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At least 919 records · Page 51

THE IMACS CLUSTER BUILDING SURVEY. III. THE STAR FORMATION HISTORIES OF FIELD GALAXIES

Using data from the IMACS Cluster Building Survey and from nearby galaxy surveys, we examine the evolution of the rate of star formation in field galaxies from z = 0.60 to the present. Fitting the luminosity function to a standard Schechter form, we find a rapid evolution of M{sub B}{sup *} consistent with that found in other deep surveys; at the present epoch M{sub B}{sup *} is evolving at the rate of 0.38 Gyr{sup -1}, several times faster than the predictions of simple models for the evolution of old, coeval galaxies. The evolution of the distribution of specific star formation rates (SSFRs) is also too rapid to explain by such models. We demonstrate that starbursts cannot, even in principle, explain the evolution of the SSFR distribution. However, the rapid evolution of both M{sub B}{sup *} and the SSFR distribution can be explained if some fraction of galaxies have star formation rates characterized by both short rise and fall times and by an epoch of peak star formation more recent than the majority of galaxies. Although galaxies of every stellar mass up to 1.4 Multiplication-Sign 10{sup 11} M{sub Sun} show a range of epochs of peak star formation, the fraction of ''younger'' galaxies falls from about 40% at a mass of 4 Multiplication-Sign 10{sup 10} M{sub Sun} to zero at a mass of 1.4 Multiplication-Sign 10{sup 11} M{sub Sun }. The incidence of younger galaxies appears to be insensitive to the density of the local environment; but does depend on group membership: relatively isolated galaxies are much more likely to be young than are group members.

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THE IMACS CLUSTER BUILDING SURVEY. IV. THE LOG-NORMAL STAR FORMATION HISTORY OF GALAXIES

We present here a simple model for the star formation history (SFH) of galaxies that is successful in describing both the star formation rate density (SFRD) over cosmic time, as well as the distribution of specific star formation rates (sSFRs) of galaxies at the current epoch, and the evolution of this quantity in galaxy populations to a redshift of z = 1. We show first that the cosmic SFRD is remarkably well described by a simple log-normal in time. We next postulate that this functional form for the ensemble is also a reasonable description for the SFHs of individual galaxies. Using the measured sSFRs for galaxies at z {approx} 0 from Paper III in this series, we then construct a realization of a universe populated by such galaxies in which the parameters of the log-normal SFH of each galaxy are adjusted to match the sSFRs at z {approx} 0 as well as fitting, in ensemble, the cosmic SFRD from z = 0 to z = 8. This model predicts, with striking fidelity, the distribution of sSFRs in mass-limited galaxy samples to z = 1; this match is not achieved by other models with a different functional form for the SFHs of individual galaxies, but with the same number of degrees of freedom, suggesting that the log-normal form is well matched to the likely actual histories of individual galaxies. We also impose the sSFR versus mass distributions at higher redshifts from Paper III as constraints on the model, and show that, as previously suggested, some galaxies in the field, particularly low mass galaxies, are quite young at intermediate redshifts. As emphasized in Paper III, starbursts are insufficient to explain the enhanced sSFRs in intermediate redshift galaxies; we show here that a model using only smoothly varying log-normal SFHs for galaxies, which allows for some fraction of the population to have peak star formation at late times, does however fully explain the observations. Finally, we show that this model, constrained in detail only at redshifts z < 1, also produces the main sequence of star-formation observed at 1.5 < z < 2.5, again suggesting that the log-normal SFHs are a close approximation to the actual histories of typical galaxies.

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THE DEPENDENCE OF STAR FORMATION EFFICIENCY ON GAS SURFACE DENSITY

Studies by Lada et al. and Heiderman et al. have suggested that star formation mostly occurs above a threshold in gas surface density {Sigma} of {Sigma}{sub c} {approx} 120 M{sub Sun} pc{sup -2} (A{sub K} {approx} 0.8). Heiderman et al. infer a threshold by combining low-mass star-forming regions, which show a steep increase in the star formation rate per unit area {Sigma}{sub SFR} with increasing {Sigma}, and massive cores forming luminous stars which show a linear relation. We argue that these observations do not require a particular density threshold. The steep dependence of {Sigma}{sub SFR}, approaching unity at protostellar core densities, is a natural result of the increasing importance of self-gravity at high densities along with the corresponding decrease in evolutionary timescales. The linear behavior of {Sigma}{sub SFR} versus {Sigma} in massive cores is consistent with probing dense gas in gravitational collapse, forming stars at a characteristic free-fall timescale given by the use of a particular molecular tracer. The low-mass and high-mass regions show different correlations between gas surface density and the area A spanned at that density, with A {approx} {Sigma}{sup -3} for low-mass regions and A {approx} {Sigma}{sup -1} for the massive cores; this difference, along with the use of differing techniques to measure gas surface density and star formation, suggests that connecting the low-mass regions with massive cores is problematic. We show that the approximately linear relationship between dense gas mass and stellar mass used by Lada et al. similarly does not demand a particular threshold for star formation and requires continuing formation of dense gas. Our results are consistent with molecular clouds forming by galactic hydrodynamic flows with subsequent gravitational collapse.

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Radio constraints on heavily obscured star formation within dark gamma-ray burst host galaxies

Highly dust-obscured starbursting galaxies (submillimeter galaxies and their ilk) represent the most extreme sites of star formation in the distant universe and contribute significantly to overall cosmic star formation beyond z > 1.5. Some stars formed in these environments may also explode as gamma-ray bursts (GRBs) and contribute to the population of 'dark' bursts. Here we present Very Large Array wideband radio-continuum observations of 15 heavily dust-obscured Swift GRBs to search for radio synchrotron emission associated with intense star formation in their host galaxies. Most of these targets (11) are not detected. Of the remaining four objects, one detection is marginal, and for two others we cannot yet rule out the contribution of a long-lived radio afterglow. The final detection is secure, but indicates a star formation rate (SFR) roughly consistent with the dust-corrected UV-inferred value. Most galaxies hosting obscured GRBs are therefore not forming stars at extreme rates, and the amount of optical extinction seen along a GRB afterglow sightline does not clearly correlate with the likelihood that the host has a sufficiently high SFR to be radio-detectable. While some submillimeter galaxies do readily produce GRBs, these GRBs are often not heavily obscured—suggesting that the outer (modestly obscured) parts of these galaxies overproduce GRBs and the inner (heavily obscured) parts underproduce GRBs relative to their respective contributions to star formation, hinting at strong chemical or initial mass function gradients within these systems.

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A CANDELS-3D-HST synergy: Resolved star formation patterns at 0.7 < z < 1.5

We analyze the resolved stellar populations of 473 massive star-forming galaxies at 0.7 < z < 1.5, with multi-wavelength broadband imaging from CANDELS and Hα surface brightness profiles at the same kiloparsec resolution from 3D-HST. Together, this unique data set sheds light on how the assembled stellar mass is distributed within galaxies, and where new stars are being formed. We find the Hα morphologies to resemble more closely those observed in the ACS I band than in the WFC3 H band, especially for the larger systems. We next derive a novel prescription for Hα dust corrections, which accounts for extra extinction toward H II regions. The prescription leads to consistent star formation rate (SFR) estimates and reproduces the observed relation between the Hα/UV luminosity ratio and visual extinction, on both a pixel-by-pixel and a galaxy-integrated level. We find the surface density of star formation to correlate with the surface density of assembled stellar mass for spatially resolved regions within galaxies, akin to the so-called 'main sequence of star formation' established on a galaxy-integrated level. Deviations from this relation toward lower equivalent widths are found in the inner regions of galaxies. Clumps and spiral features, on the other hand, are associated with enhanced Hα equivalent widths, bluer colors, and higher specific SFRs compared to the underlying disk. Their Hα/UV luminosity ratio is lower than that of the underlying disk, suggesting that the ACS clump selection preferentially picks up those regions of elevated star formation activity that are the least obscured by dust. Our analysis emphasizes that monochromatic studies of galaxy structure can be severely limited by mass-to-light ratio variations due to dust and spatially inhomogeneous star formation histories.

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Tracing the mass growth and star formation rate evolution of massive galaxies from Z ∼ 6 to Z ∼ 1 in the Hubble ultra-deep field

We present an analysis of an H {sub 160}-selected photometric catalog of galaxies in the Hubble Ultra-Deep Field, using imaging from the WFC3/IR camera on the Hubble Space Telescope in combination with archival ultraviolet, optical, and near-infrared imaging. Using these data, we measure the spectral energy distributions of ∼1500 galaxies to a limiting H {sub 160} magnitude of 27.8, from which we fit photometric redshifts and stellar population estimates for all galaxies with well-determined Spitzer IRAC fluxes, allowing for the determination of the cumulative mass function within the range 1 < z < 6. By selecting samples of galaxies at a constant cumulative number density, we are able to explore the coevolution of stellar masses and star formation rates (SFRs) for progenitor galaxies and their descendants from z ∼ 6. We find a steady increase in the SFRs of galaxies at constant number density from z ∼ 6 to z ∼ 3, accompanied by gradually declining specific star formation rates (sSFRs) during this same period. The peak epoch of star formation is also found to shift to later times for galaxies with increasing number densities, in agreement with the expectations from cosmic downsizing. The observed SFRs can fully account for the mass growth to z ∼ 2 among galaxies with cumulative number densities greater than 10{sup –3.5} Mpc{sup –3}. For galaxies with a lower constant number density (higher mean mass), we find the observed stellar masses are ∼three times greater than that which may be accounted for by the observed star formation alone at late times, implying that growth from mergers plays an important role at z < 2. We additionally observe a decreasing sSFR, equivalent to approximately one order of magnitude, from z ∼ 6 to z ∼ 2 among galaxies with number densities less than 10{sup –3.5} Mpc{sup –3}, along with significant evidence that at any redshift the sSFR is higher for galaxies at higher number density. The combination of these findings can qualitatively explain the previous findings of a specific star formation rate plateau at high redshift. Tracing the evolution of the fraction of quiescent galaxies for samples matched in cumulative number density over this redshift range, we find no unambiguous examples of quiescent galaxies at z > 4.

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Inside-out planet formation

The compact multi-transiting planet systems discovered by Kepler challenge planet formation theories. Formation in situ from disks with radial mass surface density, Σ, profiles similar to the minimum mass solar nebula but boosted in normalization by factors ≳ 10 has been suggested. We propose that a more natural way to create these planets in the inner disk is formation sequentially from the inside-out via creation of successive gravitationally unstable rings fed from a continuous stream of small (∼cm-m size) 'pebbles', drifting inward via gas drag. Pebbles collect at the pressure maximum associated with the transition from a magnetorotational instability (MRI)-inactive ('dead zone') region to an inner MRI-active zone. A pebble ring builds up until it either becomes gravitationally unstable to form an ∼1 M {sub ⊕} planet directly or induces gradual planet formation via core accretion. The planet may undergo Type I migration into the active region, allowing a new pebble ring and planet to form behind it. Alternatively, if migration is inefficient, the planet may continue to accrete from the disk until it becomes massive enough to isolate itself from the accretion flow. A variety of densities may result depending on the relative importance of residual gas accretion as the planet approaches its isolation mass. The process can repeat with a new pebble ring gathering at the new pressure maximum associated with the retreating dead-zone boundary. Our simple analytical model for this scenario of inside-out planet formation yields planetary masses, relative mass scalings with orbital radius, and minimum orbital separations consistent with those seen by Kepler. It provides an explanation of how massive planets can form with tightly packed and well-aligned system architectures, starting from typical protoplanetary disk properties.

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Cosmological constraints from galaxy clustering and the mass-to-number ratio of galaxy clusters: marginalizing over the physics of galaxy formation

Many approaches to obtaining cosmological constraints rely on the connection between galaxies and dark matter. However, the distribution of galaxies is dependent on their formation and evolution as well as on the cosmological model, and galaxy formation is still not a well-constrained process. Thus, methods that probe cosmology using galaxies as tracers for dark matter must be able to accurately estimate the cosmological parameters. This can be done without knowing details of galaxy formation a priori as long as the galaxies are well represented by a halo occupation distribution (HOD). We apply this reasoning to the method of obtaining Ω {sub m} and σ{sub 8} from galaxy clustering combined with the mass-to-number ratio of galaxy clusters. To test the sensitivity of this method to variations due to galaxy formation, we consider several different models applied to the same cosmological dark matter simulation. The cosmological parameters are then estimated using the observables in each model, marginalizing over the parameters of the HOD. We find that for models where the galaxies can be well represented by a parameterized HOD, this method can successfully extract the desired cosmological parameters for a wide range of galaxy formation prescriptions.

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The role of turbulence in star formation laws and thresholds

The Schmidt-Kennicutt relation links the surface densities of gas to the star formation rate in galaxies. The physical origin of this relation, and in particular its break, i.e., the transition between an inefficient regime at low gas surface densities and a main regime at higher densities, remains debated. Here, we study the physical origin of the star formation relations and breaks in several low-redshift galaxies, from dwarf irregulars to massive spirals. We use numerical simulations representative of the Milky Way and the Large and Small Magellanic Clouds with parsec up to subparsec resolution, and which reproduce the observed star formation relations and the relative variations of the star formation thresholds. We analyze the role of interstellar turbulence, gas cooling, and geometry in drawing these relations at 100 pc scale. We suggest in particular that the existence of a break in the Schmidt-Kennicutt relation could be linked to the transition from subsonic to supersonic turbulence and is independent of self-shielding effects. With this transition being connected to the gas thermal properties and thus to the metallicity, the break is shifted toward high surface densities in metal-poor galaxies, as observed in dwarf galaxies. Our results suggest that together with the collapse of clouds under self-gravity, turbulence (injected at galactic scale) can induce the compression of gas and regulate star formation.

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Modeling jet and outflow feedback during star cluster formation

Powerful jets and outflows are launched from the protostellar disks around newborn stars. These outflows carry enough mass and momentum to transform the structure of their parent molecular cloud and to potentially control star formation itself. Despite their importance, we have not been able to fully quantify the impact of jets and outflows during the formation of a star cluster. The main problem lies in limited computing power. We would have to resolve the magnetic jet-launching mechanism close to the protostar and at the same time follow the evolution of a parsec-size cloud for a million years. Current computer power and codes fall orders of magnitude short of achieving this. In order to overcome this problem, we implement a subgrid-scale (SGS) model for launching jets and outflows, which demonstrably converges and reproduces the mass, linear and angular momentum transfer, and the speed of real jets, with ∼1000 times lower resolution than would be required without the SGS model. We apply the new SGS model to turbulent, magnetized star cluster formation and show that jets and outflows (1) eject about one-fourth of their parent molecular clump in high-speed jets, quickly reaching distances of more than a parsec, (2) reduce the star formation rate by about a factor of two, and (3) lead to the formation of ∼1.5 times as many stars compared to the no-outflow case. Most importantly, we find that jets and outflows reduce the average star mass by a factor of ∼ three and may thus be essential for understanding the characteristic mass of the stellar initial mass function.

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The formation of massive primordial stars in the presence of moderate UV backgrounds

Radiative feedback produced by stellar populations played a vital role in early structure formation. In particular, photons below the Lyman limit can escape the star-forming regions and produce a background ultraviolet (UV) flux, which consequently may influence the pristine halos far away from the radiation sources. These photons can quench the formation of molecular hydrogen by photodetachment of H{sup –}. In this study, we explore the impact of such UV radiation on fragmentation in massive primordial halos of a few times 10{sup 7} M {sub ☉}. To accomplish this goal, we perform high resolution cosmological simulations for two distinct halos and vary the strength of the impinging background UV field in units of J {sub 21} assuming a blackbody radiation spectrum with a characteristic temperature of T {sub rad} = 10{sup 4} K. We further make use of sink particles to follow the evolution for 10,000 yr after reaching the maximum refinement level. No vigorous fragmentation is observed in UV-illuminated halos while the accretion rate changes according to the thermal properties. Our findings show that a few 10{sup 2}-10{sup 4} solar mass protostars are formed when halos are irradiated by J {sub 21} = 10-500 at z > 10 and suggest a strong relation between the strength of the UV flux and mass of a protostar. This mode of star formation is quite different from minihalos, as higher accretion rates of about 0.01-0.1 M {sub ☉} yr{sup –1} are observed by the end of our simulations. The resulting massive stars are potential cradles for the formation of intermediate-mass black holes at earlier cosmic times and contribute to the formation of a global X-ray background.

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Star formation trends in the unrelaxed, post-merger cluster A2255

The effects of dense environments on normal field galaxies are still up for debate despite much study since Abell published his catalog of nearby clusters in 1958. There are changes in color, morphology, and star formation properties when galaxies fall into groups and clusters, but the specifics of how and where these modifications occur are not fully understood. To look for answers, we focused on star-forming galaxies in A2255, an unrelaxed cluster thought to have recently experienced a merger with another cluster or large group. We used Hα, MIPS 24 μm, and WISE 22 μm to estimate total star formation rates (SFRs) and Sloan Digital Sky Survey photometry to find stellar masses (M {sub *}) for galaxies out to ∼5 r {sub 200}. We compared the star-forming cluster galaxies with the field SFR-mass distribution and found no enhancement or suppression of star formation in currently star-forming galaxies of high mass (log (M {sub *}/M {sub ☉}) ≳ 10). This conclusion holds out to very large distances from the cluster center. However, the core (r {sub proj} < 3 Mpc) has a much lower fraction of star-forming galaxies than anywhere else in the cluster. These results indicate that for the mass range studied here, the majority of the star formation suppression occurs in the core on relatively short timescales, without any enhancement prior to entering the central region. If any significant enhancement or quenching of star formation occurs, it will be in galaxies of lower mass (log (M {sub *}/M {sub ☉}) < 10).

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Induced core formation time in subcritical magnetic clouds by large-scale trans-Alfvénic flows

We clarify the mechanism of accelerated core formation by large-scale nonlinear flows in subcritical magnetic clouds by finding a semi-analytical formula for the core formation time and describing the physical processes that lead to them. Recent numerical simulations show that nonlinear flows induce rapid ambipolar diffusion that leads to localized supercritical regions that can collapse. Here, we employ non-ideal magnetohydrodynamic simulations including ambipolar diffusion for gravitationally stratified sheets threaded by vertical magnetic fields. One of the horizontal dimensions is eliminated, resulting in a simpler two-dimensional simulation that can clarify the basic process of accelerated core formation. A parameter study of simulations shows that the core formation time is inversely proportional to the square of the flow speed when the flow speed is greater than the Alfvén speed. We find a semi-analytical formula that explains this numerical result. The formula also predicts that the core formation time is about three times shorter than that with no turbulence, when the turbulent speed is comparable to the Alfvén speed.

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Near 3:2 and 2:1 mean motion resonance formation in the systems observed by Kepler

The Kepler mission has released ∼4229 transiting planet candidates. There are approximately 222 candidate systems with three planets. Among them, the period ratios of planet pairs near 1.5 and 2.0 reveal that two peaks exist for which the proportions of the candidate systems are ∼7.0% and 18.0%, respectively. In this work, we study the formation of mean motion resonance (MMR) systems, particularly for the planetary configurations near 3:2 and 2:1 MMRs, and we concentrate on the interplay between the resonant configuration and the combination of stellar accretion rate, stellar magnetic field, speed of migration, and additional planets. We perform more than 1000 runs by assuming a system with a solar-like star and three surrounding planets. From the statistical results, we find that under the formation scenario, the proportions near 1.5 and 2.0 can reach 14.5% and 26.0%, respectively. In addition, M-dot =0.1×10{sup −8} M{sub ⊙} yr{sup −1} is propitious toward the formation of 3:2 resonance, whereas M-dot =2×10{sup −8} M{sub ⊙} yr{sup −1} contributes to the formation of 2:1 resonance. The speed-reduction factor of type I migration f {sub 1} ≥ 0.3 facilitates 3:2 MMRs, whereas f {sub 1} ≥ 0.1 facilitates 2:1 MMRs. If additional planets are present in orbits within the innermost or beyond the outermost planet in a three-planet system, 3:2:1 MMRs can be formed, but the original systems trapped in 4:2:1 MMRs are not affected by the supposed planets. In summary, we conclude that this formation scenario will provide a likely explanation for Kepler candidates involved in 2:1 and 3:2 MMRs.

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How dead are dead galaxies? Mid-infrared fluxes of quiescent galaxies at redshift 0.3 < z < 2.5: implications for star formation rates and dust heating

We investigate star formation rates (SFRs) of quiescent galaxies at high redshift (0.3 < z < 2.5) using 3D-HST WFC3 grism spectroscopy and Spitzer mid-infrared data. We select quiescent galaxies on the basis of the widely used UVJ color-color criteria. Spectral energy distribution (SED) fitting (rest-frame optical and near-IR) indicates very low SFRs for quiescent galaxies (sSFR ∼ 10{sup –12} yr{sup –1}). However, SED fitting can miss star formation if it is hidden behind high dust obscuration and ionizing radiation is re-emitted in the mid-infrared. It is therefore fundamental to measure the dust-obscured SFRs with a mid-IR indicator. We stack the MIPS 24 μm images of quiescent objects in five redshift bins centered on z = 0.5, 0.9, 1.2, 1.7, 2.2 and perform aperture photometry. Including direct 24 μm detections, we find sSFR ∼ 10{sup –11.9} × (1 + z){sup 4} yr{sup –1}. These values are higher than those indicated by SED fitting, but at each redshift they are 20-40 times lower than those of typical star-forming galaxies. The true SFRs of quiescent galaxies might be even lower, as we show that the mid-IR fluxes can be due to processes unrelated to ongoing star formation, such as cirrus dust heated by old stellar populations and circumstellar dust. Our measurements show that star formation quenching is very efficient at every redshift. The measured SFR values are at z > 1.5 marginally consistent with the ones expected from gas recycling (assuming that mass loss from evolved stars refuels star formation) and well below that at lower redshifts.

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ACCRETION-INHIBITED STAR FORMATION IN THE WARM MOLECULAR DISK OF THE GREEN-VALLEY ELLIPTICAL GALAXY NGC 3226?

We present archival Spitzer photometry and spectroscopy and Herschel photometry of the peculiar ''Green Valley'' elliptical galaxy NGC 3226. The galaxy, which contains a low-luminosity active galactic nucleus (AGN), forms a pair with NGC 3227 and is shown to lie in a complex web of stellar and H I filaments. Imaging at 8 and 16 μm reveals a curved plume structure 3 kpc in extent, embedded within the core of the galaxy and coincident with the termination of a 30 kpc long H I tail. In situ star formation associated with the infrared (IR) plume is identified from narrowband Hubble Space Telescope (HST) imaging. The end of the IR plume coincides with a warm molecular hydrogen disk and dusty ring containing 0.7-1.1 × 10{sup 7} M {sub ☉} detected within the central kiloparsec. Sensitive upper limits to the detection of cold molecular gas may indicate that a large fraction of the H{sub 2} is in a warm state. Photometry derived from the ultraviolet (UV) to the far-IR shows evidence for a low star-formation rate of ∼0.04 M {sub ☉} yr{sup –1} averaged over the last 100 Myr. A mid-IR component to the spectral energy distribution (SED) contributes ∼20% of the IR luminosity of the galaxy, and is consistent with emission associated with the AGN. The current measured star formation rate is insufficient to explain NGC 3226's global UV-optical ''green'' colors via the resurgence of star formation in a ''red and dead'' galaxy. This form of ''cold accretion'' from a tidal stream would appear to be an inefficient way to rejuvenate early-type galaxies and may actually inhibit star formation.

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STAR FORMATION IN DISK GALAXIES. III. DOES STELLAR FEEDBACK RESULT IN CLOUD DEATH?

Stellar feedback, star formation, and gravitational interactions are major controlling forces in the evolution of giant molecular clouds (GMCs). To explore their relative roles, we examine the properties and evolution of GMCs forming in an isolated galactic disk simulation that includes both localized thermal feedback and photoelectric heating. The results are compared with the three previous simulations in this series, which consists of a model with no star formation, star formation but no form of feedback, and star formation with photoelectric heating in a set with steadily increasing physical effects. We find that the addition of localized thermal feedback greatly suppresses star formation but does not destroy the surrounding GMC, giving cloud properties closely resembling the run in which no stellar physics is included. The outflows from the feedback reduce the mass of the cloud but do not destroy it, allowing the cloud to survive its stellar children. This suggests that weak thermal feedback such as the lower bound expected for a supernova may play a relatively minor role in the galactic structure of quiescent Milky-Way-type galaxies, compared to gravitational interactions and disk shear.

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A STAR FORMATION LAW FOR DWARF IRREGULAR GALAXIES

The radial profiles of gas, stars, and far-ultraviolet radiation in 20 dwarf Irregular galaxies are converted to stability parameters and scale heights for a test of the importance of two-dimensional (2D) instabilities in promoting star formation. A detailed model of this instability involving gaseous and stellar fluids with self-consistent thicknesses and energy dissipation on a perturbation crossing time gives the unstable growth rates. We find that all locations are effectively stable to 2D perturbations, mostly because the disks are thick. We then consider the average volume densities in the midplanes, evaluated from the observed H i surface densities and calculated scale heights. The radial profiles of the star-formation rates are equal to about 1% of the H i surface densities divided by the free fall times at the average midplane densities. This 1% resembles the efficiency per unit free fall time commonly found in other cases. There is a further variation of this efficiency with radius in all of our galaxies, following the exponential disk with a scale length equal to about twice the stellar mass scale length. This additional variation is modeled by the molecular fraction in a diffuse medium using radiative transfer solutions for galaxies with the observed dimensions and properties of our sample. We conclude that star formation is activated by a combination of three-dimensional gaseous gravitational processes and molecule formation. Implications for outer disk structure and formation are discussed.

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