The Large Deviation Principle for Coarse-Grained Processes

The large deviation principle is proved for a class of $L^2$-valued processes that arise from the coarse-graining of a random field. Coarse-grained processes of this kind form the basis of the analysis of local mean-field models in statistical mechanics by exploiting the long-range nature of the interaction function defining such models. In particular, the large deviation principle is used in a companion paper to derive the variational principles that characterize equilibrium macrostates in statistical models of two-dimensional and quasi-geostrophic turbulence. Such macrostates correspond to large-scale, long-lived flow structures, the description of which is the goal of the statistical equilibrium theory of turbulence. The large deviation bounds for the coarse-grained process under consideration are shown to hold with respect to the strong $L^2$ topology, while the associated rate function is proved to have compact level sets with respect to the weak topology. This compactness property is nevertheless sufficient to establish the existence of equilibrium macrostates for both the microcanonical and canonical ensembles.Comment: 19 page

Large Deviation Principles and Complete Equivalence and Nonequivalence Results for Pure and Mixed Ensembles

We consider a general class of statistical mechanical models of coherent structures in turbulence, which includes models of two-dimensional fluid motion, quasi-geostrophic flows, and dispersive waves. First, large deviation principles are proved for the canonical ensemble and the microcanonical ensemble. For each ensemble the set of equilibrium macrostates is defined as the set on which the corresponding rate function attains its minimum of 0. We then present complete equivalence and nonequivalence results at the level of equilibrium macrostates for the two ensembles.Comment: 57 page

MOSFIRE Spectroscopy of Quiescent Galaxies at 1.5 < z < 2.5. II - Star Formation Histories and Galaxy Quenching

We investigate the stellar populations for a sample of 24 quiescent galaxies at 1.5 < z < 2.5 using deep rest-frame optical spectra obtained with Keck MOSFIRE. By fitting templates simultaneously to the spectroscopic and photometric data, and exploring a variety of star formation histories, we obtain robust measurements of median stellar ages and residual levels of star formation. After subtracting the stellar templates, the stacked spectrum reveals the Halpha and [NII] emission lines, providing an upper limit on the ongoing star formation rate of 0.9 +/- 0.1 Msun/yr. By combining the MOSFIRE data to our sample of Keck LRIS spectra at lower redshift, we analyze in a consistent manner the quiescent population at 1 < z < 2.5. We find a tight relation (with a scatter of 0.13 dex) between the stellar age and the rest-frame U-V and V-J colors, which can be used to estimate the age of quiescent galaxies given their colors. Applying this age--color relation to large, photometric samples, we are able to model the number density evolution for quiescent galaxies of various ages. We find evidence for two distinct quenching paths: a fast quenching that produces compact post-starburst systems, and a slow quenching of larger galaxies. Fast quenching accounts for about a fifth of the growth of the red sequence at z~1.4, and half at z~2.2. We conclude that fast quenching is triggered by dramatic events such as gas-rich mergers, while slow quenching is likely caused by a different physical mechanism.Comment: 28 pages, 15 figures, accepted in Ap

Velocity Dispersions and Dynamical Masses for a Large Sample of Quiescent Galaxies at z > 1: Improved Measures of the Growth in Mass and Size

We present Keck LRIS spectroscopy for a sample of 103 massive galaxies with redshifts 0.9 < z < 1.6. Of these, 56 are quiescent with high signal-to-noise absorption line spectra, enabling us to determine robust stellar velocity dispersions for the largest sample yet available beyond a redshift of 1. Together with effective radii measured from deep Hubble Space Telescope images, we calculate dynamical masses and address key questions relating to the puzzling size growth of quiescent galaxies over 0 < z < 2. We examine the relationship between stellar and dynamical masses at high redshift, finding that it closely follows that determined locally. We also confirm the utility of the locally-established empirical calibration which enables high-redshift velocity dispersions to be estimated photometrically, and we determine its accuracy to be 35%. To address recent suggestions that progenitor bias - the continued arrival of recently-quenched larger galaxies - can largely explain the size evolution of quiescent galaxies, we examine the growth at fixed velocity dispersion assuming this quantity is largely unaffected by the merger history. We demonstrate that significant size and mass growth have clearly occurred in individual systems. Parameterizing the relation between mass and size growth over 0 < z < 1.6 as R \propto M^alpha, we find alpha = 1.6 +- 0.3, in agreement with theoretical expectations from simulations of minor mergers. Relaxing the assumption that the velocity dispersion is unchanging, we examine growth assuming a constant ranking in galaxy velocity dispersion. This approach is applicable only to the large-dispersion tail of the distribution, but yields a consistent growth rate of alpha = 1.4 +- 0.2. Both methods confirm that progenitor bias alone is insufficient to explain our new observations and that quiescent galaxies have grown in both size and stellar mass over 0 < z < 1.6.Comment: Updated to match the published versio

MOSFIRE Spectroscopy of Quiescent Galaxies at 1.5 < z < 2.5. I - Evolution of Structural and Dynamical Properties

We present deep near-infrared spectra for a sample of 24 quiescent galaxies in the redshift range 1.5 < z < 2.5 obtained with the MOSFIRE spectrograph at the W. M. Keck Observatory. In conjunction with a similar dataset we obtained in the range 1 < z < 1.5 with the LRIS spectrograph, we analyze the kinematic and structural properties for 80 quiescent galaxies, the largest homogeneously-selected sample to date spanning 3 Gyr of early cosmic history. Analysis of our Keck spectra together with measurements derived from associated HST images reveals increasingly larger stellar velocity dispersions and smaller sizes to redshifts beyond z~2. By classifying our sample according to Sersic indices, we find that among disk-like systems the flatter ones show a higher dynamical to stellar mass ratio compared to their rounder counterparts which we interpret as evidence for a significant contribution of rotational motion. For this subset of disk-like systems, we estimate that V/sigma, the ratio of the circular velocity to the intrinsic velocity dispersion, is a factor of two larger than for present-day disky quiescent galaxies. We use the velocity dispersion measurements also to explore the redshift evolution of the dynamical to stellar mass ratio, and to measure for the first time the physical size growth rate of individual systems over two distinct redshift ranges, finding a faster evolution at earlier times. We discuss the physical origin of this time-dependent growth in size in the context of the associated reduction of the systematic rotation.Comment: Updated to match the published versio

Discovery of a Strongly Lensed Massive Quiescent Galaxy at z=2.636: Spatially Resolved Spectroscopy and Indications of Rotation

We report the discovery of RG1M0150, a massive, recently quenched galaxy at z=2.636 that is multiply imaged by the cluster MACSJ0150.3-1005. We derive a stellar mass of log M_*=11.49+0.10-0.16 and a half-light radius of R_e,maj =1.8+-0.4 kpc. Taking advantage of the lensing magnification, we are able to spatially resolve a remarkably massive yet compact quiescent galaxy at z>2 in ground-based near-infrared spectroscopic observations using Magellan/FIRE and Keck/MOSFIRE. We find no gradient in the strength of the Balmer absorption lines over 0.6 R_e - 1.6 R_e, which are consistent with an age of 760 Myr. Gas emission in [NII] broadly traces the spatial distribution of the stars and is coupled with weak Halpha emission (log [NII]/Halpha = 0.6+-0.2), indicating that OB stars are not the primary ionizing source. The velocity dispersion within the effective radius is sigma_e = 271+-41 km/s. We detect rotation in the stellar absorption lines for the first time beyond z~1. Using a two-integral Jeans model that accounts for observational effects, we measure a dynamical mass of log M_dyn =11.24+-0.14 and V/sigma=0.70+-0.21. This is a high degree of rotation considering the modest observed ellipticity of 0.12+-0.08, but it is consistent with predictions from dissipational merger simulations that produce compact remnants. The mass of RG1M0150 implies that it is likely to become a slowly rotating elliptical. If it is typical, this suggests that the progenitors of massive ellipticals retain significant net angular momentum after quenching which later declines, perhaps through accretion of satellites.Comment: Accepted to ApJ Letters; updated to include revisions from the referee process, including an improved Fig.

Stellar populations from spectroscopy of a large sample of quiescent galaxies at z > 1: Measuring the contribution of progenitor bias to early size growth

We analyze the stellar populations of a sample of 62 massive (log Mstar/Msun > 10.7) galaxies in the redshift range 1 < z < 1.6, with the main goal of investigating the role of recent quenching in the size growth of quiescent galaxies. We demonstrate that our sample is not biased toward bright, compact, or young galaxies, and thus is representative of the overall quiescent population. Our high signal-to-noise ratio Keck LRIS spectra probe the rest-frame Balmer break region which contains important absorption line diagnostics of recent star formation activity. We obtain improved measures of the various stellar population parameters, including the star-formation timescale tau, age and dust extinction, by fitting templates jointly to both our spectroscopic and broad-band photometric data. We identify which quiescent galaxies were recently quenched and backtrack their individual evolving trajectories on the UVJ color-color plane finding evidence for two distinct quenching routes. By using sizes measured in the previous paper of this series, we confirm that the largest galaxies are indeed among the youngest at a given redshift. This is consistent with some contribution to the apparent growth from recent arrivals, an effect often called progenitor bias. However, we calculate that recently-quenched objects can only be responsible for about half the increase in average size of quiescent galaxies over a 1.5 Gyr period, corresponding to the redshift interval 1.25 < z < 2. The remainder of the observed size evolution arises from a genuine growth of long-standing quiescent galaxies.Comment: Accepted for publication in the Astrophysical Journal, 14 pages, 11 figure

High angular resolution observation of the Sunyaev-Zel'dovich effect in the massive z=0.83 cluster ClJ0152-1357

X-ray observations of galaxy clusters at high redshift (z>0.5) indicate that they are more morphologically complex and less virialized than those at low-redshift. We present the first subarcmin resolution at 18 GHz observations of the Sunyaev-Zel'dovich (SZ) effect for ClJ0152-1357 using the Australia Telescope Compact Array. ClJ0152-1357 is a massive cluster at redshift z=0.83 and has a complex structure including several merging subclumps which have been studied at optical, X-ray, and radio wavelengths. Our high-resolution observations indicate a clear displacement of the maximum SZ effect from the peak of X-ray emission for the most massive sub-clump. This result shows that the cluster gas within the cluster substructures is not virialised in ClJ0152-1357 and we suggest that it is still recovering from a recent merger event. A similar offset of the SZ effect has been recently seen in the `bullet cluster' by Malu et al. This non-equilibrium situation implies that high resolution observations are necessary to investigate galaxy cluster evolution, and to extract cosmological constraints from a comparison of the SZ effect and X-ray signals.Comment: 5 pages, 4 figures, submitted to ApJ

Electroweak Precision Data and Gravitino Dark Matter

Electroweak precision measurements can provide indirect information about the possible scale of supersymmetry already at the present level of accuracy. We review present day sensitivities of precision data in mSUGRA-type models with the gravitino as the lightest supersymmetric particle (LSP). The chi^2 fit is based on M_W, sin^2 theta_eff, (g-2)_mu, BR(b -> s gamma) and the lightest MSSM Higgs boson mass, M_h. We find indications for relatively light soft supersymmetry-breaking masses, offering good prospects for the LHC and the ILC, and in some cases also for the Tevatron.Comment: 4 pages, 1 figure. Talk given at the LCWS06 March 2006, Bangalore, India. References adde