Galactic Center Research Articles

Galaxy Spectra neural Network (GaSNet). II. Using deep learning for spectral classification and redshift predictions

ABSTRACT The size and complexity reached by the large sky spectroscopic surveys require efficient, accurate, and flexible automated tools for data analysis and science exploitation. We present the Galaxy Spectra Network/GaSNet-II, a supervised multinetwork deep learning tool for spectra classification and redshift prediction. GaSNet-II can be trained to identify a customized number of classes and optimize the redshift predictions. Redshift errors are determined via an ensemble/pseudo-Monte Carlo test obtained by randomizing the weights of the network-of-networks structure. As a demonstration of the capability of GaSNet-II, we use 260k Sloan Digital Sky Survey spectra from Data Release 16, separated into 13 classes including 140k galactic, and 120k extragalactic objects. GaSNet-II achieves 92.4 per cent average classification accuracy over the 13 classes and mean redshift errors of approximately 0.23 per cent for galaxies and 2.1 per cent for quasars. We further train/test the pipeline on a sample of 200k 4MOST (4-metre Multi-Object Spectroscopic Telescope) mock spectra and 21k publicly released DESI (Dark Energy Spectroscopic Instrument) spectra. On 4MOST mock data, we reach 93.4 per cent accuracy in 10-class classification and mean redshift error of 0.55 per cent for galaxies and 0.3 per cent for active galactic nuclei. On DESI data, we reach 96 per cent accuracy in (star/galaxy/quasar only) classification and mean redshift error of 2.8 per cent for galaxies and 4.8 per cent for quasars, despite the small sample size available. GaSNet-II can process ∼40k spectra in less than one minute, on a normal Desktop GPU. This makes the pipeline particularly suitable for real-time analyses and feedback loops for optimization of Stage-IV survey observations.

Intermediate-mass Black Hole Progenitors from Stellar Collisions in Dense Star Clusters

Very massive stars (VMSs) formed via a sequence of stellar collisions in dense star clusters have been proposed as the progenitors of massive black hole seeds. VMSs could indeed collapse to form intermediate-mass black holes, which would then grow by accretion to become the supermassive black holes observed at the centers of galaxies and powering high-redshift quasars. Previous studies have investigated how different cluster initial conditions affect the formation of a VMS, including mass segregation, stellar collisions, and binaries, among others. In this study, we investigate the growth of VMSs with a new grid of Cluster Monte Carlo star cluster simulations—the most expansive to date. The simulations span a wide range of initial conditions, varying the number of stars, cluster density, stellar initial mass function (IMF), and primordial binary fraction. We find a gradual shift in the mass of the most massive collision product across the parameter space; in particular, denser clusters born with top-heavy IMFs provide strong collisional regimes that form VMSs with masses easily exceeding 1000 M ⊙. Our results are used to derive a fitting formula that can predict the typical mass of a VMS formed as a function of the star cluster properties. Additionally, we study the stochasticity of this process and derive a statistical distribution for the mass of the VMS formed in one of our models, recomputing the model 50 times with different initial random seeds.

Strong lensing of tidal disruption events: Detection rates in imaging surveys

Tidal disruption events (TDEs) are multi-messenger transients in which a star is tidally destroyed by a supermassive black hole at the center of galaxies. The Rubin Observatory Legacy Survey of Space and Time (LSST) is anticipated to detect hundreds to thousands of TDEs annually, such that the first gravitationally lensed TDE may be observed in the coming years. Using Monte-Carlo simulations, we quantify the rate of both unlensed and lensed TDEs as a function of limiting magnitudes in four different optical bands ($u$, $g$, $r$, and $i$) for a range of TDE temperatures that match observations. Dependent on the temperature and luminosity model, we find that $g$ and $r$ bands are the most promising bands with unlensed TDE detections that can be as high as $ sim $ annually. By populating a cosmic volume with realistic distributions of TDEs and galaxies that can act as gravitational lenses, we estimate that a few lensed TDEs (depending on the TDE luminosity model) can be detected annually in $g$ or $r$ bands in the LSST survey, with TDE redshifts in the range of $ sim 0.5$ to $ sim 2$. The ratio of lensed to unlensed detections indicates that we may detect $ sim 1$ lensed event for every $10^ $ unlensed events, which is independent of the luminosity model. The number of lensed TDEs decreases as a function of the image separations and time delays, and most of the lensed TDE systems are expected to have image separations below $ sim and time delays within sim 30$ days. At fainter limiting magnitudes, the $i$ band becomes notably more successful. These results suggest that strongly lensed TDEs are likely to be observed within the coming years and such detections will enable us to study the demographics of black holes at higher redshifts through the lensing magnifications. Our simulated catalogs of lensed TDEs are publicly available.

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.

Compactness of supermassive dark objects at galactic centers

We define compactness of a gravitational lens as the scaled closest distance of approach (i.e., r0/ M) of the null geodesic giving rise to an image. We model 40 supermassive dark objects as Schwarzschild lenses and compute compactness of lenses (determined by the formation of the first-order relativistic image). We then obtain a novel formula for the compactness of a lens as a function of mass to the distance ratio ( M/ Dd) and the ratio of lens–source to the observer–source distances ( Dds/ Ds). This formula yields a very important result: Just an observation of a relativistic image would give an incredibly accurate upper bound to the physical compactness (the ratio of the radius to mass) of the lens without having any knowledge of mass of the lens, angular source position, and observer–source and lens–source distances. Similarly, we show that the observation of the second-order relativistic image would give a lower value of upper bound to the physical compactness. These results, though obtained for supermassive dark objects at galactic centers, are valid for any object compact enough to give rise to relativistic images.

Multiple-scale gas infall through gravity torques on Milky Way twins

One of the main problems raised by the feeding of super-massive black holes (SMBHs) at the centres of galaxies is the huge angular momentum of the circumnuclear gas and of the gas reservoir in the galaxy disk. Because viscous torques are not efficient at kiloparsec or 100 pc scales, the angular momentum must be exchanged through gravity torques that arise from the non-axisymmetric patterns in the disks. Our goal here is to quantify the efficiency of bars and spirals in driving the gas towards the centre at different scales in galaxies. We selected a sample of nearby galaxies considered to be analogues of the Milky Way, that is, galaxies of late morphological type Sbc. Their bar strength was variable, either SB, or SAB, or SA, so that we were able to quantify the influence of the bar. The gravitational potential was computed from deprojected red images, either from Hubble Space Telescope or Legacy survey, depending on the spatial resolution and field of view considered. The torques were computed on the gas through CO emission maps from ALMA at different resolutions. Halpha maps from MUSE were used, when available. Eight out of ten galaxies are barred. The torques are found to be negative in the eight barred objects at kiloparsec scales, between corotation and the inner Lindblad resonance (ILR), with a loss of angular momentum in a few rotations. Inside the ILR, the torques are negative in only five cases, with a timescale of one to two rotations. The torques are positive for the galaxies without bars. The torques applied on the ionized gas are comparable to what is deduced from molecular gas. The bars are confirmed to be the essential pattern in the SMBH feeding at kiloparsec and 100 pc scales; higher-resolution gas maps are required to explore scales of 10 pc.

The first high-redshift cavity power measurements of cool-core galaxy clusters with the International LOFAR Telescope

Radio-mode feedback associated with the active galactic nuclei (AGNs) at the cores of galaxy clusters injects a large amount of energy into the intracluster medium (ICM), offsetting radiative losses through X-ray emission. This mechanism prevents the ICM from rapidly cooling down and fueling extreme starburst activity as it accretes onto the central galaxies, and it is therefore a key ingredient in the evolution of galaxy clusters. However, the influence and mode of feedback at high redshifts (z ∼ 1) remains largely unknown. Low-frequency sub-arcsecond-resolution radio observations taken with the International LOFAR Telescope have demonstrated their ability to assist X-ray observations with constraining the energy output from the AGNs (or “cavity power”) in galaxy clusters, thereby enabling research at higher redshifts than before. In this pilot project, we tested this hybrid method on a high-redshift (0.6 < z < 1.3) sample of 13 galaxy clusters for the first time with the aim of verifying the performance of this method at these redshifts and providing the first estimates of the cavity power associated with the central AGN for a sample of distant clusters. We were able to detect clear radio lobes in three out of 13 galaxy clusters at redshifts of 0.7 < z < 0.9, and we used these detections in combination with ICM pressures surrounding the radio lobes obtained from standard profiles to calculate the corresponding cavity powers of the AGNs. Combining our results with the literature, the current data appear to suggest that the average cavity power peaked at a redshift of z ∼ 0.4 and slowly decreases toward higher redshifts. However, we require more and tighter constraints on the cavity volume and a better understanding of our observational systematics to confirm any deviation of the cavity power trend from a constant level.

All-sky three-dimensional dust density and extinction Maps of the Milky Way out to 2.8 kpc

ABSTRACT Three-dimensional dust density maps are crucial for understanding the structure of the interstellar medium of the Milky Way and the processes that shape it. However, constructing these maps requires large data sets and the methods used to analyse them are computationally expensive and difficult to scale up. As a result, it has only recently become possible to map kiloparsec-scale regions of our Galaxy at parsec-scale grid sampling. We present all-sky three-dimensional dust density and extinction maps of the Milky Way out to 2.8 kpc in distance from the Sun using the fast and scalable Gaussian Process algorithm Dustribution. The sampling of the three-dimensional map is l, b, d = 1° × 1° × 1.7 pc. The input extinction and distance catalogue contains 120 million stars with photometry and astrometry from Gaia DR2, 2MASS and AllWISE. This combines the strengths of optical and infrared data to probe deeper into the dusty regions of the Milky Way. We compare our maps with other published 3D dust maps. All maps quantitatively agree at the 0.001 mag pc−1 scale with many qualitatively similar features, although each map also has its own features. We recover Galactic features previously identified in the literature. Moreover, we also see a large under-density that may correspond to an inter-arm or -spur gap towards the Galactic Centre.

Diffuse interstellar bands in the near-infrared: expanding the reddening range

ABSTRACT We have investigated the behaviour of three strong near-infrared diffuse interstellar bands (DIBs) at λ13177 Å, λ14680 Å, and λ15272 Å, on a larger sample of sightlines and over a wider range of extinctions than previously studied, utilizing spectra from three observatories. We applied two telluric correction techniques to reduce atmospheric contamination and have used Gaussian fits to characterize the DIB profiles and measure equivalent widths. We confirmed strong and approximately linear correlations with reddening of the λ13177 Å, λ14680 Å, and λ15272 Å DIBs, extending them to higher reddening values and strengthening their link to interstellar matter. Modelling of the λ14680 Å DIB profiles revealed intrinsic variations, including line broadening, linked to their formation processes. This effect is particularly pronounced in the Galactic Centre (GC) environment, where multiple diffuse molecular clouds along the line of sight contribute to line broadening. We have detected one new DIB candidate at λ14795 Å on sightlines with high reddening.

Dark supernova remnant buried in the Galactic Center “Brick” G0.253+0.016 revealed by an expanding CO-line bubble

Dark supernova remnant buried in the Galactic Center “Brick” G0.253+0.016 revealed by an expanding CO-line bubble

Analytical models of supermassive black holes in galaxies surrounded by dark matter halos

In this Letter, we present five analytical models in closed forms, each representing a supermassive black hole (SMBH) located at the center of a galaxy surrounded by dark matter (DM) halo. The density profile of the halo vanishes inside twice the Schwarzschild radius of the hole and satisfies the weak, strong, and dominant energy conditions. The spacetime are asymptotically flat, and the difference among the models lies in the slopes of the density profiles in the spike and regions far from the center of the galaxy. Three of them represent cusp models, whereas the other two represent core models. With the well-known (generalized) Newman-Janis algorithm, rotating SMBHs with DM halos can be easily constructed from these models.

Magnetic field at the Galactic centre from multiwavelength dust polarization

ABSTRACT We have mapped the magnetic field (B-field) for a region of about 30 pc around the centre of our Galaxy, which encompasses the circumnuclear disc (CND), the minispiral, and the 20 and 50 km s−1 molecular clouds, using thermal dust polarization observations obtained from SOFIA/HAWC+ and JCMT/SCUPOL. We decompose the spectra of 12CO (J = 3 → 2) transition from this region into individual cloud components and find the polarization observed at different wavelengths might be tracing completely different layers of dust along the line of sight. We use modified Davis–Chandrasekhar–Fermi methods to measure the strength of B-field projected in the plane of the sky ($B_{{}_{\mathrm{POS}}}$). The mean $B_{{}_{\mathrm{POS}}}$ of the CND and the minispiral, probed at 53 μm is of the order of ∼2 mG. $B_{{}_{\mathrm{POS}}}\!\!\!\lt \!1$ mG close to the Galactic Centre, in the region of the ionized mini-cavity within the CND, and increases outwards. However, the longer wavelength polarization at 216 μm appears to come from a dust layer that is cooler and behind the CND and has a stronger B-field of about 7 mG. The B-field strength is lowest along the Eastern Arm of the minispiral, which is also the only region with Alfvén Mach number, $\mathcal {M}_{\mathrm{A}}\gt 1$ and mass-to-flux ratio, λ ≳ 1. Such an observed weak B-field could be a result of the low resolution of the observation, where the tangled B-fields due to the strong turbulence in the high density clumps of the CND are lost within the beam size of the observation.

WISE2MBH: a scaling-based algorithm for probing supermassive black hole masses through WISE catalogues

ABSTRACT Supermassive Black Holes (SMBHs) are commonly found at the centres of massive galaxies. Estimating their masses (MBH) is crucial for understanding galaxy-SMBH co-evolution. We present WISE2MBH, an efficient algorithm that uses cataloged Wide-field Infrared Survey Explorer (WISE) magnitudes to estimate total stellar mass (M*) and scale this to bulge mass (MBulge), and MBH, estimating the morphological type (TType) and bulge fraction (B/T) in the process. WISE2MBH uses scaling relations from the literature or developed in this work, providing a streamlined approach to derive these parameters. It also distinguishes QSOs from galaxies and estimates the galaxy TType using WISE colours with a relation trained with galaxies from the 2MASS Redshift Survey. WISE2MBH performs well up to z ∼ 0.5 thanks to K-corrections in magnitudes and colours. WISE2MBH MBH estimates agree very well with those of a selected sample of local galaxies with MBH measurements or reliable estimates: a Spearman score of ∼0.8 and a RMSE of ∼0.63 were obtained. When applied to the ETHER sample at z ≤ 0.5, WISE2MBH provides ∼1.9 million MBH estimates (78.5 per cent new) and ∼100 thousand upper limits. The derived local black hole mass function (BHMF) is in good agreement with existing literature BHMFs. Galaxy demographic projects, including target selection for the Event Horizon Telescope, can benefit from WISE2MBH for up-to-date galaxy parameters and MBH estimates. The WISE2MBH algorithm is publicly available on GitHub.

Investigating the shadows and strong gravitational lensing of modified Bardeen black holes

This study is dedicated to exploring the distinctive observational features affected by the modified Bardeen black hole through meticulous analysis of its shadow and strong gravitational lensing observations. We thoroughly investigated the impact of the black hole’s parameters q, g and μ on its shadow radius through numerical simulations and graphical representations. Utilizing the Event Horizon Telescope (EHT) data, we constrained the modified Bardeen black hole parameter μ of the modified Bardeen black hole within specific ranges: 0.24 ≤ μ ≤ 1.16 for M87*; and 0.036 ≤ μ ≤ 0.51 for Sgr A *, while maintaining the fixed values g = 0.2 and q = 0.3. This restriction of the modified Bardeen black hole parameter μ by the EHT findings illustrates the viability of modified Bardeen black holes as astrophysical candidates. Additionally, we study strong gravitational lensing and its various observables for the modified Bardeen black hole, comparing its behavior to other astrophysical black holes such as the Schwarzschild (μ = 0 = q) and Bardeen (μ = 0) black holes. By examining the astrophysical ramifications through strong gravitational lensing, considering supermassive black holes at the center of nearby galaxies, we uncovered that the modified Bardeen black hole exhibits distinct characteristics, offering a quantitative distinction from other black holes such as the Schwarzschild and Bardeen black holes. These findings in astrophysical consequences provide a promising pathway to differentiate the modified black hole from its counterparts in the realm of general relativity.

Partial tidal disruption events: the elixir of life

ABSTRACT In our Galactic Centre, about $10\,000$ to $100\,000$ stars are estimated to have survived tidal disruption events, resulting in partially disrupted remnants. These events occur when a supermassive black hole (SMBH) tidally interacts with a star, but not enough to completely disrupt the star. We use the 1D stellar evolution code Kepler and the 3D smoothed particle hydrodynamics code Phantom to model the tidal disruption of 1, 3, and $10\, \mathrm{M}_\odot$ stars at zero-age main sequence (ZAMS), middle-age main sequence (MAMS), and terminal-age main sequence (TAMS). We map the disruption remnants into Kepler in order to understand their post-distribution evolution. We find distinct characteristics in the remnants, including increased radius, rapid core rotation, and differential rotation in the envelope. The remnants undergo composition mixing that affects their stellar evolution. Although the remnants formed by disruption of ZAMS models evolve similarly to unperturbed models of the same mass, for MAMS and TAMS stars, the remnants have higher luminosity and effective temperature. Potential observational signatures include peculiarities in nitrogen and carbon abundances, higher luminosity, rapid rotation, faster evolution, and unique tracks in the Hertzsprung–Russell diagram.

Revisiting the accretion disc spectra of dwarf novae and nova-like variables: implications for the standard disc model

ABSTRACT Accretion discs are fundamental to much of astronomy. They can occur around stars, both young and old, around compact objects they provide a window into the extremes of physics, and around supermassive black holes in galaxy centres, they generate spectacular luminosities that can outshine the entire galaxy. However, our understanding of the inner workings of accretion discs remains far from complete. Here, we revisit a conundrum in the observations of some of the simplest accreting systems: the cataclysmic variables (CVs). The high-accretion-rate states of (non-magnetic) CVs can be divided into the short-lived outbursts (∼a week), typical of dwarf novae (DNe), and the long-lived (and sometimes perpetual) high states of nova-like (NL) CVs. Since both sorts of high-state occur in approximately steady-state accretion discs with similar properties and accretors, we would expect them to display similar spectral energy distributions. However, previous analyses based on UV spectra from the International Ultraviolet Explorer have shown that their spectral energy distributions are different. We perform a re-analysis of the data using up to date calibrations and distance (and thus dereddening) estimates to test whether this difference persists and whether it is statistically significant over the sample. We find that it does persist, and it is statistically significant. We propose routes to investigating this discrepancy further and discuss the implications this has for other accreting systems, such as X-ray binaries, active galactic nuclei, and protoplanetary discs.

WISDOM project XX. – Strong shear tearing molecular clouds apart in NGC 524

ABSTRACT Early-type galaxies (ETGs) are known to harbour dense spheroids of stars but scarce star formation (SF). Approximately a quarter of these galaxies have rich molecular gas reservoirs yet do not form stars efficiently. We study here the ETG NGC 524, with strong shear suspected to result in a smooth molecular gas disc and low star-formation efficiency (SFE). We present new spatially resolved observations of the 12CO(2-1)-emitting cold molecular gas from the Atacama Large Millimeter/sub-millimeter Array (ALMA) and of the warm ionized-gas emission lines from SITELLE at the Canada–France–Hawaii Telescope. Although constrained by the resolution of the ALMA observations (≈37 pc), we identify only 52 GMCs with radii ranging from 30 to 140 pc, a low mean molecular gas mass surface density 〈Σgas〉 ≈ 125 M⊙ pc−2 and a high mean virial parameter 〈αobs, vir〉 ≈ 5.3. We measure spatially resolved molecular gas depletion times (τdep ≡ 1/SFE) with a spatial resolution of ≈100 pc within a galactocentric distance of 1.5 kpc. The global depletion time is ≈2.0 Gyr but τdep increases towards the galaxy centre, with a maximum τdep, max ≈ 5.2 Gyr. However, no pure H ii region is identified in NGC 524 using ionized-gas emission-line ratio diagnostics, so the τdep inferred are in fact lower limits. Measuring the GMC properties and dynamical states, we conclude that shear is the dominant mechanism shaping the molecular gas properties and regulating SF in NGC 524. This is supported by analogous analyses of the GMCs in a simulated ETG similar to NGC 524.

Portrait of a Black Hole: The first image of the behemoth at the center of the Milky Way opens new possibilities for understanding the nature of black holes.

Portrait of a Black Hole: The first image of the behemoth at the center of the Milky Way opens new possibilities for understanding the nature of black holes.

Periodicity from X-ray sources within the inner Galactic disk

Aims. For many years it had been claimed that the Galactic ridge X-ray emission at the Galactic Center (GC) is truly diffuse in nature. However, with the advancement of modern X-ray satellites, it has been found that most of the diffuse emission actually comprises thousands of previously unresolved X-ray point sources. Furthermore, many studies suggest that a vast majority of these X-ray point sources are magnetic cataclysmic variables (CVs) and active binaries. One unambiguous way to identify these magnetic CVs and other sources is by detecting their X-ray periodicity. Therefore, we systematically searched for periodic X-ray sources in the inner Galactic disk, including the GC region. Methods. We used data from our ongoing XMM-Newton Heritage Survey of the inner Galactic disk (350° ≲l ≲ +7° and −1° ≲b ≲ +1°) plus archival XMM-Newton observations of the GC. We computed the Lomb-Scargle periodogram for the soft (0.2–2 keV), hard (2–10 keV), and total (0.2–10 keV) band light curves to search for periodicities. Furthermore, we modeled the power spectrum using a power-law model to simulate 1000 artificial light curves and estimate the detection significance of the periodicity. We fitted the energy spectra of the sources using a simple power-law model plus three Gaussians, at 6.4, 6.7, and 6.9 keV, for the iron K emission complex. Results. We detected periodicity in 26 sources. For 14 of them, this is the first discovery of periodicity. For the other 12 sources, we found periods similar to those already known, indicating no significant period evolution. The intermediate polar (IP) type sources display relatively hard spectra compared to polars. We also searched for the Gaia counterparts of the periodic sources to estimate their distances using the Gaia parallax. We found a likely Gaia counterpart for seven sources. Conclusions. Based on the periodicity, hardness ratio, and the equivalent width of Fe K line emission, we have classified the sources into four categories: IPs, polars, neutron star X-ray binaries, and unknown. Of the 14 sources for which we detect the periodicity for the first time, four are likely IPs, five are likely polars, two are neutron star X-ray binaries, and three are of an unknown nature.

Dynamical friction in dark matter superfluids: The evolution of black hole binaries

The theory of superfluid dark matter is characterized by self-interacting sub-eV particles that thermalize and condense to form a superfluid core in galaxies. Massive black holes at the center of galaxies, however, modify the dark matter distribution and result in a density enhancement in their vicinity known as dark matter spikes. The presence of these spikes affects the evolution of binary systems by modifying their gravitational wave emission and inducing dynamical friction effects on the orbiting bodies. In this work, we assess the role of dynamical friction for bodies moving through a superfluid core enhanced by a central massive black hole. As a first step, we compute the dynamical friction force experienced by bodies moving in a circular orbit. Then, we estimate the gravitational wave dephasing of the binary, showing that the effect of the superfluid drag force is beyond the reach of space-based experiments like LISA, contrarily to collisionless dark matter, therefore providing an opportunity to distinguish these dark matter models.