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Cosmological simulations are an important theoretical pillar for understanding nonlinear structure formation in our Universe and for relating it to observations on large scales. In several papers, we introduce our MillenniumTNG (MTNG) project that provides a comprehensive set of high-resolution, large volume simulations of cosmic structure formation aiming to better understand physical processes on large scales and to help interpreting upcoming large-scale galaxy surveys. We here focus on the full physics box MTNG740 that computes a volume of $(740\,\mathrm{Mpc})^3$ with a baryonic mass resolution of $3.1\times~10^7\,\mathrm{M_\odot}$ using \textsc{arepo} with $80.6$~billion cells and the IllustrisTNG galaxy formation model. We verify that the galaxy properties produced by MTNG740 are consistent with the TNG simulations, including more recent observations. We focus on galaxy clusters and analyse cluster scaling relations and radial profiles. We show that both are broadly consistent with various observational constraints. We demonstrate that the SZ-signal on a deep lightcone is consistent with Planck limits. Finally, we compare MTNG740 clusters with galaxy clusters found in Planck and the SDSS-8 RedMaPPer richness catalogue in observational space, finding very good agreement as well. However, {\it simultaneously} matching cluster masses, richness, and Compton-$y$ requires us to assume that the SZ mass estimates for Planck clusters are underestimated by $0.2$~dex on average. Thanks to its unprecedented volume for a high-resolution hydrodynamical calculation, the MTNG740 simulation offers rich possibilities to study baryons in galaxies, galaxy clusters, and in large scale structure, and in particular their impact on upcoming large cosmological surveys., Comment: 18 pages, 14 figures, accepted for publication by MNRAS, comments welcome

We introduce the star formation and Supernova (SN) feedback model of the SATIN (Simulating AGNs Through ISM with Non-Equilibrium Effects) project to simulate the evolution of the star forming multi-phase interstellar medium (ISM) of entire disk galaxies. This galaxy-wide implementation of a successful ISM feedback model naturally covers an order of magnitude in gas surface density, shear and radial motions. It is implemented in the adaptive mesh refinement code RAMSES at a peak resolution of 9 pc. New stars are represented by star cluster (sink) particles with individual SN delay times for massive stars. With SN feedback, cooling and gravity, the galactic ISM develops a realistic three-phase structure. The star formation rates naturally follow observed scaling relations for the local Milky Way gas surface density. SNe drive additional turbulence in the warm (300 K < $T$ < 10$^4$ K) gas and increase the kinetic energy of the cold gas, cooling out of the warm phase. The majority of the gas leaving the galactic ISM is warm and hot with mass loading factors of $3 \le \eta \le 10$. While the hot gas is leaving the system, the warm and cold gas falls back onto the disc in a galactic fountain flow., Comment: Submitted to MNRAS

We investigated isolated sodium/chloride aqueous droplets at the microscopic level, which comprise from about 5k to 1M water molecules and whose salt concentrations are 0.2$m$ (brackish water) and 0.6$m$ (sea water), by means of molecular dynamics simulations based on an \emph{ab initio}-based polarizable force field. The size of our largest droplets is at the submicron particle marine aerosol scale. From our simulations, we investigated ion spatial distributions, ion aggregates (size, composition, lifetime and distribution), droplet surface potentials and the densities of the water vapor surrounding the droplets. Regarding ions, they form a weak electrostatic double layer extending from the droplet boundary to 2~nm within the droplet interior. Free $\mathrm{Na^+}$ and ion aggregates are more repelled from the boundary than free $\mathrm{Cl^-}$. Most of the droplet properties depend on the droplet radius $R$ according to the standard formula $A=A_\infty(1 - 2 \delta/R) $, where $A_\infty$ is the bulk magnitude of the quantity $A$ and $\delta$ is a length at most at the~nm scale. Regarding the water vapor densities they obey a Kelvin relation corresponding to a surface tension whose Tolman length is negative and at the 1~nm scale. That length is about one order of magnitude larger than for pure water droplets, however it is weak enough to support the reliability of a standard Kelvin term (based on planar interface surface tensions and water densities) and of the related K{\"o}lher equation to model sub-micron salty aerosols., Comment: 54 pages, 10 figures, 3 tables

We study the radial and azimuthal mass distribution of the lensing galaxy in WFI2033-4723. Mindful of the fact that modeling results depend on modeling assumptions, we examine two very different recent models: simply parametrized (SP) models from the H0LiCOW collaboration, and pixelated free-form (FF) GLASS models. In addition, we fit our own models which are a compromise between the astrophysical grounding of SP, and the flexibility of FF approaches. Our models consist of two offset parametric mass components, and generate many solutions, all fitting the quasar point image data. Among other results, we show that to reproduce point image properties the lensing mass must be lopsided, but the origin of this asymmetry can reside in the main lens plane or along the line of sight. We also show that there is a degeneracy between the slope of the density profile and the magnitude of external shear, and that the models from various modeling approaches are connected not by the mass sheet degeneracy, but by a more generalized transformation. Finally, we discuss interpretation degeneracy which afflicts all mass modeling: inability to correctly assign mass to the main lensing galaxy vs. nearby galaxies or line of sight structures. While this may not be a problem for the determination of $H_0$, interpretation degeneracy may become a major issue for the detailed study of galaxy structure., Comment: 13 pages, 7 figures, submitted to OJA

Fossil groups are considered the end product of natural galaxy group evolution in which group members sink towards the centre of the gravitational potential due to dynamical friction, merging into a single, massive, and X-ray bright elliptical. Since gravitational lensing depends on the mass of a foreground object, its mass concentration, and distance to the observer, we can expect lensing effects of such fossil groups to be particularly strong. This paper explores the exceptional system $\mathrm{J}143454.4+522850$. We combine gravitational lensing with stellar population-synthesis to separate the total mass of the lens into stars and dark matter. The enclosed mass profiles are contrasted with state-of-the-art galaxy formation simulations, to conclude that SW05 is likely a fossil group with a high stellar to dark matter mass fraction $0.027\pm0.003$ with respect to expectations from abundance matching $0.012\pm0.004$, indicative of a more efficient conversion of gas into stars in fossil groups., Comment: 8 pages, 9 figures, submitted to MNRAS

We present a determination of the Hubble constant from the joint, free-form analysis of 8 strongly, quadruply lensing systems. In the concordance cosmology, we find $H_0 = 71.8^{+3.9}_{-3.3}\,\mathrm{km}\,\mathrm{s}^{-1}\,\mathrm{Mpc}^{-1}$ with a precision of $4.97\%$. This is in agreement with the latest measurements from Supernovae Type Ia and Planck observations of the cosmic microwave background. Our precision is lower compared to these and other recent time-delay cosmography determinations, because our modelling strategies reflect the systematic uncertainties of lensing degeneracies. We furthermore are able to find reasonable lensed image reconstructions by constraining to either value of $H_0$ from local and early Universe measurements. This leads us to conclude that current lensing constraints on $H_0$ are not strong enough to break the "Hubble tension" problem of cosmology., Comment: 19 pages, 11 figures, published in MNRAS

In the coming years, strong gravitational lens discoveries are expected to increase in frequency by two orders of magnitude. Lens-modelling techniques are being developed to prepare for the coming massive influx of new lens data, and blind tests of lens reconstruction with simulated data are needed for validation. In this paper we present a systematic blind study of a sample of 15 simulated strong gravitational lenses from the EAGLE suite of hydrodynamic simulations. We model these lenses with a free-form technique and evaluate reconstructed mass distributions using criteria based on shape, orientation, and lensed image reconstruction. Especially useful is a lensing analogue of the Roche potential in binary star systems, which we call the $\textit{lensing Roche potential}$. This we introduce in order to factor out the well-known problem of steepness or mass-sheet degeneracy. Einstein radii are on average well recovered with a relative error of ${\sim}5\%$ for quads and ${\sim}25\%$ for doubles; the position angle of ellipticity is on average also reproduced well up to $\pm10^{\circ}$, but the reconstructed mass maps tend to be too round and too shallow. It is also easy to reproduce the lensed images, but optimising on this criterion does not guarantee better reconstruction of the mass distribution., Comment: 20 pages, 12 figures. Published in MNRAS. Agrees with published version

We have developed a symbolic algebra approach to automatically produce, verify, and optimize computer code for the Fast Multipole Method (FMM) operators. This approach allows for flexibility in choosing a basis set and kernel, and can generate computer code for any expansion order in multiple languages. The procedure is implemented in the publicly available Python program Mosaic. Optimizations performed at the symbolic level through algebraic manipulations significantly reduce the number of mathematical operations compared with a straightforward implementation of the equations. We find that the optimizer is able to eliminate 20-80% of the floating-point operations and for the expansion orders $p \le 10$ it changes the observed scaling properties. We present our approach using three variants of the operators with the Cartesian basis set for the harmonic potential kernel $1/r$, including the use of totally symmetric and traceless multipole tensors., Comment: Updated to final version submitted to Computer Physics Communications. Accepted on 20 November 2019

We report modelling follow-up of recently-discovered gravitational-lens candidates in the Canada France Hawaii Telescope Legacy Survey. Lens modelling was done by a small group of specially-interested volunteers from the SpaceWarps citizen-science community who originally found the candidate lenses. Models are categorised according to seven diagnostics indicating (a) the image morphology and how clear or indistinct it is, (b) whether the mass map and synthetic lensed image appear to be plausible, and (c) how the lens-model mass compares with the stellar mass and the abundance-matched halo mass. The lensing masses range from ~10^11 Msun to >10^13 Msun. Preliminary estimates of the stellar masses show a smaller spread in stellar mass (except for two lenses): a factor of a few below or above ~10^11 Msun. Therefore, we expect the stellar-to-total mass fraction to decline sharply as lensing mass increases. The most massive system with a convincing model is J1434+522 (SW05). The two low-mass outliers are J0206-095 (SW19) and J2217+015 (SW42); if these two are indeed lenses, they probe an interesting regime of very low star-formation efficiency. Some improvements to the modelling software (SpaghettiLens), and discussion of strategies regarding scaling to future surveys with more and frequent discoveries, are included., Comment: 16 pages, 10 figures, 1 table, online supplement table_1.csv contains additional detailed numbers shown in table 1 and figure 7

We measure the projected density profile, shape and alignment of the stellar and dark matter mass distribution in 11 strong-lens galaxies. We find that the projected dark matter density profile - under the assumption of a Chabrier stellar initial mass function - shows significant variation from galaxy to galaxy. Those with an outermost image beyond $\sim 10$ kpc are very well fit by a projected NFW profile; those with images within 10 kpc appear to be more concentrated than NFW, as expected if their dark haloes contract due to baryonic cooling. We find that over several half-light radii, the dark matter haloes of these lenses are rounder than their stellar mass distributions. While the haloes are never more elliptical than $e_{dm} = 0.2$, their stars can extend to $e_* > 0.2$. Galaxies with high dark matter ellipticity and weak external shear show strong alignment between light and dark; those with strong shear ($\gamma \gtrsim 0.1$) can be highly misaligned. This is reassuring since isolated misaligned galaxies are expected to be unstable. Our results provide a new constraint on galaxy formation models. For a given cosmology, these must explain the origin of both very round dark matter haloes and misaligned strong-lens systems., Comment: 16 pages, 7 figures, 4 tables. Accepted for publication by MNRAS

We develop a method to enable collaborative modelling of gravitational lenses and lens candidates, that could be used by non-professional lens enthusiasts. It uses an existing free-form modelling program (glass), but enables the input to this code to be provided in a novel way, via a user-generated diagram that is essentially a sketch of an arrival-time surface. We report on an implementation of this method, SpaghettiLens, which has been tested in a modelling challenge using 29 simulated lenses drawn from a larger set created for the Space Warps citizen science strong lens search. We find that volunteers from this online community asserted the image parities and time ordering consistently in some lenses, but made errors in other lenses depending on the image morphology. While errors in image parity and time ordering lead to large errors in the mass distribution, the enclosed mass was found to be more robust: the model-derived Einstein radii found by the volunteers were consistent with those produced by one of the professional team, suggesting that given the appropriate tools, gravitational lens modelling is a data analysis activity that can be crowd-sourced to good effect. Ideas for improvement are discussed, these include (a) overcoming the tendency of the models to be shallower than the correct answer in test cases, leading to systematic overestimation of the Einstein radius by 10 per cent at present, and (b) detailed modelling of arcs., Comment: 10 pages, 12 figures

We present an implementation of the fast multipole method for computing coulombic electrostatic and polarization forces from polarizable force-fields based on induced point dipole moments. We demonstrate the expected $O(N)$ scaling of that approach by performing single energy point calculations on hexamer protein subunits of the mature HIV-1 capsid. We also show the long time energy conservation in molecular dynamics at the nanosecond scale by performing simulations of a protein complex embedded in a coarse-grained solvent using a standard integrator and a multiple time step integrator. Our tests show the applicability of FMM combined with state-of-the-art chemical models in molecular dynamical systems., Comment: 11 pages, 8 figures, accepted by J. Chem. Phys

We use a new non-parametric gravitational modelling tool -- \Glass{} -- to determine what quality of data (strong lensing, stellar kinematics, and/or stellar masses) are required to measure the circularly averaged mass profile of a lens and its shape. \Glass{} uses an under-constrained adaptive grid of mass pixels to model the lens, searching through thousands of models to marginalise over model uncertainties. Our key findings are as follows: (i) for pure lens data, multiple sources with wide redshift separation give the strongest constraints as this breaks the well-known mass-sheet or steepness degeneracy; (ii) a single quad with time delays also performs well, giving a good recovery of both the mass profile and its shape; (iii) stellar masses -- for lenses where the stars dominate the central potential -- can also break the steepness degeneracy, giving a recovery for doubles almost as good as having a quad with time delay data, or multiple source redshifts; (iv) stellar kinematics provide a robust measure of the mass at the half light radius of the stars $r_{1/2}$ that can also break the steepness degeneracy if the Einstein radius $r_E \neq r_{1/2}$; and (v) if $r_E \sim r_{1/2}$, then stellar kinematic data can be used to probe the stellar velocity anisotropy $\beta$ -- an interesting quantity in its own right. Where information on the mass distribution from lensing and/or other probes becomes redundant, this opens up the possibility of using strong lensing to constrain cosmological models., Comment: 18 pages, 11 figures, accepted to MNRAS

We present a novel proposal strategy for the Metropolis-Hastings algorithm designed to efficiently sample general convex polytopes in 100 or more dimensions. This improves upon previous sampling strategies used for free-form reconstruction of gravitational lenses, but is general enough to be applied to other fields. We have written a parallel implementation within the lens modeling framework GLASS. Testing shows that we are able to produce uniform uncorrelated random samples which are necessary for exploring the degeneracies inherent in lens reconstruction., Comment: 10 pages, 9 figures. Accepted for publication in MNRAS

A nearby star having a near-transit of a galaxy will cause a time-dependent weak lensing of the galaxy. Because the effect is small, we refer to this as weak microlensing. This could provide a useful method to weigh low-mass stars and brown dwarfs. We examine the feasibility of measuring masses in this way and we find that a star causes measurable weak microlensing in a galaxy even at 10 Einstein radii away. Of order one magnitude I < 25 galaxy comes close enough to one or other of the ~100 nearest stars per year., Comment: Accepted for publication in MNRAS (4 pages, 5 figures, 1 table)

This paper examines free-form modeling of gravitational lenses using Bayesian ensembles of pixelated mass maps. The priors and algorithms from previous work are clarified and significant technical improvements are made. Lens reconstruction and Hubble Time recovery are tested using mock data from simple analytic models and recent galaxy-formation simulations. Finally, using published data, the Hubble Time is inferred through the simultaneous reconstruction of eleven time-delay lenses. The result is H_0^{-1}=13.7^{+1.8}_{-1.0} Gyr., Comment: 24 pages, 9 figures. Accepted to ApJ