The Kinematics of CIV in Star-Forming Galaxies at z~1.2

We present the first statistical sample of rest-frame far-UV spectra of star-forming galaxies at z~1. These spectra are unique in that they cover the high-ionization CIV{\lambda}{\lambda}1548, 1550 doublet. We also detect low-ionization features such as SiII{\lambda}1527, FeII{\lambda}1608, AlII{\lambda}1670, NiII{\lambda}{\lambda}1741, 1751 and SiII{\lambda}1808, and intermediate-ionization features from AlIII{\lambda}{\lambda}1854, 1862. Comparing the properties of absorption lines of lower- and higher- ionization states provides a window into the multi-phase nature of circumgalactic gas. Our sample is drawn from the DEEP2 survey and spans the redshift range 1.01 < z < 1.35 ( = 1.25). By isolating the interstellar CIV absorption from the stellar P-Cygni wind profile we find that 69% of the CIV profiles are blueshifted with respect to the systemic velocity. Furthermore, CIV shows a small but significant blueshift relative to FeII (offset of the best-fit linear regression -76 $\pm$ 26 km/s). At the same time, the CIV blueshift is on average comparable to that of MgII{\lambda}{\lambda}2796, 2803. At this point, in explaining the larger blueshift of CIV absorption at the ~ 3-sigma level, we cannot distinguish between the faster motion of highly-ionized gas relative to gas traced by FeII, and filling in on the red side from resonant CIV emission. We investigate how far-UV interstellar absorption kinematics correlate with other galaxy properties using stacked spectra. These stacking results show a direct link between CIV absorption and the current SFR, though we only observe small velocity differences among different ionization states tracing the outflowing ISM.Comment: 21 pages, 14 figures, ApJ, accepte

Young and intermediate-age massive star clusters

An overview of our current understanding of the formation and evolution of star clusters is given, with main emphasis on high-mass clusters. Clusters form deeply embedded within dense clouds of molecular gas. Left-over gas is cleared within a few million years and, depending on the efficiency of star formation, the clusters may disperse almost immediately or remain gravitationally bound. Current evidence suggests that a few percent of star formation occurs in clusters that remain bound, although it is not yet clear if this fraction is truly universal. Internal two-body relaxation and external shocks will lead to further, gradual dissolution on timescales of up to a few hundred million years for low-mass open clusters in the Milky Way, while the most massive clusters (> 10^5 Msun) have lifetimes comparable to or exceeding the age of the Universe. The low-mass end of the initial cluster mass function is well approximated by a power-law distribution, dN/dM ~ M^{-2}, but there is mounting evidence that quiescent spiral discs form relatively few clusters with masses M > 2 x 10^5 Msun. In starburst galaxies and old globular cluster systems, this limit appears to be higher, at least several x 10^6 Msun. The difference is likely related to the higher gas densities and pressures in starburst galaxies, which allow denser, more massive giant molecular clouds to form. Low-mass clusters may thus trace star formation quite universally, while the more long-lived, massive clusters appear to form preferentially in the context of violent star formation.Comment: 21 pages, 3 figures. To appear as invited review article in a special issue of the Phil. Trans. Royal Soc. A: Ch. 9 "Star clusters as tracers of galactic star-formation histories" (ed. R. de Grijs). Fully peer reviewed. PDFLaTeX, requires rspublic.cls style fil

Biases in metallicity measurements from global galaxy spectra: the effects of flux-weighting and diffuse ionized gas contamination

Galaxy metallicity scaling relations provide a powerful tool for understanding galaxy evolution, but obtaining unbiased global galaxy gas-phase oxygen abundances requires proper treatment of the various line-emitting sources within spectroscopic apertures. We present a model framework that treats galaxies as ensembles of HII and diffuse ionized gas (DIG) regions of varying metallicities. These models are based upon empirical relations between line ratios and electron temperature for HII regions, and DIG strong-line ratio relations from SDSS-IV MaNGA IFU data. Flux-weighting effects and DIG contamination can significantly affect properties inferred from global galaxy spectra, biasing metallicity estimates by more than 0.3 dex in some cases. We use observationally-motivated inputs to construct a model matched to typical local star-forming galaxies, and quantify the biases in strong-line ratios, electron temperatures, and direct-method metallicities as inferred from global galaxy spectra relative to the median values of the HII region distributions in each galaxy. We also provide a generalized set of models that can be applied to individual galaxies or galaxy samples in atypical regions of parameter space. We use these models to correct for the effects of flux-weighting and DIG contamination in the local direct-method mass-metallicity and fundamental metallicity relations, and in the mass-metallicity relation based on strong-line metallicities. Future photoionization models of galaxy line emission need to include DIG emission and represent galaxies as ensembles of emitting regions with varying metallicity, instead of as single HII regions with effective properties, in order to obtain unbiased estimates of key underlying physical properties.Comment: 37 pages, 29 figures, 4 tables. Accepted to ApJ. See Figures 15-17 for typical global galaxy biases in strong-line ratios, electron temperatures, and direct-method metallicitie

The Direct Detection of Lyman Continuum Emission from Star-forming Galaxies at z~3

We present the results of rest-frame UV spectroscopic observations of a sample of 14 z ~ 3 star-forming galaxies in the SSA 22a field. These spectra are characterized by unprecedented depth in the Lyman continuum region. For the first time, we have detected escaping ionizing radiation from individual galaxies at high redshift, with 2 of the 14 objects showing significant emission below the Lyman limit. We also measured the ratio of emergent flux density at 1500 Å to that in the Lyman continuum region, for the individual detections (C49 and D3) and the sample average. If a correction for the average IGM opacity is applied to the spectra of the objects C49 and D3, we find f_(1500)/f_(900,corr,C49) = 4.5 and f_(1500)/f_(900,corr,D3) = 2.9. The average emergent flux density ratio in our sample is = 22, implying an escape fraction ~4.5 times lower than inferred from the composite spectrum from Steidel and coworkers. If this new estimate is representative of LBGs, their contribution to the metagalactic ionizing radiation field is J_ν(900) ~ 2.6 × 10^(-22) ergs s^(-1) cm^(-2) Hz^(-1) sr^(-1), comparable to the contribution of optically selected quasars at the same redshift. The sum of the contributions from galaxies and quasars is consistent with recent estimates of the level of the ionizing background at z ~ 3, inferred from the H I Lyα forest optical depth. There is significant variance among the emergent far-UV spectra in our sample, yet the factors controlling the detection or nondetection of Lyman continuum emission from galaxies are not well determined. Because we do not yet understand the source of this variance, significantly larger samples will be required to obtain robust constraints on the galaxy contribution to the ionizing background at z ~ 3 and beyond

The Kinematics of Morphologically Selected z~2 Galaxies in the GOODS-N Field

We present near-IR spectra of H-alpha emission from 13 galaxies at z~2 in the GOODS-N field. The galaxies were selected primarily because they appear to have elongated morphologies, and slits were aligned with the major axes (as determined from the rest-frame UV emission) of 11 of the 13. If the galaxies are elongated because they are highly inclined, alignment of the slit and major axis should maximize the observed velocity and reveal velocity shear, if present. In spite of this alignment, we see spatially resolved velocity shear in only two galaxies. We show that the seeing makes a large difference in the observed velocity spread of a tilted emission line, and use this information to place limits on the velocity spread of the ionized gas of the galaxies in the sample: we find that all 13 have v_{0.5} < 110 km/s, where v_{0.5} is the velocity shear (half of the velocity range of a tilted emission line) that would be observed under our best seeing conditions of ~0.5". When combined with previous work, our data also indicate that aligning the slit along the major axis does not increase the probability of observing a tilted emission line. We then focus on the one-dimensional velocity dispersion \sigma, which is much less affected by the seeing, and see that the elongated subsample exhibits a significantly lower velocity dispersion than galaxies selected at random from our total H-alpha sample, not higher as one might have expected. We also see some evidence that the elongated galaxies are less reddened than those randomly selected using only UV colors. Both of these results are counter to what would be expected if the elongated galaxies were highly inclined disks. It is at least as likely that the galaxies' elongated morphologies are due to merging subunits.Comment: 9 pages, 5 figures. Accepted for publication in Ap

Fine-Structure FeII* Emission and Resonant MgII Emission in z = 1 Star-Forming Galaxies

We present a study of the prevalence, strength, and kinematics of ultraviolet FeII and MgII emission lines in 212 star-forming galaxies at z = 1 selected from the DEEP2 survey. We find FeII* emission in composite spectra assembled on the basis of different galaxy properties, indicating that FeII* emission is prevalent at z = 1. In these composites, FeII* emission is observed at roughly the systemic velocity. At z = 1, we find that the strength of FeII* emission is most strongly modulated by dust attenuation, and is additionally correlated with redshift, star-formation rate, and [OII] equivalent width, such that systems at higher redshifts with lower dust levels, lower star-formation rates, and larger [OII] equivalent widths show stronger FeII* emission. We detect MgII emission in at least 15% of the individual spectra and we find that objects showing stronger MgII emission have higher specific star-formation rates, smaller [OII] linewidths, larger [OII] equivalent widths, lower dust attenuations, and lower stellar masses than the sample as a whole. MgII emission strength exhibits the strongest correlation with specific star-formation rate, although we find evidence that dust attenuation and stellar mass also play roles in the regulation of MgII emission. Future integral field unit observations of the spatial extent of FeII* and MgII emission in galaxies with high specific star-formation rates, low dust attenuations, and low stellar masses will be important for probing the morphology of circumgalactic gas.Comment: 29 pages, 22 figures, 2 tables; accepted to Ap

The Inverse Shapley Value Problem

For $f$ a weighted voting scheme used by $n$ voters to choose between two candidates, the $n$ \emph{Shapley-Shubik Indices} (or {\em Shapley values}) of $f$ provide a measure of how much control each voter can exert over the overall outcome of the vote. Shapley-Shubik indices were introduced by Lloyd Shapley and Martin Shubik in 1954 \cite{SS54} and are widely studied in social choice theory as a measure of the "influence" of voters. The \emph{Inverse Shapley Value Problem} is the problem of designing a weighted voting scheme which (approximately) achieves a desired input vector of values for the Shapley-Shubik indices. Despite much interest in this problem no provably correct and efficient algorithm was known prior to our work. We give the first efficient algorithm with provable performance guarantees for the Inverse Shapley Value Problem. For any constant \eps > 0 our algorithm runs in fixed poly$(n)$ time (the degree of the polynomial is independent of \eps) and has the following performance guarantee: given as input a vector of desired Shapley values, if any "reasonable" weighted voting scheme (roughly, one in which the threshold is not too skewed) approximately matches the desired vector of values to within some small error, then our algorithm explicitly outputs a weighted voting scheme that achieves this vector of Shapley values to within error \eps. If there is a "reasonable" voting scheme in which all voting weights are integers at most \poly(n) that approximately achieves the desired Shapley values, then our algorithm runs in time \poly(n) and outputs a weighted voting scheme that achieves the target vector of Shapley values to within error $\eps=n^{-1/8}.

The nonlinear Bernstein-Schr\"odinger equation in Economics

In this paper we relate the Equilibrium Assignment Problem (EAP), which is underlying in several economics models, to a system of nonlinear equations that we call the "nonlinear Bernstein-Schr\"odinger system", which is well-known in the linear case, but whose nonlinear extension does not seem to have been studied. We apply this connection to derive an existence result for the EAP, and an efficient computational method.Comment: 8 pages, submitted to Lecture Notes in Computer Scienc

Probing the Ionization State of the Universe at z>6

We present high signal-to-noise ratio Keck ESI spectra of the two quasars known to have Gunn-Peterson absorption troughs, SDSS J1030+0524 (z=6.28) and SDSS J1148+5251 (z=6.37). The Ly alpha and Ly beta troughs for SDSS J1030+0524 are very black and show no evidence for any emission over a redshift interval of ~0.2 starting at z=6. On the other hand, SDSS J1148+5251 shows a number of emission peaks in the Ly beta Gunn-Peterson trough along with a single weak peak in the Ly alpha trough. The Ly alpha emission has corresponding Ly beta emission, suggesting that it is indeed a region of lower optical depth in the intergalactic medium at z=6.08. The stronger Ly beta peaks in the spectrum of SDSS J1148+5251 could conceivably also be the result of "leaks" in the IGM, but we suggest that they are instead Ly alpha emission from an intervening galaxy at z=4.9. This hypothesis gains credence from a strong complex of C IV absorption at the same redshift and from the detection of continuum emission in the Ly alpha trough at the expected brightness. If this proposal is correct, the quasar light has probably been magnified through gravitational lensing by the intervening galaxy. The Stromgren sphere observed in the absorption spectrum of SDSS J1148+5251 is significantly smaller than expected based on its brightness, which is consistent with the hypothesis that the quasar is lensed. If our argument for lensing is correct, the optical depths derived from the troughs of SDSS J1148+5251 are only lower limits (albeit still quite strong, with tau(LyA)>16 inferred from the Ly beta trough.) The Ly beta absorption trough of SDSS J1030+0524 gives the single best measurement of the IGM transmission at z>6, with an inferred optical depth tau(LyA)>22.Comment: To appear in July 2003 AJ, 34 pages, 11 figures; minor changes/typos fixe