EDGE: The sensitivity of ultra-faint dwarfs to a metallicity-dependent initial mass function

Motivated by the observed bottom-light initial mass function (IMF) in faint dwarfs, we study how a metallicity-dependent IMF affects the feedback budget and observables of an ultra-faint dwarf galaxy. We model the evolution of a low-mass (⁠≈8×108M⊙⁠) dark matter halo with cosmological, zoomed hydrodynamical simulations capable of resolving individual supernovae explosions, which we complement with an empirically motivated subgrid prescription for systematic IMF variations. In this framework, at the low gas metallicities typical of faint dwarfs, the IMF of newborn stellar populations becomes top-heavy, increasing the efficiency of supernova and photoionization feedback in regulating star formation. This results in a 100-fold reduction of the final stellar mass of the dwarf compared to a canonical IMF, at fixed dynamical mass. The increase in the feedback budget is none the less met by increased metal production from more numerous massive stars, leading to nearly constant iron content at z = 0. A metallicity-dependent IMF therefore provides a mechanism to produce low-mass (⁠M⋆∼103M⊙⁠), yet enriched (⁠[Fe/H]≈−2⁠) field dwarf galaxies, thus opening a self-consistent avenue to populate the plateau in [Fe/H] at the faintest end of the mass–metallicity relation

VINTERGATAN III: how to reset the metallicity of the Milky Way

Using the cosmological zoom simulation VINTERGATAN, we present a new scenario for the onset of star formation at the metal-poor end of the low-[$\alpha$/Fe] sequence in a Milky Way-like galaxy. In this scenario, the galaxy is fueled by two distinct gas flows. One is enriched by outflows from massive galaxies, but not the other. While the former feeds the inner galactic region, the latter fuels an outer gas disk, inclined with respect to the main galactic plane, and with a significantly poorer chemical content. The first passage of the last major merger galaxy triggers tidal compression in the outer disk, which increases the gas density and eventually leads to star formation, at a metallicity 0.75 dex lower than the inner galaxy. This forms the first stars of the low-[$\alpha$/Fe] sequence. These in situ stars have halo-like kinematics, similarly to what is observed in the Milky Way, due to the inclination of the outer disk which eventually aligns with the inner one via gravitational torques. We show that this tilting disk scenario is likely to be common in Milky-Way like galaxies. This process implies that the low-[$\alpha$/Fe] sequence is populated in situ, simultaneously from two formation channels, in the inner and the outer galaxy, with distinct metallicities. This contrasts with purely sequential scenarios for the assembly of the Milky Way disk and could be tested observationally.Comment: MNRAS in press. Movies available at http://www.astro.lu.se/~florent/vintergatan.ph

EDGE: The sensitivity of ultra-faint dwarfs to a metallicity-dependent initial mass function

We study how an observationally-motivated, metallicity-dependent initial mass function (IMF) affects the feedback budget and observables of an ultra-faint dwarf galaxy. We model the evolution of a low-mass ($\approx 8 \, \times \, 10^{8} \, \rm M_{\odot}$) dark matter halo with cosmological, zoomed hydrodynamical simulations capable of resolving individual supernovae explosions. We complement the EDGE galaxy formation model from Agertz et al. (2020) with a new prescription for IMF variations according to Geha et al. (2013). At the low metallicities typical of faint dwarf galaxies, the IMF becomes top-heavy, increasing the efficiency of supernova and photo-ionization feedback in regulating star formation. This results in a 100-fold reduction of the final stellar mass of the dwarf compared to a canonical IMF, at fixed dynamical mass. The increase in the feedback budget is nonetheless met by increased metal production from more numerous massive stars, leading to nearly constant iron content at $z=0$. A metallicity-dependent IMF therefore provides a mechanism to produce low-mass ($\rm M_{\star}\sim 10^3 \rm M_{\odot}$), yet enriched ($\rm [Fe/H]\approx -2$) field dwarf galaxies, thus opening a self-consistent avenue to populate the plateau in $\rm [Fe/H]$ at the faintest end of the mass-metallicity relation.Comment: Main text 7 pages. Submitted to MNRAS, comments welcom

VINTERGATAN II: the history of the Milky Way told by its mergers

Using the VINTERGATAN cosmological zoom simulation, we explore the contributions of the in situ and accreted material, and the effect of galaxy interactions and mergers in the assembly of a Milky Way-like galaxy. We find that the initial growth phase of galaxy evolution, dominated by repeated major mergers, provides the necessary physical conditions for the assembly of a thick, kinematically hot disk populated by high-[$\alpha$/Fe] stars, formed both in situ and in accreted satellite galaxies. We find that the diversity of evolutionary tracks followed by the simulated galaxy and its progenitors leads to very little overlap of the in situ and accreted populations for any given chemical composition. At a given age, the spread in [$\alpha$/Fe] abundance ratio results from the diversity of physical conditions in VINTERGATAN and its satellites, with an enhancement in [$\alpha$/Fe] found in stars formed during starburst episodes. Later, the cessation of the merger activity promotes the in situ formation of stars in the low-[$\alpha$/Fe] regime, in a radially extended, thin and overall kinematically colder disk, thus establishing chemically bimodal thin and thick disks, in line with observations. We draw links between notable features in the [Fe/H] - [$\alpha$/Fe] plane with their physical causes, and propose a comprehensive formation scenario explaining self-consistently, in the cosmological context, the main observed properties of the Milky Way.Comment: MNRAS in press. Movies available at http://www.astro.lu.se/~florent/vintergatan.ph

EDGE: The origin of scatter in ultra-faint dwarf stellar masses and surface brightnesses

We demonstrate how the least luminous galaxies in the Universe, ultra-faint dwarf galaxies, are sensitive to their dynamical mass at the time of cosmic reionization. We select a low-mass ($\sim \text{1.5} \times 10^{9} \, \text{M}_{\odot}$) dark matter halo from a cosmological volume, and perform zoom hydrodynamical simulations with multiple alternative histories using "genetically modified" initial conditions. Earlier forming ultra-faints have higher stellar mass today, due to a longer period of star formation before their quenching by reionization. Our histories all converge to the same final dynamical mass, demonstrating the existence of extended scatter ($\geq$ 1 dex) in stellar masses at fixed halo mass due to the diversity of possible histories. One of our variants builds less than 2 % of its final dynamical mass before reionization, rapidly quenching in-situ star formation. The bulk of its final stellar mass is later grown by dry mergers, depositing stars in the galaxy's outskirts and hence expanding its effective radius. This mechanism constitutes a new formation scenario for highly diffuse ($\text{r}_{1 /2} \sim 820 \, \text{pc}$, $\sim 32 \, \text{mag arcsec}^2$), metal-poor ($\big[ \mathrm{Fe}\, / \mathrm{H} \big]= -2.9$), ultra-faint ($\mathcal{M}_V= -5.7$) dwarf galaxies within the reach of next-generation low surface brightness surveys.Comment: Minor edits to match the published ApJL version. Results unchange

VINTERGATAN I: The origins of chemically, kinematically and structurally distinct discs in a simulated Milky Way-mass galaxy

Spectroscopic surveys of the Milky Way's stars have revealed spatial, chemical and kinematical structures that encode its history. In this work, we study their origins using a cosmological zoom simulation, VINTERGATAN, of a Milky Way-mass disc galaxy. We find that in connection to the last major merger at $z\sim 1.5$, cosmological accretion leads to the rapid formation of an outer, metal-poor, low-[$\alpha$/Fe] gas disc around the inner, metal-rich galaxy containing the old high-[$\alpha$/Fe] stars. This event leads to a bimodality in [$\alpha$/Fe] over a range of [Fe/H]. A detailed analysis of how the galaxy evolves since $z\sim 1$ is presented. We demonstrate the way in which inside-out growth shapes the radial surface density and metallicity profile and how radial migration preferentially relocates stars from the inner to the outer disc. Secular disc heating is found to give rise to increasing velocity dispersions and scaleheights with stellar age, which together with disc flaring explains several trends observed in the Milky Way, including shallower radial [Fe/H]-profiles above the midplane. We show how the galaxy formation scenario imprints non-trivial mappings between structural associations (i.e. thick and thin discs), velocity dispersions, $\alpha$-enhancements, and ages of stars, e.g. the most metal-poor stars in the low-[$\alpha$/Fe] sequence are found to have a scaleheight comparable to old high-[$\alpha$/Fe] stars. Finally, we illustrate how at low spatial resolution, comparable to the thickness of the galaxy, the proposed pathway to distinct sequences in [$\alpha$/Fe]-[Fe/H] cannot be captured.Comment: 20 pages, MNRAS submitted, comments welcome. Movies available at http://www.astro.lu.se/~florent/vintergatan.ph

Exact S-matrices for supersymmetric sigma models and the Potts model

We study the algebraic formulation of exact factorizable S-matrices for integrable two-dimensional field theories. We show that different formulations of the S-matrices for the Potts field theory are essentially equivalent, in the sense that they can be expressed in the same way as elements of the Temperley-Lieb algebra, in various representations. This enables us to construct the S-matrices for certain nonlinear sigma models that are invariant under the Lie ``supersymmetry'' algebras sl(m+n|n) (m=1,2; n>0), both for the bulk and for the boundary, simply by using another representation of the same algebra. These S-matrices represent the perturbation of the conformal theory at theta=pi by a small change in the topological angle theta. The m=1, n=1 theory has applications to the spin quantum Hall transition in disordered fermion systems. We also find S-matrices describing the flow from weak to strong coupling, both for theta=0 and theta=pi, in certain other supersymmetric sigma models.Comment: 32 pages, 8 figure

EDGE: The shape of dark matter haloes in the faintest galaxies

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 $f_{\rm gas}(r<R_{\rm half}) < 0.06$. These dwarfs are drawn from the Engineering Dwarfs at Galaxy formation's Edge (EDGE) project, using high resolution simulations that allow us to resolve DM halo shapes within the half light radius ($\sim 100\,$pc). We show that gas-poor ultra-faints ($M_{\rm 200c} \leqslant 1.5\times10^9\,$M$_\odot$; $f_{\rm gas} < 10^{-5}$) retain their pristine prolate DM halo shape even when gas, star formation and feedback are included. This could provide a new and robust test of DM models. By contrast, gas-rich ultra-faints ($M_{\rm 200c} > 3\times10^9\,$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 MNRA

Truthmakers and modality

This paper attempts to locate, within an actualist ontology, truthmakers for modal truths: truths of the form or . In section 1 I motivate the demand for substantial truthmakers for modal truths. In section 2 I criticise Armstrong’s account of truthmakers for modal truths. In section 3 I examine essentialism and defend an account of what makes essentialist attributions true, but I argue that this does not solve the problem of modal truth in general. In section 4 I discuss, and dismiss, a theistic account of the source of modal truth proposed by Alexander Pruss. In section 5 I offer a means of (dis)solving the problem