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Aaron D. Ludlow

Publications and source records attributed to Aaron D. Ludlow.

At least 19 recordsLinked to original sources

The origin of the stellar mass-size relation of satellite galaxies in the COLIBRE simulations

We study the stellar mass-size relation of satellite galaxies in the COLIBRE suite of cosmological hydrodynamical simulations. Satellites deviate from the relation that holds for centrals galaxies, where at the high mass end, $\log (M_*/{\rm M}_\odot) > 10.5$, sizes (defined as the 3D half-mass radius $r_{\rm h,*}$) increase systematically with mass ($r_{\rm h,*} \propto M_*^{0.5}$), whereas at lower masses, $8 < \log(M_*/{\rm M}_\odot) < 10.5$, the relation flattens and galaxy size becomes, on average, almost independent of mass ($r_{\rm h,*} \approx 3$ kpc). At $z=0$, dwarf satellites (defined as those with $8 < \log(M_*/{\rm M}_\odot) < 9$) are systematically larger than centrals of similar $M_*$. This trend reverses for bright satellites ($9 < \log(M_*/{\rm M}_\odot) < 10.5$), which are typically smaller than centrals of similar mass. We trace these trends to evolutionary processes affecting satellites after infall into the haloes of more massive hosts. At infall, dwarf satellites are typically gas-rich, dark matter-dominated systems with relatively large baryon-induced cores. These satellites quench rapidly after losing their gas to ram pressure, which prompts an immediate impulsive expansion due to the shallowing central potential, followed by secular expansion as their cored dark matter haloes are gradually stripped by tides. In contrast, the inner regions of bright satellites are baryon-dominated and resilient to tides. Centrally concentrated star formation increases their stellar mass, leading to smaller sizes and higher stellar metallicities (by $\approx 0.2$ dex) than those of centrals of similar mass. These distinct satellite evolutionary pathways lead to identifiable features in the mass-size-metallicity relations that may be compared with observations.

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The evolution of the sizes and angular momentum content of galaxies in the COLIBRE simulations

We analyse the sizes and specific angular momentum content of galaxies in the Colibre cosmological hydrodynamical simulations spanning two orders of magnitude in mass resolution. We compare the predicted size-mass and angular momentum-mass relations to a broad range of observational measurements spanning redshifts $z=0$ to $4$. At $z=0$, Colibre reproduces observed size-mass relations over the sampled mass range $10^8 \lesssim M_\star/{\rm M_\odot}\lesssim 10^{11.5}$, and for multiple size definitions, including two- and three-dimensional stellar half-mass radii, half-light radii across several wavelengths, as well as alternative measures such as baryonic half-mass radii and characteristic radii defined by stellar surface density thresholds. The simulations also recover the observed segregation of galaxies in the size-mass plane by morphological type and star formation rate, and reproduce the distinct, approximately parallel sequences followed by star-forming discs and quenched spheroids in the stellar specific angular momentum-mass plane. The angular momentum content of star-forming Colibre galaxies matches that of observed systems out to $z\approx 1.5$. At higher redshifts, massive galaxies ($ 10^{9.5}\lesssim M_\star/{\rm M_\odot}\lesssim 10^{11}$) in the simulations are somewhat smaller than observed, and the separation between star-forming and passive populations in the size-mass plane is reduced relative to observations, while at lower masses the agreement remains good. This apparent discrepancy may reflect the effects of dust attenuation, which is neglected in our analysis and may preferentially obscure the central regions of observed systems. Overall, our findings highlight the close connection between galaxy size, angular momentum, and morphology over cosmic time.

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The weak connection between the stellar haloes and merger histories of Milky Way-mass galaxies

Stellar haloes form through the disruption of satellite galaxies over time, making them a promising observable for constraining galaxy merger histories. We use a dynamical decomposition technique to isolate the stellar haloes of Milky Way-mass galaxies in the $100\,{\rm Mpc}$ EAGLE simulation and study their relationship to the merger histories of their hosts. We define the stellar halo as the stellar mass that is bound to the central subhalo but not associated with the disc or bulge components of a galaxy, and we quantify their merger histories using the most significant merger since $z=1$. Surprisingly, we find that the fraction of a galaxy's total stellar mass in the stellar halo, $f_{\rm SH}$, is not a reliable indicator of its merger activity. Contrary to common assumptions, disc galaxies with low $f_{\rm SH}$ do not necessarily have quiescent merger histories. In fact, roughly one quarter experienced a merger at $z \leq 1$ with a satellite whose stellar mass was at least 10 per cent of the host galaxy's stellar mass. These galaxies undergo mergers with satellites on circular orbits that are roughly co-planar with the pre-existing disc and thereby avoid contributing mass to the stellar halo. Instead, such mergers build thick, extended discs and supply fresh gas that often triggers a significant episode of star formation in the disc. Our results suggest that disc galaxies with low-mass stellar haloes, such as the Milky Way, can have varied and active merger histories, and that stellar haloes may not be a reliable tool for inferring galaxy merger histories.

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The active role of co-evolving haloes in stellar bar formation

We use idealised N-body simulations of equilibrium discs in live and static haloes to study how dark matter co-evolution impacts the assembly of stellar particles into a bar and the halo response. Initial conditions correspond to a marginally unstable disc according to commonly used disc stability criteria, and are evolved for the equivalent of about 150 disc dynamical times (10Gyr). An extensive convergence study ensures accurate modelling of the bar formation process. Live haloes lead to the formation of a strong bar, but the same disc remains unbarred when evolved in a static halo. Neither seeded disc instabilities, nor longer (60Gyr) simulations result in the formation of a bar when the halo is static. When the live halo is replaced with a static analogue at later times the previously robust bar slowly dissipates, suggesting: (1) the co-evolution of the disc and halo is critical for the assembly and long-term survival of bars in marginally unstable discs; and (2) global disc stability criteria must be modified for discs in the presence of live haloes. In our live halo runs, a "dark bar" grows synchronously with the stellar bar. Processes that inhibit the transfer of angular momentum between the halo and disc may stabilise a galaxy against bar formation, and can lead to the dissolution of the bar itself. This raises further questions about the puzzling stability of observed discs that are marginally unstable, but unbarred.

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Identifying the discs, bulges, and intra-halo light of simulated galaxies through structural decomposition

We perform a structural decomposition of galaxies identified in three cosmological hydrodynamical simulations by applying Gaussian Mixture Models (GMMs) to the kinematics of their stellar particles. We study the resulting disc, bulge, and intra-halo light (IHL) components of galaxies whose host dark matter haloes have virial masses in the range $M_{200}=10^{11}$-- $10^{15}\,{\rm M_\odot}$. Our decomposition technique isolates galactic discs whose mass fractions, $f_{\rm disc}$, correlate strongly with common alternative morphology indicators; for example, $f_{\rm disc}$ is approximately equal to $κ_{\rm co}$, the fraction of stellar kinetic energy in co-rotation. The primary aim of our study, however, is to characterise the IHL of galaxies in a consistent manner and over a broad mass range, and to analyse its properties from the scale of galactic stellar haloes up to the intra-cluster light. Our results imply that the IHL fraction, $f_{\rm IHL}$, has appreciable scatter and is strongly correlated with galaxy morphology: at fixed stellar mass, the IHL of disc galaxies is typically older and less massive than that of spheroids. Above $M_{200}\approx 10^{13}\,{\rm M_\odot}$, we find, on average, $f_{\rm IHL}\approx 0.45$, albeit with considerable scatter. The transition radius beyond which the IHL dominates the stellar mass of a galaxy is roughly $30\,{\rm kpc}$ for $M_{200}\lesssim 10^{12.8}\,{\rm M_\odot}$, but increases strongly towards higher masses. However, we find that no alternative IHL definitions -- whether based on the ex-situ stellar mass, or the stellar mass outside a spherical aperture -- reproduce our dynamically-defined IHL masses.

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The impact of stochastic modeling on the predictive power of galaxy formation simulations

All modern galaxy formation models employ stochastic elements in their sub-grid prescriptions to discretise continuous equations across the time domain. In this paper, we investigate how the stochastic nature of these models, notably star formation, black hole accretion, and their associated feedback, that act on small ($<$ kpc) scales, can back-react on macroscopic galaxy properties (e.g. stellar mass and size) across long ($>$ Gyr) timescales. We find that the scatter in scaling relations predicted by the EAGLE model implemented in the SWIFT code can be significantly impacted by random variability between re-simulations of the same object, even when galaxies are resolved by tens of thousands of particles. We then illustrate how re-simulations of the same object can be used to better understand the underlying model, by showing how correlations between galaxy stellar mass and black hole mass disappear at the highest black hole masses ($M_{\rm BH} > 10^8$ M$_\odot$), indicating that the feedback cycle may be interrupted by external processes. We find that although properties that are collected cumulatively over many objects are relatively robust against random variability (e.g. the median of a scaling relation), the properties of individual galaxies (such as galaxy stellar mass) can vary by up to 25\%, even far into the well-resolved regime, driven by bursty physics (black hole feedback) and mergers between galaxies. We suggest that studies of individual objects within cosmological simulations be treated with caution, and that any studies aiming to closely investigate such objects must account for random variability within their results.

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Spurious heating of stellar motions by dark matter particles in cosmological simulations of galaxy formation

We use two cosmological simulations to study the impact of spurious heating of stellar motions within simulated galaxies by dark matter (DM) particles. The simulations share the same numerical and subgrid parameters, but one used a factor of 7 more DM particles. Many galaxy properties are unaffected by spurious heating, including their masses, star formation histories, and the spatial distribution of their gaseous baryons. The distribution and kinematics of stellar and DM particles, however, are affected. Below a resolution-dependent virial mass, $M_{200}^{\rm spur}$, galaxies have higher characteristic velocities, larger sizes, and more angular momentum in the simulation with lower DM mass resolution; haloes have higher central densities and lower velocity dispersions. Above $M_{200}^{\rm spur}$, galaxies and haloes have similar properties in both runs. The differences arise due to spurious heating, which transfers energy from DM to stellar particles, causing galaxies to heat up and haloes to cool down. The value of $M_{200}^{\rm spur}$ can be derived from an empirical disc heating model, and coincides with the mass below which the predicted {\em spurious} velocity dispersion exceeds the {\em measured} velocity dispersion of simulated galaxies. We predict that galaxies in the $100^3\, {\rm Mpc}^3$ \eagle\, run and IllustrisTNG-100 are robust to spurious collisional effects at their half-mass radii provided $M_{200}^{\rm spur}\approx 10^{11.7}{\rm M_\odot}$; for the $25^3\, {\rm Mpc}^3$ \eagle\, run and IllustrisTNG-50, we predict $M_{200}^{\rm spur}\approx 10^{11}{\rm M_\odot}$. Suppressing spurious heating at smaller/larger radii, or for older/younger stellar populations, requires haloes to be resolved with more/fewer DM particles.

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The physical drivers of gas turbulence in simulated disc galaxies

We use the EAGLE cosmological simulations to study the evolution of the vertical velocity dispersion of cold gas, $σ_{z}$, in central disc galaxies and its connection to stellar feedback, gravitational instabilities, cosmological gas accretion and galaxy mergers. To isolate the impact of feedback, we analyse runs that turn off stellar and (or) AGN feedback in addition to a run that includes both. The evolution of $σ_z$ and its dependence on stellar mass and star formation rate in EAGLE are in good agreement with observations. Galaxies hosted by haloes of similar virial mass, $\rm M_{200}$, have similar $σ_z$ values even in runs where feedback is absent. The prevalence of local instabilities in discs is uncorrelated with $σ_z$ at low redshift and becomes only weakly correlated at high redshifts and in galaxies hosted by massive haloes. $σ_z$ correlates most strongly with the specific gas accretion rate onto the disc as well as with the degree of misalignment between the inflowing gas and the disc's rotation axis. These correlations are significant across all redshifts and halo masses, with misaligned accretion being the primary driver of high gas turbulence at redshifts $z \lesssim 1$ and for halo masses $\rm M_{200} \lesssim 10^{11.5} M_{\odot}$. Galaxy mergers increase $σ_z$, but because they are rare in our sample, they play only a minor role in its evolution. Our results suggest that the turbulence of cold gas in EAGLE discs results from a complex interplay of different physical processes whose relative importance depends on halo mass and redshift.

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The impact of spurious collisional heating on the morphological evolution of simulated galactic discs

We use a suite of idealised N-body simulations to study the impact of spurious heating of star particles by dark matter particles on the kinematics and morphology of simulated galactic discs. We find that spurious collisional heating leads to a systematic increase of the azimuthal velocity dispersion ($σ_ϕ$) of stellar particles and a corresponding decrease in their mean azimuthal velocities ($\overline{v}_ϕ$). The rate of heating is dictated primarily by the number of dark matter halo particles (or equivalently, by the dark matter particle mass at fixed halo mass) and by radial gradients in the local dark matter density along the disc; it is largely insensitive to the stellar particle mass. Galaxies within haloes resolved with fewer than $\approx 10^6$ dark matter particles are particularly susceptible to spurious morphological evolution, irrespective of the total halo mass (with even more particles required to prevent heating of the galactic centre). Collisional heating transforms galactic discs from flattened structures into rounder spheroidal systems, causing them to lose rotational support in the process. It also affects the locations of galaxies in standard scaling relations that link their various properties: at fixed stellar mass, it increases the sizes of galaxies, and reduces their mean stellar rotation velocities and specific angular momenta. Our results urge caution when extrapolating simulated galaxy scaling relations to low masses where spurious collisional effects can bias their normalisation, slope and scatter.

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The cosmology dependence of the concentration-mass-redshift relation

The concentrations of dark matter haloes provide crucial information about their internal structure and how it depends on mass and redshift -- the so-called concentration-mass-redshift relation, denoted $c(M,z)$. We present here an extensive study of the cosmology-dependence of $c(M,z)$ that is based on a suite of 72 gravity-only, full N-body simulations in which the following cosmological parameters were varied: $σ_{8}$, $Ω_{\mathrm{M}}$, $Ω_{\mathrm{b}}$, $n_{\mathrm{s}}$, $h$, $M_ν$, $w_{0}$ and $w_{\mathrm{a}}$. We characterize the impact of these parameters on concentrations for different halo masses and redshifts. In agreement with previous works, and for all cosmologies studied, we find that there exists a tight correlation between the characteristic densities of dark matter haloes within their scale radii, $r_{-2}$, and the critical density of the Universe at a suitably defined formation time. This finding, when combined with excursion set modelling of halo formation histories, allows us to accurately predict the concentrations of dark matter haloes as a function of mass, redshift, and cosmology. We use our simulations to test the reliability of a number of published models for predicting halo concentration and highlight when they succeed or fail to reproduce the cosmological $c(M,z)$ relation.

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Drivers of asymmetry in synthetic H I emission-line profiles of galaxies in the EAGLE simulation

We study the shapes of spatially integrated H I emission-line profiles of galaxies in the EAGLE simulation using three separate measures of the profile's asymmetry. We show that the subset of EAGLE galaxies whose gas fractions and stellar masses are consistent with those in the xGASS survey also have similar H I line asymmetries. Central galaxies with symmetric H I line profiles typically correspond to rotationally supported H I and stellar disks, but those with asymmetric line profiles may or may not correspond to dispersion-dominated systems. Galaxies with symmetric H I emission lines are, on average, more gas rich than those with asymmetric lines, and also exhibit systematic differences in their specific star formation rates, suggesting that turbulence generated by stellar or AGN feedback may be one factor contributing to H I line asymmetry. The line asymmetry also correlates strongly with the dynamical state of a galaxy's host dark matter halo: older, more relaxed haloes host more-symmetric galaxies than those hosted by unrelaxed ones. At fixed halo mass, asymmetric centrals tend to be surrounded by a larger number of massive subhaloes than their symmetric counterparts, and also experience higher rates of gas accretion and outflow. At fixed stellar mass, central galaxies have, on average, more symmetric H I emission lines than satellites; for the latter, ram pressure and tidal stripping are significant sources of asymmetry.

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Spurious heating of stellar motions in simulated galactic disks by dark matter halo particles

We use idealized N-body simulations of equilibrium stellar disks embedded within course-grained dark matter haloes to study the effects of spurious collisional heating on disk structure and kinematics. Collisional heating artificially increases the vertical and radial velocity dispersions of disk stars, as well as the thickness and size of disks; the effects are felt at all galacto-centric radii. The integrated effects of collisional heating are determined by the mass of dark matter halo particles (or equivalently, by the number of particles at fixed halo mass), their local density and characteristic velocity dispersion, but are largely insensitive to the stellar particle mass. The effects can therefore be reduced by increasing the mass resolution of dark matter in cosmological simulations, with limited benefits from increasing the baryonic (or stellar) mass resolution. We provide a simple empirical model that accurately captures the effects of spurious collisional heating on the structure and kinematics of simulated disks, and use it to assess the importance of disk heating for simulations of galaxy formation. We find that the majority of state-of-the-art zoom simulations, and a few of the highest-resolution, smallest-volume cosmological runs, are in principle able to resolve thin stellar disks in Milky Way-mass haloes, but most large-volume cosmological simulations cannot. For example, dark matter haloes resolved with fewer than $\approx 10^6$ particles will collisionally heat stars near the stellar half-mass radius such that their vertical velocity dispersion increases by $\gtrsim 10$ per cent of the halo's virial velocity in approximately one Hubble time.

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Pre-processing, group accretion and the orbital trajectories of associated subhaloes

We use a high-resolution cosmological dark matter-only simulation to study the orbital trajectories of haloes and subhaloes in the environs of isolated hosts. We carefully tally all apsis points and use them to distinguish haloes that are infalling for the first time from those that occupy more evolved orbits. We find that roughly 21 per cent of subhaloes within a host's virial radius are currently on first infall, and have not yet reached their first orbital pericentre; roughly 44 per cent are still approaching their first apocentre after infall. For the range of host masses studied, roughly half of all accreted systems were pre-processed prior to infall, and about 20 per cent were accreted in groups. We confirm that the entire population of accreted subhaloes -- often referred to as "associated" subhaloes -- extend far beyond the virial radii of their hosts, with roughly half currently residing at distances that exceed $\approx 1.2\times r_{200}$. Many of these backsplash haloes have gained orbital energy since infall, and occupy extreme orbits that carry them well past their initial turnaround radii. Such extreme orbits are created during the initial accretion and dissolution of loosely bound groups, but also through penetrating encounters between subhaloes on subsequent orbits. The same processes may also give rise to unexpectedly abrupt losses of orbital energy. These effects combine, giving rise to a large variation in the ratio of sequent apocentres for accreted systems. We find that, within 2 virial radii from host centres, the concentrations of first-infall halos are remarkably similar those of isolated field halos, whereas backsplash haloes, as well as systems that were pre-processed, are considerably more concentrated.

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Observational constraints on the slope of the radial acceleration relation at low accelerations

The radial acceleration relation (RAR) locally relates the `observed' acceleration inferred from the dynamics of a system to the acceleration implied by its baryonic matter distribution. The relation as traced by galaxy rotation curves is one-to-one with remarkably little scatter, implying that the dynamics of a system can be predicted simply by measuring its density profile as traced by e.g. stellar light or gas emission lines. Extending the relation to accelerations below those usually probed by practically observable kinematic tracers is challenging, especially once accounting for faintly emitting baryons, such as the putative warm-hot intergalactic medium, becomes important. We show that in the low-acceleration regime, the (inverted) RAR predicts an unphysical, declining enclosed baryonic mass profile for systems with `observed' acceleration profiles steeper than $g_{\rm obs}\propto r^{-1}$ (corresponding to density profiles steeper than isothermal - $ρ(r)\propto r^{-2}$). If the RAR is tantamount to a natural law, such acceleration profiles cannot exist. We apply this argument to test the compatibility of an extrapolation of the rotation curve-derived RAR to low accelerations with data from galaxy-galaxy weak lensing, dwarf spheroidal galaxy stellar kinematic, and outer Milky~Way dynamical measurements, fully independent of the uncertainties inherent in direct measurements of the baryonic matter distribution. In all cases we find that the data weakly favour a break to a steeper low-acceleration slope. Improvements in measurements and modelling of the outer Milky~Way, and weak lensing, seem like the most promising path toward stronger constraints on the low-acceleration behaviour of the RAR.

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The orbital evolution of UFDs and GCs in an evolving Galactic potential

We use the second Gaia data release to investigate the kinematics of 17 ultra-faint dwarf galaxies (UFDs) and 154 globular clusters (GCs) in the Milky Way, focusing on the differences between static and evolving models of the Galactic potential. An evolving potential modifies a satellite's orbit relative to its static equivalent, though the difference is small compared to existing uncertainties on orbital parameters. We find that the UFD Boötes II is likely on its first passage around the Milky Way. Depending on the assumed mass of the Milky Way, the UFDs Triangulum II, Hydrus I, Coma Berenices, Draco II, and Ursa Major II, as well as the GC Pyxis, may also be on first infall so may be useful for constraining the mass of the Galaxy. We identify a clear kinematic distinction between metal-rich (${\rm [Fe/H]}>-1.1$) and metal-poor GCs (${\rm [Fe/H]}\leq-1.1$). Although most metal-rich clusters occupy predominately prograde orbits, with low eccentricities ($e\approx 0.35$) and similar specific angular momenta and orbital planes as the Galactic disc, 7 show potentially retrograde orbits, the origin of which is unclear. Metal-poor clusters have more diverse orbits, higher eccentricities ($e\approx 0.65$), and half have orbital planes offset from the disc by 60 to 120 degrees. The UFDs have similar $θ$ and $ϕ$ to the metal-poor GCs, suggesting a similar origin. We provide a catalogue of orbital parameters for UFDs and GCs for two different Galaxy masses and their observational uncertainties.

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A comparison of $\text{H}_2$ formation models at high redshift

Modelling the molecular gas that is routinely detected through CO observations of high-redshift galaxies constitutes a major challenge for ab initio simulations of galaxy formation. We carry out a suite of cosmological hydrodynamic simulations to compare three approximate methods that have been used in the literature to track the formation and evolution of the simplest and most abundant molecule, H$_2$. Namely, we consider: i) a semi-empirical procedure that associates H$_2$ to dark-matter haloes based on a series of scaling relations inferred from observations, ii) a model that assumes chemical equilibrium between the H$_2$ formation and destruction rates, and iii) a model that fully solves the out-of-equilibrium rate equations and accounts for the unresolved structure of molecular clouds. We study the impact of finite spatial resolution and show that robust H$_2$ masses at redshift $z\approx 4$ can only be obtained for galaxies that are sufficiently metal enriched in which H$_2$ formation is fast. This corresponds to H$_2$ reservoirs with masses $M_{\mathrm{H_2}}\gtrsim 6\times 10^9 \mathrm{M}_\odot$. In this range, equilibrium and non-equilibrium models predict similar molecular masses (but different galaxy morphologies) while the semi-empirical method produces less H$_2$. The star formation rates as well as the stellar and H$_2$ masses of the simulated galaxies are in line with those observed in actual galaxies at similar redshifts that are not massive starbursts. The H$_2$ mass functions extracted from the simulations at $z\approx 4$ agree well with recent observations that only sample the high-mass end. However, our results indicate that most molecular material at high $z$ lies yet undetected in reservoirs with $10^9<M_{\mathrm H_2}<10^{10} \mathrm{M}_\odot$.

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To beta or not to beta: can higher-order Jeans analysis break the mass-anisotropy degeneracy in simulated dwarfs?

We test a non-parametric higher-order Jeans analysis method, GravSphere, on 32 simulated dwarf galaxies comparable to classical Local Group dwarfs like Fornax. The galaxies are selected from the APOSTLE suite of cosmological hydrodynamics simulations with Cold Dark Matter (CDM) and Self-Interacting Dark Matter (SIDM) models, allowing us to investigate cusps and cores in density distributions. We find that, for CDM dwarfs, the recovered enclosed mass profiles have a bias of no more than 10 per cent, with a 50 per cent scatter in the inner regions and a 20 per cent scatter near the half-light radius, consistent with standard mass estimators. The density profiles are also recovered with a bias of no more than 10 per cent and a scatter of 30 per cent in the inner regions. For SIDM dwarfs, the mass and density profiles are recovered within our 95 per cent confidence intervals, but are biased towards cuspy dark matter distributions. This is mainly due to a lack of sufficient constraints from the data. We explore the sources of scatter in the accuracy of the recovered profiles and suggest a $χ^2$ statistic to separate successful models from biased ones. Finally, we show that the uncertainties on the mass profiles obtained with GravSphere are smaller than those for comparable Jeans methods, and that they can be further improved if stronger priors, motivated by cosmological simulations, are placed on the velocity anisotropy. We conclude that GravSphere is a promising Jeans-based approach for modelling dark matter distributions in dwarf galaxies.

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Numerical convergence of hydrodynamical simulations of galaxy formation: the abundance and internal structure of galaxies and their cold dark matter haloes

We address the issue of numerical convergence in cosmological smoothed particle hydrodynamics simulations using a suite of runs drawn from the EAGLE project. Our simulations adopt subgrid models that produce realistic galaxy populations at a fiducial mass and force resolution, but systematically vary the latter in order to study their impact on galaxy properties. We provide several analytic criteria that help guide the selection of gravitational softening for hydrodynamical simulations, and present results from runs that both adhere to and deviate from them. Unlike dark matter-only simulations, hydrodynamical simulations exhibit a strong sensitivity to gravitational softening, and care must be taken when selecting numerical parameters. Our results--which focus mainly on star formation histories, galaxy stellar mass functions and sizes--illuminate three main considerations. First, softening imposes a minimum resolved escape speed, $v_ε$, due to the binding energy between gas particles. Runs that adopt such small softening lengths that $v_ε\gt 10\,{\rm km s^{-1}}$ (the sound speed in ionised $\sim 10^4\,{\rm K}$ gas) suffer from reduced effects of photo-heating. Second, feedback from stars or active galactic nuclei may suffer from numerical over-cooling if the gravitational softening length is chosen below a critical value, $ε_{\rm eFB}$. Third, we note that small softening lengths exacerbate the segregation of stars and dark matter particles in halo centres, often leading to the counter-intuitive result that galaxy sizes {\em increase} as softening is reduced. The structure of dark matter haloes in hydrodynamical runs respond to softening in a way that reflects the sensitivity of their galaxy populations to numerical parameters.

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