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

We determine the response of a self-similar isothermal stellar system to small adiabatic gravitational perturbations. For odd spherical harmonics, the response is identical to the response of the analogous isothermal fluid system. For even spherical harmonics, the response can be regarded as an infinite series of wavetrains in $\\log r$, implying alternating compression and rarefaction in equal logarithmic radius intervals. Partly because of the oscillatory nature of the solutions, tidal fields from external sources are not strongly amplified by an intervening isothermal stellar system, except at radii $\\lta 10^{-3.5}$ times the satellite radius; at some radii the stellar system can even screen the external tidal field in a manner analogous to Debye screening. As Weinberg has pointed out, individual resonances in a stellar system can strongly amplify external tidal fields over a limited radial range, but we cannot address this possibility because we examine only adiabatic perturbations. We also discuss the application of our method to the halo response caused by the slow growth of an embedded thin disk.

/pdf/linear-response-of-galactic-haloes-to-adiabatic-2f6j8s7ist.pdf

Linear response of galactic haloes to adiabatic gravitational perturbations

Some quadruple star systems in the hierarchical 2+2 configuration exhibit orbit-orbit resonances between the two compact binaries. We show that the most important resonances occur at period ratios of 1:1, 3:2 and 2:1. We describe the conditions required for capture and show that they can be satisfied at the 3:2 and 2:1 resonances in binaries that migrate significantly in semimajor axis after circularization, probably through magnetic braking or gravitational radiation.

Resonant capture in quadruple stellar systems

The broad emission lines commonly seen in quasar spectra have velocity widths of a few percent of the speed of light, so special- and general-relativistic effects have a significant influence on the line profile. We have determined the redshift of the broad Hβ line in the quasar rest frame (determined from the core component of the [O III] line) for over 20,000 quasars from the Sloan Digital Sky Survey Data Release 7 quasar catalog. The mean redshift as a function of line width is approximately consistent with the relativistic redshift that is expected if the line originates in a randomly oriented Keplerian disk that is obscured when the inclination of the disk to the line of sight exceeds ~30°-45°, consistent with simple active galactic nucleus unification schemes. This result also implies that the net line-of-sight inflow/outflow velocities in the broad-line region are much less than the Keplerian velocity when averaged over a large sample of quasars with a given line width.

/pdf/relativistic-redshifts-in-quasar-broad-lines-59ilgimz5t.pdf

Relativistic Redshifts in Quasar Broad Lines

The shearing sheet is a model dynamical system that is used to study the small-scale dynamics of astrophysical disks. Numerical simulations of particle trajectories in the shearing sheet usually employ the leapfrog integrator, but this integrator performs poorly because of velocity-dependent (Coriolis) forces. We describe two new integrators for this purpose; both are symplectic, time-reversible and second-order accurate, and can easily be generalized to higher orders. Moreover, both integrators are exact when there are no small-scale forces such as mutual gravitational forces between disk particles. In numerical experiments these integrators have errors that are often several orders of magnitude smaller than competing methods. The first of our new integrators (SEI) is well-suited for disks in which the typical inter-particle separation is large compared to the particles' Hill radii (e.g., planetary rings), and the second (SEKI) is designed for disks in which the particles are on bound orbits or the separation is smaller than the Hill radius (e.g., irregular satellites of the giant planets).

Symplectic integrators in the shearing sheet

https://physicstoday.scitation.org/doi/pdf/10.1063/1.1457268

Scott Tremaine

Papers

Linear response of galactic haloes to adiabatic gravitational perturbations

Resonant capture in quadruple stellar systems

Relativistic Redshifts in Quasar Broad Lines

Symplectic integrators in the shearing sheet

Structure and Interpretation of Classical Mechanics