaxies.