Collisionless Dark Matter Research Articles

Evolution of the phase-space density and the Jeans scale for dark matter derivedfrom the Vlasov-Einstein equation

We discuss solutions of Vlasov-Einstein equation for collisionless dark matter particles in the context of a flat Friedmann universe. We show that, after decoupling from the primordial plasma, the dark matter phase-space density indicator Q = ρ/(σ1D2)3/2 remains constant during the expansion of the universe, prior to structure formation. This well known result is valid for non-relativistic particles and is not ``observer dependent'' as in solutions derived from the Vlasov-Poisson system. In the linear regime, the inclusion of velocity dispersion effects permits to define a physical Jeans length for collisionless matter as function of the primordial phase-space density indicator: λJ = (5π/G)1/2Q−1/3ρdm−1/6. The comoving Jeans wavenumber at matter-radiation equality is smaller by a factor of 2-3 than the comoving wavenumber due to free-streaming, contributing to the cut-off of the density fluctuation power spectrum at the lowest scales. We discuss the physical differences between these two scales. For dark matter particles of mass equal to 200 GeV, the derived Jeans mass is 4.3 × 10−6M⊙.

A new approach to simulating collisionless dark matter fluids

Recently, we have shown how current cosmological N-body codes already follow the fine grained phase-space information of the dark matter fluid. Using a tetrahedral tesselation of the three-dimensional manifold that describes perfectly cold fluids in six-dimensional phase space, the phase-space distribution function can be followed throughout the simulation. This allows one to project the distribution function into configuration space to obtain highly accurate densities, velocities, and velocity dispersions. Here, we exploit this technique to show first steps on how to devise an improved particle-mesh technique. At its heart, the new method thus relies on a piecewise linear approximation of the phase space distribution function rather than the usual particle discretisation. We use pseudo-particles that approximate the masses of the tetrahedral cells up to quadrupolar order as the locations for cloud-in-cell (CIC) deposit instead of the particle locations themselves as in standard CIC deposit. We demonstrate that this modification already gives much improved stability and more accurate dynamics of the collisionless dark matter fluid at high force and low mass resolution. We demonstrate the validity and advantages of this method with various test problems as well as hot/warm-dark matter simulations which have been known to exhibit artificial fragmentation. This completely unphysical behaviour is much reduced in the new approach. The current limitations of our approach are discussed in detail and future improvements are outlined.

Beyond collisionless dark matter: Particle physics dynamics for dark matter halo structure

Dark matter (DM) self-interactions have important implications for the formation and evolution of structure, from dwarf galaxies to clusters of galaxies. We study the dynamics of self-interacting DM via a light mediator, focusing on the quantum resonant regime where the scattering cross section has a non-trivial velocity dependence. While there are long-standing indications that observations of small scale structure in the Universe are not in accord with the predictions of collisionless DM, theoretical study and simulations of DM self-interactions have focused on parameter regimes with simple analytic solutions for the scattering cross section, with constant or classical velocity (and no angular) dependence. We devise a method that allows us to explore the velocity and angular dependence of self-scattering more broadly, in the strongly-coupled resonant and classical regimes where many partial modes are necessary for the achieving the result. We map out the entire parameter space of DM self-interactions --- and implications for structure observations --- as a function of the coupling and the DM and mediator masses. We derive a new analytic formula for describing resonant s-wave scattering. Finally, we show that DM self-interactions can be correlated with observations of Sommerfeld enhancements in DM annihilation through indirect detection experiments.

Interaction between collisionless galactic discs and non-axisymmetric dark matter haloes

Using $N$-body simulations ($N\sim 10^6 - 10^7$), we examine how a non-axisymmetric dark halo affects the dynamical evolution of the structure in collisionless (stellar) discs. We demonstrate how the model parameters such as mass of the halo, initial conditions in the disc and the halo axes ratio affect morphology and kinematics of the stellar discs. We show that a non-axisymmetric halo can generate a large-scale spiral density pattern in the embedded stellar disc. The pattern is observed in the disc for many periods of its revolution, even if the disc is gravitationally over-stable. The growth of the spiral arms is not accompanied by significant dynamical heating of the disc, irrelevant to its initial parameters. We also investigate transformation of the dark halo's shape driven by the long-lived spiral pattern in the disc . We show that the analysis of the velocity field in the stellar disc and in the spiral pattern gives us a possibility to figure out the spatial orientation of the triaxial-shaped dark halo and to measure the triaxiality.

Direct detection of self-interacting dark matter

Self-interacting dark matter offers an interesting alternative to collisionless dark matter because of its ability to preserve the large-scale success of the cold dark matter model, while seemingly solving its challenges on small scales. We present here the first study of the expected dark matter detection signal taking into account different self-scattering models. We demonstrate that models with constant and velocity dependent cross sections, which are consistent with observational constraints, lead to distinct signatures in the velocity distribution, because non-thermalised features found in the cold dark matter distribution are thermalised through particle scattering. Depending on the model, self-interaction can lead to a 10% reduction of the recoil rates at high energies, corresponding to a minimum speed that can cause recoil larger than 300 km/s, compared to the cold dark matter case. At lower energies these differences are smaller than 5% for all models. The amplitude of the annual modulation signal can increase by up to 25%, and the day of maximum amplitude can shift by about two weeks with respect to the cold dark matter expectation. Furthermore, the exact day of phase reversal of the modulation signal can also differ by about a week between the different models. In general, models with velocity dependent cross sections peaking at the typical velocities of dwarf galaxies lead only to minor changes in the detection signals, whereas allowed constant cross section models lead to significant changes. We conclude that different self-interacting dark matter scenarios might be distinguished from each other through the details of direct detection signals. Furthermore, detailed constraints on the intrinsic properties of dark matter based on null detections, should take into account the possibility of self-scattering and the resulting effects on the detector signal.

Collisionless stellar hydrodynamics as an efficient alternative to N-body methods

For simulations that deal only with dark matter or stellar systems, the conventional N-body technique is fast, memory efficient, and relatively simple to implement. However when including the effects of gas physics, mesh codes are at a distinct disadvantage compared to SPH. Whilst implementing the N-body approach into SPH codes is fairly trivial, the particle-mesh technique used in mesh codes to couple collisionless stars and dark matter to the gas on the mesh, has a series of significant scientific and technical limitations. These include spurious entropy generation resulting from discreteness effects, poor load balancing and increased communication overhead which spoil the excellent scaling in massively parallel grid codes. We propose the use of the collisionless Boltzmann moment equations as a means to model collisionless material as a fluid on the mesh, implementing it into the massively parallel FLASH AMR code. This approach, which we term "collisionless stellar hydrodynamics" enables us to do away with the particle-mesh approach. Since the parallelisation scheme is identical to that used for the hydrodynamics, it preserves the excellent scaling of the FLASH code already demonstrated on peta-flop machines. We find the classic hydrodynamic equations and Boltzmann moment equations can be reconciled under specific conditions, allowing us to generate analytic solutions for collisionless systems using conventional test problems. We confirm the validity of our approach using a suite of demanding test problems, including the use of a modified Sod shock test. We conclude by demonstrating the ability of our code to model complex phenomena by simulating the evolution of a spiral galaxy whose properties agree with those predicted by swing amplification theory. (Abridged)

ON DARK PEAKS AND MISSING MASS: A WEAK-LENSING MASS RECONSTRUCTION OF THE MERGING CLUSTER SYSTEM A520,

Merging clusters of galaxies are unique in their power to directly probe and place limits on the self-interaction cross-section of dark matter. Detailed observations of several merging clusters have shown the intracluster gas to be displaced from the centroids of dark matter and galaxy density by ram pressure, while the latter components are spatially coincident, consistent with collisionless dark matter. This has been used to place upper limits on the dark matter particle self-inteaction cross-section of order 1 cm^2/g. The cluster Abell 520 has been seen as a possible exception. We revisit A520 presenting new HST ACS mosaic images and a Magellan image set. We perform a detailed weak lensing analysis and show that the weak lensing mass measurements and morphologies of the core galaxy-filled structures are mostly in good agreement with previous works. There is however one significant difference -- we do not detect the previously claimed "dark core" that contains excess mass with no significant galaxy overdensity at the location of the X-ray plasma. This peak has been suggested to be indicative of a large self-interaction cross-section for dark matter (at least ~5 sigma larger than the upper limit of 0.7 cm^2/g determined by observations of the Bullet Cluster). We find no such indication and instead find that the mass distribution of A520, after subtraction of the X-ray plasma mass, is in good agreement with the luminosity distribution of the cluster galaxies. We conclude that A520 shows no evidence to contradict the collisionless dark matter scenario.

Theoretical dark matter halo density profile

We derive the density profile for collisionless dissipationless dark matter haloes in hierarchical cosmologies making use of the secondary infall (SI) model. The novelties are (i) we deal with triaxial virialized objects, (ii) their seeds in the linear regime are peaks endowed with unconvolved spherically averaged density profiles according to the peak formalism, (iii) the initial peculiar velocities are taken into account and (iv) accreting haloes are assumed to develop from the inside out, keeping the instantaneous inner system unaltered. The validity of this latter assumption is accurately checked by comparing analytical predictions on such a growth with the results of numerical simulation. We show that the spherically averaged density profile of virialized objects can be inferred with no need to specify their shape. The typical spherically averaged halo density profile is inferred, down to arbitrarily small radii, from the power spectrum of density perturbations. The predicted profile in the Λ cold dark matter cosmology is approximately described by an Einasto profile, meaning that it does not have a cusp but rather a core, where the inner slope slowly converges to zero. Down to one-hundredth the total radius, the profile has the right NFW and Einasto forms, being close to the latter down to a radius of about four orders of magnitude less. The inner consistency of the model implies that the density profiles of haloes harbour no information on their past aggregation history. This would explain why major mergers do not alter the typical density profile of virialized objects formed by SI and do not invalidate the peak formalism based on such a formation.

DISCOVERY OF A DISSOCIATIVE GALAXY CLUSTER MERGER WITH LARGE PHYSICAL SEPARATION

We present DLSCL J0916.2+2951 (z=0.53), a newly discovered major cluster merger in which the collisional cluster gas has become dissociated from the collisionless galaxies and dark matter. We identified the cluster using optical and weak lensing observations as part of the Deep Lens Survey. Our follow-up observations with Keck, Subaru, Hubble Space Telescope, and Chandra show that the cluster is a dissociative merger and constrain the dark matter self-interaction cross-section {\sigma}_{DM}m_{DM}^{-1}\leq7 cm^2g^{-1}. The system is observed at least 0.7\pm0.2 Gyr since first pass-through, thus providing a picture of cluster mergers 2-5 times further progressed than similar systems observed to date. This improved temporal leverage has implications for our understanding of merging clusters and their impact on galaxy evolution.

Dynamical effect of the turbulence of the intergalactic medium on the baryon fraction distribution

We investigate the dynamical effect of the turbulence in baryonic intergalactic medium (IGM) on the baryon fraction distribution. In the fully developed nonlinear regime, the IGM will evolve into the state of turbulence, containing strong and curved shocks, vorticity and complex structures. Turbulence would lead to the density and velocity fields of the IGM to be different from those of underlying collisionless dark matter. Consequently, the baryon fraction f_b will deviate from its cosmic mean . We study these phenomena with simulation samples produced by the weighted essentially non-oscillatory (WENO) hybrid cosmological hydrodynamic/N-body code, which is effective of capturing shocks and complex structures. We find that the distribution of baryon fraction is highly nonuniform on scales from hundreds kpc to a few of Mpc, and f_b varies from as low as 1% to a few times of the cosmic mean. We further show that the turbulence pressure in the IGM is weakly scale-dependent and comparable to the gravitational energy density of halos with mass around 10^11 h-1 M\odot . The baryon fraction in halos with mass equal to or smaller than 10^11 h^-1 M\odot should be substantially lower than f_b^cosmic. Numerical results show that f_b is decreasing from 0.8 f_b^cosmic at halo mass scales around 10^12 h^-1 M\odot to 0.3f_b^cosmic at 10^11 h^-1 M\odot and shows further decrease when halo mass is less than 10^11 h^-1 M\odot. The strong mass dependence of f_b is similar to the observed results. Although the simulated f_b in halos are higher than the observed value by a factor of 2, the turbulence of the IGM should be an important dynamical reason leading to the remarkable missing of baryonic matter in halos with mass \leq 10^12 h^-1 M\odot.

Cosmic X-ray and gamma-ray background from dark matter annihilation

(Abridged) The extragalactic background light (EBL) observed at multiple wavelengths is a promising tool to probe the nature of dark matter since it might contain a significant contribution from gamma-rays produced promptly by dark matter annihilation. Additionally, the electrons and positrons produced in the annihilation give energy to the CMB photons to populate the EBL with X-rays and gamma-rays. We here create full-sky maps of the radiation from both of these contributions using the high-resolution Millennium-II simulation. We use upper limits on the contributions of unknown sources to the EBL to constrain the intrinsic properties of dark matter using a model-independent approach that can be employed as a template to test different particle physics models (including those with a Sommerfeld enhancement). These upper limits are based on observations spanning eight orders of magnitude in energy (from soft X-rays measured by CHANDRA to gamma-rays measured by Fermi), and on expectations for the contributions from blazars and star forming galaxies. To exemplify this approach, we analyze a set of benchmark Sommerfeld-enhanced models that give the correct dark matter abundance, satisfy CMB constraints, and fit the cosmic ray spectra measured by PAMELA and Fermi without any contribution from local subhalos. We find that these models are in conflict with the EBL constraints unless the contribution of unresolved subhalos is small and the annihilation signal dominates the EBL. We conclude that provided the collisionless cold dark matter paradigm is accurate, even for conservative estimates of the contribution from unresolved subhalos and astrophysical backgrounds, the EBL is at least as sensitive a probe of these types of scenarios as the CMB. Our results disfavor an explanation of the positron excess measured by PAMELA based only on dark matter annihilation in the smooth Galactic halo.

Statistical and Dynamical Decoupling of the IGM from Dark Matter

Although the gravitational field in the universe is dominated by dark matter, cosmological observations show that the statistical properties of cosmic baryonic matter are significantly and systematically decoupled from that of the underlying dark matter. The dynamical reason of the decoupling is the difference of the nonlinear evolution of baryon fluid from that of collisionless dark matter. In highly nonlinear regime, the cosmic baryon fluid on scale free range evolves into the state of fully developed turbulence, of which the velocity field consists of shocks, vortices and complex structures. This scenario provides a coherent explanation of various phenomena referring to the statistical and dynamical decoupling of the IGM from dark matter.

Direct detection of WIMPs: implications of a self-consistent truncated isothermal model of the Milky Way's dark matter halo

Direct detection of Weakly Interacting Massive Particle (WIMP) candidates of Dark Matter (DM) is studied within the context of a self-consistent truncated isothermal model of the finite-size dark halo of the Galaxy. The halo model, based on the ``King model'' of the phase space distribution function of collisionless DM particles, takes into account the modifications of the phase-space structure of the halo due to the gravitational influence of the observed visible matter in a self-consistent manner. The parameters of the halo model are determined by a fit to a recently determined circular rotation curve of the Galaxy that extends up to ∼ 60 kpc. Unlike in the Standard Halo Model (SHM) customarily used in the analysis of the results of WIMP direct detection experiments, the velocity distribution of the WIMPs in our model is non-Maxwellian with a cut-off at a maximum velocity that is self-consistently determined by the model itself. For our halo model that provides the best fit to the rotation curve data, the 90% C.L. upper limit on the WIMP-nucleon spin-independent cross section from the recent results of the CDMS-II experiment, for example, is ∼ 5.3 × 10−8 pb at a WIMP mass of ∼ 71 GeV. We also find, using the original 2-bin annual modulation amplitude data on the nuclear recoil event rate seen in the DAMA experiment, that there exists a range of small WIMP masses, typically ∼ 2–16 GeV, within which DAMA collaboration's claimed annual modulation signal purportedly due to WIMPs is compatible with the null results of other experiments. These results, based as they are on a self-consistent model of the dark matter halo of the Galaxy, strengthen the possibility of low-mass (≲10 GeV) WIMPs as a candidate for dark matter as indicated by several earlier studies performed within the context of the SHM. A more rigorous analysis using DAMA bins over smaller intervals should be able to better constrain the ``DAMA regions'' in the WIMP parameter space within the context of our model.

Ram-pressure stripping of the cool core of the Ophiuchus Cluster

We report results from a Chandra study of the central regions of the nearby, X-ray bright, Ophiuchus Cluster (z= 0.03), the second-brightest cluster in the sky. Our study reveals a dramatic, close-up view of the stripping and potential destruction of a cool core within a rich cluster. The X-ray emission from the Ophiuchus Cluster core exhibits a comet-like morphology extending to the north, driven by merging activity, indicative of ram-pressure stripping caused by rapid motion through the ambient cluster gas. A cold front at the southern edge implies a velocity of 1000 ± 200 km s−1 (M∼ 0.6). The X-ray emission from the cluster core is sharply peaked. As previously noted, the peak is offset by 4 arcsec (∼2 kpc) from the optical centre of the associated cD galaxy, indicating that ram pressure has slowed the core, allowing the relatively collisionless stars and dark matter to carry on ahead. The cluster exhibits the strongest central temperature gradient of any massive cluster observed to date: the temperature rises from 0.7 keV within 1 kpc of the brightness peak to 10 keV by 30 kpc. A strong metallicity gradient is also observed within the same region. This supports a picture in which the outer parts of the cool core have been stripped by ram pressure due to its rapid motion. The cooling time of the innermost gas is very short, ∼5 × 107 yr. Within the central 10 kpc radius, multiple small-scale fronts and a complex thermodynamic structure are observed, indicating significant motions. These may be excited by the separation of the X-ray peak from the cD galaxy and its associated dark matter potential. Beyond the central 50 kpc, and out to a radius of ∼150 kpc, the cluster appears relatively isothermal and has near constant metallicity. The exception is a large, coherent ridge of enhanced metallicity observed to trail the cool core and which is likely to have been stripped from it.

Acquired scaling relations in dark matter turbulence

Variety of scaling relations are observed in astronomical objects. We study a consistent understanding of them from a simple proposal that the collision-less dark matter fluid terns into a turbulent state, i.e. cosmic dark turbulence. This happens most likely when the density fluctuations cross the caustic surface toward the non-linear regime. Collision-less dark turbulence may not be eddy-dominant. We first derive Kolmogorov scaling laws from the gravitational Navier-Stokes equation by the method similar to the case in Smoluchowski coagulation equation. Then we apply this to several observations such as the scale-dependent velocity dispersion, mass-luminosity ratio, magnetic fields, and mass-angular momentum relation, power spectrum of density fluctuations. They all conclude a single value for a constant energy flow per mass: 0.3cm2/sec3. This value may deeply related with the speed of the hierarchical coalescence process in the cosmic structure formation.

EFFECTS OF BARYON DISSIPATION ON THE DARK MATTER VIRIAL SCALING RELATION

We investigate effects of baryon dissipation on the dark matter virial scaling relation between total mass and velocity dispersion and the velocity bias of galaxies in groups and clusters using self-consistent cosmological simulations. We show that the baryon dissipation increases the velocity dispersion of dark matter within the virial radius by 5% - 10%. The effect is mainly driven by the change in density and gravitational potential in inner regions of cluster, and it is larger in lower mass systems where gas cooling and star formation are more efficient. We also show that the galaxy velocity bias depends on how galaxies are selected. Galaxies selected based on their stellar mass exhibit no velocity bias, while galaxies selected based on their total mass show positive bias of ~10%, consistent with previous results based on collisionless dark matter- only simulations. We further find that observational estimates of galaxy velocity dispersion are unbiased with respect to the velocity dispersion of dark matter, provided galaxies are selected using their stellar masses and and their velocity dispersions are computed with more than twenty most massive galaxies. Velocity dispersions estimated with fewer galaxies, on the other hand, can lead to significant underestimate of dynamical masses. Results presented in this paper should be useful in interpretating high-redshift groups and clusters as well as cosmological constraints derived from upcoming optical cluster surveys.

Gravity modification with Yukawa-type potential: dark matter and mirror gravity

The nature of the gravitational interaction between ordinary and dark matter is still open. Any deviation from universality or the Newtonian law also modifies the standard assumption of collisionless dark matter. On the other hand, obtaining a Yukawa-like large-distance modification of the gravitational potential is a nontrivial problem, that has so far eluded a consistent realization even at linearized level. We propose here a theory providing a Yukawa-like potential, by coupling non-derivatively the two metric fields related respectively to the visible and dark matter sectors, in the context of massive gravity theories where the local Lorentz invariance is broken by the different coexisting backgrounds. This gives rise to the appropriate mass pattern in the gravitational sector, producing a healthy theory with the Yukawa potential. Our results are of a special relevance in the scenario of dark matter originated from the mirror world, an exact duplicate of the ordinary particle sector.

Cosmic dark turbulence

We aim for a consistent understanding of various scaling relations reported for self-gravitating systems, based on the proposal that the collisionless dark matter fluid turns into a turbulent state, i.e. dark turbulence, after crossing the caustic surface in the non-linear stage. Kolmogorov scaling laws with a constant energy flow per mass of 0.3 cm<sup>2<sup/>/s<sup>3<sup/> are suggested from observations.

Galaxy Distribution as a Probe of the Ringlike Dark Matter Structure in the Galaxy Cluster Cl 0024+17

In a galaxy cluster, galaxies are mostly collisionless particles in recent epochs. They resemble collisionless cold dark matter particles in some way. Therefore, the spatial distributions of dark matter and cluster galaxies might be expected to possess similar features in the gravitational potential of a cluster. Here we use the galaxy distribution in cluster Cl 0024+17 to probe for the ringlike dark matter structure recently discovered by means of strong and weak lensing observations. The galaxies are taken from the catalog of Czoske et al., which contains 650 objects with measured redshifts, of which ~300 galaxies have redshifts in the range 0.37 < z < 0.41 (and are therefore probable cluster members). We find that, at about the 3 σ level, the ringlike structure seen in the dark matter measurement is not observed in the projected two-dimensional galaxy distribution.

Third-order cosmological perturbations of zero-pressure multi-component fluids: puregeneral relativistic non-linear effects

The present expansion stage of the universe is believed to be mainly governed bythe cosmological constant, collisionless dark matter and baryonic matter. Thelatter two components are often modeled as zero-pressure fluids. In our previouswork we have shown that to second order in the cosmological perturbations, therelativistic equations for the density and velocity perturbations of the zero-pressure,irrotational, multi-component fluids in a spatially near flat background withoutgravitational waves effectively coincide with the Newtonian equations. As the Newtonianequations only have quadratic order non-linearity, it is of practical interest toderive the third-order perturbation terms in a general relativistic treatment, whichcorrespond to pure general relativistic corrections. In our previous work we haveshown that even in a single-component fluid there exist a substantial numberof pure relativistic third-order correction terms. We have, however, shown thatthose correction terms are independent of the horizon scale, and are quite small(∼5 × 10−5 smaller compared with the relativistic/Newtonian second-order terms) near thehorizon scale due to the weak level anisotropy of the cosmic microwave backgroundradiation. Here, we present pure general relativistic correction terms appearing inthe third-order perturbations of the multi-component zero-pressure fluids. Theforms of the pure general relativistic correction terms are quite similar to theones in a single-component situation. The third-order correction terms involveonly the ‘linear order spatial curvature perturbation in the comoving gauge’φv which has the order of the ‘perturbed Newtonian gravitational potential divided byc2 ’, and thus is small on nearly all scales. Consequently, we show that, as ina single-component situation, the third-order correction terms are quite small(∼5 × 10−5 smaller) near the horizon, and independent of the horizon scale. We emphasize that theseresults are based on our proper choice of perturbation variables and gauge conditions fordescribing the relativistic perturbations. Still, there do exist a substantial number of puregeneral relativistic correction terms in third-order perturbations which couldpotentially become important in future development of precision cosmology. Althoughφv is small on nearly all scales, our third-order corrections are applicable only in weaklynon-linear regimes where perturbation analysis is viable. We include the cosmologicalconstant in all our analyses.