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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

DESI mock challenge: Halo and galaxy catalogues with the bias assignment method

We present a novel approach to the construction of mock galaxy catalogues for large-scale structure analysis based on the distribution of dark matter halos obtained with effective bias models at the field level. We aim to produce mock galaxy catalogues capable of generating accurate covariance matrices for a number of cosmological probes that are expected to be measured in current and forthcoming galaxy redshift surveys (e.g. two- and three-point statistics). The construction of the catalogues shown in this paper is part of a mock-comparison project within the Dark Energy Spectroscopic Instrument (DESI) collaboration. We use the bias assignment method ( BAM ) to model the statistics of halo distribution through a learning algorithm using a few detailed N-body simulations, and approximated gravity solvers based on Lagrangian perturbation theory. We introduce cosmic-web-dependent corrections to modelling redshift-space distortions at the N-body level – both in the halo and galaxy distributions –, as well as a multi-scale approach for accurate assignment of halo properties. Using specific models of halo occupation distributions to populate halos, we generate galaxy mocks with the expected number density and central-satellite fraction of emission-line galaxies, which are a key target of the DESI experiment. BAM generates mock catalogues with per cent accuracy in a number of summary statistics, such as the abundance, the two- and three-point statistics of halo distributions, both in real and redshift space. In particular, the mock galaxy catalogues display ~3%-10% accuracy in the multipoles of the power spectrum up to scales of k ~ 0.4 h -1 Mpc. We show that covariance matrices of two- and three-point statistics obtained with BAM display a similar structure to the reference simulation. BAM offers an efficient way to produce mock halo catalogues with accurate two- and three-point statistics and is able to generate a variety of multi-tracer catalogues with precise covariance matrices of several cosmological probes. We discuss future developments of the algorithm towards mock production in DESI and other galaxy-redshift surveys.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

COMPASO : A new halo finder for competitive assignment to spherical overdensities

We describe a new method (compaso) for identifying groups of particles in cosmological N-body simulations. compaso builds upon existing spherical overdensity (SO) algorithms by taking into consideration the tidal radius around a smaller halo before competitively assigning halo membership to the particles. In this way, the compaso finder allows for more effective deblending of haloes in close proximity as well as the formation of new haloes on the outskirts of larger ones. This halo-finding algorithm is used in the abacussummit suite of N-body simulations, designed to meet the cosmological simulation requirements of the Dark Energy Spectroscopic Instrument (DESI) survey. compaso is developed as a highly efficient on-the-fly group finder, which is crucial for enabling good load-balancing between the GPU and CPU and the creation of high-resolution merger trees. In this paper, we describe the halo-finding procedure and its particular implementation in abacus, accompanying it with a qualitative analysis of the finder. We test the robustness of the compaso catalogues before and after applying the cleaning method described in an accompanying paper and demonstrate its effectiveness by comparing it with other validation techniques. We then visualize the haloes and their density profiles, finding that they are well fit by the NFW formalism. Finally, we compare other properties such as radius–mass relationships and two-point correlation functions with that of another widely used halo finder, rockstar.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

The kinematic properties of Milky Way stellar halo populations

ABSTRACT In the Gaia era, stellar kinematics are extensively used to study Galactic halo stellar populations, to search for halo structures, and to characterize the interface between the halo and hot disc populations. We use distribution function-based models of modern data sets with 6D phase space data to qualitatively describe a variety of kinematic spaces commonly used in the study of the Galactic halo. Furthermore, we quantitatively assess how well each kinematic space can separate radially anisotropic from isotropic halo populations. We find that scaled action space (the ‘action diamond’) is superior to other commonly used kinematic spaces at this task. We present a new, easy to implement selection criterion for members of the radially anisotropic Gaia–Enceladus merger remnant. Assuming a 1:1 ratio of Gaia–Enceladus stars to more isotropic halo, we find our selection achieves a sample purity of 86 per cent in our models with respect to contamination from the more isotropic halo. We compare this criterion to literature criteria, finding that it produces the highest purity in the resulting samples, at the expense of a modest reduction in completeness. We also show that selection biases that underlie nearly all contemporary spectroscopic data sets can noticeably impact the E−Lz distribution of samples in a manner that may be confused for real substructure. We conclude by providing recommendations for how authors should use stellar kinematics in the future to study the Galactic stellar halo.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Contribution of Gaia Sausage to the Galactic Stellar Halo Revealed by K Giants and Blue Horizontal Branch Stars from the Large Sky Area Multi-Object Fiber Spectroscopic Telescope, Sloan Digital Sky Survey, and Gaia

We explore the contribution of the Gaia Sausage to the stellar halo of the Milky Way by making use of a Gaussian mixture model (GMM) and applying it to halo star samples of Large Sky Area Multi-Object Fiber Spectroscopic Telescope K giants, Sloan Extension for Galactic Understanding and Exploration K giants, and Sloan Digital Sky Survey blue horizontal branch stars. The GMM divides the stellar halo into two parts, of which one represents a more metal-rich and highly radially biased component associated with an ancient, head-on collision referred to as the Gaia Sausage, and the other one is a more metal-poor and isotropic halo. A symmetric bimodal Gaussian is used to describe the distribution of spherical velocity of the Gaia Sausage, and we find that the mean absolute radial velocity of the two lobes decreases with the Galactocentric radius. We find that the Gaia Sausage contributes about 41%–74% of the inner (Galactocentric radius r gc < 30 kpc) stellar halo. The fraction of stars of the Gaia Sausage starts to decline beyond r gc ~ 25–30 kpc, and the outer halo is found to be significantly less influenced by the Gaia Sausage than the inner halo. After the removal of halo substructures found by integrals of motion, the contribution of the Gaia Sausage falls slightly within r gc ~ 25 kpc but is still as high as 30%–63%. Finally, we select several possible Sausage-related substructures consisting of stars on highly eccentric orbits. The GMM/Sausage component agrees well with the selected substructure stars in their chemodynamical properties, which increases our confidence in the reliability of the GMM fits.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Toward Accurate Modeling of Galaxy Clustering on Small Scales: Halo Model Extensions and Lingering Tension

This paper represents an effort to provide robust constraints on the galaxy–halo connection and simultaneously test the Planck ΛCDM cosmology using a fully numerical model of small-scale galaxy clustering. We explore two extensions to the standard Halo Occupation Distribution model: assembly bias, whereby halo occupation depends on both halo mass and the larger environment, and velocity bias, whereby galaxy velocities do not perfectly trace the velocity of the dark matter within the halo. Moreover, we incorporate halo mass corrections to account for the impact of baryonic physics on the halo population. We identify an optimal set of clustering measurements to constrain this "decorated" HOD model for both low- and high-luminosity galaxies in SDSS DR7. We find that, for low-luminosity galaxies, a model with both assembly bias and velocity bias provides the best fit to the clustering measurements, with no tension remaining in the fit. In this model, we find evidence for both central and satellite galaxy assembly bias at the 99% and 95% confidence levels, respectively. In addition, we find evidence for satellite galaxy velocity bias at the 99.9% confidence level. For high-luminosity galaxies, we find no evidence for either assembly bias or velocity bias, but our model exhibits significant tension with SDSS measurements. We find that all of these conclusions still stand when we include the effects of baryonic physics on the halo mass function, suggesting that the tension we find for high-luminosity galaxies may be due to a problem with our assumed cosmological model.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Strong Dark Matter Self-interactions Diversify Halo Populations within and surrounding the Milky Way

Abstract We perform a high-resolution cosmological zoom-in simulation of a Milky Way (MW)–like system, which includes a realistic Large Magellanic Cloud analog, using a large differential elastic dark matter self-interaction cross section that reaches ≈100 cm 2 g −1 at relative velocities of ≈10 km s −1 , motivated by the diverse and orbitally dependent central densities of dwarf galaxies within and surrounding the MW. We explore the effects of dark matter self-interactions on satellite, splashback, and isolated halos through their abundance, central densities, maximum circular velocities, orbital parameters, and correlations between these variables. We use an effective constant cross section model to analytically predict the stages of our simulated halos’ gravothermal evolution, demonstrating that deviations from the collisionless R max – V max relation can be used to select deeply core-collapsed halos, where V max is a halo’s maximum circular velocity, and R max is the radius at which it occurs. We predict that a sizable fraction (≈20%) of subhalos with masses down to ≈10 8 M ⊙ is deeply core collapsed in our SIDM model. Core-collapsed systems form ≈10% of the isolated halo population down to the same mass; these isolated, core-collapsed halos would host faint dwarf field galaxies with extremely steep central density profiles. Finally, most halos with masses above ≈10 9 M ⊙ are core-forming in our simulation. Our study thus demonstrates how self-interactions diversify halo populations in an environmentally dependent fashion within and surrounding MW-mass hosts, providing a compelling avenue to address the diverse dark matter distributions of observed dwarf galaxies.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Merger Response of Halo Anisotropy Properties

Anisotropy properties—halo spin, shape, position offset, velocity offset, and orientation—are an important family of dark matter halo properties that indicate the level of directional variation of the internal structures of halos. These properties reflect the dynamical state of halos, which in turn depends on the mass assembly history. In this work, we study the evolution of anisotropy properties in response to merger activity using the IllustrisTNG simulations. We find that the response trajectories of the anisotropy properties significantly deviate from secular evolution. These trajectories have the same qualitative features and timescales across a wide range of merger and host properties. We propose explanations for the behavior of these properties and connect their evolution to the relevant stages of merger dynamics. We measure the relevant dynamical timescales. We also explore the dependence of the strength of the response on time of merger, merger ratio, and mass of the main halo. These results provide insight into the physics of halo mergers and their effects on the statistical behavior of halo properties. This study paves the way toward a physical understanding of scaling relations, particularly to how systematics in their scatter are connected to the mass assembly histories of halos.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Testing the parametric model for self-interacting dark matter using matched halos in cosmological simulations

Here, we systemically evaluate the performance of the self-interacting dark matter (SIDM) halo model proposed in Ref.Yang et al. (2023) with matched halos from high-resolution cosmological CDM and SIDM simulations. The model incorporates SIDM effects along mass evolution histories of CDM halos and it is applicable to both isolated halos and subhalos. We focus on the accuracy of the model in predicting halo density profiles at z = 0 and the evolution of maximum circular velocity. We find the model predictions agree with the simulations within 10%–50% for most of the simulated (sub)halos, 50%–100% for extreme cases. This indicates that the model effectively captures the gravothermal evolution of the halos with very strong, velocity-dependent self-interactions. For an example application, we apply the model to study the impact of various SIDM scenarios on strong lensing perturber systems, demonstrating its utility in predicting SIDM effects for small-scale structure analyses. Our findings confirm that the model is an effective tool for mapping CDM halos into their SIDM counterparts.

Yang, Daneng [Chinese Academy of Sciences, Nanjing↗
DOE OSTI2022

The dark matter halo masses of elliptical galaxies as a function of observationally robust quantities

Context. The assembly history of the stellar component of a massive elliptical galaxy is closely related to that of its dark matter halo. Measuring how the properties of galaxies correlate with their halo mass can therefore help to understand their evolution. Aims. We investigate how the dark matter halo mass of elliptical galaxies varies as a function of their properties, using weak gravitational lensing observations. To minimise the chances of biases, we focus on the following galaxy properties that can be determined robustly: the surface brightness profile and the colour. Methods. We selected 2409 central massive elliptical galaxies (log M*/M ⊙ ≳ 11.4) from the Sloan Digital Sky Survey spectroscopic sample. We first measured their surface brightness profile and colours by fitting Sérsic models to photometric data from the Kilo-Degree Survey (KiDS). We fitted their halo mass distribution as a function of redshift, rest-frame r-band luminosity, half-light radius, and rest-frame u - g colour, using KiDS weak lensing measurements and a Bayesian hierarchical approach. For the sake of robustness with respect to assumptions on the large-radii behaviour of the surface brightness, we repeated the analysis replacing the total luminosity and half-light radius with the luminosity within a 10 kpc aperture, L r, 10 , and the light-weighted surface brightness slope, Γ 10 . Results. We did not detect any correlation between the halo mass and either the half-light radius or colour at fixed redshift and luminosity. Using the robust surface brightness parameterisation, we found that the halo mass correlates weakly with L r,10 and anti-correlates with Γ 10 . At fixed redshift, L r, 10 and Γ 10 , the difference in the average halo mass between galaxies at the 84th percentile and 16th percentile of the colour distribution is 0.00 ± 0.11 dex. Conclusion. Our results indicate that the average star formation efficiency of massive elliptical galaxies has little dependence on their final size or colour. This suggests that the origin of the diversity in the size and colour distribution of these objects lies with properties other than the halo mass.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Galaxy formation with wave/fuzzy dark matter: The core-halo structure and the solitonic imprint

Dark matter-dominated cores have long been claimed for the well-studied local group dwarf galaxies. More recently, extended stellar halos have been uncovered around several of these dwarfs through deeper imaging and spectroscopy. Such core-halo structures (inner flat core and a characteristic r −3 asymptotic outer halo profile) are not a feature of conventional cold dark matter (CDM). In contrast, smooth and prominent dark matter cores are predicted for wave/fuzzy dark matter (ψDM). The question arises as to what extent the visible stellar profiles should reflect this dark matter core structure. Here we compare cosmological hydrodynamical simulations of CDM, “WDM” (model used as a proxy for ψDM) & ψDM, aiming to predict the stellar profiles for these three DM scenarios. We show that cores surrounded by extended halos are distinguishable for ψDM, where the stellar density is enhanced in the core due to the presence of the relatively dense soliton. Our analysis demonstrates that, in our simulations, a distinctive core-halo structure does not appear in the case of CDM in the DM, gas, or stars. Whereas we do find a core-halo transition for DM, gas, and stars for ψDM, and the scale of this transition is in line with the predicted core radius set by the soliton scale anticipated for the adopted boson mass of 2.5×10 −22 eV. The presence of a core-halo structure in the stellar profile for Galaxy 1 for ψDM is visible for the most massive and the first galaxy to form in the simulation. Clearly, further simulations are needed to establish how strict this possible relationship is between the DM and stellar core-halo profile as a potential observational discriminator. Furthermore, we observe the anticipated asymmetry for ψDM due to the soliton's motion (jumping and random walk), a distinctive characteristic not found in the symmetric distributions of stars in the warm and CDM models.

dark matter↗
DOE OSTI2025

Accurately simulating core-collapse self-interacting dark matter halos

The properties of satellite halos provide a promising probe for dark matter (DM) physics. Observations have motivated current efforts to explain surprisingly compact DM halos. If DM is not collisionless, but has strong self-interactions, halos can undergo gravothermal collapse, leading to higher densities in the central region of the halo. However, it is challenging to model this collapse phase from first principles. To improve on this, we sought to better understand the numerical challenges and convergence properties of self-interacting dark matter (SIDM) N-body simulations in the collapse phase. Especially, our aim was to better understand the evolution of satellite halos. To do so, we ran SIDM N-body simulations of a low-mass halo in isolation and within an external gravitational potential. The simulation set-up was motivated by the perturber of the stellar stream GD-1. We find that the halo evolution is very sensitive to energy conservation errors, and a SIDM kernel size that is too large can artificially speed up the collapse. Moreover, we demonstrate that the King model can describe the density profile at small radii for the late stages that we have simulated. Furthermore, for our most highly resolved simulation (N = 5 × 10 7 ) we have made the data public. It can serve as a benchmark. Overall, we find that the current numerical methods do not suffer from convergence problems in the late collapse phase and provide guidance on how to choose numerical parameters, for example that the energy conservation error is better kept well below 1%. This allows simulations to be run of halos that become concentrated enough to explain observations of GD-1-like stellar streams or strong gravitational lensing systems.

dark matter↗
DOE OSTI2020

Connecting SDSS central galaxies to their host haloes using total satellite luminosity

ABSTRACT The total luminosity of satellite galaxies around a central galaxy, Lsat, is a powerful metric for probing dark matter haloes. We utilize data from the Sloan Digital Sky Survey and DESI Legacy Imaging Surveys to explore the relationship between Lsat and galaxy properties for a sample of 117 966 central galaxies with z ≤ 0.15. At fixed stellar mass, we find that every galaxy property we explore correlates with Lsat, suggesting that dark matter haloes can influence them. We quantify these correlations by computing the mutual information between Lsat and secondary properties and explore how this varies as a function of stellar mass and star-formation activity. We find that absolute r-band magnitude correlates more strongly with Lsat than stellar mass across all galaxy populations; and that effective radius, velocity dispersion, and Sérsic index do so as well for star-forming and quiescent galaxies. Lsat is influenced by the mass of the host halo as well as the halo formation history, with younger haloes having higher Lsat. Lsat cannot distinguish between these two effects, but measurements of galaxy large-scale environment can break this degeneracy. For star-forming centrals, Reff, σv, and Sérsic index all correlate with large-scale density, implying that the halo age affects these properties. For quiescent galaxies, all secondary properties are independent of environment, implying that correlations with Lsat are driven only by halo mass. These results are a significant step forward in quantifying the extent of the galaxy–halo connection, and present a new test of galaxy formation models.

Alpaslan, Mehmet↗
DOE OSTI2022

Beyond mass: detecting secondary halo properties with galaxy-galaxy lensing

ABSTRACT Secondary halo properties beyond mass, such as the mass accretion rate (MAR), concentration, and the half mass scale, are essential in understanding the formation of large-scale structure and dark matter haloes. In this paper, we study the impact of secondary halo properties on the galaxy-galaxy lensing observable, ΔΣ. We build an emulator trained on N-body simulations to model ΔΣ and quantify the impact of different secondary parameters on the ΔΣ profile. We focus on the impact of MAR on ΔΣ. We show that a 3σ detection of variations in MAR at fixed halo mass could be achieved with the Hyper Suprime Cam survey assuming no baryonic effects and a proxy for MAR with scatter <1.5. We show that the full radial profile of ΔΣ depends on secondary properties at fixed halo mass. Consequently, an emulator that can perform full shape fitting yields better than two times improvement upon the constraints on MAR than only using the outer part of the halo. Finally, we highlight that miscentring and MAR impact the radial profile of ΔΣ in a similar fashion, implying that miscentring and MAR need to be modelled jointly for unbiased estimates of both effects. We show that present-day lensing data sets have the statistical capability to place constraints on halo MAR within our assumptions. Our analysis opens up new possibilities for observationally measuring the assembly history of the dark matter haloes that host galaxies and clusters.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Halo effective field theory analysis of one-neutron knockout reactions of Be 11 and C 15

Background: One-nucleon knockout reactions provide insightful information on the single-particle structure of nuclei. When applied to one-neutron halo nuclei, they are purely peripheral, suggesting that they could be properly modeled by describing the projectile within a halo effective field theory (halo-EFT). Purpose: We reanalyze the one-neutron knockout measurements of 11 Be and 15 C —both one-neutron halo nuclei—on beryllium at about 60 MeV/nucleon. We consider halo-EFT descriptions of these nuclei which already provide excellent agreement with breakup and transfer data. Method: Here we include a halo-EFT description of the projectile within an eikonal-based model of the reaction and compare its outcome to existing data. Results: Excellent agreement with experiment is found for both nuclei. The asymptotic normalization coefficients inferred from this comparison confirm predictions from ab initio nuclear-structure calculations and values deduced from transfer data. Conclusions: Halo-EFT can be reliably used to analyze one-neutron knockout reactions measured for halo nuclei and test predictions from state-of-the-art nuclear structure models on these experimental data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Position-dependent Voronoi probability distribution functions for matter and halos

Here, we measure the Voronoi density probability distribution function (PDF) for both dark matter and halos in N-body simulations. For the dark matter, Voronoi densities represent the matter density field smoothed on a uniform mass scale, which approximates the Lagrangian density field. For halos, the Voronoi densities contain information about the local environment of each halo. We measure the halo virial masses, the total amount of dark matter within each halo Voronoi cell, and the halo Voronoi cell volumes, and we show how halo abundances depend on these three quantities. We then study the position-dependent Voronoi density PDF, measured within finite subregions of the Universe, using separate universe simulations. We demonstrate that the spatial variation of the position-dependent PDF is due to large-scale density fluctuations, indicating that the position-dependent PDF is a biased tracer of large-scale structure. We measure this bias for the dark matter, and interpret it as the bias of regions of the Lagrangian density field that are selected based on density. For the halos, this bias can be interpreted as a form of assembly bias. We present the mapping from late-time to early-time Voronoi density for each simulation dark matter particle, which is highly stochastic. We compare the median of this stochastic map with spherical collapse calculations and discuss challenges involved in modeling the evolution of the density field on these scales.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

The Odd Dark Matter Halos of Isolated Gas-rich Ultradiffuse Galaxies

Abstract We analyze circular velocity profiles of seven ultradiffuse galaxies (UDGs) that are isolated and gas-rich. Assuming that the dark matter halos of these UDGs have a Navarro–Frenk–White (NFW) density profile or a Read density profile (which allows for constant-density cores), the inferred halo concentrations are systematically lower than the cosmological median, even as low as −0.6 dex (about 5 σ away) in some cases. Alternatively, similar fits can be obtained with a density profile that scales roughly as 1/ r 2 for radii larger than a few kiloparsecs. Both solutions require the radius where the halo circular velocity peaks ( R max ) to be much larger than the median expectation. Surprisingly, we find an overabundance of such large- R max halos in the IllustrisTNG dark-matter-only simulations compared to the Gaussian expectation. These halos form late and have higher spins compared to median halos of similar masses. The inner densities of the most extreme among these late-forming halos are higher than their NFW counterparts, leading to a ∼1/ r 2 density profile. However, the two well-resolved UDGs in our sample strongly prefer lower dark matter densities in the center than the simulated ones. Comparing to IllustrisTNG hydrodynamical simulations, we also find a tension in getting both low enough circular velocities and high enough halo mass to accommodate the measurements. Our results indicate that the gas-rich UDGs present a significant challenge for galaxy formation models.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

The AGORA High-resolution Galaxy Simulations Comparison Project. V. Satellite Galaxy Populations in a Cosmological Zoom-in Simulation of a Milky Way–Mass Halo

We analyze and compare the satellite halo populations at z ~ 2 in the high-resolution cosmological zoom-in simulations of a 10 12 M ⊙ target halo (z = 0 mass) carried out on eight widely used astrophysical simulation codes (Art-I, Enzo, Ramses, Changa, Gadget-3, Gear, Arepo-t, and Gizmo) for the AGORA High-resolution Galaxy Simulations Comparison Project. We use slightly different redshift epochs near z = 2 for each code (hereafter "z ~ 2") at which the eight simulations are in the same stage in the target halo's merger history. After identifying the matched pairs of halos between the CosmoRun simulations and the DMO simulations, we discover that each CosmoRun halo tends to be less massive than its DMO counterpart. When we consider only the halos containing stellar particles at z ~ 2, the number of satellite galaxies is significantly fewer than that of dark matter halos in all participating AGORA simulations and is comparable to the number of present-day satellites near the Milky Way or M31. The so-called "missing satellite problem" is fully resolved across all participating codes simply by implementing the common baryonic physics adopted in AGORA and the stellar feedback prescription commonly used in each code, with sufficient numerical resolution (≲100 proper pc at z = 2). We also compare other properties such as the stellar mass–halo mass relation and the mass–metallicity relation. Our work highlights the value of comparison studies such as AGORA, where outstanding problems in galaxy formation theory are studied simultaneously on multiple numerical platforms.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1976

Suppression of bar instability by a massive halo

Numerical experiments are performed to determine the effect of a spherical uniform-density mass distribution or halo on the evolution of stellar disks. For a halo with radius much smaller than that of the disk, the large-scale bar-forming instability is prevented by a fixed halo (or core) component containing 60% of the total system mass. Similar results are obtained for a halo component corresponding to the Schmidt (1965) model of the Galaxy. For a uniform-density spherical halo with radius equal to that of the stellar disk, a halo component containing only 40% of the total mass is sufficient to stabilize the bar-forming mode. These results indicate that a large halo is more effective in stabilizing against bar formation than a more centrally condensed core-halo.

Hohl, F.↗