Search

Ongoing large stellar spectroscopic surveys of the Milky Way seek to reconstruct the major events in the assembly history of the Galaxy. Chemical and kinematic observations can be used to separate the contributions of different progenitor galaxies to the present-day stellar halo. Here we compute the number of progenitors that contribute to the accreted stellar halos of simulated Milky Way-like galaxies as a function of radius (the radial diversity) in three suites of models: Bullock & Johnston, Aquarius and Auriga. We show that there are significant differences between the predictions of these three models, beyond the halo-to-halo scatter expected in $\Lambda$CDM. Predictions of diversity from numerical simulations are sensitive to model-dependent assumptions regarding the efficiency of star formation in dwarf galaxies. We compare, at face value, to current constraints on the radial diversity of the Milky Way's accreted halo. These constraints imply that the halo of our Galaxy is dominated by $\sim2$ progenitors in the range $8-45\,\mathrm{kpc}$, in contrast to averages of $7$ progenitors in the Bullock & Johnston models, $3.5$ in Aquarius and $4.2$ in Auriga over the same region. We additionally find that the models with radial diversity most similar to that of the Milky Way are predominantly those with ongoing merger events. The Milky Way therefore appears unusual in having an accreted stellar halo dominated by a small number of progenitors accreted at very early times., Comment: 20 pages, 10 figures, submitted to ApJ. This paper describes the first public release of the particle-tagging stellar halo data from Cooper et al. (2010), see https://github.com/nthu-ga/aquarius-halos

In a hierarchically formed Universe, galaxies accrete smaller systems that tidally disrupt as they evolve in the host's potential. We present a complete catalogue of disrupting galaxies accreted onto Milky Way-mass haloes from the Auriga suite of cosmological magnetohydrodynamic zoom-in simulations. We classify accretion events as intact satellites, stellar streams, or phase-mixed systems based on automated criteria calibrated to a visually classified sample, and match accretions to their counterparts in haloes re-simulated at higher resolution. Most satellites with a bound progenitor at the present day have lost substantial amounts of stellar mass -- 67 per cent have $f_\text{bound} < 0.97$ (our threshold to no longer be considered intact), while 53 per cent satisfy a more stringent $f_\text{bound} < 0.8$. Streams typically outnumber intact systems, contribute a smaller fraction of overall accreted stars, and are substantial contributors at intermediate distances from the host centre ($\sim$0.1 to $\sim$0.7$R_\text{200m}$, or $\sim$35 to $\sim$250 kpc for the Milky Way). We also identify accretion events that disrupt to form streams around massive intact satellites instead of the main host. Streams are more likely than intact or phase-mixed systems to have experienced preprocessing, suggesting this mechanism is important for setting disruption rates around Milky Way-mass haloes. All of these results are preserved across different simulation resolutions, though we do find some hints that satellites disrupt more readily at lower resolution. The Auriga haloes suggest that disrupting satellites surrounding Milky Way-mass galaxies are the norm and that a wealth of tidal features waits to be uncovered in upcoming surveys., Comment: 16+4 pages, 13+2 figures, 1+1 tables. Submitted to MNRAS, comments are welcome

Galaxies like the Milky Way are surrounded by complex populations of satellites at all stages of tidal disruption. In this paper, we present a dynamical study of the disrupting satellite galaxies in the Auriga simulations that are orbiting 28 distinct Milky Way-mass hosts across three resolutions. We find that the satellite galaxy populations are highly disrupted. The majority of satellites that remain fully intact at present day were accreted recently without experiencing more than one pericentre ($n_{\rm peri} \lesssim 1$) and have large apocentres ($r_{\rm apo} \gtrsim 200$ kpc) and pericentres ($r_{\rm peri} \gtrsim 50$ kpc). The remaining satellites have experienced significant tidal disruption and, given full knowledge of the system, would be classified as stellar streams. We find stellar streams in Auriga across the range of pericentres and apocentres of the known Milky Way dwarf galaxy streams and, interestingly, overlapping significantly with the Milky Way intact satellite population. We find no significant change in satellite orbital distributions across resolution. However, we do see substantial halo-to-halo variance of $(r_\text{peri}, r_\text{apo})$ distributions across host galaxies, as well as a dependence of satellite orbits on host halo mass - systems disrupt at larger pericentres and apocentres in more massive hosts. Our results suggest that either cosmological simulations (including, but not limited to, Auriga) are disrupting satellites far too readily, or that the Milky Way's satellites are more disrupted than current imaging surveys have revealed. Future observing facilities and careful mock observations of these systems will be key to revealing the nature of this apparent discrepancy., Comment: 16 pages, 10 figures, 1 table, submitted to MNRAS

We assessed the ability to recover chemical bimodalities in integral-field spectroscopy (IFS) observations of edge-on galaxies, using 24 Milky Way-mass galaxies from the AURIGA zoom-in cosmological simulations. We first analyzed the distribution of single stellar particles in the [Mg/Fe] - [Fe/H] plane. Then we produced mock IFS [Mg/Fe] and [Fe/H] maps of galaxies seen edge on, and considered integrated stellar-population properties (projected and spatially binned). We investigated how the distribution of stars in the [Mg/Fe] - [Fe/H] plane is affected by edge-on projection and spatial binning. Bimodality is preserved while distributions change their shapes. Naturally, broad distributions of individual star particles are narrowed into smaller [Mg/Fe] and [Fe/H] ranges for spatial bins. We observe continuous distributions, bimodal in most cases. The overlap in [Fe/H] is small, and different [Mg/Fe] components show up as peaks instead of sequences (even when the latter are present for individual particles). The larger the spatial bins, the narrower the [Mg/Fe] - [Fe/H] distribution. This narrowing helps amplify the density of different [Mg/Fe] peaks, often leading to a clearer bimodality in mock IFS observations than for original star particles. We have also assessed the correspondence of chemical bimodalities with the distinction between geometric thick and thin disks. Their individual particles have different distributions but mostly overlap in [Mg/Fe] and [Fe/H]. However, integrated properties of geometric thick and thin disks in mock maps do mostly segregate into different regions of the [Mg/Fe] - [Fe/H] plane. In bimodal distributions, they correspond to the two distinct peaks. Our results show that this approach can be used for bimodality studies in future IFS observations of edge-on external galaxies., Comment: 12 pages, 6 figures, accepted for publication in Astronomy & Astrophysics

We study the dependence of the physical and observable properties of the CGM on its halo mass. We analyse 22 simulations from the Auriga suite of high resolution cosmological `zoom-in' simulations at $z=0$ with halo masses $10^{10}~\text{M}_{\odot}\leq\text{M}_{\mathrm{200c}}\leq10^{12}~\text{M}_{\odot}$. We find a larger scatter in temperature and smaller scatter in metallicity in more massive haloes. The scatter of temperature and metallicity as a function of radius increases out to larger radii. The median and scatter of the volume-weighted density and mass-weighted radial velocity show no significant dependence on halo mass. Our results highlight that the CGM is more multiphase in haloes of higher mass. We additionally investigate column densities for HI and the metal ions CIV, OVI, MgII and SiII as a function of stellar mass and radius. We find the HI and metal ion column densities increase with stellar mass at sufficiently large radii ($R\gtrsim{0.2}$R$_{\mathrm{200c}}$). We find good agreement between our HI column densities and observations outside $20$% of the virial radius and overpredict within $20$%. MgII and SiII are similarly overpredicted within $20$% of the virial radius, but drop off steeply at larger radii. Our OVI column densities underpredict observations for stellar masses between $10^{9.7}~\text{M}_{\odot}\leq\text{M}_{\star}<10^{10.8}~\text{M}_{\odot}$ with reasonable agreement at $10^{10.8}~\text{M}_{\odot}$. CIV column densities agree with observational detections above a halo mass of $10^{9.7}~\text{M}_{\odot}$. We find that OVI (MgII) traces the highest (lowest) temperatures, and lowest (highest) density and metallicity. OVI and CIV are photo-ionized (collisionally ionized) at low (high) halo masses with a transition to higher temperatures at $10^{11}~\text{M}_{\odot}$. However, there is no clear trend for the radial velocity of the ions., Comment: 15 pages, 8 figures. Submitted for publication in MNRAS

Optimizing risk-averse objectives in discounted MDPs is challenging because most models do not admit direct dynamic programming equations and require complex history-dependent policies. In this paper, we show that the risk-averse {\em total reward criterion}, under the Entropic Risk Measure (ERM) and Entropic Value at Risk (EVaR) risk measures, can be optimized by a stationary policy, making it simple to analyze, interpret, and deploy. We propose exponential value iteration, policy iteration, and linear programming to compute optimal policies. In comparison with prior work, our results only require the relatively mild condition of transient MDPs and allow for {\em both} positive and negative rewards. Our results indicate that the total reward criterion may be preferable to the discounted criterion in a broad range of risk-averse reinforcement learning domains.

The operation of upcoming ultra-high-energy cosmic-ray, gamma-ray, and neutrino radio-detection experiments, like the Giant Radio Array for Neutrino Detection (GRAND), poses significant computational challenges involving the production of numerous simulations of particle showers and their detection, and a high data throughput. GRANDlib is an open-source software tool designed to meet these challenges. Its primary goal is to perform end-to-end simulations of the detector operation, from the interaction of ultra-high-energy particles, through -- by interfacing with external air-shower simulations -- the ensuing particle shower development and its radio emission, to its detection by antenna arrays and its processing by data-acquisition systems. Additionally, GRANDlib manages the visualization, storage, and retrieval of experimental and simulated data. We present an overview of GRANDlib to serve as the basis of future GRAND analyses., Comment: 11 pages, 9 figures, plus appendices

Self-play via online learning is one of the premier ways to solve large-scale two-player zero-sum games, both in theory and practice. Particularly popular algorithms include optimistic multiplicative weights update (OMWU) and optimistic gradient-descent-ascent (OGDA). While both algorithms enjoy $O(1/T)$ ergodic convergence to Nash equilibrium in two-player zero-sum games, OMWU offers several advantages including logarithmic dependence on the size of the payoff matrix and $\widetilde{O}(1/T)$ convergence to coarse correlated equilibria even in general-sum games. However, in terms of last-iterate convergence in two-player zero-sum games, an increasingly popular topic in this area, OGDA guarantees that the duality gap shrinks at a rate of $O(1/\sqrt{T})$, while the best existing last-iterate convergence for OMWU depends on some game-dependent constant that could be arbitrarily large. This begs the question: is this potentially slow last-iterate convergence an inherent disadvantage of OMWU, or is the current analysis too loose? Somewhat surprisingly, we show that the former is true. More generally, we prove that a broad class of algorithms that do not forget the past quickly all suffer the same issue: for any arbitrarily small $\delta>0$, there exists a $2\times 2$ matrix game such that the algorithm admits a constant duality gap even after $1/\delta$ rounds. This class of algorithms includes OMWU and other standard optimistic follow-the-regularized-leader algorithms., Comment: 27 pages, 4 figures

The Dark Energy Spectroscopic Instrument Milky Way Survey (DESI MWS) will explore the assembly history of the Milky Way by characterising remnants of ancient dwarf galaxy accretion events and improving constraints on the distribution of dark matter in the outer halo. We present mock catalogues that reproduce the selection criteria of MWS and the format of the final MWS data set. These catalogues can be used to test methods for quantifying the properties of stellar halo substructure and reconstructing the Milky Way's accretion history with the MWS data, including the effects of halo-to-halo variance. The mock catalogues are based on a phase-space kernel expansion technique applied to star particles in the Auriga suite of six high-resolution $\Lambda$CDM magneto-hydrodynamic zoom-in simulations. They include photometric properties (and associated errors) used in DESI target selection and the outputs of the MWS spectral analysis pipeline (radial velocity, metallicity, surface gravity, and temperature). They also include information from the underlying simulation, such as the total gravitational potential and information on the progenitors of accreted halo stars. We discuss how the subset of halo stars observable by MWS in these simulations corresponds to their true content and properties. These mock Milky Ways have rich accretion histories, resulting in a large number of substructures that span the whole stellar halo out to large distances and have substantial overlap in the space of orbital energy and angular momentum., Comment: Accepted for publication in MNRAS, 31 pages, 27 figues, 7 tables. The mock catalogues are available at https://data.desi.lbl.gov/public/papers/mws/auridesi/v1

Galactic bars drive the internal evolution of spiral galaxies, while their formation is tightly coupled to the properties of their host galaxy and dark matter halo. To explore what drives bar formation in the cosmological context and how these structures evolve throughout cosmic history, we use the Auriga suite of magneto-hydrodynamical cosmological zoom-in simulations. We find that bars are robust and long-lived structures, and we recover a decreasing bar fraction with increasing redshift which plateaus around $\sim20\%$ at $z\sim3$. We find that bars which form at low and intermediate redshifts grow longer with time, while bars that form at high redshifts are born `saturated' in length, likely due to their merger-induced formation pathway. This leads to a larger bar-to-disc size ratio at high redshifts as compared to the local Universe. We subsequently examine the multi-dimensional parameter space thought to drive bar formation. We find that barred galaxies tend to have lower Toomre $Q$ values at the time of their formation, while we do not find a difference in the gas fraction of barred and unbarred populations when controlling for stellar mass. Barred galaxies tend to be more baryon-dominated at all redshifts, assembling their stellar mass earlier, while galaxies that are baryon-dominated but that do not host a bar, have a higher ex-situ bulge fraction. We explore the implications of the baryon-dominance of barred galaxies on the Tully-Fisher relation, finding an offset from the unbarred relation; confirming this in observations would serve as additional evidence for dark matter, as this behaviour is not readily explained in modified gravity scenarios., Comment: 21 pages including Appendices, 17 figures, submitted to MNRAS

The ability to build and leverage world models is essential for a general-purpose AI agent. Testing such capabilities is hard, in part because the building blocks of world models are ill-defined. We present Elements of World Knowledge (EWOK), a framework for evaluating world modeling in language models by testing their ability to use knowledge of a concept to match a target text with a plausible/implausible context. EWOK targets specific concepts from multiple knowledge domains known to be vital for world modeling in humans. Domains range from social interactions (help/hinder) to spatial relations (left/right). Both, contexts and targets are minimal pairs. Objects, agents, and locations in the items can be flexibly filled in enabling easy generation of multiple controlled datasets. We then introduce EWOK-CORE-1.0, a dataset of 4,374 items covering 11 world knowledge domains. We evaluate 20 openweights large language models (1.3B--70B parameters) across a battery of evaluation paradigms along with a human norming study comprising 12,480 measurements. The overall performance of all tested models is worse than human performance, with results varying drastically across domains. These data highlight simple cases where even large models fail and present rich avenues for targeted research on LLM world modeling capabilities., Comment: 21 pages (11 main), 7 figures. Authors Anna Ivanova, Aalok Sathe, Benjamin Lipkin contributed equally

We investigate the growth of stellar discs in Milky Way-mass galaxies using the magnetohydrodynamical simulations of the Auriga Project in a full cosmological context. We focus on the gas accretion process along the discs, calculating the net, infall and outflow rates as a function of galactocentric distance, and investigate the relation between them and the star formation activity. The stellar distributions of around 70% of the simulated galaxies exhibit an ``inside-out'' pattern, with older (younger) stellar populations preferentially located in the inner (outer) disc regions. In all cases, we find a very tight correlation between the infall, outflow and net accretion rates, as well as between these three quantities and the star formation rate. This is because the amount of gas which is ultimately available for star formation in each radial ring depends not only on the infall rates, but also on the amount of gas leaving the disc in outflows, which directly relates to the local star formation level. Therefore, any of these rates can be used to identify galaxies with inside-out growth. For these galaxies, the correlation between the dominant times of accretion/star formation and disc radius is well fitted by a linear function. We also find that, when averaged over galaxies with formation histories similar to the Milky Way, the simulated accretion rates show a similar evolution (both temporally- and radially-integrated) to the usual accretion prescriptions used in chemical evolution models, although some major differences arise at early times and in the inner disc regions., Comment: 19 pages, 13 figures

Language models are rarely shown fruitful mistakes while training. They then struggle to look beyond the next token, suffering from a snowballing of errors and struggling to predict the consequence of their actions several steps ahead. In this paper, we show how language models can be taught to search by representing the process of search in language, as a flattened string -- a stream of search (SoS). We propose a unified language for search that captures an array of different symbolic search strategies. We demonstrate our approach using the simple yet difficult game of Countdown, where the goal is to combine input numbers with arithmetic operations to reach a target number. We pretrain a transformer-based language model from scratch on a dataset of streams of search generated by heuristic solvers. We find that SoS pretraining increases search accuracy by 25% over models trained to predict only the optimal search trajectory. We further finetune this model with two policy improvement methods: Advantage-Induced Policy Alignment (APA) and Self-Taught Reasoner (STaR). The finetuned SoS models solve 36% of previously unsolved problems, including problems that cannot be solved by any of the heuristic solvers. Our results indicate that language models can learn to solve problems via search, self-improve to flexibly use different search strategies, and potentially discover new ones.

The Wide-field Spectroscopic Telescope (WST) is proposed as a new facility dedicated to the efficient delivery of spectroscopic surveys. This white paper summarises the initial concept as well as the corresponding science cases. WST will feature simultaneous operation of a large field-of-view (3 sq. degree), a high multiplex (20,000) multi-object spectrograph (MOS) and a giant 3x3 sq. arcmin integral field spectrograph (IFS). In scientific capability these requirements place WST far ahead of existing and planned facilities. Given the current investment in deep imaging surveys and noting the diagnostic power of spectroscopy, WST will fill a crucial gap in astronomical capability and work synergistically with future ground and space-based facilities. This white paper shows that WST can address outstanding scientific questions in the areas of cosmology; galaxy assembly, evolution, and enrichment, including our own Milky Way; origin of stars and planets; time domain and multi-messenger astrophysics. WST's uniquely rich dataset will deliver unforeseen discoveries in many of these areas. The WST Science Team (already including more than 500 scientists worldwide) is open to the all astronomical community. To register in the WST Science Team please visit https://www.wstelescope.com/for-scientists/participate, Comment: 194 pages, 66 figures. Comments are welcome (wstelescope@gmail.com)

In this paper, we introduce the first algorithmic framework for Blackwell approachability on the sequence-form polytope, the class of convex polytopes capturing the strategies of players in extensive-form games (EFGs). This leads to a new class of regret-minimization algorithms that are stepsize-invariant, in the same sense as the Regret Matching and Regret Matching$^+$ algorithms for the simplex. Our modular framework can be combined with any existing regret minimizer over cones to compute a Nash equilibrium in two-player zero-sum EFGs with perfect recall, through the self-play framework. Leveraging predictive online mirror descent, we introduce Predictive Treeplex Blackwell$^+$ (PTB$^+$), and show a $O(1/\sqrt{T})$ convergence rate to Nash equilibrium in self-play. We then show how to stabilize PTB$^+$ with a stepsize, resulting in an algorithm with a state-of-the-art $O(1/T)$ convergence rate. We provide an extensive set of experiments to compare our framework with several algorithmic benchmarks, including CFR$^+$ and its predictive variant, and we highlight interesting connections between practical performance and the stepsize-dependence or stepsize-invariance properties of classical algorithms.

Questions combine our mastery of language with our remarkable facility for reasoning about uncertainty. How do people navigate vast hypothesis spaces to pose informative questions given limited cognitive resources? We study these tradeoffs in a classic grounded question-asking task based on the board game Battleship. Our language-informed program sampling (LIPS) model uses large language models (LLMs) to generate natural language questions, translate them into symbolic programs, and evaluate their expected information gain. We find that with a surprisingly modest resource budget, this simple Monte Carlo optimization strategy yields informative questions that mirror human performance across varied Battleship board scenarios. In contrast, LLM-only baselines struggle to ground questions in the board state; notably, GPT-4V provides no improvement over non-visual baselines. Our results illustrate how Bayesian models of question-asking can leverage the statistics of language to capture human priors, while highlighting some shortcomings of pure LLMs as grounded reasoners., Comment: Accepted to CogSci 2024

We study the cosmological evolution of the two-point correlation functions of galactic gas-phase metal distributions using the 28 simulated galaxies from the Auriga Project. Using mock observations of the $z = 0$ snapshots to mimic our past work, we show that the correlation functions of the simulated mock observations are well matched to the correlation functions measured from local galaxy surveys. This comparison suggests that the simulations capture the processes important for determining metal correlation lengths, the key parameter in metallicity correlation functions. We investigate the evolution of metallicity correlations over cosmic time using the true simulation data, showing that individual galaxies undergo no significant systematic evolution in their metal correlation functions from $z\sim 3$ to today. In addition, the fluctuations in metal correlation length are correlated with but lag ahead fluctuations in star formation rate. This suggests that re-arrangement of metals within galaxies occurs at a higher cadence than star formation activity, and is more sensitive to the changes of environment, such as galaxy mergers, gas inflows / outflows, and fly-bys., Comment: 12 pages, 10 figures, 1 table, accepted for publication in MNRAS

Aims. Recent observational studies suggest that feedback from active galactic nuclei (AGNs) may play an important role in the formation and evolution of low-mass dwarf galaxies, an issue that has received little attention from a theoretical perspective. Methods. We investigate this using two sets of 12 cosmological magneto-hydrodynamical simulations of the formation of dwarf galaxies: one set using a version of the AURIGA galaxy formation physics model including AGN feedback and a parallel set with AGN feedback turned off. Results. We show that the full-physics AGN runs satisfactorily reproduce several scaling relations, including the M_ BH-M_*, M_ BH-sigma_* and the baryonic Tully-Fisher relation. We find that the global star formation (SF) of galaxies run with AGN is reduced compared to the one in which AGN has been turned off, suggesting that this type of feedback is a viable way of suppressing SF in low-mass dwarfs, even though none of our galaxies is completely quenched by z=0. Furthermore, we found a tight correlation between the median SF rates and the black-hole-to-stellar mass ratio (M_BH/M_star) in our simulated dwarfs. SF is suppressed due to gas heating in the vicinity of the AGN: less HI gas is available in AGN runs, though the total amount of gas is preserved across the two settings within each galaxy. This indicates that the main effect of AGN feedback in our dwarfs is to heat up and push the gas away from the galaxy's centre rather than expelling it completely. Finally, we show that the two galaxies harbouring the largest BHs have suffered a considerable (up to 65%) reduction in their central dark matter density, pinpointing the role of AGNs in determining the final dark matter mass distribution within dwarf galaxies. This pilot paper highlights the importance of modelling AGN feedback at the lowest mass scales and the impact this can have on dwarf galaxy evolution., Comment: 13 pages, 10 figures and 2 tables Submitted to A&A

We explore the chemodynamical properties of the Galaxy in the azimuthal velocity $V_\phi$ and metallicity [Fe/H] space using red giant stars from Gaia Data Release 3. The row-normalized $V_\phi$-[Fe/H] maps form a coherent sequence from the bulge to the outer disk, clearly revealing the thin/thick disk and the Splash. The metal-rich stars display bar-like kinematics while the metal-poor stars show dispersion-dominated kinematics. The intermediate-metallicity population ($-1<$[Fe/H]$<-0.4$) can be separated into two populations, one that is bar-like, i.e. dynamically cold ($\sigma_{V_R}\sim80$ $\rm km\ s^{-1}$) and fast rotating ($V_\phi\gtrsim100$ $\rm km\ s^{-1}$), and the Splash, which is dynamically hot ($\sigma_{V_R}\sim110$ $\rm km\ s^{-1}$) and slow rotating ($V_\phi\lesssim100$ $\rm km\ s^{-1}$). We compare the observations in the bulge region with an Auriga simulation where the last major merger event occurred $\sim10$ Gyr ago: only stars born around the time of the merger reveal a Splash-like feature in the $V_\phi$-[Fe/H] space, suggesting that the Splash is likely merger-induced, predominantly made-up of heated disk stars and the starburst associated with the last major merger. Since the Splash formed from the proto-disk, its lower metallicity limit coincides with that of the thick disk. The bar formed later from the dynamically hot disk with [Fe/H] $>-1$ dex, with the Splash not participating in the bar formation and growth. Moreover, with a set of isolated evolving $N$-body disk simulations, we confirm that a non-rotating classical bulge can be spun up by the bar and develop cylindrical rotation, consistent with the observation for the metal-poor stars., Comment: ApJ accepted, 20 pages, 15 figures, comments welcome

We present an extended suite of the Auriga cosmological gravo-magnetohydrodynamical "zoom-in" simulations of 40 Milky Way-mass halos and 26 dwarf galaxy-mass halos run with the moving-mesh code Arepo. Auriga adopts the $\Lambda$ Cold Dark Matter ($\Lambda$CDM) cosmogony and includes a comprehensive galaxy formation physics model following the coupled cosmic evolution of dark matter, gas, stars, and supermassive black holes which has been shown to produce numerically well-converged galaxy properties for Milky Way-mass systems. We describe the first public data release of this augmented suite of Auriga simulations, which includes raw snapshots, group catalogues, merger trees, initial conditions, and supplementary data, as well as public analysis tools with worked examples of how to use the data. To demonstrate the value and robustness of the simulation predictions, we analyse a series of low-redshift global properties that compare well with many observed scaling relations, such as the Tully-Fisher relation, the star-forming main sequence, and HI gas fraction/disc thickness. Finally, we show that star-forming gas discs appear to build rotation and velocity dispersion rapidly for $z\gtrsim 3$ before they "settle" into ever-increasing rotation-dispersion ratios ($V/\sigma$). This evolution appears to be in rough agreement with some kinematic measurements from H$\alpha$ observations, and demonstrates an application of how to utilise the released data., Comment: Matches final MNRAS version

Robust Markov Decision Processes (RMDPs) are a widely used framework for sequential decision-making under parameter uncertainty. RMDPs have been extensively studied when the objective is to maximize the discounted return, but little is known for average optimality (optimizing the long-run average of the rewards obtained over time) and Blackwell optimality (remaining discount optimal for all discount factors sufficiently close to 1). In this paper, we prove several foundational results for RMDPs beyond the discounted return. We show that average optimal policies can be chosen stationary and deterministic for sa-rectangular RMDPs but, perhaps surprisingly, that history-dependent (Markovian) policies strictly outperform stationary policies for average optimality in s-rectangular RMDPs. We also study Blackwell optimality for sa-rectangular RMDPs, where we show that {\em approximate} Blackwell optimal policies always exist, although Blackwell optimal policies may not exist. We also provide a sufficient condition for their existence, which encompasses virtually any examples from the literature. We then discuss the connection between average and Blackwell optimality, and we describe several algorithms to compute the optimal average return. Interestingly, our approach leverages the connections between RMDPs and stochastic games.

The Milky Way's last significant merger, the Gaia Enceladus/Sausage (GES), is thought to have taken place between 8-11 Gyr ago. Recent studies in the literature suggest that the bar of the Milky Way is rather old, indicating that it formed at a similar epoch to the GES merger. We investigate the possible link between these events using one of the Auriga cosmological simulations which has salient features in common with the Milky Way, including a last significant merger with kinematic signatures resembling that of the GES. In this simulation, the GES-like merger event triggers tidal forces on the disc, gas inflows and a burst of star formation, with the formation of a bar occuring within 1 Gyr of the first pericentre. To highlight the effects of the merger, we rerun the simulation from z=4 with the progenitors of the GES-like galaxy removed well before the merger time. The consequence is a delay in bar formation by around 2 Gyr, and this new bar forms without any significant external perturbers. We conclude that this Milky Way-like simulation shows a route to the real Milky Way's bar forming around the epoch of the GES merger due to tidal forces on its first pericentre. We explore all Auriga galaxies with GES-like merger events, and find that those with stellar mass ratios below 10% form bars within 1 Gyr of the merger, while bar formation is delayed in the more massive merger scenarios. These include the 4 oldest bars in the simulation suite. Lastly, we note some later morphological differences between the disc of the original simulation and our rerun, in particular that the latter does not grow radially for the final 7 Gyr. Our study suggests that the GES may therefore be responsible for the formation of the Milky Way's bar, as well as for the build-up of its extended disc., Comment: 14 pages, 9 figures, submitted to MNRAS