Mechanisms with evidence: commitment and robustness

We show that in a class of I‐agent mechanism design problems with evidence, commitment is unnecessary, randomization has no value, and robust incentive compatibility has no cost. In particular, for each agent i, we construct a simple disclosure game between the principal and agent i where the equilibrium strategies of the agents in these disclosure games give their equilibrium strategies in the game corresponding to the mechanism but where the principal is not committed to his response. In this equilibrium, the principal obtains the same payoff as in the optimal mechanism with commitment. As an application, we show that certain costly verification models can be characterized using equilibrium analysis of an associated model of evidence.Accepted manuscrip

A Model for Star Formation, Gas Flows and Chemical Evolution in Galaxies at High Redshifts

Motivated by the increasing use of the Kennicutt-Schmidt (K-S) star formation law to interpret observations of high redshift galaxies, the importance of gas accretion to galaxy formation, and the recent observations of chemical abundances in galaxies at z~2-3, I use simple analytical models to assess the consistency of these processes of galaxy evolution with observations and with each other. I derive the time dependence of star formation implied by the K-S law, and show that the sustained high star formation rates observed in galaxies at z~2-3 require the accretion of additional gas. A model in which the gas accretion rate is approximately equal to the combined star formation and outflow rates broadly reproduces the observed trends of star formation rate with galaxy age. Using an analytical description of chemical evolution, I also show that this model, further constrained to have an outflow rate roughly equal to the star formation rate, reproduces the observed mass-metallicity relation at z~2.Comment: 7 pages, 3 figures. Accepted for publication in Ap

Evidence for a Positive Cosmological Constant from Flows of Galaxies and Distant Supernovae

Recent observations of high-redshift supernovae seem to suggest that the global geometry of the Universe may be affected by a `cosmological constant', which acts to accelerate the expansion rate with time. But these data by themselves still permit an open universe of low mass density and no cosmological constant. Here we derive an independent constraint on the lower bound to the mass density, based on deviations of galaxy velocities from a smooth universal expansion. This constraint rules out a low-density open universe with a vanishing cosmological constant, and together the two favour a nearly flat universe in which the contributions from mass density and the cosmological constant are comparable. This type of universe, however, seems to require a degree of fine tuning of the initial conditions that is in apparent conflict with `common wisdom'.Comment: 8 pages, 1 figure. Slightly revised version. Letter to Natur

Wiener Reconstruction of Large-Scale Structure from Peculiar Velocities

We present an alternative, Bayesian method for large-scale reconstruction from observed peculiar velocity data. The method stresses a rigorous treatment of the random errors and it allows extrapolation into poorly sampled regions in real space or in k-space. A likelihood analysis is used to determine the fluctuation power spectrum, followed by a Wiener Filter (WF) analysis to obtain the minimum-variance mean fields of velocity and mass density. Constrained Realizations (CR) are then used to sample the statistical scatter about the WF mean field. The WF/CR method is applied as a demonstration to the Mark III data with 1200 km/s, 900 km/s, and 500 km/s resolutions. The main reconstructed structures are consistent with those extracted by the POTENT method. A comparison with the structures in the distribution of IRAS 1.2Jy galaxies yields a general agreement. The reconstructed velocity field is decomposed into its divergent and tidal components relative to a cube of +/-8000 km/s centered on the Local Group. The divergent component is very similar to the velocity field predicted from the distribution of IRAS galaxies. The tidal component is dominated by a bulk flow of 194 +/- 32 km/s towards the general direction of the Shapley concentration, and it also indicates a significant quadrupole.Comment: 28 pages and 8 GIF figures, Latex (aasms4.sty), submitted to ApJ. Postscript version of the figures can be obtained by anonymous ftp from: ftp://alf.huji.ac.il/pub/saleem

Galactic Wind Signatures around High Redshift Galaxies

We carry out cosmological chemodynamical simulations with different strengths of supernova (SN) feedback and study how galactic winds from star-forming galaxies affect the features of hydrogen (HI) and metal (CIV and OVI) absorption systems in the intergalactic medium at high redshift. We find that the outflows tend to escape to low density regions, and hardly affect the dense filaments visible in HI absorption. As a result, the strength of HI absorption near galaxies is not reduced by galactic winds, but even slightly increases. We also find that a lack of HI absorption for lines of sight (LOS) close to galaxies, as found by Adelberger et al., can be created by hot gas around the galaxies induced by accretion shock heating. In contrast to HI, metal absorption systems are sensitive to the presence of winds. The models without feedback can produce the strong CIV and OVI absorption lines in LOS within 50 kpc from galaxies, while strong SN feedback is capable of creating strong CIV and OVI lines out to about twice that distance. We also analyze the mean transmissivity of HI, CIV, and OVI within 1 h$^{-1}$ Mpc from star-forming galaxies. The probability distribution of the transmissivity of HI is independent of the strength of SN feedback, but strong feedback produces LOS with lower transmissivity of metal lines. Additionally, strong feedback can produce strong OVI lines even in cases where HI absorption is weak. We conclude that OVI is probably the best tracer for galactic winds at high redshift.Comment: 16 pages, 16 figures, ApJ in press. Higher resolution version available at http://www.ociw.edu/~dkawata/research/papers.htm

NIHAO XI: Formation of Ultra-Diffuse Galaxies by outflows

We address the origin of Ultra-Diffuse Galaxies (UDGs), which have stellar masses typical of dwarf galaxies but effective radii of Milky Way-sized objects. Their formation mechanism, and whether they are failed $\rm L_{\star}$ galaxies or diffuse dwarfs, are challenging issues. Using zoom-in cosmological simulations from the NIHAO project, we show that UDG analogues form naturally in medium-mass haloes due to episodes of gas outflows associated with star formation. The simulated UDGs live in isolated haloes of masses $10^{10-11}\rm M_{\odot}$, have stellar masses of $10^{7-8.5}\rm M_{\odot}$, effective radii larger than 1 kpc and dark matter cores. They show a broad range of colors, an average S\'ersic index of 0.83, a typical distribution of halo spin and concentration, and a non-negligible HI gas mass of $10^{7-9}\rm M_{\odot}$, which correlates with the extent of the galaxy. Gas availability is crucial to the internal processes that form UDGs: feedback driven gas outflows, and subsequent dark matter and stellar expansion, are the key to reproduce faint, yet unusually extended, galaxies. This scenario implies that UDGs represent a dwarf population of low surface brightness galaxies and should exist in the field. The largest isolated UDGs should contain more HI gas than less extended dwarfs of similar $\rm M_{\star}$.Comment: matches accepted version, MNRAS Letter 2016-10-1

A Revised Model for the Formation of Disk Galaxies: Low Spin and Dark-Halo Expansion

We use observed rotation velocity-luminosity (VL) and size-luminosity (RL) relations to single out a specific scenario for disk galaxy formation in the LCDM cosmology. Our model involves four independent log-normal random variables: dark-halo concentration c, disk spin lam_gal, disk mass fraction m_gal, and stellar mass-to-light ratio M/L_I. A simultaneous match of the VL and RL zero points with adiabatic contraction requires low-c halos, but this model has V_2.2~1.8 V_vir (where V_2.2 and V_vir are the circular velocity at 2.2 disk scale lengths and the virial radius, respectively) which will be unable to match the luminosity function (LF). Similarly models without adiabatic contraction but standard c also predict high values of V_2.2/V_vir. Models in which disk formation induces an expansion rather than the commonly assumed contraction of the dark-matter halos have V_2.2~1.2 V_vir which allows a simultaneous fit of the LF. This may result from non-spherical, clumpy gas accretion, where dynamical friction transfers energy from the gas to the dark matter. This model requires low lam_gal and m_gal values, contrary to naive expectations. However, the low lam_gal is consistent with the notion that disk galaxies predominantly survive in halos with a quiet merger history, while a low m_gal is also indicated by galaxy-galaxy lensing. The smaller than expected scatter in the RL relation, and the lack of correlation between the residuals of the VL and RL relations, respectively, imply that the scatter in lam_gal and in c need to be smaller than predicted for LCDM halos, again consistent with the idea that disk galaxies preferentially reside in halos with a quiet merger history.Comment: 28 pages, 16 figures, ApJ accepted, minor changes from unpublished version, uses emulateapj.cls, high-resolution version available at http://www.ucolick.org/~dutton/65200/hi-res-version/ms.dutton.v2_hr.p

Molecular Hydrogen and Global Star Formation Relations in Galaxies

(ABRIDGED) We use hydrodynamical simulations of disk galaxies to study relations between star formation and properties of the molecular interstellar medium (ISM). We implement a model for the ISM that includes low-temperature (T<10^4K) cooling, directly ties the star formation rate to the molecular gas density, and accounts for the destruction of H2 by an interstellar radiation field from young stars. We demonstrate that the ISM and star formation model simultaneously produces a spatially-resolved molecular-gas surface density Schmidt-Kennicutt relation of the form Sigma_SFR \propto Sigma_Hmol^n_mol with n_mol~1.4 independent of galaxy mass, and a total gas surface density -- star formation rate relation Sigma_SFR \propto Sigma_gas^n_tot with a power-law index that steepens from n_tot~2 for large galaxies to n_tot>~4 for small dwarf galaxies. We show that deviations from the disk-averaged Sigma_SFR \propto Sigma_gas^1.4 correlation determined by Kennicutt (1998) owe primarily to spatial trends in the molecular fraction f_H2 and may explain observed deviations from the global Schmidt-Kennicutt relation.Comment: Version accepted by ApJ, high-res version available at http://kicp.uchicago.edu/~brant/astro-ph/molecular_ism/rk2007.pd

Cosmological Density and Power Spectrum from Peculiar Velocities: Nonlinear Corrections and PCA

We allow for nonlinear effects in the likelihood analysis of galaxy peculiar velocities, and obtain ~35%-lower values for the cosmological density parameter Om and the amplitude of mass-density fluctuations. The power spectrum in the linear regime is assumed to be a flat LCDM model (h=0.65, n=1, COBE) with only Om as a free parameter. Since the likelihood is driven by the nonlinear regime, we "break" the power spectrum at k_b=0.2 h/Mpc and fit a power law at k>k_b. This allows for independent matching of the nonlinear behavior and an unbiased fit in the linear regime. The analysis assumes Gaussian fluctuations and errors, and a linear relation between velocity and density. Tests using proper mock catalogs demonstrate a reduced bias and a better fit. We find for the Mark3 and SFI data Om_m=0.32+-0.06 and 0.37+-0.09 respectively, with sigma_8*Om^0.6 = 0.49+-0.06 and 0.63+-0.08, in agreement with constraints from other data. The quoted 90% errors include cosmic variance. The improvement in likelihood due to the nonlinear correction is very significant for Mark3 and moderately so for SFI. When allowing deviations from LCDM, we find an indication for a wiggle in the power spectrum: an excess near k=0.05 and a deficiency at k=0.1 (cold flow). This may be related to the wiggle seen in the power spectrum from redshift surveys and the second peak in the CMB anisotropy. A chi^2 test applied to modes of a Principal Component Analysis (PCA) shows that the nonlinear procedure improves the goodness of fit and reduces a spatial gradient of concern in the linear analysis. The PCA allows addressing spatial features of the data and fine-tuning the theoretical and error models. It shows that the models used are appropriate for the cosmological parameter estimation performed. We address the potential for optimal data compression using PCA.Comment: 18 pages, LaTex, uses emulateapj.sty, ApJ in press (August 10, 2001), improvements to text and figures, updated reference

Luminescence from highly excited nanorings: Luttinger liquid description

We study theoretically the luminescence from quantum dots of a ring geometry. For high excitation intensities, photoexcited electrons and holes form Fermi seas. Close to the emission threshold, the single-particle spectral lines aquire weak many-body satellites. However, away from the threshold, the discrete luminescence spectrum is completely dominated by many-body transitions. We employ the Luttinger liquid approach to exactly calculate the intensities of all many-body spectral lines. We find that the transition from single-particle to many-body structure of the emission spectrum is governed by a single parameter and that the distribution of peaks away from the threshold is universal.Comment: 10 pages including 2 figure