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At least 1,603 records · Page 89

FIRST DETECTION OF ULTRAVIOLET EMISSION FROM A DETACHED DUST SHELL: GALAXY EVOLUTION EXPLORER OBSERVATIONS OF THE CARBON ASYMPTOTIC GIANT BRANCH STAR U Hya

We present the discovery of an extended ring of ultraviolet (UV) emission surrounding the asymptotic giant branch (AGB) star U Hya in archival observations performed by the Galaxy Evolution Explorer. This is the third discovery of extended UV emission from a carbon AGB star and the first from an AGB star with a detached shell. From imaging and photometric analysis of the FUV and NUV images, we determined that the UV ring has a radius of ∼110'', thus indicating that the emitting material is likely associated with the detached shell seen in the infrared. We find that scattering of the central point source of NUV and FUV emission by the dust shell is negligible. Moreover, we find that scattering of the interstellar radiation field by the dust shell can contribute at most ∼10% of the FUV flux. Morphological and photometric evidence suggests that shocks caused by the star's motion through space and, possibly, shock-excited H{sub 2} molecules are the most likely origins of the UV flux. In contrast to previous examples of extended UV emission from AGB stars, the extended UV emission from U Hya does not show a bow-shock-like structure, which is consistent with a lower space velocity and lower interstellar medium density. This suggests the detached dust shell is the source of the UV-emitting material and can be used to better understand the formation of detached shells.

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Alma resolves the properties of star-forming regions in a dense gas disk at z ∼ 3

We exploit long baseline ALMA submillimeter observations of the lensed star-forming galaxy SDP 81 at z = 3.042 to investigate the properties of the interstellar medium (ISM) on scales of 50–100 pc. The kinematics of the {sup 12}CO gas within this system are well described by a rotationally supported disk with an inclination-corrected rotation speed, v{sub rot} = 320 ± 20 km s{sup −1,} and a dynamical mass of M{sub dyn} = (3.5 ± 1.0)× 10{sup 10} M{sub ⊙} within a radius of 1.5 kpc. The disk is gas-rich and unstable, with a Toomre parameter, Q = 0.30 ± 0.10, and so into star-forming regions with Jeans length L{sub J} ∼ 130 pc. We identify five star-forming regions within the ISM on these scales and show that their scaling relations between luminosity, line widths, and sizes are significantly offset from those typical of molecular clouds in local galaxies (Larson’s relations). These offsets are likely to be caused by the high external hydrostatic pressure for the ISM, P{sub tot}/k{sub B}∼ 40{sub −20}{sup +30} × 10{sup 7} K cm{sup −3}, which is ∼10{sup 4}× higher than the typical ISM pressure in the Milky Way. The physical conditions of the star-forming ISM and giant molecular clouds appear to be similar to those found in the densest environments in the local universe, such as those in the Galactic center.

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IMPACT OF SUPERNOVA AND COSMIC-RAY DRIVING ON THE SURFACE BRIGHTNESS OF THE GALACTIC HALO IN SOFT X-RAYS

The halo of the Milky Way contains a hot plasma with a surface brightness in soft X-rays of the order 10{sup −12} erg cm{sup −2} s{sup −1} deg{sup −2}. The origin of this gas is unclear, but so far numerical models of galactic star formation have failed to reproduce such a large surface brightness by several orders of magnitude. In this paper, we analyze simulations of the turbulent, magnetized, multi-phase interstellar medium including thermal feedback by supernova explosions as well as cosmic-ray feedback. We include a time-dependent chemical network, self-shielding by gas and dust, and self-gravity. Pure thermal feedback alone is sufficient to produce the observed surface brightness, although it is very sensitive to the supernova rate. Cosmic rays suppress this sensitivity and reduce the surface brightness because they drive cooler outflows. Self-gravity has by far the largest effect because it accumulates the diffuse gas in the disk in dense clumps and filaments, so that supernovae exploding in voids can eject a large amount of hot gas into the halo. This can boost the surface brightness by several orders of magnitude. Although our simulations do not reach a steady state, all simulations produce surface brightness values of the same order of magnitude as the observations, with the exact value depending sensitively on the simulation parameters. We conclude that star formation feedback alone is sufficient to explain the origin of the hot halo gas, but measurements of the surface brightness alone do not provide useful diagnostics for the study of galactic star formation.

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Non-LTE modelling of cyanoacetylene: evidence for isomer-specific excitation

ABSTRACT Cyanoacetylene molecules are widespread in the interstellar medium (ISM) and several of its isomers have been detected in cold molecular clouds and circumstellar gas. Accurate estimates of the abundance ratio of cyanoacetylene isomers may provide deep insight into their environment. Such knowledge requires rigorous modelling of the emission spectra based on non-local thermodynamic equilibrium (LTE) radiative transfer calculations. To this end, we computed excitation cross-sections of HC2NC and HNC3 induced by collision with para- and ortho-H2, using a quantum mechanical close-coupling method. Then, by thermally averaging these data, we derived rate coefficients for the first 31 low-lying rotational levels of each isomer for temperatures up to 80 K. For the para-H2 collider, the propensity rules are in favour of rotational transitions involving Δj1 = 2 for both isomers, while for the ortho-H2 collider, Δj1 = 2 and Δj1 = 1 rotational transitions are favoured for HC2NC and HNC3, respectively. A comparison of rate coefficients for the HC3N isomers shows differences up to an order of magnitude, especially at low temperatures. Finally, we performed non-LTE radiative transfer calculations to assess the impact of such variations in the analysis of observations. Our simulation suggests that the lack of collisional data specific to each isomer could lead to errors up to a factor of 2–3 in the excitation temperatures. We expect that these data could help in better understanding the cyanoacetylene chemistry and constraining the nitrogen chemistry in the ISM.

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Cherenkov Telescope Array sensitivity to the putative millisecond pulsar population responsible for the Galactic Centre excess

ABSTRACT The leading explanation of the Fermi Galactic Centre γ-ray excess is the extended emission from an unresolved population of millisecond pulsars (MSPs) in the Galactic bulge. Such a population would, along with the prompt γ-rays, also inject large quantities of electrons/positrons (e±) into the interstellar medium. These e± could potentially inverse-Compton (IC) scatter ambient photons into γ-rays that fall within the sensitivity range of the upcoming Cherenkov Telescope Array (CTA). In this article, we examine the detection potential of CTA to this signature by making a realistic estimation of the systematic uncertainties on the Galactic diffuse emission model at TeV-scale γ-ray energies. We forecast that, in the event that e± injection spectra are harder than E−2, CTA has the potential to robustly discover the IC signature of a putative Galactic bulge MSP population sufficient to explain the Galactic Centre excess for e± injection efficiencies in the range of ≈2.9–74.1 per cent, or higher, depending on the level of mismodelling of the Galactic diffuse emission components. On the other hand, for spectra softer than E−2.5, a reliable CTA detection would require an unphysically large e± injection efficiency of ${\gtrsim} 158{{\ \rm per\ cent}}$. However, even this pessimistic conclusion may be avoided in the plausible event that MSP observational and/or modelling uncertainties can be reduced. We further find that, in the event that an IC signal were detected, CTA can successfully discriminate between an MSP and a dark matter origin for the radiating e±.

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Probing the progenitors of Type Ia supernovae using circumstellar material interaction signatures

This work aims to study different probes of Type Ia supernova (SN Ia) progenitors that have been suggested to be linked to the presence of circumstellar material (CSM). In particular, we have investigated, for the first time, the link between narrow blueshifted Nai D absorption profiles and the presence and strength of the broad high-velocity Caii near-infrared triplet absorption features seen in SNe Ia around maximum light. With the probes exploring different distances from the SN; Nai D > 10 17 cm, high-velocity Caii features < 10 15 cm. For this, we have used a new intermediate-resolution X-shooter spectral sample of 15 SNe Ia. We do not identify a link between these two probes, implying either that, one (or both) is not physically related to the presence of CSM or that the occurrence of CSM at the distance explored by one probe is not linked to its presence at the distance probed by the other. However, the previously identified statistical excess in the presence of blueshifted (over redshifted) Nai D absorption is confirmed in this sample at high significance and is found to be stronger in SNe Ia hosted by late-type galaxies. This excess is difficult to explain as being from an interstellar-medium origin as has been suggested by some recent modelling, as such an origin is not expected to show a bias for blueshifted absorption. However, a circumstellar origin for these features also appears unsatisfactory based on our new results, given the lack of link between the two probes of CSM investigated.

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Alignment of the magnetic field in star-forming regions and why it might be difficult to observe

ABSTRACT Magnetic fields are an important component of the interstellar medium (ISM) and exhibit strongly varying field strengths and a non-trivial correlation with the gas density. Its dynamical impact varies between individual regions of the ISM and correlates with the orientation of the field with respect to the gas structures. Using high-resolution magneto-hydrodynamical simulations of the ISM, we explore the connection between the orientation of the field and the dynamical state of the gas. We find that the onset of gravitational instability in molecular gas above a density of $\rho \sim 10^{-21}\, \mathrm{g\, cm}^{-3}$$(n\sim 400\, \mathrm{cm}^{-3})$ coincides with an alignment of the magnetic field lines and the gas flow. At this transition, the gradient of the density changes from mainly perpendicular to preferentially parallel to the field lines. A connection between the three-dimensional alignment and projected two-dimensional observables is non-trivial, because of a large dispersion of the magnetic field orientation along the line of sight. The turbulent correlation lengths can be small compared to the typical integration lengths. As a consequence, the small-scale signal of the orientation can sensitively depend on the line of sight or the dynamical state of the cloud can fluctuate stochastically or be completely averaged out. With higher spatial resolution more small-scale structures are resolved, which aggravates the link between magneto-hydrodynamical quantities and projected observables.

Girichidis, Philipp (ORCID:0000000293009914)↗

Inelastic rate coefficients for collisions of C 4 H - with H 2

Carbon-chain anions were recently detected in the interstellar medium. These very reactive species are used as tracers of the physical and chemical conditions in a variety of astrophysical environments. However, the local thermodynamic equilibrium conditions are generally not fulfilled in these environments. Therefore, collisional as well as radiative rates are needed to accurately model the observed emission lines. We determine in this work the state-to-state rate coefficients of C 4 H- in collision with both ortho- and para-H 2 . A new ab initio 4D potential energy surface was computed using explicitly correlated coupled-cluster procedures. This surface was then employed to determine rotational excitation and de-excitation cross-sections and rate coefficients for the first 21 rotational levels (up to rotational level j 1 = 20) using the close-coupling method, while the coupled-state approximation was used to extend the calculations up to j 1 = 30. State-to-state rate coefficients were obtained for the temperature range 2–100K. The differences between the ortho- and para-H 2 rate coefficients are found to be small.

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Decoding the star forming properties of gas-rich galaxy pairs

Here we extend the analysis of Bok et al. (2020) in which the H i content of isolated galaxies from the AMIGA (Analysis of the interstellar Medium in Isolated GAlaxies) sample and selected paired galaxies from ALFALFA (Arecibo Legacy Fast ALFA) were examined as a potential driver of galaxy location on the WISE (Wide-field Infrared Survey Explorer) mid-infrared SFR–M * sequence. By further characterizing the isolated and pair galaxy samples, i.e. in terms of optical galaxy morphology, a more detailed and quantitative description of local galaxy environment by way of the local number density (η) and tidal strength (Q) parameters, star formation efficiency (SFE HI ), and H i integrated profile asymmetries, we present plausible pathways for the broadening of the pair sample H i deficiency distribution towards both high and low deficiencies compared to the narrower isolated galaxy sample distribution (i.e. σ PAIRS = 0.34 versus σ AMIGA = 0.28). We associate the gas-rich tail of the pair deficiency distribution with the highest Q values, large profile asymmetries, and low SFEs. From this, we infer that merger activity is enhancing gas supplies, as well as disrupting the efficiency of star formation, via strong gravitational torques. The gas-poor wing of the deficiency distribution appears to be populated with galaxies in denser environments (with larger η values on average), more akin to groups. Despite our gas-rich selection criterion, there is a small population of early-type galaxies in the pair sample, which primarily fall in the positive deficiency wing of the distribution. These results suggest that a combination of a denser galaxy environment, early-type morphology, and higher stellar mass is contributing to the broadening of the deficiency distribution towards larger deficiencies.

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The driving mode of shock-driven turbulence

Turbulence in the interstellar medium (ISM) is crucial in the process of star formation. Shocks produced by supernova explosions, jets, radiation from massive stars, or galactic spiral-arm dynamics are amongst the most common drivers of turbulence in the ISM. However, it is not fully understood how shocks drive turbulence, in particular whether shock driving is a more solenoidal (rotational, divergence-free) or a more compressive (potential, curl-free) mode of driving turbulence. The mode of turbulence driving has profound consequences for star formation, with compressive driving producing three times larger density dispersion, and an order of magnitude higher star formation rate than solenoidal driving. Here, we use hydrodynamical simulations of a shock inducing turbulent motions in a structured, multiphase medium. This is done in the context of a laser-induced shock, propagating into a foam material, in preparation for an experiment to be performed at the National Ignition Facility (NIF). Specifically, we analyse the density and velocity distributions in the shocked turbulent medium, and measure the turbulence driving parameter $b=(\sigma _{\rho /\langle \rho \rangle }^{2\Gamma }-1)^{1/2}(1-\sigma _{\rho /\langle \rho \rangle }^{-2})^{-1/2}\mathcal {M}^{-1}\Gamma ^{-1/2}$, with the density dispersion σρ/<ρ>, the turbulent Mach number $\mathcal {M}$, and the polytropic exponent Γ. Purely solenoidal and purely compressive driving correspond to b ~ 1/3 and b ~ 1, respectively. As a result, using simulations in which a shock is driven into a multiphase medium with structures of different sizes and Γ < 1, we find b ~ 1 for all cases, showing that shock-driven turbulence is consistent with strongly compressive driving.

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Chemical abundances in Seyfert galaxies – Ⅸ. Helium abundance estimates

For the first time, the helium abundance relative to hydrogen (He/H), which relied on direct measurements of the electron temperature, has been derived in the narrow line regions (NLRs) from a local sample of Seyfert 2 nuclei. In view of this, optical emission line intensities [3000 < λ(Å) < 7000] of 65 local Seyfert 2 nuclei (z < 0.2), taken from Sloan Digital Sky Survey Data Release 15 and additional compilation from the literature, were considered. Here we used photoionization model grid to derive an Ionization Correction Factor (ICF) for the neutral helium. The application of this ICF indicates that the NLRs of Seyfert 2 present a neutral helium fraction of ~50 percent in relation to the total helium abundance. We find that Seyfert 2 nuclei present helium abundance ranging from 0.60 to 2.50 times the solar value, while ~85 percent of the sample present oversolar abundance values. The derived (He/H)–(O/H) abundance relation from the Seyfert 2 is stepper than that of star-forming regions (SFs) and this difference could be due to excess of helium injected into the interstellar medium by the winds of Wolf–Rayet stars. From a regression to zero metallicity, by using Seyfert 2 estimates combined with SFs estimates, we obtained a primordial helium mass fraction Y p = 0.2441 ± 0.0037, a value in good agreement with the one inferred from the temperature fluctuations of the cosmic microwave background by the Planck Collaboration, i.e. $Y_{p}^{Planck}$ =0.2471 ± 0.0003.

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Energy balance and Alfvén Mach numbers in compressible magnetohydrodynamic turbulence with a large-scale magnetic field

Energy equipartition is a powerful theoretical tool for understanding astrophysical plasmas. It is invoked, for example, to measure magnetic fields in the interstellar medium (ISM), as evidence for small-scale turbulent dynamo action, and, in general, to estimate the energy budget of star-forming molecular clouds. Here, in this study, we motivate and explore the role of the volume-averaged root-mean-squared (rms) magnetic coupling term between the turbulent, δB , and large-scale, B 0 , fields, $\langle$(δB·B 0 ) 2 $\rangle$$_{V}^{1/2}$. By considering the second moments of the energy balance equations we show that the rms coupling term is in energy equipartition with the volume-averaged turbulent kinetic energy for turbulence with a sub-Alfvénic large-scale field. Under the assumption of exact energy equipartition between these terms, we derive relations for the magnetic and coupling term fluctuations, which provide excellent, parameter-free agreement with time-averaged data from 280 numerical simulations of compressible magnetohydrodynamic (MHD) turbulence. Furthermore, we explore the relation between the turbulent mean field and total Alfvén Mach numbers, and demonstrate that sub-Alfvénic turbulence can only be developed through a strong, large-scale magnetic field, which supports an extremely super-Alfvénic turbulent magnetic field. This means that the magnetic field fluctuations are significantly subdominant to the velocity fluctuations in the sub-Alfvénic large-scale field regime. Throughout our study, we broadly discuss the implications for observations of magnetic fields and understanding the dynamics in the magnetized ISM.

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A GALAH view of the chemical homogeneity and ages of stellar strings identified in Gaia

ABSTRACT The advent of Gaia has led to the discovery of nearly 300 elongated stellar associations (called ‘strings’) spanning hundreds of parsecs in length and mere tens of parsecs in width. These newfound populations present an excellent laboratory for studying the assembly process of the Milky Way thin disc. In this work, we use data from GALAH DR3 to investigate the chemical distributions and ages of 18 newfound stellar populations, 10 of which are strings and 8 of which are compact in morphology. We estimate the intrinsic abundance dispersions in [X/H] of each population and compare them with those of both their local fields and the open cluster (OC) M 67. We find that all but one of these groups are more chemically homogeneous than their local fields. Furthermore, half of the strings, namely Theias 139, 169, 216, 303, and 309, have intrinsic [X/H] dispersions that range between 0.01 and 0.07 dex in most elements, equivalent to those of many OCs. These results provide important new observational constraints on star formation and the chemical homogeneity of the local interstellar medium (ISM). We investigate each population’s Li and chemical clock abundances (e.g. [Sc/Ba], [Ca/Ba], [Ti/Ba], and [Mg/Y]) and find that the ages suggested by chemistry generally support the isochronal ages in all but six structures. This work highlights the unique advantages that chemistry holds in the study of kinematically related stellar groups.

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Using host galaxy spectroscopy to explore systematics in the standardization of Type Ia supernovae

We use stacked spectra of the host galaxies of photometrically identified Type Ia supernovae (SNe Ia) from the Dark Energy Survey (DES) to search for correlations between Hubble diagram residuals and the spectral properties of the host galaxies. Utilizing full spectrum fitting techniques on stacked spectra binned by Hubble residual, we find no evidence for trends between Hubble residuals and properties of the host galaxies that rely on spectral absorption features (<1.3σ), such as stellar population age, metallicity, and mass-to-light ratio. However, we find significant trends between the Hubble residuals and the strengths of [O ii] (4.4σ) and the Balmer emission lines (3σ). These trends are weaker than the well-known trend between Hubble residuals and host galaxy stellar mass (7.2σ) that is derived from broad-band photometry. After light-curve corrections, we see fainter SNe Ia residing in galaxies with larger line strengths. We also find a trend (3σ) between Hubble residual and the Balmer decrement (a measure of reddening by dust) using H β and H γ. The trend, quantified by correlation coefficients, is slightly more significant in the redder SNe Ia, suggesting that the bluer SNe Ia are relatively unaffected by dust in the interstellar medium of the host and that dust contributes to current Hubble diagram scatter impacting the measurement of cosmological parameters.

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The density distribution and physical origins of intermittency in supersonic, highly magnetized turbulence with diverse modes of driving

The probability density function (PDF) of the logarithmic density contrast, s = ln (ρ/ρ 0 ), with gas density ρ and mean density ρ 0 , for hydrodynamical supersonic turbulence is well known to have significant non-Gaussian (intermittent) features that monotonically increase with the turbulent Mach number, M. By studying the mass- and volume-weighted s-PDF for an ensemble of 36 sub-to-trans-Alfvenic mean-field, supersonic, isothermal turbulence simulations with different modes of driving, relevant to molecular gas in the cool interstellar medium, we show that a more intricate picture emerges for the non-Gaussian nature of s. Using four independent measures of the non-Gaussian components, we find hydrodynamical-like structure in the highly magnetized plasma for M≲4. However, for M≳4, the non-Gaussian signatures disappear, leaving approximately Gaussian s-statistics – exactly the opposite of hydrodynamical turbulence in the high-M limit. We also find that the non-Gaussian components of the PDF increase monotonically with more compressive driving modes. To understand the M≲4 non-Gaussian features, we use one-dimensional pencil beams to explore the dynamics along and across the large-scale magnetic field, B 0 . Here we discuss kinetic, density, and magnetic field fluctuations from the pencil beams, and identify physical sources of non-Gaussian components to the PDF as single, strong shocks coupled to fast magnetosonic compressions that form along B 0 . We discuss the Gaussianization of the M≳4 s-fields through the lens of two phenomenologies: the self-similarity of the s-field and homogenization of the dynamical time-scales between the over- and underdense regions in the compressible gas.

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CHANG-ES XXV: H i imaging of nearby edge-on galaxies – Data Release 4

ABSTRACT We present the ${\rm H}\, {\small I}$ distribution of galaxies from the Continuum Haloes in Nearby Galaxies – an EVLA Survey (CHANG-ES). Though the observational mode was not optimized for detecting ${\rm H}\, {\small I}$, we successfully produce ${\rm H}\, {\small I}$ cubes for 19 galaxies. The moment-0 maps from this work are available on CHANG-ES data release website (i.e. https://www.queensu.ca/changes). Our sample is dominated by star-forming, ${\rm H}\, {\small I}$-rich galaxies at distances from 6.27 to 34.1 Mpc. ${\rm H}\, {\small I}$ interferometric images on two of these galaxies (NGC 5792 and UGC 10288) are presented here for the first time, while 12 of our remaining sample galaxies now have better ${\rm H}\, {\small I}$ spatial resolutions and/or sensitivities of intensity maps than those in existing publications. We characterize the average scale heights of the ${\rm H}\, {\small I}$ distributions for a subset of most inclined galaxies (inclination > 80 deg), and compare them to the radio continuum intensity scale heights, which have been derived in a similar way. The two types of scale heights are well correlated, with similar dependence on disc radial extension and star formation rate surface density but different dependence on mass surface density. This result indicates that the vertical distribution of the two components may be governed by similar fundamental physics but with subtle differences.

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State-to-state rate coefficients for HCS+ in rotationally inelastic collisions with H2 at low temperatures

ABSTRACT HCS+ ions have been detected in several regions of the interstellar medium (ISM), but an accurate determination of the chemical-physical conditions in the molecular clouds where this molecule is observed requires detailed knowledge of the collisional rate coefficients with the most common colliders in those environments. In this work, we study the dynamics of rotationally inelastic collisions of HCS+ + H2 at low temperature, and report, for the first time, a set of rate coefficients for this system. We used a recently developed potential energy surface for the HCS+–H2 van der Waals complex and computed state-to-state rotational rate coefficients for the lower rotational states of HCS+ in collision with both para- and ortho-H2, analysing the influence of the computed rate coefficients on the determination of critical densities. Additionally, the computed rate coefficients are compared with those obtained by scaling the ones from HCS+ in collision with He (an approximation that is sometimes used when data is lacking), and large differences are found. Furthermore, the approximation of using the rates for the HCO+ + H2 collision as a rough approximation for those of the HCS+ + H2 system is also evaluated. Finally, the complete set of de-excitation rate coefficients for the lowest 30 rotational states of HCS+ by collision with H2 is reported from 5 to 100 K.

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SILCC – VII. Gas kinematics and multiphase outflows of the simulated ISM at high gas surface densities

ABSTRACT We present magnetohydrodynamic (MHD) simulations of the star-forming multiphase interstellar medium (ISM) in stratified galactic patches with gas surface densities Σgas = 10, 30, 50, and 100 $\mathrm{M_\odot \, pc^{-2}}$. The silcc project simulation framework accounts for non-equilibrium thermal and chemical processes in the warm and cold ISM. The sink-based star formation and feedback model includes stellar winds, hydrogen-ionizing UV radiation, core-collapse supernovae, and cosmic ray (CR) injection and diffusion. The simulations follow the observed relation between Σgas and the star formation rate surface density ΣSFR. CRs qualitatively change the outflow phase structure. Without CRs, the outflows transition from a two-phase (warm and hot at 1 kpc) to a single-phase (hot at 2 kpc) structure. With CRs, the outflow always has three phases (cold, warm, and hot), dominated in mass by the warm phase. The impact of CRs on mass loading decreases for higher Σgas and the mass loading factors of the CR-supported outflows are of order unity independent of ΣSFR. Similar to observations, vertical velocity dispersions of the warm ionized medium (WIM) and the cold neutral medium (CNM) correlate with the star formation rate as $\sigma _\mathrm{z} \propto \Sigma _\mathrm{SFR}^a$, with a ∼ 0.20. In the absence of stellar feedback, we find no correlation. The velocity dispersion of the WIM is a factor ∼2.2 higher than that of the CNM, in agreement with local observations. For $\Sigma _\mathrm{SFR} \gtrsim 1.5 \times 10^{-2}\, \mathrm{M}_\odot \, \mathrm{yr}^{-1}\, \mathrm{kpc}^{-2}$ the WIM motions become supersonic.

Astronomy & Astrophysics↗