Prolate Halo Research Articles

Galaxy rotation favors prolate dark matter haloes

The flattening rotation velocity $v(r)\ensuremath{\rightarrow}\text{constant}$ found by Vera Rubin and collaborators and very apparent in the SPARC (Spitzer photometry accurate rotation curves) galaxy--rotation data coincides with Kepler's law in one less dimension. Thus, it is naturally reproduced by elongated dark matter distributions with the axis of prolateness perpendicular to the galactic plane. This theoretical understanding is borne out by the detailed fits to the rotation data that we here report: for equal dark matter profile, elongated distributions provide smaller ${\ensuremath{\chi}}^{2}$ than purely spherical ones. We also propose to use the geometric mean of the individual halo ellipticities, as opposed to their arithmetic average, because the ratio of the ellipsoid's minor to major half-axes $s=c/a\ensuremath{\in}(0,\ensuremath{\infty})$ corresponds to spherical haloes for $s=1$, so that the usually reported average is skewed toward oblateness and fails to reveal the large majority of prolate haloes. Several independently coded fitting exercises concur in yielding $s1$ for most of the database entries and the oblate exceptions are understood and classified. This likely prolateness is of consequence for the estimated dark matter density near Earth.

The effect of dark matter halo shape on bar buckling and boxy/peanut bulges

ABSTRACT It is well established that bars evolve significantly after they form in galaxy discs, often changing shape both in and out of the disc plane. In some cases they may bend or buckle out of the disc plane resulting in the formation of boxy/peanut/x-shape bulges. In this paper we show that the dark matter halo shape affects bar formation and buckling. We have performed N-body simulations of bar buckling in non-spherical dark matter haloes and traced bar evolution for 8 Gyr. We find that bar formation is delayed in oblate haloes, resulting in delayed buckling whereas bars form earlier in prolate haloes leading to earlier buckling. However, the duration of first buckling remains almost comparable. All the models show two buckling events but the most extreme prolate halo exhibits three distinct buckling features. Bars in prolate haloes also show buckling signatures for the longest duration compared to spherical and oblate haloes. Since ongoing buckling events are rarely observed, our study suggests that most barred galaxies may have more oblate or spherical haloes rather than prolate haloes. Our measurement of BPX structures also shows that prolate haloes promote bar thickening and disc heating more than oblate and spherical haloes.

Elongated Gravity Sources as an Analytical Limit for Flat Galaxy Rotation Curves

The flattening of spiral-galaxy rotation curves is unnatural in view of the expectations from Kepler’s third law and a central mass. It is interesting, however, that the radius-independence velocity is what one expects in one less dimension. In our three-dimensional space, the rotation curve is natural if, outside the galaxy’s center, the gravitational potential corresponds to that of a very prolate ellipsoid, filament, string, or otherwise cylindrical structure perpendicular to the galactic plane. While there is observational evidence (and numerical simulations) for filamentary structure at large scales, this has not been discussed at scales commensurable with galactic sizes. If, nevertheless, the hypothesis is tentatively adopted, the scaling exponent of the baryonic Tully–Fisher relation due to accretion of visible matter by the halo comes out to reasonably be 4. At a minimum, this analytical limit would suggest that simulations yielding prolate haloes would provide a better overall fit to small-scale galaxy data.

On filaments, prolate halos and rotation curves

We propose a simple geometrical mechanism for the flattening of galactic rotation curves, the local compression of field lines around their planes induced either by the presence of thin string-like objects at the centers of galaxies or by elongated dark-matter halos, and elaborate on its possible role in Nature. We fit 83 rotation curves from the SPARC database with logarithmic potentials produced by a thin "wire" at the origin and then, after selecting 2 galaxies that yield the most interesting fits, analyze them with an alternative model, deformed versions of two popular models of dark-matter halos. Our conclusion is that the presence of a filament clearly improves the fit quality in a number of cases, while bulged dark matter profiles have a lesser effect. If taken at face value, these results would imply the presence of elongated mass distributions away from the galactic plane in a number of galaxies, and may also have some indirect impact on the controversy between cold dark matter (CDM), self-interacting dark matter (SiDM), and modified Newtonian dynamics (MOND).

Can intrinsic alignments of elongated low-mass galaxies be used to map the cosmic web at high redshift?

ABSTRACT Hubble Space Telescope observations show that low-mass ($M_*=10^9\!-\!10^{10}\, \mathrm{M}_{\odot }$) galaxies at high redshift (z = 1.0–2.5) tend to be elongated (prolate) rather than disky (oblate) or spheroidal. This is explained in zoom-in cosmological hydrodynamical simulations by the fact that these galaxies are forming in cosmic web filaments where accretion happens preferentially along the direction of elongation. We ask whether the elongated morphology of these galaxies allows them to be used as effective tracers of cosmic web filaments at high redshift via their intrinsic alignments. Using mock light cones and spectroscopically confirmed galaxy pairs from the Cosmic Assembly Near-infared Deep Extragalactic Legacy Survey (CANDELS), we test two types of alignments: (1) between the galaxy major axis and the direction to nearby galaxies of any mass and (2) between the major axes of nearby pairs of low-mass, likely prolate, galaxies. The mock light cones predict strong signals in 3D real space, 3D redshift space, and 2D projected redshift space for both types of alignments (assuming prolate galaxy orientations are the same as those of their host prolate haloes), but we do not detect significant alignment signals in CANDELS observations. However, we show that spectroscopic redshifts have been obtained for only a small fraction of highly elongated galaxies, and accounting for spectroscopic incompleteness and redshift errors significantly degrades the 2D mock signal. This may partly explain the alignment discrepancy and highlights one of several avenues for future work.

The shape of the dark matter halo revealed from a hypervelocity star

AbstractA recently discovered young, high-velocity giant star J01020100-7122208 is a good candidate of hypervelocity star ejected from the Galactic center, although it has a bound orbit. If we assume that this star was ejected from the Galactic center, it can be used to constrain the Galactic potential, because the deviation of its orbit from a purely radial orbit informs us of the torque that this star has received. Based on this assumption, we estimate the flattening of the Galactic dark matter halo by using the Gaia DR2 data and the circular velocity data. Our Bayesian analysis shows that the orbit of J01020100-7122208 favors a prolate halo within ~ 10 kpc from the Galactic center. The posterior distribution of the density flattening q shows a broad distribution at q ≳ 1 and peaks at q ≃ 1.5. Also, 98.5% of the posterior distribution is located at q > 1, highly disfavoring an oblate halo.

Mass and shape of the Milky Way’s dark matter halo with globular clusters from Gaia and Hubble

Aims. We estimate the mass of the inner (< 20 kpc) Milky Way and the axis ratio of its inner dark matter halo using globular clusters as tracers. At the same time, we constrain the distribution in phase-space of the globular cluster system around the Galaxy. Methods. We use the Gaia Data Release 2 catalogue of 75 globular clusters’ proper motions and recent measurements of the proper motions of another 20 distant clusters obtained with the Hubble Space Telescope. We describe the globular cluster system with a distribution function (DF) with two components: a flat, rotating disc-like one and a rounder, more extended halo-like one. While fixing the Milky Way’s disc and bulge, we let the mass and shape of the dark matter halo and we fit these two parameters, together with six others describing the DF, with a Bayesian method. Results. We find the mass of the Galaxy within 20 kpc to be M(<20 kpc) = 1.91−0.17+0.18×1011 M⊙, of which MDM(<20 kpc) = 1.37−0.17+0.18×1011 M⊙ is in dark matter, and the density axis ratio of the dark matter halo to be q = 1.30 ± 0.25. Assuming a concentration-mass relation, this implies a virial mass Mvir = 1.3±0.3×1012 M⊙. Our analysis rules out oblate (q < 0.8) and strongly prolate halos (q > 1.9) with 99% probability. Our preferred model reproduces well the observed phase-space distribution of globular clusters and has a disc component that closely resembles that of the Galactic thick disc. The halo component follows a power-law density profile ρ ∝ r−3.3, has a mean rotational velocity of Vrot ≃ −14km s−1 at 20 kpc, and has a mildly radially biased velocity distribution (β ≃ 0.2 ± 0.07, which varies significantly with radius only within the inner 15 kpc). We also find that our distinction between disc and halo clusters resembles, although not fully, the observed distinction in metal-rich ([Fe/H] > −0.8) and metal-poor ([Fe/H] ≤ −0.8) cluster populations.

Interpretation of halo in 19C with complex momentum representation method

The extremely neutron-rich nucleus 19C has attracted much attention for its exotic properties. The most interesting is that the ground state of 19C behaves like a one-neutron halo. In order to understand this peculiar characteristic, we apply the complex momentum representation method to explore the weakly bound structure of 19C. We have calculated the single-particle energies for the bound and resonant states together with their evolutions to deformation, and checked the occupation probabilities of major configurations in the level occupied by the valance neutron. The result suggests that 19C is a prolate halo formed by a dominant s-wave configuration.

Around the Way: Testing ΛCDM with Milky Way Stellar Stream Constraints

Abstract Recent analyses of the Pal 5 and GD-1 tidal streams suggest that the inner dark matter halo of the Milky Way is close to spherical, in tension with predictions from collisionless N-body simulations of cosmological structure formation. We use the Eris simulation to test whether the combination of dissipative physics and hierarchical structure formation can produce Milky Way–like galaxies whose dark matter halos match the tidal stream constraints from the GD-1 and Pal 5 clusters. We use a dynamical model of the simulated Eris galaxy to generate many realizations of the GD-1 and Pal 5 tidal streams, marginalize over observational uncertainties in the cluster galactocentric positions and velocities, and compare with the observational constraints. We find that the total density and potential of Eris contributed by baryons and dark matter satisfies constraints from the existing Milky Way stellar stream data, as the baryons both round and redistribute the dark matter during the dissipative formation of the galaxy, and provide a centrally concentrated mass distribution that rounds the inner potential. The Eris dark matter halo or a spherical Navarro–Frenk–White dark matter work comparably well in modeling the stream data. In contrast, the equivalent dark matter–only ErisDark simulation produces a prolate halo that cannot reproduce the observed stream data. The ongoing Gaia mission will provide decisive tests of the consistency between and Milky Way streams, and should distinguish between models like Eris and more spherical halos.

Ecology of dark matter haloes –II. Effects of interactions on the alignment of halo pairs

We use the Horizon Run 4 cosmological N -body simulation to study the effects of distant and close interactions on the alignments of the shapes, spins, and orbits of targets haloes with their neighbours, and their dependence on the local density environment and neighbour separation. Interacting targets have a significantly lower spin and higher sphericity and oblateness than all targets. Interacting pairs initially have anti-parallel spins, but the spins develop parallel alignment as time goes on. Neighbours tend to evolve in the plane of rotation of the target, and in the direction of the major axis of prolate haloes. Moreover, interactions are preferentially radial, while pairs with non-radial orbits are preferentially prograde. The alignment signals are stronger at high-mass and for close separations, and independent on the large-scale density. Positive alignment signals are found at redshifts up to 4, and increase with decreasing redshifts. Moreover, the orbits tend to become prograde at low redshift, while no alignment is found at high redshift (z = 4).

Dynamical measurement of the stellar surface density of face-on galaxies

The DiskMass survey recently provided measurements of the vertical velocity dispersions of disk stars in a sample of nearly face-on galaxies. By setting the disk scale-heights to be equal to those of edge-on galaxies with similar scale-lengths, it was found that these disks must be sub-maximal, with surprisingly low K-band mass-to-light ratios of the order of $M_\star/L_K \simeq 0.3 M_\odot/L_\odot$. This study made use of a simple relation between the disk surface density and the measured velocity dispersion and scale height of the disk, neglecting the shape of the rotation curve and the dark matter contribution to the vertical force, which can be especially important in the case of sub-maximal disks. Here, we point out that these simplifying assumptions led to an overestimation of the stellar mass-to-light ratios. Relaxing these assumptions, we compute even lower values than previously reported for the mass-to-light ratios, with a median $M_\star/L_K \simeq 0.18 M_\odot/L_\odot$, where 14 galaxies have $M_\star/L_K < 0.11$. Invoking prolate dark matter halos made only a small difference to the derived $M_\star/L_K$, although extreme prolate halos ($q>1.5$ for the axis ratios of the potential) might help. The cross-terms in the Jeans equation are also generally negligible. These deduced K-band stellar mass-to-light ratios are even more difficult to reconcile with stellar population synthesis models than the previously reported ones.

Evolution of surface deformations of weakly bound nuclei in the continuum

We study weakly-bound deformed nuclei based on the coordinate-space Skyrme Hartree-Fock-Bogoliubov approach, in which a large box is employed for treating the continuum and surface diffuseness. Approaching the limit of core-halo deformation decoupling, calculations found an exotic "egg"-like structure consisting of a spherical core plus a prolate halo in $^{38}$Ne, in which the resonant continuum plays an essential role. Generally the halo probability and the decoupling effect in heavy nuclei are reduced compared to light nuclei, due to denser level densities around Fermi surfaces. However, deformed halos in medium-mass nuclei are possible with sparse levels of negative parity, for example, in $^{110}$Ge. The surface deformations of pairing density distributions are also influenced by the decoupling effect and are sensitive to the effective pairing Hamiltonian.

GLOBAL PROPERTIES OF M31'S STELLAR HALO FROM THE SPLASH SURVEY. I. SURFACE BRIGHTNESS PROFILE

We present the surface brightness profile of M31's stellar halo out to a projected radius of 175 kpc. The surface brightness estimates are based on confirmed samples of M31 red giant branch stars derived from Keck/DEIMOS spectroscopic observations. A set of empirical spectroscopic and photometric M31 membership diagnostics is used to identify and reject foreground and background contaminants. This enables us to trace the stellar halo of M31 to larger projected distances and fainter surface brightnesses than previous photometric studies. The surface brightness profile of M31's halo follows a power-law with index -2.2 +/- 0.2 and extends to a projected distance of at least ~175 kpc (~ 2/3 of M31's virial radius), with no evidence of a downward break at large radii. The best-fit elliptical isophotes have b/a=0.94 with the major axis of the halo aligned along the minor axis of M31's disk, consistent with a prolate halo, although the data are also consistent with M31's halo having spherical symmetry. The fact that tidal debris features are kinematically cold is used to identify substructure in the spectroscopic fields out to projected radii of 90 kpc, and investigate the effect of this substructure on the surface brightness profile. The scatter in the surface brightness profile is reduced when kinematically identified tidal debris features in M31 are statistically subtracted; the remaining profile indicates a comparatively diffuse stellar component to M31's stellar halo exists to large distances. Beyond 90 kpc, kinematically cold tidal debris features can not be identified due to small number statistics; nevertheless, the significant field-to-field variation in surface brightness beyond 90 kpc suggests that the outermost region of M31's halo is also comprised to a significant degree of stars stripped from accreted objects.

NGC 5466: a unique probe of the Galactic halo shape

Abstract Stellar streams provide unique probes of galactic potentials, with the longer streams normally providing the cleaner measurements. In this Letter, we show an example of a short tidal stream that is particularly sensitive to the shape of the Milky Way's dark matter halo: the globular cluster tidal stream NGC 5466. This stream has an interesting deviation from a smooth orbit at its western edge. We show that such a deviation favours an underlying oblate or triaxial halo (irrespective of plausible variations in the Milky Way disc properties and the specific halo parametrization chosen); spherical or prolate halo shapes can be excluded at a high confidence level. Therefore, more extensive data sets along the NGC 5466 tidal stream promise strong constraints on the Milky Way halo shape.

Dynamics of particles around a pseudo-Newtonian Kerr black hole with halos

The regular and chaotic dynamics of test particles in a superposed field between a pseudo-Newtonian Kerr black hole and quadrupolar halos is detailed. In particular, the dependence of dynamics on the quadrupolar parameter of the halos and the spin angular momentum of the rotating black hole is studied. It is found that the small quadrupolar moment, in contrast with the spin angular momentum, does not have a great effect on the stability and radii of the innermost stable circular orbits of these test particles. In addition, chaos mainly occurs for small absolute values of the rotating parameters, and does not exist for the maximum counter-rotating case under some certain initial conditions and parameters. This means that the rotating parameters of the black hole weaken the chaotic properties. It is also found that the counter-rotating system is more unstable than the co-rotating one. Furthermore, chaos is absent for small absolute values of the quadrupoles, and the onset of chaos is easier for the prolate halos than for the oblate ones.

The evolution of chaos in active galaxy models with an oblate or a prolate dark halo component

AbstractThe evolution of chaotic motion in a galactic dynamical model with a disk, a dense nucleus and a flat biaxial dark halo component is investigated. Two cases are studied: (i) the case where the halo component is oblate and (ii) the case where a prolate halo is present. In both cases, numerical calculations show that the extent of the chaotic regions decreases exponentially as the scale‐length of the dark halo increases. On the other hand, a linear relationship exists between the extent of the chaotic regions and the flatness parameter of the halo component. A linear relationship between the critical value of the angular momentum and the flatness parameter is also found. Some theoretical arguments to support the numerical outcomes are presented. An estimation of the degree of chaos is made by computing the Lyapunov Characteristic Exponents. Comparison with earlier work is also made (© 2010 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

EVIDENCE FOR A TRIAXIAL MILKY WAY DARK MATTER HALO FROM THE SAGITTARIUS STELLAR TIDAL STREAM

Observations of the lengthy tidal streams produced by the destruction of the Sagittarius dwarf spheroidal (Sgr dSph) are capable of providing strong constraints on the shape of the Galactic gravitational potential. However, previous work, based on modeling different stream properties in axisymmetric Galactic models has yielded conflicting results: while the angular precession of the Sgr leading arm is most consistent with a spherical or slightly oblate halo, the radial velocities of stars in this arm are only reproduced by prolate halo models. We demonstrate that this apparent paradox can be resolved by instead adopting a triaxial potential. Our new Galactic halo model, which simultaneously fits all well-established phase space constraints from the Sgr stream, provides the first conclusive evidence for, and tentative measurement of, triaxiality in an individual dark matter halo. The Milky Way halo within ~ 60 kpc is best characterized by a minor/major axis ratio of the isovelocity contours c/a ~ 0.67, intermediate/major axis ratio b/a ~ 0.83, and triaxiality parameter T ~ 0.56. In this model, the minor axis of the dark halo is coincident with the Galactic X axis connecting the Sun and the Galactic Center to within ~ 15 degrees, while the major axis also lies in the Galactic plane, approximately along the Galactic Y axis.

MAPPING THE GALACTIC HALO. VIII. QUANTIFYING SUBSTRUCTURE

We have measured the amount of kinematic substructure in the Galactic halo using the final data set from the Spaghetti project, a pencil-beam high latitude sky survey. Our sample contains 101 photometrically selected and spectroscopically confirmed giants with accurate distance, radial velocity and metallicity information. We have developed a new clustering estimator: the "4distance" measure, which when applied to our data set leads to the identification of 1 group and 7 pairs of clumped stars. The group, with 6 members, can confidently be matched to tidal debris of the Sagittarius dwarf galaxy. Two pairs match the properties of known Virgo structures. Using models of the disruption of Sagittarius in Galactic potentials with different degrees of dark halo flattening, we show that this favors a spherical or prolate halo shape, as demonstrated by Newberg et al. (2007) using SDSS data. One additional pair can be linked to older Sagittarius debris. We find that 20% of the stars in the Spaghetti data set are in substructures. From comparison with random data sets we derive a very conservative lower limit of 10% to the amount of substructure in the halo. However, comparison to numerical simulations shows that our results are also consistent with a halo entirely built up from disrupted satellites, provided the dominating features are relatively broad due to early merging or relatively heavy progenitor satellites.

Magellanic Stream: A possible tool for studying dark halo model

We model the dynamics of Magellanic Stream with the ram-pressure scenario in the logarithmic and power-law galactic halo models and construct numerically the past orbital history of Magellanic Clouds and Magellanic Stream. The parameters of models include the asymptotic rotation velocity of spiral arms, halo flattening, core radius and rising or falling parameter of rotation curve. We obtain the best-fit parameters of galactic models through the maximum likelihood analysis, comparing the high resolution radial velocity data of HI in Magellanic Stream with that of theoretical models. The initial condition of the Magellanic Clouds is taken from the six different values reported in the literature. We find that oblate and nearly spherical shape halos provide a better fit to the observation than the prolate halos. This conclusion is almost independent of choosing the initial conditions and is valid for both logarithmic and power-law models.

Concentration, spin and shape of dark matter haloes: scatter and the dependence on mass and environment

We use a series of cosmological N-body simulations for a flat LCDM cosmology to investigate the properties of dark matter haloes in the mass range 3.0e9-3.0e13 Msun. These properties include the concentration parameter (c), the spin parameter (lambda) and the mean axis ratio (q). For the concentration-mass relation we find c~M^(-0.11) in agreement with the model proposed by Bullock et al. even if we find a lower normalization (15%). The results for lambda and q are in good agreement with previous studies, while c and lambda are anti-correlated. In an attempt to remove unrelaxed haloes, we use the offset parameter (xoff), defined as the distance between the most bound particle and the center of mass. Removing haloes with large xoff increases the c by ~10%, lowers the lambda by ~15%, and removes the most prolate haloes. In addition, it largely removes the anti-correlation between c and lambda though not entirely. We also investigate the effects of the large-scale environment. We find that more concentrated haloes live in denser environments. Note, however, that the trend is weak compared to the scatter. For the spin parameters we find no environment dependence, while there is a weak indication that the most spherical haloes reside in denser region. Finally, using a simple model for disk galaxy formation we show that haloes that host low surface brightness galaxies are expected to be hosted by a biased sub-set of haloes. Not only do these haloes have spin parameters that are larger than average, they also have c that are 15% percent lower than the average at a given halo mass. We discuss the implications of all these findings for the claimed disagreement between halo concentrations inferred from LSB rotation curves, and those expected for a LCDM cosmology. (abridged)