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Jason S. Kalirai

Publications and source records attributed to Jason S. Kalirai.

At least 37 records · Page 2Linked to original sources

Global Properties of M31's Stellar Halo from the SPLASH Survey: III. Measuring the Stellar Velocity Dispersion Profile

We present the velocity dispersion of red giant branch (RGB) stars in M31's halo, derived by modeling the line of sight velocity distribution of over 5000 stars in 50 fields spread throughout M31's stellar halo. The dataset was obtained as part of the SPLASH (Spectroscopic and Photometric Landscape of Andromeda's Stellar Halo) Survey, and covers projected radii of 9 to 175 kpc from M31's center. All major structural components along the line of sight in both the Milky Way (MW) and M31 are incorporated in a Gaussian Mixture Model, including all previously identified M31 tidal debris features in the observed fields. The probability an individual star is a constituent of M31 or the MW, based on a set of empirical photometric and spectroscopic diagnostics, is included as a prior probability in the mixture model. The velocity dispersion of stars in M31's halo is found to decrease only mildly with projected radius, from 108 km/s in the innermost radial bin (8.2 to 14.1 kpc) to $\sim 80$ to 90 km/s at projected radii of $\sim 40$ to 130 kpc, and can be parameterized with a power-law of slope $-0.12\pm 0.05$. The quoted uncertainty on the power-law slope reflects only the precision of the method, although other sources of uncertainty we consider contribute negligibly to the overall error budget.

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Can magnetic fields suppress convection in the atmosphere of cool white dwarfs? A case study on WD2105-820

Around 10% of white dwarfs exhibit global magnetic structures with fields ranging from 1 kG to hundreds of MG. Recently, the first radiation magnetohydrodynamics simulations of the atmosphere of white dwarfs showed that convection should be suppressed in their photospheres for magnetic fields with strengths B $\gtrsim$ 50 kG. These predictions are in agreement with our knowledge of stellar physics (e.g. energy transfer in strong magnetic field regions of the solar photosphere), but have yet to be directly confirmed from white dwarf observations. We obtained COS far-UV spectroscopy of the weakly magnetic, hydrogen-atmosphere, white dwarf WD2105-820 and of three additional non-magnetic, convective remnants (all in the $T_{\mathrm{eff}}$ range 9000-11,000 K). We fitted both the COS and the already available optical spectra with convective and radiative atmospheric models. As expected, we find that for two of the non-magnetic comparison stars only convective model fits predict consistent $T_{\mathrm{eff}}$ values from both the optical and the FUV spectra. In contrast, for WD2105-820 only the best fitting radiative model produced consistent results.

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Dissecting the Extended Main Sequence Turn-off of the Young Star Cluster NGC1850

We use the Wide Field Camera 3 onboard the Hubble Space Telescope to obtain deep, high-resolution photometry of the young (~ 100 Myr) star cluster NGC1850 in the Large Magellanic Cloud. We analyze the cluster colour-magnitude diagram (CMD) and find that it hosts an extended main sequence turn-off (MSTO) and a double MS. We demonstrate that these features cannot be due to photometric errors, field star contamination, or differential reddening. From a comparison with theoretical models and Monte Carlo simulations, we show that a coeval stellar population featuring a distribution of stellar rotation rates can reproduce the MS split quite well. However, it cannot reproduce the observed MSTO region, which is significantly wider than the simulated ones. Exploiting narrow-band Halpha imaging, we find that the MSTO hosts a population of Halpha-emitting stars which are interpreted as rapidly rotating Be-type stars. We explore the possibility that the discrepancy between the observed MSTO morphology and that of the simulated simple stellar population (SSP) is caused by the fraction of these objects that are highly reddened, but we rule out this hypothesis. We demonstrate that the global CMD morphology is well-reproduced by a combination of SSPs that cover an age range of ~ 35 Myr as well as a wide variety of rotation rates. We derive the cluster mass and escape velocity and use dynamical evolution models to predict their evolution starting at an age of 10 Myr. We discuss these results and their implications in the context of the extended MSTO phenomenon.

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The Panchromatic Hubble Andromeda Treasury XV. The BEAST: Bayesian Extinction and Stellar Tool

We present the Bayesian Extinction And Stellar Tool (BEAST), a probabilistic approach to modeling the dust extinguished photometric spectral energy distribution of an individual star while accounting for observational uncertainties common to large resolved star surveys. Given a set of photometric measurements and an observational uncertainty model, the BEAST infers the physical properties of the stellar source using stellar evolution and atmosphere models and constrains the line of sight extinction using a newly developed mixture model that encompasses the full range of dust extinction curves seen in the Local Group. The BEAST is specifically formulated for use with large multi-band surveys of resolved stellar populations. Our approach accounts for measurement uncertainties and any covariance between them due to stellar crowding (both systematic biases and uncertainties in the bias) and absolute flux calibration, thereby incorporating the full information content of the measurement. We illustrate the accuracy and precision possible with the BEAST using data from the Panchromatic Hubble Andromeda Treasury. While the BEAST has been developed for this survey, it can be easily applied to similar existing and planned resolved star surveys.

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Constraining Globular Cluster Age Uncertainties Using the IR Color-Magnitude Diagram

Globular Clusters (GCs) in the Milky Way are the primary laboratories for establishing the ages of the oldest stellar populations and for measuring the color-magnitude relation of stars. In infrared (IR) color-magnitude diagrams (CMDs), the stellar main sequence (MS) exhibits a "kink", due to opacity effects in M dwarfs, such that lower mass and cooler dwarfs become bluer in the IR color baseline. This diagnostic offers a new opportunity to model GC CMDs and to reduce uncertainties on cluster properties (e.g., their derived ages). In this context, we analyzed Hubble Space Telescope Wide Field Camera 3 IR archival observations of four GCs - 47Tuc, M4, NGC2808, and NGC6752 - for which the data are deep enough to fully sample the low-mass MS, reaching at least ~ 2 mag below the "kink". We derived the fiducial lines for each cluster and compared them with a grid of isochrones over a large range of parameter space, allowing age, metallicity, distance, and reddening to vary within reasonable selected ranges. The derived ages for the four clusters are respectively 11.6, 11.5, 11.2, and 12.1 Gyr and their random uncertainties are σ~ 0.7 - 1.1 Gyr. Our results suggest that the near-IR MS "kink", combined with the MS turn-off, provides a valuable tool to measure GC ages and offers a promising opportunity to push the absolute age of GCs to sub-Gyr accuracy with the next generation IR telescopes such as the James Webb Space Telescope and the Wide-Field Infrared Survey Telescope.

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An Ultramassive 1.28 M$_\odot$ White Dwarf in NGC 2099

With the Keck I Low-Resolution Imaging Spectrometer we have observed nine white dwarf candidates in the very rich open cluster NGC 2099 (M37). The spectroscopy shows seven to be DA white dwarfs, one to be a DB white dwarf, and one to be a DZ white dwarf. Three of these DA white dwarfs are consistent with singly evolved cluster membership: an ultramassive (1.28$^{+0.05}_{-0.08}$ M$_\odot$) and two intermediate-mass (0.70 and 0.75 M$_\odot$) white dwarfs. Analysis of their cooling ages allows us to calculate their progenitor masses and establish new constraints on the initial-final mass relation. The intermediate-mass white dwarfs are in strong agreement with previous work over this mass regime. The ultramassive white dwarf has $V$ = 24.5, $\sim$2 mag fainter than the other two remnants. The spectrum of this star has lower quality, so the derived stellar properties (e.g., T$_{\rm eff}$, log g) have uncertainties that are several times higher than the brighter counterparts. We measure these uncertainties and establish the star's final mass as the highest-mass white dwarf discovered thus far in a cluster, but we are unable to calculate its progenitor mass because at this high mass and cooler T$_{\rm eff}$ its inferred cooling age is highly sensitive to its mass. At the highest temperatures, however, this sensitivity of cooling age to an ultramassive white dwarf's mass is only moderate. This demonstrates that future investigations of the upper-mass end of the initial-final mass relation must identify massive, newly formed white dwarfs (i.e., in young clusters with ages 50-150 Myr).

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Two Massive White Dwarfs from NGC 2323 and the Initial-Final Mass Relation for Progenitors of 4 to 6.5 M$_\odot$

We have observed a sample of 10 white dwarf candidates in the rich open cluster NGC 2323 (M50) with the Keck Low-Resolution Imaging Spectrometer. The spectroscopy shows eight to be DA white dwarfs, with six of these having high S/N appropriate for our analysis. Two of these white dwarfs are consistent with singly evolved cluster membership, and both are high mass $\sim$1.07 M$_\odot$, and give equivalent progenitor masses of 4.69 M$_\odot$. To supplement these new high-mass white dwarfs and analyze the initial-final mass relation (IFMR), we have also looked at 30 white dwarfs from publicly available data that are mostly all high-mass ($\gtrsim$0.9 M$_\odot$). These original published data exhibited significant scatter, and to test if this scatter is true or simply the result of systematics, we have uniformly analyzed the white dwarf spectra and have adopted thorough photometric techniques to derive uniform cluster parameters for their parent clusters. The resulting IFMR scatter is significantly reduced, arguing that mass-loss rates are not stochastic in nature and that within the ranges of metallicity and mass analyzed in this work mass loss is not highly sensitive to variations in metallicity. Lastly, when adopting cluster ages based on Y$^2$ isochrones, the slope of the high-mass IFMR remains steep and consistent with that found from intermediate-mass white dwarfs, giving a linear IFMR from progenitor masses between 3 to 6.5 M$_\odot$. In contrast, when adopting the slightly younger cluster ages based on PARSEC isochrones, the high-mass IFMR has a moderate turnover near an initial mass of 4 M$_\odot$.

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Initial-Final Mass Relation for 3 to 4 M$_\odot$ Progenitors of White Dwarfs from the Single Cluster NGC 2099

We have expanded the sample of observed white dwarfs in the rich open cluster NGC 2099 (M37) with the Keck Low-Resolution Imaging Spectrometer. Of 20 white dwarf candidates, the spectroscopy shows 19 to be true white dwarfs with 14 of these having high S/N. We find 11 of these 14 to be consistent with singly evolved cluster members. They span a mass range of $\sim$0.7 to 0.95 M$_\odot$, excluding a low-mass outlier, corresponding to progenitor masses of $\sim$3 to 4 M$_\odot$. This region of the initial final mass relation (IFMR) has large scatter and a slope that remains to be precisely determined. With this large sample of white dwarfs that belong to a single age and metallicity population, we find an initial-final mass relation of (0.171$\pm$0.057)M$_{\rm initial}$+0.219$\pm$0.187 M$_\odot$, significantly steeper than the linear relation adopted over the full observed white dwarf mass range in many previous studies. Comparison of this new relation from the solar metallicity NGC 2099 to 18 white dwarfs in the metal-rich Hyades and Praesepe shows that their IFMR also has a consistently steep slope. This strong consistency also suggests that there is no significant metallicity dependence of the IFMR at this mass and metallicity range. As a result, the IFMR can be more reliably determined with this broad sample of 29 total white dwarfs giving M$_{\rm final}$=(0.163$\pm$0.022)M$_{\rm initial}$+0.238$\pm$0.071 M$_\odot$ from M$_{\rm initial}$ of 3 to 4 M$_\odot$. A steep IFMR in this mass range indicates that the full IFMR is nonlinear.

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The Panchromatic Hubble Andromeda Treasury XI: The Spatially-Resolved Recent Star Formation History of M31

We measure the recent star formation history (SFH) across M31 using optical images taken with the \texit{Hubble Space Telescope} as part of the Panchromatic Hubble Andromeda Treasury (PHAT). We fit the color-magnitude diagrams in ~9000 regions that are ~100 pc $\times$ 100 pc in projected size, covering a 0.5 square degree area (~380 kpc$^2$, deprojected) in the NE quadrant of M31. We show that the SFHs vary significantly on these small spatial scales but that there are also coherent galaxy-wide fluctuations in the SFH back to ~500 Myr, most notably in M31's 10-kpc star-forming ring. We find that the 10-kpc ring is at least 400 Myr old, showing ongoing star formation over the past ~500 Myr. This indicates the presence of molecular gas in the ring over at least 2 dynamical times at this radius. We also find that the ring's position is constant throughout this time, and is stationary at the level of 1 km/s, although there is evidence for broadening of the ring due to diffusion of stars into the disk. Based on existing models of M31's ring features, the lack of evolution in the ring's position makes a purely collisional ring origin highly unlikely. We find that the global SFR has been fairly constant over the last ~500 Myr, though it does show a small increase at 50 Myr that is 1.3 times the average SFR over the past 100 Myr. During the last ~500 Myr, ~60% of all SF occurs in the 10-kpc ring. Finally, we find that in the past 100 Myr, the average SFR over the PHAT survey area is $0.28\pm0.03$ M$_\odot$ yr$^{-1}$ with an average deprojected intensity of $7.3 \times 10^{-4}$ M$_\odot$ yr$^{-1}$ kpc$^{-2}$, which yields a total SFR of ~0.7 M$_\odot$ yr$^{-1}$ when extrapolated to the entire area of M31's disk. This SFR is consistent with measurements from broadband estimates. [abridged]

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The High-Mass Stellar Initial Mass Function in M31 Clusters

We have undertaken the largest systematic study of the high-mass stellar initial mass function (IMF) to date using the optical color-magnitude diagrams (CMDs) of 85 resolved, young (4 Myr < t < 25 Myr), intermediate mass star clusters (10^3-10^4 Msun), observed as part of the Panchromatic Hubble Andromeda Treasury (PHAT) program. We fit each cluster's CMD to measure its mass function (MF) slope for stars >2 Msun. For the ensemble of clusters, the distribution of stellar MF slopes is best described by $Γ=+1.45^{+0.03}_{-0.06}$ with a very small intrinsic scatter. The data also imply no significant dependencies of the MF slope on cluster age, mass, and size, providing direct observational evidence that the measured MF represents the IMF. This analysis implies that the high-mass IMF slope in M31 clusters is universal with a slope ($Γ=+1.45^{+0.03}_{-0.06}$) that is steeper than the canonical Kroupa (+1.30) and Salpeter (+1.35) values. Using our inference model on select Milky Way (MW) and LMC high-mass IMF studies from the literature, we find $Γ_{\rm MW} \sim+1.15\pm0.1$ and $Γ_{\rm LMC} \sim+1.3\pm0.1$, both with intrinsic scatter of ~0.3-0.4 dex. Thus, while the high-mass IMF in the Local Group may be universal, systematics in literature IMF studies preclude any definitive conclusions; homogenous investigations of the high-mass IMF in the local universe are needed to overcome this limitation. Consequently, the present study represents the most robust measurement of the high-mass IMF slope to date. We have grafted the M31 high-mass IMF slope onto widely used sub-solar mass Kroupa and Chabrier IMFs and show that commonly used UV- and Halpha-based star formation rates should be increased by a factor of ~1.3-1.5 and the number of stars with masses >8 Msun are ~25% fewer than expected for a Salpeter/Kroupa IMF. [abridged]

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Tracing the Metal-Poor M31 Stellar Halo with Blue Horizontal Branch Stars

We have analyzed new HST/ACS and HST/WFC3 imaging in F475W and F814W of two previously-unobserved fields along the M31 minor axis to confirm our previous constraints on the shape of M31's inner stellar halo. Both of these new datasets reach a depth of at least F814W$<$27 and clearly detect the blue horizontal branch (BHB) of the field as a distinct feature of the color-magnitude diagram. We measure the density of BHB stars and the ratio of BHB to red giant branch stars in each field using identical techniques to our previous work. We find excellent agreement with our previous measurement of a power-law for the 2-D projected surface density with an index of 2.6$^{+0.3}_{-0.2}$ outside of 3 kpc, which flattens to $α<$1.2 inside of 3 kpc. Our findings confirm our previous suggestion that the field BHB stars in M31 are part of the halo population. However, the total halo profile is now known to differ from this BHB profile, which suggests that we have isolated the metal-poor component. This component appears to have an unbroken power-law profile from 3-150 kpc but accounts for only about half of the total halo stellar mass. Discrepancies between the BHB density profile and other measurements of the inner halo are therefore likely due to the different profile of the metal-rich halo component, which is not only steeper than the profile of the met al-poor component, but also has a larger core radius. These profile differences also help to explain the large ratio of BHB/RGB stars in our observations.

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Extended Main Sequence Turnoffs in Intermediate-Age Star Clusters: A Correlation Between Turnoff Width and Early Escape Velocity

We present color-magnitude diagram analysis of deep Hubble Space Telescope imaging of a mass-limited sample of 18 intermediate-age (1 - 2 Gyr old) star clusters in the Magellanic Clouds, including 8 clusters for which new data was obtained. We find that ${\it all}$ star clusters in our sample feature extended main sequence turnoff (eMSTO) regions that are wider than can be accounted for by a simple stellar population (including unresolved binary stars). FWHM widths of the MSTOs indicate age spreads of 200-550 Myr. We evaluate dynamical evolution of clusters with and without initial mass segregation. Our main results are: (1) the fraction of red clump (RC) stars in secondary RCs in eMSTO clusters scales with the fraction of MSTO stars having pseudo-ages $\leq 1.35$ Gyr; (2) the width of the pseudo-age distributions of eMSTO clusters is correlated with their central escape velocity $v_{\rm esc}$, both currently and at an age of 10 Myr. We find that these two results are unlikely to be reproduced by the effects of interactive binary stars or a range of stellar rotation velocities. We therefore argue that the eMSTO phenomenon is mainly caused by extended star formation within the clusters; (3) we find that $v_{\rm esc} \geq 15$ km/s out to ages of at least 100 Myr for ${\it all}$ clusters featuring eMSTOs, while $v_{\rm esc} \leq 12$ km/s at all ages for two lower-mass clusters in the same age range that do ${\it not}$ show eMSTOs. We argue that eMSTOs only occur for clusters whose early escape velocities are higher than the wind velocities of stars that provide material from which second-generation stars can form. The threshold of 12-15 km/s is consistent with wind velocities of intermediate-mass AGB stars in the literature.

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The Quenching of the Ultra-Faint Dwarf Galaxies in the Reionization Era

We present new constraints on the star formation histories of six ultra-faint dwarf galaxies: Bootes I, Canes Venatici II, Coma Berenices, Hercules, Leo IV, and Ursa Major I. Our analysis employs a combination of high-precision photometry obtained with the Advanced Camera for Surveys on the Hubble Space Telescope, medium-resolution spectroscopy obtained with the DEep Imaging Multi-Object Spectrograph on the W.M. Keck Observatory, and updated Victoria-Regina isochrones tailored to the abundance patterns appropriate for these galaxies. The data for five of these Milky Way satellites are best fit by a star formation history where at least 75% of the stars formed by z~10 (13.3 Gyr ago). All of the galaxies are consistent with 80% of the stars forming by z~6 (12.8 Gyr ago) and 100% of the stars forming by z~3 (11.6 Gyr ago). The similarly ancient populations of these galaxies support the hypothesis that star formation in the smallest dark matter sub-halos was suppressed by a global outside influence, such as the reionization of the universe.

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Global Properties of M31's Stellar Halo from the SPLASH Survey: II. Metallicity Profile

We present the metallicity distribution of red giant branch (RGB) stars in M31's stellar halo, derived from photometric metallicity estimates for over 1500 spectroscopically confirmed RGB halo stars. The stellar sample comes from 38 halo fields observed with the Keck/DEIMOS spectrograph, ranging from 9 to 175 kpc in projected distance from M31's center, and includes 52 confirmed M31 halo stars beyond 100 kpc. While a wide range of metallicities is seen throughout the halo, the metal-rich peak of the metallicity distribution function becomes significantly less prominent with increasing radius. The metallicity profile of M31's stellar halo shows a continuous gradient from 9 to ~100 kpc, with a magnitude of -0.01 dex/kpc. The stellar velocity distributions in each field are used to identify stars that are likely associated with tidal debris features. The removal of tidal debris features does not significantly alter the metallicity gradient in M31's halo: a gradient is maintained in fields spanning 10 to 90 kpc. We analyze the halo metallicity profile, as well as the relative metallicities of stars associated with tidal debris features and the underlying halo population, in the context of current simulations of stellar halo formation. We argue that the large scale gradient in M31's halo implies M31 accreted at least one relatively massive progenitor in the past, while the field to field variation seen in the metallicity profile indicates that multiple smaller progenitors are likely to have contributed substantially to M31's outer halo.

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New Clues to the Cause of Extended Main Sequence Turn-Offs in Intermediate-Age Star Clusters in the Magellanic Clouds

We use the Wide Field Camera 3 (WFC3) onboard the Hubble Space Telescope (HST) to obtain deep, high resolution images of two intermediate-age star clusters in the Large Magellanic Cloud of relatively low mass ($\approx$ $10^4$ $M_{\odot}$) and significantly different core radii, namely NGC2209 and NGC2249. For comparison purposes, we also re-analyzed archival HST images of NGC1795 and IC2146, two other relatively low mass star clusters. From the comparison of the observed color-magnitude diagrams with Monte Carlo simulations, we find that the main sequence turnoff (MSTO) regions in NGC2209 and NGC2249 are significantly wider than that derived from simulations of simple stellar populations, while those in NGC1795 and IC2146 are not. We determine the evolution of the clusters' masses and escape velocities from an age of 10 Myr to the present age. We find that the differences among these clusters can be explained by dynamical evolution arguments if the currently extended clusters (NGC2209 and IC2146) experienced stronger levels of initial mass segregation than the currently compact ones (NGC2249 and NGC1795). Under this assumption, we find that NGC2209 and NGC2249 have estimated escape velocities $V_{\rm esc}$ $\geq$ 15 km s$^{-1}$ at an age of 10 Myr, large enough to retain material ejected by slow winds of first-generation stars, while the two clusters that do not feature extended MSTOs have $V_{\rm esc}$ $\leq$ 12 km s$^{-1}$ at that age. These results suggest that the extended MSTO phenomenon can be better explained by a range of stellar ages rather than a range of stellar rotation velocities or interacting binaries.

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The Core Mass Growth and Stellar Lifetime of Thermally Pulsing Asymptotic Giant Branch Stars

We establish new constraints on the intermediate-mass range of the initial-final mass relation by studying white dwarfs in four young star clusters, and apply the results to study the evolution of stars on the thermally pulsing asymptotic giant branch (TP-AGB). We show that the stellar core mass on the AGB grows rapidly from 10% to 30% for stars with $M_{\rm initial}$ = 1.6 to 2.0 $M_\odot$. At larger masses, the core-mass growth decreases steadily to $\sim$10% at $M_{\rm initial}$ = 3.4 $M_\odot$. These observations are in excellent agreement with predictions from the latest TP-AGB evolutionary models in Marigo et al. (2013). We also compare to models with varying efficiencies of the third dredge-up and mass loss, and demonstrate that the process governing the growth of the core is largely the stellar wind, while the third dredge-up plays a secondary, but non-negligible role. Based on the new white dwarf measurements, we perform an exploratory calibration of the most popular mass-loss prescriptions in the literature. Finally, we estimate the lifetime and the integrated luminosity of stars on the TP-AGB to peak at $t$ $\sim$ 3 Myr and $E$ = 1.2 $\times$ 10$^{10}$ $L_\odot$ yr for $M_{\rm initial}$ $\sim$ 2 $M_\odot$ ($t$ $\sim$ 2 Myr for luminosities brighter than the RGB tip at $\log(L/L_{\odot})$ $>$ 3.4), decreasing to $t$ = 0.4 Myr and $E$ = 6.1 $\times$ 10$^{9}$ $L_\odot$ yr for stars with $M_{\rm initial}$ $\sim$ 3.5 $M_\odot$. The implications of these results are discussed with respect to general population synthesis studies that require correct modeling of the TP-AGB phase of stellar evolution.

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The Formation History of the Ultra-Faint Dwarf Galaxies

We present early results from a Hubble Space Telescope survey of the ultra-faint dwarf galaxies. These Milky Way satellites were discovered in the Sloan Digital Sky Survey, and appear to be an extension of the classical dwarf spheroidals to low luminosities, offering a new front in the efforts to understand the missing satellite problem. Because they are the least luminous, most dark matter dominated, and least chemically evolved galaxies known, the ultra-faint dwarfs are the best candidate fossils from the early universe. The primary goal of the survey is to measure the star-formation histories of these galaxies and discern any synchronization due to the reionization of the universe. We find that the six galaxies of our survey have very similar star-formation histories, and that each is dominated by stars older than 12 Gyr.

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Comparing the White Dwarf Cooling Sequences in 47 Tuc and NGC 6397

Using deep Hubble Space Telescope imaging, color-magnitude diagrams are constructed for the globular clusters 47 Tuc and NGC 6397. As expected, because of its lower metal abundance, the main sequence of NGC 6397 lies well to the blue of that of 47 Tuc. A comparison of the white dwarf cooling sequences of the two clusters, however, demonstrates that these sequences are indistinguishable over most of their loci - a consequence of the settling out of heavy elements in the dense white dwarf atmosphere and the near equality of their masses. Lower quality data on M4 continues this trend to a third cluster whose metallicity is intermediate between these two. While the path of the white dwarfs in the color-magnitude diagram is nearly identical in 47 Tuc and NGC 6397, the numbers of white dwarfs along the path are not. This results from the relatively rapid relaxation in NGC 6397 compared to 47 Tuc and provides a cautionary note that simply counting objects in star clusters in random locations as a method of testing stellar evolutionary theory is likely dangerous unless dynamical considerations are included.

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