N-body Research Articles

Effects of Halo Spin on the Formation and Evolution of Bars in Disk Galaxies

The spin of dark halos has been shown to significantly affect bar formation and evolution in disk galaxies. To understand the physical role of halo spin in bar formation, we run N-body simulations of isolated, Milky Way–sized galaxies by varying the halo spin parameter in the range −0.16 ≤ λ ≤ 0.16 and the bulge mass. We find that our adopted halo alone is subject to swing amplification of an m = 2 nonaxisymmetric mode rotating in the same sense as the halo, which assists or inhibits the bar formation in a disk depending on its sense of rotation. The m = 2 mode in the disk, growing via swing amplification, interacts constructively (destructively) with the m = 2 mode in the prograde (retrograde) halo, promoting (delaying) bar formation. A bar grows by losing its angular momentum primarily to a halo. Since the halo particles inside (outside) the corotation resonance with the bar can emit (absorb) angular momentum to (from) the bar, the bar pattern speed decays more slowly for larger λ > 0, while it decreases relatively fast almost independent of λ ≤ 0. Models with a strong bar develop a boxy peanut-shaped bulge. In models without a bulge, this occurs rapidly via buckling instability, while bars with a bulge thicken gradually without undergoing buckling instability. Among the models considered in the present work, the bar in the λ = 0.06 model with a bulge of 10% of the disk mass best describes the Milky Way in terms of its length and pattern speed.

The clustering of Lyman Alpha Emitting galaxies at 𝗓=2–3

We measure the clustering of Lyman Alpha Emitting galaxies (LAEs) selected from the One-hundred-square-degree DECam Imaging in Narrowbands (ODIN) survey, with spectroscopic follow-up from Dark Energy Spectroscopic Instrument (DESI). We use DESI spectroscopy to optimize our selection and to constrain the interloper fraction and redshift distribution of our narrow-band selected sources. We select samples of 4000 LAEs at z = 2.45 and 3.1 in 9 sq.deg. centered on the COSMOS field with median Lyα fluxes of ≈ 10-16 erg s-1 cm-2. Covariances and cosmological inferences are obtained from a series of mock catalogs built upon high-resolution N-body simulations that match the footprint, number density, redshift distribution and observed clustering of the sample. We find that both samples have a correlation length of r 0 = 3.0 ± 0.2 h-1 Mpc. Within our fiducial cosmology these correspond to 3D number densities of ≈ 10-3 h3 Mpc-3 and, from our mock catalogs, biases of 1.7 and 2.0 at z = 2.45 and 3.1, respectively. We discuss the implications of these measurements for the use of LAEs as large-scale structure tracers for high-redshift cosmology.

The Solar System could have formed in a low-viscosity disc: A dynamical study from giant planet migration to the Nice model

Context. In the context of low-viscosity protoplanetary discs (PPDs), the formation scenarios of the Solar System should be revisited. In particular, the Jupiter-Saturn pair has been shown to lock in the 2:1 mean motion resonance while migrating generally inwards, making the Grand Tack scenario impossible. Aims. We explore what resonant chains of multiple giant planets can form in a low-viscosity disc, and whether these configurations can evolve into forming the Solar System in the post gas disc phase. Methods. We used hydrodynamical simulations with the code FARGOCA to study the migration of the giant planets in a disc with viscosity parameter of α = 10−4. After a transition phase to a gas-less configuration, we studied the stability of the obtained resonant chains through their interactions with a disc of leftover planetesimals by performing N-body simulations using rebound. Results. The gaps opened by giant planets are wider and deeper for lower viscosity, reducing the damping effect of the disc. Thus, when planets enter a resonance, the resonant angle remains closer to circulation, making the chain weaker. Exploring numerous configurations, we found five stable resonant chains of four or five planets. In a thin (cold) PPD, the four giant planets revert their migration and migrate outwards. After disc dispersal, under the influence of a belt of planetesimals, some resonant chains undergo an instability phase while others migrate smoothly over a billion years. For three of our resonant chains, about ~1% of the final configurations pass the four criteria to fit the Solar System. The most successful runs are obtained for systems formed in a cold PPD with a massive planetesimal disc. Conclusions. This work provides a fully consistent study of the dynamical history of the Solar System’s giant planets, from the protoplanetary disc phase up to the giant planet instability. Although building resonant configurations is difficult in low-viscosity discs, we find it possible to reproduce the Solar System from a cold, low-viscosity protoplanetary disc.

Giant planet formation in the Solar System

The formation history of Jupiter has been of interest due to its ability to shape the solar system’s history. Yet little attention has been paid to the formation and growth of Saturn and the other giant planets. Here we explore through N-body simulations the implications of the simplest disc and pebble accretion model with steady-state accretion and an assumed ring structure in the disc at 5 AU on the formation of the giant planets in the solar system. We conducted a statistical survey of different disc parameters and initial conditions of the protoplanetary disc to establish which combination best reproduces the present outer solar system. We examined the effect of the initial planetesimal disc mass, the number of planetesimals and their size-frequency distribution slope, pebble accretion prescription and sticking efficiency on the likelihood of forming gas giants and their orbital distribution. The results reveal that the accretion sticking efficiency is the most sensitive parameter to control the final masses and number of giant planets. We have been unable to replicate the formation of all three types of giant planets in the solar system in a single simulation. The probability distribution of the final location of the giant planets is approximately constant in logr, suggesting there is a slight preference for formation closer to the Sun but no preference for more massive planets to form closer. The eccentricity distribution has a higher mean for more massive planets indicating that systems with more massive planets are more violent. We compute the average formation time for proto-Jupiter to reach 10 Earth masses to be 〈tc,J〉=1.1±0.3 Myr and for proto-Saturn 〈tc,S〉=3.3±0.4 Myr, while for the ice giants this increases to 〈tc,I〉=4.9±0.1 Myr. The formation timescales of the cores of the gas giants are distinct at >95% confidence, suggesting that they formed sequentially.

KRATOS: A large suite of N-body simulations to interpret the stellar kinematics of LMC-like discs

Context. The Large and Small Magellanic Clouds (LMC and SMC, respectively) are the brightest satellites of the Milky Way (MW), and for the last thousand million years they have been interacting with one another. As observations only provide a static picture of the entire process, numerical simulations are used to interpret the present-day observational properties of these kinds of systems, and most of them have been focused on attempting to recreate the neutral gas distribution and characteristics through hydrodynamical simulations. Aims. We present KRATOS, a comprehensive suite of 28 open-access pure N-body simulations of isolated and interacting LMC-like galaxies designed for studying the formation of substructures in their discs after interaction with an SMC-mass galaxy. The primary objective of this paper is to provide theoretical models that help us to interpret the formation of general structures in an LMC-like galaxy under various tidal interaction scenarios. This is the first paper of a series dedicated to the analysis of this complex interaction. Methods. Simulations are grouped into 11 sets of up to three configurations, with each set containing (1) a control model of an isolated LMC-like galaxy; (2) a model that contains the interaction with an SMC-mass galaxy, and (3) a model where both an SMC-mass and a MW-mass galaxy may interact with the LMC-like galaxy (the most realistic model). In each simulation, we analysed the orbital history between the three galaxies and examined the morphological and kinematic features of the LMC-like disc galaxy throughout the interaction. This includes investigating the disc scale height and velocity maps. When a bar was found to develop, we characterised its strength, length, off-centredness, and pattern speed. Results. The diverse outcomes found in the KRATOS simulations, including the presence of bars, warped discs, and various spiral arm shapes, demonstrate the opportunities they offer to explore a range of LMC-like galaxy morphologies. These morphologies directly correspond to distinct disc kinematic maps, making them well-suited for a first-order interpretation of the LMC’s kinematic maps. From the simulations, we note that tidal interactions can: boost the disc scale height; both destroy and create bars; and naturally explain the off-centre stellar bars. The bar length and pattern speed of long-lived bars are not appreciably altered by the interaction. Conclusions. The high spatial, temporal, and mass resolution used in the KRATOS simulations has been shown to be appropriate for the purpose of interpreting the internal kinematics of LMC-like discs, as evidenced by the first scientific results presented in this work.

Simulating the Arrival of the Southern Substructure in the Galaxy Cluster Abell 1758

Abell 1758 (z ∼ 0.278) is a galaxy cluster composed of two structures, A1758N and A1758S, separated by ∼2.2 Mpc. The northern cluster is itself a dissociative merging cluster that has already been modeled by dedicated simulations. Recent radio observations revealed the existence of a previously undetected bridge connecting A1758N and A1758S. New simulations are now needed to take into account the presence of A1758S. We wish to evaluate which orbital configuration would be compatible with a bridge between the clusters. Using N-body hydrodynamical simulations that build upon the previous model, we explore different scenarios that could have led to the current observed configuration. Five types of orbital approaches were tested: radial, tangential, vertical, postapocentric, and outgoing. We found that the incoming simulated scenarios are generally consistent with mild enhancements of gas density between the approaching clusters. The mock X-ray images exhibit a detectable bridge in all cases. Compared to measurements of Chandra data, the amplitude of the X-ray excess is overestimated by a factor of ∼2–3 in the best simulations. The scenario of tangential approach proved to be the one that best matches the properties of the profiles of X-ray surface brightness. The scenarios of radial approach of vertical approach are also marginally compatible.

Denoising diffusion delensing: reconstructing the non-Gaussian CMB lensing potential with diffusion models

ABSTRACT Optimal extraction of cosmological information from observations of the cosmic microwave background (CMB) critically relies on our ability to accurately undo the distortions caused by weak gravitational lensing. In this work, we demonstrate the use of denoising diffusion models in performing Bayesian lensing reconstruction. We show that score-based generative models can produce accurate, uncorrelated samples from the CMB lensing convergence map posterior, given noisy CMB observations. To validate our approach, we compare the samples of our model to those obtained using established Hamiltonian Monte Carlo methods, which assume a Gaussian lensing potential. We then go beyond this assumption of Gaussianity, and train and validate our model on non-Gaussian lensing data, obtained by ray-tracing N-body simulations. We demonstrate that in this case, samples from our model have accurate non-Gaussian statistics beyond the power spectrum. The method provides an avenue towards more efficient and accurate lensing reconstruction, which does not rely on an approximate analytical description of the posterior probability. The reconstructed lensing maps can be used as an unbiased tracer of the matter distribution, and to improve delensing of the CMB, resulting in more precise cosmological parameter inference.

Redshift evolution and covariances for joint lensing and clustering studies with DESI Y1

ABSTRACT Galaxy–galaxy lensing (GGL) and clustering measurements from the Dark Energy Spectroscopic Instrument Year 1 (DESI Y1) data set promise to yield unprecedented combined-probe tests of cosmology and the galaxy–halo connection. In such analyses, it is essential to identify and characterize all relevant statistical and systematic errors. We forecast the covariances of DESI Y1 GGL + clustering measurements and the systematic bias due to redshift evolution in the lens samples. Focusing on the projected clustering and GGL correlations, we compute a Gaussian analytical covariance, using a suite of N-body and lognormal simulations to characterize the effect of the survey footprint. Using the DESI one percent survey data, we measure the evolution of galaxy bias parameters for the DESI luminous red galaxy (LRG) and bright galaxy survey (BGS) samples. We find mild evolution in the LRGs in $0.4 < z < 0.8$, subdominant to the expected statistical errors. For BGS, we find less evolution for brighter absolute magnitude cuts, at the cost of reduced sample size. We find that for a redshift bin width $\Delta z = 0.1$, evolution effects on DESI Y1 GGL is negligible across all scales, all fiducial selection cuts, all fiducial redshift bins. Galaxy clustering is more sensitive to evolution due to the bias squared scaling. Nevertheless the redshift evolution effect is insignificant for clustering above the 1-halo scale of $0.1h^{-1}$ Mpc. For studies that wish to reliably access smaller scales, additional treatment of redshift evolution is likely needed. This study serves as a reference for GGL and clustering studies using the DESI Y1 sample.

Fate of a remnant solid disk around an eccentric giant planet

The composition of giant planets' atmospheres is an important tracer of their formation history. While many theoretical studies investigate the heavy-element accretion within a gaseous protoplanetary disk, the possibility of solid accretion after disk dissipation has not been explored. Here, we focus on the case of a gas giant planet excited to an eccentric orbit and assess the likelihood of solid accretion after disk dissipation. We follow the orbital evolution of the surrounding solid materials and investigate the scattering and accretion of heavy elements in the remnant solid disks. We perform N-body simulations of planetesimals and embryos around an eccentric giant planet. We consider various sizes and orbits for the eccentric planet and determine the fate of planetesimals and embryos. We find that the orbital evolution of solids, such as planetesimals and embryos, is regulated by weak encounters with the eccentric planet rather than strong close encounters. Even in the region where the Safronov number is smaller than unity, most solid materials fall onto the central star or are ejected from the planetary system. We also develop an analytical model of the solid accretion along the orbital evolution of a giant planet, where the accretion probability is obtained as a function of the planetary mass, radius, semi-major axis, eccentricity, inclination, and solid disk thickness. Our model predicts that sim 0.01-0.1 $M_ of solids is accreted onto an eccentric planet orbiting in the outer disk ($ The accreted heavy-element mass increases (decreases) with the eccentricity (inclination) of the planet. We also discuss the possibility of collisions of terrestrial planets and find that $ of the hot Jupiters formed via high-eccentric migration collide with a planet of $10M_ However, we find that solid accretion and collisions with terrestrial planets are minor events for planets in the inner orbit, and a different accretion process is required to enrich eccentric giant planets with heavy elements.

Metallicity distributions of halo stars: do they trace the Galactic accretion history?

The standard cosmological scenario predicts a hierarchical formation for galaxies. Many substructures have been found in the Galactic halo, usually identified as clumps in kinematic spaces, like the energy-angular momentum space ($E-L_z$), under the hypothesis that these quantities should be conserved during the interaction. If these clumps also feature different chemical abundances, such as the metallicity distribution function (MDF), these two arguments together (different kinematic and chemical properties) are often used to motivate their association with distinct and independent merger debris. The aim of this study is to explore to what extent we can couple kinematic characteristics and metallicities of stars in the Galactic halo to reconstruct the accretion history of the Milky Way (MW). In particular, we want to understand whether different clumps in the $E-L_z$ space with different MDFs should be associated with distinct merger debris. We analysed dissipationless, self-consistent, high-resolution N-body simulations of a MW-type galaxy accreting a satellite with a mass ratio of 1:10, with different orbital parameters and different metallicity gradients, which were assigned a posteriori. We confirm that accreted stars from a sim 1:10 mass ratio merger event redistribute in a wide range of $E$ and $L_z$, due to the dynamical friction process, and are thus not associated with a single region. Because satellite stars with different metallicities can be deposited in different regions of the $E-L_z$ space (on average the more metal-rich ones end up more gravitationally bound to the MW), this implies that a single accretion of sim 1:10 can manifest with different MDFs, in different regions of the $E-L_z$ space. Groups of stars with different $E$, $L_z$, and metallicities may be interpreted as originating from different satellite galaxies, but our analysis shows that these interpretations are not physically motivated. In fact, as we show, the coupling of kinematic information with MDFs to reconstruct the accretion history of the MW can bias the reconstructed merger tree towards increasing the number of past accretions and decreasing the masses of the progenitor galaxies.

Halo densities and pericenter distances of the bright Milky Way satellites as a test of dark matter physics

ABSTRACT We provide new constraints on the dark matter halo density profile of Milky Way (MW) dwarf spheroidal galaxies (dSphs) using the phase-space distribution function (DF) method. After assessing the systematics of the approach against mock data from the Gaia Challenge project, we apply the DF analysis to the entire kinematic sample of well-measured MW dwarf satellites for the first time. Contrary to previous findings for some of these objects, we find that the DF analysis yields results consistent with the standard Jeans analysis. In particular, in this study we rediscover (i) a large diversity in the inner halo densities of dSphs (bracketed by Draco and Fornax), and (ii) an anticorrelation between inner halo density and pericenter distance of the bright MW satellites. Regardless of the strength of the anticorrelation, we find that the distribution of these satellites in density versus pericenter space is inconsistent with the results of the high-resolution N-body simulations that include a disc potential. Our analysis motivates further studies on the role of internal feedback and dark matter microphysics in these dSphs.

Modelling the redshift-space cluster–galaxy correlation function on Mpc scales with emulation of the pairwise velocity distribution

ABSTRACT We present a method for modelling the cluster–galaxy correlation function in redshift space, down to $\sim$ Mpc scales. The method builds upon the so-called galaxy infall kinematics (GIK) model, a parametric model for the pairwise velocities of galaxies with respect to nearby galaxy clusters. We fit the parameters of the GIK model to a suite of simulations run with different cosmologies, and use Gaussian processes to emulate how the GIK parameters depend upon cosmology. This emulator can then be combined with knowledge of the real-space clustering of clusters and galaxies, to predict the cluster–galaxy correlation function in redshift space, $\xi _\mathrm{cg}^s$. Fitting this model to an observed $\xi _\mathrm{cg}^s$ enables the extraction of cosmological parameter constraints, and we present forecasts for a survey like that currently being done by the Dark Energy Spectroscopic Instrument (DESI). We also perform tests of the robustness of our constraints from fitting to mock data extracted from N-body simulations, finding that fitting to scales $\lesssim 3 \, h^{-1}\, \mathrm{Mpc}$ leads to a biased inference on cosmology, due to model mis-specification on these scales. Finally, we discuss what steps will need to be taken in order to apply our method to real data.

Rapid formation of binary asteroid systems post rotational failure: A recipe for making atypically shaped satellites

Binary asteroid formation is a highly complex process, which has been highlighted with recent observations of satellites with unexpected shapes, such as the oblate Dimorphos by the NASA DART mission and the contact binary Selam by NASA’s Lucy mission. There is no clear consensus on which dynamical mechanisms determine the final shape of these objects. In turn, we explore a formation pathway where spin-up and rotational failure of a rubble pile asteroid lead to mass-shedding and a wide circumasteroidal debris disk in which the satellite forms. Using a combination of smooth-particle hydrodynamical and N-body simulations, we study the dynamical evolution in detail. We find that a debris disk containing matter corresponding to a few percent of the primary asteroid mass extending beyond the fluid Roche limit can consistently form both oblate and bilobate satellites via a series of tidal encounters with the primary body and mergers with other gravitational aggregates. Principally, satellites end up prolate (elongated) and on synchronous orbits, accreting mainly in a radial direction while tides from the primary asteroid keep the shape intact. However, close encounters and mergers can break the orbital state, leading to orbital migration and deformation. Satellite–satellite impacts occurring in this regime have lower impact velocities than merger-driven moon formation in e.g. planetary rings, leading to soft impacts between differently sized, non-spherical bodies. The resulting post-merger shape of the satellite is highly dependent on the impact geometry. Only moons having experienced a prior mild or catastrophic tidal disruption during a close encounter with the primary asteroid can become oblate spheroids, which is consistent with the predominantly prolate observed population of binary asteroid satellites.

Algorithm to Produce a Density Field with Given Two, Three, and Four-Point Correlation Functions

Abstract Here we show how to produce a 3D density field with a given set of higher-order correlation functions. Our algorithm enables producing any desired two-point, three-point, and four-point functions, including odd-parity for the latter. We note that this algorithm produces the desired correlations about a set of “primary” points, matched to how the spherical-harmonic-based algorithms ENCORE and CADENZA measure them. These “primary points” must be used as those around which the correlation functions are measured. We also generalize the algorithm to i) N-point correlations with N > 4, ii) dimensions other than 3, and iii) beyond scalar quantities. This algorithm should find use in verifying analysis pipelines for higher-order statistics in upcoming galaxy redshift surveys such as DESI, Euclid, Roman, and Spherex, as well as intensity mapping. In particular it may be helpful in searches for parity violation in the 4PCF of these samples, for which producing initial conditions for N-body simulations is both costly and highly model-dependent at present, and so alternative methods such as that developed here are desirable.

GalaxyFlow: upsampling hydrodynamical simulations for realistic mock stellar catalogues

ABSTRACT Cosmological N-body simulations of galaxies operate at the level of ‘star particles’ with a mass resolution on the scale of thousands of solar masses. Turning these simulations into stellar mock catalogues requires ‘upsampling’ the star particles into individual stars following the same phase-space density. In this paper, we introduce two new upsampling methods. First, we describe GalaxyFlow, a sophisticated upsampling method that utilizes normalizing flows to both estimate the stellar phase-space density and sample from it. Secondly, we improve on existing upsamplers based on adaptive kernel density estimation (KDE), using maximum likelihood estimation to fine-tune the bandwidth for such algorithms in a way that improves both the density estimation accuracy and upsampling results. We demonstrate our upsampling techniques on a neighbourhood of the Solar location in two simulated galaxies: Auriga 6 and h277. Both yield smooth stellar distributions that closely resemble the stellar densities seen in the Gaia DR3 catalogue. Furthermore, we introduce a novel multimodel classifier test to compare the accuracy of different upsampling methods quantitatively. This test confirms that GalaxyFlow more accurately estimates the density of the underlying star particles than methods based on KDE, at the cost of being more computationally intensive.

Extensive Pollution of Uranus and Neptune’s Atmospheres by Upsweep of Icy Material during the Nice Model Migration

In the Nice model of Solar System formation, Uranus and Neptune undergo an orbital upheaval, sweeping through a planetesimal disk. The region of the disk from which material is accreted by the ice giants during this phase of their evolution has not previously been identified. We perform direct N-body orbital simulations of the four giant planets to determine the amount and origin of solid accretion during this orbital upheaval. We find that the ice giants undergo an extreme bombardment event, with collision rates as high as ∼3 per hour assuming km-sized planetesimals, increasing the total planet mass by up to ∼0.35%. In all cases, the initially outermost ice giant experiences the largest total enhancement. We determine that, for some plausible planetesimal properties, the resulting atmospheric enrichment could potentially produce sufficient latent heat to alter the planetary cooling timescale according to existing models. Our findings suggest that substantial accretion during this phase of planetary evolution may have been sufficient to impact the atmospheric composition and thermal evolution of the ice giants, motivating future work on the fate of deposited solid material.

Euclid preparation

We investigate the accuracy of the perturbative galaxy bias expansion in view of the forthcoming analysis of the Euclid spectroscopic galaxy samples. We compare the performance of a Eulerian galaxy bias expansion using state-of-the-art prescriptions from the effective field theory of large-scale structure (EFTofLSS) with a hybrid approach based on Lagrangian perturbation theory and high-resolution simulations. These models are benchmarked against comoving snapshots of the flagship I N-body simulation at z = (0.9, 1.2, 1.5, 1.8), which have been populated with Hα galaxies leading to catalogues of millions of objects within a volume of about 58 h−3 Gpc3. Our analysis suggests that both models can be used to provide a robust inference of the parameters (h, ωc) in the redshift range under consideration, with comparable constraining power. We additionally determine the range of validity of the EFTofLSS model in terms of scale cuts and model degrees of freedom. From these tests, it emerges that the standard third-order Eulerian bias expansion – which includes local and non-local bias parameters, a matter counter term, and a correction to the shot-noise contribution – can accurately describe the full shape of the real-space galaxy power spectrum up to the maximum wavenumber of kmax = 0.45 h Mpc−1, and with a measurement precision of well below the percentage level. Fixing either of the tidal bias parameters to physically motivated relations still leads to unbiased cosmological constraints, and helps in reducing the severity of projection effects due to the large dimensionality of the model. We finally show how we repeated our analysis assuming a volume that matches the expected footprint of Euclid, but without considering observational effects, such as purity and completeness, showing that we can get constraints on the combination (h, ωc) that are consistent with the fiducial values to better than the 68% confidence interval over this range of scales and redshifts.

On the statistical theory of self-gravitating collisionless dark matter flow: High order kinematic and dynamic relations

Dark matter, if it exists, accounts for five times as much as ordinary baryonic matter. To better understand the self-gravitating collisionless dark matter flow on different scales, a statistical theory involving kinematic and dynamic relations must be developed for different types of flow, e.g., incompressible, constant divergence, and irrotational flow. This is mathematically challenging because of the intrinsic complexity of dark matter flow and the lack of a self-closed description of flow velocity. This paper extends our previous work on second-order statistics Xu [Phys. Fluids 35, 077105 (2023)] to kinematic relations of any order for any type of flow. Dynamic relations were also developed to relate statistical measures of different orders. The results were validated by N-body simulations. On large scales, we found that (i) third-order velocity correlations can be related to density correlation or pairwise velocity; (ii) the pth-order velocity correlations follow ∝a(p+2)/2 for odd p and ∝ap/2 for even p, where a is the scale factor; (iii) the overdensity δ is proportional to density correlation on the same scale, ⟨δ⟩∝⟨δδ′⟩; (iv) velocity dispersion on a given scale r is proportional to the overdensity on the same scale. On small scales, (i) a self-closed velocity evolution is developed by decomposing the velocity into motion in haloes and motion of haloes; (ii) the evolution of vorticity and enstrophy are derived from the evolution of velocity; (iii) dynamic relations are derived to relate second- and third-order correlations; (iv) while the first moment of pairwise velocity follows ⟨ΔuL⟩=−Har (H is the Hubble parameter), the third moment follows ⟨(ΔuL)3⟩∝εuar that can be directly compared with simulations and observations, where εu≈10−7 m2/s3 is the constant rate for energy cascade; (v) the pth order velocity correlations follow ∝a(3p−5)/4 for odd p and ∝a3p/4 for even p. Finally, the combined kinematic and dynamic relations lead to exponential and one-fourth power-law velocity correlations on large and small scales, respectively.

An implementation of nDGP gravity in Pinocchio

In this paper we investigate dark matter structure formation in the normal branch of the Dvali-Gabadadze-Porrati (nDGP) model using the PINOCCHIO algorithm. We first present 2nd order Lagrangian perturbation theory for the nDGP model, which shows that the 1st- and 2nd-order growth functions in nDGP are larger than those in ΛCDM. We then examine the dynamics of ellipsoidal collapse in nDGP, which is accelerated compared to ΛCDM due to enhanced gravitational interactions. Running the nDGP-PINOCCHIO code with a box size of 512 Mpc h -1 and 10243 particles, we analyze the statistical properties of the output halo catalogs, including the halo power spectrum and halo mass function. The calibrated PINOCCHIO halo power spectrum agrees with N-body simulations within 5% in the comoving wavenumber range k<0.3 (h Mpc-1) at redshift z=0. The agreement is extended to smaller scales for higher redshifts. For the cumulative halo mass function, the agreement between N-body and PINOCCHIO is also within the simulation scatter.

How the presence of a giant planet affects the outcome of terrestrial planet formation simulations

The architecture and masses of planetary systems in the habitable zone could be strongly influenced by the presence of outer giant planets. Here, we investigate the impact of outer giants on terrestrial planet formation, under the assumption that the final assembly of the planetary system is set by a giant impact phase. Utilizing a state-of-the-art N-body simulation software, GENGA, we interpret how the late stage of terrestrial planet formation contributes to diversity among planetary systems. We designed two global model setups: 1) we placed a gas giant on the outer side of planetesimals and embryo disk and 2) we only included planetesimals and embryos, but no giant. For the model including the outer giant, we studied the effect of different giant initial masses in the range of 1.0–3.0 Jupiter masses, as well as a range of orbital radii from 2.0–5.8 AU. We also studied the influence of different initial positions of planetesimals and embryos on the results. Our N-body simulation time is approximately 50 Myr. The results show that the existence of an outer giant will promote the interaction between planetesimals and embryos, making the orbits of the formed terrestrial planets more compact. However, placing the giant planet too close to the planetesimals and embryo disk suppresses the formation of massive rocky planets. In addition, under the classical theory, where planetary embryos and planetesimals collide to form terrestrial planets, our results show that the presence of a giant planet actually decreases the gap complexity of the inner planetary system.