Statistical mechanics of collisionless orbits. III. Comparison with N-body simulations

We compare the DARKexp differential energy distribution, N(E) \propto \exp(\phi_0-E)-1, obtained from statistical mechanical considerations, to the results of N-body simulations of dark matter halos. We first demonstrate that if DARKexp halos had anisotropic velocity distributions similar to those of N-body simulated halos, their density and energy distributions could not be distinguished from those of isotropic DARKexp halos. We next carry out the comparison in two ways, using (1) the actual energy distribution extracted from simulations, and (2) N-body fitting formula for the density distribution as well as N(E) computed from the density using the isotropic Eddington formula. Both the methods independently agree that DARKexp N(E) with \phi_0\approx 4-5 is an excellent match to N-body N(E). Our results suggest (but do not prove) that statistical mechanical principles of maximum entropy can be used to explain the equilibrated final product of N-body simulations.Comment: 17 pages, 7 figures; ApJ, in pres

Non-universality of dark-matter halos: cusps, cores, and the central potential

Dark-matter halos grown in cosmological simulations appear to have central NFW-like density cusps with mean values of $d\log\rho/d\log r \approx -1$, and some dispersion, which is generally parametrized by the varying index $\alpha$ in the Einasto density profile fitting function. Non-universality in profile shapes is also seen in observed galaxy clusters and possibly dwarf galaxies. Here we show that non-universality, at any given mass scale, is an intrinsic property of DARKexp, a theoretically derived model for collisionless self-gravitating systems. We demonstrate that DARKexp - which has only one shape parameter, $\phi_0$ - fits the dispersion in profile shapes of massive simulated halos as well as observed clusters very well. DARKexp also allows for cored dark-matter profiles, such as those found for dwarf spheroidal galaxies. We provide approximate analytical relations between DARKexp $\phi_0$, Einasto $\alpha$, or the central logarithmic slope in the Dehnen-Tremaine analytical $\gamma$-models. The range in halo parameters reflects a substantial variation in the binding energies per unit mass of dark-matter halos.Comment: ApJ, in press, 10 pages, 7 figure

Why does the Jeans Swindle work?

When measuring the mass profile of any given cosmological structure through internal kinematics, the distant background density is always ignored. This trick is often refereed to as the "Jeans Swindle". Without this trick a divergent term from the background density renders the mass profile undefined, however, this trick has no formal justification. We show that when one includes the expansion of the Universe in the Jeans equation, a term appears which exactly cancels the divergent term from the background. We thereby establish a formal justification for using the Jeans Swindle.Comment: 5 pages, 2 figures, Accepted for publication in MNRAS Letter

Ursa Major II - Reproducing the observed properties through tidal disruption

Recent deep photometry of the dwarf spheroidal Ursa Major II's morphology, and spectroscopy of individual stars, have provided a number of new constraints on its properties. With a velocity dispersion $\sim$6 km s$^{-1}$, and under the assumption that the galaxy is virialised, the mass-to-light ratio is found to be approaching $\sim$2000 - apparently heavily dark matter dominated. Using N-Body simulations, we demonstrate that the observed luminosity, ellipticity, irregular morphology, velocity gradient, and the velocity dispersion can be well reproduced through processes associated with tidal mass loss, and in the absence of dark matter. These results highlight the considerable uncertainty that exists in measurements of the dark matter content of Ursa Major II. The dynamics of the inner tidal tails, and tidal stream, causes the observed velocity dispersion of stars to be boosted to values of $>$5 km s$^{-1}$ ($>$20 km s$^{-1}$ at times). This effect is responsible for raising the velocity dispersion of our model to the observed values in UMaII. We test an iterative rejection technique for removing unbound stars from samples of UMaII stars whose positions on the sky, and line-of-sight velocities, are provided. We find this technique is very effective at providing an accurate bound mass from this information, and only fails when the galaxy has a bound mass less than 10$$ of its initial mass. However when $<2$ mass remains bound, mass overestimation by $>$3 orders of magnitude are seen. Additionally we find that mass measurements are sensitive to measurement uncertainty in line-of-sight velocities. Measurement uncertainties of 1-4 km s$^{-1}$ result in mass overestimates by a factor of $\sim$1.3-5.7.Comment: 17 pages, 12 figures, accepted to MNRAS: 23rd, May, 201

Gravitational redshift of galaxies in clusters as predicted by general relativity

The theoretical framework of cosmology is mainly defined by gravity, of which general relativity is the current model. Recent tests of general relativity within the \Lambda Cold Dark Matter (CDM) model have found a concordance between predictions and the observations of the growth rate and clustering of the cosmic web. General relativity has not hitherto been tested on cosmological scales independent of the assumptions of the \Lambda CDM model. Here we report observation of the gravitational redshift of light coming from galaxies in clusters at the 99 per cent confidence level, based upon archival data. The measurement agrees with the predictions of general relativity and its modification created to explain cosmic acceleration without the need for dark energy (f(R) theory), but is inconsistent with alternative models designed to avoid the presence of dark matter.Comment: Published in Nature issued on 29 September 2011. This version includes the Letter published there as well as the Supplementary Information. 23 pages, 7 figure

The Distance to NGC 4993: The Host Galaxy of the Gravitational-wave Event GW170817

The historic detection of gravitational waves from a binary neutron star merger (GW170817) and its electromagnetic counterpart led to the first accurate (sub-arcsecond) localization of a gravitational-wave event. The transient was found to be $\sim$10" from the nucleus of the S0 galaxy NGC 4993. We report here the luminosity distance to this galaxy using two independent methods. (1) Based on our MUSE/VLT measurement of the heliocentric redshift ($z_{\rm helio}=0.009783\pm0.000023$) we infer the systemic recession velocity of the NGC 4993 group of galaxies in the cosmic microwave background (CMB) frame to be $v_{\rm CMB}=3231 \pm 53$ km s$^{-1}$. Using constrained cosmological simulations we estimate the line-of-sight peculiar velocity to be $v_{\rm pec}=307 \pm 230$ km s$^{-1}$, resulting in a cosmic velocity of $v_{\rm cosmic}=2924 \pm 236$ km s$^{-1}$ ($z_{\rm cosmic}=0.00980\pm 0.00079$) and a distance of $D_z=40.4\pm 3.4$ Mpc assuming a local Hubble constant of $H_0=73.24\pm 1.74$ km s$^{-1}$ Mpc$^{-1}$. (2) Using Hubble Space Telescope measurements of the effective radius (15.5" $\pm$ 1.5") and contained intensity and MUSE/VLT measurements of the velocity dispersion, we place NGC 4993 on the Fundamental Plane (FP) of E and S0 galaxies. Comparing to a frame of 10 clusters containing 226 galaxies, this yields a distance estimate of $D_{\rm FP}=44.0\pm 7.5$ Mpc. The combined redshift and FP distance is $D_{\rm NGC 4993}= 41.0\pm 3.1$ Mpc. This 'electromagnetic' distance estimate is consistent with the independent measurement of the distance to GW170817 as obtained from the gravitational-wave signal ($D_{\rm GW}= 43.8^{+2.9}_{-6.9}$ Mpc) and confirms that GW170817 occurred in NGC 4993.Comment: 9 pages, 5 figure

Interloper treatment in dynamical modelling of galaxy clusters

The aim of this paper is to study the efficiency of different approaches to interloper treatment in dynamical modelling of galaxy clusters. Using cosmological N-body simulation of standard LCDM model we select 10 massive dark matter haloes and use their particles to emulate mock kinematic data in terms of projected galaxy positions and velocities as they would be measured by a distant observer. Taking advantage of the full 3D information available from the simulation we select samples of interlopers defined with different criteria. The interlopers thus selected provide means to assess the efficiency of different interloper removal schemes. We study direct methods of interloper removal based on dynamical or statistical restrictions imposed on ranges of positions and velocities available to cluster members. In determining these ranges we use either the velocity dispersion criterion or a maximum velocity profile. We find that the direct methods exclude on average 60-70 percent of unbound particles producing a sample of contamination as low as 2-3 percent. We also test the dependence of the commonly used virial mass and projected mass estimators on the presence of interlopers. We find that both are sensitive mainly to unbound particles and their ratio is a good indicator of the presence of unbound particles in the sample. Finally we consider indirect methods of interloper treatment which are applied to the data stacked from many objects. In these approaches interlopers are treated in a statistical way as a uniform background which modifies the distribution of cluster members. We find that unbound particles constitute a sample of interlopers with the most uniform distribution. We estimate the probability of finding an interloper as a function of the distance from the object centre

A new derivation of the Hubble constant from γ\gamma-ray attenuation using improved optical depths for the Fermi and CTA era

We present $\gamma$-ray optical-depth calculations from a recently published extragalactic background light (EBL) model built from multiwavelength galaxy data from the Hubble Space Telescope Cosmic Assembly Near-Infrared Deep Extragalactic Legacy Survey (HST/CANDELS). CANDELS gathers one of the deepest and most complete observations of stellar and dust emissions in galaxies. This model resulted in a robust derivation of the evolving EBL spectral energy distribution up to $z\sim 6$, including the far-infrared peak. Therefore, the optical depths derived from this model will be useful for determining the attenuation of $\gamma$-ray photons coming from high-redshift sources, such as those detected by the Large Area Telescope on board the Fermi Gamma-ray Space Telescope, and for multi-TeV photons that will be detected from nearby sources by the future Cherenkov Telescope Array. From these newly calculated optical depths, we derive the cosmic $\gamma$-ray horizon and also measure the expansion rate and matter content of the Universe including an assessment of the impact of the EBL uncertainties. We find $H_{0}=61.9$ $^{+2.9}_{-2.4}$ km s$^{-1}$ Mpc$^{-1}$ when fixing $\Omega_{m}=0.32$, and $H_{0}=65.6$ $^{+5.6}_{-5.0}$ km s$^{-1}$ Mpc$^{-1}$ and $\Omega_{m}=0.19\pm 0.07$, when exploring these two parameters simultaneously.Comment: 11 pages, 8 figures, 1 tables; Accepted by MNRA