https://biblio.ugent.be/publication/685594/file/1130605.pdf

Review of Particle Physics

We use high-resolution N-body simulations to study the equilibrium density profiles of dark matter halos in hierarchically clustering universes. We find that all such profiles have the same shape, independent of the halo mass, the initial density fluctuation spectrum, and the values of the cosmological parameters. Spherically averaged equilibrium profiles are well fitted over two decades in radius by a simple formula originally proposed to describe the structure of galaxy clusters in a cold dark matter universe. In any particular cosmology, the two scale parameters of the fit, the halo mass and its characteristic density, are strongly correlated. Low-mass halos are significantly denser than more massive systems, a correlation that reflects the higher collapse redshift of small halos. The characteristic density of an equilibrium halo is proportional to the density of the universe at the time it was assembled. A suitable definition of this assembly time allows the same proportionality constant to be used for all the cosmologies that we have tested. We compare our results with previous work on halo density profiles and show that there is good agreement. We also provide a step-by-step analytic procedure, based on the Press-Schechter formalism, that allows accurate equilibrium profiles to be calculated as a function of mass in any hierarchical model.

https://iopscience.iop.org/article/10.1086/304888/pdf

A Universal Density Profile from Hierarchical Clustering

We discuss the cosmological simulation code GADGET-2, a new massively parallel TreeSPH code, capable of following a collisionless fluid with the N-body method, and an ideal gas by means of smoothed particle hydrodynamics (SPH). Our implementation of SPH manifestly conserves energy and entropy in regions free of dissipation, while allowing for fully adaptive smoothing lengths. Gravitational forces are computed with a hierarchical multipole expansion, which can optionally be applied in the form of a TreePM algorithm, where only short-range forces are computed with the ‘tree’ method while long-range forces are determined with Fourier techniques. Time integration is based on a quasi-symplectic scheme where long-range and short-range forces can be integrated with different time-steps. Individual and adaptive short-range time-steps may also be employed. The domain decomposition used in the parallelization algorithm is based on a space-filling curve, resulting in high flexibility and tree force errors that do not depend on the way the domains are cut. The code is efficient in terms of memory consumption and required communication bandwidth. It has been used to compute the first cosmological N-body simulation with more than 10 10 dark matter particles, reaching a homogeneous spatial dynamic range of 10 5 per dimension in a three-dimensional box. It has also been used to carry out very large cosmological SPH simulations that account for radiative cooling and star formation, reaching total particle numbers of more than 250 million. We present the algorithms used by the code and discuss their accuracy and performance using a number of test problems. GADGET-2 is publicly released to the research community. Ke yw ords: methods: numerical ‐ galaxies: interactions ‐ dark matter.

/pdf/the-cosmological-simulation-code-gadget-2-48ba4eyb8k.pdf

The Cosmological simulation code GADGET-2

This paper describes the Seventh Data Release of the Sloan Digital Sky Survey (SDSS), marking the completion of the original goals of the SDSS and the end of the phase known as SDSS-II. It includes 11,663 deg^2 of imaging data, with most of the ~2000 deg^2 increment over the previous data release lying in regions of low Galactic latitude. The catalog contains five-band photometry for 357 million distinct objects. The survey also includes repeat photometry on a 120° long, 2°.5 wide stripe along the celestial equator in the Southern Galactic Cap, with some regions covered by as many as 90 individual imaging runs. We include a co-addition of the best of these data, going roughly 2 mag fainter than the main survey over 250 deg^2. The survey has completed spectroscopy over 9380 deg^2; the spectroscopy is now complete over a large contiguous area of the Northern Galactic Cap, closing the gap that was present in previous data releases. There are over 1.6 million spectra in total, including 930,000 galaxies, 120,000 quasars, and 460,000 stars. The data release includes improved stellar photometry at low Galactic latitude. The astrometry has all been recalibrated with the second version of the USNO CCD Astrograph Catalog, reducing the rms statistical errors at the bright end to 45 milliarcseconds per coordinate. We further quantify a systematic error in bright galaxy photometry due to poor sky determination; this problem is less severe than previously reported for the majority of galaxies. Finally, we describe a series of improvements to the spectroscopic reductions, including better flat fielding and improved wavelength calibration at the blue end, better processing of objects with extremely strong narrow emission lines, and an improved determination of stellar metallicities.

/pdf/the-seventh-data-release-of-the-sloan-digital-sky-survey-5cm9fqkek5.pdf

The Seventh Data Release of the Sloan Digital Sky Survey

The cold dark matter model has become the leading theoretical picture for the formation of structure in the Universe. This model, together with the theory of cosmic inflation, makes a clear prediction for the initial conditions for structure formation and predicts that structures grow hierarchically through gravitational instability. Testing this model requires that the precise measurements delivered by galaxy surveys can be compared to robust and equally precise theoretical calculations. Here we present a simulation of the growth of dark matter structure using 2,1603 particles, following them from redshift z = 127 to the present in a cube-shaped region 2.230 billion lightyears on a side. In postprocessing, we also follow the formation and evolution of the galaxies and quasars. We show that baryon-induced features in the initial conditions of the Universe are reflected in distorted form in the low-redshift galaxy distribution, an effect that can be used to constrain the nature of dark energy with future generations of observational surveys of galaxies.

/pdf/simulations-of-the-formation-evolution-and-clustering-of-1yahvmv5qk.pdf

Simulations of the formation, evolution and clustering of galaxies and quasars

The ring systems of Saturn and Uranus exhibit several sharp edges across which the optical depth drops from order unity to essentially zero. At least two and perhaps all of these features are associated with the location of orbital resonances between a satellite and the ring particles. It is remarkable that the optical depth varies on a distance scale which is much finer than that over which angular momentum can be transferred between a satellite and the ring material. The important features of this phenomenon are: (1) A perturbed band of width Δa/a ≃ (M_s/M_p)^(½) adjacent to the edge within which the angular momentum transfer occurs. (2) Streamlines perturbed such that the angular momentum luminosity decreases smoothly across the band to zero at the edge even though the optical depth remains constant. (3) Dynamical equilibrium requires a relation between the random velocity, the rate of deformation and the optical depth.

Sharp Edges of Planetary Rings

Supermassive black holes at the centres of galaxies are often surrounded by dense star clusters. For a wide range of cluster properties and orbital radii the resonant relaxation times in these clusters are much shorter than the Hubble time. Since resonant relaxation conserves semimajor axes, these clusters should be in the maximum-entropy state consistent with the given semimajor axis distribution. We determine these maximum-entropy equilibria in a simplified model in which all of the stars have the same semimajor axes. We find that the cluster exhibits a phase transition from a disordered, spherical, high-temperature equilibrium to an ordered low-temperature equilibrium in which the stellar orbits have a preferred orientation or line of apsides. Here `temperature' is a measure of the non-Keplerian or self-gravitational energy of the cluster; in the spherical state, temperature is a function of the rms eccentricity of the stars. We explore a simple two-parameter model of black-hole star clusters -- the two parameters are semimajor axis and black-hole mass --- and find that clusters are susceptible to the lopsided phase transition over a range of ~100 in semimajor axis, mostly for black-hole masses less than $10^{7.5}$ solar masses.

Order-disorder phase transition in black hole star clusters - III. A mono-energetic cluster

The Stability of a Family of Elliptical Stellar Disks

The two-dimensional analogs to Riemann S-type ellipsoids are considered as simple fluid models for galactic bars. Their equilibrium is discussed and their evolution under the effects of viscosity, gravitational radiation, and external torques from other components of the galaxy is computed. As a bar loses angular momentum due to external torques, it generally becomes less elongated, and its figure speed may either increase or decrease.

The Riemann disks. I - Equilibrium and secular evolution

Self-consistent dynamic models of the M31 nucleus were constructed which satisfy Stratoscope II and ground-based photometry, as well as ground-based velocity dispersion measurements. Two models designed to yield the highest and lowest mass-to-light ratios (M/L) consistent with observations are concentrated on. It is found that self-consistent static models of the M31 nucleus can be constructed with a nuclear mass-to-blue magnitude ratio between 0 and 50, and that it is very difficult to construct high M/L models with plausible evolutionary histories. The low values of M/L that were found suggest that the nucleus must be composed of stars on nearly radial orbits whose apocenters lie well outside the observable part of the nucleus. Such nuclei may be formed either during core collapse of a preexisting dense nucleus or by orbital decay of globular clusters in a triaxial bulge.

Scott Tremaine

Papers

Sharp Edges of Planetary Rings

Order-disorder phase transition in black hole star clusters - III. A mono-energetic cluster

The Stability of a Family of Elliptical Stellar Disks

The Riemann disks. I - Equilibrium and secular evolution

The dynamics of the nucleus of M31