Dark Matter Halo Models Research Articles

Time delay of light in the gravitational lensing of supermassive black holes in dark matter halos

AbstractThe dark matter halo has non-negligible effects on the gravitational lensing of supermassive black hole in the galaxy center. Our work presents a study on the time-delay of light in gravitational lensing of black holes enclosed by dark matter halos. To provide a precise description on the distribution of dark matter in galaxies, we choose several famous phenomenological dark matter halo models in astrophysics, including the NFW, Beta, Burkert and Moore models, to carry out the present study. Through numerically calculating the time-delay of light in gravitational lensing, a comparative analysis of the dark matter effects within different halo models has been performed. Assuming typical length scales associated with the galactic gravitational lensing, numerical results indicate that the NFW, Beta, Burkert and Moore dark matter halos can significantly enhance the time delay of light in gravitational lenisng of central supermassive black holes. The enhancing effect becomes more pronounced with a small dark matter halo scale and an increasing dark matter halo mass.

Gravitational lensing of spherically symmetric black holes in dark matter halos

The gravitational lensing of supermassive black holes surrounded by dark matter halo has attracted a great number of interests in recent years. However, many studies employed simplified dark matter density models, which makes it very hard to give a precise prediction on the dark matter effects in real astrophysical galaxies. In this work, to more accurately describe the distribution of dark matter in real astrophysical galaxies, we study the gravitational lensing of black holes in astrophysical dark matter halo models (Beta, Burkert, Brownstein, and Moore). The deflection angle is obtained using a generalized Gibbons-Werner approach. The visual angular positions and the Einstein rings are also calculated by adopting the gravitational lens equation. Specifically, we choose the supermassive black holes in Milky Way Galaxy, Andromeda galaxy (M31), Virgo galaxy (M87), and ESO138-G014 galaxy as examples, including the corresponding fitted value of dark matter halos. The results suggest that the dark matter halo described by the Beta model has non-negligible influences on the gravitational deflection angle and gravitational lensing observations. However, the Burkert, Brownstein, and Moore models have relatively small influences on angular position of images and the Einstein ring.

Challenges in modeling the dark matter halo of NGC 1052–DF2: Cored versus cuspy halo models

Aims. The discovery of NGC 1052−DF2 and subsequent modeling have shown that NGC 1052−DF2 is deficient in dark matter and is in conflict with the standard stellar-to-halo mass ratio. In this work, we aim to resolve the degeneracy between the dynamical models on the mass estimate of the NGC 1052−DF2. Methods. We constructed mass models of NGC 1052−DF2 using an anisotropic distribution function with a radially varying anisotropy parameter and studied the effect of the various model parameters on the dark matter estimates. We used the observed stellar photometry as an input parameter to construct the distribution function and employed a Markov chain Monte Carlo (MCMC) method to estimate the dark matter model parameters. Results. We find that mass models with a cuspy dark matter halo have comparable χ2 to models with zero dark matter. Moreover, the cuspy dark matter halo fails to consistently account for the observed velocity dispersion in the inner and outer regions of the galaxy. Consequently, we rule out the possibility of a cuspy dark matter halo for describing the mass models of NGC 1052−DF2. Our study shows that the cored dark matter halo model with a total mass of log(MDM/M⊙) = 10.5 explains the observed kinematics but requires an extraordinarily large scale length (20 kpc) and an outer cutoff radius (26 kpc). While the cored mass model provides a comparatively better fit, our findings emphasize that the mass models are largely unconstrained by the available kinematic data. Our results suggest that NGC 1052−DF2 may not only have an ultra-diffuse stellar distribution but that it can, within uncertainties in the available kinematic data, potentially host an ultra-diffuse dark matter distribution compatible with the standard stellar-to-halo mass relation (SHMR) predicted by galaxy formation and evolution models.

Modelling Einstein cluster using Einasto profile

We demonstrate a general relativistic approach to model dark matter halos using the Einstein cluster, with the matter stress-energy generated by collisionless particles moving on circular geodesics in all possible angular directions and orbital radii. Such matter, as is known, allows an anisotropic pressure profile with non-zero tangential but zero radial pressure. We use the Einasto density profile for the Einstein cluster. Analytical studies on its properties (metric functions) and stability issues are investigated. Further, to establish this model (with the Einasto profile) as one for a dark matter halo,we use the SPARC galactic rotation curve data and estimate the best-fit values for the model parameters. General relativistic features (beyond the Keplerian velocities) such as the tangential pressure profile, are quantitatively explored. Thus, Einstein clusters with the Einasto profile, which tally well with observations, may be considered as a viable model for dark matter halos.

A parametric model for self-interacting dark matter halos

We propose a parametric model for studying self-interacting dark matter (SIDM) halos. The model uses an analytical density profile, calibrated using a controlled N-body SIDM simulation that covers the entire gravothermal evolution, including core-forming and -collapsing phases. By normalizing the calibrated density profile, we obtain a universal description for SIDM halos at any evolution phase. The model allows us to infer properties of SIDM halos based on their cold dark matter (CDM) counterparts. As a basic application, we only require two characteristic parameters of an isolated CDM halo at z = 0. We then extend the model to incorporate effects induced by halo mass changes, such as major mergers or tidal stripping, making it applicable to both isolated halos and subhalos. The parametric model is tested and validated using cosmological zoom-in SIDM simulations available in the literature.

Constraining the halo-ISM connection through multi-transition carbon monoxide line-intensity mapping

Line-intensity mapping (LIM) surveys will characterise the cosmological large-scale structure of emissivity in a range of atomic and molecular spectral lines, but existing literature rarely considers whether these surveys can recover excitation properties of the tracer gas species, such as the carbon monoxide (CO) molecule. Combining basic empirical and physical assumptions with the off-the-shelf Radex radiative transfer code or a Gaussian process emulator of Radex outputs, we devise a basic dark matter halo model for CO emission by tying bulk CO properties to halo properties, exposing physical variables governing CO excitation as free parameters. The CO Mapping Array Project (COMAP) is working towards a multi-band survey programme to observe both CO(1–0) and CO(2–1) at z ∼ 7. We show that this programme, as well as a further `Triple Deluxe' extension to higher frequencies covering CO(3–2), is fundamentally capable of successfully recovering the connection between halo mass and CO abundances, and constraining the molecular gas kinetic temperature and density within the star-forming interstellar medium in ways that single-transition CO LIM cannot. Given a fiducial thermal pressure of ∼ 104 K cm-3 for molecular gas in halos of ∼ 1010 M ⊙, simulated multi-band COMAP surveys successfully recover the thermal pressure within 68% interval half-widths of 0.5–0.6 dex. Construction of multi-frequency LIM instrumentation to access multiple CO transitions is crucial in harnessing this capability, as part of a cosmic statistical probe of gas metallicity, dust chemistry, and other physical parameters in star-forming regions of the first galaxies and proto-galaxies out of reionisation.

Galaxy Rotation Curve Fitting Using Machine Learning Tools

Galaxy rotation curve (RC) fitting is an important technique which allows the placement of constraints on different kinds of dark matter (DM) halo models. In the case of non-phenomenological DM profiles with no analytic expressions, the art of finding RC best-fits including the full baryonic + DM free parameters can be difficult and time-consuming. In the present work, we use a gradient descent method used in the backpropagation process of training a neural network, to fit the so-called Grand Rotation Curve of the Milky Way (MW) ranging from ∼1 pc all the way to ∼105 pc. We model the mass distribution of our Galaxy including a bulge (inner + main), a disk, and a fermionic dark matter (DM) halo known as the Ruffini-Argüelles-Rueda (RAR) model. This is a semi-analytical model built from first-principle physics such as (quantum) statistical mechanics and thermodynamics, whose more general density profile has a dense core–diluted halo morphology with no analytic expression. As shown recently and further verified here, the dark and compact fermion-core can work as an alternative to the central black hole in SgrA* when including data at milliparsec scales from the S-cluster stars. Thus, we show the ability of this state-of-the-art machine learning tool in providing the best-fit parameters to the overall MW RC in the 10−2–105 pc range, in a few hours of CPU time.

Normalized additional velocity distribution: Testing the radial profile of dark matter halos and MOND

We propose a complementary and fast approach to study galaxy rotation curves directly from the sample data, instead of individual fits. With this approach, some relevant tests can be done analytically. It is based on a dimensionless difference between the observational rotation curve and the expected one from the baryonic matter ($\delta V^2$) as a function of the normalized radius $r_n$ (i.e., for all galaxies, $0 < r_n < 1$). Using 153 galaxies from the SPARC galaxy sample, we find the observational distribution of $\delta V^2$. Considering radii with $0.2 < r_n < 0.9$, most of the SPARC data are close to the curve $\delta V^2 = r_n^{0.42}$, and about $95\%$ of the SPARC data is between the curves $\delta V^2 = r_n^{2.2}$ and $\delta V^2 = 2 r_n^{0.38} - r_n^{1.9} $. We consider three well known dark matter halo models (NFW, Burkert and DC14), a simple dark matter rotation curve profile for the purpose of model comparison (Arctan$_\alpha$) and one modified gravity model without dark matter (MOND). By comparing the observational data distribution with the model-inferred data, we confirm that the NFW halo lacks the necessary diversity to reproduce several observed rotation curves, while Burkert and DC14 models have better concordance with observational data. The lowest $\delta V^2$ curves that can be found from NFW are linear on the normalized radius (i.e., $\delta V^2_{NFW} = r_n$), while for Burkert $\delta V^2_{Bur} = r_n^2$ (this result is independent of the halo density parameter, i.e., $\rho_{c}$ or $\rho_{s}$). MOND only covers the very central region of the observed distribution, hence it also lacks the necessary diversity, which in turn is related to larger $\chi^2$ values. In a second paper, the method will be extended to consider other classes of modified gravity models.

Dark matter profiles of SPARC galaxies: a challenge to fuzzy dark matter

ABSTRACT Stellar and gas kinematics of galaxies are a sensitive probe of the dark matter distribution in the halo. The popular fuzzy dark matter models predict the peculiar shape of density distribution in galaxies: specific dense core with sharp transition to the halo. Moreover, fuzzy dark matter predicts scaling relations between the dark matter particle mass and density parameters. In this work, we use a Bayesian framework and several dark matter halo models to analyse the stellar kinematics of galaxies using the Spitzer Photometry and Accurate Rotation Curves data base. We then employ a Bayesian model comparison to select the best halo density model. We find that more than half of the galaxies prefer the fuzzy dark model against standard dark matter profiles (NFW, Burkert, and cored NFW). While this seems like a success for fuzzy dark matter, we also find that there is no single value for the particle mass that provides a good fit for all galaxies.

The Effects of Dark Matter upon Neutron Stars’ Properties

The nature of Dark Matter remains elusive despite all of our efforts. This missing matter of the universe cannot be directly observed, but we can see its gravitational effects. Galaxies and Clusters of Galaxies are most likely to contain Dark Matter that is trapped to their Gravitational Field. This leads us to the natural conclusion that Compact Objects might contain Dark Matter too. Neutron Stars are the natural laboratories that we can test our theories and receive crucial observational data. Thus, many models of Dark Matter have been produced to check the existence of Dark Matter in those stars. Since we know for sure the varying parameters of Neutron Stars (Radii, Mass, Λ etc.), by inserting Dark Matter to our equations we can see the differences we obtain in the aforementioned parameters. In this study, we chose to work with the Dark Matter Halo model, where a Neutron Star’s gravitational field is able to trap Dark Matter, but the latter expands way beyond the star’s radius, creating a Dark Halo around the Neutron Star. By studying the various parameters of the Star, we can obtain crucial information about the whole structure and the nature of Dark Matter.

Improved mixed dark matter halo model for ultralight axions

We present a complete halo model for mixed dark matter composed of cold dark matter (CDM) and ultralight axionlike particles (ULAs). Our model treats ULAs as a biased tracer of CDM, in analogy to treatments of massive neutrinos and neutral hydrogen. The model accounts for clustering of ULAs around CDM host halos, and fully models the cross correlations of both components. The model inputs include the ULA Jeans scale, and soliton density profile. Our model can be used to predict the matter power spectrum, $P(k)$, on nonlinear scales for subpopulations of ULAs across the mass range ${10}^{\ensuremath{-}33}\text{ }\text{ }\mathrm{eV}\ensuremath{\le}m\ensuremath{\le}{10}^{\ensuremath{-}21}\text{ }\mathrm{eV}$, and can be calibrated against future mixed DM simulations to improve its accuracy. The mixed DM halo model also allows us to assess the importance of various approximations.

Effect of a high-precision semianalytical mass function on the merger rate of primordial black holes in dark matter halos

In this work, we study the effect of a high-precision semianalytical mass function on the merger rate of primordial black holes (PBHs) in dark matter halos. For this purpose, we first explain a theoretical framework for dark matter halo models and introduce relevant quantities such as the halo density profile, the concentration parameter, and a high-precision semianalytical function, namely Del Popolo (DP) mass function. In the following, we calculate the merger rate of PBHs in the framework of ellipsoidal-collapse dark matter halo models while considering the DP mass function, and compare it with our previous study for the Sheth-Tormen (ST) mass function. The results show that by taking the mass of PBHs as ${M}_{\mathrm{PBH}}=30{M}_{\ensuremath{\bigodot}}$, the DP mass function can potentially amplify the merger rate of PBHs. Moreover, we calculate the merger rate of PBHs for the DP mass function as a function of their mass and fraction and compare it with the black hole mergers recorded by the Laser Interferometer Gravitational-Wave Observatory (LIGO)-Virgo detectors during the latest observing run. Our findings show that the merger rate of PBHs will fall within the LIGO-Virgo band if ${f}_{\mathrm{PBH}}\ensuremath{\gtrsim}\mathcal{O}({10}^{\ensuremath{-}1})$. This implies that the DP mass function can be used to strengthen constraints on the fraction of PBHs.

The Merger Rate of Primordial Black Hole–Neutron Star Binaries in Ellipsoidal-collapse Dark Matter Halo Models

In this work, we calculate the merger rate of primordial black hole–neutron star (PBH–NS) binaries within the framework of ellipsoidal-collapse dark matter models and compare it with that obtained from spherical-collapse dark matter halo models. Our results exhibit that ellipsoidal-collapse dark matter halo models can potentially amplify the merger rate of PBH–NS binaries in such a way that it is very close to the range estimated by the LIGO–Virgo observations. In contrast, spherical-collapse dark matter halo models cannot justify PBH–NS merger events as consistent results with the latest gravitational wave data reported by the LIGO–Virgo collaborations. In addition, we calculate the merger rate of PBH–NS binaries as a function of PBH mass and fraction within the context of ellipsoidal-collapse dark matter halo models. The results indicate that PBH–NS merger events with masses of M PBH ≤ 5M ⊙, M NS ≃ 1.4M ⊙ will be consistent with the LIGO–Virgo observations if f PBH ≃ 1.

Predictive model of fermionic dark matter halos with a quantum core and an isothermal atmosphere

We develop a thermodynamical model of fermionic dark matter halos at finite temperature. Statistical equilibrium states may be justified by a process of violent collisionless relaxation in the sense of Lynden-Bell or from a collisional relaxation of nongravitational origin if the fermions are self-interacting. The most probable state (maximum entropy state) generically has a "core-halo" structure with a quantum core (fermion ball) surrounded by an isothermal atmosphere. The quantum core is equivalent to a polytrope of index $n=3/2$. The Pauli exclusion principle creates a quantum pressure that prevents gravitational collapse and solves the core-cusp problem of the cold dark matter model. The isothermal atmosphere (which is similar to the NFW profile of cold dark matter) accounts for the flat rotation curves of the galaxies at large distances. We numerically solve the equation of hydrostatic equilibrium with the Fermi-Dirac equation of state and determine the density profiles and rotation curves of fermionic dark matter halos.

Constraint on the early-formed dark matter halos using the free-free emission in the Planck foreground analysis

We provide a new constraint on the small-scale density fluctuations, evaluating the diffuse background free-free emission from dark matter halos in the dark ages. If there exists a large amplitude of the matter density fluctuations on small scales, the excess enhances the early formation of dark matter halos. When the virial temperature is sufficiently high, the gas in a halo is heated up and ionized by thermal collision. The heated ionized gas emits photons by the free-free process. We would observe the sum of these photons as the diffuse background free-free emission. Assuming the analytical dark matter halo model including the gas density and temperature profile, we calculate the intensity of the diffuse background free-free emission from early-formed dark matter halos in the microwave frequency range. Comparing with the recent foreground analysis on cosmic microwave background, we obtain the constraint on the excess of the density fluctuations on small scales. Our constraint corresponds to $P_\zeta \lesssim 10^{-7}$ for $k \simeq 1-100~\mathrm{Mpc}^{-1}$ with assuming the delta-function-type curvature power spectrum. Therefore, our constraint is the most stringent constraint on the perturbations below $1~\rm Mpc$ scales.

Primordial black hole merger rate in self-interacting dark matter halo models

We study the merger rate of primordial black holes (PBHs) in self-interacting dark matter (SIDM) halo models. To explore a numerical description for the density profile of SIDM halo models, we use the result of a previously performed simulation for SIDM halo models with $\sigma/m=10~{\rm cm^{2}g^{-1}}$. We also propose a concentration-mass-time relation that can explain the evolution of the halo density profile related to SIDM models. Furthermore, we investigate the encounter condition of PBHs that may have been randomly distributed in the medium of dark matter halos. Under these assumptions, we calculate the merger rate of PBHs within each halo considering SIDM halo models and compare the results with that obtained for cold dark matter (CDM) halo models. To do this, we employ the definition of the time after halo virialization as a function of halo mass. We indicate that SIDM halo models for $f_{\rm PBH}>0.32$ can generate sufficient PBH mergers in such a way that those exceed the one resulted from CDM halo models. By considering the spherical-collapse halo mass function, we obtain similar results for the cumulative merger rate of PBHs. Moreover, we calculate the redshift evolution of the PBH total merger rate. To determine a constraint on the PBH abundance, we study the merger rate of PBHs in terms of their fraction and masses and compare those with the black hole merger rate estimated by the Advanced LIGO (aLIGO)-Advanced Virgo (aVirgo) detectors during the third observing run. The results demonstrate that within the context of SIDM halo models, the merger rate of $10~M_{\odot}-10~M_{\odot}$ events can potentially fall within the aLIGO-aVirgo window. We also estimate a relation between the fraction of PBHs and their masses, which is well consistent with our findings.

A fully Lagrangian, non-parametric bias model for dark matter halos

We present a non-parametric Lagrangian biasing model and fit the ratio of the halo and mass densities at the field level using the mass-weighted halo field in the AbacusSummit simulations at z=0.5. Unlike the perturbative halo bias model that has been widely used in interpreting the observed large-scale structure traced by galaxies, we find a non-negative halo-to-mass ratio that increases monotonically with the linear overdensity δ1 in the initial Lagrangian space. The bias expansion, however, does not guarantee non-negativity of the halo counts, and may lead to rising halo number counts at negative overdensities. The shape of the halo-to-mass ratio is unlikely to be described by a polynomial function of δ1 and other quantities. Especially for massive halos with 6×1012 h-1 M⊙, the halo-to-mass ratio starts soaring up at δ1>0, substantially different from the predictions of the bias expansion. We show that for the halo masses we consider (M>3×1011 h-1 M⊙) a non-parametric halo-to-mass ratio as a function of δ1 and its local derivative ∇^2δ1 can recover the halo power spectra to sub-percent level accuracy for wavenumbers k=0.01-0.1 h Mpc-1 given a proper smoothing scale to filter the initial density field, even though we do not fit the power spectrum directly. However, there is mild dependence of the recovery of the halo power spectrum on the smoothing scale and other input parameters. At k<0.01 h Mpc-1 and for massive halos with M>6×1012 h-1 M⊙, our non-parametric model leads to a few percent overestimation of the halo power spectrum, indicating the need for larger or multiple smoothing scales. The halo-to-mass ratios obtained qualitatively agree with intuitions from extended Press-Schechter theory. We compare our framework to the bias expansion and discuss possible extensions.

A Hydro-particle-mesh Code for Efficient and Rapid Simulations of the Intracluster Medium

Abstract We introduce the cosmological HYPER code based on an innovative hydro-particle-mesh (HPM) algorithm for efficient and rapid simulations of gas and dark matter. For the HPM algorithm, we update the approach of Gnedin &amp; Hui to expand the scope of its application from the lower-density intergalactic medium (IGM) to the higher-density intracluster medium (ICM). While the original algorithm tracks only one effective particle species, the updated version separately tracks the gas and dark matter particles, as they do not exactly trace each other on small scales. For the approximate hydrodynamics solver, the pressure term in the gas equations of motion is calculated using robust physical models. In particular, we use a dark matter halo model, ICM pressure profile, and IGM temperature–density relation, all of which can be systematically varied for parameter-space studies. We show that the HYPER simulation results are in good agreement with the halo model expectations for the density, temperature, and pressure radial profiles. Simulated galaxy cluster scaling relations for Sunyaev–Zel’dovich (SZ) and X-ray observables are also in good agreement with mean predictions, with scatter comparable to that found in hydrodynamic simulations. HYPER also produces lightcone catalogs of dark matter halos and full-sky tomographic maps of the lensing convergence, SZ effect, and X-ray emission. These simulation products are useful for testing data analysis pipelines, generating training data for machine learning, understanding selection and systematic effects, and for interpreting astrophysical and cosmological constraints.

Quenching Factor consistency across several NaI(Tl) crystals

Testing the DAMA/LIBRA annual modulation result independently of dark matter particle and halo models has been a challenge for twenty years. Using the same target material, NaI(Tl), is required and presently two experiments, ANAIS-112 and COSINE-100, are running for such a goal. A precise knowledge of the detector response to nuclear recoils is mandatory because this is the most likely channel to find the dark matter signal. The light produced by nuclear recoils is quenched with respect to that produced by electrons by a factor that has to be measured experimentally. However, current quenching factor measurements in NaI(Tl) crystals disagree within the energy region of interest for dark matter searches. To disentangle whether this discrepancy is due to intrinsic differences in the light response among different NaI(Tl) crystals, or has its origin in unaccounted for systematic effects will be key in the comparison among the different experiments. We present measurements of the quenching factors for five small NaI(Tl) crystals performed in the same experimental setup to control systematics. Quenching factor results are compatible between crystals and no clear dependence with energy is observed from 10 to 80 keVnr.

Annual modulation results from three-year exposure of ANAIS-112

ANAIS (Annual modulation with NaI Scintillators) is a dark matter direct detection experiment consisting of 112.5 kg of NaI(Tl) detectors in operation at the Canfranc Underground Laboratory (LSC), in Spain, since August 2017. ANAIS' goal is to confirm or refute in a model independent way the DAMA/LIBRA positive result: an annual modulation in the low-energy detection rate having all the features expected for the signal induced by dark matter particles in a standard galactic halo. This modulation, observed for about 20 years, is in strong tension with the negative results of other very sensitive experiments, but a model-independent comparison is still lacking. By using the same target material, NaI(Tl), such comparison is more direct and almost independent on dark matter particle and halo models. Here, we present the annual modulation analysis corresponding to three years of ANAIS data (for an effective exposure of 313.95 kg$\times$y), applying a blind procedure which updates that developed for the 1.5 years analysis, and later applied to 2 years. The analysis also improves the background modelling in the fitting of the region of interest rates. We obtain for the best fit in the [1-6] keV ([2-6] keV) energy region a modulation amplitude of -0.0034$\pm$0.0042 cpd/kg/keV (0.0003$\pm$0.0037 cpd/kg/keV), supporting the absence of modulation in our data, and incompatible with DAMA/LIBRA result at 3.3 (2.6) $\sigma$, for a sensitivity of 2.5 (2.7) $\sigma$. Moreover, we include two complementary analyses: a phase-free annual modulation search and the exploration of the possible presence of a periodic signal at other frequencies. Finally, we carry out several consistency checks of our result, and we update the ANAIS-112 projected sensitivity for the scheduled 5 years of operation.