arXiv subjects

Andrew Wetzel

Publications and source records attributed to Andrew Wetzel.

At least 145 records · Page 8Linked to original sources

arXiv2020

Self-consistent proto-globular cluster formation in cosmological simulations of high-redshift galaxies

We report the formation of bound star clusters in a sample of high-resolution cosmological zoom-in simulations of z>5 galaxies from the FIRE project. We find that bound clusters preferentially form in high-pressure clouds with gas surface densities over 10^4 Msun pc^-2, where the cloud-scale star formation efficiency is near unity and young stars born in these regions are gravitationally bound at birth. These high-pressure clouds are compressed by feedback-driven winds and/or collisions of smaller clouds/gas streams in highly gas-rich, turbulent environments. The newly formed clusters follow a power-law mass function of dN/dM~M^-2. The cluster formation efficiency is similar across galaxies with stellar masses of ~10^7-10^10 Msun at z>5. The age spread of cluster stars is typically a few Myrs and increases with cluster mass. The metallicity dispersion of cluster members is ~0.08 dex in [Z/H] and does not depend on cluster mass significantly. Our findings support the scenario that present-day old globular clusters (GCs) were formed during relatively normal star formation in high-redshift galaxies. Simulations with a stricter/looser star formation model form a factor of a few more/fewer bound clusters per stellar mass formed, while the shape of the mass function is unchanged. Simulations with a lower local star formation efficiency form more stars in bound clusters. The simulated clusters are larger than observed GCs due to finite resolution. Our simulations are among the first cosmological simulations that form bound clusters self-consistently in a wide range of high-redshift galaxies.

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arXiv2020

Variations in the slope of the resolved star-forming main sequence: a tool for constraining the mass of star-forming regions

The correlation between galaxies' integrated stellar masses and star formation rates (the `star formation main sequence'; SFMS) is a well-established scaling relation. Recently, surveys have found a relationship between the star formation rate and stellar mass surface densities on kpc and sub-kpc scales (the `resolved SFMS'; rSFMS). In this work, we demonstrate that the rSFMS emerges naturally in FIRE-2 zoom-in simulations of Milky Way-mass galaxies. We make SFR and stellar mass maps of the simulated galaxies at a variety of spatial resolutions and star formation averaging time-scales and fit the rSFMS using multiple methods from the literature. While the absolute value of the SFMS slope depends on the fitting method, the slope is steeper for longer star formation time-scales and lower spatial resolutions regardless of the fitting method employed. We present a toy model that quantitatively captures the dependence of the simulated galaxies' rSFMS slope on spatial resolution and use it to illustrate how this dependence can be used to constrain the characteristic mass of star-forming clumps.

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arXiv2019

Astro2020 APC White Paper: Theoretical Astrophysics 2020-2030

The past two decades have seen a tremendous investment in observational facilities that promise to reveal new and unprecedented discoveries about the universe. In comparison, the investment in theoretical work is completely dwarfed, even though theory plays a crucial role in the interpretation of these observations, predicting new types of phenomena, and informing observing strategies. In this white paper, we argue that in order to reach the promised critical breakthroughs in astrophysics over the next decade and well beyond, the national agencies must take a serious approach to investment in theoretical astrophysics research. We discuss the role of theory in shaping our understanding of the universe, and then we provide a multi-level strategy, from the grassroots to the national, to address the current underinvestment in theory relative to observational work.

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arXiv2019

Stars made in outflows may populate the stellar halo of the Milky Way

We study stellar-halo formation using six Milky Way-mass galaxies in FIRE-2 cosmological zoom simulations. We find that $5-40\%$ of the outer ($50-300$ kpc) stellar halo in each system consists of $\textit{in-situ}$ stars that were born in outflows from the main galaxy. Outflow stars originate from gas accelerated by super-bubble winds, which can be compressed, cool, and form co-moving stars. The majority of these stars remain bound to the halo and fall back with orbital properties similar to the rest of the stellar halo at $z=0$.In the outer halo, outflow stars are more spatially homogeneous, metal rich, and alpha-element-enhanced than the accreted stellar halo. At the solar location, up to $\sim 10 \%$ of our kinematically-identified halo stars were born in outflows; the fraction rises to as high as $\sim 40\%$ for the most metal-rich local halo stars ([Fe/H] $> -0.5$). We conclude that the Milky Way stellar halo could contain local counterparts to stars that are observed to form in molecular outflows in distant galaxies. Searches for such a population may provide a new, near-field approach to constraining feedback and outflow physics. A stellar halo contribution from outflows is a phase-reversal of the classic halo formation scenario of Eggen, Lynden-Bell $\&$ Sandange, who suggested that halo stars formed in rapidly $\textit{infalling}$ gas clouds. Stellar outflows may be observable in direct imaging of external galaxies and could provide a source for metal-rich, extreme velocity stars in the Milky Way.

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arXiv2019

Reconciling observed and simulated stellar halo masses

We use cosmological hydrodynamical simulations of Milky-Way-mass galaxies from the FIRE project to evaluate various strategies for estimating the mass of a galaxy's stellar halo from deep, integrated-light images. We find good agreement with integrated-light observations if we mimic observational methods to measure the mass of the stellar halo by selecting regions of an image via projected radius relative to the disk scale length or by their surface density in stellar mass . However, these observational methods systematically underestimate the accreted stellar component, defined in our (and most) simulations as the mass of stars formed outside of the host galaxy, by up to a factor of ten, since the accreted component is centrally concentrated and therefore substantially obscured by the galactic disk. Furthermore, these observational methods introduce spurious dependencies of the estimated accreted stellar component on the stellar mass and size of galaxies that can obscure the trends in accreted stellar mass predicted by cosmological simulations, since we find that in our simulations the size and shape of the central galaxy is not strongly correlated with the assembly history of the accreted stellar halo. This effect persists whether galaxies are viewed edge-on or face-on. We show that metallicity or color information may provide a way to more cleanly delineate in observations the regions dominated by accreted stars. Absent additional data, we caution that estimates of the mass of the accreted stellar component from single-band images alone should be taken as lower limits.

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arXiv2019

Constraining Star Formation Histories of Blue Galaxies using the Scatter between Stellar Mass and Halo Mass

We present constraints on the timescale of star formation variability and the correlation between star formation and host halo accretion histories of star-forming (SF) central galaxies from the scatter of the stellar-to-halo mass relation (SHMR). SF galaxies are found to have a tight relationship between their star formation rates and stellar masses on the so-called "star-forming sequence" (SFS), which characterizes their SF histories and $M_*$ growths. Meanwhile, observed SHMR constraints connect $M_*$ growth to halo accretion history. Combining these observed trends with a cosmological $N$-body simulation, we present flexible models that track the SF, $M_*$, and halo accretion histories of SF central galaxies at $z<1$ while reproducing the observed stellar mass function and SFS in SDSS DR7. We find that the scatter in SHMR at $M_h=10^{12}M_\odot$, $σ_{M_*|M_h=10^{12}M_\odot}$, is sensitive to the timescale of star formation variability, $t_{\rm duty}$, and the correlation coefficient, $r$, between SF and halo accretion histories: shorter $t_{\rm duty}$ and higher $r$ both result in tighter $σ_{M_*|M_h=10^{12}M_\odot}$. To reproduce a constant 0.2 dex scatter over $z=1-0$, our models require $t_{\rm duty}\leq1.5$ Gyr for $r=0.99$ or $r>0.6$ for $t_{\rm duty}=0.1$ Gyr. For $r\sim0.6$, as found in the literature, $t_{\rm duty}<0.2$ Gyr is necessary. Meanwhile, to reproduce the tightening of $σ_{M_*|M_h=10^{12}M_\odot}=0.35$ to 0.2 dex from $z=1-0$ in hydrodynamical simulations, our models require $t_{\rm duty}=0.1$ Gyr for $r>0.5$. Although, the lack of consensus on $σ_{M_*|M_h=10^{12}M_\odot}$ at $M_h=10^{12}M_\odot$ and at $z=1$ from observations and galaxy formation models remains the main bottleneck in precisely constraining $r$ and $t_{\rm duty}$, we demonstrate that SHMR can be used to constrain the SF and host halo accretion histories of SF central galaxies.

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arXiv2019

Dwarf Galaxies in CDM, WDM, and SIDM: Disentangling Baryons and Dark Matter Physics

We present a suite of FIRE-2 cosmological zoom-in simulations of isolated field dwarf galaxies, all with masses of $M_\mathrm{halo} \approx 10^{10}\,$M$_\odot$ at $z=0$, across a range of dark matter models. For the first time, we compare how both self-interacting dark matter (SIDM) and/or warm dark matter (WDM) models affect the assembly histories as well as the central density structure in fully hydrodynamical simulations of dwarfs. Dwarfs with smaller stellar half-mass radii (r$_{1/2}<500$ pc) have lower $σ_\star/V_\mathrm{max}$ ratios, reinforcing the idea that smaller dwarfs may reside in halos that are more massive than is naively expected. The majority of dwarfs simulated with self-interactions actually experience contraction of their inner density profiles with the addition of baryons relative to the cores produced in dark-matter-only runs, though the simulated dwarfs are always less centrally dense than in $Λ$CDM. The V$_{1/2}-$r$_{1/2}$ relation across all simulations is generally consistent with observations of Local Field dwarfs, though compact objects such as Tucana provide a unique challenge. Spatially-resolved rotation curves in the central regions ($<400$ pc) of small dwarfs could provide a way to distinguish between CDM, WDM, and SIDM, however: at the masses probed in this simulation suite, cored density profiles in dwarfs with small r$_{1/2}$ values can only originate from dark matter self-interactions.

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arXiv2019

Star formation at the edge of the Local Group: a rising star formation history in the isolated galaxy WLM

We present the star formation history (SFH) of the isolated (D~970 kpc) Local Group dwarf galaxy WLM measured from color-magnitude diagrams constructed from deep Hubble Space Telescope imaging. Our observations include a central (0.5 $r_h$) and outer field (0.7 $ r_h$) that reach below the oldest main sequence turnoff. WLM has no early dominant episode of star formation: 20% of its stellar mass formed by ~12.5 Gyr ago (z~5). It also has an SFR that rises to the present with 50% of the stellar mass within the most recent 5 Gyr (z<0.7). There is evidence of a strong age gradient: the mean age of the outer field is 5 Gyr older than the inner field despite being only 0.4 kpc apart. Some models suggest such steep gradients are associated with strong stellar feedback and dark matter core creation. The SFHs of real isolated dwarf galaxies and those from the the Feedback In Realistic Environment suite are in good agreement for $M_{\star}(z=0) \sim 10^7-10^9 M_{\odot}$, but in worse agreement at lower masses ($M_{\star}(z=0) \sim 10^5-10^7 M_{\odot}$). These differences may be explainable by systematics in the models (e.g., reionization model) and/or observations (HST field placement). We suggest that a coordinated effort to get deep CMDs between HST/JWST (crowded central fields) and WFIRST (wide-area halo coverage) is the optimal path for measuring global SFHs of isolated dwarf galaxies.

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arXiv2019

Dark and luminous satellites of LMC-mass galaxies in the FIRE simulations

Within $Λ$CDM, dwarf galaxies like the Large Magellanic Cloud (LMC) are expected to host numerous dark matter subhalos, several of which should host faint dwarf companions. Recent Gaia proper motions confirm new members of the LMC-system in addition to the previously known SMC, including two classical dwarf galaxies ($M_\ast$ > $10^5$ M$_{\odot}$; Carina and Fornax) as well as several ultra-faint dwarfs (Car2, Car3, Hor1, and Hyd1). We use the Feedback In Realistic Environments (FIRE) simulations to study the dark and luminous (down to ultrafaint masses, $M_\ast$ ~ $6\times10^3$ M$_{\odot}$) substructure population of isolated LMC-mass hosts ($M_\text{200}$ = $1-3\times10^{11}$ M$_{\odot}$) and place the Gaia + DES results in a cosmological context. By comparing number counts of subhalos in simulations with and without baryons, we find that, within 0.2 $r_\text{200}$, LMC-mass hosts deplete ~30% of their substructure, significantly lower than the ~70% of substructure depleted by Milky Way (MW) mass hosts. For our highest resolution runs ($m_\text{bary}$ = 880 M$_{\odot}$), ~5-10 subhalos form galaxies with $M_\ast$ > $10^4$ M$_{\odot}$, in agreement with the 7 observationally inferred pre-infall LMC companions. However, we find steeper simulated luminosity functions than observed, hinting at observation incompleteness at the faint end. The predicted DM content for classical satellites in FIRE agrees with observed estimates for Carina and Fornax, supporting the case for an LMC association. We predict that tidal stripping within the LMC potential lowers the inner dark matter density of ultra faint companions of the LMC. Thus, in addition to their orbital consistency, the low densities of dwarfs Car2, Hyd1, and Hyd2 reinforce their likelihood of Magellanic association.

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arXiv2019

Astro2020 APC White Paper: The Early Career Perspective on the Coming Decade, Astrophysics Career Paths, and the Decadal Survey Process

In response to the need for the Astro2020 Decadal Survey to explicitly engage early career astronomers, the National Academies of Sciences, Engineering, and Medicine hosted the Early Career Astronomer and Astrophysicist Focus Session (ECFS) on October 8-9, 2018 under the auspices of Committee of Astronomy and Astrophysics. The meeting was attended by fifty six pre-tenure faculty, research scientists, postdoctoral scholars, and senior graduate students, as well as eight former decadal survey committee members, who acted as facilitators. The event was designed to educate early career astronomers about the decadal survey process, to solicit their feedback on the role that early career astronomers should play in Astro2020, and to provide a forum for the discussion of a wide range of topics regarding the astrophysics career path. This white paper presents highlights and themes that emerged during two days of discussion. In Section 1, we discuss concerns that emerged regarding the coming decade and the astrophysics career path, as well as specific recommendations from participants regarding how to address them. We have organized these concerns and suggestions into five broad themes. These include (sequentially): (1) adequately training astronomers in the statistical and computational techniques necessary in an era of "big data", (2) responses to the growth of collaborations and telescopes, (3) concerns about the adequacy of graduate and postdoctoral training, (4) the need for improvements in equity and inclusion in astronomy, and (5) smoothing and facilitating transitions between early career stages. Section 2 is focused on ideas regarding the decadal survey itself, including: incorporating early career voices, ensuring diverse input from a variety of stakeholders, and successfully and broadly disseminating the results of the survey.

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arXiv2019

The OSIRIS Lens-Amplified Survey (OLAS) I: Dynamical Effects of Stellar Feedback in Low Mass Galaxies at z ~ 2

We introduce the OSIRIS Lens-Amplified Survey (OLAS), a kinematic survey of gravitationally lensed galaxies at cosmic noon taken with Keck adaptive optics. In this paper we present spatially resolved spectroscopy and nebular emission kinematic maps for 17 star forming galaxies with stellar masses 8 < log($M_*$/$M_{\odot}$) < 9.8 and redshifts 1.2 < z < 2.3. OLAS is designed to probe the stellar mass ($M_*$) and specific star formation rate (sSFR) range where simulations suggest that stellar feedback is most effective at driving gaseous outflows that create galaxy-wide potential fluctuations which can generate dark matter cores. We compare our kinematic data with the trend between sSFR, $M_*$ and H$α$ velocity dispersion, $σ$, from the Feedback In Realistic Environments (FIRE) simulations. Our observations reveal a correlation between sSFR and sigma at fixed $M_*$ that is similar to the trend predicted by simulations: feedback from star formation drives star-forming gas and newly formed stars into more dispersion dominated orbits. The observed magnitude of this effect is in good agreement with the FIRE simulations, in which feedback alters the central density profiles of low mass galaxies, converting dark matter cusps into cores over time. Our data support the scenario that stellar feedback drives gaseous outflows and potential fluctuations, which in turn drive dark matter core formation in dwarf galaxies.

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arXiv2019

Formation, vertex deviation and age of the Milky Way's bulge: input from a cosmological simulation with a late-forming bar

We present the late-time evolution of m12m, a cosmological simulation of a Milky Way-like galaxy from the FIRE project. The simulation forms a bar after redshift z = 0.2. We show that the evolution of the model exhibits behaviours typical of kinematic fractionation, with a bar weaker in older populations, an X-shape traced by the younger, metal-rich populations and a prominent X-shape in the edge-on mean metallicity map. Because of the late formation of the bar in m12m, stars forming after 10 Gyr (z = 0.34) significantly contaminate the bulge, at a level higher than is observed at high latitudes in the Milky Way, implying that its bar cannot have formed as late as in m12m. We also study the model's vertex deviation of the velocity ellipsoid as a function of stellar metallicity and age in the equivalent of Baade's Window. The formation of the bar leads to a non-zero vertex deviation. We find that metal-rich stars have a large vertex deviation (~ 40 degrees), which becomes negligible for metal-poor stars, a trend also found in the Milky Way, despite not matching in detail. We demonstrate that the vertex deviation also varies with stellar age and is large for stars as old as 9 Gyr, while 13 Gyr old stars have negligible vertex deviation. When we exclude stars that have been accreted, the vertex deviation is not significantly changed, demonstrating that the observed variation of vertex deviation with metallicity is not necessarily due to an accreted population.

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arXiv2019

Astro2020 Science White Paper: Construction of an L* Galaxy: the Transformative Power of Wide Fields for Revealing the Past, Present and Future of the Great Andromeda System

The Great Andromeda Galaxy (M31) is the nexus of the near-far galaxy evolution connection and a principal data point for near-field cosmology. Due to its proximity (780 kpc), M31 can be resolved into individual stars like the Milky Way (MW). Unlike the MW, we have the advantage of a global view of M31, enabling M31 to be observed with techniques that also apply to more distant galaxies. Moreover, recent evidence suggests that M31 may have survived a major merger within the last several Gyr, shaping the morphology of its stellar halo and triggering a starburst, while leaving the stellar disk largely intact. The MW and M31 thus provide complementary opportunities for in-depth studies of the disks, halos, and satellites of L* galaxies. Our understanding of the M31 system will be transformed in the 2020s if they include wide field facilities for both photometry (HST-like sensitivity and resolution) and spectroscopy (10-m class telescope, >1 sq. deg. field, highly multiplexed, R~ 3000 to 6000). We focus here on the power of these facilities to constrain the past, present, and future merger history of M31, via chemo-dynamical analyses and star formation histories of phase-mixed stars accreted at early times, as well as stars in surviving tidal debris features, M31's extended disk, and intact satellite galaxies that will eventually be tidally incorporated into the halo. This will yield an unprecedented view of the hierarchical formation of the M31 system and the subhalos that built it into the L* galaxy we observe today.

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arXiv2019

Star formation histories of dwarf galaxies in the FIRE simulations: dependence on mass and Local Group environment

We study star formation histories (SFHs) of $\simeq500$ dwarf galaxies (stellar mass $M_\ast = 10^5 - 10^9\,M_\odot$) from FIRE-2 cosmological zoom-in simulations. We compare dwarfs around individual Milky Way (MW)-mass galaxies, dwarfs in Local Group (LG)-like environments, and true field (i.e. isolated) dwarf galaxies. We reproduce observed trends wherein higher-mass dwarfs quench later (if at all), regardless of environment. We also identify differences between the environments, both in terms of "satellite vs. central" and "LG vs. individual MWvs. isolated dwarf central." Around the individual MW-mass hosts, we recover the result expected from environmental quenching: central galaxies in the "near field" have more extended SFHs than their satellite counterparts, with the former more closely resemble isolated ("true field") dwarfs (though near-field centrals are still somewhat earlier forming). However, this difference is muted in the LG-like environments, where both near-field centrals and satellites have similar SFHs, which resemble satellites of single MW-mass hosts. This distinction is strongest for $M_\ast = 10^6 - 10^7\,M_\odot$ but exists at other masses. Our results suggest that the paired halo nature of the LG may regulate star formation in dwarf galaxies even beyond the virial radii of the MW and Andromeda. Caution is needed when comparing zoom-in simulations targeting isolated dwarf galaxies against observed dwarf galaxies in the LG.

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arXiv2019

A Predicted Correlation Between Age Gradient and Star Formation History in FIRE Dwarf Galaxies

We explore the radial variation of star formation histories in dwarf galaxies simulated with Feedback In Realistic Environments (FIRE) physics. The sample contains 9 low-mass field dwarfs with M_ star = 10^5 - 10^7 M_sun from previous FIRE results, and a new suite of 17 higher mass field dwarfs with M_star = 10^7 - 10^9 M_sun introduced here. We find that age gradients are common in our dwarfs, with older stars dominant at large radii. The strength of the gradient correlates with overall galaxy age such that earlier star formation produces a more pronounced gradient. The relation between formation time and strength of the gradient is driven by both mergers and star-formation feedback. Mergers can both steepen and flatten the age gradient depending on the timing of the merger and star formation history of the merging galaxy. In galaxies without significant mergers, early feedback pushes stars to the outskirts at early times. Interestingly, among galaxies without mergers, those with large dark matter cores have flatter age gradients because these galaxies have more late-time feedback. If real galaxies have age gradients as we predict, stellar population studies that rely on sampling a limited fraction of a galaxy can give a biased view of its global star formation history. We show that central fields can be biased young by a few Gyrs while outer fields are biased old. Fields positioned near the 2D half-light radius will provide the least biased measure of a dwarf galaxy's global star formation history.

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arXiv2018

Be it therefore resolved: Cosmological Simulations of Dwarf Galaxies with Extreme Resolution

We study a suite of extremely high-resolution cosmological FIRE simulations of dwarf galaxies ($M_{\rm halo} \lesssim 10^{10}$$M_{\odot}$), run to $z=0$ with $30 M_{\odot}$ resolution, sufficient (for the first time) to resolve the internal structure of individual supernovae remnants within the cooling radius. Every halo with $M_{\rm halo} \gtrsim 10^{8.6} M_{\odot}$ is populated by a resolved {\em stellar} galaxy, suggesting very low-mass dwarfs may be ubiquitous in the field. Our ultra-faint dwarfs (UFDs; $M_{\ast}<10^{5}\,M_{\odot}$) have their star formation truncated early ($z\gtrsim2$), likely by reionization, while classical dwarfs ($M_{\ast}>10^{5} M_{\odot}$) continue forming stars to $z<0.5$. The systems have bursty star formation (SF) histories, forming most of their stars in periods of elevated SF strongly clustered in both space and time. This allows our dwarf with $M_{\ast}/M_{\rm halo} > 10^{-4}$ to form a dark matter core $>200$pc, while lower-mass UFDs exhibit cusps down to $\lesssim100$pc, as expected from energetic arguments. Our dwarfs with $M_{\ast}>10^{4}\,M_{\odot}$ have half-mass radii ($R_{\rm 1/2}$) in agreement with Local Group (LG) dwarfs; dynamical mass vs. $R_{1/2}$ and the degree of rotational support also resemble observations. The lowest-mass UFDs are below surface brightness limits of current surveys but are potentially visible in next-generation surveys (e.g. LSST). The stellar metallicities are lower than in LG dwarfs; this may reflect pre-enrichment of the LG by the massive hosts or Pop-III stars. Consistency with lower resolution studies implies that our simulations are numerically robust (for a given physical model).

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arXiv2018

FIRE-2 Simulations: Physics versus Numerics in Galaxy Formation

The Feedback In Realistic Environments (FIRE) project explores feedback in cosmological galaxy formation simulations. Previous FIRE simulations used an identical source code (FIRE-1) for consistency. Motivated by the development of more accurate numerics - including hydrodynamic solvers, gravitational softening, and supernova coupling algorithms - and exploration of new physics (e.g. magnetic fields), we introduce FIRE-2, an updated numerical implementation of FIRE physics for the GIZMO code. We run a suite of simulations and compare against FIRE-1: overall, FIRE-2 improvements do not qualitatively change galaxy-scale properties. We pursue an extensive study of numerics versus physics. Details of the star-formation algorithm, cooling physics, and chemistry have weak effects, provided that we include metal-line cooling and star formation occurs at higher-than-mean densities. We present new resolution criteria for high-resolution galaxy simulations. Most galaxy-scale properties are robust to numerics we test, provided: (1) Toomre masses are resolved; (2) feedback coupling ensures conservation, and (3) individual supernovae are time-resolved. Stellar masses and profiles are most robust to resolution, followed by metal abundances and morphologies, followed by properties of winds and circum-galactic media (CGM). Central (~kpc) mass concentrations in massive (L*) galaxies are sensitive to numerics (via trapping/recycling of winds in hot halos). Multiple feedback mechanisms play key roles: supernovae regulate stellar masses/winds; stellar mass-loss fuels late star formation; radiative feedback suppresses accretion onto dwarfs and instantaneous star formation in disks. We provide all initial conditions and numerical algorithms used.

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arXiv2018

How To Model Supernovae in Simulations of Star and Galaxy Formation

We study the implementation of mechanical feedback from supernovae (SNe) and stellar mass loss in galaxy simulations, within the Feedback In Realistic Environments (FIRE) project. We present the FIRE-2 algorithm for coupling mechanical feedback, which can be applied to any hydrodynamics method (e.g. fixed-grid, moving-mesh, and mesh-less methods), and black hole as well as stellar feedback. This algorithm ensures manifest conservation of mass, energy, and momentum, and avoids imprinting 'preferred directions' on the ejecta. We show that it is critical to incorporate both momentum and thermal energy of mechanical ejecta in a self-consistent manner, accounting for SNe cooling radii when they are not resolved. Using idealized simulations of single SN explosions, we show that the FIRE-2 algorithm, independent of resolution, reproduces converged solutions in both energy and momentum. In contrast, common 'fully-thermal' (energy-dump) or 'fully-kinetic' (particle-kicking) schemes in the literature depend strongly on resolution: when applied at mass resolution >100 solar masses, they diverge by orders-of-magnitude from the converged solution. In galaxy-formation simulations, this divergence leads to orders-of-magnitude differences in galaxy properties, unless those models are adjusted in a resolution-dependent way. We show that all models that individually time-resolve SNe converge to the FIRE-2 solution at sufficiently high resolution. However, in both idealized single-SN simulations and cosmological galaxy-formation simulations, the FIRE-2 algorithm converges much faster than other sub-grid models without re-tuning parameters.

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