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We present a new multi-dimensional, robust, and cell-centered finite-volume scheme for the ideal MHD equations. This scheme relies on relaxation and splitting techniques and can be easily used at high order. A fully conservative version is not entropy satisfying but is observed experimentally to be more robust than standard constrained transport schemes at low plasma beta. At very low plasma beta and high Alfv\'en number, we have designed an entropy-satisfying version that is not conservative for the magnetic field but preserves admissible states and we switch locally a-priori between the two versions depending on the regime of plasma beta and Alfv\'en number. This strategy is robust in a wide range of standard MHD test cases, all performed at second order with a classic MUSCL-Hancock scheme., Comment: accepted in JCP

We present results of our dynamical stream modelling for the North West Stream in the outer halo of the Andromeda galaxy (M31). Comprising two main segments, the North West Stream was thought to be a single structured arching around M31. However, recent evidence suggests that it is two separate, unrelated, streams. To test this hypothesis we use observational data from 6 fields associated with the upper segment of the North West Stream together with 8 fields and 5 globular clusters associated with the lower segment to constrain model orbits. We fit both segments of the stream using a fixed potential model for M31 and an orbit integrator to compare orbits with the observed streams. We measure the central tracks and predict proper motions for for the upper segment (lower segment) finding ${\mu^*_{\alpha}}$ = 0.078$^{+0.015}_{-0.012}$ (0.085$^{+0.001}_{-0.002}$) mas/yr and ${\mu_{\delta}}$ = $-$0.05$^{+0.008}_{-0.009}$ ($-$0.095$^{+0.003}_{-0.005}$) mas/yr. Our results support the hypothesis that the dwarf spheroidal galaxy Andromeda XXVII is the progenitor of the upper segment of the North West Stream and that the upper and lower segments do not comprise a single structure. We propose that the upper segment, which appears to be on an infall trajectory with M31, be renamed the "Andromeda XXVII Stream" and the lower segment, also apparently infalling towards M31, retain the name "North West Stream"., Comment: 20 pages, 14 figures

Collisionless Dark Matter Only (DMO) structure formation simulations predict that Dark Matter (DM) haloes are prolate in their centres and triaxial towards their outskirts. The addition of gas condensation transforms the central DM shape to be rounder and more oblate. It is not clear, however, whether such shape transformations occur in `ultra-faint' dwarfs, which have extremely low baryon fractions. We present the first study of the shape and velocity anisotropy of ultra-faint dwarf galaxies that have gas mass fractions of $f_{\rm gas}(r 3\times10^9\,$M$_\odot$; $f_{\rm gas} > 10^{-4}$) become rounder and more oblate within $\sim 10$ half light radii. Finally, we find that most of our simulated dwarfs have significant radial velocity anisotropy that rises to $\tilde{\beta} > 0.5$ at $R \gtrsim 3 R_{\rm half}$. The one exception is a dwarf that forms a rotating gas/stellar disc because of a planar, major merger. Such strong anisotropy should be taken into account when building mass models of gas-poor ultra-faints., Comment: 16 pages and 11 figures (excluding appendices), accepted by MNRAS

The Eridanus II (EriII) 'ultra-faint' dwarf has a large ($15\,\text{pc}$) and low mass ($4.3\times10^3\,\text{M}_\odot$) star cluster (SC) offset from its centre by $23\pm3\,\text{pc}$ in projection. Its size and offset are naturally explained if EriII has a central dark matter core, but such a core may be challenging to explain in a $\Lambda$CDM cosmology. In this paper, we revisit the survival and evolution of EriII's SC, focussing for the first time on its puzzlingly large ellipticity ($0.31^{+0.05}_{-0.06}$). We perform a suite of 960 direct $N$-body simulations of SCs, orbiting within a range of spherical background potentials fit to ultra-faint dwarf (UFD) galaxy simulations. We find only two scenarios that come close to explaining EriII's SC. In the first, EriII has a low density dark matter core (of size $\sim70\,\text{pc}$ and density $\lesssim2\times10^8\,\text{M}_{\odot}\,\text{kpc}^{-3}$). In this model, the high ellipticity of EriII's SC is set at birth, with the lack of tidal forces in the core allowing its ellipticity to remain frozen in for long times. In the second, EriII's SC orbits in a partial core, with its high ellipticity owing to its imminent tidal destruction. However, this latter model struggles to reproduce the large size of EriII's SC, and it predicts substantial tidal tails around EriII's SC that should have already been seen in the data. This leads us to favour the cored model. We discuss potential caveats to these findings, and the implications of the cored model for galaxy formation and the nature of dark matter., Comment: 16 pages, 12 figures + appendices. Published with MNRAS. Comments welcome

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., Comment: 14 pages, 13 figures, submitted to MNRAS

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., Comment: Accepted in MNRAS

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., Comment: Submitted for publication in MNRAS

We present new chemo--kinematics of the Hercules dwarf galaxy based on Keck II-- DEIMOS spectroscopy. Our 21 confirmed members have a systemic velocity of $v_{\mathrm{Herc}}=46.4\pm1.3$ kms$^{-1}$ and a velocity dispersion $\sigma_{v,\mathrm{Herc}}=4.4^{+1.4}_{-1.2}$ kms$^{-1}$. From the strength of the Ca II triplet, we obtain a metallicity of [Fe/H]= $-2.48\pm0.19$ dex and dispersion of $\sigma_{\rm{[Fe/H]}}= 0.63^{+0.18}_{-0.13}$ dex. This makes Hercules a particularly metal--poor galaxy, placing it slightly below the standard mass--metallicity relation. Previous photometric and spectroscopic evidence suggests that Hercules is tidally disrupting and may be on a highly radial orbit. From our identified members, we measure no significant velocity gradient. By cross--matching with the second \textit{Gaia} data release, we determine an uncertainty--weighted mean proper motion of $\mu_{\alpha}^*=\mu_{\alpha}\cos(\delta)=-0.153\pm{0.074}$ mas yr$^{-1}$, $\mu_{\delta}=-0.397\pm0.063$ mas yr$^{-1}$. This proper motion is slightly misaligned with the elongation of Hercules, in contrast to models which suggest that any tidal debris should be well aligned with the orbital path. Future observations may resolve this tension., Comment: Submitted to MNRAS. 17 pages, 14 figures

We present a kinematic and spectroscopic analysis of 38 red giant branch stars, in 7 fields, spanning the dwarf spheroidal galaxy Andromeda XXVII and the upper segment of the North West Stream. Both features are located in the outer halo of the Andromeda galaxy at a projected radius of 50-80 kpc, with the stream extending for $\sim$3$^{\circ}$ on the sky. Our data is obtained as part of the PAndAS survey and enables us to confirm that Andromeda XXVII's heliocentric distance is 827 $\pm$ 47 kpc and spectroscopic metallicity is -2.1$^{+0.4}_{-0.5}$. We also re-derive Andromeda XXVII's kinematic properties, measuring a systemic velocity = -526.1$^{+10.0}_{-11.0}${\kms} and a velocity dispersion that we find to be non-Gaussian but for which we derive a formal value of 27.0$^{+2.2}_{-3.9}${\kms}. In the upper segment of the North West Stream we measure mean values for the metallicity = -1.8$\pm$0.4, systemic velocity = -519.4 $\pm$4.0{\kms} and velocity dispersion = 10.0$\pm$4.0{\kms}. We also detect a velocity gradient of 1.7$\pm$0.3 {\kms} kpc$^{-1}$ on an infall trajectory towards M31. With a similar gradient, acting in the same direction, in the lower segment we suggest that the North West Stream is not a single structure. As the properties of the upper segment of the North West Stream and Andromeda XXVII are consistent within ~90\% confidence limits, it is likely that the two are related and plausible that Andromeda XXVII is the progenitor of this stream., Comment: 15 pages, 10 figures

We present a new technique to probe the central dark matter (DM) density profile of galaxies that harnesses both the survival and observed properties of star clusters. As a first application, we apply our method to the `ultra-faint' dwarf Eridanus II (Eri II) that has a lone star cluster ~45 pc from its centre. Using a grid of collisional $N$-body simulations, incorporating the effects of stellar evolution, external tides and dynamical friction, we show that a DM core for Eri II naturally reproduces the size and the projected position of its star cluster. By contrast, a dense cusped galaxy requires the cluster to lie implausibly far from the centre of Eri II (>1 kpc), with a high inclination orbit that must be observed at a particular orbital phase. Our results, therefore, favour a dark matter core. This implies that either a cold DM cusp was `heated up' at the centre of Eri II by bursty star formation, or we are seeing an evidence for physics beyond cold DM., Comment: Minor changes to match the version in press in MNRAS

We present a novel positive potential-density pair expansion for modelling galaxies, based on the Miyamoto-Nagai (MN) disc. By using three sets of such discs, each one of them aligned along each symmetry axis, we are able to reconstruct a broad range of potentials that correspond to density profiles from exponential discs to 3D power law models with varying triaxiality (henceforth simply "twisted" models). We increase the efficiency of our expansion by allowing the scale length parameter of each disc to be negative. We show that, for suitable priors on the scale length and height parameters, these "MNn discs" have just one negative density minimum. This allows us to ensure global positivity by demanding that the total density at the global minimum is positive. We find that at better than 10\% accuracy in our density reconstruction, we can represent a radial and vertical exponential disc over $0.1-10$ scale lengths/heights with 4 MNn discs, an NFW profile over $0.1-10$ scale lengths with 4 MNn discs, and a twisted triaxial NFW profile with 3 MNn discs per symmetry axis. Our expansion is efficient, fully analytic, and well-suited to reproducing the density distribution and gravitational potential of galaxies from discs to ellipsoids., Comment: 8 pages, 8 figures. Accepted for publication in Monthly Notices of the Royal Astronomical Society