arXiv subjects

Walter Dehnen

Publications and source records attributed to Walter Dehnen.

At least 55 records · Page 3Linked to original sources

arXiv2017

A study of symplectic integrators for planetary system problems: error analysis and comparisons

The symplectic Wisdom-Holman map revolutionized long-term integrations of planetary systems. There is freedom in such methods of how to split the Hamiltonian and which coordinate system to employ, and several options have been proposed in the literature. These choices lead to different integration errors, which we study analytically and numerically. The Wisdom-Holman method in Jacobi coordinates and the method of Hernandez, H16, compare favorably and avoid problems of some of the other maps, such as incorrect center-of-mass position or truncation errors even in the one-planet case. We use H16 to compute the evolution of Pluto's orbital elements over 500 million years in a new calculation.

astro-ph.EP↗

arXiv2016

Collisionless loss-cone refilling: there is no final parsec problem

Coalescing massive black hole binaries, formed during galaxy mergers, are expected to be a primary source of low frequency gravitational waves. Yet in isolated gas-free spherical stellar systems, the hardening of the binary stalls at parsec-scale separations owing to the inefficiency of relaxation-driven loss-cone refilling. Repopulation via collisionless orbit diffusion in triaxial systems is more efficient, but published simulation results are contradictory. While sustained hardening has been reported in simulations of galaxy mergers with $N \sim 10^6$ stars and in early simulations of rotating models, in isolated non-rotating triaxial models the hardening rate continues to fall with increasing N, a signature of spurious two-body relaxation. We present a novel approach for studying loss cone repopulation in galactic nuclei. Since loss cone repopulation in triaxial systems owes to orbit diffusion, it is a purely collisionless phenomenon and can be studied with an approximated force calculation technique, provided the force errors are well behaved and sufficiently small. We achieve this using an accurate fast multipole method and define a proxy for the hardening rate that depends only on stellar angular momenta. We find that the loss cone is efficiently replenished even in very mildly triaxial models (with axis ratios 1 : 0.9 : 0.8). Such triaxiality is unavoidable following galactic mergers and can drive binaries into the gravitational wave regime. We conclude that there is no final parsec problem.

astro-ph.GA↗

arXiv2016

Symplectic fourth-order maps for the collisional N-body problem

We study analytically and experimentally certain symplectic and time-reversible N-body integrators which employ a Kepler solver for each pair-wise interaction, including the method of Hernandez & Bertschinger (2015). Owing to the Kepler solver, these methods treat close two-body interactions correctly, while close three-body encounters contribute to the truncation error at second order and above. The second-order errors can be corrected to obtain a fourth-order scheme with little computational overhead. We generalise this map to an integrator which employs a Kepler solver only for selected interactions and yet retains fourth-order accuracy without backward steps. In this case, however, two-body encounters not treated via a Kepler solver contribute to the truncation error.

math.NA↗

arXiv2016

Indirect Dark Matter Detection for Flattened Dwarf Galaxies

Gamma-ray experiments seeking to detect evidence of dark matter annihilation in dwarf spheroidal galaxies require knowledge of the distribution of dark matter within these systems. We analyze the effects of flattening on the annihilation (J) and decay (D) factors of dwarf spheroidal galaxies with both analytic and numerical methods. Flattening has two consequences: first, there is a geometric effect as the squeezing (or stretching) of the dark matter distribution enhances (or diminishes) the J-factor; second, the line of sight velocity dispersion of stars must hold up the flattened baryonic component in the flattened dark matter halo. We provide analytic formulae and a simple numerical approach to estimate the correction to the J- and D-factors required over simple spherical modeling. The formulae are validated with a series of equilibrium models of flattened stellar distributions embedded in flattened dark-matter distributions. We compute corrections to the J- and D-factors for the Milky Way dwarf spheroidal galaxies under the assumption that they are all prolate or all oblate and find that the hierarchy of J-factors for the dwarf spheroidals is slightly altered (typical correction factors for an ellipticity of $0.4$ are $0.75$ for the oblate case and $1.6$ for the prolate case). We demonstrate that spherical estimates of the D-factors are very insensitive to the flattening and introduce uncertainties significantly less than the uncertainties in the D-factors from the other observables for all the dwarf spheroidals (for example, ${}^{+10\mathrm{\,percent}}_{-3\mathrm{\,percent}}$ for a typical ellipticity of $0.4$). We conclude by investigating the spread in correction factors produced by triaxial figures and provide uncertainties in the J-factors for the dwarf spheroidals using different physically-motivated assumptions for their intrinsic shape and axis alignments. (abridged)

astro-ph.GA↗

arXiv2015

Misaligned gas discs around eccentric black-hole binaries and implications for the final-parsec problem

We investigate the evolution of low mass (Md /Mb = 0.005) misaligned gaseous discs around eccentric supermassive black hole (SMBH) binaries. These are expected to form from randomly oriented accretion events onto a SMBH binary formed in a galaxy merger. When expanding the interaction terms between the binary and a circular ring to quadrupole order and averaging over the binary orbit, we expect four non-precessing disc orientations: aligned or counter-aligned with the binary, or polar orbits around the binary eccentricity vector with either sense of rotation. All other orientations precess around either of these, with the polar precession dominating for high eccentricity. These expectations are borne out by smoothed particle hydrodynamics simulations of initially misaligned viscous circumbinary discs, resulting in the formation of polar rings around highly eccentric binaries in contrast to the co-planar discs around circular binaries. Moreover, we observe disc tearing and violent interactions between differentially precessing rings in the disc significantly disrupting the disc structure and causing gas to fall onto the binary with little angular momentum. While accretion from a polar disc may not promote SMBH binary coalescence (solving the `final-parsec problem'), ejection of this infalling low-angular momentum material via gravitational slingshot is a possible mechanism to reduce the binary separation. Moreover, this process acts on dynamical rather than viscous time scales, and so is much faster.

astro-ph.HE↗

arXiv2014

A fast multipole method for stellar dynamics

The approximate computation of all gravitational forces between $N$ interacting particles via the fast multipole method (FMM) can be made as accurate as direct summation, but requires less than $\mathcal{O}(N)$ operations. FMM groups particles into spatially bounded cells and uses cell-cell interactions to approximate the force at any position within the sink cell by a Taylor expansion obtained from the multipole expansion of the source cell. By employing a novel estimate for the errors incurred in this process, I minimise the computational effort required for a given accuracy and obtain a well-behaved distribution of force errors. For relative force errors of $\sim10^{-7}$, the computational costs exhibit an empirical scaling of $\propto N^{0.87}$. My implementation (running on a 16 core node) out-performs a GPU-based direct summation with comparable force errors for $N\gtrsim10^5$.

astro-ph.IM↗

arXiv2013

Black hole foraging: feedback drives feeding

We suggest a new picture of supermassive black hole (SMBH) growth in galaxy centers. Momentum-driven feedback from an accreting hole gives significant orbital energy but little angular momentum to the surrounding gas. Once central accretion drops, the feedback weakens and swept-up gas falls back towards the SMBH on near-parabolic orbits. These intersect near the black hole with partially opposed specific angular momenta, causing further infall and ultimately the formation of a small-scale accretion disk. The feeding rates into the disk typically exceed Eddington by factors of a few, growing the hole on the Salpeter timescale and stimulating further feedback. Natural consequences of this picture include (i) the formation and maintenance of a roughly toroidal distribution of obscuring matter near the hole; (ii) random orientations of successive accretion disk episodes; (iii) the possibility of rapid SMBH growth; (iv) tidal disruption of stars and close binaries formed from infalling gas, resulting in visible flares and ejection of hypervelocity stars; (v) super-solar abundances of the matter accreting on to the SMBH; and (vi) a lower central dark-matter density, and hence annihilation signal, than adiabatic SMBH growth implies. We also suggest a simple sub-grid recipe for implementing this process in numerical simulations.

astro-ph.CO↗

arXiv2012

Gravitational Collapse in One Dimension

We simulate the evolution of one-dimensional gravitating collisionless systems from non- equilibrium initial conditions, similar to the conditions that lead to the formation of dark- matter halos in three dimensions. As in the case of 3D halo formation we find that initially cold, nearly homogeneous particle distributions collapse to approach a final equilibrium state with a universal density profile. At small radii, this attractor exhibits a power-law behavior in density, ρ(x) \propto |x|^(-γ_crit), γ_crit \simeq 0.47, slightly but significantly shallower than the value γ = 1/2 suggested previously. This state develops from the initial conditions through a process of phase mixing and violent relaxation. This process preserves the energy ranks of particles. By warming the initial conditions, we illustrate a cross-over from this power-law final state to a final state containing a homogeneous core. We further show that inhomogeneous but cold power-law initial conditions, with initial exponent γ_i > γ_crit, do not evolve toward the attractor but reach a final state that retains their original power-law behavior in the interior of the profile, indicating a bifurcation in the final state as a function of the initial exponent. Our results rely on a high-fidelity event-driven simulation technique.

astro-ph.CO↗

arXiv2012

Improving convergence in smoothed particle hydrodynamics simulations without pairing instability

The numerical convergence of smoothed particle hydrodynamics (SPH) can be severely restricted by random force errors induced by particle disorder, especially in shear flows, which are ubiquitous in astrophysics. The increase in the number NH of neighbours when switching to more extended smoothing kernels at fixed resolution (using an appropriate definition for the SPH resolution scale) is insufficient to combat these errors. Consequently, trading resolution for better convergence is necessary, but for traditional smoothing kernels this option is limited by the pairing (or clumping) instability. Therefore, we investigate the suitability of the Wendland functions as smoothing kernels and compare them with the traditional B-splines. Linear stability analysis in three dimensions and test simulations demonstrate that the Wendland kernels avoid the pairing instability for all NH, despite having vanishing derivative at the origin (disproving traditional ideas about the origin of this instability; instead, we uncover a relation with the kernel Fourier transform and give an explanation in terms of the SPH density estimator). The Wendland kernels are computationally more convenient than the higher-order B-splines, allowing large NH and hence better numerical convergence (note that computational costs rise sub-linear with NH). Our analysis also shows that at low NH the quartic spline kernel with NH ~= 60 obtains much better convergence then the standard cubic spline.

astro-ph.IM↗

arXiv2012

The mass distribution of the Fornax dSph: constraints from its globular cluster distribution

Uniquely among the dwarf spheroidal (dSph) satellite galaxies of the Milky Way, Fornax hosts globular clusters. It remains a puzzle as to why dynamical friction has not yet dragged any of Fornax's five globular clusters to the centre, and also why there is no evidence that any similar star cluster has been in the past (for Fornax or any other dSph). We set up a suite of 2800 N-body simulations that sample the full range of globular-cluster orbits and mass models consistent with all existing observational constraints for Fornax. In agreement with previous work, we find that if Fornax has a large dark-matter core then its globular clusters remain close to their currently observed locations for long times. Furthermore, we find previously unreported behaviour for clusters that start inside the core region. These are pushed out of the core and gain orbital energy, a process we call 'dynamical buoyancy'. Thus a cored mass distribution in Fornax will naturally lead to a shell-like globular cluster distribution near the core radius, independent of the initial conditions. By contrast, CDM-type cusped mass distributions lead to the rapid infall of at least one cluster within Δt = 1-2Gyr, except when picking unlikely initial conditions for the cluster orbits (\sim 2% probability), and almost all clusters within Δt = 10Gyr. Alternatively, if Fornax has only a weakly cusped mass distribution, dynamical friction is much reduced. While over Δt = 10Gyr this still leads to the infall of 1-4 clusters from their present orbits, the infall of any cluster within Δt = 1-2Gyr is much less likely (with probability 0-70%, depending on Δt and the strength of the cusp). Such a solution to the timing problem requires that in the past the globular clusters were somewhat further from Fornax than today; they most likely did not form within Fornax, but were accreted.

astro-ph.CO↗

arXiv2011

Modeling disc non-axisymmetries: multiple patterns, radial migration, and thick discs

Disc non-axisymmetrc components, such as spirals and central bars, are nowadays known to play an important role in shaping galactic discs. Here we use Tree-SPH N-body simulations to examine the effect of these perturbers on two aspects: the occurrence of multiple patterns in discs and the effects of radial migration on disc thickening. We find that, in addition to a central bar, multiple spiral patterns and lopsided modes develop in all models. Interaction among these asymmetric features results in a large scale stellar migration. However, we show that, despite the strong radial mixing, discs cannot be thickened sufficiently to match observed thick discs. We relate this to the adiabatic cooling as stars migrate radially outwards. We also find that the bulge contribution to a thick-disc component for an Sa-type galaxy at ~2.5 disc scale-lengths is less than 1% and zero in the case of a Milky Way-like, Sb-type. Our findings cast doubt on the plausibility of thick disc formation via stellar radial migration.

astro-ph.GA↗

arXiv2011

Weakening dark-matter cusps by clumpy baryonic infall

We consider the infall of a massive clump into a dark-matter halo as a simple and extreme model for the effect of baryonic physics (neglected in gravity-only simulations of large-scale structure formation) on the dark-matter. We find that such an infalling clump is extremely efficient in altering the structure of the halo and reducing its central density: a clump of 1% the mass of the halo can remove about twice its own mass from the inner halo and transform a cusp into a core or weaker cusp. If the clump is subsequently removed, mimicking a galactic wind, the central halo density is further reduced and the mass removed from the inner halo doubled. Lighter clumps are even more efficient: the ratio of removed mass to clump mass increases slightly towards smaller clump masses. This process is the more efficient the more radially anisotropic the initial dark-matter velocities. While such a clumpy infall may be somewhat unrealistic, it demonstrates that the baryons need to transfer only a small fraction of their initial energy to the dark matter via dynamical friction to explain the discrepancy between predicted dark-matter density profiles and those inferred from observations of dark-matter dominated galaxies.

astro-ph.CO↗

arXiv2011

N-body simulations of gravitational dynamics

We describe the astrophysical and numerical basis of N-body simulations, both of collisional stellar systems (dense star clusters and galactic centres) and collisionless stellar dynamics (galaxies and large-scale structure). We explain and discuss the state-of-the-art algorithms used for these quite different regimes, attempt to give a fair critique, and point out possible directions of future improvement and development. We briefly touch upon the history of N-body simulations and their most important results.

astro-ph.IM↗

arXiv2010

Inviscid SPH

In smooth-particle hydrodynamics (SPH), artificial viscosity is necessary for the correct treatment of shocks, but often generates unwanted dissipation away from shocks. We present a novel method of controlling the amount of artificial viscosity, which uses the total time derivative of the velocity divergence as shock indicator and aims at completely eliminating viscosity away from shocks. We subject the new scheme to numerous tests and find that the method works at least as well as any previous technique in the strong-shock regime, but becomes virtually inviscid away from shocks, while still maintaining particle order. In particular sound waves or oscillations of gas spheres are hardly damped over many periods.

astro-ph.IM↗

arXiv2009

Tailoring triaxial N-body models via a novel made-to-measure method

The made-to-measure N-body method (Syer & Tremaine 1996) slowly adapts the particle weights of an N-body model, whilst integrating the trajectories in an assumed static potential, until some constraints are satisfied, such as optimal fits to observational data. I propose a novel technique for this adaption procedure, which overcomes several limitations and shortcomings of the original method. The capability of the new technique is demonstrated by generating realistic N-body equilibrium models for dark-matter haloes with prescribed density profile, triaxial shape, and slowly outwardly growing radial velocity anisotropy

astro-ph.GA↗

arXiv2007

Initial conditions for disc galaxies

We present a general recipe for constructing N-body realizations of galaxies comprised of near-spherical and disc components. First, an exact spherical distribution function for the spheroids (halo & bulge) is determined, such that it is in equilibrium with the gravitational monopole of the disc components. Second, an N-body realisation of this model is adapted to the full disc potential by growing the latter adiabatically from its monopole. Finally, the disc is sampled with particles drawn from an appropriate distribution function, avoiding local-Maxwellian approximations. We performed test simulations and find that the halo and bulge radial density profile very closely match their target model, while they become slightly oblate due to the added disc gravity. Our findings suggest that vertical thickening of the initially thin disc is caused predominantly by spiral and bar instabilities, which also result in a radial re-distribution of matter, rather than scattering off interloping massive halo particles.

astro-ph↗

arXiv2006

The velocity dispersion and mass profile of the Milky Way

We re-analyse the velocity-dispersion profile sigma(r) at radii r>10 kpc in the Galactic stellar halo, recently derived by Battaglia et al. (2005), who concluded that, for constant velocity anisotropy of the tracers, these data rule out a flat circular-speed curve for the Milky Way. However, we demonstrate that if one makes the natural assumption that the tracer density is truncated at r_t >~ 160 kpc and falls off significantly more steeply than r^-3.5 at r >~ 80 kpc, then these data are consistent with a flat circular-speed curve and a constant velocity anisotropy comparable to that observed for halo stars in the Solar neighbourhood. We also consider a more detailed mass model with an exponential stellar disc and an extended non-isothermal dark-matter halo. In this two-component model, the Milky Way's virial radius and mass are r_vir = 200 kpc and M_vir = 1.5 x 10^12 M_sun. Still assuming the tracers' velocity anisotropy to be constant (at beta=0.5) we again find good agreement with the observed sigma(r), so long as the tracer density is truncated near the virial radius. These data by themselves do not allow to differentiate between different dark-halo or total-mass models for the Milky Way, nor between different velocity-anisotropy profiles for the tracers.

astro-ph↗

arXiv2005

Probing dark matter with X-ray binaries

Low-mass X-ray binaries (LMXBs), which occur in old stellar populations, have velocities exceeding those of their parent distribution by at least 20 km/s. This makes them ideal probes for dark matter, in particular in dwarf spheroidals (dSph), where the LMXBs should penetrate well outside the visible galaxy. We argue that the most likely explanation of the observation of LMXBs in the Sculptor dSph by Maccarone et al (2005) is the presence of a dark matter halo of >~ 10^9 Msun, corresponding to a total-mass to light ratio of >~ 600 (M/L_V)_sun. In this case there should be an extended halo of LMXBs which may be observable.

astro-ph↗