Feedback from supernovae is often invoked as an important process in limiting star formation, removing gas from galaxies and hence as a determining process in galaxy formation. Here we report on numerical simulations investigating the interaction between supernova explosions and the natal molecular cloud. We also consider the cases with and without previous feedback from the high-mass star in the form of ionising radiation and stellar winds. The supernova is able to find weak points in the cloud and create channels through which it can escape, leaving much of the well shielded cloud largely unaffected. This effect is increased when the channels are pre-existing due to the effects of previous stellar feedback. The expanding supernova deposits its energy in the gas that is in these exposed channels, and hence sweeps up less mass when feedback has already occurred, resulting in faster outflows with less radiative losses. The full impact of the supernova explosion is then able to impact the larger scale of the galaxy in which it abides. We conclude that supernova explosions only have moderate effects on their dense natal environments but that with pre-existing feedback, the energetic effects of the supernova are able to escape and affect the wider scale medium of the galaxy.
Using a semianalytical approach based on the thin-shell approximation, we calculate the long-term evolution of supernova remnants (SNRs) while also accounting for the cosmic rays (CRs) accelerated at their blast waves. Our solution reproduces the results of state-of-the-art hydro simulations across the adiabatic and radiative stages for the gas-only case, and it predicts that typical CR acceleration efficiencies ($\approx 10\%$ ) can boost SNR momentum deposition by a factor of 2--3. This enhancement can become as large as an order of magnitude in environments in which the gas experiences more…
The cataclysmic explosions of massive stars as supernovae are one of the key ingredients of galaxy formation. However, their evolution is not well understood in the presence of magnetic fields or cosmic rays (CRs). We study the expansion of individual supernova remnants (SNRs) using our suite of 3D hydrodynamical (HD), magnetohydrodynamical (MHD) and CRMHD simulations generated using RAMSES. We explore multiple ambient densities, magnetic fields and fractions of supernova energy deposited as CRs ($χ_{\rm CR}$), accounting for cosmic ray anisotropic diffusion and streaming. All our runs have co…
We use magnetohydrodynamical simulations of converging warm neutral medium flows to analyse the formation and global evolution of magnetised and turbulent molecular clouds subject to supernova feedback from massive stars. We show that supernova feedback alone fails to disrupt entire, gravitationally bound, molecular clouds, but is able to disperse small--sized (~10 pc) regions on timescales of less than 1 Myr. Efficient radiative cooling of the supernova remnant as well as strong compression of the surrounding gas result in non-persistent energy and momentum input from the supernovae. However,…
Molecular cloud structure is regulated by stellar feedback in various forms. Two of the most important feedback processes are UV photoionisation and supernovae from massive stars. However, the precise response of the cloud to these processes, and the interaction between them, remains an open question. In particular, we wish to know under which conditions the cloud can be dispersed by feedback, which in turn can give us hints as to how feedback regulates the star formation inside the cloud. We perform a suite of radiative magnetohydrodynamic simulations of a 10^5 solar mass cloud with embedded …
We present a novel set of stellar feedback models, implemented in the moving-mesh code Arepo, designed for galaxy formation simulations with near-parsec (or better) resolution. These include explicit sampling of stars from the IMF, allowing feedback to be linked to individual massive stars, an improved method for the modelling of H II regions, photoelectric heating from a spatially varying FUV field and supernova feedback. We perform a suite of 32 simulations of isolated $M_\mathrm{vir} = 10^{10}\,\mathrm{M_\odot}$ galaxies with a baryonic mass resolution of $20\,\mathrm{M_\odot}$ in order to …
Supernovae are the most energetic stellar events and influence the interstellar medium by their gasdynamics and energetics. By this, both also affect the star formation positively and negatively. In this paper, we review the development of the complexity of investigations aiming at understanding the interchange between supernovae and their released hot gas with the star-forming molecular clouds. Commencing from analytical studies the paper advances to numerical models of supernova feedback from superbubble scales to galaxy structure. We also discuss parametrizations of star-formation and super…
We explore the interplay between supernovae and the ionizing radiation of their progenitors in star forming regions. The relative contributions of these stellar feedback processes are not well understood, particularly on scales greater than a single star forming cloud. We focus predominantly on how they affect the interstellar medium. We re-simulate a 500 pc^2 region from previous work that included photoionization and add supernovae. Over the course of 10 Myr more than 500 supernovae occur in the region. The supernovae remnants cool very quickly in the absence of earlier photoionization, but …
We explore when supernovae can (and cannot) regulate the star formation and bulge growth in galaxies based on a sample of 18 simulated galaxies. The simulations include key physics such as evaporation and conduction, neglected in prior work, and required to correctly model superbubbles resulting from stellar feedback. We show that for galaxies with virial masses $>10^{12}\;M_\odot$, supernovae alone cannot prevent excessive star formation. This failure occurs due to a shutdown of galactic winds, with wind mass loadings falling from $η\sim10$ to $η<1$. In more massive systems, this transfer of …
Feedback from supernovae (SNe) is an essential mechanism that self-regulates the growth of galaxies, and a better model of SN feedback is still needed in galaxy formation simulations. In the first part of this paper, using an Eulerian hydrodynamic code Athena++, we find universal scaling relations for the time evolution of momentum and radius for a superbubble, when the momentum and time are scaled by those at the shell-formation time. In the second part of this paper, we develop an SN feedback model based on the Athena++ simulation results utilizing Voronoi tessellation around each star parti…
Integral field units enable resolved studies of a large number of star-forming regions across entire nearby galaxies, providing insight on the conversion of gas into stars and the feedback from the emerging stellar populations over unprecedented dynamic ranges in terms of spatial scale, star-forming region properties, and environments. We use the VLT/MUSE legacy data set covering the central $35$ arcmin$^{2}$ (${\sim}12$ kpc$^{2}$) of the nearby galaxy NGC 300 to quantify the effect of stellar feedback as a function of the local galactic environment. We extract spectra from emission line regio…
The fraction of hydrogen ionizing photons escaping from galaxies into the intergalactic medium is a critical ingredient in the theory of reionization. We use two zoomed-in, high-resolution (4 pc), cosmological radiation hydrodynamic simulations with adaptive mesh refinement to investigate the impact of two physical mechanisms (supernova feedback and runaway OB stars) on the escape fraction (f_esc) at the epoch of reionization (z>7). We implement a new, physically motivated supernova feedback model that can approximate the Sedov solutions at all (from the free expansion to snowplow) stages. We …
Supernova (SN) explosions are a major feedback mechanism regulating star formation in galaxies through their momentum input. We review the observations of SNRs in radiative stages in the Milky Way to validate the theoretical results on the momentum/energy injection from a single SN explosion. For seven SNRs where we can observe fast-expanding, atomic radiative shells, we show that the shell momentum inferred from HI 21 cm line observations is in the range of (0.5--4.5)$\times 10^5$ $M_\odot$ km s$^{-1}$. In two SNRs (W44 and IC 443), shocked molecular gas with momentum comparable to that of th…
We have recently improved our model of active galactic nucleus (AGN) by attaching the supermassive black hole (SMBH) to a massive nuclear star cluster (NSC). Here we study the effects of this new model in massive, gas-rich galaxies with several simulations of different feedback recipes with the hydrodynamics code RAMSES. These simulations are compared to a reference simulation without any feedback, in which the cooling halo gas is quickly consumed in a burst of star formation. In the presence of strong supernovae (SN) feedback, we observe the formation of a galactic fountain that regulates sta…
What exactly controls star formation in the Galaxy remains controversial. In particular, the role of feedback and magnetic field are still partially understood. We investigate the role played by supernovae feedback and magnetic field onto the star formation and the structure of the Galactic disk. We perform numerical simulations of the turbulent, magnetized, self-gravitating, multi-phase, supernovae regulated ISM within a 1 kpc stratified box. We implemented various schemes for the supernovae. This goes from a random distribution at a fixed rate to distributions for which the supernovae are sp…
We compare 5 sub-grid models for supernova (SN) feedback in adaptive mesh refinement (AMR) simulations of isolated dwarf and L-star disk galaxies with 20-40 pc resolution. The models are thermal dump, stochastic thermal, 'mechanical' (injecting energy or momentum depending on the resolution), kinetic, and delayed cooling feedback. We focus on the ability of each model to suppress star formation and generate outflows. Our highest-resolution runs marginally resolve the adiabatic phase of the feedback events, which correspond to 40 SN explosions, and the first three models yield nearly identical …
A recent comparison by Merritt et al. 2020 of simulated and observed Milky Way-mass galaxies has identified a significant tension between the outskirts ($r>20\kpc$) of the stellar halos in simulated and observed galaxies. Using observations from the Dragonfly telescope and simulated galaxies from the Illustris-TNG100 project, Merritt et al. 2020 finds that the outskirts of stellar halos in simulated galaxies have surface densities $1-2$ dex higher than observed galaxies. In this paper, we compare two suites of 15 simulated Milky Way-like galaxies, each drawn from the same initial conditions, s…
We address a simple model where the Kennicutt-Schmidt (KS) relation between the macroscopic densities of star-formation rate (SFR, $ρ_{\rm sfr}$) and gas ($n$) in galactic discs emerges from self-regulation of the SFR via supernova feedback. It arises from the physics of supernova bubbles, insensitive to the microscopic SFR recipe and not explicitly dependent on gravity. The key is that the filling factor of SFR-suppressed supernova bubbles self-regulates to a constant, $f\sim 0.5$. Expressing the bubble fading radius and time in terms of $n$, the filling factor is $f \propto S\,n^{-s}$ with $…
While feedback from massive stars exploding as supernovae (SNe) is thought to be one of the key ingredients regulating galaxy formation, theoretically it is still unclear how the available energy couples to the interstellar medium and how galactic scale outflows are launched. We present a novel implementation of six sub-grid SN feedback schemes in the moving-mesh code Arepo, including injections of thermal and/or kinetic energy, two parametrizations of delayed cooling feedback and a `mechanical' feedback scheme that injects the correct amount of momentum depending on the relevant scale of the …
We compare an analytic model for the evolution of supernova-driven superbubbles with observations of local and high-redshift galaxies, and the properties of intact HI shells in local star-forming galaxies. Our model correctly predicts the presence of superwinds in local star-forming galaxies (e.g., NGC 253) and the ubiquity of outflows near $z \sim 2$. We find that high-redshift galaxies may `capture' 20-50\% of their feedback momentum in the dense ISM (with the remainder escaping into the nearby CGM), whereas local galaxies may contain $\lesssim$10\% of their feedback momentum from the centra…
Most of the massive elliptical galaxies in the universe stopped forming stars billions of years ago, even though plenty of hot gas remains available for star formation. Here we present compelling evidence indicating that quenching of star formation depends on both black-hole feedback and Type Ia supernova heating. We analyze Chandra X-ray observations of ten massive ellipticals, five with extended, potentially star-forming multiphase gas and five single-phase ellipticals with no star formation. The ratio of cooling time to freefall time at 1--10 kpc in the multiphase galaxies is tc/tff ~10, in…
We use local Cartesian simulations with a vertical gravitational potential to study how supernova (SN) feedback in stratified galactic discs drives turbulence and launches galactic winds. Our analysis includes three disc models with gas surface densities ranging from Milky Way-like galaxies to gas-rich ultra-luminous infrared galaxies (ULIRGs), and two different SN driving schemes (random and correlated with local gas density). In order to isolate the physics of SN feedback, we do not include additional feedback processes. We find that, in these local box calculations, SN feedback excites rela…
We perform high resolution N-body+SPH simulations of isolated Milky-Way-like galaxies and major mergers between them, to investigate the effect of feedback from both an active galactic nucleus (AGN) and supernovae on the galaxy's evolution. Several AGN methods from the literature are used independently and in conjunction with supernova feedback to isolate the most important factors of these feedback processes. We find that in isolated galaxies, supernovae dominate the suppression of star formation but the star formation rate is unaffected by the presence of an AGN. In mergers the converse is t…
We report the results of our study of fractional entropy enhancement in the intra-cluster medium (ICM) of the clusters from the representative XMM-Newton cluster structure survey (REXCESS). We compare the observed entropy profile of these clusters with that expected for the ICM without any feedback, as well as with the introduction of preheating and entropy change due to gas cooling. We make the first estimate of the total, as well as radial, non-gravitational energy deposition up to r500 for a large, nearly flux-limited, sample of clusters. We find that the total energy deposition correspondi…
We have used the NIHAO simulations to explore how supernovae (SNe) affect star formation in galaxies. We find that SN feedback operates on all scales from the interstellar medium (ISM) to several virial radii. SNe regulate star formation by preventing condensation of HI into H$_2$ and by moving cold neutral gas to the hot HII phase. The first effect explains why the cold neutral gas in dwarf galaxies forms stars inefficiently. The second maintains the hot ISM of massive galaxies (HII vents out at lower masses). At $v_{\rm vir}\simeq 67{\rm\,km\,s}^{-1}$, the outflow rate follows the relation: …
We describe a new method for adding a prescribed amount of kinetic energy to simulated gas modeled on a cartesian grid by directly altering grid cells' mass and velocity in a distributed fashion. The method is explored in the context of supernova feedback in high-resolution ($\sim 10$ pc) hydrodynamic simulations of galaxy formation. Resolution-dependence is a primary consideration in our application of the method and simulations of isolated explosions (performed at different resolutions) motivate a resolution-dependent scaling for the injected fraction of kinetic energy that we apply in cosmo…
Stellar winds and supernova (SN) explosions of massive stars ("stellar feedback") create bubbles in the interstellar medium (ISM) and insert newly produced heavy elements and kinetic energy into their surroundings, possibly driving turbulence. Most of this energy is thermalized and immediately removed from the ISM by radiative cooling. The rest is available for driving ISM dynamics. In this work we estimate the amount of feedback energy retained as kinetic energy when the bubble walls have decelerated to the sound speed of the ambient medium. We show that the feedback of the most massive star …
Massive black holes (BHs) inhabit local galaxies, including the Milky Way and some dwarf galaxies. BH formation, occurring at early cosmic times, must account for the properties of BHs in today's galaxies, notably why some galaxies host a BH, and others do not. We investigate the formation, distribution and growth of BH `seeds' by using the adaptive mesh refinement code Ramses. We develop an implementation of BH formation in dense, low-metallicity environments, as advocated by models invoking the collapse of the first generation of stars, or of dense nuclear star clusters. The seed masses are …
Impulsive supernova feedback and non-standard dark matter models, such as self-interacting dark matter (SIDM), are the two main contenders for the role of the dominant core formation mechanism at the dwarf galaxy scale. Here we show that the impulsive supernova cycles that follow episodes of bursty star formation leave distinct features in the distribution function of stars: groups of stars with similar ages and metallicities develop overdense shells in phase space. If cores are formed through supernova feedback, we predict the presence of such features in star-forming dwarf galaxies with core…
Using high-resolution simulations from the FIRE-2 (Feedback In Realistic Environments) project, we study the effects of discreteness in stellar feedback processes on the evolution of galaxies and the properties of the interstellar medium (ISM). We specifically consider the discretization of supernovae (SNe), including hypernovae (HNe), and sampling the initial mass function (IMF). We study these processes in cosmological simulations of dwarf galaxies with $z=0$ stellar masses $M_{\ast}\sim 10^{4}-3\times10^{6}\,M_\odot$ (halo masses $\sim 10^{9}-10^{10}\,M_\odot$). We show that the discrete na…
Using a 1D Lagrangian code specifically designed to assess the impact of multiple, time-resolved supernovae (SNe) from a single star cluster on the surrounding medium, we test three commonly used feedback recipes: delayed cooling (e.g., used in the GASOLINE-2 code), momentum-energy injection (a resolution-dependent transition between momentum-dominated feedback and energy-dominated feedback used, e.g., in the FIRE-2 code), and simultaneous energy injection (e.g., used in the EAGLE simulations). Our work provides an intermediary test for these recipes: we analyse a setting that is more complex …
While the evolution of superbubbles driven by clustered supernovae has been studied by numerous authors, the resulting radial momentum yield is uncertain by as much as an order of magnitude depending on the computational methods and assumed properties of the surrounding interstellar medium (ISM). In this work, we study the origin of these discrepancies, and seek to determine the correct momentum budget for a homogeneous ISM. We carry out 3D hydrodynamic (HD) and magnetohydrodynamic (MHD) simulations of clustered supernova explosions, using a Lagrangian method and checking for convergence with …
We present a semi-analytical model of high redshift galaxy formation. In our model the star formation inside a galaxy is regulated by the feedback from supernova (SNe) driven outflows. We derive a closed analytical form for star formation rate in a single galaxy taking account of the SNe feedback in a self-consistent manner. We show that our model can explain the observed correlation between the stellar mass and the circular velocity of galaxies from dwarf galaxies to massive galaxies of $10^{12} M_\odot$. For small mass dwarf galaxies additional feedback other than supernova feedback is neede…
Supernova (SN) feedback plays a crucial role in simulations of galaxy formation. Because blastwaves from individual SNe occur on scales that remain unresolved in modern cosmological simulations, SN feedback must be implemented as a subgrid model. Differences in the manner in which SN energy is coupled to the local interstellar medium and in which excessive radiative losses are prevented have resulted in a zoo of models used by different groups. However, the importance of the selection of resolution elements around young stellar particles for SN feedback has largely been overlooked. In this wor…
Does supernova feedback regulate the star formation rate in dwarf galaxies?
Universidad Nacional Autónoma de México. Instituto de Radioastronomía y Astrofísica（墨西哥国立自治大学射电天文与天体物理研究所）；Centre de Recherche Astrophysique de Lyon UMR5574, ENS de Lyon, Univ. Lyon1, CNRS, Université de Lyon（里昂天体物理研究中心（UMR5574），里昂高等师范学院，里昂第一大学，法国国家科学研究中心，里昂大学）
Energetic feedback from supernovae (SNe) and from active galactic nuclei (AGN) are both important processes that are thought to control how much gas is able to condense into galaxies and form stars. We show that although both AGN and SNe suppress star formation, they mutually weaken one another's effect by up to an order of magnitude in haloes in the mass range for which both feedback processes are efficient (10^11.25 M_sun < m_200 < 10^12.5 M_sun). These results demonstrate the importance of the simultaneous, non-independent inclusion of these two processes in models of galaxy formation to es…
The characterization of the large amount of gas residing in the galaxy halos, the so called circumgalactic medium (CGM), is crucial to understand galaxy evolution across cosmic time. We focus here on the the cool ($T\sim10^4$ K) phase of this medium around star-forming galaxies in the local universe, whose properties and dynamics are poorly understood. We developed semi-analytical parametric models to describe the cool CGM as an outflow of gas clouds from the central galaxy, as a result of supernova explosions in the disc (galactic wind). The cloud motion is driven by the galaxy gravitational …
It is a major open question which physical processes stop the accretion of gas onto giant molecular clouds (GMCs) and limit the efficiency at which gas is converted into stars within these GMCs. While feedback from supernova explosions has been the popular feedback mechanism included in simulations of galaxy formation and evolution, `early' feedback mechanisms such as stellar winds, photoionisation and radiation pressure are expected to play an important role in dispersing the gas after the onset of star formation. These feedback processes typically take place on small scales ($\sim 10-100$ pc…
According to star formation histories (SFHs), Local Group dwarf galaxies can be broadly classified in two types: those forming most of their stars before $z=2$ (${\it fast}$) and those with more extended SFHs (${\it slow}$). The most precise SFHs are usually derived from deep but not very spatially extended photometric data; this might alter the ratio of old to young stars when age gradients are present. Here we correct for this effect and derive the mass formed in stars by $z=2$ for a sample of 16 Local Group dwarf galaxies. We explore early differences between ${\it fast}$ and ${\it slow}$ d…
Feedback from supernovae is essential to understanding the self-regulation of star formation in galaxies. However, the efficacy of the process in a cosmological context remains unclear due to excessive radiative losses during the shock propagation. To better understand the impact of SN explosions on the evolution of galaxies, we perform a suite of high-resolution (12 pc), zoom-in cosmological simulations of a Milky Way-like galaxy at z=3 with adaptive mesh refinement. We find that SN explosions can efficiently regulate star formation, leading to the stellar mass and metallicity consistent with…
The Characteristic Mass and Energy Conversion Efficiency in the Cusp-Core Transition of Dark Matter Haloes: Implications for Scaling Relations and Supernova feedbacks
University of Tsukuba（筑波大学）；National Institute of Technology, Sendai College（国立仙台高等专门学校）；Tohoku University（东北大学）；The University of Tokyo（东京大学）
Using idealized 1-D Eulerian hydrodynamic simulations, we contrast the behavior of isolated supernovae with the superbubbles driven by multiple, collocated supernovae. Continuous energy injection via successive supernovae going off within the hot/dilute bubble maintains a strong termination shock. This strong shock keeps the superbubble over-pressured and drives the outer shock well after it becomes radiative. Isolated supernovae, in contrast, with no further energy injection, become radiative quite early ($\lesssim 0.1$ Myr, 10s of pc), and stall at scales $\lesssim 100$ pc. We show that isol…
We study the magnetic field evolution of an isolated spiral galaxy, using isolated Milky Way-mass galaxy formation simulations and a novel prescription for magnetohydrodynamic (MHD) supernova feedback. Our main result is that a galactic dynamo can be seeded and driven by supernova explosions, resulting in magnetic fields whose strength and morphology is consistent with observations. In our model, supernovae supply thermal energy, and a low level magnetic field along with their ejecta. The thermal expansion drives turbulence, which serves a dual role by efficiently mixing the magnetic field int…
The recently launched James Webb Space Telescope promises unparalleled advances in our understanding of the first stars and galaxies, but realizing this potential requires cosmological simulations that capture the key physical processes that affected these objects. Here we show that radiative transfer and subgrid turbulent mixing are two such processes. By comparing simulations with and without radiative transfer but with exactly the same physical parameters and subgrid turbulent mixing model, we show that tracking radiative transfer suppresses the Population III (Pop III) star formation densi…
We present numerical simulations of a 15 solar mass star in a suite of idealised environments in order to quantify the amount of energy transmitted to the interstellar medium (ISM). We include models of stellar winds, UV photoionisation and the subsequent supernova based on theoretical models and observations of stellar evolution. The system is simulated in 3D using RAMSES-RT, an Adaptive Mesh Refinement Radiation Hydrodynamics code. We find that stellar winds have a negligible impact on the system owing to their relatively low luminosity compared to the other processes. The main impact of pho…
We study the obscuring structure of circumnuclear disks (CNDs) by considering supernova (SN) feedbacks from nuclear starburst and the effect of anisotropic radiative pressure from AGNs. We suppose that the mass accretion onto a central supermassive black hole (SMBH) is triggered by SN-driven turbulence within CNDs, and we explore how the structures of CNDs depend on the BH mass ($M_{\rm BH}$) and AGN luminosity ($L_{\rm AGN}$). We find that the obscuring fraction ($f_{\rm obs}$) peaks at $\sim10\%$ of the Eddington luminosity ($L_{\rm Edd}$), and its maximal value is $f_\mathrm{obs} \sim 0.6$ …
The mass-dependent interplay of active galacitc nuclei and supernova feedback in shaping the $L_{\rm X}$--$T$ relation of early-type galaxies
Shanghai Astronomical Observatory, Chinese Academy of Sciences（中国科学院上海天文台）；University of Chinese Academy of Sciences（中国科学院大学）；Center for Astronomy and Astrophysics and Department of Physics, Fudan University（复旦大学天文与天体物理中心及物理系）；National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台）
Supernova (SN) explosions play an important role in the development of galactic structures. The energy and momentum imparted on the interstellar medium (ISM) in so-called "supernova feedback" drives turbulence, heats the gas, enriches it with heavy elements, can lead to the formation of new stars or even suppress star formation by disrupting stellar nurseries. In the numerical simulation at the sub-galactic level, not including the energy and momentum of supernovas in the physical description of the problem can also lead to several problems that might partially be resolved by including a descr…
We present a suite of 16 high-resolution hydrodynamic simulations of an isolated dwarf galaxy (gaseous and stellar disk plus a stellar bulge) within an initially cuspy dark matter (DM) halo, including self-interactions between the DM particles (SIDM); as well as stochastic star formation and subsequent supernova feedback (SNF), implemented using the stellar feedback model SMUGGLE. The simulations start from identical initial conditions and we regulate the strength of SIDM and SNF by systematically varying the SIDM momentum transfer cross section and the gas density threshold for star formation…
We use sub-parsec resolution hydrodynamic resimulations of a Milky Way (MW) like galaxy at high redshift to investigate the formation of the MW satellite galaxies. More specifically, we assess the impact of supernova feedback on the dwarf progenitors of these satellite, and the efficiency of a simple instantaneous reionisation scenario in suppressing star formation at the low-mass end of this dwarf distribution. Identifying galaxies in our high redshift simulation and tracking them to z=0 using a dark matter halo merger tree, we compare our results to present-day observations and determine the…
