arXiv subjects

Bert Vandenbroucke

Publications and source records attributed to Bert Vandenbroucke.

At least 19 recordsLinked to original sources

arXiv2026

The FLAMINGO simulations data release

We describe the public release of $>2.3$ petabytes of data from the FLAMINGO cosmological simulations. The suite consists of hydrodynamical simulations that include radiative cooling, star formation, stellar mass loss and the resulting chemical enrichment, supernova feedback, and two implementations of AGN feedback. Neutrinos are simulated explicitly using particles. Data products include snapshots, halo and galaxy catalogues, HEALPix all-sky lightcone maps, particle data for lightcone maps, and power spectra. The FLAMINGO set includes 22 hydrodynamical simulations. In addition, there are 16 gravity-only simulations, including the $10080^3$ particles FLAMINGO-10k run, with initial conditions that match those of the corresponding hydrodynamical runs. The fiducial hydrodynamical simulations span three numerical resolutions that have each been calibrated to reproduce the present-day galaxy stellar mass function and gas fractions in low-redshift clusters. Other simulations systematically vary the galaxy stellar mass function, cluster gas fractions, cosmology (including neutrino masses), and/or the nature of dark matter, in volumes of 1Gpc$^3$. The release includes hitherto unpublished simulations that use extra dark matter particles. While we provide a facility for downloading complete simulation outputs, we recognise that for many users this will not be possible due to limited local storage or network bandwidth. We implement a web service that enables users to explore available outputs and selectively download datasets or parts of datasets.

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arXiv2026

FLAMINGO: The thermal history of the Universe from tSZ effect cross-correlations and its dependencies on cosmology and baryon physics

The cross-correlation between tracers of large-scale structure, such as galaxies or quasars, and the thermal Sunyaev-Zel'dovich (tSZ) signal yields a measure of the bias-weighted mean electron pressure, $\langle b_\mathrm{h} P_\mathrm{e} \rangle$, where $b_\mathrm{h}$ is the halo bias and $P_\mathrm{e}$ is the electron pressure. With a model for the bias, one can derive the thermal history, $\mathrm{d}y/\mathrm{d}z$, where $y$ is the Compton parameter and $z$ is redshift. We explore how these quantities depend on redshift, cosmology, and the physics of galaxy formation using the FLAMINGO suite of cosmological hydrodynamical simulations, which spans a range of cosmological parameters and baryonic feedback implementations in volumes of up to $(2.8\,\text{Gpc})^3$. We find that $\langle b_\mathrm{h} P_\mathrm{e} \rangle$ depends steeply on $S_8 \equiv σ_8\sqrt{Ω_\mathrm{m}/0.3}$, with an effective scaling $\langle b_\mathrm{h} P_\mathrm{e} \rangle \propto S_8^{ε(z)}$, where the exponent $ε(z) \approx 3$ over the redshift range $0.1 \leq z \leq 1$. Compared with existing cross-correlation measurements using tracer samples from SDSS, BOSS, eBOSS, DES, and DESI cross-correlated with tSZ measurements from Planck, we find that models with a low-$S_8$ cosmology and strong feedback are preferred, with a joint fit yielding $S_8 = 0.72^{+0.03}_{-0.03}$ and a normalised group-mass halo baryon fraction $f_b(10^{13}\,M_\odot, z=0.1)/(Ω_b/Ω_m) = 0.10^{+0.09}_{-0.05}$ . Contrary to most probes of feedback which sample smaller scales (e.g., X-ray measurements), we show that feedback boosts $\langle b_\mathrm{h} P_\mathrm{e} \rangle$, thus providing a novel test of feedback models. Overall, our results show the thermal history provides a route to jointly constrain cosmological parameters and test models of galaxy formation.

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arXiv2025

SOAP: A Python Package for Calculating the Properties of Galaxies and Halos Formed in Cosmological Simulations

Modern large scale cosmological hydrodynamic simulations require robust tools capable of analysing their data outputs in a parallel and efficient manner. We introduce SOAP (Spherical Overdensity and Aperture Processor), a Python package designed to compute halo and galaxy properties from SWIFT simulations after being post-processed with a subhalo finder. SOAP takes a subhalo catalogue as input and calculates a wide array of properties for each object. SOAP offers parallel processing capabilities via mpi4py for efficient handling of large datasets, and allows for consistent property calculation across multiple halo finders. SOAP supports various halo definitions, including spherical overdensities and fixed physical apertures, providing flexibility for diverse observational comparisons. The package is compatible with both dark matter-only and full hydrodynamic simulations, producing HDF5 catalogues that are integrated with the swiftsimio package for seamless unit handling.

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arXiv2025

The FLAMINGO project: the coupling between baryonic feedback and cosmology in light of the $S_8$ tension

Large-scale structure surveys have reported measurements of the density of matter, $Ω_\mathrm{m}$, and the amplitude of clustering, $σ_8$, that are in tension with the values inferred from observations of the cosmic microwave background. While this may be a sign of new physics that slows the growth of structure at late times, strong astrophysical feedback processes could also be responsible. In this work, we argue that astrophysical processes are not independent of cosmology and that their coupling naturally leads to stronger baryonic feedback in cosmological models with suppressed structure formation or when combined with a mechanism that removes dark matter from halos. We illustrate this with two well-motivated extensions of the Standard Model known to suppress structure formation: massive neutrinos and decaying dark matter. Our results, based on the FLAMINGO suite of hydrodynamical simulations, show that the combined effect of baryonic and non-baryonic suppression mechanisms is greater than the sum of its parts, particularly for decaying dark matter. We also show that the dependence of baryonic feedback on cosmology can be modelled as a function of the ratio $f_\mathrm{b}/c^2_\mathrm{v}\sim f_\mathrm{b}/(Ω_\mathrm{m}σ_8)^{1/4}$ of the universal baryon fraction, $f_\mathrm{b}$, to a velocity-based definition of halo concentration, $c^2_\mathrm{v}$, giving an accurate fitting formula for the baryonic suppression of the matter power spectrum. Although the combination of baryonic and non-baryonic suppression mechanisms can resolve the tension, the models with neutrinos and decaying dark matter are challenged by constraints on the expansion history.

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arXiv2024

Time-dependent metal ionization and the persistence of collisionally excited emission lines in the diffuse ionized gas of star forming galaxies

We extend our time-dependent hydrogen ionization simulations of diffuse ionized gas to include metals important for collisional cooling and diagnostic emission lines. The combination of heating from supernovae and time-dependent collisional and photoionization from midplane OB stars produces emission line intensities (and emission line ratios) that follow the trends observed in the Milky Way and other edge-on galaxies. The long recombination times in low density gas result in persistent large volumes of ions with high ionization potentials, such as O III and Ne III. In particular, the vertically extended layers of Ne III in our time-dependent simulations result in [Ne III] 15$μ$m/[Ne II] 12$μ$m emission line ratios in agreement with observations of the edge-on galaxy NGC 891. Simulations adopting ionization equilibrium do not allow for the persistence of ions with high ionization states and therefore cannot reproduce the observed emission lines from low density gas at high altitudes.

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arXiv2024

The FLAMINGO Project: Galaxy clusters in comparison to X-ray observations

Galaxy clusters are important probes for both cosmology and galaxy formation physics. We test the cosmological, hydrodynamical FLAMINGO simulations by comparing to observations of the gaseous properties of clusters measured from X-ray observations. FLAMINGO contains unprecedented numbers of massive galaxy groups ($>10^6$) and clusters ($>10^5$) and includes variations in both cosmology and galaxy formation physics. We predict the evolution of cluster scaling relations as well as radial profiles of the temperature, density, pressure, entropy, and metallicity for different masses and redshifts. We show that the differences between volume-, and X-ray-weighting of particles in the simulations, and between cool-core non cool-core samples, are similar in size as the differences between simulations for which the stellar and AGN feedback has been calibrated to produce significantly different gas fractions. Compared to thermally-driven AGN feedback, kinetic jet feedback calibrated to produce the same gas fraction at $R_{\rm 500c}$ yields a hotter core with higher entropies and lower densities, which translates into a smaller fraction of cool-core clusters. Stronger feedback, calibrated to produce lower gas fractions and hence lower gas densities, results in higher temperatures, entropies, and metallicities, but lower pressures. The scaling relations and thermodynamic profiles show almost no evolution with respect to self-similar expectations, except for the metallicity decreasing with redshift. We find that the temperature, density, pressure, and entropy profiles of clusters in the fiducial FLAMINGO simulation are in excellent agreement with observations, while the metallicities in the core are too high.

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arXiv2024

The persistence of high altitude non-equilibrium diffuse ionized gas in simulations of star forming galaxies

Widespread, high altitude, diffuse ionized gas with scale heights of around a kiloparsec is observed in the Milky Way and other star forming galaxies. Numerical radiation-magnetohydrodynamic simulations of a supernova-driven turbulent interstellar medium show that gas can be driven to high altitudes above the galactic midplane, but the degree of ionization is often less than inferred from observations. For computational expediency, ionizing radiation from massive stars is often included as a post-processing step assuming ionization equilibrium. We extend our simulations of a Milky Way-like interstellar medium to include the combined effect of supernovae and photoionization feedback from midplane OB stars and a population of hot evolved low mass stars. The diffuse ionized gas has densities below 0.1 ${\rm cm^{-3}}$, so recombination timescales can exceed millions of years. Our simulations now follow the time-dependent ionization and recombination of low density gas. The long recombination timescales result in diffuse ionized gas that persists at large altitudes long after the deaths of massive stars that produce the vast majority of the ionized gas. The diffuse ionized gas does not exhibit the large variability inherent in simulations that adopt ionization equilibrium. The vertical distribution of neutral and ionized gas is close to what is observed in the Milky Way. The volume filling factor of ionized gas increases with altitude resulting in the scale height of free electrons being larger than that inferred from H$α$ emission, thus reconciling the observations of ionized gas made in H$α$ and from pulsar dispersion measurements.

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arXiv2024

SWIFT: A modern highly-parallel gravity and smoothed particle hydrodynamics solver for astrophysical and cosmological applications

Numerical simulations have become one of the key tools used by theorists in all the fields of astrophysics and cosmology. The development of modern tools that target the largest existing computing systems and exploit state-of-the-art numerical methods and algorithms is thus crucial. In this paper, we introduce the fully open-source highly-parallel, versatile, and modular coupled hydrodynamics, gravity, cosmology, and galaxy-formation code SWIFT. The software package exploits hybrid shared- and distributed-memory task-based parallelism, asynchronous communications, and domain-decomposition algorithms based on balancing the workload, rather than the data, to efficiently exploit modern high-performance computing cluster architectures. Gravity is solved for using a fast-multipole-method, optionally coupled to a particle mesh solver in Fourier space to handle periodic volumes. For gas evolution, multiple modern flavours of Smoothed Particle Hydrodynamics are implemented. SWIFT also evolves neutrinos using a state-of-the-art particle-based method. Two complementary networks of sub-grid models for galaxy formation as well as extensions to simulate planetary physics are also released as part of the code. An extensive set of output options, including snapshots, light-cones, power spectra, and a coupling to structure finders are also included. We describe the overall code architecture, summarise the consistency and accuracy tests that were performed, and demonstrate the excellent weak-scaling performance of the code using a representative cosmological hydrodynamical problem with $\approx$$300$ billion particles. The code is released to the community alongside extensive documentation for both users and developers, a large selection of example test problems, and a suite of tools to aid in the analysis of large simulations run with SWIFT.

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arXiv2024

Inferring the dark matter splashback radius from cluster gas and observable profiles in the FLAMINGO simulations

The splashback radius, coinciding with the minimum in the dark matter radial density gradient, is thought to be a universal definition of the edge of a dark matter halo. Observational methods to detect it have traced the dark matter using weak gravitational lensing or galaxy number counts. Recent attempts have also claimed the detection of a similar feature in Sunyaev-Zel'dovich (SZ) observations of the hot intracluster gas. Here, we use the FLAMINGO simulations to investigate whether an extremum gradient in a similar position to the splashback radius is predicted to occur in the cluster gas profiles. We find that the minimum in the gradient of the stacked 3D gas density and pressure profiles, and the maximum in the gradient of the entropy profile, broadly align with the splashback feature though there are significant differences. While the dark matter splashback radius varies with specific mass accretion rate, in agreement with previous work, the radial position of the deepest minimum in the log-slope of the gas density is more sensitive to halo mass. In addition, we show that a similar minimum is also present in projected 2D pseudo-observable profiles: emission measure (X-ray); Compton-$y$ (SZ) and surface mass density (weak lensing). We find that the latter traces the dark matter results reasonably well albeit the minimum occurs at a slightly smaller radius. While results for the gas profiles are largely insensitive to accretion rate and various observable proxies for dynamical state, they do depend on the strength of the feedback processes.

astro-ph.CO↗

arXiv2024

The FLAMINGO project: Baryonic impact on weak gravitational lensing convergence peak counts

Weak gravitational lensing convergence peaks, the local maxima in weak lensing convergence maps, have been shown to contain valuable cosmological information complementary to commonly used two-point statistics. To exploit the full power of weak lensing for cosmology, we must model baryonic feedback processes because these reshape the matter distribution on non-linear and mildly non-linear scales. We study the impact of baryonic physics on the number density of weak lensing peaks using the FLAMINGO cosmological hydrodynamical simulation suite. We generate ray-traced full-sky convergence maps mimicking the characteristics of a Stage IV weak lensing survey. We compare the number densities of peaks in simulations that have been calibrated to reproduce the observed galaxy mass function and cluster gas fraction or to match a shifted version of these, and that use either thermally driven or jet AGN feedback. We show that the differences induced by realistic baryonic feedback prescriptions (typically $5 - 30\%$ for $κ= 0.1 - 0.4$) are smaller than those induced by reasonable variations in cosmological parameters ($20 - 60\%$ for $κ= 0.1 - 0.4$) but must be modeled carefully to obtain unbiased results. The reasons behind these differences can be understood by considering the impact of feedback on halo masses, or by considering the impact of different cosmological parameters on the halo mass function. Our analysis demonstrates that, for the range of models we investigated, the baryonic suppression is insensitive to changes in cosmology up to $κ\approx 0.4$ and that the higher $κ$ regime is dominated by Poisson noise and cosmic variance.

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arXiv2023

FLAMINGO: Calibrating large cosmological hydrodynamical simulations with machine learning

To fully take advantage of the data provided by large-scale structure surveys, we need to quantify the potential impact of baryonic effects, such as feedback from active galactic nuclei (AGN) and star formation, on cosmological observables. In simulations, feedback processes originate on scales that remain unresolved. Therefore, they need to be sourced via subgrid models that contain free parameters. We use machine learning to calibrate the AGN and stellar feedback models for the FLAMINGO cosmological hydrodynamical simulations. Using Gaussian process emulators trained on Latin hypercubes of 32 smaller-volume simulations, we model how the galaxy stellar mass function and cluster gas fractions change as a function of the subgrid parameters. The emulators are then fit to observational data, allowing for the inclusion of potential observational biases. We apply our method to the three different FLAMINGO resolutions, spanning a factor of 64 in particle mass, recovering the observed relations within the respective resolved mass ranges. We also use the emulators, which link changes in subgrid parameters to changes in observables, to find models that skirt or exceed the observationally allowed range for cluster gas fractions and the stellar mass function. Our method enables us to define model variations in terms of the data that they are calibrated to rather than the values of specific subgrid parameters. This approach is useful, because subgrid parameters are typically not directly linked to particular observables, and predictions for a specific observable are influenced by multiple subgrid parameters.

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arXiv2023

The FLAMINGO project: cosmological hydrodynamical simulations for large-scale structure and galaxy cluster surveys

We introduce the Virgo Consortium's FLAMINGO suite of hydrodynamical simulations for cosmology and galaxy cluster physics. To ensure the simulations are sufficiently realistic for studies of large-scale structure, the subgrid prescriptions for stellar and AGN feedback are calibrated to the observed low-redshift galaxy stellar mass function and cluster gas fractions. The calibration is performed using machine learning, separately for three resolutions. This approach enables specification of the model by the observables to which they are calibrated. The calibration accounts for a number of potential observational biases and for random errors in the observed stellar masses. The two most demanding simulations have box sizes of 1.0 and 2.8 Gpc and baryonic particle masses of $1\times10^8$ and $1\times10^9 \text{M}_\odot$, respectively. For the latter resolution the suite includes 12 model variations in a 1 Gpc box. There are 8 variations at fixed cosmology, including shifts in the stellar mass function and/or the cluster gas fractions to which we calibrate, and two alternative implementations of AGN feedback (thermal or jets). The remaining 4 variations use the unmodified calibration data but different cosmologies, including different neutrino masses. The 2.8 Gpc simulation follows $3\times10^{11}$ particles, making it the largest ever hydrodynamical simulation run to $z=0$. Lightcone output is produced on-the-fly for up to 8 different observers. We investigate numerical convergence, show that the simulations reproduce the calibration data, and compare with a number of galaxy, cluster, and large-scale structure observations, finding very good agreement with the data for converged predictions. Finally, by comparing hydrodynamical and `dark-matter-only' simulations, we confirm that baryonic effects can suppress the halo mass function and the matter power spectrum by up to $\approx20$ per cent.

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arXiv2023

The FLAMINGO project: revisiting the $S_8$ tension and the role of baryonic physics

A number of recent studies have found evidence for a tension between observations of large-scale structure (LSS) and the predictions of the standard model of cosmology with the cosmological parameters fit to the cosmic microwave background (CMB). The origin of this '$S_8$ tension' remains unclear, but possibilities include new physics beyond the standard model, unaccounted for systematic errors in the observational measurements and/or uncertainties in the role that baryons play. Here we carefully examine the latter possibility using the new FLAMINGO suite of large-volume cosmological hydrodynamical simulations. We project the simulations onto observable harmonic space and compare with observational measurements of the power and cross-power spectra of cosmic shear, CMB lensing, and the thermal Sunyaev-Zel'dovich (tSZ) effect. We explore the dependence of the predictions on box size and resolution, cosmological parameters including the neutrino mass, and the efficiency and nature of baryonic 'feedback'. Despite the wide range of astrophysical behaviours simulated, we find that baryonic effects are not sufficiently large to remove the $S_8$ tension. Consistent with recent studies, we find the CMB lensing power spectrum is in excellent agreement with the standard model, whilst the cosmic shear power spectrum, tSZ effect power spectrum, and the cross-spectra between shear, CMB lensing, and the tSZ effect are all in varying degrees of tension with the CMB-specified standard model. These results suggest that some mechanism is required to slow the growth of fluctuations at late times and/or on non-linear scales, but that it is unlikely that baryon physics is driving this modification.

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arXiv2023

Non-linear CMB lensing with neutrinos and baryons: FLAMINGO simulations vs. fast approximations

Weak lensing of the cosmic microwave background is rapidly emerging as a powerful probe of neutrinos, dark energy, and new physics. We present a fast computation of the non-linear CMB lensing power spectrum which combines non-linear perturbation theory at early times with power spectrum emulation using cosmological simulations at late times. Comparing our calculation with lightcones from the FLAMINGO 5.6 Gpc cube dark-matter-only simulation, we confirm its accuracy to 1% (2%) up to multipoles L = 3000 (L = 5000) for a nuLambdaCDM cosmology consistent with current data. Clustering suppression due to small-scale baryonic phenomena such as feedback from active galactic nuclei can reduce the lensing power by of order 10%. To our perturbation theory and emulator-based calculation we add SP(k), a new fitting function for this suppression, and confirm its accuracy compared to the FLAMINGO hydrodynamic simulations to 4% at L = 5000, with similar accuracy for massive neutrino models. We further demonstrate that scale-dependent suppression due to neutrinos and baryons approximately factorize, implying that a careful treatment of baryonic feedback can limit biasing neutrino mass constraints.

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arXiv2022

SOFIA/HAWC+ observations of the Crab Nebula: dust properties from polarised emission

Supernova remnants (SNRs) are well-recognised dust producers, but their net dust production rate remains elusive due to uncertainties in grain properties that propagate into observed dust mass uncertainties, and determine how efficiently these grains are processed by reverse shocks. In this paper, we present a detection of polarised dust emission in the Crab pulsar wind nebula, the second SNR with confirmed polarised dust emission after Cassiopeia A. We constrain the bulk composition of the dust with new SOFIA/HAWC+ polarimetric data in band C 89 um and band D 154 um. After correcting for synchrotron polarisation, we report dust polarisation fractions ranging between 3.7-9.6 per cent and 2.7-7.6 per cent in three individual dusty filaments at 89 and 154 um, respectively. The detected polarised signal suggests the presence of large (> 0.05-0.1 um) grains in the Crab Nebula. With the observed polarisation, and polarised and total fluxes, we constrain the temperatures and masses of carbonaceous and silicate grains. We find that the carbon-rich grain mass fraction varies between 12 and 70 per cent, demonstrating that carbonaceous and silicate grains co-exist in this SNR. Temperatures range from 40 K to 70 K and from 30 K to 50 K for carbonaceous and silicate grains, respectively. Dust masses range from 10^{-4} Msol to 10^{-2} Msol for carbonaceous grains and to 10^{-1} Msol for silicate grains, in three individual regions.

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arXiv2021

Modelling of ionising feedback with Smoothed Particle Hydrodynamics and Monte Carlo Radiative Transfer on a Voronoi grid

The ionising feedback of young massive stars is well known to influence the dynamics of the birth environment and hence plays an important role in regulating the star formation process in molecular clouds. For this reason, modern hydrodynamics codes adopt a variety of techniques accounting for these radiative effects. A key problem hampering these efforts is that the hydrodynamics are often solved using smoothed particle hydrodynamics (SPH), whereas radiative transfer is typically solved on a grid. Here we present a radiation-hydrodynamics (RHD) scheme combining the SPH code Phantom and the Monte Carlo Radiative Transfer (MCRT) code CMacIonize, using the particle distribution to construct a Voronoi grid on which the MCRT is performed. We demonstrate that the scheme successfully reproduces the well-studied problem of D-type H II region expansion in a uniform density medium. Furthermore, we use this simulation setup to study the robustness of the RHD code with varying choice of grid structure, density mapping method, and mass and temporal resolution. To test the scheme under more realistic conditions, we apply it to a simulated star-forming cloud reminiscing those in the Central Molecular Zone of our galaxy, in order to estimate the amount of ionised material that a single source could create. We find that a stellar population of several $10^3~\rm{M_{\odot}}$ is needed to noticeably ionise the cloud. Based on our results, we formulate a set of recommendations to guide the numerical setup of future and more complex simulations of star forming clouds.

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arXiv2021

Polarised emission from aligned dust grains in nearby galaxies: predictions from the Auriga simulations

(Aims) In this work, we predict the far-infrared polarisation signal emitted by non-spherical dust grains in nearby galaxies. We determine the angular resolution and sensitivity required to study the magnetic field configuration in these galaxies. (Methods) We post-process a set of Milky Way like galaxies from the Auriga project, assuming a dust mix consisting of spheroidal dust grains that are partially aligned with the model magnetic field. We constrain our dust model using Planck 353 GHz observations of the Milky Way. This model is then extrapolated to shorter wavelengths that cover the peak of interstellar dust emission and to observations of arbitrarily oriented nearby Milky Way like galaxies. (Results) Assuming an intrinsic linear polarisation fraction that does not vary significantly with wavelength for wavelengths longer than 50 micron, we predict a linear polarisation fraction with a maximum of $10-15\%$ and a median value of $\approx{}7\%$ for face-on galaxies and $\approx{}3\%$ for edge-on galaxies. The polarisation fraction anti-correlates with the line of sight density and with the angular dispersion function which expresses the large scale order of the magnetic field perpendicular to the line of sight. The maximum linear polarisation fraction agrees well with the intrinsic properties of the dust model. The true magnetic field orientation can be traced along low density lines of sight when it is coherent along the line of sight. These results also hold for nearby galaxies, where a coherent magnetic field structure is recovered over a range of different broad bands. (Conclusions) Polarised emission from non-spherical dust grains accurately traces the large scale structure of the galactic magnetic field in Milky Way like galaxies, with expected maximum linear polarisation fractions of $10-15\%$. To resolve this maximum, a spatial resolution of at least 1 kpc is required.

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arXiv2021

SpheCow: flexible dynamical models for galaxies and dark matter haloes

Simple but flexible dynamical models are useful for many purposes, including serving as the starting point for more complex models or numerical simulations of galaxies, clusters, or dark matter haloes. We present SpheCow, a new light-weight and flexible code that allows one to easily explore the structure and dynamics of any spherical model. Assuming an isotropic or Osipkov-Merritt anisotropic orbital structure, the code can automatically calculate the dynamical properties of any model with either an analytical density profile or an analytical surface density profile as starting point. We have extensively validated SpheCow using a combination of comparisons to analytical and high-precision numerical calculations, as well as the calculation of inverse formulae. SpheCow contains readily usable implementations for many standard models, including the Plummer, Hernquist, NFW, Einasto, Sérsic, and Nuker models. The code is publicly available as a set of C++ routines and as a Python module, and it is designed to be easily extendable, in the sense that new models can be added in a straightforward way. We demonstrate this by adding two new families of models in which either the density slope or the surface density slope is described by an algebraic sigmoid function. We advocate the use of the SpheCow code to investigate the full dynamical structure for models for which the distribution function cannot be expressed analytically and to explore a much wider range of models than is possible using analytical models alone.

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