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A FRAMEWORK FOR INTERPRETING FAST RADIO TRANSIENTS SEARCH EXPERIMENTS: APPLICATION TO THE V-FASTR EXPERIMENT

We define a framework for determining constraints on the detection rate of fast transient events from a population of underlying sources, with a view to incorporate beam shape, frequency effects, scattering effects, and detection efficiency into the metric. We then demonstrate a method for combining independent data sets into a single event rate constraint diagram, using a probabilistic approach to the limits on parameter space. We apply this new framework to present the latest results from the V-FASTR experiment, a commensal fast transients search using the Very Long Baseline Array (VLBA). In the 20 cm band, V-FASTR now has the ability to probe the regions of parameter space of importance for the observed Lorimer and Keane fast radio transient candidates by combining the information from observations with differing bandwidths, and properly accounting for the source dispersion measure, VLBA antenna beam shape, experiment time sampling, and stochastic nature of events. We then apply the framework to combine the results of the V-FASTR and Allen Telescope Array Fly's Eye experiments, demonstrating their complementarity. Expectations for fast transients experiments for the SKA Phase I dish array are then computed, and the impact of large differential bandwidths is discussed.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

AN INITIAL MASS FUNCTION STUDY OF THE DWARF STARBURST GALAXY NGC 4214

The production rate of ionizing photons in young ({<=}8 Myr), unresolved stellar clusters in the nearby irregular galaxy NGC 4214 is probed using multi-wavelength Hubble Space Telescope WFC3 data. We normalize the ionizing photon rate by the cluster mass to investigate the upper end of the stellar initial mass function (IMF). We have found that within the uncertainties the upper end of the stellar IMF appears to be universal in this galaxy, and that deviations from a universal IMF can be attributed to stochastic sampling of stars in clusters with masses {approx}<10{sup 3} M{sub Sun }. Furthermore, we have found that there does not seem to be a dependence of the maximum stellar mass on the cluster mass. We have also found that for massive clusters, feedback may cause an underrepresentation in H{alpha} luminosities, which needs to be taken into account when conducting this type of analysis.

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AMI OBSERVATIONS OF THE ANOMALOUS MICROWAVE EMISSION IN THE PERSEUS MOLECULAR CLOUD

We present observations of the known anomalous microwave emission region, G159.6-18.5, in the Perseus molecular cloud at 16 GHz performed with the Arcminute Microkelvin Imager Small Array. These are the highest angular resolution observations of G159.6-18.5 at microwave wavelengths. By combining these microwave data with infrared observations between 5.8 and 160 {mu}m from the Spitzer Space Telescope, we investigate the existence of a microwave-infrared correlation on angular scales of {approx}2'. We find that the overall correlation appears to increase toward shorter infrared wavelengths, which is consistent with the microwave emission being produced by electric dipole radiation from small, spinning dust grains. We also find that the microwave-infrared correlation peaks at 24 {mu}m (6.7{sigma}), suggesting that the microwave emission is originating from a population of stochastically heated small interstellar dust grains rather than polycyclic aromatic hydrocarbons.

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AN EFFICIENT APPROXIMATION TO THE LIKELIHOOD FOR GRAVITATIONAL WAVE STOCHASTIC BACKGROUND DETECTION USING PULSAR TIMING DATA

Direct detection of gravitational waves by pulsar timing arrays will become feasible over the next few years. In the low frequency regime (10{sup -7} Hz-10{sup -9} Hz), we expect that a superposition of gravitational waves from many sources will manifest itself as an isotropic stochastic gravitational wave background. Currently, a number of techniques exist to detect such a signal; however, many detection methods are computationally challenging. Here we introduce an approximation to the full likelihood function for a pulsar timing array that results in computational savings proportional to the square of the number of pulsars in the array. Through a series of simulations we show that the approximate likelihood function reproduces results obtained from the full likelihood function. We further show, both analytically and through simulations, that, on average, this approximate likelihood function gives unbiased parameter estimates for astrophysically realistic stochastic background amplitudes.

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SHAPING THE BROWN DWARF DESERT: PREDICTING THE PRIMORDIAL BROWN DWARF BINARY DISTRIBUTIONS FROM TURBULENT FRAGMENTATION

The formation of brown dwarfs (BDs) poses a key challenge to star formation theory. The observed dearth of nearby ({<=}5 AU) BD companions to solar mass stars, known as the BD desert, as well as the tendency for low-mass binary systems to be more tightly bound than stellar binaries, has been cited as evidence for distinct formation mechanisms for BDs and stars. In this paper, we explore the implications of the minimal hypothesis that BDs in binary systems originate via the same fundamental fragmentation mechanism as stars, within isolated, turbulent giant molecular cloud cores. We demonstrate analytically that the scaling of specific angular momentum with turbulent core mass naturally gives rise to the BD desert, as well as wide BD binary systems. Further, we show that the turbulent core fragmentation model also naturally predicts that very low mass binary and BD/BD systems are more tightly bound than stellar systems. In addition, in order to capture the stochastic variation intrinsic to turbulence, we generate 10{sup 4} model turbulent cores with synthetic turbulent velocity fields to show that the turbulent fragmentation model accommodates a small fraction of binary BDs with wide separations, similar to observations. Indeed, the picture which emerges from the turbulent fragmentation model is that a single fragmentation mechanism may largely shape both stellar and BD binary distributions during formation.

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DEPENDENCE OF NEBULAR HEAVY-ELEMENT ABUNDANCE ON H I CONTENT FOR SPIRAL GALAXIES

We analyze the galactic H I content and nebular log (O/H) for 60 spiral galaxies in the Moustakas et al. (2006a) spectral catalog. After correcting for the mass-metallicity relationship, we show that the spirals in cluster environments show a positive correlation for log (O/H) on DEF, the galactic H I deficiency parameter, extending the results of previous analyses of the Virgo and Pegasus I clusters. Additionally, we show for the first time that galaxies in the field obey a similar dependence. The observed relationship between H I deficiency and galactic metallicity resembles similar trends shown by cosmological simulations of galaxy formation including inflows and outflows. These results indicate the previously observed metallicity-DEF correlation has a more universal interpretation than simply a cluster's effects on its member galaxies. Rather, we observe in all environments the stochastic effects of metal-poor infall as minor mergers and accretion help to build giant spirals.

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NEAR-INFRARED VARIABILITY AMONG YOUNG STELLAR OBJECTS IN THE STAR FORMATION REGION CYGNUS OB7

We present an analysis of near-infrared time-series photometry in J, H, and K bands for about 100 epochs of a 1 Degree-Sign Multiplication-Sign 1 Degree-Sign region of the Lynds 1003/1004 dark cloud in the Cygnus OB7 region. Augmented by data from the Wide-field Infrared Survey Explorer, we identify 96 candidate disk bearing young stellar objects (YSOs) in the region. Of these, 30 are clearly Class I or earlier. Using the Wide-Field Imaging Camera on the United Kingdom Infrared Telescope, we were able to obtain photometry over three observing seasons, with photometric uncertainty better than 0.05 mag down to J Almost-Equal-To 17. We study detailed light curves and color trajectories of {approx}50 of the YSOs in the monitored field. We investigate the variability and periodicity of the YSOs and find the data are consistent with all YSOs being variable in these wavelengths on timescales of a few years. We divide the variability into four observational classes: (1) stars with periodic variability stable over long timescales, (2) variables which exhibit short-lived cyclic behavior, (3) long-duration variables, and (4) stochastic variables. Some YSO variability defies simple classification. We can explain much of the observed variability as being due to dynamic and rotational changes in the disk, including an asymmetric or changing blocking fraction, changes to the inner disk hole size, as well as changes to the accretion rate. Overall, we find that the Class I:Class II ratio of the cluster is consistent with an age of <1 Myr, with at least one individual, wildly varying source {approx}100, 000 yr old. We have also discovered a Class II eclipsing binary system with a period of 17.87 days.

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OBSERVATIONAL TEST OF STOCHASTIC HEATING IN LOW-{beta} FAST-SOLAR-WIND STREAMS

Spacecraft measurements show that protons undergo substantial perpendicular heating during their transit from the Sun to the outer heliosphere. In this paper, we use Helios 2 measurements to investigate whether stochastic heating by low-frequency turbulence is capable of explaining this perpendicular heating. We analyze Helios 2 magnetic field measurements in low-{beta} fast-solar-wind streams between heliocentric distances r = 0.29 AU and r = 0.64 AU to determine the rms amplitude of the fluctuating magnetic field, {delta}B{sub p}, near the proton gyroradius scale {rho}{sub p}. We then evaluate the stochastic heating rate Q{sub stoch} using the measured value of {delta}B{sub p} and a previously published analytical formula for Q{sub stoch}. Using Helios measurements we estimate the ''empirical'' perpendicular heating rate Q{sub Up-Tack emp} = (k{sub B}/m{sub p}) BV (d/dr) (T{sub Up-Tack p}/B) that is needed to explain the T{sub p} profile. We find that Q{sub stoch} {approx} Q{sub emp}, but only if a key dimensionless constant appearing in the formula for Q{sub stoch} lies within a certain range of values. This range is approximately the same throughout the radial interval that we analyze and is consistent with the results of numerical simulations of the stochastic heating of test particles in reduced magnetohydrodynamic turbulence. These results support the hypothesis that stochastic heating accounts for much of the perpendicular proton heating occurring in low-{beta} fast-wind streams.

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THE EFFECTS OF EPISODIC STAR FORMATION ON THE FUV-NUV COLORS OF STAR FORMING REGIONS IN OUTER DISKS

We run stellar population synthesis models to examine the effects of a recently episodic star formation history (SFH) on UV and Hα colors of star forming regions. Specifically, the SFHs we use are an episodic sampling of an exponentially declining star formation rate (SFR; τ model) and are intended to simulate the SFHs in the outer disks of spiral galaxies. To enable comparison between our models and observational studies of star forming regions in outer disks, we include in our models sensitivity limits that are based on recent deep UV and Hα observations in the literature. We find significant dispersion in the FUV-NUV colors of simulated star forming regions with frequencies of star formation episodes of 1 × 10{sup –8} to 4 × 10{sup –9} yr{sup –1}. The dispersion in UV colors is similar to that found in the outer disk of nearby spiral galaxies. As expected, we also find large variations in L{sub H{sub α}}/L{sub FUV}. We interpret our models within the context of inside-out disk growth, and find that a radially increasing τ and decreasing metallicity with an increasing radius will only produce modest FUV-NUV color gradients, which are significantly smaller than what is found for some nearby spiral galaxies. However, including moderate extinction gradients with our models can better match the observations with steeper UV color gradients. We estimate that the SFR at which the number of stars emitting FUV light becomes stochastic is ∼2 × 10{sup –6} M{sub ☉} yr{sup –1}, which is substantially lower than the SFR of many star forming regions in outer disks. Therefore, we conclude that stochasticity in the upper end of the initial mass function is not likely to be the dominant cause of dispersion in the FUV-NUV colors of star forming regions in outer disks. Finally, we note that if outer disks have had an episodic SFH similar to that used in this study, this should be taken into account when estimating gas depletion timescales and modeling chemical evolution of spiral galaxies.

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CONSTRAINING SUB-PARSEC BINARY SUPERMASSIVE BLACK HOLES IN QUASARS WITH MULTI-EPOCH SPECTROSCOPY. I. THE GENERAL QUASAR POPULATION

We perform a systematic search for sub-parsec binary supermassive black holes (BHs) in normal broad-line quasars at z < 0.8, using multi-epoch Sloan Digital Sky Survey (SDSS) spectroscopy of the broad Hβ line. Our working model is that (1) one and only one of the two BHs in the binary is active; (2) the active BH dynamically dominates its own broad-line region (BLR) in the binary system, so that the mean velocity of the BLR reflects the mean velocity of its host BH; (3) the inactive companion BH is orbiting at a distance of a few R{sub BLR}, where R{sub BLR} ∼ 0.01-0.1 pc is the BLR size. We search for the expected line-of-sight acceleration of the broad-line velocity from binary orbital motion by cross-correlating SDSS spectra from two epochs separated by up to several years in the quasar rest frame. Out of ∼700 pairs of spectra for which we have good measurements of the velocity shift between two epochs (1σ error ∼40 km s{sup –1}), we detect 28 systems with significant velocity shifts in broad Hβ, among which 7 are the best candidates for the hypothesized binaries, 4 are most likely due to broad-line variability in single BHs, and the rest are ambiguous. Continued spectroscopic observations of these candidates will easily strengthen or disprove these claims. We use the distribution of the observed accelerations (mostly non-detections) to place constraints on the abundance of such binary systems among the general quasar population. Excess variance in the velocity shift is inferred for observations separated by longer than 0.4 yr (quasar rest frame). Attributing all the excess to binary motion would imply that most of the quasars in this sample must be in binaries, that the inactive BH must be on average more massive than the active one, and that the binary separation is at most a few times the size of the BLR. However, if this excess variance is partly or largely due to long-term broad-line variability, the requirement of a large population of close binaries is much weakened or even disfavored for massive companions. Future time-domain spectroscopic surveys of normal quasars can provide vital prior information on the structure function of stochastic velocity shifts induced by broad-line variability in single BHs. Such surveys with improved spectral quality, increased time baseline, and more epochs can greatly improve the statistical constraints of this method on the general binary population in broad-line quasars, further shrink the allowed binary parameter space, and detect true sub-parsec binaries.

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APPLICATION OF JITTER RADIATION: GAMMA-RAY BURST PROMPT POLARIZATION

A high degree of polarization of gamma-ray burst (GRB) prompt emission has been confirmed in recent years. In this paper, we apply jitter radiation to study the polarization feature of GRB prompt emission. In our framework, relativistic electrons are accelerated by turbulent acceleration. Random and small-scale magnetic fields are generated by turbulence. We further determine that the polarization property of GRB prompt emission is governed by the configuration of the random and small-scale magnetic fields. A two-dimensional compressed slab, which contains a stochastic magnetic field, is applied in our model. If the jitter condition is satisfied, the electron deflection angle in the magnetic field is very small and the electron trajectory can be treated as a straight line. A high degree of polarization can be achieved when the angle between the line of sight and the slab plane is small. Moreover, micro-emitters with mini-jet structures are considered to be within a bulk GRB jet. The jet 'off-axis' effect is intensely sensitive to the observed polarization degree. We discuss the depolarization effect on GRB prompt emission and afterglow. We also speculate that the rapid variability of GRB prompt polarization may be correlated with the stochastic variability of the turbulent dynamo or the magnetic reconnection of plasmas.

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DWARF GALAXY FORMATION WITH H{sub 2}-REGULATED STAR FORMATION. II. GAS-RICH DARK GALAXIES AT REDSHIFT 2.5

We present a cosmological hydrodynamic simulation of the formation of dwarf galaxies at redshifts z ∼> 2.5 using a physically motivated model for H{sub 2}-regulated star formation. Our simulation, performed using the Enzo code and reaching a peak resolution of 109 proper parsecs at z = 2.5, extends the results of Kuhlen et al. to significantly lower redshifts. We show that a star formation prescription regulated by the local H{sub 2} abundance leads to the suppression of star formation in dwarf galaxy halos with M{sub h} ∼< 10{sup 10} M{sub ☉} and to a large population of gas-rich 'dark galaxies' at z = 2.5 with low star formation efficiencies and gas depletion timescales >20 Gyr. The fraction of dark galaxies is 60% at M{sub h} ≅ 10{sup 10} M{sub ☉} and increases rapidly with decreasing halo mass. Dark galaxies form late and their gaseous disks never reach the surface densities, ∼> 5700 M{sub ☉} pc{sup –2} (Z/10{sup –3} Z{sub ☉}){sup –0.88}, that are required to build a substantial molecular fraction. Despite this large population of dark galaxies, we show that our H{sub 2}-regulated simulation is consistent with both the observed luminosity function of galaxies and the cosmological mass density of neutral gas at z ∼> 2.5. Moreover, our results provide a theoretical explanation for the recent detection in fluorescent Lyα emission of gaseous systems at high redshift with little or no associated star formation. We further propose that H{sub 2}-regulation may offer a fresh solution to a number of outstanding 'dwarf galaxy problems' in ΛCDM. In particular, H{sub 2}-regulation leads galaxy formation to become effectively stochastic on mass scales of M{sub h} ∼ 10{sup 10} M{sub ☉}, and thus these massive dwarfs are not 'too big to fail'.

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STOCHASTIC HEATING, DIFFERENTIAL FLOW, AND THE ALPHA-TO-PROTON TEMPERATURE RATIO IN THE SOLAR WIND

We extend previous theories of stochastic ion heating to account for the motion of ions along the magnetic field B . We derive an analytic expression for the temperature ratio T{sub i}/T{sub p} in the solar wind assuming that stochastic heating is the dominant ion heating mechanism, where T{sub i} is the perpendicular temperature of species i and T{sub p} is the perpendicular proton temperature. This expression describes how T{sub i}/T{sub p} depends upon U{sub i} and β{sub ∥p}, where U{sub i} is the average velocity along B of species i in the proton frame and β{sub ∥p} is the ratio of the parallel proton pressure to the magnetic pressure, which we take to be ∼< 1. We compare our model with previously published measurements of alpha particles and protons from the Wind spacecraft. We find that stochastic heating offers a promising explanation for the dependence of T{sub α}/T{sub p} on U{sub α} and β{sub ∥p} when the fractional cross helicity and Alfvén ratio at the proton-gyroradius scale have values that are broadly consistent with solar-wind measurements. We also predict how the temperatures of other ion species depend on their drift speeds.

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TURBULENT DISKS ARE NEVER STABLE: FRAGMENTATION AND TURBULENCE-PROMOTED PLANET FORMATION

A fundamental assumption in our understanding of disks is that when the Toomre Q >> 1, the disk is stable against fragmentation into self-gravitating objects (and so cannot form planets via direct collapse). But if disks are turbulent, this neglects a spectrum of stochastic density fluctuations that can produce rare, high-density mass concentrations. Here, we use a recently developed analytic framework to predict the statistics of these fluctuations, i.e., the rate of fragmentation and mass spectrum of fragments formed in a turbulent Keplerian disk. Turbulent disks are never completely stable: we calculate the (always finite) probability of forming self-gravitating structures via stochastic turbulent density fluctuations in such disks. Modest sub-sonic turbulence above Mach number M∼0.1 can produce a few stochastic fragmentation or 'direct collapse' events over ∼Myr timescales, even if Q >> 1 and cooling is slow (t{sub cool} >> t{sub orbit}). In transsonic turbulence this extends to Q ∼ 100. We derive the true Q-criterion needed to suppress such events, which scales exponentially with Mach number. We specify to turbulence driven by magneto-rotational instability, convection, or spiral waves and derive equivalent criteria in terms of Q and the cooling time. Cooling times ∼> 50 t{sub dyn} may be required to completely suppress fragmentation. These gravo-turbulent events produce mass spectra peaked near ∼(Q M{sub disk}/M{sub *}){sup 2} M{sub disk} (rocky-to-giant planet masses, increasing with distance from the star). We apply this to protoplanetary disk models and show that even minimum-mass solar nebulae could experience stochastic collapse events, provided a source of turbulence.

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PERPENDICULAR ION HEATING BY REDUCED MAGNETOHYDRODYNAMIC TURBULENCE

Recent theoretical studies argue that the rate of stochastic ion heating in low-frequency Alfvén-wave turbulence is given by Q = c{sub 1}((δu){sup 3}/ρ)exp (– c{sub 2}/ε), where δu is the rms turbulent velocity at the scale of the ion gyroradius ρ, ε = δu/v{sub i}, v{sub i} is the perpendicular ion thermal speed, and c{sub 1} and c{sub 2} are dimensionless constants. We test this theoretical result by numerically simulating test particles interacting with strong reduced magnetohydrodynamic (RMHD) turbulence. The heating rates in our simulations are well fit by this formula. The best-fit values of c{sub 1} are ∼1. The best-fit values of c{sub 2} decrease (i.e., stochastic heating becomes more effective) as the Reynolds number and the number of grid points in the RMHD simulations increase. As an example, in a 1024{sup 2} × 256 RMHD simulation with a dissipation wavenumber of the order of the inverse ion gyroradius, we find c{sub 2} = 0.21. We show that stochastic heating is significantly stronger in strong RMHD turbulence than in a field of randomly phased Alfvén waves with the same power spectrum, because coherent structures in strong RMHD turbulence increase orbit stochasticity in the regions where ions are heated most strongly. We find that c{sub 1} increases by a factor of ∼3 while c{sub 2} changes very little as the ion thermal speed increases from values <<v{sub A} to values ∼v{sub A}, where v{sub A} is the Alfvén speed. We discuss the importance of these results for perpendicular ion heating in the solar wind.

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THE BENEFITS OF VLBI ASTROMETRY TO PULSAR TIMING ARRAY SEARCHES FOR GRAVITATIONAL RADIATION

Precision astrometry is an integral component of successful pulsar timing campaigns. Astrometric parameters are commonly derived by fitting them as parameters of a timing model to a series of pulse times of arrival (TOAs). TOAs measured to microsecond precision over spans of several years can yield position measurements with sub-milliarcsecond precision. However, timing-based astrometry can become biased if a pulsar displays any red spin noise or a red signal produced by the stochastic gravitational wave background. We investigate how noise of different spectral types is absorbed by timing models, leading to significant estimation biases in the astrometric parameters. We find that commonly used techniques for fitting timing models in the presence of red noise (Cholesky whitening) prevent the absorption of noise into the timing model remarkably well if the time baseline of observations exceeds several years, but are inadequate for dealing with shorter pulsar data sets. Independent of timing, pulsar-optimized very long baseline interferometry (VLBI) is capable of providing position estimates precise to the sub-milliarcsecond levels needed for high-precision timing. In order to make VLBI astrometric parameters useful in pulsar timing models, the transformation between the International Celestial Reference Frame (ICRF) and the dynamical solar system ephemeris used for pulsar timing must be constrained to within a few microarcseconds. We compute a transformation between the ICRF and pulsar timing frames and quantitatively discuss how the transformation will improve in coming years. We find that incorporating VLBI astrometry into the timing models of pulsars for which only a couple of years of timing data exist will lead to more realistic assessments of red spin noise and could enhance the amplitude of gravitational wave signatures in post-fit timing residuals by factors of 20 or more.

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ON IRON MONOXIDE NANOPARTICLES AS A CARRIER OF THE MYSTERIOUS 21 μm EMISSION FEATURE IN POST-ASYMPTOTIC GIANT BRANCH STARS

A prominent mysterious emission feature peaking at ∼20.1 μm—historically known as the '21 μm' feature—is seen in over two dozen Galactic and Magellanic Cloud carbon-rich, post-asymptotic giant branch (post-AGB) stars. The nature of its carrier remains unknown since the first detection of the 21 μm feature in 1989. Over a dozen materials have been suggested as possible carrier candidates. However, none of them has been accepted: they either require too much material (compared to what is available in the circumstellar shells around these post-AGB stars), or exhibit additional emission features that are not seen in these 21 μm sources. Recently, iron monoxide (FeO) nanoparticles seem to be a promising carrier candidate as Fe is an abundant element and FeO emits exclusively at ∼21 μm. In this work, using the proto-typical protoplanetary nebula HD 56126 as a test case, we examine FeO nanoparticles as a carrier for the 21 μm feature by modeling their infrared emission, with FeO being stochastically heated by single stellar photons. We find that FeO emits too broad a 21 μm feature to explain that observed and the Fe abundance required to be locked up in FeO exceeds what is available in HD 56126. We therefore conclude that FeO nanoparticles are not likely to be responsible for the 21 μm feature.

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K{sub s} -BAND LUMINOSITY EVOLUTION OF THE ASYMPTOTIC GIANT BRANCH POPULATION BASED ON STAR CLUSTERS IN THE LARGE MAGELLANIC CLOUD

We present a study of K{sub s} -band luminosity evolution of the asymptotic giant branch (AGB) population in simple stellar systems using star clusters in the Large Magellanic Cloud (LMC). We determine physical parameters of LMC star clusters including center coordinates, radii, and foreground reddenings. Ages of 83 star clusters are derived from isochrone fitting with the Padova models, and those of 19 star clusters are taken from the literature. The AGB stars in 102 star clusters with log(age) = 7.3-9.5 are selected using near-infrared color-magnitude diagrams based on Two Micron All Sky Survey photometry. Then we obtain the K{sub s} -band luminosity fraction of AGB stars in these star clusters as a function of ages. The K{sub s} -band luminosity fraction of AGB stars increases, on average, as age increases from log(age) ∼ 8.0, reaching a maximum at log(age) ∼ 8.5, and it decreases thereafter. There is a large scatter in the AGB luminosity fraction for given ages, which is mainly due to stochastic effects. We discuss this result in comparison with five simple stellar population models. The maximum K{sub s} -band AGB luminosity fraction for bright clusters is reproduced by the models that expect the value of 0.7-0.8 at log(age) = 8.5-8.7. We discuss the implication of our results with regard to the study of size and mass evolution of galaxies.

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