arXiv subjects

Walter Dehnen

Publications and source records attributed to Walter Dehnen.

At least 37 records · Page 2Linked to original sources

arXiv2022

Age-morphology dependence of the Milky Way boxy/peanut bulge seen in Mira variables

We analyse the distribution of Mira variable stars in the central region of the Milky Way. We find that with increasing period, i.e. decreasing age, the Miras shift towards negative Galactic longitudes $\ell$. Comparing to a cosmological zoom simulation of a barred galaxy, we find that this shift with age can be explained by an age-morphology dependence of the boxy peanut/bulge. Owing to a combination of projection effects and the limitation of the range of Galactic longitudes, the near hump at $\ell>0$ is more truncated for younger populations, and the far hump at $\ell<0$ dominates the observed distributions.

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arXiv2022

Secular Dynamics around a Supermassive Black Hole via Multipole Expansion

In galactic nuclei, the gravitational potential is dominated by the central supermassive black hole, so stars follow quasi-Keplerian orbits. These orbits are distorted by gravitational forces from other stars, leading to long-term orbital relaxation. The direct numerical study of these processes is challenging because the fast orbital motion imposed by the central black hole requires very small timesteps. An alternative approach, pioneered by Gauss, is to use the secular approximation of smearing out the $N$ stars over their Keplerian orbits, using $K$ nodes along each orbit. In this study we propose three novel improvements to this method. First, we re-formulate the discretisation of the rates of change of the variables describing the orbital states to ensure that all conservation laws are exactly satisfied. Second, we replace the pairwise sum over nodes by a multipole expansion up to order $\ell_{\mathrm{max}}$, reducing the overall computational costs from $O(N^2K^2)$ to $O(NK\ell_{\mathrm{max}}^2)$. Finally, we show that the averaged dynamical system is equivalent to $2N$ interacting unit spin vectors and provide two time integrators: a second-order symplectic scheme and a fourth-order Lie-group Runge-Kutta method, both of which are straightforward to generalize to higher order. These new simulations recover the diffusion coefficients of stellar eccentricities obtained through analytical calculations of the secular dynamics.

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arXiv2021

Capture of interstellar objects II: by the Solar system

Capture of interstellar objects (ISOs) into the Solar system is dominated by ISOs with asymptotic incoming speeds $v_\infty<4\,$km\,s$^{-1}$. The capture rate is proportional to the ISO phase-space density in the Solar vicinity and does not vary along the Sun's Galactic orbit, i.e.\ is not enhanced during a passage through a cloud of ISOs (in contrast to previous suggestions). Most bound orbits crossing those of Jupiter and Saturn are fully mixed with unbound phase space, implying that they hold the same ISO phase-space density. Assuming an interstellar number density $n_{iso}\sim0.1\,$au$^{-3}$, we estimate that in 1000 years the planets capture $\sim2$ ISOs (while $\sim17$ fall into the Sun), resulting in a population of $\sim8$ captured ISOs within 5\,au of the Sun at any time, less than the number of visiting ISOs passing through the same volume on hyperbolic orbits. In terms of phase-space volume, capture onto and ejection from the Solar system are equal, such that on average ISOs will not remain captive at $a\lesssim2000\,$au for extensive periods.

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arXiv2021

Capture of interstellar objects I: the capture cross-section

We study the capture of interstellar objects (ISOs) by a planet-star binary with mass ratio $q\ll1$, semi-major axis $a_p$, orbital speed $v_c$, and eccentricity $e_p$. Very close (slingshot) and wide encounters with the planet are amenable to analytic treatment, while numerically obtained capture cross-sections $σ$ closely follow the analytical results even in the intermediate regime. Wide interactions can only generate energy changes $ΔE\lesssim qv_c^2$, when $σ\propto v_\infty^{-2} |\lnΔE|^{2/3}$ (with $v_\infty$ the ISO's incoming speed far away from the binary), which is slightly enhanced for $e_p>0$. Energy changes $ΔE\gtrsim qv_c^2$, on the other hand, require close interactions when $σ\propto (v_\infty ΔE)^{-2}$ hardly depending on $e_p$. Finally, at $ΔE\gtrsim v_c^2$, the cross-section drops to zero, depending on the planet's radius $R_p$ through the Safronov number $Θ=qa_p/R_p$. We also derive the cross-sections for collisions of ISOs with planets or moons.

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arXiv2021

The small boxy/peanut structure of the Milky Way traced by old stars

We analyse the positions of RR Lyrae stars in the central region of the Milky Way. In addition to the overall bar shape detected previously, we find evidence for a peanut shaped structure, in form of overdensities near $\ell=-2$ deg and $1$ deg at $b\sim-3.5$ deg. The corresponding physical distance between the two peaks of the peanut is $\sim0.7$ kpc, significantly shorter than that found from near-IR images (3.3 kpc) and red-clump stars. Qualitatively this is expected from `fractionation' of bar orbits, which we demonstrate to be matched in a simulation of an inside-out growing disc subsequently forming a bar.

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arXiv2021

Formation of the largest galactic cores through binary scouring and gravitational wave recoil

Massive elliptical galaxies are typically observed to have central cores in their projected radial light profiles. Such cores have long been thought to form through `binary scouring' as supermassive black holes (SMBHs), brought in through mergers, form a hard binary and eject stars from the galactic centre. However, the most massive cores, like the ~3kpc core in A2261-BCG, remain challenging to explain in this way. In this paper, we run a suite of dry galaxy merger simulations to explore three different scenarios for central core formation in massive elliptical galaxies: `binary scouring', `tidal deposition' and `gravitational wave (GW) induced recoil'. Using the Griffin code, we self-consistently model the stars, dark matter and SMBHs in our merging galaxies, following the SMBH dynamics through to the formation of a hard binary. We find that we can only explain the large surface brightness core of A2261-BCG with a combination of a major merger that produces a small ~1kpc core through binary scouring, followed by the subsequent GW recoil of its SMBH that acts to grow the core size. We show that this same model can also explain the bright `knots' observed in the core region of A2261-BCG. Key predictions of this scenario are an offset SMBH surrounded by a compact cluster of bound stars and a non-divergent central density profile. We show that the bright `knots' observed in the core region of A2261-BCG are best explained as stalled perturbers resulting from minor mergers, though the brightest may also represent ejected SMBHs surrounded by a stellar cloak of bound stars.

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arXiv2021

EDGE: Two routes to dark matter core formation in ultra-faint dwarfs

In the standard Lambda cold dark matter paradigm, pure dark matter simulations predict dwarf galaxies should inhabit dark matter haloes with a centrally diverging density `cusp'. This is in conflict with observations that typically favour a constant density `core'. We investigate this `cusp-core problem' in `ultra-faint' dwarf galaxies simulated as part of the `Engineering Dwarfs at Galaxy formation's Edge' (EDGE) project. We find, similarly to previous work, that gravitational potential fluctuations within the central region of the simulated dwarfs kinematically heat the dark matter particles, lowering the dwarfs' central dark matter density. However, these fluctuations are not exclusively caused by gas inflow/outflow, but also by impulsive heating from minor mergers. We use the genetic modification approach on one of our dwarf's initial conditions to show how a delayed assembly history leads to more late minor mergers and, correspondingly, more dark matter heating. This provides a mechanism by which even ultra-faint dwarfs ($M_* < 10^5\,\text{M}_{\odot}$), in which star formation was fully quenched at high redshift, can have their central dark matter density lowered over time. In contrast, we find that late major mergers can regenerate a central dark matter cusp, if the merging galaxy had sufficiently little star formation. The combination of these effects leads us to predict significant stochasticity in the central dark matter density slopes of the smallest dwarfs, driven by their unique star formation and mass assembly histories.

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arXiv2020

Non-parametric Triaxial Deprojection of Elliptical Galaxies

We present a grid-based non-parametric approach to obtain a triaxial three-dimensional luminosity density from its surface brightness distribution. Triaxial deprojection is highly degenerate and our approach illustrates the resulting difficulties. Fortunately, for massive elliptical galaxies, many deprojections for a particular line of sight can be discarded, because their projection along other lines of sight does not resemble elliptical galaxies. The near-elliptical isophotes of these objects imply near ellipsoidal intrinsic shapes. In fact, deprojection is unique for densities distributed on ellipsoidal shells. The constrained non-parametric deprojection method we present here relaxes this constraint and assumes that the contours of the luminosity density are boxy/discy ellipsoids with radially varying axis ratios. With this approach we are able to reconstruct the intrinsic triaxial densities of our test models, including one drawn from an $N$-body simulation. The method also allows to compare the relative likelihood of deprojections at different viewing angles. We show that the viewing orientations of individual galaxies with nearly ellipsoidal isophotal shapes can be constrained from photometric data alone.

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arXiv2020

Defeating stochasticity: coalescence timescales of massive black holes in galaxy mergers

The coalescence of massive black hole binaries (BHBs) in galactic mergers is the primary source of gravitational waves (GWs) at low frequencies. Current estimates of GW detection rates for the Laser Interferometer Space Antenna and the Pulsar Timing Array vary by three orders of magnitude. To understand this variation, we simulate the merger of equal-mass, eccentric, galaxy pairs with central massive black holes and shallow inner density cusps. We model the formation and hardening of a central BHB using the Fast Multiple Method as a force solver, which features a $O(N)$ scaling with the number $N$ of particles and obtains results equivalent to direct-summation simulations. At $N \sim 5\times 10^5$, typical for contemporary studies, the eccentricity of the BHBs can vary significantly for different random realisations of the same initial condition, resulting in a substantial variation of the merger timescale. This scatter owes to the stochasticity of stellar encounters with the BHB and decreases with increasing $N$. We estimate that $N \sim 10^7$ within the stellar half-light radius suffices to reduce the scatter in the merger timescale to $\sim 10$\%. Our results suggest that at least some of the uncertainty in low-frequency GW rates owes to insufficient numerical resolution.

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arXiv2020

Capture of interstellar objects: a source of long-period comets

We simulate the passage through the Sun-Jupiter system of interstellar objects (ISOs) similar to 1I/`Oumuamua or 2I/Borisov. Capture of such objects is rare and overwhelmingly from low incoming speeds onto orbits akin to those of known long-period comets. This suggests that some of these comets could be of extra-solar origin, in particular inactive ones. Assuming ISOs follow the local stellar velocity distribution, we infer a volume capture rate of $0.051\,\mathrm{au}^3 \mathrm{yr}^{-1}$. Current estimates for orbital lifetimes and space densities then imply steady-state captured populations of $\sim10^2$ comets and $\sim10^5$ `Oumuamua-like rocks, of which 0.033% are within 6au at any time.

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arXiv2019

The fate of planetesimal discs in young open clusters: implications for 1I/'Oumuamua, the Kuiper belt, the Oort cloud and more

We perform $N$-body simulations of the early phases of open cluster evolution including a large population of planetesimals, initially arranged in Kuiper-belt like discs around each star. Using a new, 4th-order and time-reversible $N$-body code on Graphics Processing Units (GPUs), we evolve the whole system under the stellar gravity, i.e. treating planetesimals as test particles, and consider two types of initial cluster models, similar to IC348 and the Hyades, respectively. In both cases, planetesimals can be dynamically excited, transferred between stars or liberated to become free-floating (such as A/2017 U1 or 'Oumuamua) during the early cluster evolution. We find that planetesimals captured from another star are not necessarily dynamically distinct from those native to a star. After an encounter both native and captured planetesimals can exhibit aligned periastrons, qualitatively similar to that seen in the Solar system and commonly thought to be the signature of Planet 9. We discuss the implications of our results for both our Solar system and exoplanetary systems.

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arXiv2019

Giant planets and brown dwarfs on wide orbits: a code comparison project

Gas clumps formed within massive gravitationally unstable circumstellar discs are potential seeds of gas giant planets, brown dwarfs and companion stars. Simulations show that competition between three processes -- migration, gas accretion and tidal disruption -- establishes what grows from a given seed. Here we investigate the robustness of numerical modelling of clump migration and accretion with the codes PHANTOM, GADGET, SPHINX, SEREN, GIZMO-MFM, SPHNG and FARGO. The test problem comprises a clump embedded in a massive disc at an initial separation of 120 AU. There is a general qualitative agreement between the codes, but the quantitative agreement in the planet migration rate ranges from $\sim 10$% to $\sim 50$%, depending on the numerical setup. We find that the artificial viscosity treatment and the sink particle prescription may account for much of the differences between the codes. In order to understand the wider implications of our work, we also attempt to reproduce the planet evolution tracks from our hydrodynamical simulations with prescriptions from three previous population synthesis studies. We find that the disagreement amongst the population synthesis models is far greater than that between our hydrodynamical simulations. The results of our code comparison project are therefore encouraging in that uncertainties in the given problem are probably dominated by the physics not yet included in the codes rather than by how hydrodynamics is modelled in them.

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arXiv2018

How gravitational softening affects galaxy stability I. Linear mode analysis of disc galaxies

Linear perturbation is used to investigate the effect of gravitational softening on the retrieved two-armed spiral eigenmodes of razor-thin stellar discs. We explore four softening kernels with different degrees of gravity bias, and with/without compact support (compact in the sense that they yield exactly Newtonian forces outside the softening kernel). These kernels are applied to two disc galaxy models with well-known unsoftened unstable modes. We illustrate quantitatively the importance of a vanishing linear gravity bias to yield accurate frequency estimates of the unstable modes. As such, Plummer softening, while very popular amongst simulators, performs poorly in our tests. The best results, with excellent agreement between the softened and unsoftened mode properties, are obtained with softening kernels that have a reduced gravity bias, obtained by compensating for the sub-Newtonian forces at small interparticle distances with slightly super-Newtonian forces at radii near the softening length. We present examples of such kernels that, moreover, are analytically simple and computationally cheap. Finally, these results light the way to the construction of softening methods with even smaller gravity bias, although at the price of increasingly complex kernels.

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arXiv2018

Tidal ribbons

Tidal debris from Galactic satellites generally forms one-dimensional elongated streams, since nearby Galactic orbits have almost identical frequency ratios. We show that the situation is different for orbits close to the Galactic disc, whose vertical frequency $Ω_z$ is strongly amplitude dependent. As a consequence, stars stripped from a satellite obtain a range of values for $Ω_z$ and hence of frequency ratios, and spread into two dimensions, forming a ribbon-like structure with vertical extent comparable to that of the progenitor orbit. In integrals-of-motion space, tidal ribbons are clumps, which offers the best chance of detection and allows the determination of the Galactic potential vertically across the disc.

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arXiv2018

Warp, Waves, and Wrinkles in the Milky Way

We derive unbiased distance estimates for the Gaia-TGAS dataset by correcting for the bias due to the distance dependence of the selection function, which we measure directly from the data. From these distances and proper motions, we estimate the vertical and azimuthal velocities, $W$ and $V_ϕ$, and angular momentum $L_z$ for stars in the Galactic centre and anti-centre directions. The resulting mean vertical motion $\overline{W}$ shows a linear increase with both $V_ϕ$ and $L_z$ at $10 σ$ significance. Such a trend is expected from and consistent with the known Galactic warp. This signal extends to stars with guiding centre radii $R_g<R_0$, placing the onset of the warp at $R\lesssim7{\rm kpc}$. At equally high significance, we detect a previously unknown wave-like pattern of $\overline{W}$ over guiding centre $R_g$ with amplitude $\sim1{\rm kms}^{-1}$ and wavelength $\sim2.5{\rm kpc}$. This pattern is present in both the centre and anti-centre directions, consistent with a winding (corrugated) warp or bending wave, likely related to known features in the outer disc (TriAnd and Monoceros over-densities), and may be caused by the interaction with the Sgr dwarf galaxy $\sim1{\rm Gyr}$ ago. The only significant deviation from this simple fit is a stream-like feature near $R_g\sim9{\rm kpc}$ ($|L_z|\sim2150{\rm kpckms}^{-1}$).

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arXiv2018

Feeding supermassive black holes by collisional cascades

The processes driving gas accretion on to supermassive black holes (SMBHs) are still poorly understood. Angular momentum conservation prevents gas within $\sim10\,$pc of the black hole from reaching radii $\sim10^{-3}\,$pc where viscous accretion becomes efficient. Here we present simulations of the collapse of a clumpy shell of swept-up isothermal gas, which is assumed to have formed as a result of feedback from a previous episode of AGN activity. The gas falls towards the SMBH forming clumps and streams, which intersect, collide, and often form a disc. These collisions promote partial cancellations of angular momenta, resulting in further infall and more collisions. This continued collisional cascade generates a tail of gas with sufficiently small angular momenta and provides a viable route for gas inflow to sub-parsec scales. The efficiency of this process hardly depends on details, such as gas temperature, initial virial ratio and power spectrum of the gas distribution, as long as it is not strongly rotating. Adding star formation to this picture might explain the near-simultaneous formation of the S-stars (from tidally disrupted binaries formed in plunging gas streams) and the sub-parsec young stellar disc around Sgr A$^{\!\star}$.

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arXiv2018

Tidal disruption of dwarf spheroidal galaxies: the strange case of Crater II

Dwarf spheroidal galaxies of the Local Group obey a relationship between the line-of-sight velocity dispersion and half-light radius, although there are a number of dwarfs that lie beneath this relation with suppressed velocity dispersion. The most discrepant of these (in the Milky Way) is the `feeble giant' Crater II. Using analytic arguments supported by controlled numerical simulations of tidally-stripped flattened two-component dwarf galaxies, we investigate interpretations of Crater II within standard galaxy formation theory. Heavy tidal disruption is necessary to explain the velocity-dispersion suppression which is plausible if the proper motion of Crater II is $(μ_{α*},μ_δ)=(-0.21\pm0.09,-0.24\pm0.09)\mathrm{mas\,yr}^{-1}$. Furthermore, we demonstrate that the velocity dispersion of tidally-disrupted systems is solely a function of the total mass loss even for weakly-embedded and flattened systems. The half-light radius evolution depends more sensitively on orbital phase and the properties of the dark matter profile. The half-light radius of weakly-embedded cusped systems rapidly decreases producing some tension with the Crater II observations. This tension is alleviated by cored dark matter profiles, in which the half-light radius can grow after tidal disruption. The evolution of flattened galaxies is characterised by two competing effects: tidal shocking makes the central regions rounder whilst tidal distortion produces a prolate tidally-locked outer envelope. After $\sim70$ per cent of the central mass is lost, tidal distortion becomes the dominant effect and the shape of the central regions of the galaxy tends to a universal prolate shape irrespective of the initial shape.

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arXiv2017

Towards time symmetric N-body integration

Computational efficiency demands discretised, hierarchically organised, and individually adaptive time-step sizes (known as the block-step scheme) for the time integration of N-body models. However, most existing N-body codes adapt individual step sizes in a way that violates time symmetry (and symplecticity), resulting in artificial secular dissipation (and often secular growth of energy errors). Using single-orbit integrations, I investigate various possibilities to reduce or eliminate irreversibility from the time stepping scheme. Significant improvements over the standard approach are possible at little extra effort. However, in order to reduce irreversible step-size changes to negligible amounts, such as suitable for long-term integrations of planetary systems, more computational effort is needed, while exact time reversibility appears elusive for discretised individual step sizes.

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