SPH Code Research Articles

Quasar outflows at z ≥ 6: the impact on the host galaxies

We investigate quasar outflows at $z \geq 6$ by performing zoom-in cosmological hydrodynamical simulations. By employing the SPH code GADGET-3, we zoom in the $2 R_{200}$ region around a $2 \times 10^{12} M_{\odot}$ halo at $z = 6$, inside a $(500 ~ {\rm Mpc})^3$ comoving volume. We compare the results of our AGN runs with a control simulation in which only stellar/SN feedback is considered. Seeding $10^5 M_{\odot}$ BHs at the centers of $10^{9} M_{\odot}$ halos, we find the following results. BHs accrete gas at the Eddington rate over $z = 9 - 6$. At $z = 6$, our most-massive BH has grown to $M_{\rm BH} = 4 \times 10^9 M_{\odot}$. Fast ($v_{r} > 1000$ km/s), powerful ($\dot{M}_{\rm out} \sim 2000 M_{\odot}$/yr) outflows of shock-heated low-density gas form at $z \sim 7$, and propagate up to hundreds kpc. Star-formation is quenched over $z = 8 - 6$, and the total SFR (SFR surface density near the galaxy center) is reduced by a factor of $5$ ($1000$). We analyse the relative contribution of multiple physical process: (i) disrupting cosmic filamentary cold gas inflows, (ii) reducing central gas density, (iii) ejecting gas outside the galaxy; and find that AGN feedback has the following effects at $z = 6$. The inflowing gas mass fraction is reduced by $\sim 12 \%$, the high-density gas fraction is lowered by $\sim 13 \%$, and $\sim 20 \%$ of the gas outflows at a speed larger than the escape velocity ($500$ km/s). We conclude that quasar-host galaxies at $z \geq 6$ are accreting non-negligible amount of cosmic gas, nevertheless AGN feedback quenches their star formation dominantly by powerful outflows ejecting gas out of the host galaxy halo.

The Romulus cosmological simulations: a physical approach to the formation, dynamics and accretion models of SMBHs

We present a novel implementation of supermassive black hole (SMBH) formation, dynamics, and accretion in the massively parallel tree+SPH code, ChaNGa. This approach improves the modeling of SMBHs in fully cosmological simulations, allowing for a more de- tailed analysis of SMBH-galaxy co-evolution throughout cosmic time. Our scheme includes novel, physically motivated models for SMBH formation, dynamics and sinking timescales within galaxies, and SMBH accretion of rotationally supported gas. The sub-grid parameters that regulate star formation (SF) and feedback from SMBHs and SNe are optimized against a comprehensive set of z = 0 galaxy scaling relations using a novel, multi-dimensional parameter search. We have incorporated our new SMBH implementation and parameter optimization into a new set of high resolution, large-scale cosmological simulations called Romulus. We present initial results from our flagship simulation, Romulus25, showing that our SMBH model results in SF efficiency, SMBH masses, and global SF and SMBH accretion histories at high redshift that are consistent with observations. We discuss the importance of SMBH physics in shaping the evolution of massive galaxies and show how SMBH feedback is much more effective at regulating star formation compared to SNe feedback in this regime. Further, we show how each aspect of our SMBH model impacts this evolution compared to more common approaches. Finally, we present a science application of this scheme studying the properties and time evolution of an example dual AGN system, highlighting how our approach allows simulations to better study galaxy interactions and SMBH mergers in the context of galaxy-BH co-evolution.

Cusps in the center of galaxies: a real conflict with observations or a numerical artefact of cosmological simulations?

Galaxy observations and N-body cosmological simulations produce conflicting dark matter halo density profiles for galaxy central regions. While simulations suggest a cuspy and universal density profile (UDP) of this region, the majority of observations favor variable profiles with a core in the center. In this paper, we investigate the convergency of standard N-body simulations, especially in the cusp region, following the approach proposed by [1]. We simulate the well known Hernquist model using the SPH code Gadget-3 and consider the full array of dynamical parameters of the particles. We find that, although the cuspy profile is stable, all integrals of motion characterizing individual particles suffer strong unphysical variations along the whole halo, revealing an effective interaction between the test bodies. This result casts doubts on the reliability of the velocity distribution function obtained in the simulations. Moreover, we find unphysical Fokker-Planck streams of particles in the cusp region. The same streams should appear in cosmological N-body simulations, being strong enough to change the shape of the cusp or even to create it. Our analysis, based on the Hernquist model and the standard SPH code, strongly suggests that the UDPs generally found by the cosmological N-body simulations may be a consequence of numerical effects. A much better understanding of the N-body simulation convergency is necessary before a `core-cusp problem' can properly be used to question the validity of the CDM model.

Shock-induced ejecta from a layer of spherical particles. Part I: SPH meso-scale simulation

According to the data obtained by the Photonic Doppler Velocimetry (PDV) shock wave propagation through a layer of bulked metallic particles produces dust ejecta consisting of fragments with various velocities. While velocity distribution of dust particles can be measured by the PDV, the spatial mass distribution and size distribution of the fragments are hard to derive from the PDV experimental data.To study the mechanism of ejecting and composition of ejected material, direct simulation of experimental conditions is performed with the massive-parallel SPH code. We find that the cumulative jets are produced by the collisions of neighbor spheres accelerated by a shock wave. Those of jets which are able to reach free boundary, leave the layer and decay with formation of many fragments.The data we acquire via direct numerical simulation of the described process is used as initial data for further investigation of dust motion in the air with the finite differences method.

A Study on Parallel FSI Simulations Using a SPH Code and the ADVENTURE through REVOCAP_Coupler

A Study on Parallel FSI Simulations Using a SPH Code and the ADVENTURE through REVOCAP_Coupler

CLUMPY DISKS AS A TESTBED FOR FEEDBACK-REGULATED GALAXY FORMATION

ABSTRACT We study the dependence of fragmentation in massive gas-rich galaxy disks at z > 1 on stellar feedback schemes and hydrodynamical solvers, employing the GASOLINE2 SPH code and the lagrangian mesh-less code GIZMO in finite mass mode. Non-cosmological galaxy disk runs with the standard delayed-cooling blastwave feedback are compared with runs adopting a new superbubble feedback, which produces winds by modeling the detailed physics of supernova-driven bubbles and leads to efficient self-regulation of star formation. We find that, with blastwave feedback, massive star-forming clumps form in comparable number and with very similar masses in GASOLINE2 and GIZMO. Typical clump masses are in the range 107–108 M ⊙, lower than in most previous works, while giant clumps with masses above 109 M ⊙ are exceedingly rare. By contrast, superbubble feedback does not produce massive star-forming bound clumps as galaxies never undergo a phase of violent disk instability. In this scheme, only sporadic, unbound star-forming overdensities lasting a few tens of Myr can arise, triggered by non-linear perturbations from massive satellite companions. We conclude that there is severe tension between explaining massive star-forming clumps observed at z > 1 primarily as the result of disk fragmentation driven by gravitational instability and the prevailing view of feedback-regulated galaxy formation. The link between disk stability and star formation efficiency should thus be regarded as a key testing ground for galaxy formation theory.

Strain Rate Dependant Material Model for Orthotropic Metals

In manufacturing processes anisotropic metals are often exposed to the loading with high strain rates in the range from 102 s-1 to 106 s-1 (e.g. stamping, cold spraying and explosive forming). These types of loading often involve generation and propagation of shock waves within the material. The material behaviour under such a complex loading needs to be accurately modelled, in order to optimise the manufacturing process and achieve appropriate properties of the manufactured component.The presented research is related to development and validation of a thermodynamically consistent physically based constitutive model for metals under high rate loading. The model is capable of modelling damage, failure and formation and propagation of shock waves in anisotropic metals. The model has two main parts: the strength part which defines the material response to shear deformation and an equation of state (EOS) which defines the material response to isotropic volumetric deformation [1]. The constitutive model was implemented into the transient nonlinear finite element code DYNA3D [2] and our in house SPH code. Limited model validation was performed by simulating a number of high velocity material characterisation and validation impact tests.The new damage model was developed in the framework of configurational continuum mechanics and irreversible thermodynamics with internal state variables. The use of the multiplicative decomposition of deformation gradient makes the model applicable to arbitrary plastic and damage deformations.To account for the physical mechanisms of failure, the concept of thermally activated damage initially proposed by Tuller and Bucher [3], Klepaczko [4] was adopted as the basis for the new damage evolution model. This makes the proposed damage/failure model compatible with the Mechanical Threshold Strength (MTS) model Follansbee and Kocks [5], 1988; Chen and Gray [6] which was used to control evolution of flow stress during plastic deformation. In addition the constitutive model is coupled with a vector shock equation of state which allows for modelling of shock wave propagation in orthotropic the material.Parameters for the new constitutive model are typically derived on the basis of the tensile tests (performed over a range of temperatures and strain rates), plate impact tests and Taylor anvil tests.The model was applied to simulate explosively driven fragmentation, blast loading and cold spraying impacts.

The anatomy of a star-forming galaxy: pressure-driven regulation of star formation in simulated galaxies

We explore the regulation of star formation in star-forming galaxies through a suite of high-resolution isolated galaxy simulations. We use the SPH code GASOLINE, including photoelectric heating and metal cooling, which produces a multi-phase interstellar medium. We show that representative star formation and feedback sub-grid models naturally lead to a weak, sub-linear dependence between the amount of star formation and changes to star formation parameters. We incorporate these sub-grid models into an equilibrium pressure-driven regulation framework. We show that the sub-linear scaling arises as a consequence of the non-linear relationship between scale height and the effective pressure generated by stellar feedback. Thus, simulated star-formation regulation is sensitive to how well vertical structure in the ISM is resolved. Full galaxy disks experience density waves which drive locally time-dependent star formation. We develop a simple time-dependent, pressure-driven model that reproduces the response extremely well.

Kinetic AGN feedback effects on cluster cool cores simulated using SPH

We implement novel numerical models of AGN feedback in the SPH code GADGET-3, where the energy from a supermassive black hole (BH) is coupled to the surrounding gas in the kinetic form. Gas particles lying inside a bi-conical volume around the BH are imparted a one-time velocity (10,000 km/s) increment. We perform hydrodynamical simulations of isolated cluster (total mass 10^14 /h M_sun), which is initially evolved to form a dense cool core, having central T<10^6 K. A BH resides at the cluster center, and ejects energy. The feedback-driven fast wind undergoes shock with the slower-moving gas, which causes the imparted kinetic energy to be thermalized. Bipolar bubble-like outflows form propagating radially outward to a distance of a few 100 kpc. The radial profiles of median gas properties are influenced by BH feedback in the inner regions (r<20-50 kpc). BH kinetic feedback, with a large value of the feedback efficiency, depletes the inner cool gas and reduces the hot gas content, such that the initial cool core of the cluster is heated up within a time 1.9 Gyr, whereby the core median temperature rises to above 10^7 K, and the central entropy flattens. Our implementation of BH thermal feedback (using the same efficiency as kinetic), within the star-formation model, cannot do this heating, where the cool core remains. The inclusion of cold gas accretion in the simulations produces naturally a duty cycle of the AGN with a periodicity of 100 Myr.

‘Grandeur in this view of life’:N-body simulation models of the Galactic habitable zone

We present an isolated Milky Way-like simulation in GADGET2 N-body SPH code. The Galactic disk star formation rate (SFR) surface densities and stellar mass indicative of Solar neighbourhood are used as thresholds to model the distribution of stellar mass in life friendly environments. SFR and stellar component density are calculated averaging the GADGET2 particle properties on a 2D grid mapped on the Galactic plane. The peak values for possibly habitable stellar mass surface density move from $10$ to $15$ kpc cylindrical galactocentric distance in $10$ Gyr simulated time span. At $10$ Gyr the simulation results imply the following. Stellar particles which have spent almost all of their life time in habitable friendly conditions reside typically at $\sim16$ kpc from Galactic centre and are $\sim 3$ Gyr old. Stellar particles that have spent $\ge 90 \%$ of their $4-5$ Gyr long life time in habitable friendly conditions, are also predominantly found in the outskirts of the Galactic disk. Less then $1 \%$ of these particles can be found at a typical Solar system galactocentric distance of $8-10$ kpc. Our results imply that the evolution of an isolated spiral galaxy is likely to result in galactic civilizations emerging at the outskirts of the galactic disk around stellar hosts younger than the Sun.

SPH modeling of adhesion in fast dynamics: Application to the Cold Spray process

Abstract The objective of this paper is to show, in a specific case, the importance of modeling adhesive forces when simulating the bouncing of very small particles impacting a substrate at high speed. The implementation of this model into a fast-dynamics SPH code is described. Taking the example of an impacted elastic cylinder, we show that the adhesive forces, which are surface forces, play a significant role only if the particles are sufficiently small. The effect of the choice of the type of interaction law in the cohesive zone is studied and some conclusions on the relevance of the modeling of the adhesive forces for fast-dynamics impacts are drawn. Then, the adhesion model is used to simulate the Cold Spray process. An aluminum particle is projected against a substrate made of the same material at a velocity ranging from 200 to 1000 m ⋅ s − 1 . We study the effects of the various modeling assumptions on the final result: bouncing or sticking. Increasingly complex models are considered. At a 200 m ⋅ s − 1 impact velocity, elastic behavior is assumed, the substrate being simply supported at its base and supplied with absorbing boundaries. The same absorbing boundaries are also used for all the other simulations. Then, plasticity is introduced and the impact velocity is increased up to 1000 m ⋅ s − 1 . At the highest velocities, the resulting strains are very significant. The calculations show that if the adhesion model is appropriately chosen, it is possible to reproduce the experimental observations: the particles stick to the substrate in a range of impact velocities surrounded by two velocity ranges in which the particles bounce.

Infalling clouds on to supermassive black hole binaries – I. Formation of discs, accretion and gas dynamics

There is compelling evidence that most -if not all- galaxies harbour a super-massive black hole (SMBH) at their nucleus, hence binaries of these massive objects are an inevitable product of the hierarchical evolution of structures in the universe, and represent an important but thus-far elusive phase of galaxy evolution. Gas accretion via a circumbinary disc is thought to be important for the dynamical evolution of SMBH binaries, as well as in producing luminous emission that can be used to infer their properties. One plausible source of the gaseous fuel is clumps of gas formed due to turbulence and gravitational instabilities in the interstellar medium, that later fall toward and interact with the binary. In this context, we model numerically the evolution of turbulent clouds in near-radial infall onto equal-mass SMBH binaries, using a modified version of the SPH code GADGET-3. We present a total of 12 simulations that explore different possible pericentre distances and relative inclinations, and show that the formation of circumbinary discs and discs around each SMBH ('mini-discs') depend on those parameters. We also study the dynamics of the formed discs, and the variability of the feeding rate onto the SMBHs in the different configurations.

The response of dark matter haloes to elliptical galaxy formation: a new test for quenching scenarios

We use cosmological hydrodynamical zoom-in simulations with the SPH code gasoline of four haloes of mass M_{200} \sim 10^{13}\Msun to study the response of the dark matter to elliptical galaxy formation. Our simulations include metallicity dependent gas cooling, star formation, and feedback from massive stars and supernovae, but not active galactic nuclei (AGN). At z=2 the progenitor galaxies have stellar to halo mass ratios consistent with halo abundance matching, assuming a Salpeter initial mass function. However by z=0 the standard runs suffer from the well known overcooling problem, overpredicting the stellar masses by a factor of > 4. To mimic a suppressive halo quenching scenario, in our forced quenching (FQ) simulations, cooling and star formation are switched off at z=2. The resulting z=0 galaxies have stellar masses, sizes and circular velocities close to what is observed. Relative to the control simulations, the dark matter haloes in the FQ simulations have contracted, with central dark matter density slopes d\log\rho/d\log r \sim -1.5, showing that dry merging alone is unable to fully reverse the contraction that occurs at z>2. Simulations in the literature with AGN feedback however, have found expansion or no net change in the dark matter halo. Thus the response of the dark matter halo to galaxy formation may provide a new test to distinguish between ejective and suppressive quenching mechanisms.

MODA: a new algorithm to compute optical depths in multidimensional hydrodynamic simulations

We introduce a new algorithm for the calculation of multidimensional optical depths in approximate radiative transport schemes, equally applicable to neutrinos and photons. Motivated by (but not limited to) neutrino transport in three-dimensional simulations of core-collapse supernovae and neutron star mergers, our method makes no assumptions about the geometry of the matter distribution, apart from expecting optically transparent boundaries. Based on local information about opacities, the algorithm figures out an escape route that tends to minimize the optical depth without assuming any pre-defined paths for radiation. Its adaptivity makes it suitable for a variety of astrophysical settings with complicated geometry (e.g., core-collapse supernovae, compact binary mergers, tidal disruptions, star formation, etc.). We implement the MODA algorithm into both a Eulerian hydrodynamics code with a fixed, uniform grid and into an SPH code where we make use a tree structure that is otherwise used for searching neighbours and calculating gravity. In a series of numerical experiments, we compare the MODA results with analytically known solutions. We also use snapshots from actual 3D simulations and compare the results of MODA with those obtained with other methods such as the global and local ray-by-ray method. It turns out that MODA achieves excellent accuracy at a moderate computational cost. In an appendix we also discuss implementation details and parallelization strategies.

Formation of discs around super-massive black hole binaries

AbstractWe model numerically the evolution of 104M⊙ turbulent molecular clouds in near-radial infall onto 106M⊙, equal-mass supermassive black hole binaries, using a modified version of the SPH code gadget-3. We investigate the different gas structures formed depending on the relative inclination between the binary and the cloud orbits. Our first results indicate that an aligned orbit produces mini-discs around each black hole, almost aligned with the binary; a perpendicular orbit produces misaligned mini-discs; and a counter-aligned orbit produces a circumbinary, counter-rotating ring.

Gravitational tides and dwarf spheroidal galaxies

The effect of the local environment on the evolution of dwarf spheroidal galaxies is poorly understood. We have undertaken a suite of simulations to investigate the tidal impact of the Milky Way on the chemodynamical evolution of dwarf spheroidals that resemble present day classical dwarfs using the SPH code GEAR. After simulating the models through a large parameter space of potential orbits the resulting properties are compared with observations from both a dynamical point of view, but also from the, often neglected, chemical point of view. In general, we find that tidal effects quench the star formation even inside gas-endowed dwarfs. Such quenching, may produce the radial distribution of dwarf spheroidals from the orbits seen within large cosmological simulations. We also find that the metallicity gradient within a dwarf is gradually erased through tidal interactions as stellar orbits move to higher radii. The model dwarfs also shift to higher $\langle$[Fe/H]$\rangle$/L ratios, but only when losing $>$$20\%$ of stellar mass.

Long-term variability of low-mass X-ray binaries

We consider modulations of mass captured by the compact object from the companion star's stellar wind in Low Mass X-ray Binaries with late type giants. Based on 3D simulations with two di erent hydrodynamic codes used Lagrangian and Eulerian approaches - the SPH code GADGET and the Eulerian code PLUTO, we conclude that a hydrodynamical interaction of the wind matter within a binary system even without eccentricity results in variability of the mass accretion rate with characteristic time-scales close to the orbital period. Observational appearances of this wind might be similar to that of an accretion disc corona/wind.

Kinetic or thermal AGN feedback in simulations of isolated and merging disc galaxies calibrated by the M-σ relation

(Abridged) We investigate two modes of coupling the feedback energy from a central AGN to the neighboring gas in galaxy simulations: kinetic - velocity boost, and thermal - heating. We formulate kinetic feedback models for energy-driven wind (EDW) and momentum-driven wind (MDW), using two free parameters: feedback efficiency epsilon_f, and AGN wind velocity v_w. A novel numerical algorithm is implemented in the SPH code GADGET-3, to prevent the expansion of a hole in the gas distribution around the BH. We perform simulations of isolated evolution and merger of disk galaxies, of Milky-Way mass as well as lower and higher masses. We find that in the isolated galaxy BH kinetic feedback generates intermittent bipolar jet-like gas outflows. We infer that current prescriptions for BH subgrid physics in galaxy simulations can grow the BH to observed values even in an isolated disk galaxy. The BH growth is enhanced in a galaxy merger. Comparing the [M_BH - sigma_star] relation obtained in our simulations with observational data, we conclude that it is possible to find parameter sets for a fit in all the models, except for the case with MDW feedback in a galaxy merger, in which the BH is always too massive. The BH thermal feedback implementation of Springel, Di Matteo & Hernquist (2005) within the multiphase star-formation model is found to have negligible impact on gas properties; and the effect claimed in all previous studies is attributed to gas depletion around the BH by the creation of an artificial hole. The BH mass accretion rate in our simulations exhibit heavy fluctuations. The star formation rate is quenched with feedback by removal of gas. The CGM gas at galactocentric distances (20 - 100)/h kpc are found to give the best metallicity observational diagnostic to distinguish between BH models.

SPH‐based simulation of multi‐material asteroid collisions

AbstractWe give a brief introduction to smoothed particle hydrodynamics methods for continuum mechanics. Specifically, we present our 3D SPH code to simulate and analyze collisions of asteroids consisting of two types of material: basaltic rock and ice. We consider effects like brittle failure, fragmentation, and merging in different impact scenarios. After validating our code against previously published results we present first collision results based on measured values for the Weibull flaw distribution parameters of basalt. (© 2013 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Cover Picture: Astron. Nachr. 9/2013

AbstractThe collision of a basalt asteroid with a water‐ice projectile simulated with a 3D SPH code. The damage pattern 0.6 ms after the impact is plotted (see T.L. Maindl et al., this issue, p. 996). (© 2013 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)